Free-Carrier Absorption in Silver Bromide

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Free-Carrier Absorption in Silver Bromide

RALPH M. GRANT*

Reactor Institute Delft, The Netherlands

(Received 10 April 1965)

A small but clearly evident control of infrared light being transmitted through silver bromide has beenobserved by photoelectrically inducing free-charge carriers which absorb the transmitted light.

A CCORDING to the well-known Fan Frolichl 2modified Drude Zener formula for free-carrier

absorption between the fundamental absorption edgeand the onset of lattice dispersion

e2'cra (X1) = ' X' 2. (1)

4 7rlc 3 m*I/ud2 eoN

Here, a (X)=wavelength-dependent absorption coeffi-cient; oo= ne/id, the dc conductivity [n represents thenumber of free carriers, e the electronic charge, andAd the drift mobility of the free carriers where the driftmobility is defined as the mean velocity (in the direc-tion of the field) of the carriers (v) per unit field strengthE or Ad= (v)/E]; eo=permittivity of free space; c=ve-locity of light; m*=effective electron mass; N= realpart of the index of refraction. It is evident that a (XI)can be made sufficiently large to measure,' by inducinga large number of free carriers photoelectrically.

When attempting to observe free-carrier absorptionin the silver halides, we regard silver bromide as themost probable candidate since it has a very small effec-tive mass (m*/m= 0.02).'4

Photoconductivity was observed in AgBr by Brown'et al. in 1961. Such measurements are obviously difficultto perform owing to deposition of metallic silver; how-ever, this difficulty can be largely overcome by workingwith unusually pure crystals. The surface-preparationtechnique of Childs and Slifkin' should also be used toremove surface material damaged by cutting andpolishing.

Since AgBr is of such great interest to the photo-graphic industry, its properties have been studied inconsiderable detail. The fundamental absorption edge,which has been extensively studied, lies in the vicinityof 0.48 p (2.6 eV) at 250C.5 '7-10 This value applies only

* Present address: The University of Michigan, Ann Arbor,Michigan.1 T. S. Moss, Infrared Phys. 2, 129 (1962).

2 R. M. Grant, "Photoelectrically Induced Free Carrier Modu-lation and Amplification of Light in Semiconductors," Ph.D. dis-sertation, Technical University, Delft, The Netherlands (1964).See this reference for a detailed review of classical and quantummechanical derivations of wavelength-dependent free-carrierabsorption.

3 R. P. Feynman, R. W. Hellwarth, and P. M. Platzman, Phys.Rev. 127, 1004 (1962).

4 F. C. Brown and F. E. Dart, Phys. Rev. 108, 281 (1957).5 F. C. Brown, T. Masumi, and H. H. Tippins, J. Phys. Chem.

Solids 22, 101 (1961).6 C. B. Childs and L. M. Slifkin, Rev. Sci. Instr. 34, 101 (1963).7 F. Moser and F. Urbach, Phys. Rev. 102, 1519 (1956).

at room temperature since the absorption-versus-wave-length spectrum of AgBr is strongly temperature de-pendent.5' 7-9 Because the transmittance of this materialcontinually changed owing to silver formation inducedby the excitation light, free-carrier absorption was notmeasured as a function of wavelength but rather as afunction of time, within a Xi wavelength band which ex-tended from 1.45 to 3.3 yz. This optical transmissionregion was determined by a germanium-coated band-pass filter il and the short wavelength range which ex-tended from 0.42 to 0.6 A was established with an inter-ference filter f2 immersed in a distilled-water cell.

The values of the spectral bandwidth at the one-halfmaximum transmittance level are r 2 = 0.4 /s and ri= 0.78 A, respectively. Next, having established, the X2

and Xi (excitation and transmission) characteristics ofAgBr, we must obtain values for v, T, Ad, m*/m, andN from the literature, in order to calculate (1) the den-sity of free carriers n photoelectrically generated bylight of wavelength X2, and (2) the magnitude of theabsorption coefficient a(Xi).

