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Ionic conductivity of AgBr films
SURFACE
SCIENCE 33 (1972) 461-476 0 North-Holland
IONIC
CONDUCTIVITY
R. C. BAETZOLD
Publishing Co.
OF AgBr FILMS
and J. F. HAMILTON
Research Laboratories, Eastman Kodak Company, Rochester, New York 14650, U.S.A. Received 8 March 1972; revised manuscript
received 31 July 1972
Ionic conductivity in {200} and {111) silver bromide films deposited on cleaved mica or cleaved alkali halide crystals in an oil-free system is reported. Interstitial silver ions are the majority carrier in each film, as indicated by the effect of Cd++ on conductivity. These films have a conductivity at least an order of magnitude greater than that of single crystals and a lower temperature coefficient (0.41 eV for (1 ll}, 0.4W.53 eV for (200)). The substrate for preparation of {200} films has a large effect on AgBr conductivity, which increases with increasing misfit between AgBr and substrate lattice. Values for the free energy of defect formation and potential difference between bulk and surface are reported.
1. Introduction
Conductivity in silver bromide occurs by ionic species near room temperaturel). Electronic conductivity at this temperature is much lower owing to the 2.6 eV bandgap. Measurements have been made for ionic conductivity in silver bromide single crystals and thin films 2). The single crystals are much larger than emulsion grains, but thin films can be prepared in the thickness range up to a few microns. Previous studiesz) on thin films were carried out using an oil-pumped system. Since oils and adsorbed gas molecules play an important role in several thin-film phenomena, we have undertaken the present work with an oil-free system in which the films are not exposed to atmosphere. Films of AgBr deposit epitaxially with the (111) surface on mica or the (200) surface on some alkali halides3). Domains of single-crystal areas were observed as reported before for the {ill} films; (200) films contain dislocations running through the film thickness. The silver halides belong to a class of materials in which significant amounts of ionic or defect motion can occur. Thus, the current through these materials can be carried in whole or in part by the ionic species. The conductivity (G) is given by the equation r~= AT-’
exp(-
AE/kT) (ohm-’
cm-‘),
(1)
if there is a single majority carrier l). The reciprocal temperature dependence of eq. (1) has so little effect compared to the exponential term that it is usual461
R. C. BAETZOLD ANDJ. F. HAMILTON
462
ly neglected. Some representative values for room temperature ionic conductivity of various single crystal materials are listed in table 1. These data should indicate that silver halide is by no means unique in possessing cation mobility and there are some materials with much higher conductivity. Of course, many materials have low ionic conductivity and in many cases the cation is not the majority carrier. In CdF,, for example, fluorine vacancies are the majority carriera) and in thallium halides anions are the majority carrier 5). TABLE1 Ionic conductivity Material NaCl CuCl AgBr AgCl KAg415 ((CH3)4N)zAg13115 AgI (a form) AgI (p form) AgI(y form)
Ref. 1 16 1 1 17 18 19 19 19
in single crystals at room temperature (T (ohm-‘cm-l) 2.2 x 1045 6 x 10-3 1 x 10-S 1 x 10-3 0.21 0.04 1 6 x 1O-7 2 x 10-5
Disorder Schottky Frenkel Frenkel Frenkel
_
Majority carrier cu+ Ag+ Ag+ Ag+ Ag+ Ag+ Ag+ Ag+
2. Experimental Films were prepared by evaporation at N 1 x lo-’ Torr in a Varian VI 460 vacuum system. This system is completely oil-free, using ion pumping, titanium sublimation pumping, and liquid-nitrogen-cooled vacsorb pumping. The interior parts of the system were stainless steel. Parts needed for evaporation were prepared from nickel-plated copper to reduce contamination. The films were deposited at room temperature on cleaved mica or alkali halide surfaces. After deposition, the films were heated to N 150°C for annealing and resistivity was recorded versus temperature during the cooling cycle, which lasts roughly three hours. The resistance of films was measured by applying a low frequency (N 1 cycle/set) ac potential of 3 V to the electrodes. Electrodes composed of silver or gold evaporated onto the substrate prior to film preparation were employed. In this system we found that a 3 V dc potential can cause irreversible electrolysis of the AgBr producing silver and pits due to bromine evolution. The conductivity of annealed films is found to be independent of electrode material over the temperature and thickness ranges employed in this work. Blocking effects are not observed
IONIC CONDUCTIVITY
OF
463
AgBr FILMS
with the gold electrodes presumably because a small amount of silver is reduced near the electrodes either by electrolysis or annealing. A similar explanation has been recently used in the case of AgI to explain identical conductivity results using graphite and silver electrodese). The activity of Frenkel point defects in AgBr is constant over a wide range of external halogen pressure or silver metal activity’). The present films possess a degree of non-stoichiometry in the direction of excess silver. This may arise from the fact that they are evaporated at a temperature not far below the decomposition temperature of AgBr. The excess silver is indicated by development of these films in photographic developers unless they have been treated with halogen vapor. Irreversible electrolysis is kept low by use of the ac potential. We observe in experiments with dc potentials a polarization effect with a half time of about 30 sec. Since this polarization time is much greater than the time the current flows in one direction in the ac experiments, decomposition effects should be small. The conductivity data reported have employed gold electrodes, but similar measurements were obtained when silver electrodes were used. Films were deposited at a constant rate of N 7 A/set using a Sloan crystal unit for monitoring frequency. Thicknesses of films measured this way are accurate to within - f5%. Contamination of AgBr films by Ti from the sublimation pumping has been found, causing a decrease in conductance. This problem can be avoided by using only ion pumping just before and during evaporation. Analysis of the films by spark-source mass spectrometry has shown the presence of Ti and other impurities in the 10 ppm range. This upper limit for impurities corresponds to one-tenth the concentration of calculated interstitial silver ions in the films at 400°K. An impurity such as Ti in greater than unity charge would introduce silver ion vacancies in the film. Since interstitial silver ions are shown later to be present in concentration excess over the vacancies, we judge such impurity effects to be unimportant. The ionic conductivity in AgBr (a) is obtained from the conductance (c) by
o=~=~nj~je, (con d uctance = reciprocal
resistance),
(2)
where the conductance is measured for a film of square cross-section having a thickness t. The summation.extends over all charge carriers of concentration nj; pj is their mobility and e the electronic charge. In silver halides interstitial silver ions and silver ion vacancies are the primary carriers; the former dominates in the conductivity of intrinsic materials because of its
464
R. C.
BAETZOLD
AND
.I. F. HAMILTON
greater mobility. The Frenkel equilibrium stitials (nr) and of vacancies (n,):
relates the concentration
n,nv = K .
of inter-
(3)
Addition of a divalent impurity such as Cd++ to AgBr creates vacancies, part of which are free. The Frenkel equation (3) may be used to show the dependence of conductivity on impurity content. 2.1.
