Millimeter-Wave Monolithic Schottky Diode-Grid Phase Shifter Citation Lam, Wayne W. (1987) Millimeter-Wave Monolithic Schottky Diode-Grid Phase Shifter. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/CGD0-XA98. https://resolver.caltech.edu/CaltechETD:etd-03032008-105407 Abstract Many applications at millimeter wavelengths require fast electronic phase shifters. In this study, the design of diode-grid phase shifters is presented, the fabrication of diode-grids on monolithic gallium-arsenide substrates is demonstrated, and the measurement of these grids is discussed. A new computer-aided design tool is developed to provide an interactive environment for design and to form a basis for comparing theory and experimental results. Diode-grids have been fabricated on 2 cm by 3 cm gallium-arsenide wafers with 2000 aluminum Schottky diodes. A novel small aperture reflectometer is computerized to use a wave-front division interference technique to measure the reflection coefficient of the grids. A 70° phase shift with a 6.5-dB loss was measured at 93 GHz when the bias on the diode-grid was changed from -3V to +1V. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Millimeter-Wave Diode-Grid Phase Shifter Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Electrical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Rutledge, David B. Thesis Committee: Rutledge, David B. (chair) Psaltis, Demetri Vahala, Kerry J. Yariv, Amnon Luhmann, Neville C., Jr. Bridges, William B. Nicolet, Marc-Aurele Defense Date: 31 January 1987 Funders: Funding Agency Grant Number Army Research Office (ARO) UNSPECIFIED Amoco Foundation UNSPECIFIED Record Number: CaltechETD:etd-03032008-105407 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-03032008-105407 DOI: 10.7907/CGD0-XA98 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 851 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 03 Mar 2008 Last Modified: 24 May 2024 18:50 Thesis Files Preview PDF (Lam_ww_1987.pdf) - Final Version See Usage Policy. 6MB Repository Staff Only: item control page

MILLIMETER-WAVE MONOLITHIC SCHOTTKY DIODE-GRID PHASE SHIFTER Thesis by Wayne W. Lam In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1987 (Submitted January 31, 1987) TO MY PARENTS ili Acknowledgements I would like to express my deepest thank to Professor David Rutledge, my the- sis advisor, for having given me the opportunity to be a member of his Millimeter- Wave Integrated Circuits Group. His ideas, encouragement and guidance made this work possible, and his kindness and understanding helped me grow. It has been my good fortune to have met him. I am grateful to Professor Dean Neikirk for showing me the art of fabricat- ing microbolometers. I am indebted to Dr. Chung-en Zah for teaching me the techniques of diode fabrication. Also, I would like to thank Professors William Bridges, Marc-Aurele Nicolet, and Amnon Yariv at Caltech, and to Professor Neville Luhmann, Jr., at UCLA, for the use of their equipment and facilities. Especially, I would like to extend my thanks to Howard Chen for supplying me the epitaxial wafers for my research, Frank So for doing proton bombardments, Christina Jou for helping me in diode- grid measurements. In addition, I appreciate Dr. Thomas Kuech at IBM for sending me MOCVD wafers, Kjell Stolt at TRW and Lars Eng at JPL for growing the epitaxial wafers, and Bob Rush at Hughes for proton implantation. Furthermore, I would like to thank Joyce Liddell for her secretarial assistance, Wyman Williams and Rick Compton for sharing their computer expertise, and other members of the group for their friendship and support. Iam grateful for the financial support of the Army Research Office Fellowship and the AMOCO Foundation Fellowship. And finally, I am most thankful to my parents, Hing Shing and Kor Han for giving me a better chance in life and my brother, Lawrence, for getting me interested in going to college rather than to the beach. iv Millimeter-Wave Monolithic Schottky Diode-Grid Phase Shifter Abstract Many applications at millimeter wavelengths require fast electronic phase shifters. In this study, the design of diode-grid phase shifters is presented, the fabrication of diode-grids on monolithic gallium-arsenide substrates is demon- strated, and the measurement of these grids is discussed. A new computer-aided design tool is developed to provide an interactive environment for design and to form a basis for comparing theory and experimental results. Diode-grids have been fabricated on 2cm by 3cm gallium-arsenide wafers with 2000 aluminum Schottky diodes. A novel small aperture reflectometer is computerized to use a wave-front division interference technique to measure the reflection coefficient of the grids. A 70° phase shift with a 6.5-dB loss was measured at 93 GHz when the bias on the diode-grid was changed from —3 V to +1V. Vv TABLE OF CONTENTS Acknowledgements Abstract 1. Introduction 1.1 Applications of Diode-Grids 1.2 Overview of Thesis 2. Design and Analysis of Diode-Grid Phase Shifter 2.1 Diode-Grid Model 2.2 Diode-Grid Phase Shifter 2.3 Computer-Aided Design and Analysis-TRAP 2.4 Simulated Performance of Diode-Grid Phase Shifter 3. Fabrication of Diode-Grids 3.1 Design of a Hyperabrupt Schottky Varactor Diode 3.2 Fabrication Processes 3.2.1 Self-Aligning Schottky Contact 3.2.2 Ohmic Contact 3.2.3 Proton Isolation 3.2.4 Low Frequency Varactor Parameters 3.2.5 Liquid Crystal Detection 3.3 Test Fixture 4. Diode-Grid Phase Shifter Measurements 4.1 Survey of Possible Experimental Methods 4.2 Small Aperture Reflectometer 4.3 Reflection Measurements of Bismuth on Fused Quartz 4.4 Reflection Measurements of Fused Quartz 4.5 Reflection Measurements of Diode-Grid page iii iv 12 18 18 22 25 29 36 36 46 46 49 54 54 58 60 66 66 69 78 82 86 vi 5. Discussion and Future Work Appendices (A) Varactor Diode-Grid Fabrication Procedure (B) Computer Program Listing of TRAP (C) Computer Program Listing for Reflection Measurement (D) Computer Program Listing for Diode Parameter Measurement (E) E) Computer Program Listing for Doping Profile Measurement 101 105 105 113 147 160 172 1 Chapter 1 Introduction Unique features of millimeter waves have attracted a growing interest in the wavelength region from 1mm to 10mm. Millimeter waves offer broader band- widths, higher resolution and smaller component size than microwaves, and pro- vide better penetration of fog and dust than infrared [1]. In radio astronomy, the measurement of molecular resonance lines, which occur significantly in the millimeter range, have provided important physical insights into the state of in- terstellar clouds [2]. In plasma diagnostics, the measurement of electron density and temperature profile, and fluctuation have increased the understanding of particle confinement mechanisms in a fusion plasma [3]. Thermography at mil- limeter wavelengths has been used in tumor detection [4]. Other applications including active radiometry [4], satellite communication [5], and remote-sensing of the earth’s surface [1] are beginning to receive more attention. As the number of applications increases, demands for new and improved sys- tems follow. Currently standard components available for millimeter applications are based on metal cavities, waveguides, and horns. Although they are adequate for small systems, they become quite expensive to use in large systems because intensive labor is required in machining these parts. In situations where only a limited amount of space is available, they can be very difficult to manage, since their physical dimensions tend to be much bigger than a wavelength. These are the driving forces that have led to the recently increased efforts in research and development of monolithic integrated circuits for millimeter waves. Special is- sues on this subject have appeared in the IEEE Transactions [6,7]. Recently, Stiglitz [9] presented a special report on the topic of gallium-arsenide technology and microwave and millimeter-wave monolithic integrated circuits for 1987. 1.1 Applications of Diode-Grids Much of the current research activities in monolithic integrated circuits for millimeter waves tend to revolve around a variety of planar transmission-line structures and dielectric waveguides. Recently a different structure based on integrating solid-state devices into a periodic grid has emerged. Rutledge and Schwarz demonstrated a multi-mode detector array by integrating microbolome- ters into a periodic grid [10]. Tong et al. built a two-dimensional tracking array, also with microbolometers and a periodic grid [11]. Figure 1.1 shows a periodic grid loaded with Schottky varactor-diodes, hence the name diode-grid. Designs based on the diode-grid for electronic beam-steering and frequency multiplication had been proposed [12], and the fabrication of a diode-grid was demonstrated on a 2cm by 2cm gallium-arsenide wafer with 2000 diodes {13]. Periodic grids offer many advantages. They present a planar geometry that is both simple and compact; therefore, it has a tremendous capacity for inter- connecting thousands of solid-state devices on a single substrate. The periodic grid lends itself to a variety of high-power applications, since power is distributed among a large number of electronic devices throughout a planar surface. They are exciting because they open up a new area of monolithic integrated circuits for plane waves. This provides an extra degree of freedom to the circuit designer. Ba- sically, the longitudinal dimension can be used for guiding high-frequency signals and feeding electromagnetic energy to the devices, while low-frequency control signals and bias can be routed in the transverse dimension. The system design is analogous to an optics design. Furthermore, the diode-grid approach is com- patible with the semiconductor fabrication technology. This leads to lower cost, smaller size, and more reliable components. No transmission lines or waveguides are used. This makes fabrication simpler and losses lower. Figure 1.1. Part of a periodic diode-grid fabricated on a gallium-arsenide wafer. 4 One of the applications of the diode-grid is in electronic beam-steering. Cur- rently, beam-steering plays a vital role in advanced radars that track and image multiple objects simultaneously. The key element that enables a beam of radi- ation to be steered at electronic speeds is the phase shifter. Typically, many thousands of phase-shifting elements are required. Conventional phase-shifters based on microwave hybrids of striplines and waveguides lead to high cost and system interconnecting complexity as the wavelength approaches 1 mm. Recently Horn et al. [14] demonstrated an electronically modulated line scanning antenna. However, many applications require more gain than a line source can provide. The use of variable-permittivity media for phase-shifting is an intriguing alter- native possibility [15,16]. Figure 1.2 shows a varactor-diode grid design for elec- tronic beam-steering. In the beam-steering array, the incident beam reflects off the programmable diode-grid phase-shifting surface, where changing the dc bias on the diodes changes the reactance, and this controls the phase of the reflected waves. A linear variation of the phase across the aperture sets the direction of the reflected beam. In addition, a quadratic variation of the phase across the aperture focuses the reflected beam. No transmission lines or waveguides are required. This architecture makes the system design simpler and the fabrica- tion cost lower. Since the power is distributed among all the diodes, the power handling capability can be designed specifically for a particular application by choosing the array size properly. Another application of the diode-grid is in harmonic power generation. As the wavelength approaches 1mm, the varactor multiplier plays an important role in providing local power to heterodyne receivers because other sources present many undesirable features. Tubes require cumbersome and dangerous high-voltage sup- plies, Impatt oscillators are generally too noisy, and Gunn oscillators are not able to provide sufficient power at frequencies above 100 GHz. Recently, Archer [17] Reflected beams Incident beam Quartz cover Diode grids Metal mounting block VL LF A a a Figure 1.2. Electronically programmable beam-steering array. 6 summarized state-of-the-art performances for millimeter wavelength frequency multiplier. They are primarily based on using a single whisker-contacted varac- tor diode chip in a cross-waveguide configuration. Although very high conversion efficiency has been obtained, they are basically limited to milliwatts of output power. The fundamental limitation is that only a few varactors can be used simul- taneously in a practical manner. However, power can be increased significantly when thousands of varactors are combined together in a suitable manner for syn- chronous operation. Figure 1.3 shows a second harmonic power-combiner that uses an array of nonlinear capacitors to generate and spatially combine power at the harmonic frequencies. In this frequency doubler design, power at the fun- damental frequency enters through the input filter, arrives at the varactor-diode grid, and pumps the nonlinear capacitance of the diodes to generate power at harmonics. The second harmonic is spatially combined and transmitted through the output filter. Loading a grid with negative resistance diodes offers the possibility of dc- to-rf power conversion that is analogous to a laser. Currently, oscillators with single electronic device such as Gunn or IMPATT diode are highly developed. However, they are capable of providing continuous-wave power only from about 500mW at 40GHz to 10mW at 230GHz [18]. Many applications in radars, imaging arrays, and heterodyne receivers require much more power than this. Although a number of power-combining circuits have been demonstrated includ- ing chip-level, circuit-level, and spatial power-combining [19], they do not take full advantage of what the solid-state semiconductor technology can offer. Re- cently Wandinger and Nalbandian demonstrated a dual oscillator quasi-optical power-combining resonator at 60 GHz with dielectric antennas [20]. However, ex- tending this approach to higher-level combining would be expensive and difficult. Mink investigated theoretically a very interesting distributed source planar array Output Harmonic Output Filter TT Input Fundamental Input Figure 1.3. Second harmonic power-combiner. _—_ Output power Gunn diode array KS .GC|CQQWG]Mq Tuning mirror Partially transparent reflector Figure 1.4. Gunn-diode resonator. 9 resonator [21]. Figure 1.4 shows a Gunn diode-grid resonator. Power generated by the Gunn diodes are combined in a semi-confocal cavity. A metal mirror is used as a tuning short for matching the impedance of the Gunn diode. Power can be coupled out through a partially transparent mirror. In addition, a union of the Gunn diode-grid resonator and the harmonic power-combiner would be an exciting all solid-state alternative for high-power local oscillator source. Another interesting application of the diode-grid is in signal detection. Re- cently, Zah et al. [22] demonstrated a one-dimensional Schottky-diode imaging array at 90 GHz. Figure 1.5 shows a typical lens-coupled optical system that has been used in imaging experiments today [23,24]. The idea is to focus en- ergy onto an imaging array at the focal plane, so that an image of the object can be constructed at electronic speed. Figure 1.6 is a close-up view of a two- dimensional imaging array based on the diode-grid approach. The idea is to use the horizontally connected diodes in the back layer as tuning elements for the vertically connected diodes in the front layer. The intersection of a column and a row defines a pixel element. The amplitude at each pixel can be measured from the column with the proper dc bias applied to the corresponding row. Further- more, being able to ascertain informations from each unit cell of a finite periodic structure raises the possibility of studying edge effects due to finite periodic- ity. This should provide important insight into future works concerning circuit interactions between diode-grids on different planes. Finally, applications of the diode-grid, analogous to holography and nonlinear optics, also appear possible. In optical phase conjugation, a nonlinear medium is used to generate the complex conjugate of a wave. This is useful in real-time imaging through a phase distorting medium [25]. The technique of using a non- linear surface for generating a phase-conjugated wave has been demonstrated at optical wavelengths [26]. Figure 1.7 shows how this can be done with a varactor- Objective lens ve QQ be Object plane 10 7 2-D Imaging array Figure 1.5. Two-dimensional imaging system. 11 ee mmn© ome oo ammns Comme se » Bias rows \eypoeee Detector columns Figure 1.6. Two-dimensional imaging array. 12 diode grid at millimeter wavelengths. The idea is to mix the signal-beam with a normally incident pump-beam on the surface of the varactor diode-grid, so that a hologram in the form of reflectivity modulation is developed. During this mixing process, the phase-conjugated beam is generated and the replica of the signal beam is reproduced as the conjugated beam evolves through the phase- distorting medium. Also signal amplification can be obtained. 1.2 Overveiw of Thesis The numerous potential applications of the diode-grid is the motivation be- hind this research. The purpose of this thesis is to lay down the groundwork and to demonstrate feasibility. Chapter 2 presents design considerations, a model of the diode-grid, and computer simulations of the reflection phase-shifter for elec- tronic beam-steering. The approach is based on a transmission-line equivalent circuit. In designing the grid structures, together with the substrate, dielectric slabs, filters and mirrors, a computer-aided design program was developed to provide an interactive environment for the user and to form a basis for compar- ing theoretical and experimental results. The software documentation is given in the appendix. Chapter 3 describes the design of a truncated hyperabrupt doping distribution for making a Schottky-barrier varactor diode. Essential parts of the diode fabri- cation are discussed. Zah’s self-aligning process as described by Zah et al. [22] is used to fabricate the aluminum Schottky diodes. Monolithic diode-grids have been fabricated on 2cm by 3cm gallium-arsenide wafers with 2000 varactor diodes. Although the diode fabrication yield as high as 98% has been achieved, the remaining bad diodes, which tend to be short circuits, usually render the grid useless. Therefore, a liquid-crystal detection technique was developed to iden- tify the shorted diodes, which are subsequently removed by an ultrasonic probe. 13 —.P Pump beam \ \-7 — a * » < \ \ \ \ v4 V7 \ os L—-- a \ «-4 | _ aes | Signal Phase Conjugate beam distorting beam medium Figure 1.7. Phase-conjugating diode-grid. Nonlinear diode-grid surface 14 The diode series resistance is calculated from the current-voltage measurement at DC, and the doping distribution is extracted from the capacitance-voltage measurement at 1 MHz. Detailed procedures are given in the appendix. Chapter 4 begins with a survey of possible existing experimental methods for testing the diode-grid and concludes that none was practical for testing our diode-grid samples because the sample sizes are typically small and irregular in a laboratory environment. Therefore, a novel small aperture quasi-optical reflectometer was developed to meet this need. It uses a wave-front division interference technique to measure the reflection coefficient of a surface. The technique was first applied to measure the reflection coefficient of bismuth on quartz. The purpose was to get an indication of its validity and limitations. Then it was used for testing the diode-grids. Results measured at 90 GHz are curve-fitted with a theory based on a transmission-line equivalent circuit model. The best-fit grid parameters are compared with parameters measured at low frequency. [1] [2] (10) [11] 15 References P. Bhartia and I. J. Bahl, Millimeter Wave Engineering and Applications, Chap. 1, pp. 1-8, John Wiley & Sons, Inc., New York, 1984. C. H. Townes, “The Challenge of Astronomy to Millimeter-Wave Technology,” IEEE Trans. on Microwave Theory and Tech., MT T-24, pp. 709-711, 1976. N. C. Luhmann, Jr. “Instrumentation and Techniques for Plasma Diagnos- tics: An Overview,” Infrared and Millimeter Waves, Chap. 1, pp. 1-66, K. J. Button, ed., Academic Press, Inc., New York, 1983. J. Edrich, “Centimeter and Millimeter-Wave Thermography—A Survey on Tumor Detection,” J. Microwave Power, Vol. 14, pp. 95-104, 1979. W. J. Wilson, R. J. Howard, A. C. Ibbott, G. S. Parks, and W. B. Ricketts, “Millimeter-Wave Imaging Sensor,” IEEE Trans. on Microwave Theory and Tech. MT T-34, pp. 1026-1035, 1986. K. Miyanchi, “Millimeter-Wave Communication,” Infrared and Millimeter Waves, Chap. 1, pp. 1-94, K. J. Button, ed., Academic Press, Inc., New York, 1983. Special Issue on Microwave and Millimeter-Wave Integrated circuits. IEEE Trans. on Microwave Theory and Tech. MTT-26, pp. 705-843, 1978. Special Issue on Millimeter-Waves. IEEE Trans. on Microwave Theory and Tech. MTT-31, pp. 89-238, 1983. M. R. Stiglitz, “GaAs Technology and MIMIC, 1987,” Microwave Journal, September, pp. 42-66, 1986. D. B. Rutledge and S. E. Schwarz, “Planar Multimode Detector Arrays for Infrared and Millimeter-wave Applications,” IEEE J. Quantum Electronics, QE-17, pp. 407-414, 1981. P. P. Tong, D. P. Neikirk, D. Psaltis, K. Wagner, and P. E. Young, “Tracking [12] [13] [14] [21] 16 Antenna Arrays for Near-Millimeter Waves,” IEEE Trans. on Antennas and Propagat., AP-31, pp. 512-515, 1983. W. W. Lam, C. F. Jou, N. C. Luhmann, Jr., and D. B. Rutledge, “Diode Grids For Electronic Beam Steering And F requency Multiplication,” Int. J. of Infrared and Millimeter Waves, Vol. 7, pp. 27-41, 1986. W. W. Lam, H. Chen, D. B. Rutledge, C. F. Jou, N. C. Luhmann, Jr., “Progress in Diode Grids for Electronic Beam Steering and Frequency Mul- tiplication,” 11th Int. Conf. on Infrared and Millimeter Waves, pp. 177-179, Pisa, Italy, Oct. 1986. R. E. Horn, H. Jacobs, K. L. Klohn, and E. Freibergs, “Single Frequency Electronic-Modulated Analog Line Scanning Using a Dielectric Antenna,” IEEE Trans. on Microwave Theory and Tech., MT T-30, pp. 816-820, 1982. H. Buscher, “Electrically Controllable Liquid Artificial Dielectric Media,” IEEE Trans. on Microwave Theory and Tech., MT'T-27, pp. 540-545, 1979. R. H. Park, “Radant Lens: Alternative to Expensive Phased Arrays,” Mi- crowave Journal, September, pp. 101-105, 1980. J. W. Archer, “Low-Noise Heterodyne Receivers for Near-Millimeter-Wave Radio Astronomy,” Proceedings of the IEEE, vol. 73, pp. 109-130, 1985. J.C. Wiltse, “Introduction and Overview of Millimeter Waves,” Infrared and Millimeter Waves, Chap. 1, pp. 1-17, K. J. Button, ed., Academic Press, Inc., New York, 1981. K. Chang and C. Sun, “Millimeter-Wave Power-Combining Techniques,” IEEE Trans. on Microwave Theory and Tech., MTT-31, pp. 91-107, 1983. L. Wandinger and V. Nalbandian, “Millimeter-Wave Power Combiner Using Quasi-Optical Techniques,” IEEE Trans. on Microwave Theory and Tech., MTT-31, pp. 189-193, 1983. J. W. Mink, “Quasi-Optical Power Combining of Solid-State Millimeter- Wave [22] [23] [24] [25] [26] 17 Sources,” IEEE Trans. on Microwave Theory and Tech., MTT-34, pp. 189- 193, 1986. C. Zah, D. Kasilingam, J. S. Smith, D. B. Rutledge, T. Wang, and S. E. Schwarz, “Millimeter-Wave Monolithic Schottky Diode Imaging arrays,” Int. J. of Infrared and Millimeter Waves, Vol. 6, pp. 981-997, 1985. D. P. Neikirk, D. B. Rutledge, M. S. Muha, H. Park, and C. X. Yu, “Far- Infrared Imaging Antenna Arrays,” Appl. Phys. Lett., Vol. 40, pp. 203-205, 1982. D. B. Rutledge, D. P. Neikirk and D. P. Kasilingam, “Integrated-Circuit Antennas,” Infrared and Millimeter Waves, Vol. 10, chap. 1, pp. 1-90, K. J. Button, ed., Academic Press, Inc. New York, 1983. A. Yariv, “Phase Conjugate Optics and Real-Time Holography,” IEEE J. of Quantum Electronics, QE-14, pp. 650-660, 1978. B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunow, “Introduction to Op- tical Phase Conjugation,” Principles of Phase Conjugation, Springer-Verlag, New York, 1984. 18 Chapter 2 Design and Analysis of Diode-Grid Phase Shifter Many types of periodic grids have been used in infrared and millimeter-wave applications, including the Jerusalem-cross for band-reject filters [1], discs for artificial dielectrics [2], inductive wires for polarizers [3], inductive and capacitive strips for polarization independent beam splitters [4] and multiplexers [5], and metal meshes for output couplers for lasers [6]. The periodic grid that we use in designing our diode-grid phase shifter is a square mesh of metal strips on a gallium-arsenide substrate as shown in figure 2.la. The vertical strips add inductance to cancel the diode capacitance. The horizontal strips provide the bias but should not otherwise affect the circuit. Design considerations include the grid period, angle of incidence, and dielectric constant. The design approach is based on an equivalent circuit model and the transmission-line theory. In designing the diode-grid phase shifter for electronic beam-steering, we developed a computer-aided design program to provide an interactive environment for the designer and to form a basis for comparing theoretical and experimental results. 