Optical and electrical properties of boronimplanted amorphous germanium thin filmsGordon Wood Anderson, John E. Davey, James Comas, Nelson S. Saks, and William H. Lucke Citation: Journal of Applied Physics 45, 4528 (1974); doi: 10.1063/1.1663082 View online: http://dx.doi.org/10.1063/1.1663082 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/45/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Nanoporosity induced by ion implantation in deposited amorphous Ge thin films J. Appl. Phys. 111, 113515 (2012); 10.1063/1.4725427 Enhanced magnetic and electrical properties in amorphous Ge:Mn thin films by non-magnetic codoping J. Appl. Phys. 111, 033916 (2012); 10.1063/1.3679076 Influence of boron-interstitials clusters on hole mobility degradation in high dose boron-implanted ultrashallowjunctions J. Appl. Phys. 107, 123711 (2010); 10.1063/1.3446844 Electrical characteristics of thin boron carbonitride films on Ge(100) and Si(100) J. Vac. Sci. Technol. B 27, 2366 (2009); 10.1116/1.3253534 Impact of boron-interstitial clusters on Hall scattering factor in high-dose boron-implanted ultrashallow junctions J. Appl. Phys. 105, 043711 (2009); 10.1063/1.3079505

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Optical and electrical properties of boron-implanted amorphous germanium thin films

Gordon Wood Anderson, John E. Davey, James Comas, Nelson S. Saks, and William H. Lucke

Naval Research Laboratory, Washington, D. C. 20375 (Received 16 May 1974)

Amorphous germanium films were implanted to high boron levels, _102l/cm3 peak concentrations. Before and after implantation the conductivity measurements fit the relation logo - T-1/4 and no evidence of intravalence absorption was observed indicating that the Fermi level was near the center of the band gap. Thermoelectric power measurements indicated that the samples were weakly n type before implantation and p type after implantation. The position of the fundamental absorption edge shifted to lower energy upon implantation 'and to higher energies upon subsequent anneals. Implanted recrystallized films were strongly p type, exhibited intra valence absorption, and had very low de activation energies,

INTRODUCTION

The recent widespread interest in amorphous semi­conductors has included considerable work on amor­phous germanium because it is, in principle, a simpler material than most amorphous semiconductors and has a crystalline analog. lOne of the early questions related to the basic properties of the material and to the poten­tial electronic switching applications was to determine the nature of the valence-band structure. 2-10 Theoretical calculations indicated that structure should be present in the valence band of the amorphous material. 1-3 In parti­cular, the degeneracy of the r 25' and r 15 states at the top of the valence band should be split by spin orbit coupling in amorphous germanium as it is in crystalline germa­nium, though experimental results have not verified the point. 4-6,10 In the present study amorphous germanium films were ion implanted to high llB concentrations, _1021/cm3 peak density, and thus made p type in order to study the valence-band structure modee by optical methods and to correlate these optical results with the electrical properties of the films.

EXPERIMENTAL Samples were prepared by evaporation of intrinsic

crystalline germanium on room-temperature substrates in an ion-pumped vacuum system having a base pres­sure of 5 xlO-9 _1 xlO-B Torr. Pressures during evapo­ration were in the 5 xl0-B-2 x 10-7 -Torr range. Evapo­ration sources were tungsten filaments, and deposition rates were 1-10 A/sec. To avoid oxygen contamination of the films extensive precautions were taken including vacuum out gassing of the filaments and the germanium before deposition. Samples prepared for electrical and near-infrared and visible optical measurements were deposited on smooth sapphire substrates. To obtain samples as large as 6 mm in diameter for infrared measurements, special techniques were developed. The samples were deposited on collodion films suspended on 100-mesh molybdenum microscope grids which in turn were supported by tantalum plates with 6-7-mm aper­tures. The collodion films were then removed in an acetone vapor bath leaving stress-free floating amor­phous germanium films supported by the grid structures alone for infrared measurements.

