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Thin films of lithium cobalt oxide
SOLID STATE lowlcs
Solid State Ionics 58 ( 1992 ) 11 S- 122 North-Holland
Thin films of lithium cobalt oxide Guang
Wei, Terry E. Haas and Ronald
B. Goldner
Electra-Optics Technology Center and Department of Chemistry, Tufts University, Medford, MA 02155, USA Received
6 April 1992; accepted
for publication
2 1 April 1992
Thin films of lithium cobalt oxide have been prepared by rf sputtering from crystalline LiCoOz. Chemical analysis shows that the films as deposited are deficient in lithium. X-ray diffraction suggests that the films retain the basic rhombohedral structure of LiCoOz. A plausible structure defect model for these lithium deficient films is that of a disordered a-NaFeO, structure. Little absorption and moderate reflectivity are found in the transmission and reflectance spectra in the infrared range. The visible absorption corresponds to a direct allowed optical transition with an energy gap of 2.2 eV. Electrical conductivity measurements of the films show that at 300 K the films behave as semiconductors, with an activation energy of 0.12 eV. Ionic conductivity does not contribute significantly to the measured conductivity. Thermopower measurements indicate that the films are ptype conductors and suggest a narrow conduction band.
1. Introduction We have for several years been engaged in research on a completely inorganic electrochromic device for optical transmission modulation. This device, which has been given the name “Smart Window” [ 11, consists of a stack of live layers of thin films, two transparent (electron) conductor layers (TC), an electrochromic layer (EC), an ion conductor layer (IC) and a counter electrode layer (CE) as shown in fig. 1. The electrochromic and counterelectrode layer must each be a mixed conductor, capable of efficient transport of both ions and electrons. Numerous candidate materials have been explored for each of these
TC CE IC EC TC Glass
Substrate
Fig. 1. Schematic drawing of the structure of an electrochromic smart window. TC = transparent conductor, EC= electrochromic electrode, IC=ion conductor, CE=counterelectrode. 0167-2738/92/$05.00
0 1992 Elsevier Science Publishers
layers, and satisfactory or plausible materials exist for each of them, with some reservations. The layer for which the least satisfactory candidates currently exist is the counterelectrode. The device is converted to its “colored” (actually, reflective, in our case) state by insertion of electrons and charge-balancing lithium ions into polycrystalline tungsten trioxide, converting it to a “tungsten bronze”. Typically the counterelectrode materials have been optically passive, that is, showing little optical modulation upon oxidation or reduction. Clearly it would be desirable if the CE material were to behave in a manner complementary to that of the EC material, i.e., to “color” upon oxidation, while the W03 is reduced. If one takes the view that the electrons being introduced into the W03 are populating an initially empty broad band, leading to free electron behavior, it can be viewed as conversion from a filled band, closed shell structure, to an n-type degenerate semiconductor. The complementary behavior would then be removal of electrons from a filled band, closed-shell structure to give a p-type degenerate semiconductor. It was with this view in mind that we undertook a search to identify possible new candidate materials which might serve as counterelectrodes and behave in this complementary fashion. Transition metal oxides were natural targets of in-
B.V. All rights reserved.
116
G. Wei et al. /Thin films oflithium cobalt oxide
vestigation because they can comfortably exist in multiple oxidation states, and in general they have larger band gaps than other transition metal compounds. A number of AM02 compounds with lithium ions as the alkali metal, A, have been studied extensively [ 2-41. Among LiMOI compounds, LiCoO, has been studied as a potential battery anode material for high energy density batteries [ 3 1. For a strictly stoichiometric phase LiCo02, the trivalent cobalt ions Co3+ are in the low spin state t$,, which corresponds to a completely filled band [ 5 1. Nonstoichiometry in the alkali metal sublattice results in the presence of tetravalent cobalt Co4+ ions and corresponds to a partially filled band, t& as shown in fig. 2. During the insertion and extraction of lithium ions, equivalent numbers of electrons are injected into or extracted from the material by an external circuit. The Fermi level and the band population can thus be modulated by these electrons. Therefore we have anticipated that the color of the material would change following the lithium intercalation and that the material will be p-type in its delithiated states. For these reasons, LiCoOZ was chosen for investigation as the counterelectrode material for the smart window device. In this paper we present results on the fabrication of lithium cobalt oxide thin films and investigations of the intrinsic properties of these films. In a subsequent paper we shall describe the electrochemistry of the thin films, the variations in their optical properties with removal and insertion of lithium, and relate this information
(a) density
of states
(b) density
of states
Fig. 2. Schematic representation of the band structure corresponding to a degenerate p-type conductor behavior expected for (a) LiCoOz, and (b) delithiated LiCoOz.
to a band structure which we have calculated crystalline lithium cobalt oxide.