2.1 Diode-Grid Model We model the diode-grid with an equivalent circuit based on the transmission- line theory because it is relatively easy to incorporate both the diode model and supporting substrate into the analysis. Figure 2.1b shows a simple model of the diode-grid on a dielectric slab. The grid is represented by an inductor in series with a diode, and the substrate is represented by a section of transmission line with a characteristic impedance equal to the wave impedance in the dielectric. The inductance-per-unit length of the metal strip for normal incidence is given 19 —a=500um—> f IAASASSS ANAARARAALARARRABALBRAES WWARARRARARRARRARRRRRRER we 2Oum A \ WARRARAARRRRRRRRRRR N+ Inductive Bios ] N Leads ——> N Diodes | ANAS ARRAR AAA RA NEARRARRRRRRRRRRRRRRARRERRS . SAASASASSSSSSSSSSS es AURA RRRURARRRRRRRARRRRRRERER Figure 2.1. (a) Grid dimensions for a 90 GHz programmable phase shifter. The incident electric field is assumed to be vertically polarized. (b) Transmission-line model of an inductive grid, loaded with diodes, and supported by a substrate. 20 by a quasi-static approximation, L= soln [ese (=)]. (2.1) where w is the strip width, a is the grid period, and yz. is the magnetic per- meability. MacFarlane [7] derived this formula based on conforma] mapping of an inductive grating in a parallel plane metal waveguide. It does not take into account the angle of incidence, the polarization, the effect of the dielectric in- terface, the parasitic capacitance across the diode, or the effect of the horizontal cross strip. These effects have been considered in the literature [8,9]. Since they amount to a correction of less than 10%, they have been neglected in our initial designs of the diode-grid. This enables us to see the effects’ of design changes faster and therefore to get a quicker turn-around time in doing the design of the diode-grid phase shifter. The grid period, a, should be somewhat smaller than a substrate wavelength to avoid exciting substrate modes. We can decide how much smaller by con- sidering figure 2.2, which shows the spatial frequencies of the grid. The spatial frequencies for the incident radiation lie within a circle of radius 1 /Ao centered at the origin. This radiation excites currents, which, because of the periodic nature of the grid, have spatial frequencies that lie within similar circles centered on the reciprocal lattice points of the grid. The reciprocal lattice is a square lattice, with a period of 1/a. The spatial frequencies for the substrate modes lie within the doughnut-shaped regions that are also centered on the reciprocal lattice points. The inner radius of the doughnuts is 1/A. and the outer radius is n/X., where n is the refractive index of the substrate. To avoid exciting substrate modes, the small circles should not intersect the doughnuts. This means the grid period XY nv an AS 22 should satisfy ° < ——_.. 2.2 For gallium-arsenide, which has a refractive index of 3.6, the grid period should be less than 0.22A.. 2.2 Diode-Grid Phase Shifter Figure 2.3 shows the diode-grid phase shifter design. It consists of a fused- quartz cover, two diode-grids, and a metal mirror. The circuit is analogous to Garver’s microwave phase shifter [10]. The quartz layer acts as a protective cover as well as an impedance transformer. The metal mirror prevents radiation from escaping and serves as a heat sink and mechanical support. Another inherent feature of this design is that the mirror also shorts out the second harmonic at the diode-grids. This reduces conversion losses to the second harmonic; therefore, it is more attractive for high power-operation. Figure 2.4a shows the transmission-line model. The mirror is electrically an open-circuit, because it is a quarter-wavelength behind the back diode-grid. At the front diode-grid, the back grid appears electrically as a parallel load, but with the impedance inverted (figure 2.4b). The total normalized reactance X; is the parallel combination of 7X and 1/j7X, or xX (2.3) X, ranges from —oo as X approaches —1, to +oo as X approaches +1. This allows a full 360° phase shift as the normalized grid reactance goes from —1 to +1. The grid reactance, X, is normalized relative to the characteristic impedance of the substrate. In gallium-arsenide this corresponds to a grid reactance sweep between —1072 to +1079. For the grid dimensions in figure 2.1, the inductive 23 Fused-quartz cover GaAs wafer Diode grid Metal mounting block Figure 2.3. Side view of the programmable diode-grid phase shifter for elec- tronic beam steering. 24 Ke) 4g Aq/q><— a> (b) Figure 2.4. (a) Transmission-line model of the diode-grid phase shifter. (b) An idealized equivalent circuit for the diode-grid phaser shifter. 25 reactance due to the strip is 160. This means that the diode capacitance should vary from 7fF to 35fF. This type of capacitance ratio has been demonstrated with the hyperabrupt junction Schottky varactor diode [11]. The design allows a spatial phase variation in one dimension only. Two- dimensional phase variation can be achieved by biasing the diodes individually rather than row by row, or by cascading two such phase shifters. The design also does not control sidelobes because there is no adjustment for amplitudes. However, it should be possible to reduce sidelobes by tapering the radiation feeding the array with an externally designed collimating lens. 2.3 Computer-Aided Design and Analysis - TRAP Since calculations of reflection modulus and phase of multi-layerd media are tedious and time consuming, we have developed a computer-aided design pro- gram that provides an interactive environment for the user to design his circuits and to compare the theoretical and experimental results. TRAP (transmission, reflection, absorption, and phase) was developed to analyze the square grid, to- gether with the substrate, dielectric slabs, filters, and mirror. It is an interactive graphics program written in Turbo Pascal for the IBM personal computer. The user types a descriptive command line via the line editor in TRAP. Commands may include lossy dielectrics, lumped elements, and a mirror. The angle of inci- dence, polarization, wavelength, and layer thicknesses can be varied linearly. The calculated results are displayed as the computations are made. Three real-time keyboard commands are available to stop, speed up, or slow down the simula- tion. On the average it takes about 30 seconds per layer to complete a plot on an IBM-XT. The programmed optimization routine is based on a multi-dimensional simplex algorithm [12]. It allows the user to fit a model based on transmission-line theory to the measured reflectance and phase of reflection from a multi-layered 26 medium. TRAP calculates the transmittance, absorptance, reflection coefficient of a layered medium by generalizing Berning’s algorithm [13] to include the ef- fects due to periodic grids at the interfaces. This algorithm is numerically more efficient than the conventional cascade matrix approach. Equivalent circuit mod- els are derived from physical dimensions of thin screens such as the square grid. One model is based on MacFarlane’s quasi-static formula of a strip [7], and the other model is based on a modification of Eisenhart and Khan’s theory of a post in a waveguide [9]. In addition the circuit model of a Jerusalem-cross based on Arnaud and Pelow [1] is also available. The solution for plane wave propagation in a multi-layered medium is a well known boundary value problem in wave analysis. However, in electromagnetic engineering, it is more desirable to make an analogy between the plane wave so- lutions and the waves along a transmission-line. The electric and magnetic fields are analogous to the voltage and current in a transmission line, and the ratio is called the impedance. The analogy is useful because it allows the designer to take advantage of existing impedance matching techniques in the field of transmission line design and analysis. To exploit this analogy fully, the concept of admittance, the ratio of magnetic field to electric field, is used because the multi-layered me- dia is plane-parallel, which means its equivalent circuit is parallel. Therefore, it is more desirable to use admittance because parallel admittances add. The method of calculation for wave reflection from multi-layered media is discussed next to establish the notation. Figure 2.5 shows a schematic of a multi-layered medium with thin structures such as a lossy film or a periodic grid at the interface between two layers. The waves are incident from the left. The boundaries are labeled from 0 to N , with 0 being the interface of the incident medium and N being the interface of the final medium. The angle of incidence is 8,, and the complex refractive index 27 A A A A A A No ny Ns nj Ny Ney ee ee ee ee ee es ee eee eee 8, Ag Ay A, A A, AL AQ 0) { 2 Hi j N-1 N Figure 2.5. Schematic diagram of a multi-layered medium. 28 of the j** layer is ny = n; + tk;, where n; is the refractive index and k; is the absorption index of the j** layer. The physical thickness of the jg’ layer is 1;, and its electrical length is oj; = 2nf;l;. All admittances are normalized to the characteristic admittance in the vacuum. The normalized admittance for a thin structure at the j** interface is y;. The calculation of the reflection coefficient, transmittance, and absorptance begins from the final medium on the right and works its way back toward the incident medium on the left. The normalized admittance of the final medium is initialized to Yn = finii + yn. The normalized admittance looking from the j* interface toward the right is given by the recursive relation, . . Y;cosd; +1h,, sind; Yj-1 = Gj—] + 1b;_4 => Noy = $3 y. . 9; fjp cos $; + tY; sin d; + Yj-1) (2.42) where nh; cos 6; for TE polaraization fijp = ; (2.46) n;/ cos 0; for TM polarization and 9; satisfies Snell’s Law of Refraction, fo Sin 8, = fi; sin 8;. (2.4c) The reflection coefficient at the input surface of the multi-layered medium is calculated from (2.5) The transmittance at the output surface is given by T = (1- |p|?) ) IT vs (2.6a) 29 where #; is the ratio of time average of the magnitude of Poynting’s vector at the j** and (j — 1)** interfaces and is given by the formula, a; a;_1|cos¢; + 1Y; sin 0; /A;|?° ~; = (2.66) Using the Law of the Conservation of Energy, the total absorptance in the layered medium is given as, A=1-T—|pj?. (2.7) 2.4 Simulated Performance of Diode-Grid Phase Shifter Figure 2.6 shows a simulation of the diode-grid phase shifter. The assumed metal parameters are based on the skin-effect formulas for gold. Dielectric prop- erties are taken from Afsar and Button’s data [14]. The result indicates that the phase of reflection varies linearly from —180° to +180° as the grid reactance sweeps from a normalized reactance of —1 to +1 (—1079 to +1072 for the gallium-arsenide substrate). The reflection efficiency varies from a low of 0.49 to a high of 0.57, with an average loss of 2.7dB. Of this loss, all but a tenth of a dB is due to the series resistance of the diode (assumed to be 109). Figure 2.7 shows a family of diode-grid phase shifter performances for normal incidence in air. Gallium-arsenide is assumed for the diode-grid substrate. The grid reactance is assumed to vary from —1072 to +107 , and resistance is as- sumed to vary from 10 to 502). The refractive index of the quarter-wavelength dielectric cover is assumed to vary from 2.26 to 2.34. These indices satisfy the condition, 2o( 22)" (RP + 22) = 22 (2.8) Ze a —_ [ed ° where the Z, is the effective characteristic wave impedance of the diode-grid substrate, Z, is the effective characteristic wave impedance of the quarter-wave 30 Relative bias voltage (V) -5 -4 -3 -2 -| O 1.0 l I I I 180 _ Oo 0.8F o 19 8 L x w= O0.6/F- . ae @ a O Cc c 2 S oat 5 O o : — F & 0.2b 90 & 0.0 l -| -100 -50 O 50 lOO 80 Total grid reactance, 2 Figure 2.6. Simulated results of the programmable diode-grid phase shifter. The initial quarter-wave transformer layer is fused quartz, the angle of incidence in the air is 45°, and the polarization is TE. 31 dielectric cover, Z; is the effective characteristic wave impedance of the incident medium, and R is the series resistance of the diode-grid. It is interesting to note that the use of these refractive indices equalizes the reflection losses by having the impedance looking into the diode-grid phase shifter to revolve around the center of the Smith chart. Also, the required refractive indices are slightly larger than the refractive index usually required for an anti-reflection coating. Although the required refractive indices are not too practical from the material point of view, the same effect of equalizing the reflection loss can be obtained by adjusting the angle of incidence in air. When this is done for TE polarized waves, the angle of incidence is about 36° for crystal-quartz, and about 52° for fused quartz. From Figure 2.7 we can see that the maximum and minimum reflection losses occurs around 0° and +110°, respectively. Figure 2.8 shows these reflection losses as a function of R/AX, the ratio of the real part to the total change in the imaginary part of the diode-grid impedance. They vary almost linearly in R/AX from 0.05 to 0.5. The slope for the maximum loss curve is 29.5, and for the minimum loss curve, 24.2. 32 Figure 2.7. Reflection loss of the diode-grid phase shifter 33 16 Lj t t Ls e ee Calculated maximum loss ° © © o Calculated minimum loss 14 - {2 |= 10 8 = Reflection loss, dB re) i l I ] i ie) Of 0.2 0.3 O4 O5 R/AX Figure 2.8. Reflectance loss of the diode-grid phase shifter as a function of the ratio of diode-grid series resistance to reactance. [1] [2] [10] [11] 34 References J. A. Arnaud and A. Pelow, “Resonant-Grid Quasi-Optical Diplexers,” Bell Sys. Tech. J., Vol. 54, pp. 263-283, 1975. R. E. Collin, Field Theory of Guided Waves, Chap. 12, McGraw-Hill, New York, 1960. G. Latmiral and A. Sposito, “ Radar Corner Reflector for Linear or Circular Polarization,” J. of Res. of NBS, Vol. 66D, pp. 23-29, 1962. R. Watanabe, “A Novel Polarization Independent Beam Splitter,” IEEE Trans. Mircrowave Theory and Tech., MTT-28, pp. 685-689, 1980. N. Nakajima and R. Watanabe, “A Quasi-Optical Circuit Circuit Technology for Shortmillimeter-Wavelength Multiplexers,” IEEE Trans. Microwave and Tech., MT'T-28, pp. 897-905, 1981. R. Ulrich, T. J. Bridges, and M. A. Pollack, “Variable Metal Mesh Coupler for Far Infrared Lasers,” Appl. Opt., Vol. 11, pp. 2511-2516, 1970. G. G. MacFarlane, “Quasi-Stationary Field Theory and Its Application to Diaphragms and Junctions in Transmission Lines and Wave Guides,” Proc. Inst. Elect. Eng., 93, Part 3A, pp. 1523-1527, 1946. J. R. Wait, “Impedance of a Wire Grid Parallel to a Dielectric Interface,” IRE Trans. on Microwave Theory and Tech., MT'T-5, pp.99-102, 1957. D. B. Rutledge and S. E. Schwarz, “Planar Multimode Detector Arrays for Infrared and Millimeter- Wave Applications,” IEEE J. of Quantum Electronics QE-17, pp. 407-414, 1981. R. V. Garver, “360° Varactor Linear Phase Modulator,” IEEE Trans. on Microwave and Tech., MTT-17, pp. 137-147, 1969. A. Y. Cho and F. K. Reinhart, “Interface and Doping Profile Characteris- tics with Molecular-Beam Epitaxy of GaAs: GaAs Voltage Varactor,” J. of 35 Applied Physics, Vol. 45, pp. 1812-1817, 1974. [12] J. A. Berning and P. H. Berning, “Thin Film Calculations using the IBM 650 Electronic Calculator,” J. of the Opt. Soc. of America, Vol. 50, pp. 813-815, 1960. [13] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, Chap. 10, pp. 274-334, Cambridge University Press, New York, 1986. [14] M. N. Afsar and K. J. Button, “Precise Millimeter-Wave Measurements for Complex Refractive Index, Complex Dielectric Permittivity and Loss Tan- gent of GaAs, Si, SiOz, Al203, BeO, Macor, and Glass,” IEEE Trans. on Microwave Theory Tech., MTT-31, pp. 217-223, 1983. 36 Chapter 3 Fabrication of Diode-Grids Monolithic diode-grids have been fabricated on 2cm by 3cm gallium-arsenide (GaAs) wafers with 2000 aluminum Schottky-barrier varactor diodes. The self- aligning technique, which Zah had developed in our group [1], is used to fabricate the diodes. The best fabrication yield for individual diodes in an array was 98%. A liquid crystal detection technique was developed to identify the diodes that are shorted in the grid, and subsequently an ultrasonic probe is used to remove the bad diodes. The design of the varactor diode with a truncated- hyperabrupt doping profile is discussed. The doping profile is measured with a mercury probe. The diode series resistance is calculated from the current- voltage (IV) characteristics measured at DC, and the capacitance parameters are calculated from the capacitance-voltage (CV) characteristics measured at 1MHz. The detailed procedures are given in the appendix. 3.1 Design of a Hyperabrupt Schottky Varactor Diode Figure 3.1 shows SEM photographs of the Schottky-barrier varactor diode on GaAs. The diode consists of a Schottky contact with a shape of a strip, which is surrounded by an ohmic contact. The width of the strip is defined by a self-aligning technique, and its length is defined by proton bombardment. This is the key of Zah’s process, which enables us to make a small planar diode for millimeter-wave applications. The area of the strip is about 18 um?; its small rectangular geometry gives a low spreading resistance since the periphery-to- area ratio is high. The metal for the Schottky contact is aluminum (Al), and the metal for the ohmic contact is gold-germanium/nickel/gold (AuGe/Ni/Au). The metalization extends from the diode and becomes part of inductive lead of the 37 Figure 3.1. SEM photographs of a planar Schottky-barrier varactor diode. (a) Diode is located at the tip of the strip. (b) Close-up view of diode. 38 diode-grid. The other part of the inductive lead is gold. For a large capacitance variation, the varactor is designed with a hyperabrupt doping profile; that is, the net doping concentration of the epitaxy decreases with the distance from the metal semiconductor interface. The three most important circuit parameters of a varactor are the breakdown voltage V;, the zero bias capacitance C., and the series resistance R,. They affect the amount of power the varactor will handle, the level of impedance the varac- tor will present, and the amount of power the varactor will dissipate in a circuit. These parameters can be calculated and optimized when the doping concentra- tion as a function of the distance from the junction is specified. Norwood and Shatz [2] analyzed an ideal hyperabrupt doping profile that is described math- ematically by an m** power law. In practice, a truncated-hyperabrupt doping profile must be used. Figure 3.2 shows the truncated-hyperabrupt doping profile. The doping concentration is given by Nz O0<zr< 24 Nu= | ) (3.1) no(£)" Zizr< Teps where z, is the zero bias depletion width, N, is the doping concentration at the surface, T.; is the epitaxial thickness, and m is the doping profile exponent. The method of design is based on Lundien et al.’s [3] design algorithm of an exponentially retrograded doping profile. In the depletion approximation, the one-dimensional Poisson equation, d?*¢ q dx2 Es Na; (3.2) is integrated, where ¢ is the electric potential, g is the electronic charge, and e, is the dielectric permittivity of the semiconductor. The boundary conditions are 39 Ng = No(x/xe)™ Ng» dopant concentration X, distance from surface Figure 3.2. A truncated-hyperabrupt impurity doping distribution designed for a varactor diode. 40 $(z = 0) = Oand ¢(z = Waep) = ¢; —V, where ; is the junction potential, Waep is the depletion width of the space-charge region, and V is the applied voltage. This leads to a complicated algebraic relation, V = F(W4ey), which is used to compute the corresponding CV relation A C=€, W dep , (3.3) where A is area of the varactor. The calculated CV characteristic is checked for self-consistency by the following expression [4], —c3 N _ (=) rn oh dV The profile computed from the above is compared with the original profile. The (3.4) resistance due to the undepleted epitaxial layer is calculated from, Tepi dz Rep: =| me 3.5 ? Waep QUnNgA ( ) where yy is the electron mobility, and Tepi is the epitaxial thickness. An emperical expression for the electron mobility is used 104 kn = = I+ 1017 where Nj is in units of cm~? and yy is in units of cm? (Vs)~} [5]. The break- (3.6) down voltage is computed as the applied voltage at which the ionization integral -(at5) ] dz = 1, (3.7) becomes unity, Weps I= [ Aexp 41 where E(x) is the electric field in units of V(cm)~!, A = 3.5 x 10° cm™!, and b = 6.85 x 10° V(cm)~! [6]. The integrals are integrated numerically with an algorithm based on Simpson’s rule [7]. The electric field is obtained from the one-dimensional Poisson equation. The boundary conditions are imposed by matching the fields at z = x, and by setting the field to zero at x = Wepi- The expressions obtained are checked with those obtained from Gauss’s law. A simple graphical procedure is used as a guide to design the truncated- hyperabrupt profile for a varactor. The design parameters are the surface con- centration (N.), the doping profile exponent (m), the zero bias depletion width (z.), and the epitaxial thickness. A figure of merit for a varactor is the dynamic cutoff frequency, which is defined by Penfield and Rafus [8] to be, f.= Smaz — Smin .= oem on , (3.8) where Smaz is the reciprocal of minimum capacitance, Syin is the reciprocal of the maximum capacitance, and R, is the series resistance of the varactor. Other quantities including series resistance, capacitance tuning ratio, and avalanche integral are also calculated to indicate design margins and tradeoffs. Figure 3.3 shows a contour plot of dynamic cutoff frequency as a function of surface concentration and doping profile exponent. An approximated junction potential for Al on GaAs is 0.94 V from Eglash et al. [9]. The maximum ca- pacitance is taken to be the zero bias capacitance, which is assumed to be 30fF because this gives the desired reactance at 90 GHz for our experiments. The epi- taxial thickness is 0.65 ym. This thickness is chosen because it is thick enough to give a capacitance ratio of 5 and thin enough for proton isolation. The calcula- tion also assumes a parasitic resistance of 7M and a parasitic capacitance of 3fF. The solid line indicates that the ionization integral is unity (J = 1) and divides 42 7 8 E 2 ro) = AL 4 x fe] = 6 3F 1 2 = ®D e 5 2b : = a [e) QA - Tr 4 O -2 -1 O Doping profile exponent, m Figure 3.3. A contour plot of dynamic cutoff frequency in units of THz as a function of surface concentration and doping profile exponent in the region where the ionization integral is less than unity (I < 1). The solid line corresponds to the (I = 1) and the shaded region corresponds to the (I> 1). 43 the space into safe and unsafe regions of operation. Safe means that the entire epitaxial layer can be depleted without avalanche breakdown or with (I < 1). Qualitatively speaking, the closer N, and m approach the solid line, the greater the chance of reaching avalanche breakdown. The bigger N, is, the bigger the capacitance ratio, which is good for phase-shifting, while (—0.5 < m< —0.3) is more favorable for second harmonic conversion efficiency [10]. The final design of the truncated-hyperabrupt doping profile varactor is N, = 1.5 x 1017 cm7?, m= 1.0, z =0.1ym, and T,,; = 0.65 um. An extra 0.05 pm is added as safety margin for back depletion from the n+ layer. The thickness of the n* layer is 1.8um. This gives a total epitaxial thickness of 2.5 uum, which is close to the limit of the proton isolation capability available to us. The doping concentration for the nt layer is designed to be 3 x 10!8cm-3. A mercury probe is used to measure the CV characteristic and the doping profile [10]. Figure 3.4 shows the measured CV characteristic. The ratio of the capacitance at zero bias to the capacitance at breakdown is about 4.5 and this is close to what the simulation predicts. The breakdown voltage is about 9V, and this corresponds to what the simulation predicts when the ionization integral is about 0.4. This comparison is based on averaging the calculated results at m = —1.1 and m = —0.9. Figure 3.5 shows the corresponding measured doping profile and compares it to the profiles that were designed and measured with a Polaron profiler. Basically, a back-to-back Schottky diode is formed on the surface of the wafer with a small and a large mercury dot, which are held there by a vacuum. Then the small signal capacitance of this diode structure is measured as a function of the DC bias. The advantage of this technique is that it is non- destructive. Occasionally, the doping profile is available from a Polaron profiler for comparison. This provides a more complete measure because it includes the nt layer; however, this is a destructive technique since it requires etching away 44 250 T T T T 200+ 4 cL es = ©O 150 mn . ~ a r ° < £ . S 100 + = Q. ° & i SOF ,. eet! 4 O I I 1 I -10 -8 -§ -4 -2 O Bias voltage, V(volt.) Figure 3.4. Measured capacitance-voltage characteristic at 1 MHz from a GaAs wafer with a truncated-hyperabrupt doping profile. 45 19 10'rc T 1 5 Designed ] 5 ——~- Measured by mercury probe a m ———: Measured by polaron profiler 7 10} oe I I Dopant concentration, Nj (cm *) riritl { of l { 1 i 0 0.2 04 0.6 0.8 {0 Depth, x (um) Figure 3.5. A comparison of designed doping profile with the measured doping profiles from a mercury probe and a Polaron profiler. 46 the substrate in determining the depth. The doping profile is calculated from the measured CV characteristic according to Equation (4). This is run by an IBM-PC that controls an HP4280A C-meter for CV measurements. The CV program is given in the appendix. 3.2 Fabrication Processes Having determined the CV characteristic and doping profile of the wafer, we evporated a 2000 A thick layer of aluminum. Although in-situ molecular beam epitaxy (MBE) aluminum is superior [1,12], it is not as readily available. Fig- ure 3.6 summarizes all the different layers of the starting material for fabricating the diode-grid. The aluminum is on an 0.7 um layer of n-type GaAs with a hy- perabrupt doping profile. The n-type GaAs is on an 1.8 pm layer of n* GaAs with a doping concentration of 1x 10!8cem-*, Howard Chen, of Professor Yariv’s group at Caltech, and Kjell Stolt of TRW grew the epitaxial layers on chrome- doped semi-insulating GaAs with MBE for us. Wafers as large as 2cm by 3cm have been used to fabricate the diode-grids. The diodes are fabricated with a self-aligning process that Zah developed (1]. 