The thickness of the films deposited on sapphire sub­strates was measured after removal from the vacuum

4528 Journal of Applied Physics, Vol. 45, No.1 0, October 1974

system by interferometric techniques. Particular care was taken to obtain uniformly thick samples under the conditions described above. The source-to-substrate distance was lOt in. except in the case of sample 41-C for which it was 6 in. In the case of the free floating films, optically flat glass plates were placed adjacent to the grids during evaporation. An evaluation of the film profile on the plates allowed quantitative determi­nation of film uniformities on the adjacent grid struc­tures. The films deposited on glass and the correspond­ing free floating films were scanned using a Joyce Loebl model III CS recording double -beam microdensitometer which measures optical density in the visible-wavelength range, the optical density being linearly proportional to thickness in this range for amorphous germanium. The films deposited on glass were then overcoated with an opaque layer of Silver, and the film thickness was mea­sured at several pOints along the profile with a CEJ interferometer. The free floating film thickness was then determined from the microdensitometer trace. 11

Film uniformity over at-in. -diam grid was found to be uniform within about 30 A for 3000-A films.

The films were studied using x-ray diffraction and reflection electron diffraction in order to establish structural properties. All films deposited in the manner described were amorphous. A particle size of about 20 A was determined by Scherrer analysis of trans­mission electron diffraction patterns for germanium films deposited at substrate temperatures less than 200°C.

The boron implants were performed USing convention­al ion-implantation facilities. Well-resolved llB ion beams passed through two in-line liquid-nitrogen traps, one of which served as a target chamber, before strik­ing the target. The target was placed in the well of a retractable cold tube, and its Faraday-cup geometry allowed for beam integration. With this trapping system targets could be implanted for extended periods without the formation of detectable surface films. The incident energy of the llB beam was chosen so that the peak of the implanted concentration profile was near the center of the film (Fig. 1). The implanted llB concentration profiles were obtained using secondary ion mass spec­troscopy (SIMS). Surface sputtering effects were in­vestigated USing masking and interferometric tech­niques. No detectable sputtering effects were observed.

Copyright © 1974 American Institute of Physics 4528

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z 0

fi a:: 10 I-Z LIJ 8 0 z 6 0 0

LIJ > ~ ...J LIJ a::

10 z 0

ti 8 a:: I-z LIJ

6 0 z 0 0

LIJ 4 > i= <[

2 ...J W a::

0

Ge FILM #IO-C

"e+ 40 keV 1.4 x 1016 e+ Icm2

DEPTH (ANGSTROMS)

Ge FILM #41-C

lIe+ 90 keV

1.9 x 1016 e+/cm2

ANNEALED

DEPTH (ANGSTROMS)

FIG. 1. Boron ion relative concentration profiles in amorphous implanted unannealed film 10-C and polycrystalline implanted film 41-C annealed at 525°C having thicknesses of about 3000 and 6900 A, respectively, implantation doses of 1.4 x1016 and 1. 9 x1016/cm2 , respectively, and implantation energies of 40 and 90 keV, respectively.

Optical absorption spectra in the range 0.05-0.7 eV were measured uSing a Perkin Elmer 112 spectrometer with a CsBr prism .. Absorption spectra in the range O. 46 -2. 0 e V we re measured uSing a Cary 14 spec­trometer. All optical measurements were made at room temperature.

Transport measurements were made in an oil-free vacuum system with a base pressure of 1 X10-7 Torr. The samples and a copper-constantan thermocouple were attached to a large copper block to ensure good thermal contact between the samples and thermocouple. The thermocouple was calibrated to an accuracy of ± 1 KO over the temperature range 77 -500 oK, and the samples were shielded from light during experiments. Contacts were made by spot welding gold wires to the samples and were Ohmic. Before annealing, the contacts were removed and a small area of the film surrounding each contact was sputter etched from the substrate to prevent possible diffusion of the gold into the film during anneal­ing. Resistivity and thermoelectric power measure­ments were carried out USing two contacts made as described above, and Hall-effect measurements were made utilizing the Van der Pauw technique.

Annealing of the films was done in the high-vacuum system described above. The rate of change of tempera-

4529 J. Appl. Phys., Vol. 45, No. 10, October 1974

ture during both heating and cooling was typically 1-2 KO/min, and the annealing times were 15-24 h.