for
2. Experimental 2.1. Film preparation A number of techniques for preparing lithium cobalt oxide thin films were explored. These included thermal evaporation, rf sputtering, spray pyrolysis and the sol-gel method. Although films were successfully made by each of these techniques, the films made using the rf sputtering technique showed the highest optical quality. The films were a light bronze to brown in color. These films also were deemed to be the most promising candidate for the CE layer, and thus were the films whose properties were most extensively investigated. Unless stated otherwise, all references to film examinations are to sputtered films. The rf sputtering target was made by placing LiCoO, powder, prepared by a published method [ 31, in a shallow stainless steel dish. The target was positioned.about 8 cm below the substrate holder. A grounded stainless steel aperture was installed to concentrate the plasma over the powder and to minimize any sputtering from parts other than the powder target. After the chamber was evacuated to about lO-‘j Torr, a sputtering gas mixture of 14 mTorr O2 and 6 mTorr Ar was introduced. The rf power was 100 W. The substrate was heated and kept at 300” C during the deposition, and the temperature was monitored by a thermocouple mounted on the heater. Under these conditions, a sputtering time of two hours generally resulted in a deposit thickness of about 1500 A. Deposits were made on glass, quartz, a transparent conductor on glass (indium tin oxide, ITO), single crystal NaCl or a nickel film on glass, depending on the application intended for the sample. The ITO/glass substrates were 1 mm thick sodalime glass microscope slides coated with about 1500 A of IT0 prepared by rf sputtering, and had a sheet resistance of lo-20 n/O. 2.2. Film characterizations X-ray diffraction patterns for the films and for LiCoOZ powder were obtained using a Nicolet 12
G. Wei et al. / Thin films of lithium cobalt oxide
powder diffractometer, using a thin film attachment for those samples. The transmission spectra of the films deposited on glass substrate were obtained over the range 0.4 to 3.2 urn using a Beckman DK-1 A spectrophotometer. Specular reflectance spectra covering the same spectral range were determined using Beckman DK2 and Cary 17 spectrophotometers. The electrical conductivity of the as-deposited thin film was measured by a four-point probe technique over the temperature range of 4 K to 293 K and 300 K to 430 K. Thermopower measurements were made using a thermopower apparatus built in house, utilizing a temperature differential of lo-20°C over a temperature range from 150 to 350 K. Complete chemical analyses were important for characterization of the films. Lithium and cobalt content in both powder and film samples was measured by atomic absorption (AA), utilizing a Buck 100 single beam AA spectrometer, in solutions prepared by dissolving the films or powder in hydrochloric acid. The average oxidation number of cobalt was obtained by a titration experiment, and could then be used with the metal analyses to infer the oxygen content of the thin films by charge balance relationships. A titration technique using Fe2+ from ferrous ammonium sulfate as the reducing agent and Ce4+ from ceric sulfate as the titrant for determining average oxidation state was developed. This technique was based on the principle utilized by earlier workers [ 51 for application to bulk materials. Specifically, the samples were dissolved with hydrochloric acid in the presence of a known excess amount of Fe’+. The excess was then back-titrated with Ce4+ to determine the total oxidizing power of the cobalt present. (Both Co3+ and Co4+ are reduced by the ferrous ion to Co’+ ). A microsyringe of 1uQ precision was used in the back titration. The amount of material in the film samples was so miniscule that a visual end-point indicator could not be used, so the end-point of the titration was determined by twoelectrode potentiometry [ 71 with a polarizing current limited to 100 nA. The sensitivity of this technique was very good, and end-point determination within 0.05 umol was readily achieved.
117
3. Results and discussion 3. I. Chemical
analysis
Lithium cobalt oxide is a known material, well characterized and straightforward to synthesize with a reasonable degree of purity. In consequence, proof of the material by both physical characteristics such as X-ray diffraction and by analysis is straightforward. On the other hand, thin films were completely unknown prior to this work, and therefore it is vital to provide as much characterization, including complete elemental composition, as possible. A method for complete chemical analysis of lithium cobalt oxide in both its powder and film forms was therefore developed in our laboratory, as described above. For the bulk powder samples, the oxygen content could also be inferred from the mass balance, in addition to the oxidation state method. By mass balance, oxygen mass is assumed to be the difference between total mass and mass of cobalt and lithium, the latter determined by AA. The mass balance technique could not be applied to the films because the mass of the film could not be measured with sufficient accuracy. The titration method used to determine the oxidation number of cobalt in the powder was the same as that used for the analysis of the films. The composition of the starting powder was LiCoO, within experimental error by both mass balance and oxidation state determinations of oxygen content. In this analysis, the principal source of error is the uncertainty in the total cobalt content measurement by AA, which was estimated to be l-2%. In the film analysis, powder samples whose stoichiometry had already been determined were used as witness samples to give us some confidence in the titration method. A charge balance relationship was used to infer the oxygen content, z, in the samples. The usual oxidation states of -2 and + 1 were assigned to oxygen and lithium, respectively, and the cobalt oxidation number, n, was determined by the titration method. Thus the following charge balance equation was used: x+ny=2z, where x and y are the lithium and cobalt content of the sample, respectively, as determined by AA. The analytical results show that the films as de-
118
G. Wei et al. / Thinjlms
posited are deficient in lithium relative to the composition of the starting target material. The Li:Co ratio was about 0.4. The 0: Co ratio was about 1.92. It was observed that under the deposition condition which we used, the cobalt oxidation state value reached a maximum value of + 3.46. Therefore the cobalt in the films has a mixed oxidation state, equivalent to about half of the cobalt being in the + 4 state and half in the + 3 state. 3.2. Structural examination The structure of the lithium cobalt oxide powder which was used as the target material and the rfsputtered thin film made by the method as described above were examined by X-ray diffraction. The lower part of fig. 3 shows the X-ray diffraction pattern of the sample of lithium cobalt oxide powder, made from Li2C03+Co304. All the peaks match well, in d spacing and intensity, with the JCPDS file 16-427 with indexed peaks for LiCoOZ with the a-NaFeO, crystalline structure. This confirms that the lithium cobalt oxide powder synthesized in our laboratory is a polycrystalline powder LiCoO, with a single phase of the rhombohedral a-NaFe02 structure. The upper part of fig. 3 shows the X-ray diffrac-
Fig. 3. X-ray diffraction patterns for powder and thin film lithium trace for a sputtered lithium cobalt oxide film.
of lithium
cobalt oxide
tion pattern of a sputtered film with an approximate thickness of 2000 A. Comparing the two patterns, it is seen that all the prominent diffraction peaks of the film correspond to peaks in the LiCoOZ powder structure. This clearly suggests that the rf sputtered films share the basic rhombohedral structure of the target material ( LiCoOZ). Comparison of the X-ray intensities obtained from the films with those from the powder shows much higher relative intensities for the (001) reflections suggesting some preference for (001) orientation in the deposit. By combining the results of the chemical analysis and the X-ray experiments, we can develop a reasonable picture of a possible structure of these lithium deficient films. We start from the a-NaFeO, structure, which is an ordered superstructure of the sodium chloride structure, with lithium and cobalt arranged in alternate ( 111) planes. We will describe the structure of the lithium cobalt oxide film having a composition LixCoOZ_,, by a close packed struccontaining vacancies. The composition ture LixCo02_-y could then be written in two ways: Li,V L,(L-x3CoOz-,Vo~,,
or
LLVbc I -_x-.~.~Co02--y.