SPACE-CHARGE LAYERS
The charge carriers in AgBr form within the bulk in equal concentration. At a surface, however, there is the possibility of differences in concentration since the interstitial Ag+ and vacancy are not required to form simultaneouslys-10). When a point defect is formed at the surface a charge-compensating surface site is created. For example, an interstitial silver ion may be generated from a positive kink site. The effective charge of this site prior to the process is taken as +3 and the effective charge after interstitial formation would then be -3. Other kinds of sites may be involved in interstitial formation, such as the domain boundaries or edge dislocations mentioned previously. The parts of the models used to describe these phenomena will be presented to aid in interpreting our data. The mathematical model of space-charge layers in ionic crystals has been discussed. Lehovecs) and Kliewers) have considered intrinsic and extrinsic crystals in which the surface provides an unlimited source of sites for defect formation. A recent treatment by Poeppel and Blakely lo) discusses the situation which arises when the surface provides a limited number of sites for defect formation. Both treatments will be utilized for analysis of data. Frenkel defects are responsible for ionic conductivity in the silver halides. The concentration of interstitial silver ions (n,) or vacancies (n,) is dependent on the space-charge potential [4(X)] by the relations n, = 22 exp { - p [AC; + e$ (X)]}
ny=zexp{-p[AG:-e~(x)l},
,
(44 (4b)
where j?= llkt, Z is the number of AgBr ion-pairs per unit volume, AC, is the standard free energy change of interstitial formation and AC, is the standard free energy change of vacancy formation. The free energy terms are defined by Poeppel and Blakely lo) in terms of the number of surface sites per unit area capable of forming an interstitial (NJ and the number of these sites which bind an Ag+ ion (n,), AC; = AC, + kT In
IONIC
CONDUClWITY
OF
AG;=AG,-kTln
AgBr
465
FILMS
,
where AG; is the standard free energy change of interstitial AG; is the standard free energy change of vacancy formation surface under consideration. Note that when n, =+NS, the entropy terms for surface A sketch of the dependence of n, and n, on distance from the case AG; < AG; is shown in fig. 1. A solution for the potential C#I (X) may be obtained using tion, - 47rp v=4 = ~ E&O ’
formation and at the particular sites are zero. the surface for Poisson’s equa-
(6)
where p = charge density, E= dielectric constant, and E,-,= permittivity of free space.
Concentration
Potential
oI-x A
Fig. 1.
Sketch of space charge layer in AgBr.
This has been solved for pure AgBr crystals and crystals containing divalent cations. When this process has been completed, substitution of 4 (X) into eq. (5) gives the complete dependence of defect concentration on position as sketched in fig. 1. The space-charge region extends a distance roughly equal to the Debye distance A, where 1
=
&co expCB (W
Be2 22 In
+ 441 * > ’
these equations the difference in potential between bulk and the surface
466
R. C.
where defects are created
BAETZOLD
AND
J. F. HAMILTON
(4m) is given by
4, = ;
(AG: - AG;).
(8)
3. Results Measurements of conductance are made after films have been annealed by heating to 150°C. Data recorded during evaporation indicate negligible conductance until an average thickness of 200-500 A of AgBr is deposited. Apparently, at this thickness the islands of AgBr coalesce, forming continuous pathways for conduction. Conductance increases sharply at this point, then levels off, varying linearly with thickness. The conductance recorded during deposition increases with evaporation rate and a significant decrease in conductance is observed at the conclusion of evaporation. The change in conductance at the conclusion of evaporation would require a 17°C change in temperature of the entire film if the effect is to be attributed to heating of the film by condensing molecules. Since this temperature change is large in relation to the observed times for heat transfer in the system, it is unlikely that the observed conductivity change is due entirely to a heating effect.
I
I
_-A-
.__________--A--@ I
I
1000
5000
Thickness,
Fig. 2.
Conductance
:
A
(c) versus thickness for {111)AgBr films on mica.
IONIC
3.1. fill)
CONDUCTIVITY
OF &@r
FILMS
467
FILMSON MICA
The conductance of {111) AgBr films on mica exhibits a thickness-dependent and thickness-independent part as shown in fig. 2. This behavior was observed before in an oil-diffusion system. The data plotted in fig. 2 indicate that both slope and intercept are temperature dependent. This type of thickness dependence is in accord with ionic conduction by a surface component and a thickness-dependent component. The activation energy of the surface space-charge component is 0.36kO.07 and that of the bulk component is 0.41 f0.05. These values are obtained from the plots in fig. 3 and are considerably less than the intrinsic activation energy, 0.79 eV, found in bulk single crystals. In addition, the concentration of interstitial silver ions is greater in the bulk of films than in single crystals. Employing our measured values for c in eq. (2) and values for the mobilityrr) we calculate values for the concentration of interstitial silver ions in table 2. These defect concentrations in the film indicate that the vacancy concentration is less than the interstitial silver
103/T Fig. 3.
Dependence
(OK)
of bulk conductivity (0) and surface conductance for {lll)AgBr films.
(c) on temperature
468
R. C. BAETZOLD
AND
TABLE
J. F. HAMILTON
2
AgBr film and single crystal data Single crystal
AE(ev) o(308 “IQ no(400 OK) m(333"K)
0.79 2.2 x 10-s 2.6 x 1017 7.3 x 10’5
Oil system
Present work
0.35 2.5 x 1O-5
0.36 1.0 x 10-s 2.1 x 1018 5.4 x 10’7
_
ion concentration in order to maintain the Frenkel equilibrium. Therefore we believe that both on the surface and in the bulk, interstitial Agf can form by some means independent of mobile vacancy formation. The com~nsating negative charge is localized at surface defects, such as kink sites, domain boundaries, or edge dislocations. According to this assumption, the activation energy for conduction due to the surface component of fig. 3 is AE = A,??”-I- AG; = 0.36,
(9)
where the activation energy for motion (AE”) is taken to be the previously measured valuerf) 0.145 eV. This gives the result AG;=O.Zl eV. Since the Frenkel defect formation energy 1) is 1.06 eV and AG;+AG:=AG,+AG,-liTln2,
(IO)
we evaluate AG:=0.85 eV. Eq. (8) predicts that Cp, =0.32 eV. The Debye thickness, which extends the distance of the space-charge layer, is calculated from eq. (7) to be ,X= 4600 A at 308 “K and ;1= 520 A at 400°K. The value of the activation energy for conductivity in these films indicates a different mechanism for carrier formation than in intrinsic AgBr. The primary carrier is interstitial Ag”, as will be demonstrated by the effect of CdBr, on ionic conductivity. Two possible causes of the extrinsic conductivity are impurities or structure of the films which permits interstitials to form independently of vacancies. The present data are compared with data for films prepared in an oildiffusion system and with single-crystal results in table 2. Apparently, ionic conductivity is changed only slightly using the oil system. There are large differences in behavior between films and single crystals. Conductivity is higher for thin films and the activation energy is much lower. In addition to these results, we have exposed fresh AgBr films to atmosphere before annealing. The effects observed are small decreases in conductivity of exposed films, apparently indicating that the effects on mechanisms of interstitial formation and movement are minor. Larger decreases
IONIC~~NDKJ~TMTY~F
AgBr
469
FILMS
in conductivity are observed in films prepared at base pressures greater than 5 x lo-’ Torr. This behavior is probably due to contamination. The space charge component of conductance can be used to give the area density of carriers in the space charge layer (n,). The surface component (intercept of fig. 2) Intercept = n,pte
(11)
is used to derive the result n4 = 1.4 x 1013 carriers/cm’
at 400°K)
n, = 3.0 x 1012 carriers/cm’
at 308°K.