RESULTS Optical absorption spectra of free floating films about

3000 J... thick were measured in the intermediate infrared region, 0.05-0.7 eV, before and after implantation and after successive anneals at 130, 235, 335, and 525°C (Fig. 2). The films were amorphous after annealing at 335°C, but were poly crystalline after annealing at 525°C. For all films studied in this spectral range, interference fringes and no evidence of intravalence absorption were observed before annealing at 525°C. After annealing at 525 °C, the films exhibited typical intravalence absorption (Fig. 2) with shoulders at about 0.22 and 0.41 eV and a strong absorption at less than 0.2 eV. The values of the index of refraction of the films, measured at about 0.55 eV, were 4.10,4.19, 4.12,4.07,4.07, and 3.64 as-deposited, after implan­tation, and after annealing at 130, 235, 335, and 525°C, respectively. Intravalence absorption was not observed in unimplanted films which were annealed at 525°C and were thus polycrystalline.

Optical absorption spectra of films deposited on sapphire substrates were measured in the range 0.46-2.0 eV in order to determine the change in energy of the position of the fundamental absorption edge before and after implantation and after successive anneals at the temperatures listed above. Again, the films were amor­phous after annealing at 335°C but polycrystalline after

WAVELENGTH (microns) 532

1.5

>- 1.0 t: en z UJ Cl ...J « u i= 0.. 0

0.5

O.O~ ___ ----:=,,=, ____ ~,.--___ -...J ___ ---I

0.0

FIG. 2. Absorption spectra of stress-free floating sample 37-C after implantation for two conditions: lower curve, cir­cles, 0, unannealed, amorphous; upper curve, triangles, ~, annealed at 525°C, polycrystalline.

Anderson et al. 4529

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E ~104 ~ t--" z w u LL l.L w 810 3

B i= 0.. 0:: o 12 <I:

102

0.8

• UNIMPLANTED, (130°C ANNEAL) o IMPLANTED

o 235° C ANNEAL • 335 ° C ANNEAL

o 525° C ANNEAL

1.2 ENERGY (eV)

1.6

FIG. 3. Absorption spectra of sample 41-C for several condi­tions. Left to right at K value 5 xl03 cm- I : 0, open circles, implanted, unannealed; ., closed circles, unimplanted, unan­nealed; .0., open triangles, after implantation and 525·C anneal; LJ, open squares, after implantation and 235·C anneal; "', closed triangles, after implantation and 335°C anneal. Data after implantation and 130·C anneal, not shown, corresponded closely to data before implantation, closed circles, •.

annealing at 525 ec. These films had thicknesses of about 0.67-0.70 fl, and the results for sample 41-C having a thickness of 0.688 f.1. are shown in Fig. 3. To correct for reflection losses and any band-tailing effects, a straight horizontal line was drawn through the mean pOints of the optical density maxima and minima at long wavelengths, extended to the range of the absorp­tion edge, and subtracted from the measured optical density to obtain a corrected optical density. In the low absorption range in which interference fringes were important, the measured optical density was taken to be the mean point between the envelopes of the fringes. The absorption coefficient K was then calculated directly from the corrected optical density. Absorption coeffi­cient values less than about 2.5 x 102 _1. 0 x103 cm-l are not very accurate due to the small sample thicknesses and the nature of the calculations.

The position of the fundamental absorption edge shifted about 0.05 eV lower in energy upon implantation and then to successively higher energies upon succes­sively higher temperature anneals (Fig. 3). After the 130 ec anneal, the fundamental edge data nearly coin­Cided with the data measured before implantation and are not shown; upon annealing at 235 and 335 ec, the position of the edge shifted, respectively, about 0.08 and 0.03 eV higher in energy with respect to the position after the previous anneal. In addition, the shape of the absorption edge was broader after successively higher

4530 J. Appl. Phys., Vol. 45, No. 10, October 1974

temperature anneals. After annealing at 525 ec, how­ever, the sample was polycrystalline, and the absorp­tion edge was sharper and shifted to a position in energy above that after annealing at 130 ec and below that after annealing at 235°C.

The electrical resistivity p as a function of tempera­ture is shown in Fig. 4 for two unannealed samples, 68-Cl and 68-C2, unimplanted and implanted, respec­tively, which were deposited at the same time and had thicknesses of about 3000 A. The resistivity at room temperature was decreased by about a factor of 40 after implantation. The dc activation energies at room tem­perature were 0.15 and 0.20 eV for samples 68-C1 and 68 -C2, respectively, before annealing. Thus the dc activation energy was increased upon implantation. To values were 1. 00 xl 08 and 2.44 xl 08 eK for the unim­planted and implanted samples, respectively, yielding values for the density of states at the Fermi level, N(EF ) , of 1. 60 x 1018 and 6.55 XI017/cm3 eV, respective­ly. To values were obtained from the slopes of the curves in Fig. 4 which fit the condition

p=poexp[(To!T)1/4] (1)

as proposed by several researchers12-

15 for low tem­peratures and recently for amorphous germanium in the temperature range studied in this work. 16,17 N(E F) was determined from the relation17

(2)

where k is the Boltzman constant and a-I is a term de­pending on the overlap of the electronic wave functions

107,---.----------.----------.-----------.---.