cobalt oxide. The lower trace is for the powder
material,
the upper
G. Wei et al. / Thin films of lithium cobalt oxide
In these formulations VLi represents a lithium cation vacancy at the octahedral sites. V, represents an anion vacancy in the close packed structure framework formed by the oxygen anions. In the first case the oxygen deficiency, y, appears structurally as point defects, specifically as oxygen vacancies, and the cobalt atoms and lithium atoms and vacancies can be considered to lie in their respective planes. By contrast, in the second case all the available oxygen is arranged in an undisturbed cubic close packed array. As is well known, in a close packed system the number of octahedral holes is equal to the number of close-packed spheres. Thus in this second case there are only 2-Y octahedral sites, instead of 2. The X-ray results discussed earlier suggest retention of the basic rhombohedral structure of the compound, and we thus assume the existence of complete layers of cobalt on one side of the oxygen plane. However, there are now only ( l-Y/2) octahedral sites available to the cobalt atoms in a “cobalt” plane, and the rest of them, Y/2, will have to occupy octahedral sites in the other layer of octahedral sites, together with the X lithium cations. From the conservation of the total available sites in one, cation layer, the number of X, Y, V,, should satisfy the following relationship: x+;+v,+;. Thus the number of vacancies, VL,, in the mixed occupied octahedral layer will be V,, = 1 - X-Y. The elemental distribution in this close packed ionic structure can then be described as follows: (V1-,-,Li,Coy,2) (Li, Co layer)
(CoI-,,Z) (Co layer)
119
gation results on Nao.,CoOz cobalt bronze by Stoklosa et al. [ 81. In their thermogravimetric and electrical conductivity study, they concluded that, except for sodium vacancies resulting from the nonstoichiometry in the sodium sublattice, the predominant ionic defects in the cobalt bronze are cobalt ions substituted at sodium sites, and that oxygen vacancies as point defects did not exist. 3.3. Optical properties Figs. 4 and 5 show the transmission and reflection spectra, respectively, of a 2000 A thick as-deposited film on a glass substrate, over the spectral range of 400 to 2500 nm. The film has high 65% transmission and 30-35% spectral reflectance throughout the in-
“d:
2.5
3
: 5
Wavelength (micrometers)
Fig. 4. Transmission ide film.
spectrum
for a sputtered
lithium cobalt ox-
(OZ-,) (0 layer)
Essentially this structural description suggests that the layer which would be a lithium cation layer in a perfectly ordered crystalline film structure is actually a mixed layer occupied by lithium and cobalt, i.e., Li,CoOZ_,, has a disordered a-NaFeO, structure. For the rf-deposited films, the x and y values are approximately 0.4 and 0.08 respectively. The model, therefore, proposes that 96% of the cobalt atoms are located in the cobalt only octahedral layer, but the remaining 4% are distributed in the other octahedral layer together with the lithium atoms. This structure defect model for the rf sputtered lithium cobalt oxide thin film is consistent with the defect investi-
0.3 0.2 0.1 I
OO 4
0.5
1
1.5
2
2.5
3
: 5
Wavelength (micrometers) Fig. 5. Specular balt oxide film.
reflection
spectrum
for a sputtered
lithium
co-
120
G. Wei et al. / Thin films of lithium cobalt oxide
frared range, thus the film shows very little absorption in this near infrared range. The absolute absorption coefficient spectrum was determined directly from the T(n), R (1) readings using the equation [ 91: a(A)=--
iln(*),
(1)
where r(n) and R(l) are the transmittance and reflectance spectra of the film. The film thickness d was obtained from a prolilometer measurement and confirmed by scanning electron microscopy. The absorption coefficient data was then fitted with the optical transition model [ 10,111: a(L) - (hv-E,,)”
.
(2)
The analysis showed that the spectral variations in the absorption coefficient can be described by this equation with n = l/2. A plot of cy2versus E is shown in fig. 6. This absorption coefficient dependence of the wavelength is that expected of a direct allowed transition. The extrapolation of the straight line region of the plot to (Y=O gives the direct allowed energy gap of 2.2 eV. The very high value of the absorption coefficient (exceeding 10’ cm-’ at the higher photon energies) is also consistent with this conclusion, since such a high value is expected only for direct allowed transitions. Therefore we can conclude that the strong absorption in the spectrum of these films is due to a direct allowed transition, with an energy gap of 2.2 eV. The slowly rising absorption edge, the so-called band tails are probably caused by defects or disor-
dered energy states near the band edge. In a disordered system, the energy bands are perturbed by the formation of states extending the bands into the energy gap forming the tails as is illustrated in the figure below. The analytical and structural results virtually require extensive disorder, and such tailing should therefore be expected. 3.4. Conductivity The electrical conductivity of an as-deposited thin film was measured by the four-point probe technique over the temperature range of 4 K to 293 K is shown in fig. 7. The material exhibited semiconducting behavior, i.e., the conductivity increased with temperature. In the range 4-l 30 K, the conductivity remained constant. Had the carriers been totally localized, the conductivity would have gone to zero at very low temperature. Thus the observation of finite conductivity at 4 K is strong evidence of the existence of extended states (i.e., free carriers). This justified application of a free electron model and band structure description to this system in the transport properties analysis. Above 130 K the conductivity increased with temperature. The conductivity in the temperature range 130-250 K does not follow simple Arrhenius activated conduction. Rather it exhibits a more complex behavior in a transition to activated conduction above about 270 K. The results shown in fig. 8 by a plot of lna versus 1/T can be fitted to eq. (3) [ 121, with an activation energy of 0.12 eV: 0.25
3V
25
0.21
5-
-0
0.5
1
1.5
2
2.5
Temperature (K)
Photon Energy (eV) Fig. 6. Square of the absorption ergy for the spectrum of lithium
coeffkient as a function of encobalt oxide from figs. 3 and 4.
Fig. 7. Conductivity 298 K.
of a thin film of lithium cobalt oxide, 4 K to
121
G. Wei et al. / Thin.films of lithium cobalt oxide
K, the lithium ion mobility, ,ULi,is 2 X 1O-6 cm*/Vs. The chemical analysis on the films and crystallographic data for the bulk solid allow us to estimate number density of lithium to be 1 x 1O**which gives an estimated ionic conductivity of 2 x 10P3 S cm- ‘. This is two to three orders of magnitude smaller than the conductivity measured in this temperature range, and allows us to confidently conclude that the measured conductivity is electronic, not ionic. -1.84 26
2.7
2.8
2.9 mx
Fig. 8. Log (conductivity) 300-430 K.
a=aexp(
-EJk,T)
3 3.1 1000
versus 1/r,
3.2
3.3
for the temperature
.
