L. G. SCHULZ

Eq. (5), which was used to calculate k, is concernedwith reflectivity. The information given by any re-flection experiment is limited to that part of the surfacelayer to which the incident energy penetrates. Recenttheoretical work21-13 has shown that when the meanfree path of the conduction electrons in the metal ismuch longer than the skin depth, anomalous skineffects can be expected. In particular, the value of kdetermined by a reflection measurement will be lowerthan the bulk value. It was found that transmission

21 G. E. H. Reuter and E. H. Sondheimer, Proc. Roy. Soc.(London) A195, 336 (1948).

22 T. Holstein, Phys. Rev. 88, 1427 (1952).23 R. B. Dingle, Physica 19, 311 (1953).

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

experiments24 gave higher values of k than did reflectionexperiments but only in the region where absorptionis caused primarily by free electron damping. Includedon the graphs in Figs. 4 to 7 are the k values calculatedfrom the Drude free electron theory.6 For Ag at thelongest wavelengths, the experimental values approachthe calculated ones; for Au the deviation is more pro-nounced; and for Cu a big difference remains even at1g. The case of Al is exceptional in that effects otherthan those due to free electrons are appreciable evenat longer wavelengths.

This research was supported in part by U. S. AirForce Contract Number AF33 (038)-6534.

24 To be given later.

VOLUME 44, NUMBER 5 MAY, 1954

Optical Constants of Silver, Gold, Copper, and Aluminum.II. The Index of Refraction n

L. G. SCHULZ AND F. R. TANGHERLINIInstitute for te Study of Metals, The University of Chicago, Chicago, Illinois

(Received November 12, 1953)

The reflectivities of Ag, Au, Cu, and Al were measured at an angle of incidence of 450, in the wavelengthrange of 0.4 0,u to 0.9 5/u at glass-metal and air-metal interfaces. These reflectivities, together with previouslydetermined values of the absorption coefficient k, were used to calculate the index of refraction n. Sampleswere prepared by evaporation and deposition from the vapor. The important experimental results are:(1) The ratios of the reflectivities in the s plane to those in the p plane agreed with the theoretical values.This result indicates that the boundary conditions required for the application of the equations of electro-magnetic theory have been satisfied. (2) Ageing and annealing resulted in increased reflectivity at bothair-metal and glass-metal interfaces. (3) The values of n obtained from aged or annealed samples werein many cases considerably lower than previously published values.

INTRODUCTION

THE experiments which will be described wereT undertaken for three reasons: First, to developmethods for the accurate measurement of reflectivity;second, to use the method to obtain more accuratevalues for the index of refraction of metals; and third,to explore the possibility of using oblique illuminationfor studying the structure of metal surfaces. Althoughit was not the purpose to develop alternatives to theusual polarimetric method' for determining opticalconstants, it was found that new methods are capableof giving results comparable to, or superior, in accuracyto those found with older methods. The value of theabsorption coefficient k determined earlier,2 togetherwith the index of refraction obtained here, makesavailable a complete set of optical constants. In additionto their interest in the field of optics, accurate deter-minations of optical constants of metals are of impor-

I W. Knig, Handbuch der Physik (Verlag Julius Springer,Berlin, 1928), Vol. 20, Chap. 6.

2 L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954).

tance in the theory of metals.3 -6 Much of the experi-mental work involved a study of the effect of annealingand ageing on evaporated metal films.

PREPARATION AND ANNEALING OF THE SAMPLES

The metals were deposited from the vapor in avacuum of about 10-5 mm of Hg onto part of each ofthe hypotenuse faces of right-angle prisms (see Fig. 1B).Ag, Au, and Cu were evaporated from shallow v-shapedtroughs of sheet molybdenum, and Al from 40-miltungsten wire. The deposits were usually about 1500Ato 2000A in thickness, i.e., considerably more thanopaque.