3.2.1 Self-Aligning Schottky Contact Figure 3.7 shows how the self-aligning process works. A photoresist is pat- terned to protect the aluminum Schottky contact during wet etching and to serve as a lift-off mask when the metalization for the ohmic contact is evaporated. The structure is formed by first etching the aluminum until it cuts under the photore- sist and then etching the n-layer until it reaches the nt layer and cuts under the photoresist. When AuGe/Ni/Au is evaporated over this structure, a small gap is created between the Schottky metal and the ohmic metal; hence, the Schottky contact is self-aligned to the ohmic contact. 47 Aluminum L LLL LLL LLL Lo De, 7. COMMA DADS SIITOCO? | - n layer 7 ry n* layer v Semi-Insulating GaAs TN 0.2 um O.7pm 1.8um Figure 3.6 A side view of the starting material with 2000 A of evaporated aluminum on the n-type GaAs epitaxy. 48 AuGe/Ni/Au evaporation Photo - Semi-insulating GaAs With Aluminum AuGe/Ni/Au ohmic contact Figure 3.7. Zah’s self-aligning process for defining the width of the Schottky contact. 49 In the past, the lead for the Schottky contact was patterned first and then the width of Schottky contact and the ohmic contact were defined by the self- aligning process as described above. Also in-situ MBE aluminum was used. In my experience of using evaporated aluminum, I find it better to etch the width of the Schottky contact and the ohmic contact first and then pattern the lead for the Schottky contact. This has the following advantages. Since a small amount of aluminum is removed in defining the contacts, there is still a significant amount of aluminum left over. If over-etching occurs, one can repeat this step several times until the desired result is obtained. More importantly, etching becomes easier to control because etching tended to be less uniform, when the lead for the Schottky contact was etched before the width of the Schottky contact and the ohmic contact were etched. This is probably due to bubbles formed and trapped at the corner of the photoresist pattern. Figure 3.8 illustrates this problem. Having patterned the lead for the Schottky contact, we then developed the photoresist mask for self-aligning the diode contacts via etching. This exposes a small piece of aluminum to be etched away. Figure 3.8a shows the top view of this. When the wafer is dipped into aluminum etchant, it was found that about 20% of the diodes tended to be incompletely etched. Typically a small patch of aluminum is left behind as shown in figure 3.8b. If the wafer is etched again, then those diodes that were etched completely will be over-etched. If the wafer is not etched again, then those diodes with a small patch of aluminum cause an electrical short when the ohmic metalization is evaporated. This problem is corrected by simply reversing these two steps. 3.2.2 Ohmic Contact The technique of using AuGe/Ni/Au to form an ohmic contact on n-type GaAs in a furnace is followed [13]. The thicknesses for the metalizations are 700 A e diode. (b) Af ol of AuGe (88% Au and 12% Ge by weight), 300 A of Ni and 2000A of Au. They are evaporated consecutively without breaking the vacuum. The metalizations for the bonding pads are also evaporated at the same time. This is because the alloy process makes the bonding pads adhere to the substrate better and roughens the surface of bonding pads so that they are easier for ultrasonic wire bonding. The alloying process is done in a furnace at 460°C for 10 minutes with flowing forming-gas. As the AuGe alloy begins to melt, gallium diffuses into the metal [14]. Germanium diffuses into the crystal lattice and dopes the GaAs. Nickel enhances this diffusion and keeps the metal ‘wet’ onto the surface from segregating in lumps, and gold serves as a capping layer to increase the conductivity. Making a good ohmic contact is important in achieving a low series resistance for the varactor diode. Factors that influence the quality of an ohmic contact are well documented [14,15]. One of the most important factor that influences the quality of an ohmic contact is the alloying temperature. Other parameters including the type of metalization and its composition and thickness, ambient gas, alloying time etc. can easily be reproduced based on published literature. There is a wide variation in the temperature used by various laboratories, be- cause the equipment and the way in which alloy temperature is measured are not the same; therefore, it is necessary to calibrate the temperature of our furnace controller. The basic technique of using a linear resistor array to measure the contact resistance is used [14]. Figure 3.9 is a photograph of the actual array fabricated on a GaAs wafer. The ohmic contacts are AuGe/Ni/Au alloyed on a mesa of nt GaAs epitaxy. An HP3478A multimeter with a 4-wire measure- ment capability is used to measure the resistance between the ohmic contacts. The measured resistance as a function of distance gives the contact resistivity. The furnace controller is calibrated by measuring the contact resistivity of the 52 Figure 3.9. Photograph of the resistor array used in measuring contact re- sistance. Square ohmic contacts are separated by increasing distances. Each resistor array is isolated by mesa etch. 53 10 T if t T I q xxx Measured [0/16/86 e «oe Measured 10/85 Contact resistivity (;22-cm*) 0 L i t I ! ! 420 440 460 480 500 520 Controller temperature, (C’) Figure 3.10. Temperature calibration curve of the furnace controller used in alloying ohmic contacts. 54 ohmic contacts alloyed at various temperatures. Figure 3.10 shows the tempera- ture calibration curve for our furnace controller. A minimum contact resistivity of 4u0(cm)* was measured at an alloying temperature of 460°C. The actual temperature was estimated to be 430°C. 3.2.3 Proton Isolation Figure 3.11 shows the proton isolation process used in defining the length of the diode. Figure 3.12 shows a 7 um thick photoresist patterned to protect the diode from the protons. The implanted protons convert the n-type semiconductor into a high resistivity dielectric by creating deep levels that trap free carriers [15]. Two consecutive proton bombardments are used in order to completely isolate the epitaxial layers. The implantation parameters are 1.) dose=4 x 10!4 cm~? and energy=330 keV, and 2.) dose=4 x 1014 cm=? and energy=200 keV. This was done for us by Frank So and Ali Ghaffari in Dr. Nicolet’s group at Caltech and Bob Rush at Hudges. The temperature reached during implantation is high enough to harden the photoresist, so an oxygen plasma is used to remove the photoresist. 3.2.4 Low Frequency Varactor Parameters After proton isolation, low frequency parameters of the varactor are mea- sured. A number of varactors are sampled through out the wafer in order to assess the amount of nonuniformity, and to find an average and a standard devi- ation for the nonuniformity. Figure 3.13 shows a contour plot of measured series resistance as a function of position on the wafer. The measured series resistance is based on an algorithm that curve-fits the measured IV characteristic with the following equation [1] I = I,exp|(V — IR,)/nVr] - 1, (3.9) 55 | | | | Proton implantation Thick photoresist RASSASAAAGSS SS IXXIXSERERLRSLE SERRE Semi-insulating GaAs Ne WN Aluminum AuGe/Ni/Au ohmic contact Proton bombard region Figure 3.11. Schematic diagram of proton bombardment for defining the length of the Schottky contact. 56 Figure 3.12. SEM photograph of a 7 wm thick photoresist mask for protecting the Schottky contact in defining its length. 57 ate SS VU, PrTiItty wt Yi Figure 3.13. A contour map of the diode series resistance in units of ohms. Tick marks correspond to diode positions on the wafer. 58 where I, is the reverse saturation current, R, is the series resistance, n is the ideality factor, g is the electronic charge, k is the Boltzman constant, and T is the temperature. Figure 3.14 shows a contour plot of zero bias capacitance measured at 1 MHz as a function of position for the same wafer. The diode parameters vary considerably. This is mainly due to mask variation and misalignment dur- ing fabrication. The measured diode series resistance is 789 with a standard deviation of 19, zero bias capacitance is 30{F with a standard deviation of 10fF, and breakdown voltage is 5.1V with a standard deviation of 1.9V. This is based on sampling 95 out of 2000 possible diodes. The diodes have a soft breakdown characteristic. This is probably due to contamination because alu- minum is evaporated in a oil diffusion-pumped system at 3 x 10~® Torr. Similar observations were reported in the literature [9,17,18]. Attempts to use refrac- tory metals such as titanium and molybdenum were made, but no significant improvements have been obtained. The series resistance is quite high because the n* concentration is only about 1 x 10/8 cm-?. The low breakdown voltage limits the capacitance variation from 14.5fF at —5.1V to 52.1{F at +0.4V. This corresponds to a capacitance ratio of 3.7. These measurements are computer- ized. An IBM personal computer is used to control an HP4145B semiconductor parameter analyzer to make the IV measurement and an HP4280A C-meter to make the CV measurement. Software documentations are given in the appendix. 3.2.5 Liquid Crystal Detection A layer of 2000 A thick gold and a layer of 100 A thick chrome are evaporated to define the periodic grid that connects the varactors row by row. The chrome acts as an adhesion layer between gold and GaAs. Despite the fact that the yield of the number of devices with a diode characteristic is quite high, the remaining bad diodes, which tend to be electrical shorts, render the entire diode- 59 3.6 Perr yperered 38 ool Figure 3.14. 10~'* farads. Tick marks correspond to diode positions on the wafer. Lirirtdir yy) AVN | A contour map of the diode zero bias capacitance in units of 60 grid almost functionless, because they are connected in parallel. To overcome this, a liquid crystal detection technique is developed to identify the shorted diodes [19]. Figure 3.15 is a photograph of a shorted diode that was found using this method. A layer of liquid crystal for 28-30°C range is spun onto the wafer. Then current is injected into the rows that are shorted. Because the shorted diodes draw most of the current and therefore dissipate most of the heat, the color of the liquid crystal changes from red to blue as the temperature rises within the vicinity of the shorted diode. Once the short is found, an ultrasonic probe is used to remove the defective diode. 3.3 Test Fixture Figure 3.16 shows a section of the diode-grid fabricated on a GaAs wafer. Figure 3.17 shows the diode-grid, glued on a glass slide with photoresist at the edge of a pc-board. This is convenient because the photoresist can be dissolved in acetone quite easily. There are a total of 50 DC bias lines available. Two edge connectors are used to feed the bias lines from the variable bias controller, which consists of an array of variable resistors driven by programmmable constant current sources. Electronic relays are used to provide low-frequency modulation of the DC bias for situations that require a reference signal. 61 Shorted diodels 1mm Figure 3.15. Photograph of a shorted diode found by a liquid crystal detection technique. 62 Figure 3.16. Photograph of a diode-grid with AuGe/Ni/Au bonding pads. 63 Figure 3.17. Photograph of a diode-grid mounted on a pe-board with 50 DC bias lines available. 64 References [1] C. E. Zah, “Millimeter-Wave Monolithic Schottky Diode Imaging Arrays,” Ph. D. Thesis, Chap. 3, pp.38-51, California Institute of Technology, Cali- fornia, 1986. [2] M. H. Norwood and E. Shatz, “Voltage Variable Capacitor Tuning: A Re- view,” Proceedings of the IEEE, Vol. 56, pp. 788-798, 1968. [3] K. Lundien, R. J. Mattauch, J. Archer, and R. Malik, “Hyperabrupt Junction Varactor Diodes for Millimeter-Wavelength Harmonic Generators,” IEEE Trans. on Microwave Theory and Tech., MTT-31, pp. 235-238, 1983. [4] R. S.Muller and T. I. Kamins, Device Electronics for Integrated Circuits, Chap. 2, pp. 65-104, John Wiley & Sons, Inc., New York, 1977. [5] C. R. Hilsum, “Simple empirical relationship between mobility and carrier concentration,” Electronics Letters, Vol. 10, pp. 259-260, 1974. [6] S. M. Sze and G. Gibbons, “Avalanche Breakdown Voltages of Abrupt and Linearly Graded p-n Juntions in Ge, Si, GaAs, and GaP,” Appl. Phys. Lett., Vol. 8, pp. 111-113, 1966. [7] W.H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, Chap. 4, pp. 102-130, Cambridge University Press, New York, 1986. [8] P. Penfield, Jr., and R. P. Rafuse, Varactor Applications, Chap. 4, pp. 57-91, Massachusetts Institute of Technology Press, Massachusetts, 1962. [9] S. J. Eglash, M. D. Williams, P. H. Mahowald, N. Newman, I. Lindau, and W. E. Spicer, “Aluminum Schottky Barrier Formation on Arsenic Capped and Heat Cleaned MBE GaAs(100),” J. of Vac. Sci. Technol., Vol. B2(3), pp. 481-486, 1984. [10] T. C. Leonard, “Prediction of Power and Efficiency of Frequency Doublers [12] [13] [14] [15] [16] (17] [18] [19] 65 Using Varactors Exhibiting a General N onlinearity,” Proceedings of the IEEE, Vol. 51, pp. 1135-1139, 1963. M. Binet, “Fast and Non-destructive Method of C(V) Profiling of Thin Semi- conductor Layers on an Insulating Substrate,” Electronics Letters, Vol. 11, pp. 580-581, 1975. A. Y. Cho and P. D. Dernier, “Single-crystal-aluminum Schottky-barrier diodes prepared by molecular-beam-epitaxy (MBE) on GaAs,” J. of Appl. Phys., Vol. 49, pp. 3328-3332, 1978. M. Heiblum, M. I. Nathan, and C. A. Chang, “Characteristics of AuGeNi Ohmic Contacts to GaAs,” Solid State Elect., Vol. 25, pp. 185-195, 1982. R. E. Williams, Gallium Arsenide Processing Techniques, Chap. 11, pp. 225-257, Artech House, Inc., Massachusetts, 1984. N. Yokoyama, S. Ohkawa, and H. Ishikawa, “Effects of the Heating Rate in Alloying of Au-Ge to n-Type GaAs on the Ohmic Properties,” Japan J. of Appl. Phys., Vol. 14, pp. 1071-1072, 1975. J. P. Donnelly and F. J. Leonberger, “Multiple-Energy Proton Bombardment in nt-GaAs,” Solid-State Electronics, Vol. 20, pp. 183-189, 1976. Y. Sato, M. Uchida, K. Shimada, M. Ida, and T. Imai, “GaAs Schottky Barrier Diode, ECL-1314,” Rev. of the Electrical Communication Lab., Vol. 18, pp. 638-644, 1970. M. Ida, M. Uchida, K. Shimada, K. Asai, and S. Ishida, “Fabrication Tech- nology of Stable Schottky Barrier Gates for Gallium Arsenide MESFETS,” Solid-State Electronics Vol. 24, pp. 1099-1105, 1981. J. L. Fergason, “Liquid Crystal in Nondestructive Testing,” Applied Optics, Vol. 7, pp. 1729-1737, 1968. 66 Chapter 4 Diode-Grid Phase Shifter Measurements In proposing a new design, the experimental procedure for testing the as- sumed model is also necessary. In the process of developing the experimental procedure, what is available in the laboratory often plays a role in deciding the experimental method. This chapter begins with a survey of possible existing methods of measurement for testing the diode-grids, and concludes that they are not suitable in our work. This is mainly due to the fact that wafers available to do our experiments were usually small and irregular in shape. Consequently, a small aperture reflectometer that uses a wave-front division interference technique was developed to measure the reflection coefficient of the diode-grid. The validity of this method is illustrated by reflection measurements of thin-film bismuth on fused quartz and its limitations are indicated by reflection measurements of fused quartz. The experimental procedure consists of curve-fitting the measured RF reflection coefficient with an equivalent circuit model based on transmission-line theory and comparing the best-fitted parameters with the corresponding param- eters measured at low frequency. 4.1 Survey of Possible Experimental Methods One of the possible methods of testing the diode-grid is based on simulation of a planar periodic array in waveguide {1]. Such simulation permits the use of a few elements in a waveguide to represent a large number of elements in an infinite periodic array. In the waveguide simulator, the array impedance can be measured. However, precision waveguide machining and sample mounting are required to duplicate the details of the array. Furthermore, a scaled model is probably required as the frequency approaches 100 GHz, and it is more desirable 67 if the measurement can be made directly on the diode-grid itself. Therefore, methods based on quasi-optical techniques become more attractive. In principle, various quasi-optical methods for measuring the complex di- electric constant of a material can be extended to test the diode-grid. They have demonstrated remarkable accuracy in dielectric measurements at millime- ter wavelengths. The semi-confocal open-resonator [2] and quasi-optical network analyzer [3,4] produce results with uncertainty of about 1% in the real part of dielectric permittivity and 10% in the loss tangent. The Mach-Zehnder interfer- ometer [5], and Michelson interferometer [6] provide five or six significant figures for refractive index and 1% accuracy in loss tangent. In the semi-confocal resonator method, a sample free of any attachments is mounted on the planar mirror side of the resonator, and a change in the Q of the resonator and the resonant frequency are used to determine the complex dielectric permittivity. Jones [2] successfully demonstrated precise dielectric measurements at 35GHz. The sample should be plane-parallel with a diameter > 5cm. His sample ranged from 7cm to 7.5cm. The minimum spot size of the beam deter- mines how small a sample can be used, and at 100 GHz samples with a diameter larger than 3cm are required. This was too large for us. In the other three approaches, various optical configurations for wavefront interference are used to assess the dielectric permittivity. Their general principle of operation is interesting and will simply be illustrated with the Michelson inter- ferometer as shown in figure 4.1. An incident wave is divided into two parts by the beam splitter. One part of this wave goes to a scanning mirror and becomes the reference wave. The other part goes to the sample, reflects off the sample, and becomes the signal wave. Then the two waves recombine at the beam splitter and go to the detector. The measured intensity of the interfering signals allows one to find the reflection coefficient of the sample. To calibrate the system, the 68 IA Scanning mirror Beam splitter Source WA Reference wave — - Signal wave Sample Ww Detector Figure 4.1. Schematic representation of a Michelson interferometer. 69 microwave technique of using an open, a short, and a matched-load can be used. Placing a planar mirror at certain position along the horizontal arm of the in- terferometer allows one to define a reflection coefficient of —1. Translating the mirror by a quarter-wavelength allows one to define a reflection coefficient of +1. And removing the mirror allows one to define a zero reflection coefficient. Figure 4.2 shows an actual setup of the Michelson interferometer. Teflon lenses were included to collimate and focus the beam onto the diode-grid since the grids were typically small (2cm by 2cm). Using results published by Har- vey [7], we designed an artificial quarter-wave matching layer in the form of groves to match the surfaces of the dielectric lens. Also, absorbing materials were strategically placed to minimize any stray reflections. Despite these efforts, the measured results were inconsistent with transmission-line theory because the cal- ibration procedure was not sufficient to calibrate out those extraneous reflections coming from the dielectric lens and absorbers in the neighborhood of the diode- grid. Although more complete calibration procedures are available [6], they are very sophisticated for practical use. In addition, these methods require samples with large lateral dimensions. For example, in the multiport reflectometer [3], Stumper used samples 7cm to 8cm in diameter to make reflection measurements at 392 GHz. These are the factors that make the small aperture reflectometer attractive for samples that are small and irregular in shape. 4.2 Small Aperture Reflectometer Figure 4.3 shows a small aperture reflectometer developed to measure the reflection coefficient of the diode-grid. The idea is to use an absorbing screen with a hole in the center to divide an incident wave-front into two parts. The wave that reflects off the absorber is the reference, while the other part reflecting off the sample is the signal. The interference of these two reflected waves is 70 Figure 4.2. Photograph of a Michelson Interferometer for millimeter waves. 71 ‘JayaWMOJOPoI oinjiade [Tews e jo uoljezUaseidal syewWaYS Jaquosqy JopNaap epoig y OADM uodshy JOpONUd} IV . jouBIS @-=}t-w => Jayow 4Oy OADM 40}D|OS} J8MOq] pupog M QOUdIOJONY > "Sh oINSLT ree apoid JOJ41UU 9|qDAOW\ 72 measured as the sample is translated relative to the absorber. An absorbing screen is chosen to approximately balance the energy in the two reflected waves so that the measured intensity has sufficient contrast. The phase and amplitude of the reflection coefficient of the sample can be found by least-square fitting each interference pattern or by a simple four-point method [8]. The scanning mirror serves as a tuning parameter as well as a standard load for calibration. The system alignment and calibration can be done quite quickly, and the measurement can be computerized. Figure 4.4 shows an actual setup for the small aperture reflectometer. Initially a Varian klystron source with 100 mW of output power was used, but later it was found that a Hughes Gunn-diode source with 10 mW of output power was sufficient to do the measurement. The input power is sampled by a 10-dB directional coupler and monitored by an HP432A power meter thru a Hughes thermistor head. The frequency is measured by a Hughes wave-meter before and is checked after the experiment to determine the appropriate step size and to ensure that no significant frequency shift occurs. The measured input powers are used to normalize the measured intensities. The area of the transmitting horn is 4cm?. The intensity of the interference pattern is measured by a receiving horn that feeds into a zero bias detector. The output isa DC signal, which is monitored by a HP 3478A multimeter. An IBM-PC is used to control the equipment. It uses a Capital Equipment interface board to communicate with HP equipment and a Data Translation A/D and D/A converter to control the stepper motors, which have a resolution of 1 wm. Figure 4.5a shows the translation stage. Figure 4.5b shows the absorbing screen that is placed next to the diode-grid, which is located at a distance of 82cm away from the horns. This corresponds to six times the far field condition. To accommodate different sizes and shapes of diode-grid, a small replaceable template of absorber is used in conjunction with a bigger 73 Figure 4.4. Photographs of the small aperture reflectometer setup. (a) Overall view. (b) Close-up view of the test fixture and minature microscope. 74 Figure 4.5. (a) Sideview of the computer-controlled translation stage. (b) The absorbing screen that is used to divide an incident wavefront in the small aperture reflectometer. 75 absorbing screen. Both the diode-grid and the scanning mirror are aligned with a Helium-Neon laser. The mirror is made by evaporating 2 um of gold on glass. The initial distance between the sample and the scanning mirror is measured by a miniature microscope with a resolution of 25 wm. The effect of interference can be demonstrated by plotting the power detected by the diode detector as a function of the mirror position. Figure 4.6 shows that the received power varies sinusoidally with the mirror position. The maxima cor- respond to constructive interference, while the minima correspond to destructive interference. Physically, more energy is deflected at the peaks and less energy is deflected at the valleys into the field of view of the detector. Since the re- flection coefficient of the sample is proportional to the complex amplitude of the interference pattern, one way to find the amplitude and phase is simply to fit a sinusoidal curve through the measured data. This is shown in figure 4.6 with a solid line. However, the curve-fitting process is time-consuming. Figure 4.7 shows pictorially another method in which both the amplitude and the phase of a sinusoid can be calculated. This is called the four point method, and it is based on simple phasor trigonometry. It was developed by Wyant [8] in optical interferometry for three-dimensional sensing. When the intensity of the sinusoid is sampled four times consecutively at 90° intervals, both the amplitude and phase of the sinusoid can be calculated by the law of tangents and the Pythagorean theorem. The 90° phase shifts can be introduced in the form of optical path delay by translating the sample relative to the screen at intervals of one-eighth of a wavelength. Both the curve-fitting method and the four-point method have been used, and they agree to within 2% for amplitude and 3° for phase. The four-point method is preferred since it is faster. Also, it is interesting to note that the use of the four-point method in the small aperture reflectometer makes the system analogous to a six-port network analyzer. However, in the small 76 100 ] 1 ] x x x Measured intensity Curve-fitted intensity Measured signal, mV 00 0.7 14 2) Mirror position, mm Figure 4.6. An interference pattern measured at 93 GHz. 27 34 77 Measured sinusoid i Vy \ 8 Phasor representation 2A Intl, I,+I, cm Ze. Aa cy IAN XN Figure 4.7. A pictorial illustration of the four-point method. 