I
3.6. Thermopower
3.4
range
(3)
3.5. Carrier concentration and mobility We can utilize some of the results discussed above to estimate carrier concentration, and hence mobility. The titration experiment results show that 46% of the cobalt in the sample was in a 4+ oxidation state, and the atomic absorption results gave the total cobalt contained in the sample. Thus, making the reasonable assumption that one Co4+ ion generates one hole as the carrier and using the crystallographic data for the powder [ 131, the carrier concentration of the film can be estimated to be 1.OS x 1O**cmA3. At room temperature, the conductivity is approximately 0.5 S cm-‘. From a=e[p]p ( [p] =hole concentration), we can estimate the hole mobility to be 3 x 10-4cm2/V-s. An attempt was made to measure the Hall mobility, but the effect was below the measurable level. From an estimate of the minimum observable signal in the apparatus, about 10 FV, we were able to place an upper bound on the hole mobility of about 6 x 1O-4 cm’/V-s, a value quite consistent with that estimated above. It is worth noting here that the contribution of the lithium ion conductivity to total conductivity can be estimated, using previously measured values for the mobility of the lithium ions in crystalline LiCo02. The ionic conductivity, and the mobility of the lithium ions, have been independently measured by two groups, with excellent agreement in their experimental results [ 14,15 1. At 300
Fig. 9 shows the thermopower of an rf sputtered lithium cobalt oxide film as a function of temperature. We note first that the sign of the low temperature thermopower clearly indicates that the charge carriers are positive, i.e., the material is behaving as a p-type semiconductor. This result is in good agreement with literature reports on thermopower in Li,Co02 [ 16,171. In view of the mobility estimates given above, the large carrier concentration and moderate conductivity, the small absolute value of the thermopower suggests that the carriers (holes) have a large effective mass. Our band structure model, the electronic conductivity value and the large carrier concentration all suggest that the film is a degenerate semiconductor. A very general model for the thermopower of such materials is available [ l&l9 ] but accurate evaluation requires knowledge about the scattering mechanisms prevalent in the material. Nevertheless, using the experimental value for cy at 300 K, 0.1 mV/K, this model for the thermopower does indeed suggest
+ TI---..-...---..-....-.----------+---..--. -----.----.--. 0.15/ 0.1i
z
e
I
G
0.05
.
t
.
8_
z
!s a, -0.05
ir
i -0.v
-0.157 295
*+
+I
330
I 335
l
l
I
+
a.
+
l
* l*
300
305
310
315
320
325
Temperature (Kj Fig. 9. Thermopower
of a thin film of lithium cobalt oxide.
122
G. Wei et al. /
Thinfilmsof lithium cobalt oxide
a large value of effective mass is required for any of the possible scattering mechanisms to explain the observation. For the various possible scattering mechanisms, the temperature dependence of the thermopower can be fit by values of effective mass, m*, in the range of 8 to 25 times the electron rest mass m,, confirming the qualitative prediction above, and consistent with the very narrow bands from a density of states calculation [ 201. The reversal of sign of the thermopower seen in fig. 9 is also not uncommon. It has been observed in various compounds, including one example closely related to the present material, the polycrystalline powder I(o&o02 [ 2 1] _
4. Summary We have demonstrated in this work that it is possible to make thin films of a mixed lithium cobalt oxide material which appears to retain the basic rhombohedral structure found in crystalline LiCoOZ, despite being deficient in lithium. These rfsputtered films have optical and electron transport properties consistent with the existence of narrow bands and an allowed (i.e., direct) band gap transition in the visible region, while showing little absorption and moderate reflectivity in the near infrared. These properties, taken together with the electrochemical properties to be described in a subsequent paper [ 201, suggest that this material has promise as a counterelectrode in a “smart window” application.
Acknowledgments The authors would like to thank Robert E. Powers of the Department of Physics, Boston University for assistance with the conductivity and Hall mobility measurments. Our colleagues Floyd Arntz, Ralph Chapman and Kwok Wong, of the Tufts EOTC, and Bill Page, Ellen Candela and Charles Amass of the Tufts Chemistry Department have given invaluable advice, aid, and have lent patient and willing ears.
We would also like to thank Andrew Siegel of Loral for his help with instrument design problems. Grateful acknowledgement is also made of support from the U.S. Department of Energy under Grant FG0385SFl5927. References [ 1] R.B. Goldner, T.E. Haas, G. Seward, K.K. Wong, P. Norton, G. Foley, G. Berera, G. Wei, S. Schulz and R. Chapman, Solid State Ionics 28-30 (1988) 1715. [ 21 K. Vidyasagar and J. Gopalakrishnan, J. Solid State Chem. 42 (16982) 217. [3] K. Mizushima, P.C. Jones, P.J. Wiseman and J.B. Goodenough, Mat. Res. Bull 15 ( 1980) 783; Solid State Ionics 3/4 (1981) 171. [4] T.A. Hewston and B.L. Chamberland, J. Phys. Chem. Solids 48 (1987) 97. [S] W.D. Johnston, R.R. Heikes and D. Sesttich, Phys. Chem. Solids 7 (1958) 1. [6] M. Oku, J. Solid State Chem. 23 (1978) 177. [7] A.J. Bard and L.R. Faulkner, Electrochemical Methods (Wiley, New York, 1980). [ 81 A. Stoklosa, J. Molenda and Do Than, Solid State Ionics 15 (1985)211. [ 91 G.R. Fowles, Introduction to Modem Optics (Dover, New York, 1975). [ lo] R.H. Bube, Electronic Properties of Crystalline Solids (Academic, New York, 1969) p. 415. [ 111 J.I. Pankove, Optical Processes in Semiconductors (Dover, NewYork, 1971). [ 121 M. Ali Omar, Elementary Solid State Physics (AddisonWesley, Reading, MA, 1975) p. 275. [ 131 H.J. Orman and P.J. Wiseman, Acta Cryst. C40 (1984) 12. [ 141 M.S.G.R. Thomas, P.G. Bruce, and J.B. Goodenough, Solid State Ionics 17 (1985) 13 [ 15 ] A.H. Honders, J.M. der Kinderen, A.H. van Heeren, J.H. W. de Wit and G.H.J. Broers, Solid State Ionics 15 ( 1985) 265 and 18/19 (1986) 794. [ 161 A.H. Honders, J.M. der Kinderen, A.H. van Heeren, J.H.W. de Wit, and G.H.J. Broers, Solid State Ionics 14 (1984) 205. [ 171 H.N. M&eon, M. Zanne, C. Gleitzer and J. Aubry, Bull. Sot. Chim. Fr. (1975) 2426. [ 18 ] R.A. Smith, Semiconductors (Cambridge University Press, Cambridge, 1978). [ 191 J.M. Ziman, Electrons and Phonons (Oxford University Press, Oxford, 1960). [20] G. Wei, T.E. Haas and R.B. Goldner, J. Electrochem. Sot. ( 1992), to be published. [ 2 11 C. Delmas, C. Fouassier and P. Hagenmuller, J. Solid State Chem. 13 (1975) 165.
