Electroplated gold and copper contacts to cadmium sulfide

Electroplated gold and copper contacts to cadmium sulfide


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1 (1964) 5470;

@I North-Holland


Co., Amsterdam


A. M. GOODMAN RCA ~abora~o~je.~,Pri~e~~ff~?, N. J.

Received 25 Aoril $963 Rectifying contacts have been prepared by electroplating gold and copper onto crystallographically oriented, single crystal, cadmium sulfide blocks. Differential capacitance, current-voltage, and photoelectric measurements were made in an attempt to determine dyl, the net work function of the metal with respect to the semiconductor at the contact. The differential capacitancemeasurements could be interpreted in terms of a unique value of dp for any given contact. However, neither the current-voltage measurements nor the photo-electric measurements could be easily interpreted in terms of the simple Bethe diode theory for a single value of &J. It is concluded that there is good evidence for the existence of patches of different Ap at plated gold and copper contacts to cadmium sulfide. The effective values of& determined by the different measurements range from - 0.75 to 1.2 volts for gold and from * 0.6 to 0.S volts for copper.

1. Introduction Williams and Bubel) have shown that copper, gold and other metals electroplated onto the faces of conducting cadmium sulfide crystals produce rectifying metal-semiconductor contacts. Their attempts to estimate the value of LIP (see fig. 1) at a copper-cadmium sulfide contact were inconclusive; i.e., two different values (0.4 and 1.1 V) were obtained from different considerations. The present work was undertaken to more closely characterize such contacts by measurements of their electrical and photoel~tric properties. Rectifying contacts were prepared by el~troplating gold and copper onto crysta~lographically oriented, single crystal, cadmium sulfide blocks. Differential capacitance, current-voltage and photoelectric measurements were then made in an attempt to determine dp. The details of the fabrication, measurements and interpretation are given in the following sections.

* The research reported in this paper has been sponsored U.S. Army Ordnance District, Philadelphia, Pennsylvania ORD-32X3RD 54

in whole or in part by the under contract DA36-034-







; F

Fig. 1.



level diagram for a rectifying with forward bias V.



2. Sample Preparation The metal contacts were plated on crystallographically oriented single crystal CdS blocks. The blocks werecut from a large single crystal boule purchased from the Eagle-Picher Co. Spectrographic analysis of two samples from the boule showed the following impurities in parts per million: Fe(0.3 to 3.0), Si(1 to lo), Mg(0.3 to 3), Cu( < I), and Zn(5 to 50). The blocks were rectangular in shape and approximately 2 x 3 x 6 mma, with the large faces oriented perpendicular to the 0001, lOi0, and 1120 axes. After cutting, the blocks were polished with Linde A and then Linde B abrasives to remove the saw marks. A schematic construction drawing of the samples is shown in fig. 2. Unless otherwise specified the following fabrication procedure was usually employed: The block was cemented to a glass slide with a transparent cement (Goodyear VPE200X). Measurements of the optical transmission of a typical glass-cement-CdS “sandwich”, as a function of wavelength, showed that it was flat within f 2% from 0.6~ to 2.4~. The sample was then etched in 9N HCl to remove the surface layer damaged in polishing. The surface adjacent to the glass was not etched since it was protected from the etch by the cement. Copper foil strips were cemented to the glass slide to provide ‘terminals’ for the ohmic contacts which were made by brushing on a liquid In-Ga mixture as shown. Glyptal was painted on to form wells on the CdS surface. Inside each well (usually two for each sample) a surface of N I to 5 x lo-” m2 was isolated for making the plated contact, The isolated sur-





faces were etched for one minute (by placing a drop of 6N HCl inside each well), washed with triple distilled water and air dried just prior to plating. The gold contacts were plated from gold cyanide solution and the copper contacts from acid copper sulphate solution in a manner similar to that described in ref. 1. A drop of plating solution was placed in the well so that it covered the CdS surface at the bottom. Connection was made from the




Fig. 2.




