PART 11. DEFECT EQUILIBRIA IN ACCEPTOR- DOPED BARIUM TITANATE

Transcription

1 Philips Res. Repts 31, , 1976 PART 11. DEFECT EQULBRA N ACCEPTOR- DOPED BARUM TTANATE by J. DANELS *) Abstract The defect model developed for BaTi0 3 in part of this series of articles is extended to acceptor-doped BaTi0 3 Although at high temperatures (about 1300 "C) the effect ofthe acceptors on the conductivity is relatively small because of their ionization energy (about 2.2 ev), quenching to room temperature has remarkable consequences: the concentrations of electrons can be reduced so drastically by the acceptor doping that even specimens prepared in a reducing atmosphere remain insulators. These conceptions of the model are confirmed by experiments with Ga-doped BaTi03 1. ntroduetion Measurements of the electrical conductivity of BaTi0 3 ceramics which at elevated temperatures (T > 900 C), are in equilibrium with the oxygen partial pressure, P02' of the surrounding atmosphere have greatly contributed to an understanding of defect distributions and the electrical properties resulting from them 1,2,3). The p-type conductivity observed at high oxygen partial pressures, i.e. 1 atm O 2, is due to acceptor-type vacancies in the barium sublattice, while n-type conductivity at low oxygen partial pressures is brought about by 'donortype oxygen vacancies lying energetically just below the conduction band. The incorporation of higher-valent ions at (Ba, Ti) sites enables the number of donors to be increased and thus the n-type conductivity to be increased as well 3,4,5,6,7,8). On the basis of the same principle it should be possible to increase the p-type conductivity if lower-valent ions replace BaH or Ti 4 + ions. Thus the incorporation of, for example, Na+ at BaH sites or of Ga3+ or Fe3+ at Ti4+ sites should create additional foreign acceptors, the ionization of which would increase the concentration of holes. However, specimens exhibiting appreciable p-type conductivity at room temperature have never been found, so that the energy of ionization of the acceptors (barium vacancies or foreign atoms) is most likely relatively high (> 1 ev). n spite of the fact that p-type conductivity has never been observed at room temperature, there are two aspects which may lead to interesting applications of such materials: (i) A BaTi0 3 ceramic p-doped in this way may perhaps be important as a *) Present address: Fachhochschule Kiel, D 2300 Kiel, W. Germany.

2 506.DANELS dielectric material which can be sintered in a reducing atmosphere and still remains high-ohmic. The p-type doping would in this case serve to compensate for the oxygen vacancies formed during sintering at low oxygen partial pressures. Such a dielectric would be very interesting indeed for use in multilayer capacitors: a cheap product could be made by sintering in a reducing atmosphere with base metal electrodes (e.g. nickel). nvestigations concerned with this problem have been published. nitially the work did not lead to success, because the high concentrations of acceptors used had a negative influence on the dielectric properties of the matrix 9). Recently, however, these difficulties seem to have been overcome 10.11). (ii) Small additions of acceptor-type ions (iron, copper, manganese) improve the properties of PTC resistors lz) and intergranular capacitors 13) produced by sintering of BaTi0 3 doped with 0.3 mol % Sb or La. Difficulties in the interpretation of the phenomena arise above all from the fact that the concentration of acceptors is about one order of magnitude less than the concentration used for n-type doping. For this reason it was assumed until now that acceptors were not dissolved in the lattice but segregated as a second phase at the grain boundaries. n the present report the effect of small additions of acceptors on the conductivity of BaTi0 3 is investigated. The defect model developed in part of this series of articles 3) will first of all be used to treat the problem of p-type doping in a model. With the example of Ga-doped BaTi0 3 ceramics we shall then see how far the results of the model calculations are confirmed by the experiments and contribute to the development of dielectric materials which remain high-ohmic after sintering in a reducing atmosphere. The consequences of slight amounts of acceptor dopes in PTC materials will be dealt with in more detail in part V of this series of articles. 2. Defect model By means of the simplifications arrived at in part, we shall consider only vacancies in the barium and oxygen sublattices, the concentrations of which are related by the modified Schottky condition (of part V) The concentrations of the neutral oxygen vacancies, [V0], and of barium vacancies, [VBa], are determined only by the oxygen partial pressure, Poz' and in accordance with part they satisfy and (1) [Vo]=K 1 Poz-t (2) (3)

