Investigation of the valence band structure of PbSe by optical and transport measurement
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Investigation of the valence band structure of PbSe by optical and transport measurement Thomas C. Chasapis1, Yeseul Lee1, Georgios S. Polymeris2, Eleni C. Stefanaki2, Euripides Hatzikraniotis2, Xiaoyuan Zhou3, Ctirad Uher3, Konstantinos M. Paraskevopoulos2 and Mercouri G. Kanatzidis1 1 Department of Chemistry, Northwestern University, Evanston, Illinois, 60208, U.S.A. 2 Physics Department, Aristotle University of Thessaloniki, GR- 54124, Thessaloniki, Greece 3 Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A. ABSTRACT We investigated the valence band structure of PbSe by a combined study of the optical and transport properties of p-type Pb1-xNaxSe, with Na concentrations ranging from 0 – 4%, yielding carrier densities in a wide range of 1018 – 1020 cm-3. Room temperature infrared reflectivity studies showed that the susceptibility (or conductivity) effective mass m* increases from ~ 0.06mo to ~ 0.5mo on increasing Na content from 0.08% to 3%. The Seebeck coefficient scales with doping in the whole temperature range, yielding lower values for higher Na contents, while the Hall coefficient increases on heating from room temperature showing a peak close to 650 K. The room temperature Pisarenko plot is well described by the simple parabolic band model up to ~ 1·1020 cm-3. In order to describe the behaviour in the whole concentration range, the application of the two band model, i.e. light hole and heavy hole, was used giving density of states effective masses 0.28mo and 2.5mo for the two bands respectively. INTRODUCTION The lead chalcogenides, such as PbTe and PbSe have been under consideration for several decades as semiconductors of potential interest in the field of thermoelectrics. Between them PbSe has several advantages with respect to thermoelectric application since Se is much more abundant than Te and has lower thermal conductivity, which is beneficial for a larger figure of merit [1-4]. Recent calculations suggest that p-type doped PbSe with carrier densities 1.2 – 1.7·1020 cm-3 may reach ZT ~ 2 at temperatures near 1000 K due to the appearance of a flat, high mass, high DOS band of ~ 0.35 eV (at 0 K) below the L point valence band edge, which enhances the thermopower [5]. Using first-principles approach Peng et al. [1] explored the band structure of Na doped PbSe demonstrating also the existence of flat bands that lead to increased DOS and larger Seebeck coefficients relative to the pristine material. Wang et al. studied the thermoelectric properties of NaxPb1-xSe system with carrier densities up to 2.6·1020 cm-3 and found that their room temperature Seebeck data versus hole carrier density (i.e. the Pisarenko plot) may be explained well by a single parabolic model [6]. The deviations observed at higher temperatures were attributed to the contribution of a second heavy hole band. The application of both a single non-parabolic band model and a two-band model in the case of the room temperature Pisarenko plot of the KxPb1-xSe system with hole densities up to ~ 1.5·1020 cm-3 showe
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