Solid State Ionics 58 ( 1992 ) 11 S- 122 North-Holland
Thin films of lithium cobalt oxide Guang
Wei, Terry E. Haas and Ronald
B. Goldner
Electra-Optics Technology Center and Department of Chemistry, Tufts University, Medford, MA 02155, USA Received
6 April 1992; accepted
for publication
2 1 April 1992
Thin films of lithium cobalt oxide have been prepared by rf sputtering from crystalline LiCoOz. Chemical analysis shows that the films as deposited are deficient in lithium. X-ray diffraction suggests that the films retain the basic rhombohedral structure of LiCoOz. A plausible structure defect model for these lithium deficient films is that of a disordered a-NaFeO, structure. Little absorption and moderate reflectivity are found in the transmission and reflectance spectra in the infrared range. The visible absorption corresponds to a direct allowed optical transition with an energy gap of 2.2 eV. Electrical conductivity measurements of the films show that at 300 K the films behave as semiconductors, with an activation energy of 0.12 eV. Ionic conductivity does not contribute significantly to the measured conductivity. Thermopower measurements indicate that the films are ptype conductors and suggest a narrow conduction band.
1. Introduction We have for several years been engaged in research on a completely inorganic electrochromic device for optical transmission modulation. This device, which has been given the name “Smart Window” [ 11, consists of a stack of live layers of thin films, two transparent (electron) conductor layers (TC), an electrochromic layer (EC), an ion conductor layer (IC) and a counter electrode layer (CE) as shown in fig. 1. The electrochromic and counterelectrode layer must each be a mixed conductor, capable of efficient transport of both ions and electrons. Numerous candidate materials have been explored for each of these
TC CE IC EC TC Glass
Substrate
Fig. 1. Schematic drawing of the structure of an electrochromic smart window. TC = transparent conductor, EC= electrochromic electrode, IC=ion conductor, CE=counterelectrode. 0167-2738/92/$05.00
0 1992 Elsevier Science Publishers
layers, and satisfactory or plausible materials exist for each of them, with some reservations. The layer for which the least satisfactory candidates currently exist is the counterelectrode. The device is converted to its “colored” (actually, reflective, in our case) state by insertion of electrons and charge-balancing lithium ions into polycrystalline tungsten trioxide, converting it to a “tungsten bronze”. Typically the counterelectrode materials have been optically passive, that is, showing little optical modulation upon oxidation or reduction. Clearly it would be desirable if the CE material were to behave in a manner complementary to that of the EC material, i.e., to “color” upon oxidation, while the W03 is reduced. If one takes the view that the electrons being introduced into the W03 are populating an initially empty broad band, leading to free electron behavior, it can be viewed as conversion from a filled band, closed shell structure, to an n-type degenerate semiconductor. The complementary behavior would then be removal of electrons from a filled band, closed-shell structure to give a p-type degenerate semiconductor. It was with this view in mind that we undertook a search to identify possible new candidate materials which might serve as counterelectrodes and behave in this complementary fashion. Transition metal oxides were natural targets of in-
B.V. All rights reserved.
116
G. Wei et al. /Thin films oflithium cobalt oxide
vestigation because they can comfortably exist in multiple oxidation states, and in general they have larger band gaps than other transition metal compounds. A number of AM02 compounds with lithium ions as the alkali metal, A, have been studied extensively [ 2-41. Among LiMOI compounds, LiCoO, has been studied as a potential battery anode material for high energy density batteries [ 3 1. For a strictly stoichiometric phase LiCo02, the trivalent cobalt ions Co3+ are in the low spin state t$,, which corresponds to a completely filled band [ 5 1. Nonstoichiometry in the alkali metal sublattice results in the presence of tetravalent cobalt Co4+ ions and corresponds to a partially filled band, t& as shown in fig. 2. During the insertion and extraction of lithium ions, equivalent numbers of electrons are injected into or extracted from the material by an external circuit. The Fermi level and the band population can thus be modulated by these electrons. Therefore we have anticipated that the color of the material would change following the lithium intercalation and that the material will be p-type in its delithiated states. For these reasons, LiCoOZ was chosen for investigation as the counterelectrode material for the smart window device. In this paper we present results on the fabrication of lithium cobalt oxide thin films and investigations of the intrinsic properties of these films. In a subsequent paper we shall describe the electrochemistry of the thin films, the variations in their optical properties with removal and insertion of lithium, and relate this information
(a) density
of states
(b) density
of states
Fig. 2. Schematic representation of the band structure corresponding to a degenerate p-type conductor behavior expected for (a) LiCoOz, and (b) delithiated LiCoOz.
to a band structure which we have calculated crystalline lithium cobalt oxide.
for
2. Experimental 2.1. Film preparation A number of techniques for preparing lithium cobalt oxide thin films were explored. These included thermal evaporation, rf sputtering, spray pyrolysis and the sol-gel method. Although films were successfully made by each of these techniques, the films made using the rf sputtering technique showed the highest optical quality. The films were a light bronze to brown in color. These films also were deemed to be the most promising candidate for the CE layer, and thus were the films whose properties were most extensively investigated. Unless stated otherwise, all references to film examinations are to sputtered films. The rf sputtering target was made by placing LiCoO, powder, prepared by a published method [ 31, in a shallow stainless steel dish. The target was positioned.about 8 cm below the substrate holder. A grounded stainless steel aperture was installed to concentrate the plasma over the powder and to minimize any sputtering from parts other than the powder target. After the chamber was evacuated to about lO-‘j Torr, a sputtering gas mixture of 14 mTorr O2 and 6 mTorr Ar was introduced. The rf power was 100 W. The substrate was heated and kept at 300” C during the deposition, and the temperature was monitored by a thermocouple mounted on the heater. Under these conditions, a sputtering time of two hours generally resulted in a deposit thickness of about 1500 A. Deposits were made on glass, quartz, a transparent conductor on glass (indium tin oxide, ITO), single crystal NaCl or a nickel film on glass, depending on the application intended for the sample. The ITO/glass substrates were 1 mm thick sodalime glass microscope slides coated with about 1500 A of IT0 prepared by rf sputtering, and had a sheet resistance of lo-20 n/O. 2.2. Film characterizations X-ray diffraction patterns for the films and for LiCoOZ powder were obtained using a Nicolet 12
G. Wei et al. / Thin films of lithium cobalt oxide
powder diffractometer, using a thin film attachment for those samples. The transmission spectra of the films deposited on glass substrate were obtained over the range 0.4 to 3.2 urn using a Beckman DK-1 A spectrophotometer. Specular reflectance spectra covering the same spectral range were determined using Beckman DK2 and Cary 17 spectrophotometers. The electrical conductivity of the as-deposited thin film was measured by a four-point probe technique over the temperature range of 4 K to 293 K and 300 K to 430 K. Thermopower measurements were made using a thermopower apparatus built in house, utilizing a temperature differential of lo-20°C over a temperature range from 150 to 350 K. Complete chemical analyses were important for characterization of the films. Lithium and cobalt content in both powder and film samples was measured by atomic absorption (AA), utilizing a Buck 100 single beam AA spectrometer, in solutions prepared by dissolving the films or powder in hydrochloric acid. The average oxidation number of cobalt was obtained by a titration experiment, and could then be used with the metal analyses to infer the oxygen content of the thin films by charge balance relationships. A titration technique using Fe2+ from ferrous ammonium sulfate as the reducing agent and Ce4+ from ceric sulfate as the titrant for determining average oxidation state was developed. This technique was based on the principle utilized by earlier workers [ 51 for application to bulk materials. Specifically, the samples were dissolved with hydrochloric acid in the presence of a known excess amount of Fe’+. The excess was then back-titrated with Ce4+ to determine the total oxidizing power of the cobalt present. (Both Co3+ and Co4+ are reduced by the ferrous ion to Co’+ ). A microsyringe of 1uQ precision was used in the back titration. The amount of material in the film samples was so miniscule that a visual end-point indicator could not be used, so the end-point of the titration was determined by twoelectrode potentiometry [ 71 with a polarizing current limited to 100 nA. The sensitivity of this technique was very good, and end-point determination within 0.05 umol was readily achieved.