3 DOPED BARUM TTANATE CERAMCS, PART T 507 onization of the neutral defects leads to charged vacancies which, together with the electrons and holes as well as possibly present ionized donors D' and acceptors A' (caused by foreign ions with donor or acceptor character) form the complete equation of electroneutrality: n + [VBa']+ 2[VBa"] + [A'] = p + [Vo'] + 2[Vo"] + [D']. (4) As was explained in pari, the mass-action constants of singly and doubly charged oxygen vacancies, Vo' and V0", and of singly and doubly charged barium vacancies, VBa' and VBa", corresponding to the individual terms of (4) can be calculated from experimental values or taken from the literature. A further finding was [VBa']~ [VBa"] in the case of undoped material, so that the term [VBa"] in (4) can be neglected. f additionally foreign acceptor-type ions are incorporated in the material in a total concentration of [Atot], the concentrations of the neutral and of the ionized acceptors, [A] and [A'] are determined by the following relations: and with the law of mass action From (5) and (6) it follows that [A] + [A'] = [Atot], A~A' +h, (5) [A'] p[a] = KA' [A] = [Atot]p(p + K~, and [A'] = [Atot]KA(P + K~ (7) KA = NA exp (-EAkT) is the mass-action constant of the ionization of the acceptors. NA can be put equal to N«, the density of states in the valence band, for which a value of about' cm- 3 is assumed 3). Substitution of (7) in (4) and the assumptions that [VBa']» [VBa"] and [D'] = 0, as well as utilisation of (2) to (8) of part, lead to an equation which can be solved for n. From this the conductivity can now be calculated with #n = #p = 0.1 cm 2 fv s. The mass-action constants Ks, K>Kl,..., Ks are taken to have the same values as in part. A new, unknown value is EA' the ionization energy of the acceptors. Figure 1 shows [A] and [A'] thus calculated, and fig. 2 the calculated conductivity of BaTi0 3 at 1300 oe with an acceptor concentration of 0.8 mol % (1.3' cm=") as a function ofthe oxygen partial pressure for various values of EA' The parameter EA was varied stepwise between 0.1 and 2.5 ev. n the case of values of EA between 0.1 and 1 ev the acceptors are largely ionized in the entire range ofpartial pressures (fig. ). This leads to an appreciable increase in p-type conduction at high oxygen partial pressures and hence to a shift in the minimum of the conductivity, amino towards lower values of the oxygen partial pressure (fig. 2). With EA > 1 ev there is a rapid decrease in [A']: and hence in p-type conduction, at high oxygen partial pressures. At low oxygen (6)

4 508 1.DANELS partial pressures the major proportion of the acceptors is ionized, but because of the high concentration of electrons the effect on the conductivity is very slight. With EA = 2.5 ev the calculated values of the conductivity coincide with those of undoped material: the effect of the acceptors has disappeared. f the concentration of acceptors is increased, the minimum of the conductivity is shifted on the oxygen pressure scale to lower partial pressures. The value of O"mlm however, is determined by np = Kh irrespective of the doping. For the essential object of the investigations it is not merely the picture at high temperatures, e.g. at or just below the sintering temperature, which is decisive. Of greater importance are the electrical properties of the ceramic at room temperature after sintering. To describe this in the model, we must first know how the defects behave during cooling, viz. whether in the limiting case (a) the vacancies remain in equilibrium with the atmosphere during cooling, or whether (b) the high-temperature concentrations of the atomic defects are frozen and only the electronic equilibria are reestablished. Without knowing the processes of diffusion we can only discuss what electrical conductivity ought to be observed if the specimens are quenched from high ~ ~21 BaTi % acc. at C ---A ---A' poatm) -5 0 Fig. 1. BaTi0 3 specimen doped with 0.8 mol % foreign acceptors, at 1300 C: distribution of the neutral [A] and ionized [A'l foreign acceptors as a function of the oxygen partial pressure Po]. with different ionization energies, BA-