A value of v=0.6"1*2 has been given for the AgBrquantum yield. However, this value will depend stronglyon the nature of the surface.

Values of r, the bulk lifetime, can be as short as 10-5sec, as quoted by Mitchell.' 3 By employing the morerecent surface-preparation technique given by Childsand Slifkin6 on crystals with less than six parts permillion polyvalent-metal impurity content, we can ob-tain longer lifetimes. (Crystals containing more than6 ppm polyvalent-metal impurity color rather rapidly.)Childs and Slifkin have pointed out that extremelypure, carefully polished silver chloride crystals (whichhave properties very similar to silver bromide) must beused to obtain large densities of free carriers withoutformation of excessive silver' at the same time. Suchhigh-quality crystals are not commercially available; how-ever, the Eastman Kodak Company of Rochester, NewYork, kindly supplied us with one of their extremely

S. Tutihasi, Phys. Rev. 105, 882 (1957).R. E. Slade and F. C. Toy, Proc. Roy. Soc. (London) A97,

181 (1920).10 F. R. Kessler, J. Phys. Chem. Solids 8, 275 (1959)."W. Lehfeldt, Nachr. Akad. Wiss. G6ttingen, II Math.-Physik

Kl. 1, 171 (1935).i2 D. C. Burnham, F. C. Brown, and R. S. Knox, Phys. Rev. 119,

1560 (1960)."J. W. Mitchell, Progress in Semiconductors (Heywood and

Company Ltd., London, 1958), p. 3.14 C. Kittel, Introduction to Solid State Physics (John Wiley &

Sons, Inc., New York, 1961), p. 500.

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VOLUME 55, NUMBER 11 NOVEM BER 1 965

RALPH M. GRANT

FIG. 1. Schematic diagram of experimental arrangement.

pure AgBr crystals, originally purified for their ownresearch. This crystal was cut with a diamond saw andthe severely strained surface was predominately re-moved by polishing cloths wet with a 5%, by weight,sodium thiosulfate solution. This reaction 2 AgBr+Na2 S2 03 > Ag 2S20 3+2 NaBr was stopped by swab-bing the surface of the crystal with a soft tissue damp-ened in distilled water. Such swabbing also helped toclear away the remaining chemical solution. It is ob-viously impossible to remove all damage caused bydiamond-saw cutting; however the major portion of thedamage was eliminated" by the careful removal ofa couple of mm from the broad surface of the crystal.In future experiments crystals should be cut with acotton thread moistened with a 3% solution of potas-sium cyanide' to avoid the damage caused by diamond-saw cutting.

According to Feyninan el al., 3 the ratio of effectivemass to free-electron mass (m*/m=0.20) agrees withresults presented earlier, in 1957, by Brown and Dart.4

Some other values are z*/rn= 0.43,16 m*/m= 0.78,1711/in= 0.30,18 and mit*/m= 0.4.s

Values of the drift mobility are typically given be-tween Pd= 220 cm2/V sec and 250 cm2 /V sec.4 "9-22

15 Before one or two mm of the AgBr surface were removed bypolishing with the thiosulfate solution, the crystals colored quiterapidly; however, after the damaged surface was removed, thesilver deposit appeared only after extensive exposure to very in-tense visible light. This silver deposit was visible only upon thesurface of the crystal; the interior was not visibly altered. A re-polished crystal, which had been exposed to highly intense visiblelight for many minutes had an infrared Xi transmittance which wasvery nearly the same as that of the originally polished crystal.This indicated that there was no appreciable silver deposit in theinterior or on the back surface of the crystal, and that the frontsurface of the crystal had been restored to approximately the con-dition of the first polishing.