Since the part of the metal deposit in immediatecontact with the glass substrate is of great importance,every effort was made to keep the glass-metal interface

3C. F. E. Simons, Physica 10, 141 (1943).4 F. Seitz, Modern Theory of Solids (McGraw-Hill Book Com-

pany, Inc., New York, 1941), Chap. 17.5 N. F. Mott and H. Jones, The Theory of the Properties of

Metals and Alloys (Oxford University Press, New York, 1936),Chap. 3.

6 A. H. Wilson, Theory of Metals (Cambridge University Press,Cambridge, 1946), Chap. 4.

362 Vol. 44

INDEX OF REFRACTION -q OF Ag, Au, Cu Al

free from contamination. The metal charge was prefusedin an initial evacuation of the evaporation equipment;and in the second evacuation, during which depositiontook place, a movable barrier placed over the glasssurfaces intercepted the initial metal vapor. To minimizeroughness7 at the air-metal interface the metals weredeposited as rapidly as the equipment permitted, whichwas about 1000A in 30 seconds. A suitable jig was usedto support a unit of four prisms.

Annealing was carried out in a metallurgical typefurnace which could be evacuated to about 10-6 mm ofHg. The usual treatment was to heat a sample forperiods of 30 hours, the temperature for each periodbeing 20C higher than the preceding one. Reflectivitymeasurements were made between each annealingperiod. It was found that the maximum temperaturebefore deterioration of the films began was about 130C.Above this temperature the reflectivities in the s and pplanes no longer had the proper ratio. While not beingtested the samples were kept in a desiccator; the longestageing period was two years.

EXPERIMENTAL ARRANGEMENTS FORMEASURING REFLECTIVITY

The drawings of Figs. 1 (A) and 1 (B) show thearrangement of a sample formed from four right-angleprisms. In passing through the prisms the beam Biexperienced four total reflections at glass-air interfaces;beam B 2 , on the other hand, was reflected four times atglass-metal interfaces. By raising and lowering thefour prisms as a unit either B1 or B 2 could be directedinto a Pulfrich photometer' (see Fig. 2). The quotientof B2/B 1 is very nearly equal to the fourth power of theglass-metal-glass reflectivity (a small correction mustbe made for multiple reflections). For the case of ahigh reflectivity the four-prism sample was used, butfor lower reflectivities one to three of the sampleprisms were replaced by blanks (no metal on thehypotenuse face). For comparing the reflectivities oftwo metals the arrangement of drawing C and D wasemployed.

Reflection at air-metal interfaces was measured withthe arrangement of Figs. 1 (E) and 1 (F). The mirrors Ml,M 2 , and M 3 of drawing E were aligned so that thecenter ray of the beam leaving M 3 was continuouswith that incident on Ml. After measuring the lightintensity through the mirror system in both the s andp planes, the mirror M 2 was shifted to the position M 2

of drawing F and the sample (I, II, III, and IV) wasadded. The principle of the procedure is the same asthat used by Strong9 except that 450 incidence isemployed here.

7 R. S. Sennett and G. D. Scott, J. Opt. Soc. Am. 40, 203 (1950).8W. West, Physical Methods of Organic Chemistry, edited by

Arnold Weissberger (Interscience Publishers, Inc., New York,1946), p. 852.

9 John Strong, Procedures in Experimental Physics (Prentice-Hall, Inc., New York, 1938), Chap. 9.

(A) (B)

8 4~~~~~~~4

(C)

M2

(E)

(D)

(F)

FIG. 1. Drawings showing the optical path through the samples.The prisms of (A) and (B) were placed close to one another butnot in optical contact. The glass blocks of (C) and. (D) are shownwith four internal reflections in each, but they could also be turnedto give two or six reflections in each. These blocks were 4 in. X in.X 8 in. The sample of F labeled I-II-III-IV was formed from thefour prisms used in (A) and (B). The square face of each prismwas 1.25 in. on an edge.