drawing of electroplated sulfide single crystal.




to a cadmium

negative terminal of a battery to one of the ohmic contacts and the positive connection was made through a platinum anode wire inserted into the drop of plating solution. The contact area was determined by taking a photomicrograph of known magnification and measuring the area with a planimeter. Sometimes the same block was used for more than one set of contacts. In these cases, the “old” In-Ga contacts were removed with KOH and the ‘old’ plated contacts were removed by dissolving them in KCN. The block was then repolished and re-etched and the original fabrication process repeated. The measurements to be described were generally made within 24 hours after the contact


3. Measurements 3.1.


and Preliminary Discussion


3.1.1. DifSerentiaE Capacitance The differential



C was determined

as a function

of bias voltage


V for each contact. been described

The technique

in a previous

01 -4 Fig. 3.






and details

of these measurements


paper2). A typical set of data is shown in fig. 3.






Variation of l/C” with bias voltage for gold-cadmium


sulfide contact Sal - 1.

A compilation of the results (bulk carrier density N, depth of the Fermi level below the conduction band in the bulk c, the “true” barrier height including the effect of the reserve layer Vm, and dqc = V,, + [) is given in table 1. A comparison was made on one sample between the value of N determined by the differential capacitance measurement technique and the carrier density value determined by a Hall measurement. The capacitance measurement gave N = 8.1 x lost m-s as compared to a Hall measurement value3) of (7.1 f 1.5) x 1021 m-s showing good agreement. The area values marked with superscript ‘a’ in table 1 may be somewhat

!; -4

Fig. 4.







of l/C2 with bias voltage for a gold plated contact to an unetched cadmium sulfide surface.

1.15 1.34 1.6 1.48 1.02 2.81

2.24 2.54 2.68” 2.08” 2.06’1 2.06

1.31 1.21 1.23 1.14 2.61 2.62

Boll - 3a Bal -5a Boll - 5b Bw.3-la Ba3 - lb Bal-5b

Ca2 - 4a Ca2 - 4b CM-2a CiuS - 2b Ca5 - 3b Cor8 - la

Sal -- la Sa3 -- 1 Sal-la So14-lb j Su4 .-4a So14- 4b



3.8 x lo-” ! 3.8 x lo-” 3.8 x IO-” j 5.8 x IO-”

0.79 0.77



0.86 0.85


3.9 % 1O-1 i 0.81 6 x 1O-5 / 0.87

0.122 0.127

0.805 0.93 0.750 I 0.88

I 1.2 x 1O-3 j

20 17


2.9 x 10-S 1.6 x 10-3

0001s FACE 0.850 0.96 0.840 0.97 0.895 1.02

55 21 20




j 0.89 i 0.83



/ 0.75


/ 0.79 / 0.78

! 0.77


0.88 0.83


0.77 0.73

0.80 0.79


4.2 x 10”



0.75 0.80



1.06 1.11


0.85 0.75




1.185 1.061



1.49 1.46




6 x 10” 1.18 / 1.56 3.8 % IO“ 1.09 ’ 1.18

x lo*

2.4 x lo5

10s 1.8 x 105

0.66 ! 8


i 0.87 0.76

0.76 / 3.6 x 104 1.10 -_ -


1.35 1.14


[email protected] !rt w

I 0.74 1.2 X 105 1.04 / 0.73 2 x 105 1.09


dp( -,-) flp(t f j d&O) j vi / fi co 09 !a 0’) (A/m”) WI

2.6 x IO--3 3.4 X IO--3 I 1.3 X 10-3 0.76 6 x 10-3 1.3 x lo-’ ’ 7.7 x lo-” ; 0.74


0.105 0.134 0.125

1.00 1.14 1.18 1.01 1.16 1.18


I 39 ; 13 18

0.164 / 0.835 0.156 0.985 0.159 1.025 0.155 0.855 0.154 1.005 0.153 : 1.025

1120 FACE

1.13 1.6 x IO-” 1.11 1.00 11.03 x lO+ 1.0 x 10.31 6.1 x 10-a 1.00 j 1.9 x 10-z 1.25 x 10-3 / 8 x 1O-4

