Resistivity and Recombinations in Extremely Thin Metallic Layers Citation Anderson, Alfred Bernard C. (1933) Resistivity and Recombinations in Extremely Thin Metallic Layers. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8bv8-t136. https://resolver.caltech.edu/CaltechTHESIS:09122024-220022323 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Millikan, Robert Andrews Thesis Committee: Unknown, Unknown Defense Date: 1 January 1933 Record Number: CaltechTHESIS:09122024-220022323 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:09122024-220022323 DOI: 10.7907/8bv8-t136 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16723 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 13 Sep 2024 18:13 Last Modified: 13 Sep 2024 18:14 Thesis Files PDF - Final Version See Usage Policy. 23MB Repository Staff Only: item control page

RESISTIVITY AND RECOMBINATIONS IN EXTREMELY THIN METALLIC LAYERS Thesis by Alfred B. C. Anderson In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1933 List of Illustrations Figure (1) Patch structure of thin films 23 (2) Chamber 25 (3) Assembly of apparatus 26 (4) Diagram illustrating method of rnaking electrical contact with adsorbed layers 24 (5) Assembly of crystal holder 29 (6) Detail of crystal holder 30 (?) Diagram showing mounting and base for both furnaces, the shutter and slit number (1) 33 Diagram. showing shutter, slit number (1), and their mountings 33.5 (9) 118.gnetic control of shutter 34 (10) Mounting and electrical connections of the two furnaces 35 (11) Shape of strip from which furnace number (1) is made 40 (12) Final appearance of furnace number (1) 40 ( 13) Upper view of furnace number ( 2) 40 (14) IDwer view of furnace number (2) 40 (15) Circuit diagram of induction furnace 46 (16) Circuit diagram for measuring conductivity 48 (17) Detail of calibration condenser and switch housing 51 (18) Detail of the apparatus for the control of the electrometer sensitivity 52 Dependence of resistivity on time (0 to 8 atomic layers) 56 Dependence of resistivity on time (8 to 34 atomic layers) 56 (8) (19) (20) List of Illustrations (continued) (21) (22) (23) Dependence of resistivity on time (19 to 53 atomic layers) 56 Dependence of resistivity on time (0 to 54 atomic layers) 58 Dependence of resistivity 9n time (?8 to 205 atomic layers) 58 {2.4) Dependence of resistivity on time (251 to 330 atomic layers) 58 (25) Dependence of the coefficient of recombination on the number of unaged particles 58 Diagram showing linearity between (R) and (t) for thin films on calcite (up to 330 layers) 59 Dependence of the coefficient of recombination on the number of sublayers 58 Dependence of resistivity on thickness (0 to 50 atomic layers on calcite) 60 Dependence of resistivity on thiclmess (0 to 330 atomic layers on calcite and Oto 380 atomic layers on glass) 60 Dependence of resistivity on time (Ag films on glass) 61 (26) {2?) (28) (29) (30) 1 Outline of Contents Table of contents I List of illustrations IV I. ·Introduction (A) Sunnnary of previous work 4 (B) Factors effecting the properties of extremely. thin films ? Former methods of determining fi 1m thickness 12 II. Situation of the problem of thin films at the outset of the present investigations 14 III. Purpose of this investigation 15 ( C) IV. V. Past theories of the abnormal behavior of resistance as a function of thickness (A) J, J, Thomson Theory 1? (B) Non-conducting layer theory l? (C) Granular theory 18 Theory and formulae proposed by author, accounting for the new aging effect (A) For extremely thin films ( 0 to 50 layers) 18 (B) For thin films (greater than 50 layers thick) 20 General description of apparatus used in the past together with its limitations 23 VI. Apparatus (A) (B) Evaporation chamber (a) General arrangement of parts 23 (b) Details of crystal holder 28 (c) Details of shutter and second slit defining area of evaporation 31 2 (d) Furnaces (1) ( C) (D) (2) Furnace (F1 ) for depositing stable electrical connections with the adsorbed film 38 (3) Furnace (F2 ) for depositing adsorbed layers and determining film thickness 39 (a) Cleaning of glass and metal-ware 44 (b) Outgasing with induction furnace 45 (c) Details of construction of induction 45 furnace Measurement of conductivity of adsorbed films (a) General description of method used 45 (b) Electrical connections 47 (c) Procedure used in measuring conductivity 49 Determination of the capacity of the entire system 49 Construction details of calibration, condenser and switch housing 50 (e) ( f) VII. 32 Precautions taken to minimize film-contamination ( d) (E) Mounting and electrical circuit Construction details of apparatus for varying electrometer sensitivity Method of setting up apparatus and taking readings 53 Experimental results and conclusions (A) Dependence of resistivity on time - extremely thin films on calcite (Oto 50 layers) (1) Data; conventions for terms used; and definitions 55 3 (2) (3) (4) (B) (F) . (G) Dependence of resistivity on thickness 57 Dependence of recombination coefficient on number of free particles present on surface 58 (1) Data 58 (2) Aging~ Dependence of resistivity on time 58 Coefficient of recombination of thin films (a) Dependence of recombination coefficient on the number of uncombined atoms on the surface 00 (b) Dependence of the recombination coefficient on the total number of atoms on the surface 60 Dependence of resistivity on film thickness Calcite backing 60 Dependence of resistivity on time - Ag film on glass backing 61 Dependence of resistivity on thickness - Ag film on glass backing 61 Ohm's Law and thin films 61 (H) VIII 57 Dependence of resistivity on time - thin films on calcite (0 to 330 layers} (3) (E) Aging - Dependence of resistivity on time General Conclusions 62 Summary 62 Aclmowledgeme:b.ts 68 Appendix 69 . ·- · - . ,. ~·. !."; -: .... • J • ..·... . :.;/,..., . &'> .: __.J. AIE/1/AtfE Tll'IE nl/CKIY~SS OF FIG. (CALOTE 19 ii, 1,;; 6ACK/IYG) 10 RR O!rrE,f>EtYT lll!Ct'lfESSE.1 RLM, /IV LAYE/f'S lhPKATLf wmKJur 6WAC.(~ ON P/f'El'IOUSLY, FULLY A6-.E~ FftM /{I/HERALS TllJ /IYOICNE M f - /1<,,VBM ~ IAYEKS. CeRJsl- ,!1Ne('AJ5 l11'8A'i/Ck ffl f~.,, f'~U,7JT ........ - 13 ,3, :to >-14--~- ,:r, - ' IS.,, :--r .a, lf", 5o F/G.~a (96} loJ , --- X!if(2M) 3-1,J. @ 6o '" ,4 1 I ~ I .'-!"-+--I /J '!H-H--1-+ ~/J~ ;! !: Pl. H81 15. 0 FIil y f GE. ALM. s1tED •Essl a SJ l(f LA r, '<J 041 fi/1-(E FIL/'! "/IC/Uf {J. ,4CA,=rs I _IIY[J{C/1 y t'"j _lA ERSj _.,/ IO RA}Kc'~ 1,rofc rt! ~,M} :,/.Z ,-/ FIG. 2/ <~71)-!J Jl:!'l . , I. 4 I. Introduction. Thin metallic films show many strange and peculiar proper- ties that differ considerably from those exhibited by a massive chunk of the same metal. These properties have been the object of much investigation in the past and may be briefly summarized: (1) The si:ecific resistance remains constant with decrease of thickness down to a certain value, often called the critical thickness, at which point it suddenly jumps towards infinity. (2) This critical thickness is variously estimated in the neighborhood of 70 x 10-8 cm. It seems to depend upon a number of variables: the kind of metal; the experimental conditions; and the way the measurements are made. (3) All films show irreversible changes of resistance with temperature; with the passage of heavy current; and with time. (4) The presence of a gas affects the properties and structure of the film. (5) The crystal structure of the film is determined by the mean film thickness; the type of backing; and the temperature at which the film is formed. As the above fiNe points - .unlike the following one - will be discussed more fully later, references are omitted. (6) Finally the thermoelectric power( 1 ); the change of resistance in a magnetic field - Hall effect( 2 - • .lS); and the photoelectrical and optical properties - for which Schulze( 19 ) gives a 5 "10 most complete bibliography including aboutAworkers - show peculiarities. As the major interest in this article will be centered about the resistance properties of thin films, particularly those depending on ~hickness and aging, previous results for these will be analysed and discussed more in detail. The best method of approach is from the standpoint of the critical thickness, since most investigators give their resistances in arbitrary units which are impossible to evaluate; and, as will be seen, aging runs hand in hand with the critical thickness. In the following is given a tabulated historical summary of the critical thickness as a function of the kind of metal, the method of producing the film, together with the name of the investigator and the year in which he obtained the results. Numbers in ( ) indicate reference in bibliography C.T. denotes critical thickness in mµ Metal Wet process Sputtering (Ni) Moreau (4), 1901, deposited Ni on Ag mirrors. C.T. = 24. Reide {10), 1914, C.T. = 3 (11), 1918, C.T. = 1.25 (11), 1924, C~T. = 3.0 All these were sputtered in H2 • ill curves show peculiarities which are probably due to a metal hydride. Evaporation 6 (Ca) Reide (10), 1914, C.T. = 2.8 Deposited as above (Pd) Pogony (46), 1916, C .T. = 25. Steinberg (48), 1923, C.T. = 12. Only the backing was outgased. The walls and tube were of brass. (Pt) (1) Patterson (45), 1902 C.T. = 4. (2) Reide (10), 1914, Weber and Oosterhuis (47), C.T. = 1.2 1917, C.T. = 12 which (3) Reide (11), 1928, agreed with 2 other trials C.T. = 2 to 3. made. Tube was baked out (4) King (6), 1917, and the measurements made C.T. 9 1.5 to 3. at 32°c. (5) Pogony (46), 1916, He also compared the C.T. = 1. conductivity of films of (6) Joliet (33), 1928, different metals at the C.T. = 2.5 same temperature: (Ag) be(7) Fery (49), 1928, gins to conduct at 2 x 108 C.T. = 3 ohms at a thickness of 12 (8) Perucca (50), 1930, molecules. At this point Finds that C.T. is 4(Pt) has a resistance of times that of gold only 300 ohms and is 2 to under similar condi-3 molecules thick. And tungsten has a resistions tance of 150 ohms and is 1 atomic layer thick. (Au) King (6), 1917, C.T. = 6 to 8. MacKeown (2), 1924 Hamburger (35), 1931, C.T. = 3.2 C.T. = 3. Perucca (50), 1931. Finds that film conducts at (¼) the thickness of Pt. (.Ag) Vincent (3), 1900, C.T.= 50. Reide (10), 1914, C.T.= 35. Wait (5), 1922, C.T.= 20. Patterson (45), 1902 Weber and Oosterhuis (47), C.T. = 5. 1917, C.T. = 6.5. King (6) ,1917, ,q.T.