78 aperture reflectometer only one detector is used, while in the six-port network analyzer four detectors are required. Reflection Measurements of Bismuth on Fused Quartz The validity of the small aperture reflectometer can be illustrated with the reflection coefficient measurement of thin-film bismuth since we can control pre- cisely the way in which the sample is prepared. Figure 4.8a shows a one-square inch thin film bismuth deposited on a 3cm square fused-quartz plate by electron- beam evaporation in a diffusion pumped vacuum system. The bismuth thickness is 608 A. Using the four-point probe procedure, we measured the sheet resistance the bismuth film via four gold deposited strips at the edge of fused quartz to be 92.2. The fused quartz material is Dynasil # 4000. It is plane-parallel to within 5m. Figure 4.8b shows the configuration in which the reflectance and phase of reflection were measured at 93 GHz. Figure 4.9 shows the result of the reflection measurement or the tuning curve. The reflectance reaches a maximum of 100% at a mirror position of 720m. This is primarily to due the effect of the mirror, which basically presents an electrical short at the plane of the bismuth film. At a mirror position of 1590 ym, the effect of the mirror is equivalent to an open circuit at the plane of the bismuth film; therefore, the reflectance reaches a minimum. The value of this minimum is determined by the sheet resistance. Theoretical curves are plotted using the measured bismuth sheet resistance (92.21), fused quartz thickness (434 um), index of refraction (1.96 from Afsar and Button [6], initial mirror position (203 um), and a best-fitted length parameter due to phase calibration (2067 um). The phase-calibration length is the distance between the input surface of the sample (bismuth film) and a reference plane at which the measured phase of reflection is 180° for the mirror. The phase-calibration length was measured to be 2019 zm, which disagrees with the best-fitted value by 48 um 79 Y Ov Incident wave Movable Yj * mirror Yy Yj —— Uy Reflected wave YU Fused quartz Bismuth (b) Figure 4.8. (a) Photograph of thin-film bismuth on fused quartz. (b) Reflection measurement configuration of bismuth at 93 GHz. 80 1.0 0.8 / 2 O6 - S @ — OFF — @ . ; o xxx Experiment O — | ] | | — 0.2 0.6 10 14 18 2.2 Mirror position, mm Figure 4.9a. Measured reflectance of thin-film bismuth on fused quartz at 93 GHz. 81 100 F I l T = x xxx Experiment S 90 — Theory = Dw 22 a L = 80 53 3 & vOFfF 60 k l I ! I — 02 0.6 1.0 1.4 18 22 Mirror position, mm Figure 4.9b. Measured phase of reflection of thin-film bismuth on fused quartz at 93 GHz. 82 in physical length or 10° in electrical length. This is about as accurate as we can measure the phase-calibration length since, a miniature microscope with a reso- lution of 25 ym is used to measure distances from the side of the sample. When the sheet resistance of thin-film bismuth is also treated as a fitting parameter, the best-fitted value is 91.69. This agrees quite well with the measured sheet resistance (92.21) at DC. 4.4 Reflection Measurements of Fused Quartz The limitation of the small aperture reflectometer is observed when it is used to measure low loss materials such as fused quartz. Figure 4.10 shows the configuration in which the reflection measurement was made at 89GHz. The reflection coefficient is measured as the mirror is tuned. Figure 4.1la shows the measured reflectance. The calculated reflectance is plotted using the measured fused quartz thickness (434 um), initial mirror position (203 wm), and refractive index for fused quartz (1.96 from Afsar and Button [6]). The calculation does not agree well with the measured reflectance when the absorption index for fused quartz (0.0005 from Afsar and Button [6]) is used. This is shown with a solid line. In order to get a better agreement, an absorption index of 0.02 must be used. This is shown in figure 4.1la with a dashed line. The dips in the measured reflectance are probably due to power leaking laterally. Figure 4.11b shows the measured phase, calibrated according to the measured phase calibration length (1105 um). It is interesting to note that the calculated phase of reflection agrees quite well with the measured phase. An explanation for this is the following. If power escapes as described above and the amount of power loss is relatively constant during a reflection measurement scan, then the measured phase is relatively unaffected because the four-point method, which takes the ratio of a difference of four intensity measurements to calculate the phase, effectively calibrates the 83 Y Incident wave Movable Y ~ Y _ | Reflected wave Figure 4.10. Reflection measurement configuration of fused quartz. 84 me ee re 8 08 b e e° ~ Cc @ oS e oS e = o7 ---- Theory (k=0.0005) ° ® . — ™ oc —— Theory (k=0.02) eee Experiment O06 F 7 O5 i | i I i 0.2 10 1.8 26 34 Figure 4.11a. Mirror position, mm Measured reflectance of fused quartz at 89 GHz. 42 85 180 F X Co) Oo | xxx Experiment — Theory g Phase of reflection, degrees vo) I Q2 1.2 1.2 26 3.4 Mirror position, mm Figure 4.11b. Measured phase of reflection of fused quartz at 89 GHz. 86 loss of power out of the calculation. This also indicates that power is most likely leaking out from the etalon formed between the quartz and the mirror. Interestingly, no dips occurred in the previous reflectance measurement of thin film bismuth on fused quartz. An explanation for this is that the thin-film bismuth, being lossy, damps out most of the power during situations that favor lateral power leakage from the etalon. 4.5 Reflection Measurements of Diode-Grids Comparisons between theory and experiment up to this point have been reasonably good. This is because the quartz plate is plane-parallel to within 5m and has a uniform layer of bismuth. On the other hand, a diode-grid has both thickness variation and nonuniform device parameters. Typically, the wafer thickness varies between 104m and 30yum. This is due to the manual lapping procedure. A total of 10 % of the diodes are expected to be open-circuited. This is due to over-etching during diode fabrication and removal of bad diodes that are shorted electrically or have a low breakdown voltage during diode testing. They tend to scatter randomly throughout the wafer. Nonuniformity of diode characteristics are also expected. They scatter less randomly throughout the wafer. This is mainly due to material properties and alignment during fabrica- tion. These factors are not readily amenable to analysis and make a comparison between theory and experiment difficult. This is why sample preparation plays such a vital role in quasi-optical dielectric measurements [2-6]. Although our calculation does not take these variations into account, they should represent some sort of average and provide useful information for the designer. A family of tuning curves were measured in order to see the effect of DC bias and millimeter frequency on the diode-grid circuit parameters. Figure 4.12a shows a diode-grid mounted on a pc-board that provides external DC bias to 87 DC bias foe grid PZ Incident wave Movable mirror _——_»> Reflected wave MG W (b) Figure 4.12. (a) Photograph of a diode-grid mounted on a pc-board. (b) Reflection measurement configuration of a diode-grid. 88 the diodes. A network of variable resistors driven by constant current sources is used to provide adjustable floating voltages to each row of the diode grid. The physical dimensions of this wafer are 2cm in width, 3cm in length and 376 um in thickness. Approximately 91 % of the varactors are functional and the rest are open-circuited. Figure 4.12b shows the configuration in which the tuning curves were made. Using a multi-dimensional simplex optimization algorithm [9], we curve-fitted the measured results with an equivalent circuit model based on a transmission-line theory. The error function was defined to be the absolute value of the difference between the measured and the calculated complex reflection coefficient. Figure 4.13 shows one of these measured tuning curves at 94GHz. This particular curve was measured with zero bias on the diode-grid. Four fitting parameters were used. The first parameter, phase calibration length, represents the thickness of a layer of air inserted in front of the diode-grid to account for the inaccuracy in phase-calibration. It allows the calculated phase of reflection to be adjusted by a constant offset. The second parameter, initial mirror position, represents the thickness of another layer of air inserted between the diode-grid and the mirror to account for the inaccuracy in measuring their initial sepa- ration. This has the effect of translating both the calculated reflectance and phase of reflection horizontally. The last two fitting parameters are the real and imaginary part of the diode-grid impedance. On this basis, theoretical curves were plotted using the best-fitted phase-calibration length (792 um), initial mir- ror position (1663 zm), diode-grid impedance (58 + 7941), the measured wafer thickness (376 um), and the index of refraction of GaAs (3.6 from Afsar and Button [6]). The measured phase-calibration length was 727 wm and the initial mirror position was 17024m. The measured diode series resistance was 782 with a standard deviation of 191M and the zero bias capacitance was 30fF with 89 Reflectance eceee Experiment = O2 Fr —— Theory 00 ! ! i ! 0.0 0.4 08 1.2 1.6 2.0 Mirror position, mm Figure 4.13a. Measured reflectance tuning curve of a diode-grid at 94 GHz. 90 40 eeoe Experiment Theory iW) O | Phase of reflection, degrees ro) nN fe) 0.0 O04 08 1.2 1.6 2.0 Mirror position, mm Figure 4.13b. Measured phase of reflection tuning curve of a diode-grid at 94 GHz. 91 a standard deviation of 10fF. This is based on sampling 95 out of 2000 possi- ble diodes. From the measured grid period (504 um), strip width (18 wm), and strip length (450 um), the strip inductance calculated from the quasi-static for- mula is 0.26 nH, which corresponds to an inductive reactance of 1531 at 94 GHz. Substracting the best-fitted diode-grid reactance from the calculated inductive reactance, we get 591 for the capacitive reactance due to the varactor. This cor- responds to 29fF, which agrees with the measured zero-bias capacitance (30 + 10fF) at 1 MHz. Following this procedure of measuring diode capacitance at Rf frequency, figure 4.14a compares the capacitance-voltage (CV) measured charac- teristic at 94 GHz with the CV characteristic measured at 1 MHz. Figure 4.14b shows the corresponding series resistance measured at 94GHz. The decreasing trend of the series resistance as a function of reverse bias is expected, since the resistance associated with the undepleted region of the diode decreases as the reverse bias increases; however, the amount of the decrement seems a little high. To investigate the phase shift capability of this diode-grid, the measured phase and amplitude of these tuning curves for a particular mirror position is plotted as a function of bias voltage. The largest phase shift occurs at a mirror position of 3.23mm. Figure 4.15 shows a comparison between experiment and theory based on transmission-line. In calculating the reflectance and phase of reflection, the assumed diode-grid parameters are based on average values of the corresponding parameters measured from the tuning curves. The average series resistance is 491, the minimum and maximum diode-grid reactance are 607M and 1051, respectively, and the average diode-grid to mirror separation is 3.16mm. However, a phase calibration length of 795 um is used. The calibration length averaged from the measured tuning curves is 761 um, which corresponds to an 8° vertical shift. Phase shift performance is about 40° and average reflection loss is 6-dB. 92 80 T T T T T xix Measured at 1MHz 60F — .4. Measured at 94 GHz 7 Capacitance, fF ro) L -—— © x 4 -—e 1 20 F —l Bias voltage, V Figure 4.14a. A comparison between the measured capacitance-voltage (CV) characteristic of a diode-grid at 94 GHz and the measured CV characteristic at 1MHz. Bars represent one standard deviation. 93 {10 T T T i q T 90 + ; Measured at DC a G eee Measured at 94 GHz ! g 5S 70F - Q ° Ww © a o e @ ® 5OF e = 9) ; . . 30 j | i 1 ] -4 -3 -2 -{ O 1 2 Bias voltage, V Figure 4.14b. A comparison between the measured resistance-voltage char- acteristic of the diode-grid at 94 GHz and the measured series resistance at DC. Bar represents one standard deviation. O4 94 03 F O02 + Reflectance fo} °o Phase of reflection, degrees ° °° Experiment —— Theory 4 Figure 4.15. Bias voltage, V A comparison of the measured and the calculated phase shift performance as a function of bias voltage at 94 GHz. 95 In exploring the frequency dependence of the diode-grid, tuning curves of the same diode-grid were measured at several frequencies with zero bias on the grid. This was done in Professor Luhmann’s laboratory at UCLA, where backward wave oscillators were available. Figure 4.16 shows the result of these measure- ments. The circles are the measured diode-grid impedance at frequencies as shown. The solid line shows the corresponding calculated diode-grid impedance, assuming a strip inductance of 0.26nH, a diode series resistance of 78, and a zero bias diode capacitance of 30 fF. The agreement is reasonably good at 90 GHz, although it deteriorates quickly as the frequency approaches 130GHz. This is expected since the effective dielectric wavelength is approaching the grid period (0.5mm). Figure 4.17 shows another configuration used in measuring phase shift per- formance of a diode-grid. A different diode-grid was used in this measurement. The largest phase shift occurred when the tuning mirror was placed 1.49mm away from the diode-grid. A 70° phase shift and an average of 6.5-dB reflec- tion loss was obtained. Figure 4.18 shows a comparison between the measured phase shift performance and calculation based on transmission-line theory. This comparison is complicated by the fact that the wafer thickness varies between 210 um to 230 um, 4 out of 35 rows of the diode-grid were shorted during the measurement, and the parasitic capacitance and series resistance of the diodes cannot be measured at low-frequency. The diode series resistance could not be measured accurately at DC because the surface of this wafer has many ripples with a feature size of about 1m. This created the problem of maintaining a good contact between the probes and the metal contacts; consequently, the con- tact resistance became too large (roughly 300) and dominated the actual diode series resistance. However, the diode series resistance was measured from a tun- ing curve at 93GHz. The measured values were 261 for the series resistance 96 ro) © © © Measurement © © © Theory 2° T Figure 4.16. A comparison of the measured and the calculated diode-grid impedance as a function of the RF frequencies. 97 Incident wave <—_—. Movable mirror > Reflected wave MQ ay Fused quartz Figure 4.17. (a) Photograph of diode-grid on fused quartz. (b) Reflection measurement configuration of diode-grid on fused quartz. 98 04 t 1 , ® O03 F 4 oO Cc g o 02 — + ® x oc oa be 4 OF 4 80 xxx Experiment _ FA —— Theory o 2 “ & s 3 40 F& = Oo ” = 20 — 6) I 1 { Bias voltage, V Figure 4.18. A comparison between the measured phase shift performance of a diode-grid in parallel with a fused quartz at 93 GHz. 99 and 621 for the reactance. Theoretical curves were plotted using the measured series resistance (261), the average wafer thickness (218 wm), and the calculated grid inductive reactance (1531). In addition, we assumed that the initial mir- ror position was 1.45 mm, the phase calibration length was 1mm, the published refractive index for fused quartz and GaAs was 1.96 and 3.6, respectively [6], and the diode capacitance varied from 35fF at 0.9V to 18fF at —2.75V. The measured initial mirror position was 1.49mm, the phase calibration length was 0.91 mm, and the average diode capacitance was 27fF at zero bias and 20fF at —3V and had a standard deviation of 15fF and 13 fF, respectively. Sensitivity analysis indicates that phase response is quite sensitive to wafer thickness and initial mirror position, shifting vertically 1° per micron for each. [1] [2] (7 (8) 100 References P. W. Hannan, “Simulation of a Phased-Array Antenna in Waveguide,” IEEE Trans. on Antennas and Propagation, AP-13, pp. 342-353, 1965. R. G. Jones, “Precise Dielectric Measurements at 35 GHz Using an Open Microwave Resonator,” Proceedings IEE, Vol. 123, no. 4, pp. 285-290, 1976. U. Stumper, “Dielectric Measurements by Multiport Reflectometers at Sub- millimeter Wavelengths,” 11th Inter. Conf. on Infrared and Millimeter Waves, Pisa, Italy, pp. 164-166, 1986. R. A. Bohlander, A. McSweeney, J. M. Newton, V. T. Brady, and R. G. Shack- elford, “A Quasi-Optical Scanning Multiport (QUOSM) Network Analyzer,” 6th Inter. Conf. on Infrared and Millimeter Waves, F-2-5, 1981. N. W. B. Stone, J. E. Harris, D. W. E. Fuller, J. G. Edwards, A. E. Costley, J. Chamberlain, T. G. Blaney, J. R. Birch, and A. E. Bailey, “Electrical Standards of Measurement,” Proc. IEE, Vol. 122, no. 10R, pp. 1054-1070, 1975. M.N. Afsar and K. J. Button, “Millimeter-Wave Dielectric Measurement of Materials” Proc. of The IEEE, Vol.73, no. 1, pp. 131-153, 1985. A. F. Harvey, “Optical Techniques at Microwave Frequencies,” Proceedings IEE, 106B, pp. 144-157, 1959. J.C. Wyant, “Interferometry for Three-Dimensional Sensing,” Test and Mea- surement World, April, pp. 66-71, 1986. W.H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, Chap. 10, pp. 274-334, Cambridge University Press, New York, 1986. 101 Chapter 5 Discussion and Future Work In this thesis, several possible applications of diode-grids were proposed. In laying down the groundwork for these applications, a model of the diode-grid was presented and subsequently used in designing a diode-grid phaser shifter. A computer-aided design tool has been developed to provide an interactive graphics environment for doing designs and to form a basis for comparing theoretical and experimental results. A small aperture reflectometer that uses a wave-front interference technique has been developed to measure the reflection coefficient of diode-grids. The measured results have shown the diode-grid model to be reasonably accurate for doing the designs. A fabrication procedure for diode-grids has been demonstrated. The combination of Zah’s self-aligning process and the liquid-crystal detection technique made it feasible. Monolithic diode-grids with 2000 Schottky varactors have been fabricated on 6cm? GaAs substrate. A phase shift of 70° with a 6.5-dB loss was measured for a single diode-grid. Further improvements remain to be done. Although the fabrication process had a reasonable yield, the quality of the diode was not as good. The diode series resistance was too high. The breakdown voltage was too low; therefore, the ratio of the capacitance at zero bias to the capacitance at breakdown was too low. The average series resistance was 262 for one grid and 78 f the other grid. The breakdown voltage for both diode-grids was about 3V. This led to a capacitance ratio of about 2. Presently these limit the performance of the diode-grid. One of the dominant factors of diode series resistance is the product of doping concentration and thickness of the nt-layer. For the diode-grid that has a series resistance of 781, the doping concentration and thickness of the n+-layer were 102 about 1x 10!® cm-3 and 1.8 wm, respectively. However, the diode series resistance can be lowered by increasing the doping concentration and thickness of nt-layer. Ballamy and Cho [1] demonstrated beam-leaded diodes with series resistances of 4 to 8. They used 1 x 10!8 cm~? for the doping concentration and 6 wm for the thickness of the n*-layer. Clifton et al. [2] fabricated a Schottky diode that had a series resistance of 70. They used 3 x 1018 cm~? for the doping concentration and 3 ym for the thickness of the n*t-layer. Jarry et al. [3] developed a mixer diode with an incredibly low series resistance that was less than 3. They used a doping concentration that was greater than 2 x 10/®cm~? and 2 to 3ym for thickness of the n*-layer. These results indicate that there is an excellent chance for improving the series resistance of our diodes. Among the factors that influence the diode breakdown voltage, contamination due to oil vapor back-streaming from the diffusion pump into the evaporating chamber was the most probable cause of our low diode breakdown voltage. The reverse breakdown characteristic was soft, and this led to a breakdown voltage of about 3V at 0.54~Apym-?. This is about 25% of Sze’s prediction, which is 12 V for avalanche breakdown in a one-sided abrupt junction diode with a dop- ing concentration of 1.5 x 10!’ cm~ [4]. The doping concentration for our diodes was 1.5 x 10!7cm~? at the GaAs surface and decreased inversely as a function of the depth in the GaAs. The low breakdown voltage can be increased by using in-situ MBE aluminum, or by evaporating the metal for the Schottky contact in an oil-free ultra high vacuum system. For example, Cho and Dernier [5] de- posited in-situ MBE aluminum on the GaAs epitaxy in the MBE growth chamber after the epitaxy was grown and before it was exposed to air. They fabricated Schottky diodes with 15 V breakdown voltage, which was about 60% of Sze’s prediction for diodes with a doping concentration of 5 x 10'©cm~?. Sato el al. [6] demonstrated that Schottky diodes fabricated in an oil vapor free vacuum had 103 a higher breakdown voltage than diodes fabricated in an oil diffusion pumped vacuum. They indicated an 3.5 V to 5.3 V improvement for their diodes, which had a doping concentration of 3.5 x 10!7cm~3. The 5.3V breakdown voltage corresponds to 75 % of Sze’s prediction. In addition, Schottky diodes with near theoretical breakdown voltage have been fabricated by other researchers. Clifton el al. [2] fabricated diodes with 10 V breakdown voltage. This was about 80% of Sze’s prediction. Immorlica and Wood [7] developed diodes with 13 V break- down voltage, and this was about 85% of Sze’s prediction. These were abrupt junction Schottky diodes. Their doping concentrations were 1.5 x 10!’ cm=? and 1x 10!7%cm-3, respectively. Their diode geometries were strips, which were sim- ilar to our diodes. Furthermore, their diode areas were about 10 pm, and proton bombardments were used for isolating their diodes. Although their methods of deposition were not given, these results do indicate that there is a good chance for improving the breakdown voltage and therefore the capacitance variation of our diodes. Based on the reasonable agreement between theory and experiment, we be- lieve our diode-grid model to be sufficiently accurate for doing the designs. Fur- thermore, works on second harmonic generation using diode-grids are being in- vestigated by Christina Jou in Professor Luhmann’s group at UCLA. They also showed a reasonable agreement between theory and experiment. For the diode- grid that had a series resistance of 78 2, the measured transmittance as a function of the position of the tuning slabs agreed well with the transmission-line model. Also, a second harmonic conversion efficiency of 16% and an output power of 0.5 W were measured at 66 GHz when a pulsed magnetron at 33 GHz was used to pump the diode-grid that had a series resistance of 261. These results indicate an exciting future for the diode-grid. In electronic beam-steering, the array design that is based on using two diode-grids appears 104 to be feasible. Diode-grids for harmonic power generation look promising. Also, the integration of other electronic devices into a periodic grid is beginning to emerge. In our group, Zorana Popovic is building a Gunn diode-grid on a Duroid substrate at 10 GHz. In any case, the future of integrating electronic devices into a periodic grid will be very exciting as well as promising. References [1] W. C. Ballamy and A. Y. Cho, “Planar Isolated GaAs Devices Produced [2] (6) by Molecular Beam Epitaxy,” IEEE Trans. on Electron Devices, ED-23, pp. 481-484, 1976. B. J. Clifton, G. D. Alley, R. A. Murphy, and I. H. Mroczkowski, “High Per- formance Quasi-Optical GaAs Monolithic Mixer at 110 GHz,” IEEE Trans. on Electron Devices, ED-28, pp. 155-157, 1981. B. Jarry, J. S. K. Mills, and F. Azan, “94 GHz Microstrip Monolithic GaAs Mixer,” IEE Electronics Letters, Vol. 22, pp. 1328-1329, 1986. S. M. Sze, “P-N Junction Diode,” Physics of Semiconductors, Chap. 2, pp. 63-132, John Wiley & Sons, Inc., 1982. A. Y. Cho and P. D. Dernier, “Single-crystal-aluminum Schottky-barrier diodes prepared by molecular-beam-epitaxy (MBE) on GaAs,” J. of Appl. Phys., Vol. 49, pp. 3328-3332, 1978. Y. Sato, M. Uchida, K. Shimada, M. Ida, and T. Imai, “GaAs Schottky Bar- rier Diode, ECL-1314,” Rev. of the Electrical Communication Lab., Vol. 18, pp. 638-644, 1970. A. A. Immorlica and E. J. Wood, “A Novel Technology for Fabrication of Beam-Leaded GaAs Schottky-Barrier Mixer Diodes,” IEEE Trans. on Elec- tron Devices, ED-25, pp.710—-713, 1978. 105 Appendix A Varactor Diode-Grid Fabrication Procedure The following contains notes on the fabrication of a Schottky-barrier varac- tor diode-grid on a semi-insulating GaAs wafer. A total of five masks is used. Because a GaAs wafer is quite large and fragile, a holder made of teflon is used to hold the wafer during rinsing and developing. Figure A.1 shows the teflon holder. A teflon tweezer is used for etching. This process evolved from Zah’s process [1]. The book by Ralph Williams is an excellent reference on GaAs pro- cessing techniques [2]. Howard Chen in Professor Yariv’s group and Dr. Kjell Stolt in TRW have been the principal suppliers of the MBE wafers. Fabrication Procedure 1. Obtain a GaAs wafer with the following layers. 