I 2.5 x lo-” i 2.1 x lo-”


0.143 0.138 0.105 0.097 0.121 0.122

5:5 39 4.8 5.7 5.9 6.2


0.146 0.142 0.142


0.985 0965 0:860 0.855

i 0.142

3.9 5.1 6.8 6.4

!FACE / 0.96 / 1.02 ! 1.10 , 1.13 I

_ .__-.__



lOi0 / 0.164 0.795 j 0.158 0.865 0.150 0.950 0.152 0.975




1. Au plated contacts to CdS

OOOiC ’ FACE 1.005 1.15 4.5 x 10-j 1.9 x 10-5 / 2.3 x lO-5 0.970 / 1.11 6.7 x 10-j 1.6 x la-5 / 1.5 x IO-j 0.875 j 0.98 0.825 I 0.93 0.760 ’ 0.88 1.2 x IO-3 1.6 x 1o--3 I.0 x JOV 0.835 , 0.96




a) See text for explanation.

1.37 1.55 3.35 2.15 2.4 1.93 2.46 1.6


N ! Area r j (m? 2: IOF) i(10”“,/m3j W) - --___-_-_--__

- la -lb - 3a - 3b - 4a _ 4b - 5a -5b

An1 Aal Aa Aa Aa Aa Aa Au3








in error due to the etching pattern on the OOOIC surface as discussed in part IV of ref. 2. The other OOOlCsurfaces were etched only briefly to avoid this effect ; the resulting l/C2 versus bias voltage plots were straight lines. In a few cases, attempts were made to plate contacts to cadmium sulfide surfaces which had not been previously etched. The platings in these cases were poorly adherent and the plots of l/C2 versus bias voltage (e.g. see fig. 4) were not straight lines nor were they explainable in terms of the discussions in reference 2. This was not investigated further and all subsequent contacts were plated on etched surfaces. 3.1.2. Current- Voltage ~eas~re~~ent~ a) Saturation current density. If a rectifying metal-semiconductor contact is described by the Bethe413) diode theory, the current density J and the applied voltage V are related by eq. (1) J = Jo [eeyjkT-



where Jo is called the saturation current density and is given by J, = [4nm*ek2 T2/h3] e-eApplkT.


Here, k is Boltzmann’s constant, T is the absolute temperature, h is Planck’s constant, e is the magnitude of the electronic charge and m* is the electron effective mass in the semiconductor. The values) m” = 0.205 x free electron mass is used in this report. Experimentally determined values of Jo may be used as a measure of dv. The quantity Jo may be determined experimentally in a number of ways all of which should give the same value if eqs. (1) and (2) are applicable. For eV/kT 9 1, In J = In Jo + eV]kT. The value of J, may be obtained from a plot of in J vs. V by extrapolating the straight line portion of the plot back to V = 0. This value will be called J, (+). The quantity J, may be determined from the slope of J vs. V at V = 0. This value will be called J&O). From eq. (1) we have Jo(O)=?

‘; = . [ 1 Y


For eV/kT e - 1, the current density should equal the saturation value. This value will be called Jo (-). Jo{--) = 6%+-kr,e. The values of dfp corresponding to these values of Jo will be &led dp (+), dv (01, and dy, (-1. It is assumed that Schottky effect and tunnelling of electrons through the




are negligible.



This may not be a valid assumption5)

and may result

in the failure of J to “saturate” completely in the reverse bias direction. Even in this case, however, it is usually possible to get an “order of magnitude” measure of JO if there is significant rectification. The contacts were generally good rectifiers and typical characteristics are shown in fig. 5. The following observations are significant and will be referred to later in the discussion: The observed forward characteristics differ to varying degrees from the idealized behavior described by eq. (1). Empiri-








Fig. 5.