=:6ti8Steinberg (48), 1923, Pogony (46), 1916, C.T. = 25. C.T. = 4.5. (Hg) Volmer and Estermann (51), 1930, C.T. = 200, Evaporated from a pool of mercury and condensed on glass at liquid air temperature. (W) Braunsfurth (51), 1930, C.T. = .8 Weber and Oosterhuis (47), 1917, C.T. = .43 Hamburger {35), 1931, C.T. = .2 Rh Braunsfurth (23), 1930, C.T. = 6. Ir-Rh Braunsfurth (23), 1930, C.T. = 2.2 The table shows a great lack of agreement among the various investigators on the critical thickness, even when they use the same method in producing the film. This, I believe, can be accounted for on the basis that not sufficient consideration was given to the following facts: (A} Occluded gases modify considerably the properties and structure of thin films: E.W. Hobbs( 20) and W. Reynolds( 2l)( 22 ) find that gas in the presence of a film causes the film to decrease its resistance with time . .And if the gas is pumped off, the resistance increases slightly with time. Braunsfurth( 23 ), Ingersoll and Hanawalt( 24 ) confirm this, and in addition show that great amounts of gas are 8 absorbed in the process of sputtering. The presence of gas has often been shown to cause changes of crystal structure and lattice constant together with the formation of compounds. G. P. Thomson( 25 ) finds that (Ni) which is normally cubic, when sputtered in (.Ar), on rocksalt is hexagonal; Ingersoll and Hanawalt( 24 ) find that (Ni) sputtered in (N2 ) or (~) has a .different structure from parent metal, and also that (Fe) and (Co) sputtered in (He) suffers an increase of lattice constant as much as 20%. Other investigators: Lauch( 27 ), Kohlschutter and No11( 28 ) and Allolio and Bredig( 29 ) obtain like results which tend to the conclusion that the presence of foreign gases, during or after the formation of the film, may produce hopelessly complicated experimental conditions. From these facts it may be concluded that experimental results gotten from films produced by the wet process or by sputtering, are open to grave criticism, as foreign atoms are always unavoidably present at a considerable density. (B) The sputtering process forms the film from small particles of the metal rather than from individual atoms: V. Kohlschutter(30) and Houllevigue( 3 l) as a result of their investigations show that a metal, when sputtered, comes down in chunks; and the size of these depends on the gas present during sputtering. (C) Properties of a filrn are very sensitive to tempera- ture changes which may cause irreversible changes in film: 9 Braunsfurth( 23 ) has shown that these films decrease their resistance with temperature, whereas, the resistance of thicker ones increases with temperature . .Also a film may take on any value for the temperature coefficient of resistance from zero to a maximum value, depending on its degree of aging. Furthermore, an hysterisis effect makes its appearance. This is evidenced by the fact that the curve representing resistance as a function of temperature always lies higher when the film is being cooled than when being heated; This is an irreversible effect and seems to be more pronounced as the quality of the vacuum improves. Like results are secured by w. Reynolds( 21 ), Bartlet( 32 ), Hamburger( 35 ), and M. F. Joliot( 33 ) who in addition show that a film will show reproducible properties at all temperatures below the maximum to which it has previously been subjected, but irreversible above this. Horowitz( 36 ) and Homburger show that films deposited at liquid air temperatures have no crystal structure, whereas, those deposited at room temperature do. Ingersoll and Sordahl( 34 ) point out that a temperature rise, always accompanying sputtering , produces a considerable change in the resistance properties of the film. The above facts lead to the conclusion that definite precautions must be made at all times to maintain the constancy of the temperature, when the effect of some other variable is 10 being investigated. In the table, with the exception of Volmer and Estermann, and Weber and Oosterhuis none of the investigators mention that any such precautions were made. {D) Films undergo spontaneous irreversible changes in structure and properties; often called aging: Hobbs( 3?) and Braunsfurth{ 23 ) find that films, immediately after their formation by sputtering, show a decrease of resistance with time. The same result is shown more clearly by Bartlett{ 32 ) and Koller( 38 ) who account for the decrease on the basis of the coalescence and crystallization of the metallic particles. These facts indicate that film-resistance depends considerably on film-aging. None of the workers mentioned in the table - as far as I have been able to determine - allow any time for aging while taking their measurements. (E) The measured film-properties depend on the backing: s. Dem~iooka( 39 ), producing her films by evaporation, and observing their structure from x-ray diffraction patterns decides that different types of ,film-backing produce different uniformities of film structure. She deposits gold films onto: an aluminum single crystal; mica; glass; and quartz, and finds that the sharpness of the x-ray diffraction patterns increase in the same order. The lattiee constant she finds, however, remains the same a:s ,· for the parent metal. The results of F. Kirchner( 4 0) make the above conclusion rather doubtful and seem to indicate that uniformity of film- 11 structure is determined principally by film-thickness. Results obtained from evaporated films and by using electron diffraction, show that - when both celluloid and mica are used as backing initially the film is colloidal; then with increase of thickness some crystallographic axis of the small nacent crystallites lines itself parallel to the backing; later, a crystallographic plane lines itself up parallel to the backing; and finally there is a complete allignment of all the small crystallites into a singlecrystal. The difference in coefficient of expansion between the film and the backing may cause strange and misleading effects: A metallic film deposited at room temperature on quartz and then cooled down to that of liquid air is placed under an increasing amount of tension, and might even finally be ruptured. This is because of the difference between the coefficient of expansion for quartz and the metallic film. Bartlett( 32 ) finds that identical films, normally with large positive temperature coefficients of resistance, when deposited on different backings do not show the saine temperature coefficient of resistance; he finds that the smaller temperature coefficient of expansion of the backing, the smaller the temperature coefficient of resistance . .AJJy tension or compression of the film should always be relieved before the filrn-properties are investigated. This can be accomplished by annealing the film or, prefferably, the film should 12 be deposited at the same tenr_perature at which its properties are to be determined. (F) The methods employed in the past for determining the thickness of extremely thin films are not all that is to be desired. Either _they are not sufficiently sensitive, or they pre- clude the possibility of keeping the film in a high vacuum. They may be divided into the following broad divisions: ( la) (1) Optical Method: (a) Interference, (b) Opacity. (2) Electrolysis. (3) Mechanical Method. Q,uinke ( 41 ) , Fizeau ( 42 ), Wernike ( 43 ) and Wiener ( 44 ) have developed methods for determining film-thickness from the interference colors. This method however is not applicable to films much thinner than the wavelength of visible light. Furthermore, each determination is extremely laborious and must be made in air outside of the apparatus, with the contamination of the film as a consequence. (lb) MacKeown( 2 ) and others have shown that there exists a lin- ear relation between film-opacity and film-thickness. This forms the basis of a method for determining film-thickness. What is done is to measure the opacity of a few thick films whose thickness can be determined by weighing. line relation is found. From these, the straight The thickness of other films are now gotten merely by measuring their opacity and extrapolating on the curve. 13 This method is likewise not adapted for extremely thin films; both because the opacity becomes iniperceptible and because thin films undergo spontaneous changes in structure with time, which change their optical properties. (2) Schulze(l9 ) describes a method for transforming thick films of known thickness into thin ones, also of known thickness, by electrolysis. The thick film, whose thickness may be determined by weighing, is placed in an electrolytic cell; and through it is passed a known current for a known time. Then applying Faraday's Law, the number of atoms removed from the film is easily calculated. This method suffers from two serious objections: The film is contaminated by foreign atoms, and the resulting film is quite non-uniform in thickness. (3) The mechanical method is the most prevalent. It presupposes the constancy of the rate of deposition, which may be determined by depositing a thick film for a known time and weighing it. The thickness of any other film, deposited at the same rate, is then merely the product of this rate and the total time of deposition. Thickness determinations in the past, by this method, have been far from satisfactory in my opinion. Those carried out by sputtering are open to the usual criticism; those by evaporation because no adequate precautions were taken to ensure a uniform rate of evaporation~ Take Oosterhuis' work as an exa1nple. He electrolysis a known amount of metal onto a tungsten filament; 14 and then by heating the filament up, evaporates this metal. He has no arrangement, such as a thermocouple, on the filament enabling him to determine its temperature. He must rely either on an optical pyrometer or the rnaintainance of the constancy of the current through the filament. With the except ion of the furnace described by Goetz ( 52 ) , none in the past - in the author's 15 opinion - eme capable of evaporating at a uniform rate. The other properties of thin films have not been investigated as thoroughly as conductivity. On the other hand, the quantitative agreement on them is found to be somewhat better. However, as they will be of no immediate interest in what follows, they will not be discussed at present. (II) Conclusions from a Consideration of Previous Work. Out of the above discussion and criticism of the sources of error inherent in the experimental methods of previous workers