The photometer, shown in Fig. 2, was equipped withfilters which had pass-bands about 70A in width athalf-maximum. (The wavelengths at which measure-ments were made are indicated in Figs. 6 and 7.) ANicol prism was added to the eyepiece to polarize thebeam in the s or p planes. Experience showed thatindividual settings of the photometer were accurate toabout 412 percent, and the average of several readingsreduced the probable error to 41 percent. A carefultest was made for stray polarization in the photometerand in the samples. With a polaroid placed in one beam(as shown in Fig. 2) and set with its transmissionplane vertical (or horizontal) the Nicol, when turned toa crossed position, transmitted less than 0.1 percent.When a sample of four glass prisms was added, thetransmitted light increased to about 0.1 percent, which

FIG. 2. Drawing showing how the sample, S or S', was insertedinto the Pulfrich photometer. A Nicol prism N mounted beyondthe eyepiece E made it possible to measure separately the reflec-tivity in the s and p planes. The polaroid, P or P', was insertedonly when testing the sample or the photometer for stray polariza-tion effects. F indicates the position at which the various filterscould be placed.

363May 1954

L. G. SCHULZ AND F. R. TANGHERLINI

.01

.00

-.01

AR -.02

-.03

-.04 _

-.05 - _

-.06 -t.01 .02 .05 .1 .2

n

could be used thereby making possible a study ofI variations over a sample surface. For accuracy and

I j/D~A. - . convenience, however, the Beckman spectrophotom-25/J- eter' 0 was found to be far superior. (A suitable mecha-

2// nism had been constructed for moving the samples.)-/ Also the wavelength range was extended beyond the

11.5 visible.

1.3 F =CALCULATIONS USING THE EQUATIONS OF// 2-. ELECTROMAGNETIC THEORY

The equations required to describe the reflection oflight at a dielectric-metal interface were selected fromthe complete list given by Konig.' The reflectivity is

.5 , 2 ! i indicated by R with s and p designating the two*5 I 2 ~' planes of polarization

FIG. 3. Graph showing the values of AR as a function of and k. The numbers on the curves indicate the k values. Note thatthe vertical scale for the positive AR region is different from thatfor the negative region. The calculations are for a vacuum-metal interface. To use the graph for the case of a dielectricother than vacuum, n and k must be normalized, that is, dividedby the index of refraction of the dielectric.

R,=R

a2 + b2_ 2a cosi+cos2i

a2 +b2+ 2a cosi+cos2 i

a2+ b2- 2a sini tani+ singi tanri

a2 +b2 +2a sini tani+sin 2 i tangi

(1)

(2)

is still less than the experimental error in the actualreflectivity measurements. The strain in the right-angleprisms, although too small to be found with the ordinarycrossed polaroid method, was easily detectable when aknife edge was used in conjunction with the polaroids.A further check of the prisms was made by comparingthe transmission in the s and p planes for glass-air-glass reflectivities; they were always found to be equal.Parts could be interchanged, such as the sampleshifted from one beam to the other, without any changein the results. By securing a sample to a metal base itcould be turned so that its plane was either horizontalor vertical.

The chief advantage of a visual type photometer forexploratory work is its extreme flexibility. For example,by a suitable arrangement of lenses a very fine beam

1.00

.99

10 20 30 40 50DEGREES

FIG. 4. Graph showing the variation ining angle of incidence for a particular seino. Note that at 450 the value of R,2 is et

The angle i is the angle of incidence. The two variablesa and b are defined by the following equations:

1a2

= - {[(n 2-k2-no 2 sin2j) 2 +4n2 k2]12no 2

+n 2 -k 2 -no 2 sin2 )}, (3)

b2 = ( [ (2

- k 2 - no2 sin2i)2+4n 2k2]12no2

-n 2 +k 2 +ne sin2 i}. (4)

Here k and n are the optical constants of the metal, andno is the index of refraction of the dielectric (glass orair). For normal incidence (i= 0°) both R, and R, reduceto Ro which is given by

k2 + (no-n) 2

k2+ (no+n)2

When i 2 and no2 are small relative to k2, a furthersimplification is possible:

_Ro= 1-4non/k 2 . (6)

