Some Theoretical Problems in Low Temperature Optical Properties of Semiconductors

Author: Pan, Dee-Son

Year: 1978

Degree: Dissertation (Ph.D.)

Advisors: McGill, Thomas C.; Smith, Darryl L.

Committee Member: Unknown, Unknown

Option: Physics

DOI: 10.7907/b3v2-pt24

Abstract

This thesis contains 5 topics investigating some theoretical problems in the low temperature behavior of electrons and holes in semiconductors.

Motivated by many recent experiments, the phonon damping of the motion of the electron hole droplet in pure Ge was investigated in chapter 1. The screening effect of the carrier phonon interaction inside the droplet was studied in the random phase approximation. This effect was found to be small for the deformation potential coupling in Ge; reducing the phonon damping by about a factor of two. The calculated damping coefficient in the low velocity case (less than sound velocity of the crystal) is in agreement with the ultrasonic absorption measurements. When the droplet velocity exceeds the sound velocity, we found that spontaneous phonon emission dominates the damping; and the damping is found to be sufficiently large to make it unlikely that velocities greater than the sound velocity will be observed experimentally.

Motivated by the recent interests of droplets in doped material and polar material, in chapter 3, we extend our investigation of damping in chapter 2 to two other damping mechanisms: impurity scatterings in doped material and piezoelectric phonon scatterings in pure polar material. The screening effect is very important for those two scattering mechanisms, since they are electrostatic in nature. The damping coefficient due to impurity scattering is calculated for Ge and GaP. The damping coefficient due to piezoelectric scattering is calculated by taking Gap as an example. We found that the piezoelectric damping is very weak in the low temperature limit (less than 10°K in GaP) due to strong screening effect when compared with the deformation potential damping. (This is an interesting contrast to the fact that the mobility of pure polar semiconductor is known to be determined by piezoelectric scattering at low temperatures, less than 100°K.)

Motivated by Haynes' rule from experiments, a study of the structure of an exciton bound to a neutral acceptor is reported in chapter 4. We chose a central-field model to calculate the ground-state energy. We found that there are no stable bound states of the system in the Hartree-Fock approximation when the electron to hole mass ratio is close to one. We include the correlation energy by using the core polarization potential method and the correlation energies for the "two electron ions". The calculated dissociation energy is then in agreement with the Haynes' rule.

A theoretical investigation of the banding of the bound excitons in doped semiconductors is presented in chapter 5. As the impurity concentration increases, one could expect, in analogy with the impurity band, banding of the bound exciton states. We estimate various matrix elements for the interactions between a bound exciton complex and a neutral impurity to first and second orders. We found that the hopping of a bound exciton between impurities is not readily feasible. (The hopping matrix element is smaller than that of a bound carrier between two ionized impurities, despite the fact that the bound exciton complex has a larger radius.) Numerical estimates of the banding of bound excitons are consistent with recent experimental observations of the smallness of the concentration broadenings of the bound exciton states.

An investigation of the phenomenon of impact ionization of excitons in Ge and Si is reported in chapter 6. The charged free carrier in an applied electric field can pick up enough energy from the field to allow it to impact ionize an exciton. For this to occur, the carrier must have an energy greater than the exciton binding energy. At low temperatures (T≤ 10°K in Ge and T≤ 30°K in Si), the energy of a significant number of carriers exceeds this threshold energy. Calculations of exciton concentration (for fixed carrier concentration} as a function of temperature and applied field strength show that a sudden drop in exciton concentration occurs when electric fields exceed a temperature dependent critical field.

Parts of this thesis either have been or will be published under the following titles:

Chapter 2: Phonon Damping of the Electron-Hole Droplet Motion, D. S. Pan, D. L. Smith and T. C. McGill, Solid State Comm.___, ___, 1977. The Damping of the EHD Motion, I. Deformation potential Coupling, D.S. Pan, D. L. Smith, and T. C. McGill, (to be published).

Chapter 3: The Damping of the EHD Motion, II. Impurity and Piezoelectric Scattering, D. S. Pan, D. L. Smith, and T. C. McGill, (to be published).

Chapter 4: Binding of an Exciton to a Neutral Acceptor, D.S. Pan, D. L. Smith, and T. C. McGill, Solid State Comm. 18, 1557, 1976.

Chapter 5: Banding of Bound Exciton States, D. S. Pan, D. L. Smith, and T. C. McGill (to be published).

Chapter 6: Impact Ionization of Excitons in Ge and Si, D. L. Smith, D. S. Pan, and T. C. McGill, Phys. Rev. 12, 4360, 1975.

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