it seems to follow: If any further progress is to be made in re- search on the properties of extremely thin films, then improved apparatus and technique must be developed. Towards the ~6complishment of this, work was started a little more than two years ag9. Preliminary runs with this apparatus brought out an aging effect of thin films never by anyone before recorded. It was found, irrnnediately following the formation of the film, that the film would begin to increase its resistance; and within an half 15 an hour or more would attain a value several hundred-fold its initial value. All films were found to exhibit this phenomena, whether they were 1 or 300 atoms thick. Previous investigators invariably find a decrease of resistance with time. The explanation for this disagreement was discovered quite by accident: One of the films exhibiting an increase of resistance with time was left overnight in the apparatus. The diffusion PUlTlJ? was turned off, but the forevac was kept on. In the morning the diffusion pump was again started and the apparatus tho'roughly re-evacuated. the old layer. Another film was deposited over I then got the decrease of resistance with time, invariably found by all others. The explanation is then: previous workers made inadequate precautions for eliminating fareign atoms. A number of attempts at studying resistance as a function of thickness convinced us that aging, far more than film-thickness, determined film-resistance. From this fact and the previous dis- cussion one sees that aging is a most fundamental property of thin films. III. All other :pl'Operties seem to depend upon it. Purpose of this Investigation. The purpose .of this investigation was to determine the dependence of aging :on(l) time; (2) film-thickness; (3) and type . of backing. The metal used was silver; and the backings glass and calcite; one, an amorphous surface; the other, crystalline. In the following will be included a description of the 16 apparatus evolved for producing the films; for measuring their conductivity; and for measuring film-thickness, of monomolecular dimensions, within an accuracy of 3% or better. A theory will be proposed leading to two formulae which satisfactorily describe the aging effe~t - the trend of resistance with time. One applies to extremely thin films and is Log R =kt+ c, where (R) is the resistance; (t) is time; (c) is a constant of integration; and (k} is a constant· which, as will be later shown, is the coefficient of recombination of atoms on the surface. The other formula applies to thicker films from,a film-thickness of 30 to 40 and up to at least 370 atomic layers, It is: R =kt+ c, where (k) is here also a constant. In addition there will be shown the dependence of the coefficient of recombination (k) on the.film-thickness and also on the mnnber of uncombined free atoms which are thrown onto the backing at one time, .And furthermore, differing radically from the results of more than a dozen other workers, there will be shown a new dependence of resistivity on thickness in which resistivity be gins to drop abruptly at a film-thickness within the same order of magnitude as the size of the ''Zwicky Block!' and, finally, observations tending to the conclusion, contrary to a previous statement by Perucca( 50), that thin filras do not obey Ohm's Law. 17 IV Past Theories of the Abnormal Behavior of Resistance as a Function of Thickness. Three distinct theories have been proposed in the past: (A) J. J. Thomson Theory: This explains the rapid increase of resistivity wi~h decrease of film-thickness on the basis of the shortening of the mean free path of the electron, in the direction perpendicular to the filln. This theory would probably be satis- factory if the film-structure were the same as it is in the bulk metal; and not, as is found, a great number of atomic pa:bches fitted together into a lace-like structure. Also, it is not satisfactory because it does not explain the sudden change of resistivity with thickness, as it is found; and also because it gives a wrong prediction for the change of the critical thickness with temperature. Recently Tisza( 53 ), on the basis of the Sonnnerfeld theory, and the shortening of the mean free path of the electron perpendicular to the film - as in Thomson's theory - has predicted a critical thickness. However, he merely gives the final formula without details; and gives no e:xp:3riTIBntal evidence to quantitatively support it. It should likewise suffer from the same objections as Thomson's theory. (B) Non-conducting Layer Theory: advanced by Perucca( 50). This is the most recent and was From experim:lntal data he arrives at the conclusion that the surface layers of all metals are non-conducting and hence possess no free electrons. Whenever the film-thickness 18 is less than twice this hypothetical value the film shows no conductivity. Such an hypothesis is untenable, as shown by Weber and Oosterhius( 47 ), and Hamburger and Reinders< 35 ). They show that films with a mean thickness of even one atomic layer show con,· ductivity. The reason for the disagreement is probably that Perucca formed his films by sputtering; whereas the others, by evaporation. (C) Granular Theory: This was proposed and given the most thorough theoretical treatment by Swan( 54 ). Other supporters of it have been Houllevigue( 3 l), King( 6 ), Reide(ll) and MacKeown( 2 ). It assumes that atoms fall on the backing at random, much like raindrops fall on the pavement. In time, due to the mutual atomic forces the atoms condense into small isolated nuclei. These nuclei continue to grow as more atoms rain on the surface; and, finally, with increase of size, they begin to make contact. At this point the resistivity drops sharply, but never attains the value found for the bulk metal. This is because the film is still porous - a remnant of its granular structure. The granular hypothesis as stated above has gained wide credence although Swan's deductions from it have had little success. V Hypotheses and Formulae Proposed, Accounting for New Aging Effect. No hypotheses or formulae have been proposed in the past to account for the new aging effect, as far as I know. This is probably because the new effect has been observed now, only for the first time. It will be shown in what follows that the effect can 19 be accounted for on the basis of the following three premises: (1) The granular hypothesis (2) the influence of the high resistant backing and (3) that atoms exert mutual forces of attraction. As these formulae will be used subseQuently in the inter- pretation and evaluation of the experimental results, the±r derivation will be given in detai1. (A) For Extremely Thin Films where the Atoms Cover a Relatively Smail Portion of the Backing. Assume that the atoms fall quite at random on the backing, and initially are arranged much as raindrops on a pavement. Immediately, because of the mutual forces of attraction, a process of coalescence of the atoms sets in, entailing a continuous decrease of the number of isolated particles on the sl.U'face. Now, assume that the mechanism of conduction is the motion of the electrons between these particles. One would therefore expect, if there are (n) free particles on the surface, that the removal of one free particle by coalescence with another would cause a (!) -fold decrease of resistance. This means that (R), n the resistance, is inversely proportional to (n): Rn= constant .Now let k = the recombination coefficient of the particles and t = the time allowed for recombination Then the fractional decrease ~f the number of free particles on the surface due to spontaneous recombination is: dn n -= - k dt 20 Integrating log n =-kt+ c. Therefore log R =kt+ c. Now R~ = constant; Experimental results later given show that this formula holds remarkably well up to at least an average thickness of 20 layers. (k) is, at the same time, both the coefficient of recombination of the particles on the surface and the slope of the curve: log R equals a function of (t). (B) For Thin Films, where the Atoms Cover a Relatively Large Portion of the Backing. This case differs from the preceding in that the small nuclei have now grown into relatively large patches separated by narrow channels of backing. This enables one to express the total resistance of the film as the sum of two quantities: (1) The resistance of that part of the line of current flow which traverses the channels, i.e., the backing, and (2) of that part which passes through the metallic patches. Using the symbols as given in the diagram, an expression will be first found for(~) - the fractional part of the line of D flow which traverses the backing in terms of the areas of the patches. Letting (A) be the inner plus the outer area, and (D) proportional to its linear dimensions; (a) the inner area, and (d) proportional to its linear dimensions 2 a_ d From geometry: A - D2 • d2 - D2 Then a - ~t,. - --A D2 PATC!f STRUCTURE Of 111111 flL/'15 ,, eLECTRODE. . I \ I I \ I ' I ~ -· ...- L ., _,. .Jl - \ I \ .. I A ' I \ <C/---.-1" ELECTRODE (l) (z) (3) of a rypicol polch (,4) 15 (Cl) + (/he ossoc/a+ed unco//en!d porflon of rhe backinc;_}. ~) 1s proporl-1onol fo -the dimensions or (o) {a) €1) . (b) NJ the 15 area proporr1onal -ft, -the (5) (~) is t&,) (L) denofes d1n-1ens1ons (D-d) a !the of current f'low. of ('A) 22 .As ( d - D) << D since (d - D) =~t a - A = (d - D)(d + D) _ 2(d - D) _ 2 A D by definition. - - D Therefore (1_) = A - a D 2A How let ( ~F ) = the resistance of unit length of a solid film and ( S&l = the resistance of unit length of clean backing. Then the part of the resistance contributed by the backing is 2 . a .Tfa . d a• rf6 (A A- a) .' and by the patches is J'/ff A ' since D2 .