5 DOPED BARUM TTANATE CERAMCS. PART T 509 temperatures to room temperature, i.e. case (b). During quenching, the hightemperature concentrations of the atomic defects are frozen: the electronic equilibria, on the other hand, will readjust. This means that the total concentration of vacancies, and. [Vo 101] = [Vo] + [Vo'] + [Vo"]' remains constant but the charge of the individual defects can be redistributed. n this respect we know from Fermi statistics that at room temperature the empty levels in the band are successively filled with electrons, starting from the bottom. This will be illustrated by means of a BaTi0 3 specimen, doped with 1% La, which, at an oxygen partial pressure of about 10-5 atm, is quenched from 1300 oe to room temperature. At 1300 oe we have as EA =O.leV.... EA =t.oev - _ -E A..t.5eV ---EA =2.0eV --E A =2.5eV -T.S BaTi03+O.8"o t3000c acc. l l' 1 if 1. -2~--1~5~---+'ro~---~s~-~O - logtopo2 (atmj Fig. 2. Calculated conductivity a at 1300 C of BaTi0 3, with 0.8 mol % foreign acceptors as a function of the oxygen partial pressure. The ionization energy of the acceptors was varied stepwise between 0.1 and 2.5 ev.

6 510.DANELS The only unoccupied levels are those of La' and VBa' (fig. 9 in part ). The electrons present at 1300 C fill up VBa' to VBa'" f n > [V Ba']' then all the La' levels are filled next, so that neutral donors are produced. This holds exactly at 0 K. At room temperature, however, on account of the lowactivation energy these will give up their electrons almost completely to the conduction band, so that semiconducting material is formed. n the case of n < [VBa' ], some of these levels remain as unoccupied acceptors: because of the high activation energy the specimens are insulators. n accordance with fig. 6b of part, specimens quenched at partial pressures of less than 10-3 atm should, on account of n > [VBa']' be semiconducting at room temperature while specimens quenched at P0 2 > 10-2 atm should, on account of n < [VBa']' be insulating. f the temperature from which the specimens are quenched increases, the transition from semiconducting to insulating is shifted to higher P0 2 values. A further result of this redistribution of the electronic charge is shown in fig. 3, in which the calculated concentrations of the conduction electrons in undoped BaTi0 3 and in BaTi0 3 doped with 0.8 mol % acceptors (EA = 2 ev) are plotted against the oxygen partial pressure at the sintering temperature of 1300 C and at 30 oe after quenching. While the high-temperature curves differ only little from each other, the electron concentration at 30 C is drastically reduced by the doping with an acceptor, rising steeply, as the oxygen partial pressure falls, from very low values to values corresponding approximately to the equilibrium values at high temperaturs. As can be seen more clearly in fig. 4, the doping with acceptors causes the location of the jump to shift quite far towards lower oxygen partial pressures. This shift is independent of the true value of EA' as long as the acceptor levels are energetically lower than the levels of the singly ionized oxygen vacancies, Vo" With a band gap of 2.9 ev and an ionization energy of 0.1 ev for Vo" this is the case if EA is less than about 2.8 ev. The cause of this behaviour is as follows. n every semiconductor at room temperature all' states below the Fermi level are occupied and those above the Fermi level are empty, if states in the immediate vicinity of the Fermi level are neglected. This means that the levels of the singly ionized oxygen vacancies V0', which at room temperature, to supply electrons to the conduction band, are occupied only if all lower levels (VBa', VBa" and A') have been filled. Thus as long as the acceptor levels are below the levels of Voo (EA < 2.8 ev), the acceptors exert their full effect. Figure 4 shows that BaTi0 3 doped with low concentrations of foreign accep-. tors, about 1 mol %, should after sintering in a reducing atmosphere (P02 ;;;:,:10-10 atm) and after quenching to room temperature be an insulating dielectric. n the actual quenching experiment, with finite cooling rates and defined gas mixtures of COC0 2 or H 2 H 2 0 the vacancy equilibria will for a