_ Ott . Since it is inconvenient to solve Eq. (1) or (2)explicitly for n in terms of R, (or R,), k, no, and i, the

X-| ]- - - experimental data, R and R, were combined in a/I manner which made it possible to use the much simpler

-_ -1- Eq. (5). A preliminary step was to define a new reflec-tivity, R= (R 8+R,). Since the difference AR=Ro-Ris relatively small, R was used in Eq. (5) to get aprovisional value of n. This n was in turn used to obtain

60 70 80 90 AR from the graph of Fig. 3. Figure 4 has been includedto show the manner in which the various R's depend onthe angle of incidence.

reflectivities with chang- --t of values for k, n, and 1 H. H. Carey and A. 0. Beckman, J. Opt. Soc. Am. 31, 682iual to R,. (1941).

R, U Ro _

.96 H

fl100~~~~~00* ~ ~~~~~..94 n-~o_

.93 ngioO

8

I' -"� Rps R

364 Vol. 44

-

INDEX OF REFRACTION 7 OF Ag, Au, Cu, Al

The method of calculating just described makes use ofthe average of R, and R,; a second method of combiningthem is to take their ratio. It is evident from Eq. (1)and (2) that RR2/R is equal to unity when i is equal to45°. Accordingly, the value of Rs2/R was used as atest to determine whether or not the reflection interfacessatisfied the boundary conditions assumed when Eqs.(1) and (2) were derived. The assumptions of particularinterest are that the interface be plane (not rough) andthat at the interface the optical properties changediscontinuously (no gradients). These conditions aresatisfied in a practical way when the roughness ampli-tude and the thickness of the transition region are verysmall relative to the wavelength of the radiation.

When using Eqs. (5) or (6) it is advantageous to keepin mind the relative magnitude of the quantitiesinvolved. Since for the metals being studied here k2 wasusually large relative to i2, the discussion will bebased on Eq. (6). It might appear from this equationthat the calculated n value would be very sensitive tok because k appears to the second power. This is indeedtrue, but k is known to a few percent, whereas 1-R isonly crudely known. It follows that in regions of highreflectivity any reasonable k value is sufficient, but thatit is highly important to measure R accurately. Sincethis is difficult, the percent error for n will usually bemany times that for k.

Because of multiple reflections between the fourprisms composing a sample, it was necessary to add acorrection to R and R 2/R,. This correction wascomputed on the basis of intensity addition. Theresults are shown in Fig. 5 for the case of all fourprisms metallized. Similar graphs were constructed forthe cases of less than four prisms metallized.

DISCUSSION OF RESULTS

Because there is no particular use for reflectivities atglass-metal interfaces measured at an angle of incidenceequal to 45°, the discussion will be concerned only withthe n values calculated from these measurements.Before considering actual cases, several general featuresof the results will be discussed.

If the experimental values of R,2/R, did not agreewith the theoretical (unity for i equal to 45°) to withinthe accuracy of the measurements, the sample wasconsidered unsatisfactory. Usually the deviations ofR, 2 /R, and R were in the same direction; both wereeither too high or too low. Annealing at temperatureshigher than 150C produced the highest values of R,but such values were not used to calculate n becausethe associated values of R 2/?R1, were above unity bymore than the experimental error. The exact nature ofthe sample defect in these cases was not discovered.On the other hand, when a sample was defectivebecause of surface roughness, both R 2 /R and Rwere low.

It was assumed that evaporated films formed onsubstrates at room temperature would be strained and

1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 0R

FIG. 5. Graph showing the corrections for the errors due tomultiple reflections between the prisms. AR and A (Rp2 /R,) areto be added to the experimental values of R and R,'/Rp, respec-tively. Included on the graph is the fractional error in R. (Thisgraph is for the case of a 4-prism sample with all prisms metallized.)