Current density versus applied voltage curves for typical gold plated contacts to cadmium sulfide. (Corrected for series resistance.)

tally, a more accurate description current density) is given by

(over 4 or more orders of magnitude


where the observed values of rl lie between 1 and 2, generally closer to I (see table 1). The value of q does not seem to be correlated wth orientation of the contact surface, measured barrier height, carrier density or any controlled parameter of the fabrication process. The significance of LIP values determined from a current-voltage characteristic for which q # I is not obvious. b) Resistance ~~rnite~forwa~~ current. If a rectifying metal-semiconductor



is biased


in the forward






the region

in which


current is limited by the series resistance, r, of the circuit, the current voltage curve becomes very nearly a straight line. The current-voltage curve in this region may be used to determine a value of A y, in the following manner: At an arbitrary current Zi, the resistive voltage drop rZi is subtracted from the terminal voltage V, (Ii) to obtain the voltage actually applied to the barrier, Vi. The current density corresponding to this point is Ji = ZJA where A is the contact area. The maximum forward current density which could Ilow through the contact if there were no barrier remaining is the unilateral random current density7) .Z, = $ NeC where 2j is the average thermal velocity of the electrons in the conduction band. It follows then (assuming Boltzmann statistics) that the actual remaining barrier at the current Zi is (W/e) In (MJZ,). The equilibrium barrier height (no applied voltage) is Vi + (kT/e) In (MJZ,). If the value of Ap determined by this method is denoted by Api, then Avi = 5 + (kTje) 111(AJ,/Zi) + 5


since v

= [8kT/nm*]*


= (kTje)111{2 [2xm*kT/h’]*/N),


we may combine

terms to obtaing) [,,,,cT’A] __

A~i = 5 + (kT/e)ln = v + (kT/e)ln

[1.2 x 106T2Am*/mZi]


where m is the free electron mass. It is clear from eq. (4) that the last term in eq. (5) must always be larger than [. To increase the forward current through quires (according to eq. (1)) an additional the barrier; the corresponding increase in plus the additional voltage drop across the stantrO)). It follows that r= where

V, is the terminal



- I’T(Zi) - kT/e [e - 1]Zi

A convenient



(see fig. 6) and

v, = e I’, (Zt) -


the contact by a factor of e reforward voltage of kTje across terminal voltage would be kT/e series resistance r (assumed con-

VT (eZ8) + kT/e (7)

e-l is obtained

by dropping

the kT/e term in eq.





(7); the error incurred[(kT/e)/(e - 1) z 15 mV at room temperature] is small enough to be neglected in many cases. A convenient graphical approximation is obtained by extrapolating the “nearly straight iine” portion of the current voltage curve back to zero current using the slope at Ii; the intercept on the voltage axis then gives Vi (approxi-


Fig. 6.

Graphical construction

for series resistance correction.

mate) as shown in fig. 6. A compilation of values of vi, Ji and dpi for some of the contacts is given in table 1. 3.1.3. Photoelectric Measurements The photoemission of electrons from a metal into a semiconductor or insulator has been discussed by Mott and Gurney ‘1) in connection with the work of Gyulaits). It was later observed by Gilleo13) and more recently by Williams and Bubei); in both of these cases a Fowler14s15) plot of the photocurrent near the long wavelength limit of the photovoltaic effect was used to determine the effective work function of a metal with respect to a semiconductor or insulator with which it was in contact. According to Fowler’s theory, the plot of log10 (photocurrent per absorbed photon) versus h (v - vo) 1 kT should be (to a good approximation) the function shown plotted in fig. 7a. Here, hv is the photon quantum energy and hvo is the work function of the metal, eAp. If the experimental data (plotted versus hv/kT) is shifted both horizontally and vertically to obtain the best fit, the value hvo is given by the amount of the horizontal shift. Alternately, the plot of (photocurrent per absorbed photon)% versus h (v - vo)/kT should be (to a good appro~mation) that shown in fig. 7b.






