Charge carrier transport with weak coupling in BaBiO3

PERGAMON

Solid State Communications 112 (1999) 45–47 www.elsevier.com/locate/ssc

Charge carrier transport with weak coupling in BaBiO3 A. Ghosh Solid State Physics Department, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700032, India Received 15 March 1999; accepted 9 June 1999 by F. Yndura´in

Abstract We have presented the electrical conductivity for the semiconducting BaBiO3 as a function of temperature. We have observed that the conductivity is nonactivated and that the variable range hopping and the small polaron hopping cannot dominate the charge transport process in BaBiO3 like other semiconductors. On the contrary, we have observed that the logarithmic conductivity is proportional to T p ; where the exponent p is independent of temperature. We have shown that the charge transport process occurs by the multiphonon assisted hopping of the charge carriers that interact weakly with phonons. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Semiconductors; D. Electronic transport; D. Electron–phonon interactions; D. Valence fluctuations

The perovskite oxide BaBiO3 is a parent compound of the copper-free superconducting oxides Ba1⫺xKxBiO3 and BaPb1⫺xBixO3 [1–3]. It is a semiconductor in spite of containing odd number of electrons in a unit formula and has been paid considerable attention because of its very interesting semiconducting properties [4–6]. The origin of the semiconducting band gap and the charge transport process in BaBiO3 has been a long standing problem. To envisage the origin of the semiconducting band gap, several studies such as EXAFS [7], neutron diffraction [8,9], Raman and optical absorption [1,10,11], X-ray absorption and photoemission [12], etc. have been reported. These studies reveal that BaBiO3 has a frozen breathing-type displacement of oxygen atoms around the Bi atoms combined with a tilting of the BiO6 octrahedra [9,12], which is thought to be responsible for the semiconducting band gap of BaBiO3. This structure can be viewed as a charge disproportionation of Bi atoms into Bi 3⫹ and Bi 5⫹ or the formation of charge density wave (CDW) at the Bi sites. The previous band structure calculation has not been successful in predicting the band gap of BaBiO3 in the cubic structure [13,14]. However, a recent theoretical band structure calculation [15] has shown an opening of the band gap when the tilting and the breathing of the BiO6 octahedra are simultaneously taken into account. On the contrary, a study of the Hall effect and thermoelectric power shows that charge carriers in BaBiO3 are holes and that the charge transport process is not like ordinary semiconductors [16]. In this paper we have

presented new insights on the charge transport process in BaBiO3. We have observed that the charge transport process in BaBiO3 cannot be dominated by the variable range hopping and small polaron hopping processes as in other semiconductors and rare earth cuprates. We have observed a T p dependence of the conductivity on temperature, where the exponent p is independent of temperature. We have shown that the multiphonon assisted hopping of charge carriers with weak interaction with phonons is the dominant charge transport process in BaBiO3. The compound BaBiO3 was prepared by the conventional solid state reaction. A mixture of high purity powders of BaCO3 and Bi2O3 was first calcined at 450⬚C for 6 h and then at 800⬚C for 12 h in air. The mixed powders were then ground and pressed into pellets of diameter 1.5 cm and thickness 1.0 mm. The pellets were then sintered at 850⬚C for 12 h in flowing oxygen gas and cooled to room temperature slowly. X-ray diffraction analysis confirmed that the samples were single-phase compounds. The electrical measurements were carried out in the temperature range 77–300 K using a standard four-probe technique. The electrical contact to the sample was made using silver paste (Acheson). Measurements were taken during the heating as well as the cooling of the samples. The measured conductivity was found to be reversible. Fig. 1 shows the temperature dependence of the electrical conductivity in the investigated temperature range. It is clear that above ⬃200 K the conductivity shows an

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A. Ghosh / Solid State Communications 112 (1999) 45–47

Fig. 1. Temperature dependence of the conductivity as a function of inverse temperature. The solid curve is the theoretical fit to the small polaron model [21] for an unreasonably larger values of n0 …6:5 × 1013 s⫺1 † than that observed experimentally.