0.2 um of in situ MBE aluminum. 0.7 wm of n layer with a hyperabrupt doping profile. 1.8 um of n* layer with 3 x 1018 cm-3 doping concentration. * Some MBE wafers have indium on the back side and some do not. If indium is present, mount the wafer on a lapping block with wax and lap away the indium on the backside of the wafer. A mixture of water and a 5ym diameter Al2O3 lapping powder made by Buehler is often used. Afterwards, acetone can be used to dissolve the wax. 2. Determine the crystal orientation of the wafer by making a strip pattern on a small chip scribed from the wafer. Note: If aluminum is present on the chip, remove the aluminum by etching it in aluminum etchant for GaAs. a. Standard lift-off photoresist process photoresist : AZ 1350J 106 spin speed : 4000 rpm prebake : 85 °C for 25 min. exposure : 25 sec. development : 30 sec. (agitate in 1:1 diluted developer.) b. Hardbake the photoresist at 125° C for 10 min. c. Using a 93% concentrated H2SO4, and a 30% concetrated H2O9, mix the solution (H2S04:H202:H20) with a ratio of 1:8:160. Stir it with a magnetic stirer in a petri-dish for an hour. The etch rate is about a quarter of a micron per min. d. Etch the wafer and rinse it in 20 beakers of DI water. e. Cleave a slice from the chip and mount it sideways on double-sided tape. Note the etched profile in a microscope. The diode orientation should be in the direction of a ‘V-groove’ etch or perpendicular to the direction of a ‘dovetail’ etch. Figure A.2 shows the etched profile. 3. If in-situ aluminum is not available, then clean the wafer throughly and evap- orate aluminum. a. Cleaning procedure. acetone ultrasonic bath : 10 min. ethanol ultrasonic bath : 5 min. hot Transene 100 bath : 5 min. cold Transene 100 bath : 30 sec. let it dry by itself b. Etch away the native oxide on the wafer for a minute in a solution of (H20:HCl) with a 1:1 ratio and rinse it with 20 beakers of DI water. c. Load the wafer into the vacuum immediately. Thermo-paste is used to mount the wafer on a glass slide, which is then mounted onto the sample holder. Evaporate 2000A thick of aluminum in a vacuum with pressure 107 below 3 x 10-© Torr. If possible, this should be done in an oil-free vacuum system at lower pressure [4,5]. The aluminum source must be cleaned by etching it in organic solvent and aluminum etchant. 4. Generate the self-aligning mask for defining the ohmic contact and the width of the Schottky contact. a. Use the standard lift-off photoresist process. (see 2a.) b. Hardbake photoresist at 125° C for 10 min. c. Etch the aluminum in Transene aluminum etchant - Type D. Typically, it takes about 60 sec. at 58° C. d. Rinse the wafer in DI water and inspect it under the microscope. Look for signs of under-etched diode tips. They tend to form short ciruits when AuGe/Ni/Au is evaporated. Typically, several rounds of etching aluminum for 10s and rinsing the wafer are required to get good results. Because the wafer is quite large, some etching nonuniformity is expected. If the situation appears desperate, dissolve the photoresist and start over again since there are “tons” of aluminum still un-etched on the wafer. This is worth the trouble because an MBE wafer is precious. 5. Etch away the n-layer until the n+-layer is exposed. a. Mix the solution (H2SO4:H202:H20) with a ratio of 1:8:160. Stir it with a magnetic stirrer in a Petridish for an hour. Note: Use the 93 % concen- trated H2SOq4, and the 30% concetrated H2Oz. b. Etch the wafer and rinse it in 20 beakers of DI water. The etch rate is a quarter of a micron per min. Generally, an extra 15 second is added to over- etch the crystal. This is just a precautionary measure for exposing thoroughly the nt layer throughout the wafer. 6. Evaporate AuGe/Ni/Au with the following thicknesses (700A /300A/2000A) at a pressure below 3 x 10~® torr. The edges of the wafer are taped with 10. 11. 108 paper so that lift-off process in acetone becomes easier. Remove the thermo-paste on the backside of the wafer with a Q-tip, that is slightly dampened with acetone. Lift off the photoresist in acetone and ethanol baths. Generate the etching mask for defining the lead of the Schottky contact. a. Use the standard lift-off photoresist process. (see 2a.) b. Hardbake the photoresist at 125°C for 10 min. c. Etch the aluminum (see 4 b.) d. Lift off the photoresist in acetone and ethanol baths. Generate the bonding pad mask with standard lift off photoresist process. Evaporate AuGe/Ni/Au with the following thicknesses (700A /300A /2000A) at pressure below 3 x 10-6 torr. The purpose for this is to make a good bonding pad. The alloying process make the metals partly dissolve into the GaAs and acquire a rough surface texture. This is worthwhile since wire bonding can be very difficult if the bond wires do not like to stick on the bonding pads. Alloy the ohmic contacts and bonding pads at 460°C for 10 min. in forming gas (15 % of No and 85% of Ha). Generate proton implantation mask with photoresist. a. Pattern implantation mask. photoresist : AZ 4620 spin speed : 4000 rpm prebake : 85°C for 1 hour exposure : 70 sec. at 20 mJ-cm~? development : 4 min. (agitate in 1:1 diluted developer) b. Optional: Some people feel that if the photoresist is flood-exposed here, then it will make the removal of the photoresist easier after ion implanta- 12. 13. 14, 15. 15. 16. 109 tion. This was not noticeable to me. c. If implantation is to be done at Caltech, obtain sample holder from Frank So or Sung Kim in Professor Nicolet’s group. Use the phospho- rus compound to define the implantation boundary. Mount the wafer onto the sample holder with thermo-paste. If implantation is to be done at Hughes, no sample holder is required. d. Implantation parameters: 330 keV at 4 x 10!4 cm~? dose 200 keV at 4 x 10!2 cm~? dose Measure the resistance between the adjacent ohmic contacts to make sure that the desired area of the wafer is completely isolated. If isolation is completed, remove the photoresist in an O2 plasma. Measure the diode parameters. If the breakdown voltage varies widely across the wafer, then probing every varactor to weed out the weak diodes becomes necessary. This can be done at UCLA, since an analytical probing station is available for fast probing. Measure the diode parameters with the HP4145B parameter analyzer and the CV characteristics with the HP4280A C-meter. See software documentation in the appendix. Here probing is quite tricky because contact resistance between the probe tip and the metal depends highly on the amount of pressure applied. Some practice is necessary to get a reasonably low contact resistance. Generate the periodic grid mask and the bonding pad mask simultaneously with the standard lift-off photoresist process. Evaporate 100A of chrome and 3000 A of gold. The lift-off here is critical. Lift-off flags must be avoided because they tend to cause electrical shorts. The cause is due to poor edge definition when the photoresist is patterned. Lap the wafer to the desired thickness. If a row of diode-grid is shorted, use liquid crystals to find shorted diodes [1] 110 and remove them from the wafer with an ultrasonic probe. It is important to prepare the sample properly. A layer of liquid crystal is spun onto the wafer at 1000 rpm. It is important to shake the bottle throughly before using it. This usually gives a nice and uniform layer. Use a Q-tip to wipe off the excess liquids on the bonding pad. Mount the wafer on a resistive heated chuck. Illuminate the wafer with a dual fiber optic lamp at approximately 30° incidence relative to the horizon. Use a curve tracer to inject current into the shorted row. Typically more than 5mA is required to see any noticeable color change. Use the Signatone 850 ultrasonic cutter to remove the bad diode. References C. E. Zah, “Fabrication Process for Monolithic Schottky Diode Imaging Ar- rays,” Ph. D. Thesis on Millimeter- Wave Monolithic Schottky Diode Imaging Arrays, Chap. 3, pp. 103-109, California Institute of Technology, Pasadena, California, 1986. R. E. Williams, Gallium Arsenide Processing Techniques, Artech House, Inc., Massachusett, 1984. A. Y. Cho and P. D. Dernier, “Single-crystal-aluminum Schottky-barrier diodes prepared by molecular-beam-epitaxy (MBE) on GaAs,” J. of Appl. Phys., Vol. 49, pp. 3328-3332, 1978. Y. Sato, M. Uchida, K. Shimada, M. Ida, and T. Imai, “GaAs Schottky Barrier Diode, ECL-1314,” Rev. of the Electrical Communication Lab., Vol. 18, pp. 638-644, 1970. M. Ida, M. Uchida, K. Shimada, K. Asai, and S. Ishida, “Fabrication Tech- nology of Stable Schottky Barrier Gates for Gallium Arsenide MESFETS,” Solid-State Electronics, Vol. 24, pp. 1099-1105, 1981. 111 Figure A.1. A teflon holder for holding the GaAs wafer during developing and rinsing. 112 (b) Figure A.2. Crystal orientation. (a) Cross-section profile of a ” V-groove”. (b) Cross-section profile of a ”dove-tail”. 113 Appendix B Computer Program Listing of TRAP program trap(input, output) ; 1 2 3 4 { TRAP is an acronym that indicates the calculation of 5 transmittance, reflectance, absorptance, and phase of 6 reflection. Because the calculation of transmittance, 7 absorptance and reflection coefficient for multi~layered 8 media is tedious and time consuming, TRAP was developed to 9 provide an interactive environment for the user to design the 10 circuit and to compare the theoretical and experimental 11 results. It is an interactive graphics program written in 12 Turbo Pascal for an IBM-PC. For the computational algorithm, 13 please see "Thin Films Calculations Using the IBM 650 14 Electronic Calculator," by Jean A. Berning and 15 Peter H. Berning in Journal of The Optical Society of America, 16 Vol. 50, Num. 8, pg. 813, Aug. of 1960. TRAP features a 17 line editor, from which the user can enter a command line 18 that describes the structures of the layered media. Commands 19 include lossy dielectric, grids, lumped elements, 20 and a mirror. The angle of incidence, polarization, 21 wavelength, and layer thicknesses can be varied linearly. 22 Keyboard commands are available to stop, speed up, 23 or slow down the simulation. TRAP also features optimization 24 capability for the user to fit a transmission-line model 25 to the measured reflectance and phase of reflection. 26 The fitting procedure is based on minimizing the absolute 27 value of the complex difference between the calculated and 28 the measured reflection coefficient. For the optimization 29 algorithm, please see Numerical Recipes by W. H. Press et al., 30 Chap. 10, pp. 274, Cambridge University Press, New York, 1986. 31 32 When the program is run, a main menu is displayed. There 33 are four options including database, simulation, optimization, 34 graphics, and quit. To make a selection, simply press the key 35 of the first letter for an option. For example pressing Q 36 exits the program. Note also that pressing Q in an option exits 37 that option, and pressing the return key repeats that option, 38 although this is not explicitly displayed in each option. 39 The database and the graphics option are menu driven and 40 allow the user to read in a set of reflection coefficient 41 data from an ASCII file and to define the vertical plotting 42 range, respectively. The data file can be viewed or edited in 43 the Turbo editor. The format of this file should be 44 (distance reflectance phase of reflection). It should 45 appear as three columns of numbers. Tyically these data are 46 measured from an experiment, but they could be generated 47 for the purpose of design and optimization. The simulation 48 option allows the user to edit a command line describing 49 the layered medium. The following are command definitions. 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 TT 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 114 Convention : 1.) parameters, ri, r2, r3, ... etc., are real numbers. 2.) i, b, f, ... etc. are definitions. 3.) , and: are delimiters. 4.) a command is usually followed by a set of parameters. irt - incident medium : ri = refractive index (default value is 1) bri,r2 ~ dielectric boundary: ri = Re(refractive index) r2 = Im(refractive index) ari,r2 - shunt admittance : ri = Re(shunt admittance) r2 = Im(shunt admittance) fri,r2 ~ final medium : ri = Re(refractive index) x2 = Im(refractive index) sri ~ TE polarization : rl = angle of incidence in degrees with respect to the surface normal. pri - IM polarization : rl = angle of incidence in degrees with respect to the surface normal. wri ~ wavelength of incidence : ri = wavelength in arbitrary units. gri,r2,r3,r4. ~ quasi-static model of a square grid : ri = length of the period. r2 = length of the gap. r3 = length of the post. r4 = series resistance. Gri,r2,r3,r4. - Eisenhart model of a square grid : ri = length of the period. r2 = length of the gap. r3 = length of the post. r4 = series resistance. tri - layer thickness : ri = wavelength in arb. units. d - plot y-axis in unit of dB. (default is tinear) xri:r2 - plot the variable (x: i,b,a, ... etc. ) on x-axis. ri = start value of x r2 = stop value of x Examples: 1.) i1 z0,.11 b3.6 t.233 zO,.11 f1 80 wi.7:2.7 2.) if b3.6 t.233 z.054,.27 bi t0:2.0 m 80 w3.36 3.) if b3.6 t.233 2.054,.1:.3 bil t1.5 m si w3.36 The first example is a bandpass filter formed by a pair of lossless inductive screens. The second example is a zero-bias diode-grid backed by a mirror that translates from 0 to 2.0 mn. The third example is a diode-grid with varying reactance and a stationary mirror tuned to 1.5 mm. These examples had been programed. To run them, enter the simulation mode and press E. The description of the multi-layered medium can be edited using a condensed version of Wordstar commands: control s - left control d - right 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 type 115 control g - delete control v - change from insert mode to overwrite mode and back. backspace - deletes left When the layer description is correct, press carriage return to enter it. You can get a screen dump by typing shift PrtSc. The optimization mode allows the user to fit a set of reflection coefficient data to a transmission-line model of the layered medium. The data can be read in from an ASCII file thru the database option. Once the data are entered, enter Q to return to main menu and press 0 to enter optimization option. The commands for optimization are similar to simulation, except that the command should be in capital letters to signify that the variable is to be optimized. Following the command symbol is the optimization range (ri;r2), where a semicolon is used to separate the minimum (ri) and the maximum (r2). Example: 4.) il bi 1.68;.69 2.042; .043, .085; .09 b3.6 t.218 bi T2.49;2.5 t0:2.0 m 80 w3.36 The fourth example illustrates an optimization command line for curve-fitting a-transmission-line model of a diode-grid with a tuning mirror to the experiment. To run this example, enter the database option, get the measured reflection coefficient from the file "diogrid.pas," return to main menu, enter the optimization mode, press the key E, enter 4, and hit return. The data file is available in the disc on the back cover of this thesis. It was obtained from an actual reflection measurement and is shown in part below. As the optimization advances, the values of each parameter of the multi-layered medium are displayed line by line on the screen. Each line represents a completed computation. The ordering of the parameters in the line starts from the right of the medium to left of the medium, and the associated error is displayed last in the line. 0.000 0.912 24.704 0.050 0.903 24.485 0.100 0.886 24.534 1.900 0.937 24.039 1.950 0.944 23.760 2.000 0.953 23.134 } line = string[250]; complex = “complex_record; 156 157 158 159 160 161 162 163 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 201 202 203 204 205 206 207 116 const complex_record = record r,i: real; end ; complex_matrix = “complex_matrix_record; complex_matrix_record = record t11,t12,t21,t22 : complex; end; char_set = set of char; gimpnp = array[1..9,1..8] of real; gimp = array[1..9] of real; glop = array[1..8] of real; rng = array[1..2,1..8] of real; structure : line = °*’; structuresave : line = ’’; xmin = 190; xmax = 550; {coordinates of graph corners} ymin = 43; ymax = 163; xd = 3; {plotting interval on x_axis} backspace = #8; enter = #13; edit_set : set of char = [“d,s,"g,7v, backspace] ; structure_set : set of char = ['-",7.%,707, 717, 2", 73°, 794°, 5, SY OR : SOR * ee "w',*h’,’b’,’t',’g’,'d',’s',’r’,'n’,’0’, "Z*,’a’,’p’,’£',’m’,’j',’q’,’G',*/','*s", *B’,'T',Z', 7A’, DT’, °F’, wed: number_set:set of char=["-",*.*,'0',°4°,°27,°3°,'4",°5", 6", °7",°8",°9°]; delimiter_set : set of char = Cet. twhy tibet, gtd’, 8’, '*p’, *o',’z’,’a’,*£",'’m',’j’,"q’,’G’,'/',’r’, m’,737 7B’ TZ, 7A, D'OR we]: command_set : set of char = Dow’, i’, "b’,'t',"g’,'d’,’a’,'’z', rn’, *o’,’s’,'p’,’f','m’,'j',’q’,’G’, 7/73’, "B’,'T', 72", 7A’, LT’, 'F', we]: label pau, main; position, pointer, positionstop : 1..150; {position in structure.} a_heap_pointer, b_heap_pointer : “integer; {pointer for garbage disposal} x, i: integer; {position along the x-axis, 0 to xmax-xmin. } t : complex_matrix; {complex transmittance matrix} reflectance, transmittance, absorptance, phase : real; error_code : integer; {for val statement} min, max : real; { minimum and maximum values of the x coordinates} c, b: char; {character read at keyboard} dB_plot : boolean; {dB plot if true} yj, re, pjao, pj, yjm1, cnj, cnje, gj, Zj, aj, cno, cnoe, yjmin, yjmid, caj, cnjp : complex; no, sj, ao, nj, 1, 1j, sjt : real; G_flag, p_flag : string(2]; p., d, v, h, QQ, ss, ccc, £1, £2, XX, BB: real; a, g. W, rs, rd, cv, sjsave : real; scan : string([5]; 209 210 117 be, bl, par : complex; mM, 0, en, positionsave, positionG, positionf : integer; zd, bev, yjsave, cnosave, ymnp, ymnm, bcsum, blsum, densum : complex; xyZ, xyz2 : complex; test_string : line; temp, la, mla, nla, ld, sine : real; yjsaver, yjsavei, cnosaver, cnosavei : real; intensity, normalization : real; on_off : integer; select : char; filename : string[15]; trp : array [1..100 , 1..3] of real; trpi, trp2, trp3 : real; data_transfer : text; data_index, ndata, data_inc : integer; find_error_flag : boolean; ref_err : real; xmi, ylmi, yrmi, xmx, ylmx, yrmx : real; ylrange, ylscale, yrrange, yrscale, xrange, xscale : real; ZZZX, ZzZy : integer; compon : array[1..20] of real; rtol, ftol : real; nmparam, idata, optimization_flag, mvertices, ndim, iter : integer; poly : glmpnp; vert : glnp; face : real; y : glnp; range : rng; range_variable : complex; range_pointer, curve_select : integer; {GRAPHICS routines} procedure draw_box (xi,y1,x2,y2,color : integer); begin draw (x1,yi,x1,y2,1); draw (xi,y2,x2,y2,1); draw (x2,y2,x2,y1,1); draw (x2,y1,x1,yi,1); end; procedure draw_x_ticks(x1,y1,x_increment ,x2 : begin while (x1<=x2) do begin draw (x1, (yi+1),x1, (y1-2) ,1); xi := x1 + x_increment; end; {while} end; {draw_x_ticks} procedure draw_y_ticks(x1,y1,y_increment,y2 : begin integer) ; integer) ; 118 while (y1<=y2) do begin draw ((x1+2) ,y1, (x1-4),y1,1); yl := yi + y_increment; end; {while} end; {draw_y_ticks} procedure draw_graph(x1,y1,x2,y2, x_increment, y_increment_left, y_increment_right :integer); begin draw_box(x1,y1-2,x2,y2+2,1); draw_x_ticks (x1,y1,x_increment ,x2); draw_x_ticks (x1,y2,x_increment ,x2); draw_y_ticks (x1,y1,y_increment_left , y2) ; draw_y_ticks (x2,y1,y_increment_right , y2) ; end; {procedure draw_graph} procedure write_x_coordinates(x1,y1,x_increment : integer; xlc,xc_increment ,x2c : real; field,fix :integer); begin repeat gotoxy((xi div 8), (y1 div 8)); write (xic:field:fix); xic := xic + xc_increment; xl := x1 + x_increment; until x1ic > x2c; end; {write_x_coordinates} procedure write_y_coordinates(xi,y1,y_increment : integer; yic,yc_increment,y2c : real; field, fix : integer); begin repeat gotoxy((xi div 8), (yi div 8)); write (y1c:field:fix); yle := yic + yc_increment; yi := yi + y_increment; until yle < y2e; end; {write_y_coordinates} function dB(x : real) : real; {give the dB difference} begin aB := 10*1n(x)/1n(10); end; {dB} procedure clean_box; begin gotoxy(2,2); write(’ *); gotoxy(2,3); write(’ "); end; procedure set_up; begin 119 315 if select = ‘'m’ then begin 316 hires; hirescolor(15); 317 draw_box(0,4,639,33,1); 318 gotoxy (2,2); 319 write(’MAIN MENU: ’); 320 write('s(simulation) d(database) '); 321 write(’o(optimization) g(graphics) '); 322 if c = ’q’ then read(kbd, select); 323 if (select = ’s’) or (select = ‘d’) then 324 begin 325 draw_graph(xmin, ymin, xmax, ymax, (xmax-xmin)div 5, 326 (ymax-ymin)div 5, (ymax-ymin)div 4); 327 if select = 's’ then begin 328 gotoxy(1,7); write(’Tran. ... .*); 329 gotoxy(1,8); write(’Refl. .. .. ..°); 330 gotoxy(1,9); write(’Abs. ee aD i 331 gotoxy(1,10); write(’Pha. ....... ‘); 332 end; 333 end; 334 end; 335 graphwindow(0,0,639,199); 336 case select of 337 *s’ : begin 338 clean_box; 339 gotoxy(2,2); write(’Key: i(nt) b(ndry) t(kns) g(rd) '); 340 writeln(’f(nl) w(vlth) m(ir) G(*) s(TE) p(T) d(B) q(it)’); 341 gotoxy(2,3); writeln(’Structure:’); 342 end; 343 *d’ : begin 344 clean_box; 345 gotoxy(2,2); write(’DATABASE: enter data_filename '); 346 end; 347 *o’ : begin 348 optimization_flag := 1; 349 clean_box; 350 gotoxy(2,2); write(’Key: i(nt) b(ndry) t(kms) g(rd) °); 351 writeln(’f(nl) w(vlth) m(ir) G(*) s(TE) p(T) d(B) q(it)’); 352 gotoxy(2,3); writeln(’Structure:’); 353 end; 354 end; {of case} 355 356 end; {set_up} 357 358 procedure write_y_axis; 359 begin 360 write_y_coordinates(xmaxt+20, ymin+7, (ymax-ymin) div 4, 361 yrmx, (yrmi-yrmx)/4,yrmi,4,0); 362 if dB_plot then 363 write_y_coordinates(xmin-20, ymint7, (ymax-ymin) div 5, 364 0,-10,-50,3,0) 365 else 366 write_y_coordinates(xmin-20, ymin+7, (ymax-ymin) div 5, 367 ylmx, (ylmi-ylmx)/5,ylmi,3,1); 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 413 414 415 416 417 418 419 420 120 end; {write_y_axis} procedure write_x_axis; begin write_x_coordinates (xmin, ymaxti4,(xmax-xmin) div 5, min, (max-min) /5,max,4,1); end; {write_x_axis} procedure plot_result(on_or_off : integer); begin graphwindow (xmin, ymin, xmax, ymax) ; trp3 := yrmx - phase*180.0/pi; if (on_off and $8) <> O then plot(x*xd,round(trp3*yrscale) ,on_or_off) ; if dB_plot then begin if odd(x) then if (on_off and $4) <> 0 then plot (x*xd, round (-dB (transmittance) /50*(ymax-ymin)) ,on_or_off); if odd(x div 2) then if (on_off and $2) <> O then plot (x*xd, round(-dB (reflectance) /50*(ymax-ymin) ) ,on_or_off); if odd(x div 3) then if (on_off and $1) <> 0 then plot (x*xd, round(-dB (absorptance) /50* (ymax-ymin) ) ,on_or_off); end {if} else begin trpi := ylmx - transmittance; trp2 := ylmx - reflectance; trp3 := ylmx - absorptance; if odd(x) then if (on_off and $4) <> O then plot (x+#xd,round(trpi*ylscale) ,on_or_off) ; if odd(x div 2) then if (on_off and $2) <> 0 then plot (x*xd,round(trp2*ylscale) ,on_or_off) ; if odd(x div 3) then if (on_off and $1) <> 0 then plot (x*xd,round(trp3*ylscale) ,on_or_off); end; {else} end; {plot_result} {COMPLEX NUMBERS routines} function co (s,t : real) : complex; {makes a complex number} var u : complex; begin new(u); u“.r := 8; u".i :=t; co := u; end; 121 function sc(s : real; t : complex) : complex; {multiply a real number s by t} var u : complex; begin new(u); u.r := 8 * t*.r; u*.i := s * t*.i; sc := u; end; function cc(s : complex) : complex; {complex conj} var u : complex; begin new(u); u*.r := s*.r; u*.i := -s*.i; ce := u; end; function ma(s : complex) : real; {magnitude} begin ma := sqrt(sqr(s*.r)+sqr(s*.i)); end; function ph(s : complex) : real; {phase in radians, (-pi,+pi]} begin if s°.r > O then ph := arctan(s*.i/s*.r); if s°.r <0 then if s*.i >= 0 then ph := arctan(s*.i/s*.r) + pi else ph := arctan(s*.i/s*.r) - pi; if s°.r = 0 then begin if s°.i > O then ph := pi/2; if s*.i <0 then ph := -pi/2; if s°.i = 0 then ph := 0; end; {real part 0} end; function su(s,t : complex) : complex; {sum} var u : complex; begin new(u); ur.r := s*.r + t*.r; u.i := s*.i + t*.i; su := u; end; function pr(s,t : complex) : complex; {product} var u : complex; begin AT4 475 476 ATT 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 §13 514 515 516 517 518 §19 520 521 522 523 524 525 526 122 new(u); ur. = s* ret? .r ~- g*.i*t*.i; ur.i := s*.rtt*.i + 8° .itt*.r; pr :=u; end; function di(s,t : complex) : complex; {difference s minus t} var u: complex; begin new(u); u>.r := s*.r - t*.3r; u*.i := s*.i - t*.i; di :=u; end; function qu(s,t : complex) : complex; {quotient s over t} var u : complex; begin new(u); u*.r r= (s*.ret*.r + s*.i*t*.i)/(sqr(t*.r) + sqr(t*.i)); urd := (-s*.ret*.i + 8°. ist? r)/(sqr(t*.r) + sqr(t*.i)); qu := u; end; function sq(s : complex) : complex; {square} var u : complex; begin new(u); u".r := 8°. .r*s*.r - g*.ixs*.i; u~.i := 2*s*.r*s*.i; 8q := U; end; function rr(s : complex) : complex; {square root in the right half plane.} var u : complex; begin new(u) ; u*.r := sqrt(ma(s))+*cos(ph(s)/2) ; u*.i := sqrt (ma(s))*sin(ph(s)/2); Ir :=u; end; function ur(s : complex) : complex; {square root in the upper half plane.} var u_: complex; theta : real; begin 527 528 529 530 531 532 §33 534 535 536 537 538 539 540 541 542 543 544 545 546 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 123 new(u); if ph(s) >= 0 then theta := ph(s)/2 else theta u".r := sqrt(ma(s))*cos(theta); u~.i := sqrt(ma(s))*sin(theta) ; ur := u; end; function Ir(s : complex) : complex; {the square root in the lower half plane.