When h (V - vd)/kT 9 1, the plot should be approximately a straight line whose (extrapolated) intercept on the abscissa gives the value h (v- v~)/lcT = 0. If one plots the experimental data versus hv, then the intercept gives the

Fig. 7. :;

Normalized ~hotocu~ent functions according to Fowler’s theory. Fowlcr function F(x) or log10 [Photocurrent per absorbed photon] [Photocurrent per absorbed photon]*.

value hvs. This method of presentation of data has been used recently by Spitzer et a1.16) and Crowell et a1.17). Photoemission measurements of this type were made on several contacts. As expected, the photocurrent was found to be linear with light intensity. The results were quite similar and a typical example is shown in fig. 8. Also, a Fowler function with a threshold energy of 1.0 e?’ is superimposed upon the experimental points. The data cannot be fitted with a single Fowler function. One possibility is that there are patches of the contact with different work functions and a superposition of Fowler functions is necessary to explain the data. Let us first, however, consider the alternatives. The discrepancy between theory and experiment may be due to the spectral dependence of the optical properties of the gold. The experimental data in fig. 8 is normalized on a per incident photon basis whereas Fowler’s theory is based on absorbed photons. The spectral dependence of the reflection at a CdS-Au interface has not been measured but it is reasonable to assume that it would be qualitatively similar to that of an air-Au interface. The fraction of light at normal incidence which enters the gold (i.e., the light





absorbed) is 1 minus the fraction reflected. This is shown for normal incidence as a function of photon quantum energy in fig. 9 for both electrolytically deposited and vapor deposited gold films. Although the data for the electrolytically deposited gold (corresponding most closely to our experimental conditions) contains too much scatter to be quantitatively useful, it is good enough to allow the following observations: The shape of the ex-

I .o



I .6




hv (eV)

Fig. 8.

[Relative photocurrent per incident photon]+ versus photon quantum energy for sample Ba4 - 5b (light incident on contact through CdS).

perimental curve of fig. 8 above 1.65 eV might be explained by a corresponding variation in fig. 9. However, it is not possible to explain the break at 1.l eV in this way. Another possibility is that the spectral variation of optical absorption produces the observed data in fig. 8, since the closer to the surface an excited electron is produced by absorption of a photon, the higher the probability of its reaching the surface without energy loss and thus, the higher the probability of escape. Fowler’s theory does not take this possibility into account. Spitzer et al. 1s) have shown that the probability of escape of excited electrons from a gold film in contact with silicon decreases exponentially with the distance the electrons must pass through the film. They find that the “electron attenuation length” L for escape for dv, = 0.79 volts is N 740A. Quinn’s theory of the range of excited electrons in metalsls) can






be used to estimate a value of L N 57OA for LIy, = 0.8. It also predicts a very strong variation 18~~9)of L with A~Jsuch that for Ap = 1.O, the estimate value of L will decrease to about 375A. On the other hand, L for an excited electron escaping over a barrier of given Ay, does not vary strongly with initial energy. For example, if Ay, = 0.8 and the initial energy is between







0.““““““““’ 0.5


1.5 hv





Fig. 9. Optical properties of gold films. Data for curve 3 taken from Hagen and Rubens, Ann. Phys. 4th series, 8 (1902) 1. All other data taken from American Institute of Physics Handbook (McGraw Hill Book Co., Inc., New York, 1957) sect. 6, p. 104 ff.