= 1.. • 'rhe total resisj;ance of the fiim is the sum of these: .' . R = , Since the patches undergo a coalescence with time, (a) changes. The rate of change of . the resistance (R) is consequently-: Let A = 1. This means t h at ·we confine our attention to a unit area of the film. Assume now that ( da) - ( the rate of contraction dt in area of the patches) - is a constant. sults will justify this. Later experirrental re- Therefore inte grati ng with respect to time: Or R =kt+ C where (k) is t h e expression in brackets~, In verifying this equation log(R) is plotted against log (t), and the curve is always found to be a 45° line. 23 VI Apparatus (A) General In the past, films have usually been produced by sputter- ing. As pointed out in the introduction this method is open to grave criticism because: (1) the unavoidable presence of gases causes many strange effects and may completely mask the property one is studying, (2) unlike the process of evaporation, where the film is formed from individual atoms, sputtering forms the fibns from small crystalline chunks or grains pulled out of the cathode, (3) the constancy of the temperature - an extremely important variable - is hard to maintain during sputtering. On the other hand, the method of evaporation has not been so widely used in the past, although it is open to none of the above criticisms. This is probably because until just recently the technique has not passed far beyond the primitive stage. It is this method we have adopted however; and as will later be shown it presents an adnurable means for determining film-thickness with an extraordinarily high precision. In what follows will be given a description of the apparatus used in depositing the films and for measuring their thickness and their conductivity. (B) Chamber (1) General Arrangement of the Parts . .An idea of this can be best gotten by referring to figure 2: (m) is the electrostatic shielding surrounding the chamber; 24 (F) the furnace support; ( e) the crystal holder; (M) the shutter; (u) its magnetic control; and (n) and (r) the water leads for cooling the crystal. The metal was evaporated from the furnace supported at (F) and condensed on the backing at the lower end of the tube (e). The stream of atoms was columm.ated by two slits: one at (S) and another at (g). Time exposure was regulated by means of the shutter (M) supported on (W) . This shutter was controlled magnet- ically from the outside by (u). Potential leads to the film were carried in through two long narrow capillaries (y) - only one is here shown, as the other is directly behind it - and connected to the rods (d) leading to the clamps ( g) . .An auxilliary furnace, inside the upper end of (W), is required for depositing electrical connections between clamps (g) and the backing. These connections consisted of relatively heavy films bridging the clamps (g) and the backing, as shown in Fig. 4. Dependable electrical connection with an adsorbed film can not be made merely by pressing electrodes against the film; the r electrodes must be welded to the film, as it were. F The reason for using an auxilliary furnace 25 DIAGRAM SHJWl;'/G ASSEMBLY ClF r/Ll'f llf?.C£R, SlltlllEI? 8 MAGIYE/7C CO!VTfil.1 r""ttR,,YK.E .5tl?RJIPT, If WATER ORCtlMTOtf , 8:ELECTtfrJSTATIC SJ-IIELDllfG . 0 I ,S- IOc,n I ,; Fig. 2 26 £ L, L I ,H SCHEMATIC DIAGRAM SIIOJr/lYG ELECTl?OSTATIC S!I/ELOIIYG Ot CMMBE~ SWITCIIES, COtYOE.f5ER5 & ELECTl?CMETER o 10cm. L__J L Fig . 3 27 was that the one below - being too far away - did not hold enough to deposit both the bridges and the adsorbed film. The space between the bridges - where the adsorbed film was to be deposited - was protected during their formation by a soft iron strip. This was afterwards rem9ved with a magnet. Constancy of the film temperature is insured by water cooling. Water is forced down the tube (n) - only the upper part is shown in the figure - to the bottom of the tube ( e), where the film-backing is held; and it is sucked out by means of a water aspirator through the larger concentric tube (r). The chamber is thoroughly shielded electrostatically. This is done in sections for convenience. They are all labeled (m). Current for the two furnaces passes in through two leads (H) - one is behind the other. Both furnaces are mounted on the same leads. Thermo couple wires to the lower furnace are introduced through two long capillaries R1R2 - one is behind the other. Figure (3) is a schematic diagram showing the chamber in its relation to the other parts of the apparatus. T1T2 T3 and U are electrostatic shields, all of which were labeled (m) in figure 2. (M) is the rotating magnet controlling the shutter; {W) repre- sents the water cooling leads; (N), the two capillaries for the therinocouple; and 11½2 the current leads to the furnaces. 28 (2) Detail of Crystal Holder rhe crystal holder ( see fi g . 5 and 6 ) serves a fourfold 1 pUTpose. It supports: the CI"JStal; the electrodes and clamps holding the crystal; the shield which protects the spaDe where the adsorbed film is later deposited - between the electrodes while the metallic bridges are being deposited; and finally the slit defining the film on t he backing . -These parts are all mounted on 4 rings (h) which fit tightly into grooves made in the quartz tube (e). Quartz was used as it must withstand wide variations of temperatUTe. Each ring , made of copper and consisting of two semicircular brackets, was held securely in its groove by two tungsten springs, as shown in the diagram. Tungsten was used as it does not loose its spring- iness at the hi gh temperatures used for out gasing . The processes of holding the film-backing and making electrical connection with the film-electrodes were combined in the two clamps (g ) spot welded to two rods (d) which slide through holes in br!lckets mounted on alternate rings (h). Tension in the clamps is maintained by using tungsten springs (f) and molybdenum elbows (g ) spotwelded onto (d). It was found imperative to have the clarnps (g ) make very close and .even contact with the film-backing (n). A satisfactory way of accomplishing this was to spotweld very carefully onto (g ), the edge of a Gem razor blade. Even the close contact secured in using the razor blade 29 !JAGl?AM S/l}lf/1/G A55l"MBLY OF RL/"I flJLOfR /l'llllfl!IG SUT ""'Z FOT£!'/T!Al ELECT/?OOES & Sf/lELD o , Sc,r, I I I I I I Fig. 5 }O 9- I , q ~ I Oi4GRAM Sll)Jtll/lG lll4/L ff flJT&TJ,fl.. I I I I I I EL£CTRrJffS, .511/EflJ & SI.IT #-2 I l..----l.-~,l---.._...K- --- 0 r-.... •---,.--. I :: ~ : I 1: •I I Fig . 6 z .,.. 31 edges was inadequate for ma.~ing dependible electrical contact with the adsorbed films. An excellent way of overcoming the difficulty was to place a shield (S) between the electrodes (L); and on each side of (S) - from the auxilia.ry:;•furnace below - to deposit a heavy metallic film bridging the backing and the electrodes (L), whereafter (S) was removed by a magnet. The adsorbed layer was then deposited betwe en the heavy metallic brid ges. This method enables . one to make dependable electrical contact with films of any thickness, no matter how small. The shield supporter (b), mounted on alternate rings (h) by means of the brackets (c), is also the slit (K) which defines the size of the adsorbed layer deposited, .AJ.l of the parts except (S) are of copper , in order to enable one to remove (S) with a magnet. are either spotwelded or silver soldered. And all permanent joints (S) is made of extremely soft transfoDmer iron and the edges of its lower side are beveled to prevent it-s becoming attached to (K) during the deposition of the electrodes. ($) Details of the Shutter and the Second Slit, Defining the Surface of Evaporation. These are shown pictorially in fi g , 7 and 8. The base for the entire nIDunting is a candle-stick-like arrangement of glass with three arms ( c 1c 2 c3 ). The whole, by means of the glass tube (D), is made an integral part of the large glass cone forming the bottom of the chamber. 32 Fitting into these cups are three pyrex rods (P). The tops of these rods fit into three steel cups on top of which is screwed a ring (T). This arrangement, it is found, gives a remarkably rigid foundation for the super structure. The slit is supported by t wo brackets (U) and (V) screwed to the ring (S). '.rhe shutter is supported on (W), at the bottom of which is a tripod N1N2 N3 which is screwed to the ring (S) by means of (W) spotwelded together from molybdenum - this metal being used as it has a very low vapor pressure at high temperatures - is the support of the shutter (M), also made of molybdenum. On the lower side of (M) is a soft iron bar by means of which (M) can be magnetically controlled from the outside. A detail of the magnetic control is given in fi g . 9. Two magnets (m) are mounted on a carriage (d) on the bottom of which is a groove (c). The whole is supported on three ball bearings (a) which roll in another groove (b) in the base plate, as shown. The ball bearing construction was necessitated as the magnets could not be conveniently mounted on an axle. (4) Furnaces (a) General Fi g . 10 shows schematically their mounting . (F1 ) deposits t he metallic bridges; (F..,) ,~ de posits the adsorbed film; one is mounted above t he other. After the bridges are deposited, the OIAGRIV1 smM!IG f!(}(JIYTIIIG a BASE RJI? 2 FtJl?!VACcS 1 Sf!UTT!:R 8- .5UTS ,_,,HOR!i!Ol'ITAL 6ECTIOM Tll/?OUG# L-L BELOW SUPPORT f'IXi' F</RtlACE "' Z (Tll!S Q'f/f EXPL.00 £0} J II II FIG FIG. G II I( L_. r!G. F t3 A TO PUMP:, AMO I. Fig. 7 I I I I I I t,,,,, SCIILf lf1? MA!/'I fJIAGRAI'/ SC,'71 Sf/tJTrER S/JPPrY?T IVR 5H(JTTER & sur ':t f -.~ :·.:·.=.:: . • /Jo •• D • . s . ..... .... '\ - ,,,,. ASSEMBLY V OIAGR/lf S/lJffll,f; Sll(JTTEI?, SI.IT '1 , 11181? SJIRJli'TS, & A.¼=MBLY 0 'I ~- Fig . 8 Sc,,-, I I rn 014Gf?AM CF APPAl?ATtl5 F@ /t/4Gll£T/C COYTRa Or SIIUTTE/rS 11/Y JIACtlt/11/ TUBES' 0 S /Oen-, I I I I I I I I I' I m d b (1 Fig . 9 110 V Q F, ' I w H,.o T,_ p K / C '-------A Cll?C{J!T /J/4Cl?AM Or rtJ!r!IAC£ Fig. 10 CO/'/TfOLS 36 one (F1) is exploded and its remainder automatically removed clearing the path between (F2 ) and the film-backing - by a remarkably simple mechanical arrangement. Its removal is accom- plished by having its ends pi voted or hinged o·n two axles (33), see Fig. 7. When (F1) is burnt in two, each half is by gravity pulled downward about its axle. Both furnaces (Fi) and (F2 ) are mounted on the same leads; a very great advantage from the standpoint of simplifying the apparatus and economizing on space. In order to accomplish this, two conditions are to be satisfied: (1) The resistance of (F1 ) must be small with respect :to (F2 ), so that - with the application of the same voltage - (F1) will become very hot while (F2 ) remains cool. (2) .And the impedance of the exterior part of the circuit including the trans~ormer must be the same order magnitude · as that of the furnaces, which are only a few thousandths of an ohm. Otherwise one finds, both from calculation and by experiment, that the burning out of one furnace automatically entails the bunnin.g out of the other. In order to satisfy condition (2) it is impossible to make use of the customary way of controlling the current in the primary circuit of the transformer 1with a rheostat. This is because the impedance in the primary is alwa~,rs reflected into the secondary. Current-control by a rheostat in the secondary is also out of the question as the current is here often grea~er than 100 amperes. What was done was to design and construct a special trans- 38 former with a turns ratio of about 400 : 1 ..... 