Here is assumed that the interstitial silver ion mobility is the same in the surface space-charge layer as in the bulk. The high-temperature data correspond to approximately 1% of the number of ions in a {11l} monolayer of AgBr. An independent check of the experimental results from eq. (11) can be made by employing
(12) which is derived by Lehovecs). We take .sO=8.84 x lo-i4 A-see/V-cm, a= 13.1, and values for 4, and I derived before. We calculate nq= 1.5 x lOi
333°K o-o-
0-0
I
1000
5000
Thickness,
Fig. 4.
Conductance
i
(c) versus thickness for {lll}AgBr Cd++.
films containing
0.003 mol %
470
R. C.
BA ETZOLD
AND
J. F. HAMILTON
carriers/cm’ at 308 “K and n, = 1.4 x 10”3 carriers/cm’ at 400°K. The comparison with earlier experimental values from eq. (11) verifies the consistency of this analysis. Rough agreement is the best that can be expected from comparison of these two methods and we attach no special significance to the fact that at 400°K the agreement is better than at 308°K. An identification of interstitial Agf as the majority carrier in the surface region of {11l> films is made by examining conductance as a function of Cd+’ concentration in the manner analogous to that used by Koch and Wagnerls) for the bulk properties of large crystals. The data in fig. 4 were obtained for AgBr samples containing 0.003 mol% Cd’ * . We describe the dependence of conductivity on divalent-impurity concentration for the case where in the pure material the primary source of interstitial Ag’ is the concentration S of immobile negative charges, as described before. In this case 9
(pure)- S,
(13)
when Cd++ ions are added, resulting in vacancy formation, electrical neutrality considerations require that S+n,=(Cd++)+pt,.
(14)
Substituting eq. (3) into eq. (14) gives $+[(Cd++)-S]n,-I(=O.
(15)
The minimum in conductance [eq. (2)] occurs when ~,,uI=nV~,. Employing this result and eq. (15) leads to the prediction of a minimum conductance when (Cd’ *) = ?zl(pure) + Kf [(~~
- (~~1.
(16)
The conductance of (1113 films containing Cd’ ’ has been separated into a bulk and surface component as in fig. 4. The slope and intercept at 400°K are 1.8 x 10T5 ohm-l cm-’ and 7 x 10-r’ ohm-‘, respectively. Corresponding values in pure AgBr indicate that the majority carrier in both surface and bulk is interstitial Ag+. We plot in fig. 5, the ratio of the bulk conductivity in doped to pure AgBr films versus Cd++ concentration at 400°K. These data agree with position of minimum calculated using eq. (16) and available values”3 ii) for pr, pLyand K, which is 0.017 mol% Cd+ ‘. The solid lines in fig. 5 arise from calculated values using eq. (15) in the limiting regions of low and high impurity.
IONICCONDUCTMTYOF AgBr
FILMS
471
Fig. 5. Log conductivity ratio for unpure to pure (c&O) versus logCd++ concentration for f 1 I1 f AgBr films at 400°K. f0 experimental points, solid lines calculated by eq. (15), $ denotes position of minimum calculated by eq. (16}.]
.05
.I
?‘oCd++ Fig. 6. Ratio of intercept (Z/Z,,,,) at 400°K in impure to pure {11 1) AgBr films at 400°K. [O experimental points, solid line calculated by eq. (15), as explained in the text.
The surface component of conductivity is plotted versus Cd’ ’ concentration in fig. 6. A negligible value for the intercept is observed at high levels of Cd++. At these Cd++ levels, vacancies are the predominant carrier in the surface region. The solid line in fig. 6 arises from solving eq. (15), assuming
412
R. C. BAETZOLD
AND
1. F. HAMILTON
uniform defect concentration in the Debye layer 1= 520 A calculated before and setting S=n,= 1.4 x lOi carriers/cm2. Apparently, this crude model of the space-charge region agrees with experiment well. We do not believe our data at lower temperature warrant analysis by this technique because of greater experimental error. Accurate data in this region would permit an evaluation of the impurity-vacancy association constant. 3.2. (200) FILMS The conductance of (200) films on a typical alkali halide substrate (KCl) is examined versus thickness in fig. 7. A zero intercept is observed within experimental error. This indicates an absence of significant surface conductivity in these films. The conductivity and activation energy for (200) AgBr
/’
/’
I’
/’
,’
333OK
_&___-c _o---cc-‘U---1000 Thickness,
Fig. 7.
5000
A
Conductance (c) versus thickness for {2OO}AgBr films on KCl.
films on various alkali halide substrates are listed in table 3. Note that conductivity seems to increase and activation energy seems to decrease as the misfit between AgBr and substrate lattice becomes greater. Interstitial silver ions are the majority carriers in these (200) films. A decrease in conductance is observed on evaporating small amounts of CdBr, with the AgBr. A minimum in conductance versus mole percent (Cd+ ‘) is observed for 5000 A thick (200) films on NaCl substrate in fig. 8. Employing eq. (16) leads to the predicted minimum at 0.0076 mol% for 400°K and 0.0005 mol% for 333°K. The experimental data in fig. 8 are consistent with
IONICcotmucrrvrrv
473
OF AgBr FILMS
TABLE3 Films of AgBr Substrate
LiF NaF NaCl KC1 KBr KI
Mica
Misfit
-31% -20% - 2.5 % -+9% i14% -t-22%
AC/C
u400 0
u3330
(ohm-km-l)
0 0.1 0.5 0.5 0.5 0.5
1.5 3.1 1.5 1.7 4.4 2.2
x x x x x x
0.3
3.4 x 10-5
(ohn-lcm-l)
10-a 10-a 10-6 10-a 10-a 10-a
I .5 5.0 3.2 2.8 7.8 3.6
x x x x x x
IO-4
0.40
zk
10-s 10-5 1O-6 1O-6 10-b
0.46 0.53 0.49 0.50 0.49
k f f zt i
3.0 x 10-4
0.03 0.05 0.04 0.07 0.07 0.07
0.41
the calculated value at 4OO”K, but a discrepancy at 333 “K similar to that observed in (111) films is noted. Some discrepancy is expected in these values because of the rough manner in which the minimum in o is determined. Alternatively, impurities in the “pure” films would reduce cr and predict a lower value of n, (pure) in the analysis by eq. (14). Nevertheless, we believe that the rough agreement in
I 0.01
I 0.02
I
0.03
Mole percent Cd* Fig. 8.