7 DOPED BARUM TlTANATE CERAMCS. PART T BaTi oC-30oC oC C t 18 ~ 17 0% acc. 16 ~L---_+'~~--~_~m~-----_5~_J--~0 - lo9lopo 2 (atm) Fig. 3. Calculated concentration of electrons n at 1300 C, and after quenching to 30 C, in undoped and acceptor-doped BaTi0 3 ro , conducting insulating (} log,opoatm) Fig. 4. Calculated insulating or conducting regions of acceptor-doped BaTi0 3 "'specimens. quenched from 1300 C to room temperature at different oxygen partial pressures.

8 512 J.DANELS time follow the lowering of the temperature and of the partial pressure. The calculations indicate that in these conditions the transition from insulating to conducting should occur at lower concentrations of acceptors than if the limiting case (b) were strictly observed (constancy of the total number of vacancies). 3. Measurements of barium titanate doped with gallium Possible dopes with acceptor character are univalent metals, with an ionic radius of about 1 A, to replace barium ions, and trivalent metals with an ionic radius of about 0.7 A to replace titanium ions. Of the trivalent cations, gallium is particularly suitable because it occurs mainly in the trivalent state and because its ionic radius (0.62 A) means a good fit at titanium sites. The preparation was analogous to the method described in part, with sintering of the specimens at 1290 oe in oxygen. The gallium dope, in the form of Ga203 (99.99%, Fluka AG, Switzerland), was weighed in following the formula Ba(Ti 1 _ x Ga x )03 with x = 0.004, and The electrical conductivity a was measured at elevated temperatures as a function of the oxygen partial pressure. The results, in figure 5, show that, at least at 1200 oe, the minima of the conductivity of doped materials are shifted o -- undoped _ 0.2% Ga _ 0.8% Ga ' o _---<.,ogo P0 2 (alm) Fig. 5. Measured conductivity of Ga-doped BaTi0 3, at high temperatures, as a function of the oxygen partial pressure.

9 DOPED BARUM TTANATE CERAMCS, PART T 513 by an order of magnitude to lower oxygen partial pressures in comparison with undoped BaTi0 3 The conductivity at the p-type side is greater by a factor of about two than that of the undoped material, on the n-type side a is less than in undoped specimens. Two causes of the small effect of doping on the conductivity at high temperatures are conceivable: (a) The dope dissolves only partly or not. at all in the material and segregates at the grain boundaries of the ceramic as a phase rich in gallium. Microprobe tests, however, provided no evidence of enrichment with gallium at particular sites of the specimen. (b) f it is therefore assumed that the gallium dissolves completely in the lattice, the phenomena can be explained only if the acceptors are far above the valence band (fig. 2). Calculations of the conductivity by means of the defect model developed in part lead to satisfactory agreement with the measured values if the ionization energy of the gallium acceptors is assumed to be about 2.2 ev. f the gallium dope is incorporated incompletely in the lattice, the energy of ionization will be correspondingly lower. Figure 6 shows that the calculations in respect of the n-type side provide a good description of the experiments but that deviations occur on the p-type BaTi03 +08% Ga _. experiment -- calculation with E'A=2.2eV o OPo2(atm) Fig. 6. Comparison of measured and calculated values of the conductivity of BaTi0 3 doped with 0.8 mol % gallium.