} var u_: complex; theta : real; begin new(u) ; if ph(s) <= 0 then theta := ph(s)/2 else theta u“.x := sqrt(ma(s))*cos(theta) ; u”.i := sqrt(ma(s))*sin(theta) ; lr := end; u; function ex(s : var u: complex; begin new(u); u-.r i= u-.i:= ex end; complex) exp(s*.r)*cos(s*.i); exp(s*.r)*sin(s*.i); [= U3 function sinh(s : var u_: complex; begin new(u); u".r:= u*.i:= sinh := end; complex) : complex; {hyperbolic cos(s*.i)*(exp(s*.r)-exp(-s*.r))/2; sin(s*.i)*(exp(s*.r)+exp(-s*.r))/2; u; function cosh(s : var u_: complex; begin new(u); u*.r:= ur.ii= cosh := end; complex) : complex; {hyperbolic cos(s*.i)*(exp(s*.i)+exp(-s*.r))/2; sin(s*.i)*(exp(s*.r)-exp(-s*.r))/2; u; function sine(s : complex) var := ph(s)/2 + pi; := ph(s)/2 - pi; : complex; {exponential function} sine} sine} : complex; {sine function} 580 581 582 583 584 585 586 587 588 589 590 691 592 593 594 595 596 597 598 599 600 601 602 603 604 606 607 608 609 610 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 124 u_: complex; begin new(u); u.r := sin(s*.r)*(exp(s*.i)+exp(-s*.i))/2; u*.i := cos(s*.r)*(exp(s*.i)-exp(-s*.i))/2; sine := u; end; function cosine(s : complex) : complex; {cosine function} var u_: complex; begin new(u); u”.r := cos(s*.r)*(exp(s*.i)+exp(-s*.i))/2; u*.i := sin(s*.r)*(-exp(s*.i)+exp(-s*.i))/2; cosine := u; end; function em(aii,a12,a21,a22: complex) :complex_matrix; {makes a complex matrix} var u : complex_matrix; function eq (s : complex) : complex; {makes an equal complex number.} var u : complex; begin new(u); u>.r r= s.r; uti := s8*.i; eq := u; end; {eq} begin new(u); with u* do begin til := eq(ail1); t12 := eq(ai2); t21 := eq(a2i); t22 := eq(a22); end; {with} cm := u; end; {cm} function mp (a,b : complex_matrix) : complex_matrix; {complex matrix product} var u_: complex_matrix; begin new(u); with u” do begin til := su(pr(a*.ti1,b*.t11) ,pr(a™.t12,b*.t21)); ti2 := su(pr(a*.ti1,b*.t12) ,pr(a*.t12,b*.t22)); t21 := su(pr(a*.t21,b*.t11) ,pr(a*.t22,b*.t21)); t22 := su(pr(a*.t21,b*.t12) ,pr(a*.t22,b*.t22)); 125 end; {with} mp := u; end; {function mp} {LINE_EDITOR routines} function edit(x,y : integer; test_string : line) var ins: boolean; {true for insert mode on} position : 1..150; row, col,px,py : integer; label quit; procedure write_cursor_position; begin gotoxy(row,col); write(’ *); gotoxy(row,col); write (position) ; end; {write_cursor_position} begin ins:= true; {insert mode on} position:= 1; row := 72; col := 4; write_cursor_position; gotoxy(x,y); write(test_string) ; repeat {draw cursor} : line; draw (8*(x+position-1)-8,8+*y-1,8*(x+position-1)-1,8+y-1, 1); draw (8*(x+position-1)-8,8*y-2,8*(x+position-1)-1,8+y-2, 1): gotoxy(x+position-1,y); read(khbd,c); {erase cursor} draw (8* (x+position-1)-8,8+*y-1,8*(x+position-1)-1,8*y-1,0); draw (8* (x+position-1)-8,8+*y-2,8+(x+position-1)-1,8+y-2,0); if c in structure_set then begin insert (c,test_string, position) ; position:= positiontt; write_cursor_position; if not(ins) then delete(test_string, position, 1); end; if c in edit_set then begin case c of “d : if position <= ord(test_string[0]) then begin position:= position+1; write_cursor_position; end; 126 686 “g : begin 687 delete (test_string, position, 1); 688 gotoxy (xtord(test_string[0]) ,y); 689 write(’ '); 690 end; 691 “vy : ins:= not(ins); 692 “s : if position > 1 then begin 693 position:= position-1; 694 write_cursor_position; 695 end; 696 backspace : if position > 1 then begin 697 position:= position-1; 698 write _cursor_position; 699 delete (test_string,position, 1); 700 gotoxy (xtord(test_string[0]) ,y); 701 write(’ °); 702 end; 703 end; {case} 704 end; 705 if c = ’e’ then begin 706 gotoxy (x,y); 707 write('There are 3 examples. Enter 0 -> quit & 1,2 or 3 -> exmpl: ’); 708 read(kbd,c); 709 case c of 710 "1? ;: test_string := ’il z0,.11 b3.6 t.233 zO,.11 f1 sO ° + 711 *w1.7:2.7'; 712 *2’ : test_string := 'i1 b3.6 t.233 z.054,.27 bi t0:2.0 ° + 713 *m sO w3.36'; 714 3’: test_string := 'i1 b3.6 t.233 z.054,.1:.3 bi t1.5 ’ + 715 *m a1 w3.36'; 716 *4’ : test_string := ’il bi T.68;.69 Z.042; .043,.085;.09 * + 717 *b3.6 t.218 bi T2.49;2.5 bi tO:2m’° + 718 *s0 w3.36'; 719 ‘5’ : test_string := ’il bi T.001;.2 b1.96 t.434 b3.6 t.231 ° + 720 "2.045; .065,.25;.31 b1 T.6;0.8 bi t0:2.0° + 721 *m 80 w3.36 010’; 722 °6’ : test_string := ’i1 bi.96 t.59 bi t0:2.3 b1.96 t.59 bi * + 723 't0:2.3 b3.23 t6.72 b1 t2.3 b3.6 t.238 ° + 724 *z.16,-.13 bil t1.15 m sO w4.6'; 725 *7’ : test_string := ‘il b1.96 t.3 b1 t0:1.2 b1.96 t.3 bi * + 726 *t0:1.2 b3.23 t6.72 bi t2.3 z.27,.29 ° + 727 °b3.6 t.238 bi t.86 m sO w2.3’; 728 end; {case} 729 gotoxy (x,y); 730 writeln(’ *); 731 if (c = ’1°) or (c = '2") or (c = °3°) or 732 (c = °4’) or (c = °5") or (c = '6’) or 733 (c = 7’) then ¢ := enter; 734 end; {if} 735 gotoxy(x,y); 736 write (test_string) ; 737 until c in [enter, ’q’]; 738 edit:= test_string; 127 739 quit: 740 end; {edit} TAL 742 743 {CALCULATION rountines} 744 745 746 function rp : real; {finds a real parameter in structure description} TAT 748 begin 749 rp := 0; 750 test_string := °’; 751 pointer := pointer + 1; 752 while not((pointer > ord(structure[0])) or 753 (structure[pointer] in delimiter_set)) do begin 754 if structure[pointer] in number_set then 755 test_string := test_string + structure[pointer]; 756 pointer:= pointer + 1; 757 end; {while} 758 if test_string <> *’ then begin 759 val(test_string, temp, error_code); 760 rp := temp; 761 end; {if} 762 if (pointer < ord(structure[0])) and (structure[pointer] = ':*) 763 then begin 764 min := temp; 765 max := rp; 766 if optimization_flag=1 then 767 rp := trp[idata,1] 768 else 769 rp := min + (max-min) *x*xd/(xmax-xmin) ; 770 end; {if} TTL end; {rp} 772 773 function cp : complex; 774 {finds a complex parameter in structure description} 775 var 776 u : complex; TTT begin 778 new(u); 779 u".r := rp; 780 if (structure[pointer] = ’,’) or (structure[pointer] = ’:') then 781 begin 782 u~.i := rp; 783 end {if} 784 else u*.i := 0; 785 cp := u; 786 end; {cp} 787 7388 function orp : real; {returns a real value for optimization} 789 begin 790 nparam := nparam + 1; 791 orp := vert{nparan]; 792 793 794 795 796 797 798 799 800 801 802 803 804 805 807 808 809 811 812 813 814 815 817 818 819 820 821 822 823 824 825 826 827 828 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 128 end; function ocp : complex; {returns a complex value for optimization} begin uparam := nparam + 1; ocp~.r := vert[nparan]; nparam := nparam + 1; ocp*.i := vert[nparan]; end; function ymnj : complex; begin la := (1*1)/(nj+*nj*a*a) ; mla := m*m*la; nla := ntn*la; ymnj := qu(co((1-mla)*nj ,0) ,1r(di(co(1,0) ,su(co(mla,0) ,co(nla,0))))): end; {equivalent characteristic admittance} procedure incident_medium; begin if structure[position] = ’i’ then cno := cc(cp) else cno := ocp; if p_flag = ’TE’ then cnoe := sc(cos(ao),cno); if p_flag = ’TM’ then cnoe ':= sc (1/cos(ao) ,cno) ; {if G_flag=’of’ then write(’i’,round(cno*.r),',',round(-cno~.i),’ *);} end; {incident_medium} procedure neff; begin caj := Ir (di(co(1,0) ,sc(sin(ao)*sin(ao) ,sq(qu(cno,cnj))))); if p_flag = ’TE’ then begin cnje := pr(cnj,caj); write(’’); end; if p_flag = ’TM’ then begin enje := qu(cnj,caj); write(’'); end; end; {effective refractive index} procedure transmit_admittance; begin if G_flag = 'on’ then begin 1d := 1/nj; mla := m*m*1ld*1d/(ax*a); nla := n*n*1ld*1ld/(a*a); Pj := sc(2*pi*lj/ld,1r(co(1-mla-nla,0))); if pj~.i <= -200 then pj*.i := -200; end else begin pj := sc(((2*pi)/1)+*1j,cnj); 129 845 end; 846 pjao := pr(pj,caj); 847 yjmin := su(pr(yj,cosine(pjao)) ,pr(pr(co(0,1),cnje) ,aine(pjao))); 848 yjmid := su(cosine(pjao) ,qu(pr(pr(co(0,1),yj),sine(pjao)) ,cnje)); 849 yjmi := qu(yjmin,yjmid); 850 end; {transmit_admittance} 851 852 procedure loss; 853 begin 854 if yjmi*.r <>0 then 855 begin 856 sjt := yj*.r/(yjmi*.r+ma(yjmid)*ma(yjmid)) ; 857 sj := sj*sjt; 858 end 859 else 860 begin 861 sj :=0; 862 end; 863 end; {loss} 864 865 procedure boundary; 866 begin 867 if structure[position] = 'b’ then cnj := cc(cp) 868 else cnj := ocp; 869 nj := cnj*.r; 870 (if G_flag='of’ then 871 write(’b’,cnj*.r:5:4,’,",-cnj*.i:5:4,’ °):} 872 if G_flag = ‘on’ then cnj := ymnj; 873 if scan = 'leftt’ then 874 begin 875 neff; 876 transmit_admittance; 877 loss; 878 yj := yjmi; 879 end; 880 end; {boundary} 881 882 procedure thickness; 883 begin 884 if structure[position] = 't’ then lj := rp 885 else 1j := orp; 886 {if G_flag='of’ then write(’t’,1j:5:4,’ °);:} 887 if scan = ’right’ then 888 begin 889 neff; 890 transmit_admittance; 891 loss; 892 yj := yjmi; 893 end; 894 end; {thickness} 895 896 procedure admittance; 897 begin 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 940 941 942 943 944 945 946 947 948 950 130 if structure[position] = ‘a’ then aj := cp else aj := ocp; {if G_flag='of’ then write('a’,aj7.r:5:3,',’,aj7.i:5:3,’ °):} yjm1 := su(yj,aj); sj := sj*(yj*.r/yjmi*.r); yj := yjmi; end; {admittance} procedure impedance; begin if structure[position] = ’z’ then zj := cp else zj := ocp; {if G_flag='of’ then write(’z’,zj*.r:5:4,',’,zj*.i:5:4,' ’):} yjm1 := su(yj,qu(co(1,0) ,zj)); sj := sj*(yj*.r/yjmi*.r); yj := yjmi; end; {admittance} function FF(t : real) : real; begin QQ := 1/sqrt(1-sqr(p/1))-1; ccc := sqr(cos({pi/2)*(t/p))); ss := i-ccec; FL := QQtecc*ccc/(1+QQ*ss*ss) ; £2 := sqr(p*cce*(1-3*ss)/(4*1)); FF := £1+f£2; end; function LL(tt : real) : real; begin LL := In(1/sin((pittt)/(2*p))); end; procedure jerusalum_grid; begin Pp := rp; d := rp; Vv := rp; h := rp; XX := (p/1)*(LL(v)+FF(v)); BB := 4*d*(LL(h)+FF(h))/1; yjmi := sulyj,co(0,1/(XX-1/BB))); sj := sj*(yj*.r/yjmi*.r); yj := yjmi; end; {jerusalum_grid} procedure quasi_static_grid; begin a := rp; & °= rp; Woi= rp; rs := xp; rd := xp; 951 952 953 954 955 956 957 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 131 cv := xp; bev := co(0, (2.0#pi*3E11/1) *cy) ; zd := sc (1/377, su(co(rs,0),qu(co(1,0) ,su(bev,co(1/rd,0))))); {if G_flag=’of’ then write(’g’ ,round(a),’ *,round(g),’ *,round(w), * *,round(rs),’ *,round(rd),’ ’,round(cv),’ *);} be := co(0, (4*a/1)*((1+nj#nj)/2)*1n(1/sin( (pig) /(2*a)))); bl := co(O,-(1/((g/1)*1n(1/(sin((pisw)/(2*a))))))); gi su(be,qu(co(1,0),su(zd,qu(co(1,0) ,b1)))); xyz := qu(co(1,0) ,gj); yjm1 := su(yj.gj); sj := sj*(yj*.xr/yjmi*.r); yj := yjmi; end; {quasi_static_grid} procedure final_mediun; begin if structure[position] = 'f’ then begin cnj := cc(cp); nj := cnj*.r; end else begin cnj := ec(ocp); nj := cnj*.r; end; {if G_flag=’of’ then write(’f*,round(cnj*.r),',’,round(-cnj*.i),’ ‘);} if G_flag = ’on’ then enj := ymnj; neff; yj := enje; end; {final_medium} procedure wavelength; begin if structure[position] = ‘w’ then 1 := rp else 1 := orp; {if G_flag=’of’ then write(’w’,round(1),’ °);} end; {wavelength} procedure te; begin ao := rp*pi/180; p_flag := ’TE’; pointer := 1; eno := cc(cp); {if G_flag='of’ then write(’s’,round(ao*180/pi),’ ');} end; {te} procedure tm; begin _ ao := rp*pi/1i80; p_flag := 'IM’; 132 1004 pointer := 1; 1008 cno := cc(cp); 1006 {if G_flag=’of’ then write(’p’ ,round(ao*180/pi),’ ');} 1007 end; {tm} 1008 1009 procedure mirror; 1010 begin 1011 yj := co(1E3,-1E3); 1012 {if G_flag='of’ then 1013 write(’m’,round(yj*.r),’,’,round(yj~.i),’ °);} 1014 end; {mirror} 1015 1016 procedure parasitic_radiation; 1017 begin 1018 par := cp; 1019 {if G_flag=’of’ then 1020 write(’r’,round(par*.r),’,’,round(par~.i),’ ’):} 1021 end; {parasitic_radiation} 1022 1023 procedure normalization_constant; 1024 begin 1025 normalization := rp; 1026 {if G_flag='of’ then write(’n’,round(normalization),’ ');} 1027 end; 1028 1029 procedure on_off_plot; 1030 begin 1031 on_off := trunc(rp); 1032 end; 1033 1034 procedure eisenhart_kahn_grid; 1035 1036 label skip; 1037 1038 function sinc2(x, y, z : real) : real; 1039 begin 1040 if x = 0 then sinc2 := i 1041 else 1042 begin 1043 sinc := sin(x*pi+y/z)/(x*pi*y/z) ; 1044 sinc2 := sinc*sinc; 1045 end; 1046 end; {sinc square} 1047 1048 procedure com_library; 1049 begin 1050 if structure[position] in command_set then begin 1051 pointer := position; 1052 case structure[position] of 1053 "i’ : incident_mediun; 1054 *b’ : boundary; 1055 *t’ : thickness; 1056 ‘a’ : admittance; 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 133 *z’ : impedance; *j’ : jerusalum_grid; "g’ : quasi_static_grid; *f£’ : final_mediun; ‘m’ : mirror; "s’ : te; *p’ : tm; ‘w’ : wavelength; *r’ : parasitic_radiation; *n’ : normalization_constant; "o’ : on_off_plot; end; {case} end; {if} end; {com_library} procedure cal_driver; begin if scan = ‘leftt’ then begin repeat {decode structure from right to left} com_library; position := position - 1; until position <= positionstop - 1; end else begin repeat {decode structure from left to right} com_library; position := position + 1; until position >= positionstop + 1; end; end; {calculation_driver} begin {special_grid} a := rp; B :* Ip; woi= rp; rs := rp; rd := rp; cv := rp; bev := co(0, (2.0*pi*3E11/1) *cv); zd := sc (1/377, su(co(rs,0) ,qu(co(1,0) ,su(bev,co(1/rd,0))))); {if G_flag=’of' then write(’G’,’ *,zound(a),’ ',round(g),’ '°, round(w),’ ’,round(rs),’ ’, round(rd),’ ‘,round(cv),’ ’);} {no choice, must store in real #, freemem cause mess} sjsave := sj; yjsaver := yj*.r; yjsavei := yj*.i; cnosaver := cno*.r; cnosavei := cno*.i; 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 134 positionsave := position; structuresave := copy(structure, 1,150); G_flag := ‘on’; positionG := pos(’G’ structure); if pos(’f’, structure) = 0 then positionf := pos(’m’, structure) else positionf := pos('f’, structure); besum := co(0,0); blsum := co(0,0); {writeln(1st,sjsave,yjsaver,yjsavei); writeln(1st,positionsave,zd*.r,zd*.i); writeln(1st, positionG, cnosaver,cnosavei); writeln(1st,a,g,w); writeln(1st,rs,rd,cv) ;} for m := 0 to 85 do begin densum := co(0,0); for n := 0 to 5 do begin pointer := 1; cnj := cc(cp); nj := cnj*.x; cnj := ymnj; neff; cno :™= cnje; scan := ‘leftt’; position := positionf; positionstop := positionG; cal_driver; write(’’); ymnp := yj; position := 1; structure[1] := 'f’: scan := ‘right’; cal_driver; write(’’); ymom := yj; if (m=0) and (n>=1) then begin besum := su(besum,sc(sinc2(n,g,a),su(ymnp, ymnm))); end; if m>=1 then begin en := 2; if n = O then en :=1; densum := su(densum,sc(en*sinc2(n,g,a),su(ymnp,ymnm))); end; end; {begin of n} if m>=1 then begin {writeln(1st, ’m=’,m, *blsum=’,blsum*.r,blsum*.i);} if m=1 then blsum := co(0,0); {writeln(1st,’m=’,m, ’blsum=',blsum*.r,blsum~.i);} blsum := su(blsum,qu(co(sinc2(m,w,a) ,0) ,densum)); {writeln(1st,’m=’,m,’blsum=’,blsum*.r,blsum~.i);} end; freemem(b_heap_pointer,-0); end; {begin of m} yj” .r := yjsaver; 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 135 yj”.i := yjeavei; sj := sjsave; cno”.r := cnosaver; cno”.i := cnosavei; position := positionsave; positionstop := 1; G_flag := ‘of’; structure := structuresave; scan := ’leftt’; {writeln(1st,sjsave,yj*.r,yj*.i); writeln(1st,positionsave,zd*.r,zd~.i); writeln(1st,positionG,cno*.r,cno*.i); writeln(1st,a,g,w); writeln(1st,rs,rd,cv);} bev := co(0,5.65E-4*cv); {modify the constant if freq change} zd := sc (1/377, su(co(rs,0) ,qu(co(1,0) ,su(bev,co(i/rd,0))))); {calculating here to avoid freemem over write} be := sc(2*(1-g/a) , besum) ; bl := qu(co(1,0),sc(2,blaum)); 8j == su(be,qu(co(1,0) ,su(zd,qu(co(1,0) ,b1)))); xyz := qu(co(1,0),gj); yjml := sulyj,gj); 8j := sj*(yj*-.r/yjmi*.r); yj := yjmi; end; {special_grid} procedure command_library; begin if structure[position] in command_set then begin pointer := position; case structure[position] of ‘i’ : incident_mediun; *I’ : incident_medium; *b’ : boundary; *B’ : boundary; *t’ : thickness; "T’ : thickness; ‘a’ : admittance; "A’ : admittance; : impedance; *Z’ : impedance; : jerusalum_grid; : quasi_static_grid; "G’ : eisenhart_kahn_ grid; *f’ : final_mediun; ’F’ : final_medium; m’ : mirror; *s’ : te; "p’ : tm; *w’ : wavelength; *W’ : wavelength; *d’ : dB_plot := true; : parasitic_radiation; 136 1216 *n’ ; normalization_constant; 1217 *o’ : on_off_plot; 1218 end; {case} 1219 end; {if} 1220 end; {command_library} 1221 1222 procedure calculation_driver; 1223 1224 begin 1225 if scan = ’leftt’ 1226 then 1227 begin 1228 repeat {decode structure from right to left} 1229 command_library; 1230 position := position - 1; 1231 until position <= positionstop - 1; 1232 end 1233 else 1234 begin 1235 repeat {decode structure from left to right} 1236 command library; 1237 position := position + 1; 1238 until position >= positionstop + 1; 1239 end; 1240 end; {calculation_driver} 1241 1242 1243 {SIMULATION rountines} 1244 1245 1246 procedure simulation; 1247 1248 label quit; 1249 var 1250 next_data : integer; 1251 1252 procedure find_trap; 1253 begin 1254 b_heap_pointer := heapptr; 1255 gotoxy (9,23); 1256 sj := 1; 1257 yj := co(0,0); 1258 position := ord(structure[0]); 1259 positionstop := 1; 1260 scan := ’leftt’; 1261 G_flag := ‘of’; 1262 calculation_driver; 1263 re := qu(di(cnoe,yj),su(cnoe,yj)); 1264 reflectance:=ma(pr(su(re,par) ,su(cc(re) ,cc(par))))/normalization; 1265 phase := ph(rc); 1266 transmittance := (1-reflectance) *sj; 1267 absorptance := i-transmittance-reflectance; 1268 end; 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 137 procedure accumulate_error; var datavalue : real; begin datavalue := trp[data_index, 2]; ref_err := ref_err + abs( reflectance - datavalue ); end; {main procedure simulation} begin dB_plot := false; write_y_axis; structure := edit(14,3, structure); x := 1; b:i= ’a’; par := co(0,0); normalization := 1.0; optimization_flag := 0; on_off := 15; ref_err := 0; data_index := 1; data_inc := round ( int( (xmax-xmin)/(xd*ndata) ) );: next_data := 1; repeat {sweep variable x} if (x = next_data) then begin if data_index <= ndata then begin find_error_flag := true; find trap; accumulate_error; find_error_flag := false; data_index := data_index + 1; next_data := next_data + data_inc; end; end; find_trap; if x>=1 then begin {gotoxy(4,13); write(’ ); gotoxy(4,13); write(ref_err:6:2); gotoxy(4,14); write(’ *); gotoxy (4,14); write(be*.i:6:4); gotoxy(4,15); write(' ); gotoxy(4,15); write(bl*.i:6:4); gotoxy(5,16); write(’ *); gotoxy(5,16); write(zd*.r:8:2); gotoxy(5,17); write(’ "); gotoxy(5,17); write(zd*~.i:8:2); gotoxy(5,18); write(’ *); gotoxy(5,18); write(XX:6:4); gotoxy(3,19); write(’ "); gotoxy(3,19); write(sj:3:2); 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 quit: 1374 end; 138 gotoxy(3,20); write(’ ');} gotoxy(3,20); write (transmittance:3:2); gotoxy(3,21); write(’ *); gotoxy(3,21); write(reflectance:3:2); gotoxy(3,22); write(' *); gotoxy (3,22); write(absorptance:3:2); gotoxy (3,23); write(’ *); gotoxy (3,23); write (round (phase*180/pi)) ; end; if x=1 then begin {gotoxy(1,13); write('er=’); gotoxy(1,14); write(’bc='); gotoxy(1,15); write(’bl='); gotoxy(1,16); write('’zdr="); gotoxy(1,17); write('zdi="); gotoxy(1,18); write(’X=’); gotoxy(1,19); write('s=');} gotoxy(1,20); write(’t=’); gotoxy(1,21); write('r="); gotoxy (1,22); write(’a=’); gotoxy(1,23); write('p=’); end; i := ((seg(heapptr*) - seg(b_heap_pointer~)) shl 4) + (ofs(heapptr*) - ofs(b_heap_pointer’)); freemem(b_heap_pointer, i); heapptr := ptr(seg(b_heap_pointer”) ,ofs(b_heap_pointer~)); freemem(b_heap_pointer,-0); {gotoxy (3,4); what for?} delay (10); if KeyPressed then read(kbd,b): case b of ’a’ : begin plot_result (1); x= xt t; end; ‘1’ : begin plot_result (0) ; read(kbd,b) ; x :=x- il; end; *r’ : begin plot_result(1); read(kbd,b); x := x + 1; end; q’ : goto quit; end; {case b} until x >= ((xmax-xmin) div xd) + 1; {end of x} write_x_axis; read(kbd,c); 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 139 {OPTIMIZATION rountines} function efunc(vertice : glnp) : real; {find error between predicted and measured} var i: integer; error, T, p: real; rm : complex; q : char; begin for i := 1 to ndim do begin vert[i] := vertice[i]; end; error := 0; optimization_flag := 1; mark(b_heap_pointer) ; for idata := 1 to ndata do begin mparam := 0; gotoxy (9,23); sj := 1.0; yj := co(0,0); position := ord(structure[0]); positionstop := 1; scan := ’leftt'; G_flag := ’of’; calculation_driver; re := qu(di(cnoe,yj),su(cnoe,yj)); r := sqrt(trp[idata,2]); face := trp[idata,3]*(pi/180.0); rm := co( r*cos(face) , r*sin(face) ); error := error + ma( di(rc,rm) ); end; {do} efunc := error; release (b_heap_pointer) ; end; procedure scalar_range; begin range_variable := cp; range[1,range_pointer] := range_variable~. range[2,range_pointer] := range_variable~. range_pointer := range_pointer + 1; end; procedure complex_range; begin scalar_range; if structure[pointer] = ’,' then begin i; 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 140 scalar_range; end else begin range[1,range_pointer] := 0; range[2,range_pointer] := 0; range_pointer := range_pointer + 1; end; end; {of complex_range} procedure initialize_optimization; var i, j : integer; temp : real; begin {rightmost parameter goes into col 1, etc. & row 1 takes minimum} range_pointer := 1; position := ord(structure([0]); positionstop := 1; scan := ’leftt’; repeat if structure[position] in command_set then begin pointer := position; case structure[position] of *I’ : complex_range:; *B’ : complex_range; *T' : scalar_range; "A’ : complex_range; *Z’ : complex_range; "F’ : complex_range; *W’ : scalar_range; end; {fof case} end; fof if} position := position - 1; until position <= positionstop - 1; ftol := 0.0001; iter := 50; ndim := range_pointer - 1; mvertices := ndim + 1; for i := 1 to mvertices do begin for j := 1 to ndim do begin if i = j then poly{i,j] := range[2,j] else poly[i,j] := range[1,j]; end; end; gotoxy(1,6); write(’ *); gotoxy(1,6); writeln(’intializating ... *); 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 141 for i := 1 to mvertices do begin for j := 1 to ndim do begin vert[j] := poly[i,j]; end; yli] := efunc(vert); end; gotoxy(1,7); writeln; for i := 1 to mvertices do begin for j := 1 to ndim do begin temp := poly[i, jl]; write(temp:6:4,' °); end; temp := y[i]; write(temp:6:4,’ °); writeln; end; writeln(’iteration cycle #0 °); writeln; writeln; end; {fof optimization} procedure amoeba; label pau, loop; const alpha = 1.0; beta = 0.5; gamma = 2.0; itmax = 500; var mpts, i, j, inhi, ilo, ihi : integer; yprr, ypr, rtol : real; pr, prr, pbar : glnp; q : char; temp : real; begin mpts := ndim + 1; iter := 0; loop: ilo := 1; if ( y{1] > y[2] ) then begin ihi := 1; inhi := 2; end else begin ihi := 2; inhi := 1; end; 142 1534 for i := 1 to mpts do 1535 begin 1536 if ( yfi] < y[ilo] ) then ilo := i; 1837 if ( y[i] > y[ihi] ) then begin 1538 inhi := ihi; 1539 ihi := i; 1540 end 1541 else begin 1542 if ( y[i] > y[inhi] ) and ( i <> ihi ) then inhi := i; 1543 end; 1544 end; 1545 rtol := 2.0 * abs( y[ihi]~y[ilo] ) / ( abs(y[ihi]) + abs(y[ilo]) ); 1546 if ( rtol < ftol ) then goto pau; 1547 if ( iter = itmax ) then 1548 begin 1549 writeln(’pause in AMOEBA - too many iterations’): 1550 readin(q); 1551 end; 1552 iter := iter + 1; 1553 for j := 1 to ndim do 1554 begin 1855 pbar[j] := 0.0; 1556 end; 1557 for j := 1 to ndim do 1558 begin 1559 begin 1560 for i := 1 to mpts do 1561 begin 1562 if ( i <> ihi ) then pbar[j] := pbar[j] + polyfi,jl]; 1563 end; 1564 end; 1565 end; 1566 for j := 1 to ndim do 1567 begin 1568 pbar[j] := pbar[j]/ndim; 1569 pr[j] := pbar[j] + alpha * ( pbar[j] - poly[ihi,j] ); 1570 end; 1571 ypr := efunc(pr); 1572 if ( ypr <= y[ilo] ) then 1573 begin 1574 {write('reflection’);} 1575 for j := 1 to ndim do 1576 begin 1577 prrf{j] := pbar[j] + gamma * ( pr[j] - pbar[j] ); 1578 end; 1579 yprr := efunc(prr); 1580 if ( yprr < yf[ilo] ) then 1581 begin 1582 {writeln(’ & expansion’) ;} 1583 for j := 1 to ndim do 1584 begin 1585 poly[ihi,j] := prr[jl; 1586 end; 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 143 ylihi] := yprr; end else begin {writeln(’ only’);} for j := 1 to ndim do begin poly[ihi,j] := pr[j]; end; ylihi] := ypr; end; end else begin if ( ypr >= y[inhi] ) then begin if ( ypr < y[ihi] ) then begin {writeln(’line contraction');} for j := 1 to ndim do begin polyfihi,j] := pr[jl]; end; ylihi] := ypr; for j := 1 to ndim do begin prr[j] := pbar[j] + beta * ( poly[ihi,j] - pbar[j] ); end; yprr := efunc(prr); if ( yprr < y[ihi] ) then begin for j := 1 to ndim do begin poly[ihi,j] := prr[jl; end; y{ihi] := yprr; end; end else begin {writeln(’surface contraction’) ;} for i := 1 to mpts do begin if ( i <> ilo ) then begin for j := 1 to ndim do begin pr[j] := ( poly[i,j] + poly[ilo,j] ) / 2; polyfi,j] := prlj]; end; yli] := efunc(pr); end; end; 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 144 end; end else begin {writeln(’reflection with mild success only’) ;} for j := 1 to ndim do begin poly[ihi,j] := pr{j]: end; y{ihi] := ypr; end; end; writeln; for i := 1 to mpts do begin for j := 1 to ndim do begin temp := poly[i,j]; write(temp:6:4,’ °); end; temp := y[i]; write(temp:6:4,' '); writeln; end; writeln(’iteration cycle #',iter,’ °); writeln; goto loop; pau: end; procedure optimization; begin dB_plot := false; structure := edit(14,3,structure); initialize_optimization; amoeba ; writeln; writeln; writeln(’Optimization finish.’); writeln('Please record optimized values.’); writeln(’Press Q to Qquit and R to continue.’): end; {DATA_BASE routines} procedure graph_units; begin gotoxy(1,2); write(’ write(’ ); gotoxy(1,2); write(’enter ylmi, ylmx, yrmi, yrmx : '); readln(ylmi, ylmx, yrmi, yrmx); 145 1693 write('select curve : (0 = refl), (1 = phase) and (2 = both) °): 1694 readln(curve_select) ; 1695 ylrange := ylmx - ylmi; ylscale := (ymax-ymin)/ylrange; 1696 yrrange := yrmx - yrmi; yrscale := (ymax-ymin) /yrrange; 1697 end; 1698 1699 procedure database; 1700 1701 var 1702 i: integer; 1703 1704 begin 1705 gotoxy (31,2); write(’ *); read (filename) ; 1706 gotoxy (12,3); writeln('inputting data from * filename) ; 1707 assign (data_transfer,filename) ; 1708 ndata := QO; 1709 reset (data_transfer); 1710 while not eof(data_transfer) do begin 1711 ndata := ndata + 1; 1712 readln(data_transfer,trp[ndata,1],trp[ndata,2] ,trp[ndata,3]); 1713 end; 1714 close(data_transfer) ; 1715 xmi := trp[1,1]; xmx := trp[ndata,1]; 1716 for i := 2 to ndata do begin 1717 if trp[i,i] > xmx then xmx := trp[i,1]; 1718 if trp[i,i] < xmi then xmi := trp[i,1]; 1719 end; 1720 graphwindow (xmin, ymin, xmax, ymax) ; 1721 xscale := (xmax - xmin)/(xmx - xmi); 1722 write_x_coordinates (xmin, ymax+14,(xmax-xmin) div 