Ratio of conductance (c/c rure) for impure to pure AgBr films on NaCl versus mole percent (Cd++). (t denotes calculated lower limit for the minimum.)
474
R. C. BAETZOLD
AND J. F. HAMILTON
position of the minimum from the two types of experiments indicates that our interpretation of the mechanism is right. The dependence of conductivity of (2001 films on substrate is shown in table 3. The misfit between AgBr lattice constant and substrate lattice constant is involved in determining cr. Apparently a misfit causes a disorder throughout the AgBr film which causes 5 to increase. An exception to this rule is ICI, in which the +22x misfit results in only a minor increase in r~ over materials with lower misfit. Possibly the AgBr lattice cannot respond to the deformation normally induced by substrate. Electron micrographs and diffraction patterns of the AgBr films on each alkali halide substrate have been made. They indicate a (200) surface on each substrate and structural features similar to those previously describeds). An attempt was made to correlate cr values with the density of dislo~tions on the f2OOj films. This attempt was unsuccessful - no correlation was found. The density of dislocations was measured to be in the range 4-8 x lo9 dislocations/cm2, showing no trend with 6. The lattice constant of AgBr on various alkali halide substrates has been examined by X-ray diffraction. We find distortion of 10000 A films of AgBr which is less than 0.1% from the bulk value. Thus, the difference in bulk conductivity on various substrates cannot be explained by lattice distortions. The surface of the evaporated AgBr as it condenses onto the film includes a transient disorder which heals in a few seconds. This is indicated by a rapid decrease of conductance when evaporation is stopped. Table 3 shows this relative change of conductance AC/Con various substrates. The loss of conductance corresponds to 2.3 x lOi Ag+ carriers, for example, on KBr substrate which represents l/1000 of an AgBr monolayer. The activation energy for conductivity in (2001 films is in the range 0.40 to 0.53 eV, depending upon the substrate. The value of the activation energy for the bulk (1 ll} films is in this range. The variation in AG; apparently TABLE
4
AgBt films on alkali halides Substrate
LiF
NaF NaCl KC1 KBr KL
0.25 0.31 0.38 0.27 0.35 0.34
0.81 0.75 0.68 0.79 0.71 0.72
0.28 0.22 0.15 0.26 0.18 0.19
IONIC
CONDUCTIVITY
OF
AgBr
FILMS
415
causes the effects observed. Values for the (200) films appearing in table 4 were calculated as before. These data apply to defect creation at the dislocation and potential is measured between bulk and the dislocation. 4. Discussion This work has shown that there are large effects on ion motion depending upon the surface. Silver ions are present in higher concentration near the { 11 l} surface in AgBr, compared to the (200) surface. A perfect (200) plane contains equal numbers of positively charged and negatively charged ions, but a perfect (111) plane consists of only one type of ion or the other. In practice a (11 l> surface is sufficiently disordered that the net surface charge is balanced by ions of the opposite charge. The number of sites for Ag+ formation is independent of surface/volume ratio in (200) films, as fig. 7 shows. Thus, the dislocations that run throughout the bulk of the film may be acting as these sites. The number of dislocations is independent of surface/volume ratio and apparently does not vary much with substrate lattice constant. The values of 4, that we derive for these films are larger than the value 0.14 eV found by Trautweilerrs) for large single crystals with no single crystallographic surface. In addition, considerable error is involved in measuring the above value for single crystals. We have also shown that IJ and AE are quite different in single crystals and the oriented films we prepare. The latter effect apparently arises from defect-generated carriers. The value of AG; for the { 11 l} films, 0.21 eV, is lower than the analogous values for (200) films in table 4. If the free energy of interstitial formation (AG,) is the same in both films, eq. (5a) suggests that the ratio n,/NS is larger in { 1111 films than (200) films. This indicates that saturation of sites by binding Ag+ is greater in { 11 l} films and may be related to the surface conductivity observed in the latter. There is the possibility that N, is very much larger for { 11 l} surfaces than for (200) surfaces, which would account for the surface conductivity phenomena observed. This situation would be consistent with a model proposedl4) for the (11 l} surface in which a nearly half full layer of Agf ions covers a full layer of Br- ions. The calculated Debye distances are less than the film thickness at high temperature, but may be comparable to the film thickness at low temperature. Though a solution for the space charge potential is more complex at low temperatures, Kliewer et a1.15) have shown there will exist a space charge region near the surface where equations similar in form to eqs. (4a) and (4b) hold. Thus, our analysis of space charge conductivity is valid.
476
R. C. BAETZOLD
AND
.I. F. HAMILTON
References 1) F. C. Brown, in: The Physics of Soliak (Benjamin, New York, 1967) ch. 10. 2) F. Trautweiler, L. E. Brady, J. W. Castle and J. F. Hamilton, in: The Structure and Chemistry of Solid Surfaces (Proc. 4th Intern. Materials Symp., Univ. of California, Berkeley, California, 1968), Ed. G. A. Somorjai (Wiley, New York, 1969) p. 83-l. 3) L. E. Brady, J. W. Castle and J. F. Hamilton, Appl. Phys. Letters 13 (1968) 76. 4) Y. T. Tan and D. Kramp, J. Chem. Phys. 53 (1970) 3691. 5) P. Suptitz and J. Teltow, Phys. Status Solidi 23 (1967) 9. 6) G. Cochrane and N. H. Fletcher, J. Phys. Chem. Solids 32 (1971) 2557. 7) F. A. Kroger, J. Phys. Chem. Solids 26 (1965) 901. 8) K. Lehovec, J. Chem. Phys. 21 (1953) 1123. 9) (a) K. L. Kliewer, J. Phys. Chem. Solids 27 (1966) 705. (b) K. L. Kliewer, J. Phys. Chem. Solids 27 (1966) 719. 10) R. B. Poeppel and J. M. Blakely, Surface Sci. 15 (1969) 507. 11) P. Muller, Phys. Status Solidi 12 (1965) 775. 12) C. Wagner and E. Koch, Z. Physik. Chem. B 38 (1937) 295. 13) F. Trautweiler, Photogr. Sci. Eng. 12 (1968) 98. 14) J. F. Hamilton and L. E. Brady, Surface Sci. 23 (1970) 389. 15) K. L. Kliewer and J. S. Koehler, Phys. Rev. 140 (1965) A 1226. 16) Y. W. Hsueh and R. W. Christy, J. Chem. Phys. 39 (1963) 3519. 17) B. B. Owens and G. R. Argue, Science 157 (1967) 308. 18) S. Geller and M. D. Lind, J. Chem. Phys. 52 (1970) 5854. 19) T. Kakahashi, K. Kawabara and 0. Yamamoto, J. Electrochem. Sot. 116 (1969) 357.