10 514.DANELS side. n all probability the reduced electroneutrality equation p = [VBa'] (in part ) requires modification and refinement in order to remove these deviations. But the essential object of this work is to describe the very favourable effect of acceptor doping on the properties at room temperature, and this is achieved very successfully with this simplified model. For that reason a refining of the defect model does not seem necessary at present. 4. Sintering in a reducing atmosphere of barium titanate doped with gallium The small effect of acceptor dopes on the conductivity at high temperatures would seem to argue against the feasibility of sintering in a reducing atmosphere a material which is insulating at room temperature. Here, however, the considerations mentioned in sec. 2 with respect to the properties of specimens quenched from high temperatures to room temperatures should be remembered. Accordingly the acceptor dope exerts its full effect at room temperature if the acceptor levels are a few tenths ev below the conduction band. The tests and calculations described in sec. 3 show that this condition is satisfied in respect of gallium-doped barium titanate MGo---o--;: _D ~_ %~-----5~0~----~100~----~~~O--~ -----<- T(Oe) Fig. 7. Temperature dependence of the electrical resistance eet) of undoped and galliumdoped BaTi0 3 sintered in reducing atmospheres of different oxygen partial pressures. MG = Mixed gas (25 vo.% H 2 75 vo1.% N 2 ).

11 DOPED BARUM TTANATE CERAMCS, PART n 515 n the course of the investigations, undoped specimens as well as specimens doped with 0.4, 0.8 and 1.6 mol % gallium were sintered in reducing atmospheres of 10-7 and atm oxygen (adjusted by means of gas mixtures of COC0 2 ) and in mixed gas (75% N 2 25% H2' P0 2 much less than atm oxygen) at 1350 C. At the end of the sintering process, the specimens were brought to room temperature at the natural cooling rate of the furnace ( Cmin in the temperature region of C, slower at lower temperatures) and investigated with respect to conductivity, and dielectric and structural properties. The resistivity of. undoped BaTi0 3 after sintering in 10-7 atm oxygen was still very high, the value being about Q cm. But sintering at atm oxygen led to dark coloured specimens with e ~ Q cm, and sintering in mixed gas to black specimens of high conductivity (e = 8.Q cm), see fig. 7. Ceramics doped with gallium, however, retained their light colour and high resistivity, e > 1011.Q cm, after sintering at oxygen partial pressures ofbetween 10-7 atm and that of mixed gas if the concentration of gallium was equal to, or greater than, 0.8 mol %. Material doped with 0.4 mol % gallium was black after sintering in mixed gas and its resistivity low (e = 8.Q cm). We see, therefore, that the problem ofpreparing BaTi0 3 ceramics which will insulate after sintering in a reducing atmosphere can be solved by the incorporation of gallium dopes of more than 0.4 mol %, and the results are in agreement with the defect model derived for BaTi0 3 Further investigations will have to deal with the question of how far gallium can be replaced by other acceptor ions and what effect the acceptor dope will have on the sintering behaviour and on the microstructure. Philips GmbH Forschungslaboratorium Aachen Aachen, November 1976 REFERENCES 1) S. A. Long and R. N. Blumenthal, J. Am. Ceram. Soc. 54, 515, 1971; ibid. 54, 577, ) A. Seuter, Philips Res. Repts Suppl. 1974, No. 3. 3) J. Daniels and K. H. Härdtl, Part ofthis series of articles. 4) P. W. Haayman, R. W. Dam and H. A. Klasens, German Patent , June 23, ) W. Heywang, Solid-State Electronics 3, 51, ) G. H. Jonker, Solid-State Electronics 7,895, ) P. Gerthsen, R. Groth and K. H. Härdtl, Phys. Stat. sol. 11, 303, ) T. Ashida and H. Toyoda, Jap. J. appl. Phys. 5,269, ) J. M. Herbert, Proc. lee 112, 1474, ) N. G. Error, J. Burn and G. H. Maher, Brit. Pat , ) J. Burn and G. H. Maher, J. Mat. Sci. 10, 633, ) H. Uecka, Ferroelectrics 7,351, ) H. Brauer, Z. angew. Phys. 23, 373, 1967; ibid. 29, 283, 1970.