117
3. Results and discussion 3. I. Chemical
analysis
Lithium cobalt oxide is a known material, well characterized and straightforward to synthesize with a reasonable degree of purity. In consequence, proof of the material by both physical characteristics such as X-ray diffraction and by analysis is straightforward. On the other hand, thin films were completely unknown prior to this work, and therefore it is vital to provide as much characterization, including complete elemental composition, as possible. A method for complete chemical analysis of lithium cobalt oxide in both its powder and film forms was therefore developed in our laboratory, as described above. For the bulk powder samples, the oxygen content could also be inferred from the mass balance, in addition to the oxidation state method. By mass balance, oxygen mass is assumed to be the difference between total mass and mass of cobalt and lithium, the latter determined by AA. The mass balance technique could not be applied to the films because the mass of the film could not be measured with sufficient accuracy. The titration method used to determine the oxidation number of cobalt in the powder was the same as that used for the analysis of the films. The composition of the starting powder was LiCoO, within experimental error by both mass balance and oxidation state determinations of oxygen content. In this analysis, the principal source of error is the uncertainty in the total cobalt content measurement by AA, which was estimated to be l-2%. In the film analysis, powder samples whose stoichiometry had already been determined were used as witness samples to give us some confidence in the titration method. A charge balance relationship was used to infer the oxygen content, z, in the samples. The usual oxidation states of -2 and + 1 were assigned to oxygen and lithium, respectively, and the cobalt oxidation number, n, was determined by the titration method. Thus the following charge balance equation was used: x+ny=2z, where x and y are the lithium and cobalt content of the sample, respectively, as determined by AA. The analytical results show that the films as de-
118
G. Wei et al. / Thinjlms
posited are deficient in lithium relative to the composition of the starting target material. The Li:Co ratio was about 0.4. The 0: Co ratio was about 1.92. It was observed that under the deposition condition which we used, the cobalt oxidation state value reached a maximum value of + 3.46. Therefore the cobalt in the films has a mixed oxidation state, equivalent to about half of the cobalt being in the + 4 state and half in the + 3 state. 3.2. Structural examination The structure of the lithium cobalt oxide powder which was used as the target material and the rfsputtered thin film made by the method as described above were examined by X-ray diffraction. The lower part of fig. 3 shows the X-ray diffraction pattern of the sample of lithium cobalt oxide powder, made from Li2C03+Co304. All the peaks match well, in d spacing and intensity, with the JCPDS file 16-427 with indexed peaks for LiCoOZ with the a-NaFeO, crystalline structure. This confirms that the lithium cobalt oxide powder synthesized in our laboratory is a polycrystalline powder LiCoO, with a single phase of the rhombohedral a-NaFe02 structure. The upper part of fig. 3 shows the X-ray diffrac-
Fig. 3. X-ray diffraction patterns for powder and thin film lithium trace for a sputtered lithium cobalt oxide film.
of lithium
cobalt oxide
tion pattern of a sputtered film with an approximate thickness of 2000 A. Comparing the two patterns, it is seen that all the prominent diffraction peaks of the film correspond to peaks in the LiCoOZ powder structure. This clearly suggests that the rf sputtered films share the basic rhombohedral structure of the target material ( LiCoOZ). Comparison of the X-ray intensities obtained from the films with those from the powder shows much higher relative intensities for the (001) reflections suggesting some preference for (001) orientation in the deposit. By combining the results of the chemical analysis and the X-ray experiments, we can develop a reasonable picture of a possible structure of these lithium deficient films. We start from the a-NaFeO, structure, which is an ordered superstructure of the sodium chloride structure, with lithium and cobalt arranged in alternate ( 111) planes. We will describe the structure of the lithium cobalt oxide film having a composition LixCoOZ_,, by a close packed struccontaining vacancies. The composition ture LixCo02_-y could then be written in two ways: Li,V L,(L-x3CoOz-,Vo~,,
or
LLVbc I -_x-.~.~Co02--y.