would contain crystal defects."- 3 The effect of anneal-ing or ageing was to remove these strains and defectsthereby producing a higher reflectivity and thereforea lower value of n. For a given metal there was alwayssome variation in the R measured on freshly preparedsamples both for the air-metal and the glass-metalinterfaces. The effect of ageing or annealing was tomake all such samples identical to within the experi-mental accuracy. Whereas the n values of preannealedsamples tended to be lower for the air-metal than forthe glass-metal interfaces, the order was reversed afterannealing. This suggested that the strain was initiallygreatest at the glass-metal interface. The best values ofn (the lowest) were obtained from glass-metal measure-

TABLE I. Values of the index of refraction n for Ag, Au, Cuand Al. These values are based on glass-metal reflectivitiesmeasured with a Beckman spectrophotometer on samples whichhad been annealed or aged and which satisfied the conditionR.'= R,. The numberlof samples (a sample consists of 4 metallizedprisms) for each metal was as follows: For Ag, 4; for Au, 2; forCu, 2; and for Al, 4.

X () Ag Au Cu Al

0.40 0.075 1.45 0.85 0.400.45 0.055 1.40 0.87 0.490.50 0.050 0.84 0.88 0.620.55 0.055 0.34 0.72 0.760.60 0.060 0.23 0.17 0.970.65 0.070 0.19 0.13 1.240.70 0.075 0.17 0.12 1.550.75 0.080 0.16 0.12 1.800.80 0.090 0.16 0.12 1.990.85 0.100 0.17 0.12 2.080.90 0.105 0.18 0.13 1.960.95 0.110 0.19 0.13 1.75

P1 P. G. Wilkinson and L. S. Birks, J. Appl. Phys. 20, 1168(1949).

12 Eber Halteman, J. Appl. Phys. 23, 150 (1952).13 R. Suhrman and G. Barth, Z. Physik 103, 157 (1936).

365May 1954

L. G. SCHULZ AND F. R. TANGHERLINI

5000 6000 7000

1.02

1.01

1.00

.99

0.

-C's (n

.98'4000

1.03

1.02

1.01

1.00

.99'4000

5000 6000 7000

5000 6000 7000

WAVELENGTH IN ANGSTROMSFIG. 6. Graph (A) shows various values for a Ag sample together with the results of two older measurements. Graphs (B)

and (C) show R8 /RP values for the same sample.

ments on aged samples; these values are given in TableI and Fig. 8.

Figure 6(A) for Ag illustrates some of the generaleffects just mentioned and also for comparison givesresults of two older investigations. 4 ,"5 Measurements

n

1.4

1.2

1.0

.8

.6

.4

.2

0 4000

on the air-metal interface after annealing are not shownsince it was assumed that exposure would alter theunprotected metal surface. It is evident that when thevalue of is small (reflectivity high), ageing causesreductions of it of nearly 50 percent. Figures 6(B) and

1.1

1.0

.9

R'/Rp

.8404000

7

.6

.5

5000 6000 7000A 404000

5000 6000 7000

5000 6000 7000

WAVELENGTH IN ANGSTROMSFIG. 7. Graph (A) shows various n values for one of the Cu samples. Graphs (B) and (C) show the R8

2/Rp values for the

air-metal interfaces of samples of Pb and Sn respectively.

14 R. Kretzmann, Ann. Physik 37, 303 (1940).15 Georg Hass, Optik 1, 2 (1946).

.22

.20

.18

.16

.14

n.12

0..10 0-

.08 -k

.06

.044000

0-1-c"'-Tr I 0T kPb-AIR

l l l l l

[ l b l

r

366 Vol. 44

INDEX OF REFRACTION OF Ag, Au, Cu, Al

6(C) show that the ratio RS 2 /R, on the average wasnear unity even for fresh samples but with ratherpronounced deviations at certain wavelengths. Aftertreatment these deviations were no longer observed.It was found that both ageing and annealing producedincreased reflectivity, but ageing gave the most con-sistent results. The initial change with time wasapproximately linear, but there was a leveling off afterabout six months.

Although the k values of Kretzmann'4 and of Hass 5

are in good agreement with the new values reported inPart I, their n values are considerably higher than thosein Fig. 6 (A). This is understandable since k is dependenton the density of free electrons in the metal 4 which isprobably independent of the structure defects. On theother hand, n depends on the conductivity of the samplewhich is highly sensitive to the presence of strains anddefects in general.