10 6

105

10

ICE

0.30 0.33

FIG. 4. Temperature dependence of electrical resistivity for two unannealed samples deposited simultaneously: upper curve, triangles, .0., sample 68-CI, unimplanted; lower curve, cir­cles, O. sample 68- C2. implanted.

Anderson et al. 4530

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-50

0

~ 50 "­> ::l

en

100

150

3.0

310

~

TEMPERATURE (OK)

270 230

" A A a b-

3.5 4.0 4.5 l000/T (OK)-1

FIG. 5. Temperature dependence of thermoelectric power, S, for two unannealed samples deposited simultaneously: upper curve, triangles, ~, sample 68-Cl, unimplanted; lower curve, circles, 0, sample 68-C2, implanted.

which was taken to be 9.4 A. 17 The temperature depen­dence of the resistivity did not fit liT or r-1

/2

conditions.

Thermoelectric power measurements were made to determine whether the films were n or p type before and after implantation, and these results are shown in Fig. 5 for samples 68-C1 and 68-C2. The unimplanted films were weakly n type as deposited, and the implanted films were p type. The thermoelectric power in the range near room temperature was nearly temperature independent.

Films were annealed at about 525°C to compare the transport properties of poly crystalline films with those of amorphous films. Typical results are shown in Table I for samples 41-C and 68-C1 which were implanted and unimplanted, respectively, and all results were obtained from Hall-effect measurements except the resistivity and dc activation energy which were measured directly. Measurements were made at room temperature except in the case of the conductivity for which the temperature was varied to determine the activation energy. Unim­planted annealed samples and the implanted annealed samples were p type. The resistivities were very lOW, 0.58 and 1.1 X 10-2 n cm for samples 68-C1 and 41-C, respectively, and the resistivity of the implanted an­nealed sample was more than a factor of 50 less than that of the unimplanted annealed sample. The carrier density of the unimplanted sample was two orders of magnitude less than that of the implanted sample. The

4531 J. Appl. Phys., Vol. 45, No. 10, October 1974

dc activation energies were very low and difficult to measure accurately.

The 11B implantation concentration profiles (Fig. 1) of an unannealed amorphous film, 10-C, and of a poly­crystalline film, 41-C, annealed at about 525°C were obtained by means of SIMS to determine the effect of annealing on the profile. Samples 10-C and 41-C were implanted at 40 and 90 keY, respectively, and had doses of 1.4 x101s and 1. 9 XlO 16/cm2

, respectively.

DISCUSSION

The SIMS results established clearly that high boron concentrations existed in the implanted films after an­nealing at 525°C as well as before annealing and that appreciable boron diffusion out of the films did not occur (Fig. 1). In the unannealed amorphous films the concen­tration profiles of the boron were consistent with theory. 18 The small peak observed near the surface was due to a scattered component of the implantation beam. The slight shift in the Gaussian distribution observed in the annealed poly crystalline film is believed to be caused by enhanced diffUSion effects associated with implantation damage.

Because the optical data showed no evidence of intra­valence absorption in the amorphous films (Fig. 2) even at the high levels of 11B implanted, -1021/cm 3 peak con­centrations, the Fermi level remained near the center of the band gap in the amorphous films after implanta­tion. Though the position of the Fermi level could have been changed appreciably within the band gap upon im­plantation, the presence of the acceptor-type boron ions did not sufficiently lower its position to permit detection of intravalence absorption as predicted by the valence­band structure model. 2,3

The shift of the position of the fundamental absorption edge to lower energy upon implantation and to succes­sively higher energies after successive anneals is con­sistent with results observed after implantation in and annealing of crystalline semiconducting materials. 19,20

Moreover, the observed increase in the index of refrac­tion upon implantation and the subsequent decreases after annealing occurred in a qualitatively consistent manner with the changes of the absorption edge position and also occurred as in crystalline materials. 19,20 From these results it is inferred that damage occurred upon implantation. The increased broadness of the edge after annealing at 235 and 335°C is attributed to the high con­centration of boron and reSidual damage effects in the films. Furthermore, the position of the edge shifted