6 with heavy taps in the secondary for obtaining the proper voltage. (Ti) in Fig . 10 represents the transformer schematically. (Ti) was used only for the upper furnace; for the lower one another one (T2 ) was used, with a 4:1 turns ratio, in combination with a vernier arrangement of rheostats ( R1¾R3 ) • Only with the latter arrangement was it found possible to obtain the required precision in the control of the current for (F2 ). The temperature of (F2 ) was determined by a platinum platinum-rhodium thermocouple (W) attached to the furnace; protected by the shield (N), and connected to the Leeds Northrup potentiometer (P) through the cold junction (M). The leads were brought into the apparatus through two long narrow capillaries (K) - one is behind the other in the figure - sealed at the ends with cotton and sealing wax. In order to simplify the subsequent removal of the wax, the cup was first filled with cotton; and then, on this, the wax was melted. (b) Furnace (F1 ) for Depositing Metallic Bridges. This consisted of a strip cut from a sheet of Ni, .003" thick, in the shape shown in Fig . (11) and bent into the shape shown in Fig . (12). Its final design was the result of a great number of trials to find a furnace which: (1) would be operated by the same leads as the lower f urnace (2) would be easily made, and replaced (3) would present a large area of evaporation and yet keep the melted metal (Ag in this case) from running to the I 39 cool ends, and there condensing and interfering with the subseg_uent removal of the furnace, ( 4) would have a much greater conductivity than the lower furnace, and yet require a relatively small current to explode it, and finally (5) would be easily and simply removed without reg_uiring any mechanical parts to get out of order. (C) Furnace F2 , For Depositing the Adsorbed Layers. The paramount reg_uirement of this furnace was that it be able to evaporate the metal at a uniform and reproducible r~te. Other desirable characteristics were: (1) small heat capacity, in order :Co minimize heat disturbances during the experiment, (2) small temperature inertia, to minimize the time reg_uired to raise it to the proper temperature (3) small volume capacity adapting it to investigations with the · precious metals whose price might make the investigation prohibitive, and finaily (4) sturdy, and requiring little attention during its operation. As none of the furnaces described in the 11 terature possess the above characteristics it was ne·cessary to develop one that did. Its final form is shown in Fig. 13 and 14. is a view from the top and Fig. 14 from the bottom. Fig.13 It was cut from a 1' x 6' strip. of Ni .003u in thickness and bent and pressed into the form shown. The thermocouple protector shown in Fig. 14, also made of Ni, was spotwelded to the bottom of the crucible. That part of it that was welded to the crucible was made of .010" thick Ni, to increase the heat conductivity between the crucible 40 _ ___.[]..._____ __, .___ F ig. 11 Fig. Fig . 13 12 Fig. 14 41 and thermocouple junction. The -riders shown prevented the molten metal from running off to the cooler parts of the two arms; and on the furnace ih its final form, w~re bent so that the lower parts ran parallel to the bottom of the furnace, thus preventing secondary evaporation onto the thermocouple junction. This type of furnace possesses an additional advantage over others. In contrast to those of the usual form, this one combines the crucible and heating element into but one unit, reducing the number of parts that might get out of order. This furnace in its final form was the result of tests carried out on a very great number of all sizes and shapes. The uniformity in the. rate of evaporation was found to be extremely ~ensitive to minute variations in its shape and desi gn; and its exact form was gotten only from a continuous observation of its behavior during operation, through the walls of the glass chamber. At times a magnifying glass was necessary to bring out defects in its design. Suffice it here to enumerate the salient sources of trouble arising: (1) Alloying: This was the first bi g trouble, and caused the Pt, Pt-Rh thermocouples to be dissolved off like sugar in_water, no matter where they were placed. (2) Surface tension: Would cause a dissymmetry in the surface of evaporation and pull molten metal into sharp corners and narrow crevices. (3) Secondary evaporation: Was the process in which atoms, 42 condensed on a hot surface, would re-evaporate onto other parts of furnace and apparatus, causing a change of furnace characteristics and short circuiting the thermocouple leads. (4) Gravity: In combination with surface tension and secondary evaporation onto the walls of crucible would, in time, cause a considerable deposit to collect at the bottom of the crucible. This would change the heat conductivity between the crucible and the thermocouple which, in time, it would dissolve off. (5) The ability of molten nietal to flow freely through microscopic holes. This required that parts spotwelded be kept free of holes. (6) The tendency of molten metal to move from the hotter to the cooler parts of the furnace - caused principally by the change of surface tension with temperature - and change the temperature distribution in the furnace. The riders at the end of crucible helped overcome this difficulty. (7) The tendency, while the furnace was being heated up, for small volcanoes to be formed around the riders and thus to pour molten metal over the sides of the crucible. (8) The fluctuation of the thermal contact between the melt and the crucible, causing - while the temperature as determined by the thermocouple remained constant - temperature changes of the melt. The following data shows the extreme uniformity of the 43 rate of evaporation obtainable with this furnace. Three indepena- ent deposits of Ag at different times but under similar conditions were deposited onto the same glass plate and weighed: (A) '. (C) (B) ( 1) Time required for deposition in hours 3.0 3.0 6.0 ( 2) Area of film in sq.ems. .?45 .688 .668 (3) Weight of film+ glass plate in grams; an average of from 5 to 10 readings .6089458 .608904 .6089749 (4) Weight of clean glass plate .6089180 .6088?5 .6089239 (5) Weight of film .00002?8 .000029 .000051 (6) Rate of deposit in layers per minute .945 1.06 .96? 'l'he weighing under (B) happened to be made during the period of earthquakes in the early part of Tuiarch 1933 and might be a bit off. (A) was made after the furnace had already been in use about 15 hours. (B) was made several weeks later after the furnace had been in use a total time of about 23 hours and (C) a few days later than (B). Comparing (A) and (C), the most dependable values and obtained at different times separated by an interval of several weeks, one finds only 2.3% deviation. Even this small deviation, I believe, is not due to the furnace but to the natural limit in the sensitivity of the microbalance. Longer time exposures or greater rates of evaporation should increase the accuracy. 44 As the shutter can be timed for 15 sec. exposures with a negligible amount of error 1one can conclude from the above that: THE THICKNESS OF A LA.YER OF MONOIV[OLECULAR ORDER OF MAGNI - TUDE CAN BE DETERMI NED', WITH GREAT CARE, TO AN ACCURACY OF 3 OR 4%. (C) Precautions Taken for Reducing the Contamination of the Film to a Minimum. The experimental results of previous workers suffer con- siderably from occluded gase~, which in the present work have been almost entirely eliminated. This was accomplished by a systematic cleaning and outgasing of the apparatus. Glass ware was cleaned according to the followi ng procedure: All parts were first dipped into hot chromic acid, then _rinsed with water, and followed by nitric acid to remove all traces of metallic deposits. The parts were again rinsed in water followed by a rinse in alcohol and dried. For those parts immediately surrounding the crystal holder, ether was used instead of alcohol. Metallic parts were cleaned in a dilute solution of nitric acid, rinsed in water, then in alcohol and dried. The cleaning of t he glass backing was carried out the s ame as for the glass ware above, and finally placed into a des s icator . The crystals used as film-bac king were freshly cleaved i mmediately before each run - without being touche d with the 45 fingers - and were then inserted as quickly as possible into the apparatus which was then immediately pumped down. Stopcock grease was applied sparingly and confined only to a very narrow band on the outer ·end of the cone leaving 3/4 of that part of the cone on the side of the chamber perfectly clean. All metal parts, especially the shutter and its attachments were thoroughly outgased at red heat by an induction furnace designed especially for that purpose. A schema.tic diagram of it is shown in figure 15. (I) is the heating coil place,d about the chamber; (H) the horngap, and (0) a blast of air to quench it; (K1 ) and C¼) the condensers; (D 1 , D2 ) choke coils and (T) the transformer. The continued sharpness of the shadows of the parts of the apparatus in the path of the atomic rays was an indication of the high vacuum maintained at all times. Another important factor contributing to the high vacuum was the great purnping speed obtainable with the apparatus. All tubes were of large diameter and practically no resistance was encountered at the liquid air trap (see fi g . (3)). (D) Measurement of Conductivity. (a) General This was done by the leakage method using an extremely sensitive string electrometer, whose current sensitivity was varied over many powers of, 10 by a specially designed bank of 46 A D, CIRCUIT Ol4CRAM or IIY!Jt/CT/011 F!Jl?IYACE w f I 110 // AC. i 0 Fig. 15 47 condensers. The string electrometer was chosen primarily be- cause of its extremely small capacity enabling one to measure resistances as high as 10 15 ohms in .a mininrum am01m.t of time. The capacity of the entire system is calibrated by a specially designed calibration condenser. Ail switches and parts are built into a single unit in order to make the electrostatic shielding as perfect as poss.ible. (b) Hookup Fig. (16) is a schema.tic drawing showing the hookup: (K) is the film backing; (E) the electrometer; {S) a switch leading to the source of plate potential which was at all times maintained so that the fibre was at zero potential; ( c1 .