Figure 7(A) for Cu shows, in addition to generaltrends, the effect of annealing on regions both of highand low values of n (low and high values of R respec-tively). For comparison purposes, the values of Lowery6

are included as they are among the lowest found in theliterature; the values of Tool17 and Meier' (Part I)are rather high.

In all essential aspects the results for Au (Table Iand Fig. 8) are similar to those of Cu. It was observedthat annealing changed the color of a film slightly:A fresh deposit was slightly orange in appearance, butafter an annealing treatment this changed to the typicalyellow of pure Au.

For Al comparison data exist only for the visibleregion. The new results (see Table I and Fig. 8) arelower than those of O'Bryan1 5 but somewhat higher thanthose reported by Hass.5 Although the reflectivitiesof glass-metal interfaces of Al samples increased some-what with ageing and annealing, the change was lessthan for the other three metals. Using the data ofTable I and Table II of Part I the calculated reflectivityat normal incidence for a vacuum-Al interface in thewavelength region of 0.40/i to 0.45,4 was 0.905 which ishigher than the experimental result of Strong9 (0.900)but lower than that of Haas5 (0.915).

DISCUSSION OF ERRORS

Auxiliary experiments were performed to obtaingeneral information on several types of surface defects.To test the effect of surface roughness, measurementswere made on films of Pb and Sn (one 4-prism sampleof each). The air-metal surfaces of Pb films are grosslyrough relative to those of Ag, Au, Cu, and Al, but stillnot so rough as to impair image formation severely.Figure 4(B) shows that the R8

2 /R, values for theair-Pb reflection averaged about 0.90. This result

16 Lowery, Wilkinson, and Smare, Phil. Mag. 22, 769 (1936).17 A. Q. Tool, Phys. Rev. 31, 1 (1910).s W. Meier, Ann. Physik 31, 1017 (1910).

19 H. O'Bryan, J. Opt. Soc. Am. 26, 122 (1936).

suggests that in the group Ag, Au, Cu, and Al the errorattributable to surface roughness must be extremelysmall, even for air-metal interfaces.

Measurements on milky white Sn films which hadvery rough surfaces led to the results given in Fig. 7 (C).This graph shows that for long wavelengths there isless diffuse scattering than for shorter ones. For bothPb and Sn measurements on glass-metal interfaces,the R8

2 /R values were essentially unity. It was impos-sible to carry through the calculations for n becausereliable k measurements were not available. It wasfound that annealing had no apparent effect on the Pbsample but that ageing produced a noticeable increaseof the reflectivity of the glass-metal interface. Onewould expect a Pb film to be free from strain but notfrom lattice defects.

To obtain a practical estimate of the experimentalerror in the measurements made with arrangements

2.0n $ 4gMICRONS

FIG. 8. Values of n for Ag, Au, Cu, and Al. It is interesting tocompare the dispersion shown here in the n values with that ofthe k values shown in Figs. 4-7 of Part I.

(A) and (B) of Fig. 1, the results for Ag and Al werecompared with those given by the arrangement shownin Figs. 1(C) and 1 (D). It was found that the ratio ofreflectivities RAg/RAI as determined by each methoddiffered by about 0.2 percent.

When all possible sources of error were considered,the probable error kin in nf was found to depend on thevalue of n in the following manner: when n> 1.0, thevalue of A\n was ±t0.03; for n values in the range of1.0 to 0.4 the value of n was +0.02; and for n<0.4the value of An was AC0.01. Although these may seemto be small absolute uncertainties, the equivalentpercentage is very great. For Ag, for example, theuncertainty is 20 percent.

CONCLUSIONS AND GENERAL REMARKS

1. The present paper and the preceding one describeaccurate procedures for determining the opticalconstants of metals. With these procedures a new set of

367May 1954

L. G. SCHULZ AND F. R. TANGHERLINI

values has been given for the wavelength region of0. 4 5A to 0. 9 0 A.