6 D. J. Howarth and E. A. Sondheimer, Proc. Roy. Soc.(London) A129, 53 (1953).

17 T. D. Schultz, Phys. Rev. 116, 526 (1959).18 F. Low and D. Pines, Phys. Rev. 98, 414 (1955).19 R. H. Bube, Pliotoconductivity of Solids (John Wiley & Sons,

Inc., New York, 1960), p. 269.

However, values as low as 62 cm 2/V sec have beenreported.-3

The last of the parameters needed for calculation isN, the index of refraction, which is well known and shallbe taken as 2.1.10

On the basis of the above parameters and Eq. (1) inaddition to a calculation of the number of free electronsgenerated by an excitation light with an irradiance ofone W/cm2 , it was theoretically evident that a smallamount of free-carrier absorption should be experiment-ally observable.2 If we define a modulation parameter

M-==(T,°- Ti')IT?, (2)

where T1? is the well known transmittance for the casewhere there are no photon-induced free carriers andT1' is the transmittance for the case where photon-in-duced free carriers are present, which can be readilycalculated by means of Eq. (1), then we may performa theoretical calculation which can be very convenientlycompared to experimental observations.

Upon inserting Eq. (1) into the above definition ofmodulation the following relationship can be readilyobtained2

M= 1-6-pnXl2 (3)

where ,= e/147r2c3m*2 deooN in cgs units. The density ofgenerated carriers n can be readily estimated on thebasis of an appropriate photoconductivity model2 andthe wavelength XI has already been established.

According to the values for v, 7, X2, XI, m*/m, Md, andN given earlier, the theoretical magnitude of M for AgBron the basis of Eq. (3) was evaluated and amounted to1.0% at an incident irradiance 12(X2) (excitation light)of 800 mW/cm2 .

Light, emitted by a longer-wavelength source, whichconsisted of a nernst filament, was focused on the en-trance slit of a single-pass monochromator which con-tained a potassium bromide prism (Fig. 1). The mono-chromatic light of irradiance Ji and wavelength XA ob-tained from the monochromator, which was chopped(200 cps) at point C in the optical diagram, was thenfocused upon the end surface of the crystal, whereuponit underwent 19 surface reflections within the crystal.The angle 0 shown in the figure was less than one degree;hence the divergence of the beam inside the crystal wasnot appreciable.

The crystal, which consisted of a thin slab with 45°angles cut on its ends to facilitate multiple internal re-flection, was mounted on a brass metal holder H. Thetemperature of this holder was held constant at 22TCby a temperature controller. In general, the crystalsused in this study were of the order of one or two centi-menters in length and one to three millimeters in thick-ness. A thin layer of pure petroleum jelly was placed

20 C. Yamanaka and T. Suita, J. Phys. Soc. Japan 10, 238 (1955).21 J. R. Haynes and W. Shockley, Phys. Rev. 82, 935 (1951).22 F. C. Brown, J. Phys. Chem. 66, 2368 (1962).

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November1965 FREE-CARRIER ABSORPTION IN SILVER BROMIDE

between the crystal and the brass crystal holder to pro-vide adhesion and better heat transfer.

The chopped light transmitted through the crystalby multiple internal reflection was refocused by a para-bolic mirror upon the detector as depicted in Fig. 1.The alternating voltage induced in the detector, afterbeing fed into a preamplifier, was further amplified bya wave analyzer tuned to the frequency of the lightchopper. The output of the wave analyzer, which servedas a tuned narrow-band voltmeter, was registered on they axis of a y-t recorder.

The shorter-wavelength light was supplied by anOsram concentrated arc xenon lamp S2. This light wasfocused on the surface of the crystal after passingthrough a shutter and filter F2. Nine of the nineteeninternal surface reflections of the longer wavelengthlight within the crystal, i.e., those on the front surfaceof the crystal, were illuminated by the excitation light;it was not possible to observe any free-carrier absorp-tion for one surface reflection only.

Now by measuring the relative transmittance of thecrystal, with and without the excitation light incidentupon the crystal, the free-carrier absorption could bemeasured.