0.8 and 1.6 eV, the estimated variation in L would be < 5OA. This would not explain the break at 1.1 eV in fig. 8. If the value of L and the optical absorption constant CLare taken into account, the Fowler function should be multiplied by the factor EL/ (1 + EL). In fig. 9, the photon penetration depth, c~-l, is plotted versus the photon quantum energy, hv. The variation in a is small and furthermore does not have the correct spectral dependence to produce the observed effect. Another consideration to be made is based on the assumption by Fowler’s theory of the Sommerfeld free electron model of a metal. Only intraband transitions are considered whereas in a real metal, strong interband transitions may become important. There is, however, no evidence for this in the





case of gold in the energy region of interest (< 1.6 eV) as can be seen from the absorption data of fig. 9. We are left with the possibility that the observed data of fig. 8 is at least partially due to a superposition of photocurrent responses for patches of the contact cussion

having 2 or more values of Acp. It is clear from the preceding disthat a quantitative analysis of the data of fig. 8 would be extremely




Fig. 10. Variation of l/C2 with bias voltage for copper plated contact to cadmium sulfide sample Ao12- lb.


Fig. 11.

Current density vs. applied voltage for copper plated contact sulfide (corrected for series resistance) sample Aa - 1b.

to cadmium


Fig. 12.


Relative photocurrent per incident photon versus photon quantum energy for sample AolZ - lb (light incident on contact through CdS).

diflicult and subject to many sources of error. The one possible exception to this is the straight line portion of the data below 1.05 eV where the optical properties are essentially constant. This leads to a value of d y, of approximately 0.8 volts for one ‘patch’ of the contact. Similar results were obtained with other samples. 3.2.



Only 2 useable copper plated contacts were fabricated. The data for the one showing the best current-voltage characteristic are shown in figs. 10,ll and 12. A compilation of the results for both contacts is given in table 2. The data for the differential capacitance and current-voltage measurements was quite similar to that for the gold contacts except that there was somewhat better agreement between the values of d 4(1obtained by the different measurements on the same contact and the values of d yt were lower than for the gold contacts. The photocurrent per incident photon did not fit a Fowler plot. It seems likely that this is largely due to the spectral variation of the optical constants of the copper. Although the data on the optical constants of copper electroplated from a CuSO, solution are not available, these data for commercial copper and evaporated copper films show large spectral variations which could partially account for the difference between our observed data and a Fowler plot, In any case, it seems reasonable to infer from




a) Poor saturation in reverse direction. b) q not constant. c) Photoelectric effect too low for useable signal-to-noise

the data of fig. 12 that the photoemission 0.7 and 0.8 volts.



value of Av is between

4. Further Discussion and Conclusions We have noted in the case of the gold contacts that the photoelectric measments strongly suggest the existence at the contact of patches of two or more work functions. In table 1, we note that there is a discrepancy between the values of Avc and the values of Aq (-), Ayl(+), and A p (0) for the various contacts with Ap, generally being larger. This is consistent with the existence of patches of different work function. Current-voltage measurements used to evaluate the saturation current density Jo would tend to “pick out” low work function patches whereas the differential capacitance measurement would tend to “see” an average value for the whole contact if the lateral dimensions of the patches were small in comparison with the space charge layer depth. Still another indication of the existence of multiple work function patches is the variation in the value of q for the various contacts. Johnson et al. 20) have shown that a distribution of patches of different work function can account for the type of current-voltage characteristic observed in the present work. For a given current-voltage characteristic, the patch distribution function is non-unique. The values of Ac,oidetermined for the various contacts are in general larger than the.Ay,(-), Acp(+), and A tp (0) values and are usually within 0.1 volts of the AC++values. This is consistent with the patch picture of the contact since the high forward current density in the Ayt measurement necessitates