2. It has been shown that the values of t obtained bya reflection method are very sensitive to the presenceof strains and crystal defects occurring in freshly pre-pared samples made with an evaporation technique.These defects can be removed, however, by annealingor by ageing to obtain the more nearly correct values ofi. The absorption coefficient k, on the other hand,appears to be independent of these defects (see Part I).

3. The ratio of reflectivities, Rs2 /R, at 450 angle ofincidence can be used to judge the suitability of adielectric-metal interface for reflectivity measurements.The samples used to prepare Table I satisfied thiscondition to within the experimental error of z40.005in R, 2/R,.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

4. As was emphasized in Part I, it is not alwayspossible to determine directly the bulk properties of ametal from surface measurements. Accordingly the11 values of Table I which are based on reflectivitymeasurements apply to the surface and may be slightlydifferent from the values associated with the interior.The k and n values of Part I and of this paper can beused for any real physical problem involving reflectionof radiation but cannot in general be used directlyto test a solid state theory of metals. The extent of thedifference in the optical constants measured at thesurface and in the interior will be considered in asubsequent paper.

This research was supported in part by U. S. AirForce Contract No. AF33 (038)-6534.

VOLUME 44, NUMBER 5 MAY, 1954

Optical Properties of Thin Films of Cadmium Sulfide

JOAN GOTTESMAN AND W. F. C. FERGUSONDepartzent of Physics, New York University, New York, New York

(Received January 8, 1954)

Thin evaporated films of CdS on glass were studied in the wavelength range 4000A to 7500A. Measure-ments of film thickness and reflectivity as a function of wavelength were used to determine the index of re-fraction and the extinction coefficient. Density measurements and aging tests were also carried out. Theeffects on film properties of a variation of the rate of deposition were investigated.

I. INTRODUCTION

INTEREST in evaporated films has been focusedmainly on the differences between dielectric or

metallic films and the bulk forms of the same substances.More recently, attempts have been made to extend therange of information about particular substances intospectral regions where these materials are too absorbingto be studied in bulk form.' Crystalline CdS has anabsorption edge at 5200A and is practically nonab-sorbing for longer wavelengths in the optical range.For wavelengths shorter than 5200A the absorption istoo high to permit direct investigation of the crystal.In the work described here, quantitative informationwas obtained about dispersion and absorption withinthe absorption region. Differences between the filmsand bulk CdS were studied, and an attempt was madeto determine some of the factors which affect filmproperties.

II. EXPERIMENTAL

The films, varying in thickness from 1200A to 6000A,were prepared on black glass specimens by evaporationin vacuum at pressures between 0.1 and 0.2 micron.Very pure CS powder (nonfluorescent) was placed in afused silica cell, and a flat spiral filament used as a

1 G. Hass and C. Salzberg, J. Opt. Soc. Am. 43, 326 (1953).

heater was suspended just above the powder. Slightdissociation of the powder apparently occurred duringevaporation, and the films became contaminated withsmall amounts of cadmium as described below. The sizeof the filament could be varied to change the rate atwhich the films were deposited.

The initial reflection measurements were made beforethe films were exposed to air. The specimen mountingwas designed to hold the glass substrate in a nearlyhorizontal position with part of its surface exposed tothe cell during deposition of the film. The specimencould then be turned to a vertical position facing theprism monochromator and photometer through a plateglass window in the vacuum chamber, and part of theuncoated surface could be exposed for comparisonmeasurements.

Reflectivities, for practically normal incidence, weremeasured by comparing the output of an RCA 931Aphotomultiplier tube for a parallel beam reflected fromthe film with the output for the same beam reflectedfrom the unfilmed glass surface. Since the dispersioncurve for the uncoated glass was known, numericalvalues of the reflectivity could be obtained for the filmon glass. A beam of 30A spectral width for yellow lightwas used to investigate the region of the spectrum be-tween 4000A and 7500A.

368 Vol. 44