SCIENCE 33 (1972) 461-476 0 North-Holland
IONIC
CONDUCTIVITY
R. C. BAETZOLD
Publishing Co.
OF AgBr FILMS
and J. F. HAMILTON
Research Laboratories, Eastman Kodak Company, Rochester, New York 14650, U.S.A. Received 8 March 1972; revised manuscript
received 31 July 1972
Ionic conductivity in {200} and {111) silver bromide films deposited on cleaved mica or cleaved alkali halide crystals in an oil-free system is reported. Interstitial silver ions are the majority carrier in each film, as indicated by the effect of Cd++ on conductivity. These films have a conductivity at least an order of magnitude greater than that of single crystals and a lower temperature coefficient (0.41 eV for (1 ll}, 0.4W.53 eV for (200)). The substrate for preparation of {200} films has a large effect on AgBr conductivity, which increases with increasing misfit between AgBr and substrate lattice. Values for the free energy of defect formation and potential difference between bulk and surface are reported.
1. Introduction
Conductivity in silver bromide occurs by ionic species near room temperaturel). Electronic conductivity at this temperature is much lower owing to the 2.6 eV bandgap. Measurements have been made for ionic conductivity in silver bromide single crystals and thin films 2). The single crystals are much larger than emulsion grains, but thin films can be prepared in the thickness range up to a few microns. Previous studiesz) on thin films were carried out using an oil-pumped system. Since oils and adsorbed gas molecules play an important role in several thin-film phenomena, we have undertaken the present work with an oil-free system in which the films are not exposed to atmosphere. Films of AgBr deposit epitaxially with the (111) surface on mica or the (200) surface on some alkali halides3). Domains of single-crystal areas were observed as reported before for the {ill} films; (200) films contain dislocations running through the film thickness. The silver halides belong to a class of materials in which significant amounts of ionic or defect motion can occur. Thus, the current through these materials can be carried in whole or in part by the ionic species. The conductivity (G) is given by the equation r~= AT-’
exp(-
AE/kT) (ohm-’
cm-‘),
(1)
if there is a single majority carrier l). The reciprocal temperature dependence of eq. (1) has so little effect compared to the exponential term that it is usual461
R. C. BAETZOLD ANDJ. F. HAMILTON
462
ly neglected. Some representative values for room temperature ionic conductivity of various single crystal materials are listed in table 1. These data should indicate that silver halide is by no means unique in possessing cation mobility and there are some materials with much higher conductivity. Of course, many materials have low ionic conductivity and in many cases the cation is not the majority carrier. In CdF,, for example, fluorine vacancies are the majority carriera) and in thallium halides anions are the majority carrier 5). TABLE1 Ionic conductivity Material NaCl CuCl AgBr AgCl KAg415 ((CH3)4N)zAg13115 AgI (a form) AgI (p form) AgI(y form)
Ref. 1 16 1 1 17 18 19 19 19
in single crystals at room temperature (T (ohm-‘cm-l) 2.2 x 1045 6 x 10-3 1 x 10-S 1 x 10-3 0.21 0.04 1 6 x 1O-7 2 x 10-5
Disorder Schottky Frenkel Frenkel Frenkel
_
Majority carrier cu+ Ag+ Ag+ Ag+ Ag+ Ag+ Ag+ Ag+
2. Experimental Films were prepared by evaporation at N 1 x lo-’ Torr in a Varian VI 460 vacuum system. This system is completely oil-free, using ion pumping, titanium sublimation pumping, and liquid-nitrogen-cooled vacsorb pumping. The interior parts of the system were stainless steel. Parts needed for evaporation were prepared from nickel-plated copper to reduce contamination. The films were deposited at room temperature on cleaved mica or alkali halide surfaces. After deposition, the films were heated to N 150°C for annealing and resistivity was recorded versus temperature during the cooling cycle, which lasts roughly three hours. The resistance of films was measured by applying a low frequency (N 1 cycle/set) ac potential of 3 V to the electrodes. Electrodes composed of silver or gold evaporated onto the substrate prior to film preparation were employed. In this system we found that a 3 V dc potential can cause irreversible electrolysis of the AgBr producing silver and pits due to bromine evolution. The conductivity of annealed films is found to be independent of electrode material over the temperature and thickness ranges employed in this work. Blocking effects are not observed
IONIC CONDUCTIVITY
OF
463
AgBr FILMS
with the gold electrodes presumably because a small amount of silver is reduced near the electrodes either by electrolysis or annealing. A similar explanation has been recently used in the case of AgI to explain identical conductivity results using graphite and silver electrodese). The activity of Frenkel point defects in AgBr is constant over a wide range of external halogen pressure or silver metal activity’). The present films possess a degree of non-stoichiometry in the direction of excess silver. This may arise from the fact that they are evaporated at a temperature not far below the decomposition temperature of AgBr. The excess silver is indicated by development of these films in photographic developers unless they have been treated with halogen vapor. Irreversible electrolysis is kept low by use of the ac potential. We observe in experiments with dc potentials a polarization effect with a half time of about 30 sec. Since this polarization time is much greater than the time the current flows in one direction in the ac experiments, decomposition effects should be small. The conductivity data reported have employed gold electrodes, but similar measurements were obtained when silver electrodes were used. Films were deposited at a constant rate of N 7 A/set using a Sloan crystal unit for monitoring frequency. Thicknesses of films measured this way are accurate to within - f5%. Contamination of AgBr films by Ti from the sublimation pumping has been found, causing a decrease in conductance. This problem can be avoided by using only ion pumping just before and during evaporation. Analysis of the films by spark-source mass spectrometry has shown the presence of Ti and other impurities in the 10 ppm range. This upper limit for impurities corresponds to one-tenth the concentration of calculated interstitial silver ions in the films at 400°K. An impurity such as Ti in greater than unity charge would introduce silver ion vacancies in the film. Since interstitial silver ions are shown later to be present in concentration excess over the vacancies, we judge such impurity effects to be unimportant. The ionic conductivity in AgBr (a) is obtained from the conductance (c) by
o=~=~nj~je, (con d uctance = reciprocal
resistance),
(2)
where the conductance is measured for a film of square cross-section having a thickness t. The summation.extends over all charge carriers of concentration nj; pj is their mobility and e the electronic charge. In silver halides interstitial silver ions and silver ion vacancies are the primary carriers; the former dominates in the conductivity of intrinsic materials because of its
464
R. C.
BAETZOLD
AND
.I. F. HAMILTON
greater mobility. The Frenkel equilibrium stitials (nr) and of vacancies (n,):
relates the concentration
n,nv = K .
of inter-
(3)
Addition of a divalent impurity such as Cd++ to AgBr creates vacancies, part of which are free. The Frenkel equation (3) may be used to show the dependence of conductivity on impurity content. 2.1.