TABLE!. Summary of data for annealed polycrystaUine films. a

Sample Conduc- Resistiv- Density Mobility dc activation tivity ity of states (cm2/ energy type (0 cm) (cm-3) V sec) (eV)

68-Cl b P type 0.58 6.0 X1017 -15 0.063 41-C c ptype 1.1 x10-2 4.4 x1019 -15 0.018

aData obtained from Hall measurements except resistivity and dc activation energy measured directly.

bUnimplanted. "Implanted.

Anderson et al. 4531

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higher in energy and the edge was sharper after crys­tallization of the samples. The data for values of ab­sorption coefficient below 103 cm-1 were not very accu­rate due to the nature of the present measurements so that it is difficult to draw conclusions about the sharp­ness and precise position of the fundamental edge at these low values of the absorption coefficient. 10,21,22 The present data suggest that the fundamental edge of the amorphous films is fairly sharp and that its position is near 0.5 eV before annealing at 235 °e. The value ob­tained for the index of refraction in unimplanted films, 4.10 at about 0.55 eV, is in good agreement with that obtained by other workers. 10

As stated above, the boron ions caused damage to the films upon implantation. There are three possible posi­tionallocations for boron implanted in the films: at in­terstitial sites; at the location of dangling bonds at voids; and at substitutional sites. The first and second possibilities would cause an increase in the resistivity and the third a decrease. The decrease in room-tem­perature resistivity by more than a factor of 40 upon implantation indicates that some boron was at substitu­tional sites.

The observation that the pOSition of the Fermi level was not suffiCiently close to the valence band to permit detection of intravalence absorption after implantation is consistent with the resistivity (Fig. 4) and thermo­electric power (Fig. 5) results. Because some boron was at substitutional sites, the pOSition of the Fermi level should have been closer to the valence band after implantation. This effect is consistent with the thermo­electric power results which showed that the implanted films were p type. A crude calculation of the Peltier coefficient from the thermoelectric power data measured after implantation (Fig. 5) gave a value of about 0.03 eV indicating that the average energy distance from the Fermi level at which conduction occurred was small. The present thermoelectric power results of the unim­planted films are in reasonable agreement with earlier results. 23

Because the resistivity fit a T- 1/ 4 condition (Fig. 4),

as predicted by several authors for variable range hop­ping in amorphous semiconductors, 12-16 before and after implantation, it is inferred that the mechanism of con­duction remained unchanged after implantation. The val­ues of To and N(F F) reported here for un implanted films, 1. 00 x108

OK and 1. 60 x1018/cm3 eV, respectively, are in good agreement with those found by other workers. 17,24 The change in slope of the temperature dependence of the resistivity to a higher value after implantation (Fig. 4), indicating a lower density of states at the Fermi level if O! is assumed to be constant (Eq. 2), appears inconSistent with the measured in­crease in conductivity. One explanation is that the value of O! was changed after implantation due to the doping or damage which occurred during implantation. The pre exponential factor may have changed upon implanta­tion as well. Thus, the observed change in the slope does not necessarily indicate a decrease in the density of states N(E F)' Such a decrease would be consistent with Mott's model of a peak in the denSity of states at the center of the band gap, though, if the position of the

4532 J. Appl. Phys., Vol. 45, No. 10, October 1974

Fermi level were lowered upon implantation. 15 It should be noted that the discussion of variable range hopping presented here may have to be modified as recent theoretical calculations are further developed. 25

The intravalence absorption observed in annealed poly crystalline films (Fig. 2) showing shoulders at about 0.22 and 0.41 eV and a strong absorption at less than 0.2 eV is in good agreement with the results for bulk p-type germanium for the transitions from the split-off band to the light-hole band and heavy-hOle band and from the light-hole band to heavy-hole band, re­spectively.26 The fact that intravalence absorption was not observed in unimplanted polycrystalline samples is an indication that appreciable amounts of boron were in substitutional sites in the implanted polycrystalline films. The large increases in conductivity and mobility and the small dc activation energies observed in both implanted and unimplanted films at room temperature (Table I) and the conversion to p-type conduction in un­implanted films after crystallization occurred as expected. 27