Since the transmittance of wavelength XI was notconstant with respect to time owing to silver formationon the surface, a single wavelength was set on the mono-chromator, within the XI range mentioned earlier. Thisvariation in the longer-wavelength transmittance due tosilver formation at the surface of the crystal was notappreciable for a properly polished crystal which hadbeen subjected to intense visible light, and was notvisible at all during the first 20 or 30 sec of measurement.

DISCUSSION OF RESULTS AND CONCLUSIONS

Figure 2 is a trace of detector voltage S versus timefor a transmission wavelength of 2.0,u. The time atwhich the excitation light is turned on is indicated byl/2 (on) and the excitation light was turned off at P12

(off). A small but definitely observable decrease in thetransmitted light beam was caused by an excitation-light irradiance /'2 of 800 mW/cm 2, which produceda value of M-+-AMmax= (7.44L2.3)% (see Eq. 2). Novisible coloration or decrease in the signal level took

FiG. 2. Signal voltage versus time for AgBr at X1 2.0 ,u, opticalslitwidth AX1=0.17 p4, &2=800 mW/cm2 , M4AM,= (7.442.3) %.

A El C D E 0 I ec

FiG. 3. Signal voltage versus time for AgBr at XI= 2.2 a, opticalslitwidth Ax 1 = 0.2 ,u, p2= 800 mW/cm 2 , M= 4.5 to M= 4.8.

place during or immediately after the first measurement.After 20 or 30 sec of continuous visible-light excitation,the transmittance of the AgBr gradually began to de-crease due to the silver formation. The measurementswere stopped, the crystal was repolished and measure-ments were repeated. Figure 3 is a trace of detectorvoltage S versus time for a transmission wavelengthof 2.2 . Values of M in this case ranged between 4.8and 4.5%.

The theoretical calculation of Mtheor= 1%o referred toearlier was based upon a model where both the trans-mitted and excitation radiation was incident upon thebroad surface of the crystal. As described in the experi-mental discussion longer wavelength radiation X1 waspassed through the crystal by multiple internal reflec-tion. To account for the multiple internal reflection,the previous value of Mtheor must be multiplied by thefactor 2 R sec. X, where R represents the number ofreflections at the surface containing free carriers and4 represents the angle between a normal to the broadsurface and the internally reflected light beam. In thisexperiment '= 450, R= 9, and hence Mth0 o, for the caseunder investigation was equal to 25.2%, based uponthe parameters discussed earlier.

For freshly prepared surfaces, measured values of Mwere not consistent, varying between 3% and 7% de-pending upon the quality of the surface. The theoreticalprediction of M= 25% is somewhat higher than the ex-perimentally observed values; however, the similaritybetween Mtheor and Me0 cp is quite good, considering thefact that comparisons between experimental and theo-retical free carrier absorption values, which are withinan order of magnitude of each other, are as good as canbe expected. Mtheor can vary appreciably depending onthe validity of the photoconductivity model employedto calculate the density of free carriers; moreover thevalues of v, the quantum yield, T, the lifetime of thefree carriers, and pd. the drift mobility of the carriers,depend critically upon the quality of the surface.

The lower experimental values for M are probably dueto the fact that the quantum yield was lower and thelifetimes of the free carriers were shorter than that ex-pected due to surface conditions which were obviouslynot ideal.

The possibility should not be overlooked that freecarriers can be generated (and most likely are, to arelatively small extent) by the transmitted radiation

4'2 (ON) 42 (OFF)

50 1 1S, I

S.,

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RALPH M. GRANT

as well as by the excitation radiation; nonetheless thenumber of free carriers so generated are probably smallin number. Since such carriers would be generated whenthe excitation light was on as well as when it is off, freecarriers produced in such a manner would act very simi-lar to naturally present free carriers rather than asphotoelectrically generated free carriers, and as suchwould not effect the desired results. Future experimentsmust be performed to learn more about the photogenera-tion of carriers by both the excitation and transmittedlight sources.