·. c4 ) a bank of condensers whose connections with the fibre of the electrometer are made by the wire switches (81 .. s 4 ) operated by 'turning the dial (D) . The dial (D) , having four CA M ~; (W1 .. w4 ) which raise and lower the phosphor bronze springs (P), causes the quartz rod to open and close the switches (s1 .. s4 ) - according to the dial setting - enabling one to put any desired capacity in parallel with the fibre and ground. (S1 ... Sg) are switches made of piano wire with pla ti mun wire tips. Wire switches were used to minimize capacity changes in the system when the switches were opened and closed; and platinum tips, to eliminate contact e.m.f. (S8 ) is the grounding switch, (f) is the calibration condenser, with guard rings (G), and charged up by the plung~r (N). The connections are such that the guard 48 510 ClliC!IIT OIACRAM ltJR ✓-~-MEA5U!?ENc/Yl Or l?E.5/.5l4'Y(£ Or AOZ'l?BEO !,4YEl?5 ----1 f'I I< H D ~ 90 11 S,., 9011 = 1 - - - ---'--------, 1\1\1\1\1\1\1\i-: + - .5,m'..a i1 1/0 oc. Fig. 16 ___J F H 49 rings are always charged to the same potential as the condenser. Fig. (3) shows the relation of the above parts to the rest of the apparatus. (P) is the electrometer, whose fibre and scale are projected by the prism (R) onto the screen (H); (E) is the calibration condenser; (F) houses the switches operated from the outside by s1S2 83 ; (T3 ) and (T4 ) go to the film and bank of I J,,_,.,.{v11,e,2/ condensers, respectively; and A, housing the bank of condensers manipulated by the dial (D). (C) Method of Measuring Conductivity and Determining the Capacity of the System. When the film-resistance is being measured 810 is thrown upwards placing a potential on the f'ilm; 8 58 7s8 are open; s9 is closed; and s 6 is opened or closed depending upon what electrometer sensitivity is desiretl. Vllien the voltage sensitivity of the electrometer is wanted, s10 is thrown downwards; ~5 and S5 are closed; and S7S3S9 are opened. When the capacity of the system is to be calibrated s10 is thrown downward and s58 6 and s8 are open. by {H) to a knovm potential. Condenser (L) is charged The charge is conununicated by s 7 to the electrometer and the rest of the system. The new potential is determined by the electrometer. Jfrom the known capacity and initial potential of {L), and the final potential of {L) and the system, the capacity of the system is readily determined. Results by this method, v1hen measuring capacities as low as 50 40 cm. agree within 1% of those obtained by another method developed in the course of the work. The other method makes use of the bank of condensers C1 .• C4 and a high resistant film. It consists in placing a standard condenser (.1 m.f.) at c4 withe the capacities of C3 C2 C1 progressively decreasing in powers of 10, and having a ' film of suitable resistance at (F). A fixed potential is applied to the film and the time noted that it requires the electrometer to charge up to a fixed potential, with each of the condensers - in turn - connected in. From these are found ratios between the time of leak, through the same film, for each pair of adjacent condensers. With these ratios, and the known capacity of c4 , the capacity of the system is readily determined. (d) Detail of Calibration Condenser and Switch Housing. Fig. 17 shows a cross section of t .he unit containing the calibration condenser grounding switch and other controls. (B) leads to the bank of condensers; (F) to the film by means of the flexible piano wire spring (u). The switches (w) are of piano wire tipped with platinum wire (P) and operated by quartz rods ( Q,) • As the grounding switch was used several thousand times during a normal run it had to be sturdy. This is brought out more clearly by the detailed sketch at the side. (e) Detail of Apparatus for Control of Electrometer Sensitivity. Fig. 18 shows a top view and a cross section through L1½z of the arrangement used for varying the electrometer sensitivity. (D) is the dial; Ki .. K4 are cams; c1 .. c4 are condensers held 51 POTENTIAL Al?l?AIYGEHEIYT ff CAL/8RAT!CrY TO CHARGE - HARD ~ BRASS IIIElll AM~R Rf/BBER CCW0,5V5f R. GtWti'h'.OHYC Slf/70/ / AND COfflrt?LS IVR Mcl!.2/iflYG RAP£<'.Y RES/STAKES GRB!Tc,P Tl/AN /OM On'MS t d II 0 10 cm . I Fi g . 17 COl'/0/:/YSER 52 r- - - - - - - - - - - - - - - - - - - - - - - G - - - - - -, ~ I ~~-~ ' I l... ---------- - - ~ -- - I I L,--::JJ_t~~~~~~~~± -,J........--l--!!,.db._ I I I I I I ~ -- - - I . __ _ _ _ _ _ _ _ _ ____, I I - - - - - _j /JIACl?AM Jl,OMIY6 AfPAft/!115 !VIP Mf?YIIYC CIIR/?flYT Sflf.5/TIJl/l-Y fff/? Jflff lrM'GcS tll?. A STR/IYG flfCT/RY'/£ /ftf r------ - - --- -- ----- G - - - - - - - - - - - 7 I I I ~:s.-~ II I IL ____ __ __ ____ __ _ _ I I I I r -- -- - - ---- - - - - - - - 1 ,....,_______ ' L - - - -1..- - - - - - - - - - - _._ : ___ . _ _ _ - - ' - , I, - -- - - - - - - ' 'J - - - - - - - - - -- - - - - - - Fig. - - - 18 o \._ 0 I I I I I I 10,,., I I I I I • 53 in place by hard rubber rods R:a and %i the (B's) are phosphor bronze springs at whose ends are quartz rods (Q) for manipulating the wire switches. The principle ot operation ~f the whole arrangrnent can be best seen from the operation of a single condenser. Take C2 and consider the lower diagram. • As the. cam (K:z) is turned mnto the position shown in the figure, (Q) - which normally presses against the piano wire (W) holding the switch open - now rises and allows ~he t _wo wires to make contact connecting C2 with the electrometer. The ·cams are so arranged on the shaft that almost any combination of condensers can be connected with the electrometer, merely by turning the dial (D). (E) Method .of Setting up the Apparatus and Taking Readings: (a) Preliminaries: (1) .Ul glassware and :rretal parts were thoroughly cleaned according to the proceedure previously outlined, before ever the apparatus was put in use, and the chamber was cleaned before each Dun. (2) Rate of evaporation of the lower furnace F2 determined by the Mechanical Method as described on page 43 . (3) New auxiliary furnace F1 inserted and loaded. (4) A freshly cleaved crystal backing inserted. (5) Apparatus pumped down. (6) Metal pellets in auxiliary furnace (F1 ) melted down to prevent their flying off during the 54 application of the induction furnace. (7) Induction furnace applied. (8) Water circulation for the cooling of the filmbacking applied ( i) Metallic ·bridges deposited by auxiliary furnace (F1) in shifts of a minute or more, to prevent crystal from heating up. {j) Auxiliary furnace exploded. (1<) Shield - for protecting space between metallic bridges above - removed. (1) Apparatus now electrostatically shielded and magnetic shutter control put around chamber. (b) Taking Readings (m) Shutter closed and lower furnace (F2 ) brought slowly up to the predetermined temperature. (n) Shutter opened and backing exposed for a definite time interval in order to deposit a known number of atoms. (o) Current to lower furnace shut off. (p) Film resistance measured from time to time until it had approached an asymtotic value. (~) Steps m, n, o, p repeated for each new deposit to be studied. (r) And at no time during a run were any of the pumps stopped; they were kept going night and day. 55 VII Experimental Results and Conclusions. (A) Dependence of Resistivity on Time - Extremely Thin Films on Calcite. (a) Data, Conventions, and Definitions. Figs. 19, 20 and 21 show the dependence of resistivity on time for extremely thin (Ag} films deposited on calcite - from 1 to 55 layers average thickness. The data from which the curves were plotted is found in section (I) of the appendix. The poten- tial applied at all times both during the formation of the film and during the conductivity measurements was 60 volts. The thickness of the film - in average number of layers is computed on the basis that the (110) plane is parallel to the backing; if future investigations prove that the (111) plane is parallel, then all film thickness given in this paper are to be increased by a constant factor. It will be noticed that instead of the resistivity of the film a quantity proportional to it is plotted. This is the pro- duct of the film resistance and the average thickness in number of layers: (R x N}i. 1 • In order to bring out the trend of the coefficient of recombination (k} with time - involved in the equation log R =kt+ c derived on page tivity is plotted. - log NR instead of the resis- And the slope of the corresponding curve is then the coefficient of recombination. From now on the following terms will have the following 56 meanings: By "aging" will be meant the change of resistance with time. By an "unaged film" will be meant one which has just been deposited and has had no time for its component atoms to recombine. By "extremely thin films" will be meant films with a thickness below 50 layers or so; by "thin films" will be meant films with a thickness greater than 50 layers and at least up to 330. The difference in experimental results for these two ranges will justify this distinction. Curve (I) of fi g . 19 represents the aging of a film having 1.45 layers average thickness. The slope representing the coeffi- cient of recombination (k) is seen to be remarkably constant for the first 40 minutes or more, whereafter the resistivity approaches an assymtotic value after 11/2 hours or more - in the curves the aging is shown only for the initial 75 minutes. Curve (II) represents the aging of film (I) - fully aged with a fresh additional deposit of 0.96 layers. It is the same as (I) in every respect except that (k) the coefficient of recombination - represented by the slope of the curve - is a bit less. Each of the succeeding curves: III ... VIII, represents the aging of' the corresponding film with 0. 