SPACE-CHARGE LAYERS
The charge carriers in AgBr form within the bulk in equal concentration. At a surface, however, there is the possibility of differences in concentration since the interstitial Ag+ and vacancy are not required to form simultaneouslys-10). When a point defect is formed at the surface a charge-compensating surface site is created. For example, an interstitial silver ion may be generated from a positive kink site. The effective charge of this site prior to the process is taken as +3 and the effective charge after interstitial formation would then be -3. Other kinds of sites may be involved in interstitial formation, such as the domain boundaries or edge dislocations mentioned previously. The parts of the models used to describe these phenomena will be presented to aid in interpreting our data. The mathematical model of space-charge layers in ionic crystals has been discussed. Lehovecs) and Kliewers) have considered intrinsic and extrinsic crystals in which the surface provides an unlimited source of sites for defect formation. A recent treatment by Poeppel and Blakely lo) discusses the situation which arises when the surface provides a limited number of sites for defect formation. Both treatments will be utilized for analysis of data. Frenkel defects are responsible for ionic conductivity in the silver halides. The concentration of interstitial silver ions (n,) or vacancies (n,) is dependent on the space-charge potential [4(X)] by the relations n, = 22 exp { - p [AC; + e$ (X)]}
ny=zexp{-p[AG:-e~(x)l},
,
(44 (4b)
where j?= llkt, Z is the number of AgBr ion-pairs per unit volume, AC, is the standard free energy change of interstitial formation and AC, is the standard free energy change of vacancy formation. The free energy terms are defined by Poeppel and Blakely lo) in terms of the number of surface sites per unit area capable of forming an interstitial (NJ and the number of these sites which bind an Ag+ ion (n,), AC; = AC, + kT In
IONIC
CONDUClWITY
OF
AG;=AG,-kTln
AgBr
465
FILMS
,
where AG; is the standard free energy change of interstitial AG; is the standard free energy change of vacancy formation surface under consideration. Note that when n, =+NS, the entropy terms for surface A sketch of the dependence of n, and n, on distance from the case AG; < AG; is shown in fig. 1. A solution for the potential C#I (X) may be obtained using tion, - 47rp v=4 = ~ E&O ’
formation and at the particular sites are zero. the surface for Poisson’s equa-
(6)
where p = charge density, E= dielectric constant, and E,-,= permittivity of free space.
Concentration
Potential
oI-x A
Fig. 1.
Sketch of space charge layer in AgBr.
This has been solved for pure AgBr crystals and crystals containing divalent cations. When this process has been completed, substitution of 4 (X) into eq. (5) gives the complete dependence of defect concentration on position as sketched in fig. 1. The space-charge region extends a distance roughly equal to the Debye distance A, where 1
=
&co expCB (W
Be2 22 In
+ 441 * > ’
these equations the difference in potential between bulk and the surface
466
R. C.
where defects are created
BAETZOLD
AND
J. F. HAMILTON
(4m) is given by
4, = ;
(AG: - AG;).
(8)
3. Results Measurements of conductance are made after films have been annealed by heating to 150°C. Data recorded during evaporation indicate negligible conductance until an average thickness of 200-500 A of AgBr is deposited. Apparently, at this thickness the islands of AgBr coalesce, forming continuous pathways for conduction. Conductance increases sharply at this point, then levels off, varying linearly with thickness. The conductance recorded during deposition increases with evaporation rate and a significant decrease in conductance is observed at the conclusion of evaporation. The change in conductance at the conclusion of evaporation would require a 17°C change in temperature of the entire film if the effect is to be attributed to heating of the film by condensing molecules. Since this temperature change is large in relation to the observed times for heat transfer in the system, it is unlikely that the observed conductivity change is due entirely to a heating effect.
I
I
_-A-
.__________--A--@ I
I
1000
5000
Thickness,
Fig. 2.
Conductance
:
A
(c) versus thickness for {111)AgBr films on mica.
IONIC
3.1. fill)
CONDUCTIVITY
OF &@r
FILMS
467
FILMSON MICA
The conductance of {111) AgBr films on mica exhibits a thickness-dependent and thickness-independent part as shown in fig. 2. This behavior was observed before in an oil-diffusion system. The data plotted in fig. 2 indicate that both slope and intercept are temperature dependent. This type of thickness dependence is in accord with ionic conduction by a surface component and a thickness-dependent component. The activation energy of the surface space-charge component is 0.36kO.07 and that of the bulk component is 0.41 f0.05. These values are obtained from the plots in fig. 3 and are considerably less than the intrinsic activation energy, 0.79 eV, found in bulk single crystals. In addition, the concentration of interstitial silver ions is greater in the bulk of films than in single crystals. Employing our measured values for c in eq. (2) and values for the mobilityrr) we calculate values for the concentration of interstitial silver ions in table 2. These defect concentrations in the film indicate that the vacancy concentration is less than the interstitial silver
103/T Fig. 3.
Dependence
(OK)
of bulk conductivity (0) and surface conductance for {lll)AgBr films.
(c) on temperature
468
R. C. BAETZOLD
AND
TABLE
J. F. HAMILTON
2
AgBr film and single crystal data Single crystal
AE(ev) o(308 “IQ no(400 OK) m(333"K)
0.79 2.2 x 10-s 2.6 x 1017 7.3 x 10’5
Oil system
Present work
0.35 2.5 x 1O-5
0.36 1.0 x 10-s 2.1 x 1018 5.4 x 10’7
_
ion concentration in order to maintain the Frenkel equilibrium. Therefore we believe that both on the surface and in the bulk, interstitial Agf can form by some means independent of mobile vacancy formation. The com~nsating negative charge is localized at surface defects, such as kink sites, domain boundaries, or edge dislocations. According to this assumption, the activation energy for conduction due to the surface component of fig. 3 is AE = A,??”-I- AG; = 0.36,
(9)
where the activation energy for motion (AE”) is taken to be the previously measured valuerf) 0.145 eV. This gives the result AG;=O.Zl eV. Since the Frenkel defect formation energy 1) is 1.06 eV and AG;+AG:=AG,+AG,-liTln2,
(IO)
we evaluate AG:=0.85 eV. Eq. (8) predicts that Cp, =0.32 eV. The Debye thickness, which extends the distance of the space-charge layer, is calculated from eq. (7) to be ,X= 4600 A at 308 “K and ;1= 520 A at 400°K. The value of the activation energy for conductivity in these films indicates a different mechanism for carrier formation than in intrinsic AgBr. The primary carrier is interstitial Ag”, as will be demonstrated by the effect of CdBr, on ionic conductivity. Two possible causes of the extrinsic conductivity are impurities or structure of the films which permits interstitials to form independently of vacancies. The present data are compared with data for films prepared in an oildiffusion system and with single-crystal results in table 2. Apparently, ionic conductivity is changed only slightly using the oil system. There are large differences in behavior between films and single crystals. Conductivity is higher for thin films and the activation energy is much lower. In addition to these results, we have exposed fresh AgBr films to atmosphere before annealing. The effects observed are small decreases in conductivity of exposed films, apparently indicating that the effects on mechanisms of interstitial formation and movement are minor. Larger decreases
IONIC~~NDKJ~TMTY~F
AgBr
469
FILMS
in conductivity are observed in films prepared at base pressures greater than 5 x lo-’ Torr. This behavior is probably due to contamination. The space charge component of conductance can be used to give the area density of carriers in the space charge layer (n,). The surface component (intercept of fig. 2) Intercept = n,pte
(11)
is used to derive the result n4 = 1.4 x 1013 carriers/cm’
at 400°K)
n, = 3.0 x 1012 carriers/cm’
at 308°K.