conduction through high work function patches as well as through the low work function patches which were manifest in the determination of d v, (-), da, (+), and dq (0). If Ji is large enough, A~Q should be a measure of the highest work function at the contact. In practice, the upper limit of Ja is imposed by heating effects causing change (usually reversible) of the current voltage characteristic with time. All of the contact measurements cited thus far have been made within approximately 24 hours after the fabrication (plating) of the contact. Measurements of differential capacitance during the next few days after fabrication show insignificant (within experimental error) changes; however, after periods of 2 to 10 weeks, significant changes in the barrier height have been found. The changes do not always occur but when present are usually decreases in barrier height of not more than N 0.15 volts. Some preliminary work has been done in an effort to determine the reason for the observed changes. The results, however, are as yet inconclusive. The effective values of Ap determined by the various methods range from - 0.75 to 1.2 volts. The spread in these effective values of Aq for a given contact seems to be smaller for the contacts made to the planes perpendicular to the C axis (0001 cadmium and sulfur) than for planes parallel to the C axis. The physical significance of this is not yet clear although such effects are not unexpected because of the differences in surface structure. One interesting speculation which has been made concerns the way in which the location of the gold (or other metal) atoms “at the surface” of a semiconductor should affect the A~J values. If the metal atom sits “outside” the surface, one might expect a different value than if it were to sit in an interstitial position in the semiconductor immediately adjacent to the surfacezl). A metal “outside” the semi-conductor could also sit in more than one position giving rise to multiple Ay, values. This could provide at least a partial explanation for observed results. Further, a change in the structure of the contact such as a recrystallization of the metal layer or an increase in the number of metal atoms sitting in interstitial positions could explain the observed time dependence of Acp,,. The results of the measurements on the copper plated contacts require little comment; the agreement between Ay, values is relatively good. If there are patches of different work function, it seems likely that the spread in values is smaller than in the case of gold. In conclusion, there is good evidence for the existence of patches of different work function at a plated gold contact to cadmium sulfideaa). The effective values of A~J determined by various techniques range from N 0.75 to 1.2 volts. The range of Ayl values determined for the copper plated contacts is from N 0.6 to 0.8 volts.





It is a pleasure to thank R. Williams, A. Rose and D. 0. North for a number of valuable discussions during the course of this work. Thanks are due also to P. Mark for his critical reading of the original manuscript. References 1) R. Williams and R. H. Bube, J. Appl. Phys. 31 (1960) 968. 2) A. M. Goodman, J. Appl. Phys. 34 (1963) 329. 3) Both the sample and the Hall measurement value were provided by R. H. Bube of RCA Laboratories. 4) H. A. Bethe, Massachusetts Institute of Technology, Radiation Laboratory Report 43112. 5) H. K. Henisch, Rectifying Semi-Conductor Contacts (Oxford University Press, London 1955) Ch. VII. 6) J. J. Hopfield and D. G. Thomas, Phys. Rev. 122 (1961) 35. 7) C. Kittel, Introduction to Solid State Physics (John Wiley and Sons, Inc., New York, 2nd ed. 1953) p. 389. 8) See reference 5, Ch. II. 9) The same result could have been obtained by direct consideration of the thermionic emission from the semiconductor into the metal at a forward voltage & applied to the barrier. 10) This is a valid assumption in most cases. The situation where this is not true has been treated theoretically by Macdonald, Solid State Electronics 5 (1962) 11. 11) N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford University Press, London, 2nd ed., 1948) p. 73. 12) Z. Gyulai, Z. Phys. 35 (1926) 411. 13) M. A. Gilleo, Phys. Rev. 91 (1953) 534. 14) R. H. Fowler, Phys. Rev. 38 (1931) 45. 15) A. L. Hughes and L. A. Du Bridge, Photoelectric Phenomena (McGraw-Hill Book Company Inc., New York, 1932) p. 241. 16) W. G. Spitzer, C. R. Crowell and M. M. Atalla, Phys. Rev. Letters 8 (1962) 57. 17) C. R. Crowell, W. G. Spitzer, L. E. Howarth and E. E. LaBate, Phys. Rev. 127 (1962) 2006. 18) J. J. Quinn, Phys. Rev. 126 (1962) 1453. 19) J. J. Quinn, persona1 communication. 20) V. A. Johnson, R. N. Smith and H. J. Yearian, J. Appl. Phys. 21 (1950) 283. 21) A. Rose, J. Phys. Chem. Solids 22 (1961) 1. 22) In contrast, there seems to be no significant patch effect present for the case of vapor coated gold contacts to cadmium sulfide. This work is still in progress and will be reported at a later date.