5, 1723 xmi, (xmx-xmi)/5,xmx,4,1); 1724 write_y_coordinates (xmin-20,ymin+7,(ymax-ymin) div 5, 1725 ylmx, (ylmi-ylmx)/5,ylmi,3,1); 1726 write_y_coordinates (xmax+20,ymin+7,(ymax-ymin) div 4, 1727 yrmx, (yrmi-yrmx)/4,yrmi,4,0); 1728 for i := 1 to ndata do begin 1729 gotoxy (47,3); writelin(i,’ *,trpli,i}]:4:2,° ‘,trp[i,2]:4:2,' °, 1730 trp[i,3]:4:2); 1731 trpi := trp[i,1] - xmi; 1732 {plot reflectance} 1733 if ( curve_select = 0 ) or ( curve_select = 2 ) then begin 1734 trp2 := ylmx - trp[i,2]; 1735 plot( round(trpitxscale) - 1, round(trp2*ylscale) , 1 ); 1736 plot( round(trp1*xscale) , round(trp2+ylscale) , 1 ); 1737 plot( round(trpi*xscale) + 1 , round(trp2+ylscale) , 1 ); 1738 plot( round(trpi*xscale) , round(trp2+ylscale) +1, 1): 1739 plot( round(trpi*xscale) , round(trp2*ylscale) - 1, 1 ); 1740 end; 1741 {plot phase} 1742 if ( curve_select = 1 ) or (curve_select = 2 ) then begin 1743 trp3 := yrmx - trp[i,3]; 1744 plot( round(trpi+xscale) - 1 , round(trp3+yrscale) + 1 , 1); 1745 plot( round(trp1*xscale) , round(trp3*yrscale ) , 1 ); 146 1746 plot( round(trpi*xscale) + 1 , round(trp3+*yrscale) - 1 1747 plot( round(trpi*xscale) + 1 , round(trp3+yrscale) + 1 1748 plot( round(trpi*xscale) - 1 , round(trp3*yrscale) - 1 1749 end; 1750 read(kbd,c): 1751 end; 1752 read(kbd,c); 1753 end; 1754 1755 1756 {MAIN PROGRAM} 1757 1758 1759 begin 1760 ylmi := 0.0; yrmi := -180.0; 1761 ylmx := 1.0; yrmx := 180.0; 1762 ylrange := ylmx - ylmi; ylscale := (ymax-ymin)/ylrange; 1763 yrrange := yrmx - yrmi; yrscale := (ymax-ymin) /yrrange; 1764 select := 'm’; 1765 ndata := 1; 1766 curve_select := 2; 1767 be := co(0.0,0.0); 1768 bl := ¢o(0.0,0.0); 1769 zd := co(0.0,0.0); 1770 XX := 0.0; 1771 Co 3= °qQ’; 1772 main : 1773 repeat 1774 set_up; 1775 if select = ’q’ then goto pau; 1776 case select of 1777 "d’ : database; 1778 *s’ : simulation; 1779 *o’ : optimization; 1780 *g’ : graph_units; 1781 *q’ : goto pau; 1782 end; 1783 if (c = 'q’) or (c = ’g’) or (c = ’o’) then select := ‘nm’: 1784 if (c = 'd’) or (c = ’s') then select := c; 1785 until c = ’q’; 1786 goto main; 1787 pau: 1788 textmode (bw80) ; 1789 end. 147 Appendix C Computer Program Listing for Reflection Measurement 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 program measure_reflection_coefficient; { The name of this program is reflmeas. It was developed to measure the reflection coefficient of the diode-grid in conjunction with the small aperture reflectometer. An IBM-PC is used to control the Data Translation A/D and D/A converter and the Hp3478A multimeter, whose address should be 23, for voltage measurements. When the program is run, it prompts the user for vertical plotting units, scanning distance in [mn], operating frequency in [GHz], etc. The measured reflection coefficients are plotted in real time. At the end of the measurement, the data can be saved in a file for later editing or processing. } type complex = “complex_record; complex_record = record r,i: real; end; complex_matrix = “complex_matrix_record: complex_matrix_record = record t11,t12,t21,+22 : complex; end; sdesc = record len : byte; addr : integer; end; datatype = array[1..100] of real; const xmin = 190; xmax = 550; ymin = 43; ymax = 163; label pau, restart, next_data; var vout, vin, gain : real; channel, dac : integer; peak, valley, i1, i2, i3, i4, pin : real; amp, face, facex, facey : real; ylstart, yrstart, ylstop, yrstop, xstart, xstop : real; q, c, select : char; dB_plot : boolean; on_off : byte; xX, xcor, ycor : integer; norm, min, max : real; 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 TT 78 79 80 8l 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 148 reflectance, transmittance, phase, absorptance : real; ndata, j : integer; lap : array [1..100 , 1..3] of real; {1 = len. , 2 = amp. ,and 3 = phase} data_transfer : text; filename : string[15]; port_num, bit_num, bit_val, port_O_byte, port_i_byte : byte; n_step, over_drive_n_step : integer; n_step_per_um, freq, inc_90, lamda : real; imirror, lprevious, lphase, lstart, Istep, lstop : real; i, mode, p_step, m_step, total_step : integer; cmd, recv, set_up_store : string[200]; cmddesc, recvdesc : sdesc; my_address, system_controller, len, status, code : integer; quote : char; offset, pnorm, initial_sep : real; function co (s,t : real) : complex; {makes a complex number} var u_: complex; begin new(u); u".r := 8; u*.i :=t; co :=u; end; function ph(s : complex) : real; {phase in radians, (-pi, +pi]} begin if s°.r > 0 then ph := arctan(s*.i/s*.r); if s°.r <0 then if s*.i >= 0 then ph := arctan(s*.i/s*.r) + pi else ph := arctan(s*.i/s*.r) - pi; if s°.r = 0 then begin if s*.i > 0 then ph := pi/2; if s°.i < 0 then ph := -pi/2: if s*.i= 0 then ph := 0; end; {real part 0} end; {of phase} procedure draw_box (x1,y1i,x2,y2,color : integer) ; begin draw (x1,y1,x1,y2,1); draw (xi,y2,x2,y2,1); draw (x2,y2,x2,y1,1); draw (x2,yi,x1,y1,1); end; procedure draw_x_ticks(x1,y1,x_increment,x2 : integer); begin while (x1<=x2) do begin draw (x1, (yit1),x1, (y1-2),1); xi := x1 + x_increment; 149 end; {while} end; {draw_x_ticks} procedure draw_y_ticks(x1,y1,y_increment,y2 : integer) ; begin while (yi<=y2) do begin draw ((x1+2),y1, (x1-4),y1,1); yi := yi + y_increment; end; {while} end; {draw_y_ticks} procedure draw_graph(xi,y1,x2,y2, x_increment, y_increment_left, y_increment_right :integer); begin draw_box(x1,y1-2,x2,y2+2,1); draw_x_ticks (x1i,y1,x_increment, x2); draw_x_ticks (x1,y2,x_increment, x2); draw_y_ticks (xi,y1,y_increment_left,y2); draw_y_ticks (x2,y1,y_increment_right , y2) ; end; {procedure draw_graph} procedure write_x_coordinates(x1,y1,x_increment : integer; xic,xc_increment ,x2c : real; field,fix :integer) ; begin repeat gotoxy((xi div 8), (y1 div 8)); write (xic:field:fix); xlc := xlc + xc_increment: xi := xi + x_increment; until xic > x2c; end; {write_x_coordinates} procedure write_y_coordinates(x1,y1,y increment integer; yic,yc_increment,y2c : real; field, fix: integer) ; begin repeat gotoxy((xi div 8), (y1 div 8)); write (yic:field:fix); yic := yic + yc_increment;: yi := yi + y_increment; until yic < y2c; end; {write_y_coordinates} function dB(x : real) : real; {give the dB difference} begin dB := 10*1n(x)/1n(10); end; {dB} procedure set_up; begin hires; hirescolor(15); draw_graph(xmin, ymin, xmax, ymax, (xmax-xmin) div 5, (ymax-ymin)div 5, (ymax-ymin)div 4); 150 gotoxy(1,7); write (’Pha. xxxxx'); gotoxy(1,8); write(’Refl. +++++ '); end; {set_up} procedure write_y_axis; begin write_y_coordinates(xmax+20, ymin+7, (ymax-ymin) div 4, yrstop, (yrstart-yrstop)/4,yrstart,4,0); if dB_plot then write_y_coordinates(xmin-20,ymint7, (ymax-ymin) div 5, 0,-10,-50,3,0) else write_y_coordinates(xmin-40, ymin+7, (ymax-ymin) div 5, ylstop, (ylstart-ylstop)/5,ylstart,3,1); end; {write_y_axis} procedure write_x_axis; begin write_x_coordinates (xmin,ymaxt14,(xmax-xmin) div 5, xstart, (xstop-xstart)/5,xstop,4,1); end; {write_x_axis} procedure initialize(var addr, level : integer); external ‘t488init’; procedure transmit(var s : sdesc; var status : integer); external ‘t488xmit’; procedure receive(var r : sdesc: var len, status : integer) ; external 't488recv’; procedure hp_vm_initialize: {Initalization procedure for Hp voltmeter} begin quote := chr(39); cmddesc.addr := ofs(cmd) + 1; recvdesc.addr := ofs(recv) + 1; my_address := 21; system_controller := 0; initialize(my_address, sysatem_controller): cmd := ’LISTEN 23° ; cmddesc.len := length(cmd); transmit (cmddesc, status); cmd := "DATA * + quote + ‘Hi Ti’ + quote + °13 10° ; cmddesc.len := length(cmd); transmit (cmddesc, status); cmd := ‘TALK 23° ; cmddesc.len := length(cmd); transmit(cmddesc, status); 151 209 end; 210 211 procedure hp_vm(var voltage : real); 212 213 begin 214 recv :=’ 215 recvdesc.len := length (recv) ; 216 receive(recvdesc,len, status) ; 217 218 recv :=' 219 recvdesc.len := length(recv) ; 220 receive (recvdesc,len,status) : 221 if recv[1] = ‘+’ then delete(recv,1,1); 222 val (recv, voltage, code) ; 223 voltage := ( voltage - offset )* 1e3 ; 224 225 end; {of hp_vm} 226 227 procedure wait_for_DIF; 228 {check data register of Data Translation board before writing to it} 229 230 var 231 ready,int : byte; 232 timeout : integer; 233 234 begin 235 ready := 0; 236 timeout := $8000; 237 while ready = 0 do 238 begin 239 int := Port[$2ED] and 2; 240 if int = 0 then ready := 1; 241 delay(1); 242 timeout := timeout+1; 243 if timeout = 32767 then 244 begin 245 writeln("Device time-out on DT-2801 board,'); 246 writeln(’during wait for DIF.'); 247 writeln; 248 ready := 1; 249 end; {if} 250 end; {while} 251 end;{procedure wait_for_DIF} 252 253 254 procedure wait_for_DOR; 255 {check if there is new data in Data Translation board} 256 257 var 258 ready,int : byte; 259 timeout : integer; 260 261 begin 152 262 ready := 0; 263 timeout :~ $8000; 264 while ready = 0 do 265 begin 266 int := Port[$2ED] and 1; 267 if int = 1 then ready := 1; 268 delay(1); 269 timeout := timeoutt1; 270 if timeout = 32767 then 271 begin 272 writeln(’Device time-out on DT-2801 board,’); 273 writeln('during wait for DOR.’); 274 writeln; 275 ready := 1; 276 end; {if} 277 end; {while} 278 end;{procedure wait_for_DOR} 279 280 281 procedure wait_for_ready; 282 {check if ready to execute another command in the 283 Data Tranlation board} 284 285 var 286 ready,int : byte; 287 timeout : integer; 288 289 begin 290 ready := 0; 291 timeout := $8000; 292 while ready = 0 do 293 begin 294 int := Port[$2ED] and 4; 295 if int = 4 then ready := 1; 296 delay (1); 297 timeout := timeouttl; 298 if timeout = 32767 then 299 begin 300 writeln(’Device time-out on DT-2801 board,’): 301 writeln(’during wait for Ready.’); 302 writeln; 303 ready := 1; 304 end; {if} 305 end; {while} 306 end;{procedure wait_for_ready} 307 308 309 procedure write_d_to_a_immediate(vout: real; dac: integer) ; 310 311 var 312 dat_low_byte, dat_high byte, ps : byte; 313 code : integer; 314 153 315 begin 316 wait_for_ready; 317 Port[$2ED] := $08; {write voltage command} 318 code := round((vout+10) #4095/20.0); 319 if code > 4095 then code := 4095; 320 if code < O then code := 0; 321 dat_high_byte := code and $0FOO shr 8; 322 dat_low._byte := code and $FF; 323 if dac = 0 then ps := $00; 324 if dac = 1 then ps := $01; 325 wait_for_DIF; 326 wait_for_DIF; 327 Port [$2EC] := ps; 328 wait_for_DIF; 329 Port[$2EC] := dat_low_byte; 330 wait_for_DIF; 331 Port [$2EC] := dat_high_byte; 332 end;{procedure write_d_to_a_immediate} 333 334 335 procedure read_a_to_d_immediate(var vin, gain : real; channel : integer) ; 336 {Read data form the Data Translation board} 337 var 338 dat_low_byte, dat_high byte, G, chan : byte; 339 code : integer; 340 tempi : real; 341 i: integer; 342 343 begin 344 tempi := 0; 345 {for i := 1 te 10 do begin} 346 wait_for_ready; 347 port [$2ED] := $0C; {A/D command} 348 wait_for_DIF; 349 if gain = 1.0 then G := $00; 350 if gain = 10.0 then G := $01; 351 if gain = 100.0 then G := $02; 352 if gain = 500.0 then G := $03; 353 port[$2EC] := G; {Gain select} 354 wait_for_DIF; 355 case channel of 356 O : chan := $00; 357 1 : chan := $01; 358 2: chan := $02; 359 3 : chan := $03; 360 4 : chan := $04; 361 5 : chan := $05; 362 6 : chan := $06; 363 7 : chan := $07; 364 end; 365 port [$2EC] := chan; {Channel select} 366 wait_for_DOR; 367 dat_low_byte := port[$2EC]; 154 368 wait_for_DOR; 369 dat_high byte := port [$2EC]; 370 code := 256 * dat_high byte + dat_low_byte; 371 tempi := tempi + 20.0 * code/65536.0; 372 vin := temp1/gain; 373 end;{procedure read_a_to_d_immediate} 374 375 376 procedure clear_DT_2801; 377 {Clear procedure for Data Translation board} 378 var 379 temp : byte; 380 381 begin 382 Port [$2ED] := $FF; 383 temp := Port[$2EC]; 384 wait_for_ready; 385 Port[$2ED] := 0; 386 wait_for_DOR; 387 temp := Port[$2Ec]; 38s end;{procedure clear_DT_2801} 389 390 procedure wait_for_keypress; 391 392 begin 393 if mode = 0 then read(kbd,q) 304 else delay(2000) ; 305 end;{procedure wait_for_keypress} 396 397 procedure write_digital_out(port_number, bit_number, on_off : byte) ; sos {Write a command to motor driver} 399 400 var 401 mask : byte; 402 begin 403 wait_for_ready; 404 port[$2ED] := $05; 405 wait_for_DIF; 406 port [$2EC] := port_number; 407 wait_for_ready; 408 port [$2ED] := $07; 409 wait_for_DIF; 410 port [$2EC] := port_number; 411 wait_for_DIF; 412 mask := 1 shl bit_number; 413 if port_number = 1 then 414 begin 415 if on_off = 1 then port_i_byte := mask or port_i_byte 416 else port_i_byte := (not mask) and port_i_byte; 417 port [$2EC] := port_1_byte; 418 end 419 else 420 begin 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 440 441 442 443 444 445 446 448 449 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 155 if on_off =1 then port_O_byte := mask or port_O_byte else port_O_byte := (not mask) and port_O_byte; port [$2EC] := port_O_byte; end; end; procedure enable_motor(port_number, on_off : byte); {Enable motor: 1 for on } begin if on_off = 1 then write_digital_out(port_number, 2, 1) else write_digital_out(port_number, 2, 0); end; procedure direction(port_number, for_bak : byte); {Motor direction: 1 for forward } begin if for_bak = 1 then write_digital_out(port_number, 5, 1) else write_digital_out(port_number, 5, 0); end; procedure scan(port_number : byte ; nistep : integer); {Move motor: 1 for move} var i: integer; begin if n_step > O then direction(port_number, 1) else direction(port_number,0); for i := 1 to abs(n_step) do begin write_digital_out(port_number, 7, 0); write_digital_out(port_number, 7, 1); delay (20); write_digital_out(port_number, 7, 0); end; end; {of scan} begin {main program} hp_vm_initialize; dB_plot := false; set_up; gotoxy(1,1); write(’enter ylstart, ylsatop, yrstart and yrstop : ’): readln(ylstart,ylstop, yrstart,yrstop) ; write_y_axis; gotoxy(1,2); write(’enter xstart and xstop : '); readIn(xstart,xstop) ; gotoxy(1,3); write(’enter mode ( manual =0 & auto=1) =: °); readin(mode) ; write_x_axis; i] fo) port_O_byte : port_i_byte : K [o) 474 475 476 ATT 478 479 480 481 482 483 484 485 486 487 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 156 clear_DT_2801; enable_motor(0,1); enable_motor(1i,1); n_step_per_um := 1.01; {Motor calibration constant} {Last calibrated on 10/86} offset := 0.10e-3; over_drive_n_step := 25; ndata := 1; total_step := 0; gotoxy(1,3); writeln(’ *); gotoxy(1,3); write(’enter frequency in GHz: '); readln(freq) ; lamda := 300.0/freq; {convert into millimeter} inc_90 := lamda/8.0; p_step := round( inc_90 * 1000.0 + n_step_per_um ); gotoxy (60,3); write(’STATE :'); if mode = 1 then begin gotoxy(1,4); write(’enter Istart, Istep, lstop : '); readln(Istart, lstep, Istop); lmirror := lstart; lprevious := lmirror; end else begin gotoxy(70,3); write(’L '); gotoxy(1,14); write(’ L > "); gotoxy(7,14); readIn(1mirror) ; lprevious := xstart; end; hp_vm_initialize; {To eliminate back-lash in the translation} scan(0,-over_drive_n_step) ; scan(0,over_drive_n_step) ; scan(0,-over_drive_n_step); scan(0,over_drive_n_step) ; scan(1,-over_drive_n_step) ; scan(1,over_drive_n_step) ; scan(1,-over_drive_n_step); scan(1,over_drive_n_step) ; gotoxy (1,4); writeln(’ *); gotoxy(1,4); write(’enter initial seperation : ’); readln(initial_sep) ; writeln(1lst,’initial seperation = *, initial_sep); writeln(lst,’ °); write(lst,’ L Pin il ); writeln(lst, ’i2 i3 i4 Phase Ampc') ; writeln(lst,’ °); next_data: restart: if ( mode = 0 ) and ( ndata <> 1 ) then begin if 157 gotoxy(70,3); write(’L '); gotoxy(1,14); write(’ L > gotoxy(7,14); readln(lmirror) ; end; m_step := round( (lmirror-lprevious) * 1000.0 + n_step_per_un ); scan(0,m_step) ; gotoxy(70,3); write(’L ’); ); gotoxy(1,14); write(’ L= '°); if mode = 1 then write(lmirror:6:3); gain := 1.0; channel := 0; gotoxy(70,3); write(’Pin’); gotoxy(1,15); write('Pin = wait_for_keypress; {hp_vm(pin) ;} ); read_a_to_d_immediate(pin, gain, channel); gotoxy(7,15); write(pin:7:6) gotoxy(70,3); write('ii ’); gotoxy(1,16); write(’ ii = wait_for_keypress; hp_vm(ii); read_a_to_d_immediate(pnorm, i1 := i1/pnorm; gotoxy(7,16); write(i1:7:6); gotoxy(70,3); write(‘'i2 ’); scan(1,p_step) ; gotoxy(1,17); write(’ i2 = wait_for_keypress; hp_vm(i2) ; read_a_to_d_immediate(pnorm, i2 := i2/pnorm; gotoxy(7,17); write(i2:7:6) ; gotoxy(70,3); write(’i3 '); scan(1,p_step) ; gotoxy(1,18); write(’ i3 = wait_for_keypress; hp_vm(i3) ; read_a_to_d_immediate(pnorm, i3 := i3/pnorm; gotoxy(7,18); write(i3:7:6); gotoxy(70,3); write(’i4 ’); scan(1,p_step); gotoxy(1,19); write(’ i4 = wait_for_keypress; q='’r’* then goto restart; hp_vm(i4); read_a_to_d_immediate(pnorm, i4 := i4/pnorm; ); gain, channel) ; ); gain, channel); *); gain, channel); gain, channel) ; 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 609 610 611 612 613 614 615 616 617 618 620 621 622 623 624 625 626 627 628 629 630 631 632 158 gotoxy(7,19); write(i4:7:6); facey := i4-i2; facex := i1-i3; face := -ph(co(facex,facey))*(180/pi) ; gotoxy(1,20); write(’Pha = *); gotoxy(7,20); write(face:4:1); xcor := round((lmirror-xstart) *(xmax-xmin) /(xstop-xstart)); ycor := round((yrstop-face) *(ymax-ymin) /(yrstop-yrstart)); graphwindow (xmin, ymin, xmax, ymax) ; plot (xcor-1,ycort+i,1); plot (xcor+1,ycor+1,1); plot(xcor,ycor,1); plot (xcor+1,ycor-1,1); plot (xcor-1,ycor-1,1); amp := sqrt(sqr(i4-i2)+sqr(i1-i3)); gotoxy(1,21); write(’Amp = ); gotoxy(7,21); write(amp:5:3); xcor := round ((1mirror-xstart) *(xmax-xmin) /(xstop-xstart)); ycor := round((ylstop-amp) *(ymax-ymin) /(ylstop-ylstart)) ; graphwindow(xmin, ymin, xmax, ymax) ; plot (xcor-1,ycor,1); plot (xcor+1,ycor,1); plot (xcor,ycor-1,1); plot (xcor,ycor+1,1); write (Lst,lmirror:6:4,° ); write (Lst,pin:7:6,' *); write(Lst,i1:7:6,’ '); write (Lst,i2:7:6,° ); write (Lst,i3:7:6,° ); write (Lst,i4:7:6,’ "); write(Lst,face:4:1,’ *); write (Lst,amp:6:3); writeln(Lst,’ ’); lap[ndata,1] := lmirror; lap[ndata,2] := amp; lap[ndata,3] := face; total_step := total_step + m_step; if ( mode = 1 ) and ( (lmirror>lstop) or (lmirror=lstop) ) then q := 's’; if q=’s’ then begin gotoxy(1,24); write(’enter impedance filename : ’); readin(filename) ; assign(data_transfer,filename); rewrite (data_transfer) ; for j := 1 to ndata do begin writeln(data_transfer,lap[j,1],’ ',lap[j,2],’ °’,lap[j,3]); end; close(data_transfer); 159 633 writeln(lst,’ °); 634 writeln(1st,'stored in filename : *,filename); 635 goto pau; 636 end; {of begin} 637 638 if q = ’q’ then goto pau; 639 gotoxy (70,3); write(’Rwd’); 640 scan(1,-3*p_step) ; 641 scan(1,-over_drive_n_step) ; 642 scan(1,over_drive_n_step); 643 lprevious := lmirror; 644 if mode = 1 then lmirror := lmirror + lstep; 645 ndata := ndata + 1; 646 goto next_data; 647 pau: 648 {Return to original positon} 649 scan(0,-total_step) ; 650 scan(0,-over_drive_n_step); 651 scan(0,over_drive_n_step) ; 652 scan(1,-3+*p_step) ; 653 scan(1,-over_drive_n_step) ; 654 scan(1,over_drive_n_step) ; 655 enable_motor(0,0); 656 enable_motor (1,0); 657 textmode (bw80) ; 658 gotoxy (1,1); 659 end. 160 Appendix D Computer Program Listing for Diode Parameter Measurement 1 program iv_measurement_of _Schottky_diode; 2 3 af The name of this program is ivdiode. It was developed for 5 measuring the circuit parameters of a Schottky diode. 6 The program is written in Turbo Pascal. An IBM-PC is used 7 to control the Hp4145A semiconductor parameter analyzer, 8 whose address is 19. The diode leads should be connected 9 to the terminals labeled as SMU1, and GND on the I-V box 10 are used. The diode parameters are calculated from the measured 11 currents and voltages. They are displayed on the monitor. 12 The diode parameters include the series resistance (Rs), 13 barrier height (Vb), n-factor (nf), and saturation current 14 (Io). The correlation coefficient (cc) of the fit is also 15 displayed. The algorithm used in this calculation 16 is given in Chung-en Zah’s Ph.D. thesis, "Millimeter-Wave 17 Monolithic Schottky Diode Imaging Arrays." The program is 18 menu driven. Default value for the diode area is 18 um#2. 19 The current ranges from 0.1 uA to 0.1 mA, and the voltage 20 ranges from 0 V to 2 V. Pressing return after the prompt 21 invokes the above default values. The data can be saved on disk, 22 retrived from disk, displayed on the monitor, or listed on the 23 printer. } 24 25 type 26 sdesc = record 27 len : byte; 28 addr : integer; 29 end; 30 datarray = array [1..100] of real; 31 32 const 33 xmin = 190; xmax = 450; 34 ymin = 23; ymax = 163; 35 xd = 3; 36 37 label 38 quit, main_menu, sub_menu, loop1, loop2; 39 40 var 41 cmd, recv : string[200]; 42 cmddesc, recvdesc : sdesc; 43 my_address, system_controller, len, status : integer; 44 quote : char; 45 first, nchar, code: integer; 46 voltage, current, va, im, vm: real; 47 filename, buffer : string[10]; 48 main_mode, sub_mode, q : char; 161 49 time_delay, j, ndata : integer; 50 v, i: datarray; 51 ia, ylstart, ylstop, xstart, xstop, ydata : real; 52 xcor, ycor, yb, ye : integer; 53 vb, area, rs, nf, gf, is : real; 54 number_transfer : file of real: 55 row, col : real; 56 57 procedure initialize(var addr, level : integer); 58 external ’t488init’; 59 60 procedure transmit(var s : sdesc; var status : integer); 61 external 't488xmit’; 62 63 procedure receive(var r : sdesc; var len, status : integer) ; 64 external 't488recv’; 65 66 procedure initialize_hp_4145a; 67 68 begin 69 time_delay := 4000; 70 quote := chr(39); 71 cmddesc.addr := ofs(cmd) + 1; 72 recvdesc.addr := ofs(recv) + 1; 73 74 my_address := 21; 75 system_controller := 0; 76 initialize(my_address, system_controller) ; 17 78 cmd := "IFC REN MTA LISTEN 19°; 79 cmddesc.len := length(cmd); 80 transmit (cmddesc, status); 81 82 cmd := ’DATA’ + quote + 'US’ + quote + ’13 10’; 83 cmddesc.len := length(cmd); 84 transmit (cmddesc, status); 85 86 cmd := "DATA’ + quote + "IT2 CAi BC’ + quote + ‘13 10’; 87 cmddesc.len := length(cmd); 88 transmit (cmddesc, status); 89 end; 90 91 procedure reset_hp_4145a; 92 93 begin 94 cmd := "MTA LISTEN 19’; 95 cmddesc.len := length(cmd); 96 transmit (cmddesc, status); 97 98 cmd := ’DATA’ + quote + "DCL SDC’ + quote + °13 10°; 99 cmddesc.len := length(cmd); 100 transmit (cmddesc, status); 101 end; {of reset_hp_4145a} 102 103 104 105 106 107 108 109 126 127 128 129 130 131 132 133 134 135 136 137 138 139 162 procedure set_voltage(volt : real); var v : string[18]; begin str(volt,v); delete(v,8,6); cmd := ’MTA LISTEN 19’; cmddesc.len := length(cmd); transmit (cmddesc, status); cmd := 'DATA’ + quote + "DV 1, 0, ' + v +", 10E-3' + quote + °13 10°; cmddesc.len := length(cmd); transmit(cmddesc, status); delay(time_delay) ; end; {of set_voltage} procedure set_current(ampere : real); var i: string[18]; begin str(ampere,i); delete(i,8,6); cmd := ’MTA LISTEN 19'; cmddesc.len := length(cmd); transmit (cmddesc, status); cmd := "DATA’ + quote + ’DI 1, 0, ' +i + "5 + quote + ‘13 10’; cmddesc.len := length(cmd); transmit (cmddesc, status); delay(time_delay) ; end; {of set_voltage} procedure measure_current(var i: real); begin cmd := ’MTA LISTEN 19’; cmddesc.len := length(cmd); transmit (cmddesc, status); cmd := 'DATA’ + quote + TI 1’ + quote + 713 10’; cmddesc.len := length(cmd) ; transmit (cmddesc, status); cmd := ‘MLA TALK 19'; cmddesc.len := length(cmd) ; transmit(cmddesc, status); 163 recv := ° , recvdesc.len := length(recv); receive (recvdesc, len, status) ; delete(recv,1,3); val(recv, current ,code) ; if current < 0 then i := current else begin delete(recv,1,1); val(recv, current ,code); i := current; end; end; {of measure_current} procedure measure_voltage(var v : real); begin cmd := ’MTA LISTEN 19°; cmddesc.len := length (cmd) ; transmit (cmddesc, status); cmd := "DATA' + quote + "TV 1’ + quote + ‘13 10’; cmddesc.len := length(cmd); transmit (cmddesc, status); cmd := ’MLA TALK 19°; cmddesc.len := length(cmd); transmit(cmddesc, status); recv := ’ , recvdesc.len := length(recv); receive (recvdesc, len, status) ; delete(recv,1,3); val(recv,voltage,code) ; if voltage < 0 then v:= voltage else begin delete(recv,1,1); val (recv, voltage, code) ; Vv := voltage; end; end; {measure_voltage} procedure clear_line; begin gotoxy(1,1); write(’ *); write(’ "); end; {clear_line} procedure display(x, y : datarray; ndata : integer) ; var cont : char; i: integer; begin 164 208 clear_line; 209 for i := 1 to ndata do begin 210 gotoxy(1,1); write(ndata,’ - ’,i,' *,y[i]:10,’ > x[i]:10); 211 read(cont); 212 end; 213 end; fof display} 214 215 procedure Isf(x, y : datarray; n : integer; var a, b, c_ : real); 216 {a = slope b = intercept c = correlation coeff. } 217 var 218 xsum, ysum, xysum, xssum, yssum : real; 219 xden, yden, rden : real: 220 i: integer; 221 222 begin 223 - xsum := 0; ysum := 0; 224 xysum := 0; 225 xssum := 0; yssum := 0; 226 for i := 1 to n do begin 227 xsum := xsum + x[il; 228 ysum := ysum + y[il; 229 xysum := xysum + x[i]*y[il; 230 xssum := xssum + x[{i]*x[iJ; 231 yssum := yssum + y[i]+y[il; 232 end; 233 xden := n * xssum - xsum * xsum; 234 yden := n * yssum - ysum * ysum; 235 rden := sqrt( xden * yden ); 236 a := ( n*xysum - xsumtysum ) / xden; 237 b := ( ysum*xssum - xysum*xsum )/ xden; 238 ¢ := ( n*xysum - xsum*ysum ) / rden; 239 end; {of lsf} 240 241 procedure curve_fit_ivdata(x, y : datarray; n : integer; 242 var rs, nf, gf, is : real); 243 { x = voltage y = current gf = goodness } 244 var 245 1x, ly, yav, dvdlni : datarray; 246 i: integer; 247 begin 248 {for i := 1 to n-1 do begin 249 dvdinifi] := ( x[it1]-x[i] ) / ( In(y[it+1])-In(y[i]) ); 250 yav[i] := ( y[it1] + y[i] ) / 2.0; 251 end; 252 lsf(yav, dvdlni, n-1, rs, nf, gf); 253 nf := nf/0.0259; This method is not accurrate because yav is used.