Here is assumed that the interstitial silver ion mobility is the same in the surface space-charge layer as in the bulk. The high-temperature data correspond to approximately 1% of the number of ions in a {11l} monolayer of AgBr. An independent check of the experimental results from eq. (11) can be made by employing
(12) which is derived by Lehovecs). We take .sO=8.84 x lo-i4 A-see/V-cm, a= 13.1, and values for 4, and I derived before. We calculate nq= 1.5 x lOi
333°K o-o-
0-0
I
1000
5000
Thickness,
Fig. 4.
Conductance
i
(c) versus thickness for {lll}AgBr Cd++.
films containing
0.003 mol %
470
R. C.
BA ETZOLD
AND
J. F. HAMILTON
carriers/cm’ at 308 “K and n, = 1.4 x 10”3 carriers/cm’ at 400°K. The comparison with earlier experimental values from eq. (11) verifies the consistency of this analysis. Rough agreement is the best that can be expected from comparison of these two methods and we attach no special significance to the fact that at 400°K the agreement is better than at 308°K. An identification of interstitial Agf as the majority carrier in the surface region of {11l> films is made by examining conductance as a function of Cd+’ concentration in the manner analogous to that used by Koch and Wagnerls) for the bulk properties of large crystals. The data in fig. 4 were obtained for AgBr samples containing 0.003 mol% Cd’ * . We describe the dependence of conductivity on divalent-impurity concentration for the case where in the pure material the primary source of interstitial Ag’ is the concentration S of immobile negative charges, as described before. In this case 9
(pure)- S,
(13)
when Cd++ ions are added, resulting in vacancy formation, electrical neutrality considerations require that S+n,=(Cd++)+pt,.
(14)
Substituting eq. (3) into eq. (14) gives $+[(Cd++)-S]n,-I(=O.
(15)
The minimum in conductance [eq. (2)] occurs when ~,,uI=nV~,. Employing this result and eq. (15) leads to the prediction of a minimum conductance when (Cd’ *) = ?zl(pure) + Kf [(~~
- (~~1.
(16)
The conductance of (1113 films containing Cd’ ’ has been separated into a bulk and surface component as in fig. 4. The slope and intercept at 400°K are 1.8 x 10T5 ohm-l cm-’ and 7 x 10-r’ ohm-‘, respectively. Corresponding values in pure AgBr indicate that the majority carrier in both surface and bulk is interstitial Ag+. We plot in fig. 5, the ratio of the bulk conductivity in doped to pure AgBr films versus Cd++ concentration at 400°K. These data agree with position of minimum calculated using eq. (16) and available values”3 ii) for pr, pLyand K, which is 0.017 mol% Cd+ ‘. The solid lines in fig. 5 arise from calculated values using eq. (15) in the limiting regions of low and high impurity.
IONICCONDUCTMTYOF AgBr
FILMS
471
Fig. 5. Log conductivity ratio for unpure to pure (c&O) versus logCd++ concentration for f 1 I1 f AgBr films at 400°K. f0 experimental points, solid lines calculated by eq. (15), $ denotes position of minimum calculated by eq. (16}.]
.05
.I
?‘oCd++ Fig. 6. Ratio of intercept (Z/Z,,,,) at 400°K in impure to pure {11 1) AgBr films at 400°K. [O experimental points, solid line calculated by eq. (15), as explained in the text.
The surface component of conductivity is plotted versus Cd’ ’ concentration in fig. 6. A negligible value for the intercept is observed at high levels of Cd++. At these Cd++ levels, vacancies are the predominant carrier in the surface region. The solid line in fig. 6 arises from solving eq. (15), assuming
412
R. C. BAETZOLD
AND
1. F. HAMILTON
uniform defect concentration in the Debye layer 1= 520 A calculated before and setting S=n,= 1.4 x lOi carriers/cm2. Apparently, this crude model of the space-charge region agrees with experiment well. We do not believe our data at lower temperature warrant analysis by this technique because of greater experimental error. Accurate data in this region would permit an evaluation of the impurity-vacancy association constant. 3.2. (200) FILMS The conductance of (200) films on a typical alkali halide substrate (KCl) is examined versus thickness in fig. 7. A zero intercept is observed within experimental error. This indicates an absence of significant surface conductivity in these films. The conductivity and activation energy for (200) AgBr
/’
/’
I’
/’
,’
333OK
_&___-c _o---cc-‘U---1000 Thickness,
Fig. 7.
5000
A
Conductance (c) versus thickness for {2OO}AgBr films on KCl.
films on various alkali halide substrates are listed in table 3. Note that conductivity seems to increase and activation energy seems to decrease as the misfit between AgBr and substrate lattice becomes greater. Interstitial silver ions are the majority carriers in these (200) films. A decrease in conductance is observed on evaporating small amounts of CdBr, with the AgBr. A minimum in conductance versus mole percent (Cd+ ‘) is observed for 5000 A thick (200) films on NaCl substrate in fig. 8. Employing eq. (16) leads to the predicted minimum at 0.0076 mol% for 400°K and 0.0005 mol% for 333°K. The experimental data in fig. 8 are consistent with
IONICcotmucrrvrrv
473
OF AgBr FILMS
TABLE3 Films of AgBr Substrate
LiF NaF NaCl KC1 KBr KI
Mica
Misfit
-31% -20% - 2.5 % -+9% i14% -t-22%
AC/C
u400 0
u3330
(ohm-km-l)
0 0.1 0.5 0.5 0.5 0.5
1.5 3.1 1.5 1.7 4.4 2.2
x x x x x x
0.3
3.4 x 10-5
(ohn-lcm-l)
10-a 10-a 10-6 10-a 10-a 10-a
I .5 5.0 3.2 2.8 7.8 3.6
x x x x x x
IO-4
0.40
zk
10-s 10-5 1O-6 1O-6 10-b
0.46 0.53 0.49 0.50 0.49
k f f zt i
3.0 x 10-4
0.03 0.05 0.04 0.07 0.07 0.07
0.41
the calculated value at 4OO”K, but a discrepancy at 333 “K similar to that observed in (111) films is noted. Some discrepancy is expected in these values because of the rough manner in which the minimum in o is determined. Alternatively, impurities in the “pure” films would reduce cr and predict a lower value of n, (pure) in the analysis by eq. (14). Nevertheless, we believe that the rough agreement in
I 0.01
I 0.02
I
0.03
Mole percent Cd* Fig. 8.