cobalt oxide. The lower trace is for the powder
material,
the upper
G. Wei et al. / Thin films of lithium cobalt oxide
In these formulations VLi represents a lithium cation vacancy at the octahedral sites. V, represents an anion vacancy in the close packed structure framework formed by the oxygen anions. In the first case the oxygen deficiency, y, appears structurally as point defects, specifically as oxygen vacancies, and the cobalt atoms and lithium atoms and vacancies can be considered to lie in their respective planes. By contrast, in the second case all the available oxygen is arranged in an undisturbed cubic close packed array. As is well known, in a close packed system the number of octahedral holes is equal to the number of close-packed spheres. Thus in this second case there are only 2-Y octahedral sites, instead of 2. The X-ray results discussed earlier suggest retention of the basic rhombohedral structure of the compound, and we thus assume the existence of complete layers of cobalt on one side of the oxygen plane. However, there are now only ( l-Y/2) octahedral sites available to the cobalt atoms in a “cobalt” plane, and the rest of them, Y/2, will have to occupy octahedral sites in the other layer of octahedral sites, together with the X lithium cations. From the conservation of the total available sites in one, cation layer, the number of X, Y, V,, should satisfy the following relationship: x+;+v,+;. Thus the number of vacancies, VL,, in the mixed occupied octahedral layer will be V,, = 1 - X-Y. The elemental distribution in this close packed ionic structure can then be described as follows: (V1-,-,Li,Coy,2) (Li, Co layer)
(CoI-,,Z) (Co layer)
119
gation results on Nao.,CoOz cobalt bronze by Stoklosa et al. [ 81. In their thermogravimetric and electrical conductivity study, they concluded that, except for sodium vacancies resulting from the nonstoichiometry in the sodium sublattice, the predominant ionic defects in the cobalt bronze are cobalt ions substituted at sodium sites, and that oxygen vacancies as point defects did not exist. 3.3. Optical properties Figs. 4 and 5 show the transmission and reflection spectra, respectively, of a 2000 A thick as-deposited film on a glass substrate, over the spectral range of 400 to 2500 nm. The film has high 65% transmission and 30-35% spectral reflectance throughout the in-
“d:
2.5
3
: 5
Wavelength (micrometers)
Fig. 4. Transmission ide film.
spectrum
for a sputtered
lithium cobalt ox-
(OZ-,) (0 layer)
Essentially this structural description suggests that the layer which would be a lithium cation layer in a perfectly ordered crystalline film structure is actually a mixed layer occupied by lithium and cobalt, i.e., Li,CoOZ_,, has a disordered a-NaFeO, structure. For the rf-deposited films, the x and y values are approximately 0.4 and 0.08 respectively. The model, therefore, proposes that 96% of the cobalt atoms are located in the cobalt only octahedral layer, but the remaining 4% are distributed in the other octahedral layer together with the lithium atoms. This structure defect model for the rf sputtered lithium cobalt oxide thin film is consistent with the defect investi-
0.3 0.2 0.1 I
OO 4
0.5
1
1.5
2
2.5
3
: 5
Wavelength (micrometers) Fig. 5. Specular balt oxide film.
reflection
spectrum
for a sputtered
lithium
co-
120
G. Wei et al. / Thin films of lithium cobalt oxide
frared range, thus the film shows very little absorption in this near infrared range. The absolute absorption coefficient spectrum was determined directly from the T(n), R (1) readings using the equation [ 91: a(A)=--
iln(*),
(1)
where r(n) and R(l) are the transmittance and reflectance spectra of the film. The film thickness d was obtained from a prolilometer measurement and confirmed by scanning electron microscopy. The absorption coefficient data was then fitted with the optical transition model [ 10,111: a(L) - (hv-E,,)”
.
(2)
The analysis showed that the spectral variations in the absorption coefficient can be described by this equation with n = l/2. A plot of cy2versus E is shown in fig. 6. This absorption coefficient dependence of the wavelength is that expected of a direct allowed transition. The extrapolation of the straight line region of the plot to (Y=O gives the direct allowed energy gap of 2.2 eV. The very high value of the absorption coefficient (exceeding 10’ cm-’ at the higher photon energies) is also consistent with this conclusion, since such a high value is expected only for direct allowed transitions. Therefore we can conclude that the strong absorption in the spectrum of these films is due to a direct allowed transition, with an energy gap of 2.2 eV. The slowly rising absorption edge, the so-called band tails are probably caused by defects or disor-
dered energy states near the band edge. In a disordered system, the energy bands are perturbed by the formation of states extending the bands into the energy gap forming the tails as is illustrated in the figure below. The analytical and structural results virtually require extensive disorder, and such tailing should therefore be expected. 3.4. Conductivity The electrical conductivity of an as-deposited thin film was measured by the four-point probe technique over the temperature range of 4 K to 293 K is shown in fig. 7. The material exhibited semiconducting behavior, i.e., the conductivity increased with temperature. In the range 4-l 30 K, the conductivity remained constant. Had the carriers been totally localized, the conductivity would have gone to zero at very low temperature. Thus the observation of finite conductivity at 4 K is strong evidence of the existence of extended states (i.e., free carriers). This justified application of a free electron model and band structure description to this system in the transport properties analysis. Above 130 K the conductivity increased with temperature. The conductivity in the temperature range 130-250 K does not follow simple Arrhenius activated conduction. Rather it exhibits a more complex behavior in a transition to activated conduction above about 270 K. The results shown in fig. 8 by a plot of lna versus 1/T can be fitted to eq. (3) [ 121, with an activation energy of 0.12 eV: 0.25
3V
25
0.21
5-
-0
0.5
1
1.5
2
2.5
Temperature (K)
Photon Energy (eV) Fig. 6. Square of the absorption ergy for the spectrum of lithium
coeffkient as a function of encobalt oxide from figs. 3 and 4.
Fig. 7. Conductivity 298 K.
of a thin film of lithium cobalt oxide, 4 K to
121
G. Wei et al. / Thin.films of lithium cobalt oxide
K, the lithium ion mobility, ,ULi,is 2 X 1O-6 cm*/Vs. The chemical analysis on the films and crystallographic data for the bulk solid allow us to estimate number density of lithium to be 1 x 1O**which gives an estimated ionic conductivity of 2 x 10P3 S cm- ‘. This is two to three orders of magnitude smaller than the conductivity measured in this temperature range, and allows us to confidently conclude that the measured conductivity is electronic, not ionic. -1.84 26
2.7
2.8
2.9 mx
Fig. 8. Log (conductivity) 300-430 K.
a=aexp(
-EJk,T)
3 3.1 1000
versus 1/r,
3.2
3.3
for the temperature
.