activated behavior with activation energy of 0.24 eV. However, below 200 K the activation energy decreases with a decrease in temperature. It is noted that the activation energy observed above 200 K is less by almost an order of magnitude than the optical gap (⬃1.9 eV) [1], which suggests the existence of some midgap states. Recent studies of the photoemission and X-ray absorption spectra [2] and band structure calculation [15] suggest that in BaBiO3 the split Bi 6s bands form a direct gap of 1.9 eV and a smaller (⬃0.9 eV) intrinsic indirect gap. It has been speculated from the combination of the photoemission [2] and the Hall effect data at high temperatures [16] that a hole accommodating polaron band is formed above the top of the occupied Bi 6s band and an electron accommodating polaron band below the bottom of the empty Bi 6s band. These polaronic levels in the gap result in the reduction of the conductivity gap from 0.9 eV of the frozen lattice to ⬃0.5 eV which provides the activation energy of 0.24 eV of the intrinsic semiconductivity above 200 K. The polaronic nature of charge carriers has been demonstrated by photoinduced changes in the optical absorption spectra [17]. However, this polaronic picture cannot reconcile with the small valence bandwidth ⬃kT and is still tentative [2]. We have examined the data in terms of theoretical models to arrive at a dominant mechanism for the charge transport. The decrease of the activation energy can be accounted for at least qualitatively in the framework of the polaron model [18–22]. If the electron–phonon interaction is strong, the carrier is spread over a single site and a small polaron is formed [18]. Several authors [18–22] have calculated the conductivity due to small polaron hopping considering strong electron–phonon coupling. We have attempted to

Fig. 2. A plot of log s versus T ⫺1/4. The solid line is a straight line fit to the data below 200 K, yielding a density of states of the order of 10 16 eV ⫺1 cm ⫺3.

interpret our data in terms of a most general small polaron model [21], which considers strong interaction of carriers (electrons or holes), with both the optical and the acoustical phonons. This model involves a number of parameters among which the optical phonon frequency determines largely the conductivity. We have shown in Fig. 1 a best fit to this model which provides an unreasonably large value of the phonon frequency. In fact, we are not successful in getting a reasonable fit of the data to the model [21] for any value of the optical phonon frequency observed experimentally [1]. In this context it is worth mentioning that the choice of the bipolaronic model [22] was also shown to be inappropriate for BaBiO3. The variable range hopping theory [23–25] was employed in the literature to interpret the charge transport process between midgap states in amorphous semiconductors [23] and in many rare earth cuprates [26–27]. We have not observed linearity in the plot of log s versus T ⫺1/4 or T ⫺1/ 2 as predicted by the variable range hopping models of Mott [23] and Efros and Shklovski [25]. However, we have observed a linearity in the log s versus T ⫺1/4 plot below 200 K (Fig. 2), which yields an unreasonably smaller value for the density of states at the Fermi level than those observed for amorphous semiconductors [23] and the rare earth cuprates [26,27]. In the following we have shown that the multiphonon assisted hopping of carriers with a weak electron–phonon coupling can interpret the data quantitatively. Many authors [19,28,29] have calculated the transition rate for the multiphonon hopping process for weak electron–phonon coupling. The conductivity for the weak coupling case can be described by

s ˆ …nc e2 R2 =6kT†n0 exp…⫺gp†…kT=hn0 †p ;

…1†

A. Ghosh / Solid State Communications 112 (1999) 45–47

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Em =hn0 ⬇ 0:12, which satisfies clearly the condition for the weak coupling [28,29]. In summary, we have performed electrical measurements on the semiconducting BaBiO3 in a wide temperature range. We have shown that the logarithmic conductivity can be described by T p, where the exponent p is independent of temperature. The observed nonactivated conductivity cannot be interpreted by the variable range hopping and the small polaron hopping theories. On the contrary, we have observed that the multiphonon assisted hopping of charge carriers with weak interaction with phonons is the dominant charge transport process in BaBiO3. Acknowledgements The assistance of Mr. M. Sural is thankfully acknowledged. Fig. 3. The logarithmic conductivity shown as a function of logarithmic temperature. The solid line is a straight line fit to the data.