In the future, better surface-preparation techniquesmust be developed before proceeding to the more im-

portant task of determining the wavelength dependenceof free-carrier absorption in AgBr.

In conclusion, free-carrier absorption has been ob-served in AgBr, where specific examples of this absorp-tion have been given for transmitted radiation of 2.0and 2 .2 gu.

ACKNOWLEDGMENT

The author is indebted to Dr. Frank Moser of theEastman Kodak Company who kindly supplied theAgBr, and to Professor H. G. Van Bueren of the Uni-versity of Utrecht, The Netherlands for many helpfulsuggestions and discussions of the results.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 55, NUMBER 11 NOVEMBER 1965

Polarization Studies in the Vacuum Ultraviolet*

R. N. HAMM, R. A. MACRAE,t AND E. T. ARAKAWA

Health Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831

(Received 10 June 1965)

A method is presented, wvell suited to the ultraviolet region, for determining the degree of polarizationproduced by a polarizer at a given wavelength and for determining the polarization introduced by a gratingmonochromator. An analysis is made of the degree of polarization required by a polarizer for use in opticalstudies to determine, for example, the reflectance of a surface for light of parallel or perpendicular polariza-tion. Data are given in the spectral region 500 to 1300 . for gold and silver reflection-type polarizers and fora grating used in the Seya geometry.

INTRODUCTION

OPTICAL studies in the vacuum ultraviolet havebeen hampered by the lack of suitable polarizers.

Investigations of solid-state properties, for example theenergy bands of crystals,' have emphasized recently theneed for polarizers for this spectral region. A LiF pile-of -plates polarizer has been used successfully from 1200to 2000 A by Walker.2 Prisms of the Wollaston designhave been constructed from MgF and used in the samewavelength region.' In this paper we report on studiesof reflection-type polarizers using silver and goldsurfaces which are stable and can be used in regions ofthe spectrum (500 to 1300 A) for which polarizers havenot previously been available. We also describe a simplemethod for analyzing the degree of polarization pro-duced by a polarizer or a grating monochromator at agiven wavelength, and examine the requirements of apolarizer which is to be used to make accurate measure-ments of optical properties depending on polarization.

* Research sponsored by the U. S. Atomic Energy Commissionunder contract with Union Carbide Corporation.

t Present address: Centiral Piedmont Communnitiity College,Charlotte, North Carolina 28204

'M. Cardona, Solid State Commun. 1, 109 (1963); J. C.Phillips, Phys. Rev. 133, A452 (1964).

2 W. C. Walker, Appl. Opt. 3, 1457 (1964).'W. C. Johnson, Jr., Appl. Opt. 3, 1375 (1964).

METHOD OF ANALYSIS

Let unpolarized light of intensity lo be incident on agrating and let the diffracted beam be reflected succes-sively by two mirrors, the polarizer and analyzer. Fourmeasurements of the reflected intensity are made, theinitial intensity being maintained constant. First, A1 isthe intensity measured with the grating and the twomirrors having a common plane of incidence. Second,the two mirrors are rotated so that their common planeof incidence is perpendicular to the grating plane ofincidence, and the intensity 12 is measured. Third, thefirst mirror, the polarizer, is rotated so that its plane ofincidence is parallel to that of the grating while thesecond mirror, the analyzer, has its plane of incidenceperpendicular; the intensity 13 is measured. Finally, 14is the intensity measured with the analyzer and gratinghaving planes of incidence perpendicular to that of thepolarizer. The measured intensities are given by thefollowing relations:

I'= -1Io[Rsrsi s+Rprprp],

12= YIoER-rpiP+Rprsfl],

13= 1Io[Rsrdxp+Rprpi;],

(la)

(lb)

(Ic)

14= 2IoERrPr+Rpy.Q, (1d)

1460 Vol. 55