96 layers added to the preceeding film, e.g. Curve (IV) represents the addition of 0.96 layers to (III) which is fully aged and already has a thickness of 3.37 layers, as indicated on the curve. Fig. 20 and 21 are continuations of fi g. 19 up to 53 layers, average thickness. As a means of comparison curve VIII is found in 57 both fig. 19 and 20, and curve A'VIII is found in both fig. 20 and 21-. The average number of layers added to the preceeding fully aged film is indicated in brackets; and the total thiclmess - of the film, without brackets. (b) Aging of Extremely Thin Films. A remarkable thing common to all--the deposits is that the resistivity during the process of aging increases several hundredfold its initial value within an hour or more. previous workers have found this. None of the many They always report a decrease of resistivity with time as mentioned in the introduction. We can likewise obtain a decrease of resistivity with time if we merely turn the diffusion pump off for a short time. The subsequent few films deposited then show a decrease of resistivity with time. (c) Resistivity as a Function of Thickness. Furthermore it is seen that each additional deposit tends to increase the film resistivity. served before. This also has never been ob- All previous workers find an infinite resistivity in this range, wijere we find a continuous increase. (d) Dependence of the Recombination Coefficient on the Number of Unaged I.ayers Deposited at One Time. This same set of curves shows that the coefficient of re- combination (k) is a constant over a considerable period of time after the film has been deposited. This is brought out by the initial straight line portion of the curves. Also (k) is seen to be independent of filln thickness and ~~ .3 .1 t> 1 2 3 0ifL7£f-l67A t :1 r/G . 2ff nvmw of r.eW taxer$ addea i» o fiJ/2 4 ~ 6 7- -r s 11£1#8& OE Jfflf t.1YE,(25 e H aged fr/rr, L~~£L? UPEh'Ofb'CE Or _RfC0#8JA1ATJOLLJf£rfiC~ ~ ~ .z /o9,,,-o- u ~ -~ ~ t- /iz~ t- ,I- @ @ @ • • au ~ q . z ✓~• -~~ -U-4.1- @ .... i~ foo 5o l~o AVEeAGE l 25o 3oO /IY LAYE,fS . FIG. 2.7 Zoo Tt-{/CK/YESS B5o '--OF REOJMB!IYAT/0/I 0/Y '!l-t/Cl(!YE55 A£TER 5 M!lltJTcS Or A;I/IG. -r _,! 24 - lEPEli'DZiYCE CF TJIE CO.f/:~OEIY: + jf> 142 .ll@f'.# • 1' r -+ .Z @/IU r4.z 4 -~ -~\.3 - - ~ ~ -----t!t: ~ ~I ij~ .8 kc-~ I.a ~~ ~ E4o' s:, ~ ~ ~ - C!/f'CL.ES_ OF llf(£ ArP.EAli'Aht'°.c ll'IDICAT_e LIKE AMO<,/'fr.:i Or OcP05IT ON TIIE PREYIC!.ISLY FVLl.!•,. A6-El) FILM 1.7.. ~ -•- . M.Wu'--2 T11£5£.....flu'.ME,£WS !YI./MERALS BcSIOE Tf/E CIRCLES I/YD-CATE TnE ,Ei':'"Ei!i' i f tAYE,f'.5' C4r£<B'JGE.) DERJ.5IT£0 2!ITO ,7/E FU.if ArED rlt.M WHa5E AVERAGE TIIKXIYE55 IJ TIIE Aff5Cls.:A j ~ 4 ,6 ~ ! ' n ,_ Lr-,- I---- -- +\- \ \ I ~J~ ,;_, ,I s, \ ~ - jl ~ I -' I --.- I ,. ll ,. ~ ~ " , __ ---+-- --!---- ·'"''I '"" ~ o, ~ I--+- ~ "' -,__ --!---- ----1----~' I ~ + I I I I I I I - ....... . ...... I l I I i I I >--!I '"' ~ I I ,... I ,, "" T I I -!! --~ l T .If t~ .I l I I I "' V I I I "' .I I I . l"o I I .I ,_ I n I .I u. ! IO, o· .I I IC \<l I ~ " I · ;--.. i I - p, I I ~- ,f.WJ-2 21, ti I I l .I ~ I ' I t In ! • I.,- 1- I l I Ill I'< oril I 1--- "- -~ . I\. ~~ l I Ii -~ ' 7 ,·c::.i r1, - ., H-- ,., o,i -;:; . I\ I..\ ~ ~-!if !.J! iii ., ::, · ~- In I ; I ~ t 1--r : , .,i;il -., t---+-- 1 ~ ' I ~ !-a-l ~- -\ \ 1-\ \, - I I --- ~- 1--r I I I I ,;;;J -"' ..: 0 t I -~i ~ ' 14,\ 0 I ' 1 I ~,~ I "1 ~ - -- ~- ---- k, >\' I ..j__ i!;i ,\ f--- ;--,--- \- +-,-. ...l.. rr lii I ] I p I N I I "i ! •l ! : r>1+--1H-+-H--+--l-\+--IH-+-H-H ---t-+-+--+--+-t----iH----t---+---l----t---+---H ,~,b"'1\-Jo--' , ~---""-t----t----l' -!H-+--1 ~ 11 11 1-.;\-1---1--1---+-- l-+H~+t-+-++.l'l+-+-t-----l---+-l----tJrHH-+H~ ,1·--++-117'l-_;1s----+--, ~l -P\i ---t----r-+--·1--t----+--"I\- l---l--+---t---i-l'IW-1,,_,_____,_._____,_-t---l--J ----l--4-----t---= ~; !• ~ ' ~,___-+-+___,.,.R,,_:,.--'-'~• - H--'\_ ~ T I~ Dr,,. \ I~ I I~ 1----l-+-- ~, +t-+---i-+-<1,1 : :\_I\ ' I~ : ; I i; ~ -ij1----t---+--1"'=1,- .! -~ : < ~ ' ~' ! ' ---1 ' +--+'-Ncl--4----l_----, ,~ 1 H--1-----1----+1'Jf,,.--H----t---+---lt-,1---+---,~ -1 r --+ - --t-• , ---"'a-1-~t-----+---1--+---,.,,+-+-+'i_._.,,,___+ ,_,;~-+--+---»,--+--+-1 +--l----+---I---+ l--l"--'=-1----H----l'>-J----+--,...-l-\-f~'-c.!---l'-.--f----t---+--l----t---'-'1',-1"', : ~ ~ 58 depends only on the nwnber of unaged layers initially deposited. This fact is clearly brought out if one correlates the slopes of different curves with the bracketed nur,ibers accompanying them, particularly in fig. ( 19) in which one sees the remarkable parallelism of all 8 curves. The quantitative dependence of the recombination coefficient (k) Oil the number of unaged layers is shown by fig. 2S. (k), the slope of the curves in fig. 19, 20 and 21, is plotted l again~ the number of unaged layers. r Each point in fig. 21~epre- sents the mean of a number of neighboring ones. One sees that the greater the number of free and lL~combined particles present the greater the rate of recombination. This fact strongly suggests that free particles on a surface obey the Mass Law. Furthermore the remarkable linearity between (k) and thickness enables one to say that k; k'd + c', where k' and c' are universal constants of the film, and (d) is film-thickness. (B) Dependence of Resistivity on Time - Thin Films on Calcite. Fig. 22, 23 and 24 represent the aging of films with thiclmesses up to 330 layers. The data from which these curves are plotted is given in section II of, the -Appendix. The same con- ventions, scale and markings apply to these curves as to the previous ones. (a) Aging of Thin Films. The aging of thin fiL'11S (greater than 50 la~ers) is like I ·1 I 11 I J I "J a -•~~..-_1+--l--l--l-~+ , l(,_,.J-+-+-+-+-HH-l--l---l--+-+-+--l-,~o,J...+l~~~,+~IT " -+--+-+-1 / µ' IL f ;j,.; fit 1\ '/ ..,, [1/ "'+ffil+l.,tt;.±i. /t.,r+--t-,;-t-t--+---tr... -+....,_r~.-+--+----+r-~111"ir¥--+-!-l.. +..,- .-1:i:r::"t-""ffif ' "° :-+.lf:--+-+--th -it; t!:!.,-,t---t--1 ti ·:. ffiltf 1/c'/ /_ I!' :fc c/ 'I• © = m Ltt ia· ""1 H;.it ~- #I rm " . :tt 1 P-_ , ~\ .. 15:c ··• ~ --..; '<:; •;,;:: fiL R:; il~-§;: b: c,, l.,f t R It:, ,i l;J, ' ft !++ llJ ~ •- • :r.< i,t 1 • •• I~ rt .. ~./ ' I'™ le!/, ,.i : ill 'f 11.l' ' t,ti 'if I~ 1,lcµtr !fl! ijj; I R . .tlJ:.FJiH;"!<.fL ~- 1ft' _, .. :tli 1, I) fl :j; I tc .n" 1 ~.f:r>- "' f 1· r,, DI! r V l:!A' r; Ii f J 1!1' {.. ·t,,.';' ·; i+· .~ Jij ;111# ti± :a ' . if. fi • , '£.lm,li+,, ITT 1 , ./l 11 . j 'tJ 17 110 .:-!! j.fitt± Ji .rt ,1 f!!c' m .:/.,, Gl 'I,~ · ri if ':' CJ,' •l;l ,i: 1 ~:' / ,, h i , , , . )' r?/: , r:1 ~ F. M". !"°J. ich v,r.c ~ i- r1A1.; I ~ PZJ [q,1/l rA ' 1:tf'j ,,g w,1;:i µ., 11.. I/ ff.4..,Jfl:._·j__,~_j__,k'.11/.,• i_'...1T~li:_J ' Jl,:t''.__1,·-1.,~¥~YJQ':~r'A.,...l~~A·~ J ·4i-c.,(""P'.t;!A.'<LfJ,,.~ " '"":..JZ lr,~Vr+ +J~4,£'.4,;;-LJt, , /115 :10 , 1, l ) f-"'J---l='IF-J+J..,iV - "--j-"'-h-"+'-±-f'--,-J C.,f,c+,-e,f-"--j/ - ' / ,= I ,j: /.o ; 7,IJQ I/ ,2 .4 .6 .8 ~-+-, 'I T l/,:lc -,f-<--+-t---+r- I /.4 I(, Fig, 26 18 .Z.o -+ -- 59 that of extremely thin filras (less than 50 layers) in that the res~stivity always increases with time; but quite unlike them, in the shape of the aging curves. We find as the thickness in- creases that the straight-line agtng curves become parabolic. This fact is shown in Fig. 23. Curve (I) is a straight line -and represents the aging of a film 8.oe layers thick, and curves VTII and IX in Fig. 24 are decidedly parabolic. The parabolic relationship is most clearly brought out in Fig. 26 in which log (NR) is now plotted as a function of log (t) rather than of just (t). These parallel straight lines show that now R =Kt+ c, where (K) and (c) are constants. There has evidently been a transition from the aging 1aw: log NR = kt+c to: R =Kt+ c. The last relationship is exactly the one derived for thick films on page 20 on the assumption that the fiilm• was composed of a number of relatively large neighboring patches, and that these were undergoing a uniform rate of contraction in area with time. The difference between the supposed mechanism of aging of extremely thin films and of thin films is that for extremely thin films we have the recombination of particles of comparable size; whereas for thin films, a coalescence or contraction of large patches covering most of the surface. (b) Coefficient of Recombination of Thin Films. (1) Dependence of Recombination Coefficient on Number of Unaged Layers. 60 The dependence of the coefficient of recombination on the number of unaged layers, for thin films, seems to be much the same as for extremely thin ones. Both cases show a larger coefficient of recombination with the presence of a larger number of unaged _layers - or what is the same thing: with the presence of a larger number of free and uncombined particles; e.g. take points XI, XIII, XIV, XV in fig. 27. It is seen that (k) is lowest when the number of uncombined layers present is least. This indicates that the recombinations, also in thin films, follow the Mass Law. (2) Dependence of the Recombination Coefficient on Film-Thickness On the other hand the dependence of (k) - the coefficient of recombination - on thickness, for thin films, is quite different fron1 that for extremely thin ones. For thin films, refering again to figure (27), there is a decided increase of (k) with thickness, irrespective of the number of unaged layers present; for extremely thin films, (k) was independent of thickness. (E) Dependence of Resistivity on Film Thickness - Calcite Backing 11he dependence of resistivity on thickness for extremely thin films (thickness up to 50 layers) is shown in fig. (28) and -Ltu...'.,.. for thick films (thickness up to 330 layers) in fig. (29). One sees that there is an increase of resistivity with thickness up to about 50 layers in both figures, representing results from two independent runs. Thereafter the resistivity remains approximately constant up to 250 layers, whereafter it I i J k:'.'. ' V I .,I I /{, . I I + ·r- c- I~ If L C 9l 15. ~- r, ..-,, tr ',.f'--r-t--;('!/-. r-r-c-r-t-r-t--t-+- _j;;-Cl 9f::::'Jfl ".l;·4/II q 1v"--i--i---i-,---,--i---r,---,-""11r-'ffi•-r· ~·' ~·, d _,v , 1~P 6 . ,/ t 14 I ll.d / 10 Zo 30 -to ,5lJ 6o 70 Fi g . ~O - ~.:,___ ____________ _ i ♦ i ; ! ! I I L i l I I i I i I f I i ' I l .I ;. OF AG~W l G 1). 