References where nc is the carrier density, R the hopping distance, and n 0 the frequency of the acoustical phonons which is most effectively coupled to carriers. The parameters p and g are given by p ˆ D=hn0 and g ˆ ln…D=Em ⫺ 1†; where D is the energy difference between adjacent sites and the parameter g or Em is a measure of the strength of the electron–phonon coupling which should satisfy the condition Em =hn0 p 1 for the weak coupling regime. As the large radius localized carriers couple only to long wavelength phonons [19], n 0 must be smaller than the maximum phonon frequency. Also the multiphonon process involves absorption and emission of p phonons, the value of p should be an integral number. However, if n 0 and D is distributed around a certain value, p must have a finite distribution and its mean value will be nonintegral. It may be noted that in this model the conductivity is proportional to T p as the carrier density nc must be given by N…EF †kT in Eq. (1). We have plotted in Fig. 3 the logarithmic conductivity as a function of logarithmic temperature in order to examine the conductivity data for BaBiO3 in the light of the above theory. It is observed in Fig. 3 that the plot is linear indicating that the conductivity is proportional to T p. The value of p ˆ 10:4 was obtained from the least square fit of the data. To confirm the validity of this model the data in Fig. 3 were fitted to this model. We have obtained from the fit the value of the coupling parameter g in the range 3.2–3.4 in the entire temperature range of measurement. In the calculation, we have employed a reasonable value of n0 ˆ 1012 s⫺1 , which is much smaller than the maximum phonon frequency [1] and a reasonable value of the carrier density nc calculated assuming one electron per Bi atom [16]. These values of g are reasonable for the weak coupling regime and provide

[1] R.J. Cava et al., Nature 332 (1988) 814. [2] A.W. Sleight, J.L. Gilson, P.E. Bierstedt, Solid State Commun. 17 (1975) 27. [3] S. Tajima et al., Phys. Rev. B 32 (1985) 6302. [4] S. Tajima et al., Phys. Rev. B 35 (1987) 696. [5] H. Namatame et al., Phys. Rev. B 48 (1993) 16 917. [6] S. Uchida, K. Kitazawa, S. Tanaka, Phase Trans. 8 (1987) 95. [7] A. Balzarotti et al., State Commun. 49 (1984) 887. [8] D.E. Cox, A.E. Sleight, Solid State Commun. 19 (1976) 969. [9] C. Chaillout et al., Solid State Commun. 65 (1988) 1363. [10] J.Th.W. de Hair, G. Blasse, Solid State Commun. 12 (1973) 727. [11] S. Uchida et al., J. Phys. Soc. Jpn. 54 (1985) 4395. [12] J.B. Boyce et al., Phys. Rev. B 44 (1991) 6961. [13] L.F. Mattheiss, D.R. Hamann, Phys. Rev. B 28 (1983) 4227. [14] K. Takegahara, Kasna, J. Phys. Soc. Jpn. 56 (1987) 1478. [15] A.I. Leiechtenstein et al., Phys. Rev. B 44 (1991) 5388. [16] H. Takagi et al., in: O. Engstorm et al. (Eds.), Proceedings of the International Conference on the Physics of Semiconductors, Stockholm, World Scientific, Singapore, 1986, p. 1815. [17] J.F. Federich et al., Phys. Rev. B 42 (1990) 923. [18] T. Holstein, Ann. Phys. (NY) 8 (1954) 343. [19] D. Emin, Adv. Phys. 24 (1975) 305. [20] D. Emin, Phys. Rev. Lett. 32 (1975) 303. [21] E. Gorham-Bergeron, D. Emin, Phys. Rev. B 15 (1977) 360. [22] D. Emin, Phys. Rev. B 48 (1993) 13691. [23] N.F. Mott, E.A. Davis, Electronic Processes in Non-Crystalline Materials, 2, 1979. [24] V. Ambegaokar et al., Phys. Rev. B 4 (1971) 2612. [25] A.L. Efros, B.I. Shklovski, J. Phys. C 8 (1975) L49. [26] M.A. Kastner et al., Phys. Rev. B 37 (1988) 111. [27] P. Lunkenheimer et al., Phys. Rev. Lett. 69 (1992) 498. [28] N. Robertson, L. Friedman, Phil. Mag. 33 (1976) 753. [29] R. Engleman, J. Jortner, Mol. Phys. 18 (1970) 145.