I
3.6. Thermopower
3.4
range
(3)
3.5. Carrier concentration and mobility We can utilize some of the results discussed above to estimate carrier concentration, and hence mobility. The titration experiment results show that 46% of the cobalt in the sample was in a 4+ oxidation state, and the atomic absorption results gave the total cobalt contained in the sample. Thus, making the reasonable assumption that one Co4+ ion generates one hole as the carrier and using the crystallographic data for the powder [ 131, the carrier concentration of the film can be estimated to be 1.OS x 1O**cmA3. At room temperature, the conductivity is approximately 0.5 S cm-‘. From a=e[p]p ( [p] =hole concentration), we can estimate the hole mobility to be 3 x 10-4cm2/V-s. An attempt was made to measure the Hall mobility, but the effect was below the measurable level. From an estimate of the minimum observable signal in the apparatus, about 10 FV, we were able to place an upper bound on the hole mobility of about 6 x 1O-4 cm’/V-s, a value quite consistent with that estimated above. It is worth noting here that the contribution of the lithium ion conductivity to total conductivity can be estimated, using previously measured values for the mobility of the lithium ions in crystalline LiCo02. The ionic conductivity, and the mobility of the lithium ions, have been independently measured by two groups, with excellent agreement in their experimental results [ 14,15 1. At 300
Fig. 9 shows the thermopower of an rf sputtered lithium cobalt oxide film as a function of temperature. We note first that the sign of the low temperature thermopower clearly indicates that the charge carriers are positive, i.e., the material is behaving as a p-type semiconductor. This result is in good agreement with literature reports on thermopower in Li,Co02 [ 16,171. In view of the mobility estimates given above, the large carrier concentration and moderate conductivity, the small absolute value of the thermopower suggests that the carriers (holes) have a large effective mass. Our band structure model, the electronic conductivity value and the large carrier concentration all suggest that the film is a degenerate semiconductor. A very general model for the thermopower of such materials is available [ l&l9 ] but accurate evaluation requires knowledge about the scattering mechanisms prevalent in the material. Nevertheless, using the experimental value for cy at 300 K, 0.1 mV/K, this model for the thermopower does indeed suggest
+ TI---..-...---..-....-.----------+---..--. -----.----.--. 0.15/ 0.1i
z
e
I
G
0.05
.
t
.
8_
z
!s a, -0.05
ir
i -0.v
-0.157 295
*+
+I
330
I 335
l
l
I
+
a.
+
l
* l*
300
305
310
315
320
325
Temperature (Kj Fig. 9. Thermopower
of a thin film of lithium cobalt oxide.
122
G. Wei et al. /
Thinfilmsof lithium cobalt oxide
a large value of effective mass is required for any of the possible scattering mechanisms to explain the observation. For the various possible scattering mechanisms, the temperature dependence of the thermopower can be fit by values of effective mass, m*, in the range of 8 to 25 times the electron rest mass m,, confirming the qualitative prediction above, and consistent with the very narrow bands from a density of states calculation [ 201. The reversal of sign of the thermopower seen in fig. 9 is also not uncommon. It has been observed in various compounds, including one example closely related to the present material, the polycrystalline powder I(o&o02 [ 2 1] _
4. Summary We have demonstrated in this work that it is possible to make thin films of a mixed lithium cobalt oxide material which appears to retain the basic rhombohedral structure found in crystalline LiCoOZ, despite being deficient in lithium. These rfsputtered films have optical and electron transport properties consistent with the existence of narrow bands and an allowed (i.e., direct) band gap transition in the visible region, while showing little absorption and moderate reflectivity in the near infrared. These properties, taken together with the electrochemical properties to be described in a subsequent paper [ 201, suggest that this material has promise as a counterelectrode in a “smart window” application.
Acknowledgments The authors would like to thank Robert E. Powers of the Department of Physics, Boston University for assistance with the conductivity and Hall mobility measurments. Our colleagues Floyd Arntz, Ralph Chapman and Kwok Wong, of the Tufts EOTC, and Bill Page, Ellen Candela and Charles Amass of the Tufts Chemistry Department have given invaluable advice, aid, and have lent patient and willing ears.
We would also like to thank Andrew Siegel of Loral for his help with instrument design problems. Grateful acknowledgement is also made of support from the U.S. Department of Energy under Grant FG0385SFl5927. References [ 1] R.B. Goldner, T.E. Haas, G. Seward, K.K. Wong, P. Norton, G. Foley, G. Berera, G. Wei, S. Schulz and R. Chapman, Solid State Ionics 28-30 (1988) 1715. [ 21 K. Vidyasagar and J. Gopalakrishnan, J. Solid State Chem. 42 (16982) 217. [3] K. Mizushima, P.C. Jones, P.J. Wiseman and J.B. Goodenough, Mat. Res. Bull 15 ( 1980) 783; Solid State Ionics 3/4 (1981) 171. [4] T.A. Hewston and B.L. Chamberland, J. Phys. Chem. Solids 48 (1987) 97. [S] W.D. Johnston, R.R. Heikes and D. Sesttich, Phys. Chem. Solids 7 (1958) 1. [6] M. Oku, J. Solid State Chem. 23 (1978) 177. [7] A.J. Bard and L.R. Faulkner, Electrochemical Methods (Wiley, New York, 1980). [ 81 A. Stoklosa, J. Molenda and Do Than, Solid State Ionics 15 (1985)211. [ 91 G.R. Fowles, Introduction to Modem Optics (Dover, New York, 1975). [ lo] R.H. Bube, Electronic Properties of Crystalline Solids (Academic, New York, 1969) p. 415. [ 111 J.I. Pankove, Optical Processes in Semiconductors (Dover, NewYork, 1971). [ 121 M. Ali Omar, Elementary Solid State Physics (AddisonWesley, Reading, MA, 1975) p. 275. [ 131 H.J. Orman and P.J. Wiseman, Acta Cryst. C40 (1984) 12. [ 141 M.S.G.R. Thomas, P.G. Bruce, and J.B. Goodenough, Solid State Ionics 17 (1985) 13 [ 15 ] A.H. Honders, J.M. der Kinderen, A.H. van Heeren, J.H. W. de Wit and G.H.J. Broers, Solid State Ionics 15 ( 1985) 265 and 18/19 (1986) 794. [ 161 A.H. Honders, J.M. der Kinderen, A.H. van Heeren, J.H.W. de Wit, and G.H.J. Broers, Solid State Ionics 14 (1984) 205. [ 171 H.N. M&eon, M. Zanne, C. Gleitzer and J. Aubry, Bull. Sot. Chim. Fr. (1975) 2426. [ 18 ] R.A. Smith, Semiconductors (Cambridge University Press, Cambridge, 1978). [ 191 J.M. Ziman, Electrons and Phonons (Oxford University Press, Oxford, 1960). [20] G. Wei, T.E. Haas and R.B. Goldner, J. Electrochem. Sot. ( 1992), to be published. [ 2 11 C. Delmas, C. Fouassier and P. Hagenmuller, J. Solid State Chem. 13 (1975) 165.