1w _ A _( ALCif/"t: • i I 1 5o loo T I i - ''I I - I i ! '---'- - ' I j 150 I ·-· - -t - -+ 6u "FAC~. - f - 200 ~ FIG. 29 300 350 61 suddenly drops, and would no doubt have continued to do so had the measurements been carried to greater thicknesses. (F) Dependence of Resistivity on Time - Ag Films Deposited on Glass', on .Amorphous Surface. The dependence of resistivity on time for li.g films - with an average number of layers from 27 to 343 - deposited on glass is shown in fig. 30. that for calcite: The dependence is a great deal like Initially there is an apparent linear relation- shi~ of log(NR) and (t), which later merges into a parabolic one. (G) Dependence of Resistivity on Thickness - Ag Films on Glass. The dependence of resistivity on film thickness is shown in figure 29. Again, as on calcite, there is the sudden drop · around 300 layers; but unlike a film on calcite, there is a continuous increase of resistivity up to 300 layers. (H} Ohm's Law and Thin Films It is here found that thin films do not obey Ohm's Law when by this one means that doubling the applied voltage will double the currents through the film. to the findings of Perucca(BO}. This statement is contrary He sputters (Au) onto a quartz fibre and happens to measure its resistance at the same voltage we use for (Ag). He finds that Ohm 1 s Law is obeyed. During the present investigations it was found that changing the voltage as little as 10 above or below the normal value applied to it during the run would cause as much as a thousandfold' increase or decrease in the current, whether the film was 62 deposited On glass or oil , calcite. The observations made may be briefly summarized: If the film normally has been kept at a potential difference of 60 volts and the voltage is suddenly dropped to 50, then a manifold decrease in conductivity will be observed. This condition is not stable and after sometime - 10 to 15 minutes or more - the conductivity apparently rises to its former value, at least in order of magnitude. If now the voltage is brought back to 60 its con- ductivity invariably rises many hundred-fold its original value. (I) General Conclusions. · The increase of resistivity with thickness - for Ag on calcite up to about 50 layers, followed by a sudden drop at 250 layers; and for (Ag) on glass, a continuous increase up to around 300 layers, followed by a sudden drop - points to the fact that the atoms deposited at random, limdergo a process of agglomeration and coalescence. Immediately~ after the initial deposit of atoms, a process begins in which each atom combines with its nei ghbor, forming nuclei over the entire surface. These nuclei in turn combine with . each other until a few large isolated nuclei are formed, giving the film an abnormally hi gh resistivity. Now, as the amount of the deposit increases, these nuclei increase in size until they become relatively large isolated patches. And finally, with in- crease of size, they make contact with each other, thus accounting for the decided drop in resistivity found at 250 layers. 63 The above picture for the mechanism of aging, was used as the basis of two formulae derived earlier in this paper, to account for the trend of resistivity with increase of time. The.s e were : ( 1) for extremely thin films log NR = kt + C, and (2) for thin films R = Kt + c. 'l'heir remarkable success in describing the experimental results is seen from a consideration • of fig. 19, 23 and 26. This seems to amply justify the proposed mechanism of aging. Such a dependence of resistivity on thickness as here found has never before been observed, as far as I know. Others invariably find an infinite resi sti vi ty up to about 25 layers. In this range we find a finite resistivity which increases with thickness. The explanation for the disagreenmnt of our results with those of previous investi gators - besides the fact that their experimental methods were open to grave criticisms, as pointed out in the introductio;n - lies partly in the fact that theirs were obtained from unstable films that had been allowed no time to age. To be sure the critical th.ickness - approximately the same for (Ag ) on both glass and calcife - at which the decided drop of resistivity occurs is only about 1/3 the thickness of the "Zwicky Block", for (Bi). But one must remember that there are no doubt variations of its size with the kind of metal; and ma.st important of all: the patches on the surface are probably not 64 flat disks at all, but pyramids. Now the volume of these are 1/3 that of a disk of the same height. This places the critical thickness found for (Ag) extraordinarily close to the size of the "Zwicky Block". Additional justification of the pyramid structure is that the resistivity of the filra on the latter part of the resistivitythickness-curve, beyond the c'ritical thickness, is many thousandfold that of the bulk metal. No doubt if the deposit had been increased sufficiently, the resistivity would have come very close to that of the bulk metal, and the pyramids would in time have become disks. Ha1nburger( 35 ) has derived a formula for the structure of thin films on strictly probability considerations, assuming that there are no force fields surrounding the atonIB, which might affect the motions of the atoms on the surface. The present re- sults show such an assumption is entirely erroneous, and cannot but lead to fallacious conclusions. In fact by its use I haven't been able to get anything but decidedly negative resistivi ties for extremely thin films, which as the thickness increases becomes abnormally hi gh positively. Contrary to the statements of everyone else, as far as I know, who has studied conductivity as a function of thickness, I do not believe that thin films have abnormally high resistivities. I believe that the patches of which the film is composed, have a resistivity quite comparable with that of the bulk metal. On the 65 basis of the film structure here postulated it is Quite evident that the resistivity one nl:lasures is not simply that of the film but is really a combination of two ,resistances: (1) the high resistance of the backing, and (2) of the metallic patches, In just what proportion each of these two contribute to the resultant resistance was shown previously, in the derivation of the formula R =Kt+ c, For all thicknesses of films, at least up to 330 layers of Ag on cal~ite, there is a definite dependence of the coefficient of recombination on the number of unaged or uncombined atoms deposited onto a surface. The general conclusion is that the rate of recombination increases with the number of uncombined atoms present. This seems to be none other than the well known Mass Law applied to thin films. For extremely thin films we found that k = k'd + c', in which (k') and (c') were universal constants for the film and (d) was the film thickness. This permits us to transform the aging formula log (NR) =kt+ C so as to apply to all film thicknesses and containing but one arbitrary constant (C), instead of two as log NR = t(k'd + c') + C formerly. This expresses the dependence of resistivity on both time and thickness, with but one arbitrary constant. There is a decided dependence of the coefficient of recombination on thickness for the thicker films above approximately 50 layers, but none below this. The general conclusion to be 66 drawn is that for a small deposit the sublayers do not have much influence on the recombination coefficient, and that the reaction is determined principally by the number of available particles; whereas for larger deposits above 50 or 60 layers, both the sublayers, and the number of available particles exert a decided influence on the rate of reaction or the so-called recombination coefficient. 67 Su:rnma:ry Improved experimental methods have been developed enabling one: (1) to deposit metallic films by evaporation with a greater freedom from film-contamination than hitherto ever attained, (2) to measure film resistance up to 1015 ohms, and (3) to determine film-thickness, of monomolecular ord.e r of magni t11de, within an accuracy of 3 or 4%. With this apparatus it was possible to obtain experimental results radically differing from those by previous wo~kers. It is shown that their results are easily obtained when extreme care is not taken in the elimination of foreign atoms. ' , It is found ( for A:g deposited .on both calcite and glass) that re sis ti vi ty increases with thi'ckness up to 250 layers, (wi'thin the sa..'1le order of magnitude as the size of the Zwicky Block) and then very suddenly drops. This is accounted for on the basis of a coalescence of the atoms into gr.anules. On the basis of hypotheses made as to the structure of extremely thin films, two formulae are derived describing the aging effect. For thin films: log R =kt+ c; for thicker films (greater than 50 layers): R = Xt + c, where k, K, and care constants and (k) is the coefficient of recombination. It is found that the coefficient of recombination increases with the number of available uncombined particles, indicating that the recombinations on a surface are governed by the Mass Law. 68 From the dependence of the coefficient of recombination on thickness for extremely thin films it is found that log NR =kt+ c can be expressed as log(NR) = (k'd + c')t + c where k' and c' are universal constants for the film; where (d) is the film thickness; (N) the thickness of the film in layers; and (c) an additive constant of integration. The recombination coefficient seems to be independent of thickness when film is less than (50) layers in thickness but starts to increase decidedly when the film-thickness is greater. This indicates that the sublayers exert an increasing effect on the rate of recombination of atoms, as the thickness of the sublayers increases . .And, finally, Ohm's Law does not hold for thin films. Acknowledgements It is a pleasure to tender to Dr. Goetz my best thanks for suggesting this problem and for his sustained interest during the course of the investigations. In conclusion, the author wishes to express his deep ~ gratitude to Dr. R. A. Tutillikan for havi ng initiated these investigations. 69 Bibliography (1) R. M. Ho·l .mes, Phys. Rev., 22, (1923). ( 2) Mackeown, Phys . Rev. , 21, (1923) and ·23, ( 1924). ( 3) Vincent, Ann. d. Chemie, 19, ( 1900). (4) Moreau, Jour. d. Physik, 10, (1900). (5) Wait, Phys. Rev., 19, (192~). (6) King, Phys. Rev., 10, (1917). ( 7) Peacock, Phys. Rev. , 27, ( 1926) . (8) 0seen, Zeit. (10) Reide, Ann. d. Phys., 45, (1914). (11) Reide, Zeit. f. Phys., 28, (1924) and 48, (1928). (12) R. L. Edwards,. Phys. Rev., 29, (1927). (13) K. J'. Miller, Phys. Rev., · 32, (1928). (14) Jewitt, Phys. Rev., 16, (1903). (15) .r. Howey, Phys. Rev., 24, (1929). (16) Richtmeyer and Curtiss, Phys. Rev., 15, (1920). (17) G. iV. Stewart, Phys. Rev., 17, (1921). 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