CONCLUSIONS

It has been shown that amorphous germanium films implanted with high concentrations of boron were changed from their n-type as-deposited characteristic to p type but still exhibited characteristics of variable­range phonon-assisted hopping conduction. Upon im­plantation the dc conductivity was increased by more than a factor of 40, indicating that some of the boron was electrically active. Intravalence absorption, even with high concentrations of boron present, was not ob­servable until the films were annealed at suffiCiently high temperatures such that they were polycrystalline. These optical and electrical results indicated that the Fermi level remained near the center of the band gap after implantation. The position of the fundamental ab­sorption edge Shifted lower in energy upon implantation and then higher after subsequent anneals. The index of refraction increased upon implantation and decreased after annealing. Results for unimplanted films were consistent with those of other recent work.

ACKNOWLEDGMENTS

The authors thank A. Addamiano for assistance in the particle size determination and H. L. Grant for excellent innovative technical assistance.

1See , for example, Proceedings of the Inter1Ultio1Ull Confer­ence on Tetrahedrally Bonded Amorphous Semiconductors, edited by M. M. Brodsky, S. Kirkpatrick, and D. Weaire (American Institute of PhYSics, New York, 1974).

2N. H. Fletcher, Proc. Phys. Soc. Lond. 91, 724 (1967). 3B. Kramer, Phys. Status Solidi B 47, 501 (1971). 4J. Tauc, R. Grigorovici, and A, Vancu, Phys. Status Solidi 15, 627 (1966).

!W.E. Spicer and T.M. Donovan, Phys. Rev. Lett. 24, 595 (1970),

6J. Tauc, A. Abraham, R. Zallen, and M. Slade, J. Non­Cryst. Solids 4, 279 (1970).

7J.C. Phillips, Phys. Status Solidi B 44, K 1 (1971), 8F. HermanandJ.P. VanDyke, Phys. Rev. Lett. 21, 1575

(1968),

Anderson et al. 4532

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9D. Brust, Phys. Rev. Lett. 23, 1232 (1969). loT.M. Donovan, W.E. Spicer, J.M. Bennett, and E.J.

Ashley, Phys. Rev. B 2, 397 (1970); T. M. Donovan, in Ref. 1.

11G. W. Anderson and H. L. Grant (unpublished). 12N. F. Mott, J. Non-Cryst. Solids 1, 1 (1968). 13V. Ambegoaker, B. I. Halperin, and J.S. Langer, J. Non­

Cryst. Solids 8-10, 492 (1972). 14M. Pollack, J. Non-Cryst. Solids 11, 1 (1972). 15N. F. Mott and E.A. Davis, Electronic Processes in Non­

Crystalline Materials (Oxford U. P. London, 1971). 16M. Pollack, M. L. Knotek, H. Kurtzman, and H. Glick,

Phys. Rev. Lett. 30, 856 (1973), 17M. L. Knotek, M. Pollack, T. M. Donovan, and H. Kurtzman,

Phys. Rev. Lett. 30, 853 (1973); M. L. Knotek, in Ref. 1. 18J. Lindhard, M. Scharff, and H.E. Schi,$tt, Kgl. Dan.

4533 J. Appl. Phys., Vol. 45, No. 10, October 1974

Vidensk. Selsk. Mat. -Fys. Medd. 33, 39 (1963). 19J.E. Davey, T. Pankey, P.R. Malmberg, and W.H. Lucke,

Appl. Phys. Lett. 17, 323 (1970). 2oA. Addamiano, G.W. Anderson, J. Comas, H.L. Hughes,

and W.H. Lucke, J. Electrochem. Soc. 119, 1355 (1972). 21M. L. Theye, Mater. Res. Bull. 6, 103 (1971). 22G.A.N. Connell and W. Paul, J. Non-Cryst. Solids 8-10,

215 (1972). 23K. L. Chopra and S. K. Bahl, Thin Solid Films 12, 211 (1972). 24J.J. Hauser and A. Staudinger, Phys. Rev. B 8, 607 (1973). 25D. Emin, Phys. Rev. Lett. 32, 303 (1974); D. Emin, in

Ref. 1. 26W. Kaiser, R.J. Collins, and H. Y. Fan, Phys. Rev. 91,

1380 (1953). 27See, for example, P.A. Walley and A.K. Jonsher, Thin

Solid Films 1, 367 (1967/68).

Anderson et al. 4533

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