} 254 for i := 1 to n-1i do begin 255 Axi] := ( ylitit]-y[i] ) / ( xfi+1]-x[i] ); 256 ly[i] := ( In(y[iti])-In(y[i]) ) / ( xfit1]-x[i] ); 257 end; 258 lsf(1lx, ly, n-1, rs, nf, gt); 259 rs := -rs/nf; 260 nf := 1/(0.0259#nf); 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 165 is := 0.0; for i := 1 to n do begin is := is + In(y[i]) - (x[i]-yLi]*rs)/(n£*0.0259) ; end; is := exp(is/n); gotoxy(1,7); write(’Rs = ’,rs:8); gotoxy(1,8); write(’nf = ’,nf:8); gotoxy(1,9); write(’Io = ',is:8); gotoxy(1,10); write(’cc = ',gf:8); end; {curve_fit_ivdata} procedure draw_box (x1,y1,x2,y2,color : integer) ; begin draw (xi,y1,x1,y2,1); draw (x1,y2,x2,y2,1); draw (x2,y2,x2,y1,1); draw (x2,yi,x1,y1,1); end; {of draw_box} procedure draw_x_ticks(x1,y1,x_increment,x2 : integer) ; begin . while (x1<=x2) do begin draw (x1, (yi+1) ,x1,(y1-2),1); xi := xi + x_increment; end; {while} end; fof draw_x_ticks} procedure draw_y_ticks(x1,y1,y_increment,y2 : integer) ; begin while (y1<=y2) do begin draw ((x1+2),yi, (x1-4),y1,1); yl := yi + y_increment; end; {while} end; fof draw_y_ticks} procedure draw_graph(x1,y1,x2,y2, x_increment, y_increment_left, y_increment_right :integer) ; begin draw_box(x1,y1-2,x2,y2+2,1); draw_x_ticks (x1,y1,x_increment ,x2) ; draw_x_ticks (x1,y2,x_increment ,x2); draw_y_ticks (x1,y1,y_increment_left,y2); draw_y_ticks (x2,y1,y_increment_right,y2); end; {of procedure draw_graph} function ten_to_power(n : integer) : real; begin ten_to_power := exp( n*In(10) ); end; {of ten_to_power} function ten_to(n : real) : real; begin 314 315 316 317 318 319 320 321 322 324 325 326 327 328 329 330 331 332 334 335 336 337 338 339 340 341 342 344 345 346 347 348 350 351 352 353 354 355 356 357 358 359 360 361 363 364 365 366 166 ten_to := exp( n*in(10) ); end; {fof ten_to} procedure write_x_coordinates(x1,y1,x_increment : integer; xic,xc_increment ,x2c : real; field,fix :integer); begin repeat gotoxy((xi div 8), (y1 div 8)); write (x1c:field:fix); xlc := xic + xc_increment; x1 := x1 + x_increment;: until x1ic > x2c; end; {of write_x_coordinates} procedure write_y_coordinates(x1,y1,y_increment integer; yic,yc_increment,y2c : real; field, fix : integer) ; begin repeat gotoxy((xi div 8), (yi div 8)); write (ylc:field:fix); yic := yle + yc_increment; yl := yi + y_increment; until yic < y2e; end; {of write_y_coordinates} procedure set_up; begin hires; hirescolor(1i5): draw_graph(xmin, ymin, xmax, ymax, (xmax-xmin)div 5, (ymax-ymin)div 6, (ymax-ymin)div 6); end; {of set_up} procedure write_y_axig; begin write_y_coordinates(xmin-40, ymin+7, (ymax-ymin) div 6, ylstop, (ylstart-ylstop)/6,ylstart,4,0); end; {of write_y_axis} procedure write_x_axis; begin write_x_coordinates (xmin, ymaxt+14,(xmax-xmin) div 5, xstart, (xstop-xstart)/5,xstop,4,1); end; {of write_x_axis} procedure plot_ivdata(x, y : datarray; n : integer); var i: integer; begin display(x, y, n); set_up; gotoxy(1,1); write(’enter ylstart ylstop xstart xstop : ’); readln(ylstart, ylstop, xstart, xstop); write_y_axis; write_x_axis; 367 368 369 370 371 372 373 374 375 376 167 for i := 1 to n do begin xcor := round((x[i]-xstart) + (xmax-xmin) /(xstop-xstart)) ; ycor := round((ylstop-1n(y[i])/1n(10.0))* (ymax-ymin) /(ylstop-ylstart)) ; graphwindow(xmin, ymin, xmax, ymax) ; plot(xcor-1,ycor,1); plot (xcor+1,ycor,1); plot (xcor,ycor-1,1); plot (xcor,ycort+i,1); end; 377 end; {plot_datafile} 378 379 procedure plot_ivcurve; 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 var i, yd : integer; amp, 1, xc : real; cont : char; begin xe := 1.0; yd :=1; repeat amp := ylstart + (ylstop-ylstart)+#xc*yd/(ymax-ymin) ; amp := ten_to(amp); 1 := 0.02594+nf*ln(amp/is + 1) + amp*rs; {clear_line; gotoxy(1,1); write(1:8,’ *,amp:8); read(cont) ;} amp := ln(amp)/1n(10.0); xcor := round((1-xstart) *(xmax-xmin) /(xstop-xstart));: ycor := round((ylstop-amp) *(ymax-ymin) /(ylstop-ylstart)) ; graphwindow(xmin, ymin, xmax, ymax) ; plot(xcor,ycor,1); xc := xe + 1.0; until xc >= int(((ymax~ymin) div yd) + 1); end; {of plot_datafile} procedure readfile(var x, y : datarray; var ndata : integer) ; i: integer; data_transfer : text; begin clear_line; gotoxy(1,1); write(’enter filename(read) : °); readln(filename) ; assign (data_transfer, filename) ; ndata := 0; reset (data_transfer); while not eof(data_transfer) do begin ndata := ndata + 1; readln(data_transfer,x[ndata] ,y[ndata]); end; close(data_transfer) ; 419 end; {of readfile} 420 421 423 424 425 426 427 428 429 430 431 432 433 434 435 436 438 439 440 441 442 443 444 445 446 447 448 449 450 452 453 454 455 456 457 458 460 461 462 463 464 465 466 467 468 469 470 471 472 168 procedure writefile(x, y : datarray; ndata : integer) ; var i: integer; data_transfer : text; begin clear_line; gotoxy(1,1); write(’enter filename(write) : °); readln(filenane) ; assign (data_transfer,filename) ; rewrite (data_transfer); for i := 1 to ndata do begin writeln(data_transfer,x[i],’ ',y[i]); end; close(data_transfer) ; end; fof writefile} procedure convert_lin_to_log(var z : datarray; ndata : integer; q : char); var i: integer; begin clear_line; gotoxy(1,1); write(’taking log(’,q,’) ... °); for i := 1 to ndata do begin z[i] := In(z{i])/1n(10.0); end; write(’done’); read (q); end; {of convert_lin_to_log} procedure calculate(var x, y : datarray; ndata : integer) ; var i: integer; begin clear_line; gotoxy(1,1); write(*log(x) or log(y) : °); read(q); if q = ‘x’ then convert_lin_to_log(x, ndata, q); if q = ‘y’ then convert_lin_to_log(y, ndata, q); end; {of calculate} procedure list(x, y : datarray; ndata : integer) ; var i: integer; begin writeln(lst,’filename : ',filename): for i := 1 to ndata do begin writeln(1st,i,’ ’,y[i]:10,’ ',x[i]:10); end; end; {of writedata} 514 516 517 518 519 520 $21 522 523 524 525 169 procedure plot_a_point(x, y : real); begin xcor := round ((x-xstart) +*(xmax-xmin) /(xstop-xstart)) ; ycor := round((ylstop-y)*(ymax-ymin) /(ylstop-ylstart)) ; graphwindow(xmin, ymin, xmax, ymax) ; plot(xcor-1,ycor,1); plot (xcort1,ycor,1); plot (xcor,ycor-1,1); plot (xcor,ycorti,1); end; {plot_a_point} procedure test(var x, y : datarray; ndata : integer) ; var i_zero : real; begin ndata := 0; i_zero := 0.0; set_up; gotoxy(1,1); write(’enter ylstart ylstop xstart xstop : '); readln(ylstart, ylstop, xstart, xstop); write_y_axis; write_x_axis; initialize_hp_4145a; set_current (i_zero); for j := trunc(ylstart)+1 to trunc(ylstop)-1 do begin ndata := ndata + 1; ia := 1.0 * ten_to_power(j); set_current (ia); measure_current (y[ndata]); measure_voltage(x[ndata]); ydata := In(y[ndata])/1n(10.0); plot_a_point (x[ndata] , ydata) ; ndata := ndata + 1; ia := 2.0 * ten_to_power(j); set_current (ia); measure_current (y[ndata]); measure_voltage(x{ndata]); ydata := in(y[ndata])/1n(10.0); plot_a_point (x[ndata] , ydata); ndata := ndata + 1; ia := 4.0 * ten_to_power(j); set_current (ia); measure_current (y[ndata]); measure_voltage(x[ndata]); ydata := In(y[ndata])/1n(10.0); plot_a_point (x[ndata] , ydata) ; end; set_current(i_zero); curve _fit_ivdata(x, y, ndata, rs, nf, gf, is); end; fof test} 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 170 procedure find_barrier_height; begin clear_line; gotoxy(1,1); write(’Enter diode area : *); readln(area); vb := (-0.0259) * In( is / (area*8.16*sqr(300)) ); gotoxy(1,12); write('Vb = ',vb:8); end; procedure create_new_buffer; var select : integer; begin clear_line; gotoxy(1,1); write(’Enter 1 for create & 0 for append to a file : '); read(select); clear_line; gotoxy(1,1); write(’Enter filename : '); readln(buffer); if select = 1 then begin assign (number_transfer,buffer) ; rewrite (number_transfer) ; close(number_transfer) ; end; write(lst,’Row Col Ra N_factor "); writeln(lst,’Is Vb CC’); end; . procedure record_diode_parameter; begin assign(number_transfer, buffer) ; reset (number_transfer) ; seek (number_transfer,filesize(number_transfer)); clear_line; gotoxy(1,1); write(’Enter row & col : ’); readln(row,col); write(number_transfer,row,col,rs,nf,is,vb, gf); write(l1st,row:2:0,’ *,co1:2:0,’ °,rs:10," ‘,nf:10," ’); writeln(1st,is:10,’ ’,vb:10,° " ,gf:10); close(number_transfer) ; end; procedure write_diode_parameter; begin write(lst,’Row Col Rs N_factor "); writeln(lst,’Is Vb CC’); clear_line; gotoxy(1,1); write(’Enter filename : °); readln(buffer); assign (number_transfer, buffer) ; reset (number_transfer); while not(eof(number_transfer)) do begin read(number_transfer,row,col,rs,nf,is,vb,gf); 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 171 write(lst,row:2:0,’ °,col:2:0," ‘,rs:10,’ '); writeln(Ist,nf:10,’ °,is:10,’ *,vb:10,’ ',gf:10); end; close(number_transfer) ; end; begin {main program} ylstart := -7.0; ylstop := -2.0; xstart := 0; xstop :=* 2.0; area := 18e-8; {um e-8} main_menu: clrscr; textmode (bw80); clear_line; gotoxy(1,1); write(’Main Menu>> (t)test-iv (r)read-iv (q)quit : ’); loop1: if not(keypressed) then goto loopi else read(kbd, main_mode) ; case main_mode of *t’ : test(v, i, ndata); r begin readfile(v, i, ndata); plot_ivdata(y, i, ndata); curve_fit_ivdata(v, i, ndata, rs, nf, gf, is); end; *q’ goto quit; end; find_barrier_height; plot_ivcurve; sub_menu: clear_line; gotoxy(1,1); write(’Sub Menu>> °); write('(d)disp (1)1st (s)sav (b)buf r(rec) w(wri) q(qit) : °); loop2: if not(keypressed) then goto loop2 else read(kbd, sub_mode): case sub_mode of ‘d’ : display(v, i, ndata); ‘1’ : list(v, i, ndata); *s’ : writefile(v, i, ndata);: *q’ : goto main_menu; *b’ : create_new_buffer; *r’ : record_diode_parameter; *w' : write_diode_parameter; end; goto sub_menu; quit: end. 172 Appendix E Computer Program Listing for Doping Profile Measurement 1 program cv_measurement_of_Schottky_diode; 2 3 a { The name of this program is cvdiode. It was developed 5 for measuring the C-V characteristics and to calculate the 6 doping profile of a diode. The program is written in 7 Turbo Pascal. An IBM-XT is used to control the Hp4280A 8 C-meter, whose address is 17. The measured data can be saved 9 on the disk, retrieved from the disk, displayed on the monitor, 10 or listed on the printer. Once a command is entered, press 11 return to invoke the command. Default value for the diode 12 area is 2.6e-3 cm*2, which is the area of the mercury 13 probe. The doping concentration ranges from 10°16 cm*-3 to 14 10°18 cm*-3, and the depth ranges from 0 um to 0.5 um. The 15 capacitance ranges from 80 pF to 400 pF, and the voltage ranges 16 from -5 V to 0.5 V at 0.5 V step increment. The duffusion barrier 17 potential is assumed to be 0.94 V for aluminum on Gads with 18 about 10°17 cm*-3 doping concentration. The zero bias 19 capacitance (Co), capacitance ratio (Cr), and capacitance 20 exponent (Gm) are determined from curve-fitting the measured 21 C-V characteristic. The correlation coefficient (cc) for this fit 22 is also displayed on the monitor. The measured doping profile is 23 least-square-fitted with the hyperabrupt doping function. } 24 25 26 27 28 type 29 sdesc = record 30 len : byte; 31 addr : integer; 32 end; 33 datarray = array[1..100] of real; 34 35 const 36 xmin = 190; xmax = 550; 37 ymin = 33; ymax = 163; 38 39 label 40 quit, loop_1, loop_2; 41 42 var 43 cmd, recv : string[200]; 44 vstart, vstop, vstep : string[18]; 45 cmddesc, recvdese : sdesc; 46 my_address, system_controller, len, status : integer; 47 quote : char; 48 i, n, first, nchar, code: integer; 173 cap, cond, volt, buffer :string[20]; capacitance, conductance, voltage : real; slope_a, gamma, intercept_b, correlation_coeff : real; c, v, g, Inv, Inc, Inxd, lnnd, nd, xd : datarray; eo, er, eq, ci, area, dcdv, nd1, nd2, nd3, cratio : real; co, nn, no, phi : real; data_transfer : text; filename : string[8]; ylstart, ylstop, ylunit, xstart, xstop, xstep, xunit : real; ndata : integer; q, cont : char; number_transfer : file of real; row, col : real; procedure initialize(var addr, level : integer); external '’t488init’; procedure transmit(var s : sdesc; var status : integer) ; external ‘t488xmit’; procedure receive(var r : sdesc; var len, status : integer) ; external ’t488recv'; function ten_to_power(n : integer) : real; begin ten_to_power := exp( n*In(10) ); end; {of ten_to_power} function ten_to(n : real) : real; begin ten_to := exp( n*1in(10) ); end; {of ten_to} procedure clear_line; begin gotoxy(1,1); write(’ "); write(’ "); end; {clear_line} procedure convert_lin_to_log(var z : datarray; ndata : integer; q : char); var i: integer; begin clear_line; gotoxy(1,1); write('taking log(’,q,’) ... °); for i := 1 to ndata do begin z{i] := In(z[i])/1n(10.0); end; write(’done’); read(q); end; {of convert_lin_to_log} procedure lsf(ndata : integer; x, y : datarray; 174 var slope, intercept, cc : real); var xsum, ysum, xysum, xssum, yssum, xden, yden, rden : real; begin xsum := 0; ysum := 0; xysum := 0; xssum := 0; yssum := 0; for i := 1 to ndata do begin xsum := xsum + x[i]; ysum := ysum + y[i]; xysum := xysum + x[i]+y(il]; xssum := xssum + x[i]*x[i]; yssum := yssum + y[i]*y[il]; end; xden := ndata*xssum-xsum*xsum; yden := ndatatyssum-ysum*ysum; rden := sqrt (xden*yden) ; slope := (ndata*xysum-xsum*ysum) /xden; intercept := (ysum*xssum-xysum*xsum) /xden; cc := (ndata*xysum-xsum*ysum) /rden; end; {of lsf} procedure draw_box (xi,y1,x2,y2,color : integer); begin draw (x1,y1,x1,y2,1); draw (x1,y2,x2,y2,1); draw (x2,y2,x2,y1,1); draw (x2,y1,x1,y1,1); end; {of draw_box} procedure draw_x_ticks(x1,y1,x_increment ,x2 : integer) ; begin while (x1<=x2) do begin draw (x1, (y1+1) ,x1, (y1-2),1); x1 := xi + x_increment; end; {while} end; {of draw_x_ticks} procedure draw_y_ticks(x1,yl,y_increment,y2 : integer); begin while (y1<=y2) do begin draw ((x1+2),y1, (x1-4) ,y1,1); yi := yl + y_increment; end; {while} end; {of draw_y_ticks} procedure draw_graph(xi,y1,x2,y2, x_increment, y_increment_left, y_increment_right :integer) ; begin draw_box(x1,y1-2,x2,y2+2,1); draw_x_ticks (x1,y1,x_increment , x2); draw_x_ticks (x1,y2,x_increment ,x2) ; draw_y_ticks (x1,y1,y_increment_left, y2) ; draw_y_ticks (x2,y1,y_increment_right, y2) ; 175 end; fof procedure draw_graph} procedure write_x_coordinates(x1,y1,x_increment integer; xic,xc_increment,x2c : real; field, fix : integer) ; begin repeat gotoxy((x1 div 8), (y1 div 8)); write (xic:field:fix); xlc := xlc + xc_increment; xi := xi + x_increment; until xilc > x2c; end; {of write_x_coordinates} procedure write_y_coordinates(x1,y1,y_increment integer; yic,yc_increment,y2c : real; field, fix : integer); begin repeat gotoxy((xi div 8), (yi div 8)); write (y1c:field:fix); yic := yic + yc_increment; yi := yi + y_increment; until yic < y2c; end; {of write_y_coordinates} procedure set_up; begin hires; hirescolor(15); draw_graph(xmin, ymin, xmax, ymax, (xmax-xmin) div 5, (ymax-ymin)div 5, (ymax-ymin)div 5); end; {of set_up} procedure write_y_axis; begin write_y_coordinates(xmin-40,ymin+7, (ymax-ymin) div 5, ylstop, (ylstart~ylstop)/5,ylstart,4,1); end; {of write_y_axis} procedure write_x_axis; begin write_x_coordinates (xmin, ymax+14,(xmax-xmin) div 5, xstart, (xstop-xstart)/5,xstop,4,2); end; {of write_x_axis} procedure write_y_axis_exp; begin write_y_coordinates(xmin-40, ymin+7, (ymax-ymin) div 2, ylstop, (ylstart-ylstop)/2,ylstart,4,1); end; {of write_y_axis_exp} procedure plot_a_pixel(x, y : real); var xcor, ycor : integer; 208 209 211 212 213 214 215 216 176 begin xcor := round((x-xstart) *(xmax-xmin) /(xstop-xstart)); ycor := round((ylstop-y)*(ymax~ymin) /(ylstop-ylstart)); graphwindow(xmin, ymin, xmax, ymax) ; plot (xcor,ycor,1); end; procedure plot_a_point(x, y : real); var xcor, ycor : integer; begin xcor := round((x-xstart)*(xmax-xmin) /(xstop-xstart)) ; ycor := round((ylstop~y)*(ymax-ymin) /(ylstop-ylstart)) ; graphwindow(xmin, ymin, xmax, ymax) ; plot (xcor-1,ycor,1); plot (xcort1,ycor,1); plot (xcor,ycor-1,1); plot (xcor,ycorti,1); end; {plot_a_point} procedure plot_datafile(x, y : datarray; ndata : integer); var i, xcor, ycor, yd : integer; amp, 1, xc : real; q : char; begin set_up; gotoxy(1,1); write(’enter ylstart ylstop xstart xstop : °); readin(ylstart, ylstop, xstart, xstop); write_y_axis; write_x_axis; for i := 1 to ndata do begin xeor := round ((x[i]-xstart) *(xmax-xmin) /(xstop-xstart)) ; ycor := round((ylstop-y[i])*(ymax-ymin) /(ylstop-ylstart)) ; graphwindow(xmin, ymin, xmax, ymax) ; plot (xcor-1,ycor,1); plot (xcor+1,ycor,1); plot (xcor, ycor-1,1); plot (xcor,ycor+1,1); end; end; {of plot_datafile} procedure readfile(var x, y : datarray; var ndata : integer); var i: integer; data_transfer : text; begin clear_line; gotoxy(1,1); write(’enter filename(read) : '); readin(filename) ; assign(data_transfer,filename) ; ndata := 0; reset (data_transfer) ; 261 262 263 264 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 177 while not eof(data_transfer) do begin ndata := ndata + 1; readln(data_transfer,x[ndata] ,y[ndata]); end; close(data_transfer) ; end; {of readfile} procedure writefile(x, y : datarray; ndata : integer); var i: integer; data_transfer : text; begin clear_line; gotoxy(1,1); write(’enter filename(write) : °); readin(filename) ; assign(data_transfer,filename); rewrite (data_transfer) ; for i := 1 to ndata do begin writeln(data_transfer,x[i],’ ’,y[i]); end; close(data_transfer) ; end; fof writefile} procedure list(x, y : datarray; ndata : integer) ; var i: integer; begin for i := 1 to ndata do begin writeln(lst,x[i],’ ’*,y[il); end; end; {of writedata} procedure display(x, y : datarray; ndata : integer); var i: integer; q : char; begin clear_line; for i := 1 to ndata do begin gotoxy(1,1); writeln(ndata,’ - °*,i,’ ',xfi],’ ’,yfil); read(q); end; end; {of display} procedure create_new_buffer; var select : integer; begin clear_line; gotoxy(1,1); write(’Enter 1 for create & 0 for append to a file : '); read(select) ; clear_line; 315 357 358 360 361 362 363 364 365 366 178 gotoxy(1,1); write(’Enter filename : *); readln(buffer): if select = 1 then begin assign (number_transfer, buffer) ; rewrite (number_transfer) : close(number_transfer) ; end; write(lst,’Row Col c.5 Co'); writeln(lst, ’*Cmi Cm2 Vb Gamma’); end; procedure record_diode_parameter; var vb, cp&, co, cmi, cm2 : real; begin assign (number_transfer, buffer); reset (number_transfer) ; seek (number_transfer,filesize(number_transfer)) ; clear_line; gotoxy(1,1); write(’Enter row & col : '); readln(row,col); vb := xstart; cp5 := c[ndata]; co := c[ndata-1]; cm1 := c[ndata-2]; cm2 := c[1]; write(number_transfer,row,col,cp5,co,cmi,cm2,vb,gamma) ; write(1st,row:2:0,’ °,col:2:0,° *,cp5:9,’ °); writeln(1st,co:9,’ *,com1:9," °,cem2:9,"’ ‘*,vb:3:1,’ >, gamma:9); close(number_transfer) ; end; procedure write_diode_parameters; var vb, cp5, cpO, cmi, cm2, gm : real; begin write(lst,’Row Col C.5 Co ’); writeln(1lst,’Cmi Cm2 Vb Gamma’); clear_line; gotoxy(1,1); write(’Enter filename : '); readln(buffer); assign (number_transfer , buffer) ; reset (number_transfer) ; while not(eof(number_transfer)) do begin read(number_transfer,row,col,cp5,cp0,cmi,cm2,vb,gm) ; write(I1st,row:2:0,’ ‘*,col:2:0,' *,cp5:9,’ °); writeln(1st,cp0:9,’ *,cm1:9,’ °,cm2:9,’ ’,vb:9,’ *,gm:9); end; close(number_transfer) ; end; procedure cvtest(var v, c : datarray; var ndata : integer); label again, loop; 179 367 var 368 cf, vf, vinc : real; 369 begin 370 again: 371 set_up; 372 yistart := 80.0; ylstop := 400.0; ylunit := te-12; 373 xstart := -5.0; xstop := 0.5; xstep := 0.5; 374 gotoxy(1,1); 375 write(’Cd_vs_Vd>> ylstart ylstop ylunit xstart xstop xstep : '); 376 readin(ylstart, ylstop, ylunit, xstart, xstop, xstep); 377 ndata := trunc( ((xstop-xstart) / xstep) ) + 1; 378 write_y_axis; 379 write_x_axis; 380 quote := chr(39); 381 cmddesc.addr := ofs(cmd) + 1; 382 recvdesc.addr := ofs(recv) + 1; 383 384 my_address := 21; 385 system_controller := 0; 386 initialize(my_address, system_controller); 387 388 cmd := 'IFC REN MTA LISTEN 17° ; 389 emddesc.len := length(cmd); 390 transmit (cmddesc, status); 391 392 cmd := "DATA ’ + quote + 'LE2 ZO’ + quote + ‘13 10° ; 393 emddesc.len := length(cmd); 394 transmit (cmddesc, status); 395 396 str(xstart,vstart); 397 str(xstop,vstop) ; 398 str(xstep,vstep); 399 cmd := "DATA * + quote + 'IB2, CE1, PS’ + vstart + ’, PP’ + vstop + 400 *, PE’ + vstep + ', PLi, PD1, TR3, SW1’ + quote + ’13 10’ ; 401 cmddesc.len := length(cmd); 402 transmit (cmddesc, status); 403 404 cmd := ’TALK 17’ ; 405 cmddesc.len := length(cmd); 406 transmit (cmddesc, status); 407 408 recv := ’ 409 recvdesc.len := length(recv); 410 receive (recvdesc,len, status) ; All for i := 1 to ndata do begin 412 recv :=’ 413 recvdesc.len := length(recv); 414 receive(recvdesc, len, status) ; 415 first := pos(’C’,recv) + 2; 416 nchar := pos(’,’,recv) - first; 417 cap := copy(recv,first+1,nchar); 418 delete(recv,1,pos(’,’,recv)); 419 first := pos(’G’,recv) + 2; 180 420 nchar := pos(’,’,recv) - first; 421 cond := copy(recv,first+1,nchar) ; 422 delete(recv,1,pos(’,’,recv) +1); 423 volt := recv; 424 if recv[i] = ’+’ then delete(volt,1,1); 425 val (cap, capacitance, code) ; 426 val (cond, conductance ,code); 427 val(volt, voltage, code) ; 428 cli] := capacitance; 429 v[i] := voltage; 430 gli] := conductance; 431 plot_a_point(v[i], cfi]/ylunit); 432 end; 433 {if v[i] is replace with v[i]-phi, fit will be better} 434 for i := 1 to ndata do begin 435 Inc[i] := In(c[i])/1n(10) ; 436 Inv[i] := In(1-(v[i]/phi))/1n(10) ; 437 end; 438 slope_a := 0; 439 intercept_b := 0; 440 correlation_coeff := 0; 441 lsf(ndata, Inv, Inc, slope_a, intercept_b, correlation_coeff); 442 gamma := -slope_a; 443 co := ten_to(intercept_b); 444 cratio := c[ndata]/c[1]; 445 gotoxy(1,5); writeln(’Cn = °,c[ndata]:8): 446 gotoxy(1,6); writeln(’Ci = ',c[1]:8); 447 gotoxy(1,7); writeln(’CR = ’ ,cratio:2:1); 448 gotoxy(1,10); writeln(’Co = *,co:8); 449 gotoxy(1,11); writeln(’Cm = ',gamma:4:3); It 450 gotoxy(1,12); writeln('’cc *,correlation_coeff:6:5); 451 vine := (xstop-xstart)/100.0; 452 vf := xstart; 453 repeat 454 cf := co / exp( gamma*(1n(1-vf/phi)) ); 455 plot_a_pixel(vf, cf/ylunit) ; 456 vf := vf + vince; 457 until (vf = xstop) or (vf > xstop); 458 loop: 459 clear_line; 460 gotoxy(1,1); write('Cd_vs_Vd>> (s)sav (d)disp '); 461 write(’ (1)1st (r)rep (w) wri (c) ert (k) kip (q) n_x : *); read(q); 462 case q of 463 "s’ : writefile(v, c, ndata); 464 *d’ : writefile(v, c, ndata); 465 ‘1’ : list(v, c, ndata); 466 ‘r’ : goto again; 467 ’w’ : write diode_parameters; 468 *c’ : create_new_buffer; 469 ’k’ : record_diode_parameter; 470 end; 471 if q <> 'q’ then goto loop; 472 end; {fof cvtest} 515 517 518 519 520 521 522 523 524 525 181 procedure read_cv(var x, y : datarray; var ndata : integer) ; label again, loop; var i: integer; cf, vf, vine : real; begin again: readfile(x, y, ndata); display(x, y, ndata); set_up; ylstart := 80.0; ylstop := 400.0; ylunit := te-12; xstart := -5.0; xstop := 0.5; gotoxy(1,1); write(’Cd_vs_Xd>> ylstart ylstop ylunit xstart xstop : ’); readln(ylstart, ylstop, ylunit, xstart, xstop); write_y_axis; write_x_axis; for i := 1 to ndata do begin plot_a_point(v[i],c[i]/ylunit) ; end; {if v[i] is replace with v[i]-phi, fit will be better} for i := 1 to ndata do begin Inc[i] := In(c[iJ)/In(10); Inv [i] In(1-(v{i]/phi))/1n(10) ; end; slope_a := 0; intercept_b := 0; correlation_coeff := 0; lsf(ndata, Inv, Inc, slope_a, intercept_b, correlation_coeff): gamma := -slope_a; co := ten_to(intercept_b); cratio := c[ndata]/c[i]; gotoxy(1,5); writeln(’Cn = ',c[ndata]:8); gotoxy(1,6); writeln(’C1 = *,c[1]:8); gotoxy(1,7); writeln(’CR = ' ,cratio:3:2): gotoxy(1,10); writeln(’Co = *,co:8); gotoxy(1,11); writeln(’Gm = *,gamma:4:3); gotoxy(1,12); writeln(’cc *, correlation_coeff:6:5): vine := (xstop-xstart)/100.0; vf := xstart; repeat cf := co / exp( gamma*(1n(1-vf/phi)) ); plot_a_pixel(vf, cf/ylunit); vf := vf + vinc; until (vf = xstop) or (vf > xstop); loop: clear_line; gotoxy(1,1); write(’Cd_vs_Vd>> (s)save (d)display '); write("(1)list (r) repeat (q)quit : *); read(q); if q = 's’ then writefile(v, c, ndata); if q = ’d’ then display(v, c¢, ndata); if q = '1’ then list(v, c, ndata); 526 527 528 529 530 531 532 533 534 535 536 537 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 182 if q = ’r’ then goto again; if q <> *q’ then goto loop end; procedure get_plot_a_file; label again, loop; var x, y : datarray; ndat : integer; q : char; begin again: readfile(x, y, ndat); display(x, y, ndat); plot_datafile(x, y, ndat); loop: clear_line; gotoxy(1,1); write(’Get & Plot>> (d)display °); write(’(1)list (xr) repeat (q)quit : '); read(q); if q = ’d’* then display(x, y, ndat); if q = ’1’ then list(x, y, ndat); if q = ’r’ then goto again; if q <> ’q’ then goto loop; end; begin {main} loop_ti: clrscr; textmode (bw80) ; phi := 0.94; {phi varies slightly with doping concentration} gotoxy(1,1); write(’Menu>> m(measure-cv) r(read-cv) p(get&plot) (q)quit : ’); read(q); case q of "m’ : cvtest(v, c, ndata); : read_cv(v, c, ndata); : get_plot_a_file; >: goto quit; end; clrscr; if q = 'p’ then goto loop_1; set_up; ylstart := 16.0; ylstop := 18.0; xstart := 0.0; xstop := 0.5; xunit := 1.0; gotoxy(1,1); write(’Nd_vs_Xd>> ylstart, ylstop, xstart, xstop, xunit [exp & um] readln(ylstart, ylstop, xstart, xstop, xunit); write_y_axis_exp; write_x_axis; eo := 8.85e-14; er := 13.1; 579 580 581 582 583 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 loo 617 qui 183 eq := 1.6e-19; area := 2.6e-3; {area of Hg probe given in manual = 2.6e-3 [cm2]} clear_line; gotoxy(1,1); write(’Nd_vs_Xd>> diode area [cm2] : *); readin(area) ; for i := 1 to ndata-1 do begin i:= ( ci] + c[itt] )/2; xd[i] := 1e4 * eo * er * area / ci; {in units of microns} dcdv := ( c[iti]-cfi] ) / ( v[iti]-v[i] ); ndi := ci/eq; {ndi := ci * ci * ci;} nd2 := ci/(eo*er); {nd2 := eq * eo *er;} ndi := ndi * nd2; {nd3 := area * area * dcdyv;} ndi := ndi * ci / area: {ndi := ndi/nd2;} nd[i] := ndi/(area * dedv); {nd[i] := ndi/nd3; units of atoms per cm-3} Innd[i] := 1n(nd[i])/1n(10.0); Inxd[i] := In(xd[i])/1n(10.0); plot_a_point (xd[i]/xunit,Innd[i]); end; slope_a := 0; intercept_b := 0; correlation_coeff := 0; lsf(ndata-1, Inxd, lInnd, slope_ a, intercept_b, correlation_coeff); nn := -slope_a; no := ten_to(intercept_b) ; gotoxy(1, 6); writeln(’No = ’,no:8); gotoxy(1,7); writeln('n *,0n:4:3); gotoxy(1,8); writelIn(’cc ’ ,correlation_coeff:6:5); p_2: clear_line; gotoxy(1,1); write('Nd_vs_Xd>> (s) save (d)display (1)list (q)quit: '); read(q); if q = 's’ then writefile(xd, nd, ndata-1); if q = ’d’ then display(xd, nd, ndata-1); if q = '1’ then list(xd, nd, ndata-1); if q <> ’q’ then goto loop_2; goto loop_i; t: 618 end,