Ratio of conductance (c/c rure) for impure to pure AgBr films on NaCl versus mole percent (Cd++). (t denotes calculated lower limit for the minimum.)
474
R. C. BAETZOLD
AND J. F. HAMILTON
position of the minimum from the two types of experiments indicates that our interpretation of the mechanism is right. The dependence of conductivity of (2001 films on substrate is shown in table 3. The misfit between AgBr lattice constant and substrate lattice constant is involved in determining cr. Apparently a misfit causes a disorder throughout the AgBr film which causes 5 to increase. An exception to this rule is ICI, in which the +22x misfit results in only a minor increase in r~ over materials with lower misfit. Possibly the AgBr lattice cannot respond to the deformation normally induced by substrate. Electron micrographs and diffraction patterns of the AgBr films on each alkali halide substrate have been made. They indicate a (200) surface on each substrate and structural features similar to those previously describeds). An attempt was made to correlate cr values with the density of dislo~tions on the f2OOj films. This attempt was unsuccessful - no correlation was found. The density of dislocations was measured to be in the range 4-8 x lo9 dislocations/cm2, showing no trend with 6. The lattice constant of AgBr on various alkali halide substrates has been examined by X-ray diffraction. We find distortion of 10000 A films of AgBr which is less than 0.1% from the bulk value. Thus, the difference in bulk conductivity on various substrates cannot be explained by lattice distortions. The surface of the evaporated AgBr as it condenses onto the film includes a transient disorder which heals in a few seconds. This is indicated by a rapid decrease of conductance when evaporation is stopped. Table 3 shows this relative change of conductance AC/Con various substrates. The loss of conductance corresponds to 2.3 x lOi Ag+ carriers, for example, on KBr substrate which represents l/1000 of an AgBr monolayer. The activation energy for conductivity in (2001 films is in the range 0.40 to 0.53 eV, depending upon the substrate. The value of the activation energy for the bulk (1 ll} films is in this range. The variation in AG; apparently TABLE
4
AgBt films on alkali halides Substrate
LiF
NaF NaCl KC1 KBr KL
0.25 0.31 0.38 0.27 0.35 0.34
0.81 0.75 0.68 0.79 0.71 0.72
0.28 0.22 0.15 0.26 0.18 0.19
IONIC
CONDUCTIVITY
OF
AgBr
FILMS
415
causes the effects observed. Values for the (200) films appearing in table 4 were calculated as before. These data apply to defect creation at the dislocation and potential is measured between bulk and the dislocation. 4. Discussion This work has shown that there are large effects on ion motion depending upon the surface. Silver ions are present in higher concentration near the { 11 l} surface in AgBr, compared to the (200) surface. A perfect (200) plane contains equal numbers of positively charged and negatively charged ions, but a perfect (111) plane consists of only one type of ion or the other. In practice a (11 l> surface is sufficiently disordered that the net surface charge is balanced by ions of the opposite charge. The number of sites for Ag+ formation is independent of surface/volume ratio in (200) films, as fig. 7 shows. Thus, the dislocations that run throughout the bulk of the film may be acting as these sites. The number of dislocations is independent of surface/volume ratio and apparently does not vary much with substrate lattice constant. The values of 4, that we derive for these films are larger than the value 0.14 eV found by Trautweilerrs) for large single crystals with no single crystallographic surface. In addition, considerable error is involved in measuring the above value for single crystals. We have also shown that IJ and AE are quite different in single crystals and the oriented films we prepare. The latter effect apparently arises from defect-generated carriers. The value of AG; for the { 11 l} films, 0.21 eV, is lower than the analogous values for (200) films in table 4. If the free energy of interstitial formation (AG,) is the same in both films, eq. (5a) suggests that the ratio n,/NS is larger in { 1111 films than (200) films. This indicates that saturation of sites by binding Ag+ is greater in { 11 l} films and may be related to the surface conductivity observed in the latter. There is the possibility that N, is very much larger for { 11 l} surfaces than for (200) surfaces, which would account for the surface conductivity phenomena observed. This situation would be consistent with a model proposedl4) for the (11 l} surface in which a nearly half full layer of Agf ions covers a full layer of Br- ions. The calculated Debye distances are less than the film thickness at high temperature, but may be comparable to the film thickness at low temperature. Though a solution for the space charge potential is more complex at low temperatures, Kliewer et a1.15) have shown there will exist a space charge region near the surface where equations similar in form to eqs. (4a) and (4b) hold. Thus, our analysis of space charge conductivity is valid.
476
R. C. BAETZOLD
AND
.I. F. HAMILTON
References 1) F. C. Brown, in: The Physics of Soliak (Benjamin, New York, 1967) ch. 10. 2) F. Trautweiler, L. E. Brady, J. W. Castle and J. F. Hamilton, in: The Structure and Chemistry of Solid Surfaces (Proc. 4th Intern. Materials Symp., Univ. of California, Berkeley, California, 1968), Ed. G. A. Somorjai (Wiley, New York, 1969) p. 83-l. 3) L. E. Brady, J. W. Castle and J. F. Hamilton, Appl. Phys. Letters 13 (1968) 76. 4) Y. T. Tan and D. Kramp, J. Chem. Phys. 53 (1970) 3691. 5) P. Suptitz and J. Teltow, Phys. Status Solidi 23 (1967) 9. 6) G. Cochrane and N. H. Fletcher, J. Phys. Chem. Solids 32 (1971) 2557. 7) F. A. Kroger, J. Phys. Chem. Solids 26 (1965) 901. 8) K. Lehovec, J. Chem. Phys. 21 (1953) 1123. 9) (a) K. L. Kliewer, J. Phys. Chem. Solids 27 (1966) 705. (b) K. L. Kliewer, J. Phys. Chem. Solids 27 (1966) 719. 10) R. B. Poeppel and J. M. Blakely, Surface Sci. 15 (1969) 507. 11) P. Muller, Phys. Status Solidi 12 (1965) 775. 12) C. Wagner and E. Koch, Z. Physik. Chem. B 38 (1937) 295. 13) F. Trautweiler, Photogr. Sci. Eng. 12 (1968) 98. 14) J. F. Hamilton and L. E. Brady, Surface Sci. 23 (1970) 389. 15) K. L. Kliewer and J. S. Koehler, Phys. Rev. 140 (1965) A 1226. 16) Y. W. Hsueh and R. W. Christy, J. Chem. Phys. 39 (1963) 3519. 17) B. B. Owens and G. R. Argue, Science 157 (1967) 308. 18) S. Geller and M. D. Lind, J. Chem. Phys. 52 (1970) 5854. 19) T. Kakahashi, K. Kawabara and 0. Yamamoto, J. Electrochem. Sot. 116 (1969) 357.