Interrelation of Electronic Properties and Defect Equilibria in PbTe

Abstract

The resistivity, Hall coefficient, and Seebeck coefficient of single crystals of PbTe were investigated in the range from 77° to 900 0 K using a capsuling arrangement which prevented tellurium loss from the specimens at elevated temperatures. The low temperature properties obtained agree with the data reported in the literature. The thermal energy gap obtained from the high temperature measurements cannot, however, be brought into agreement with the energy gap determined from room temperature absorption measurements by considering solely the excitation of electron-hole pairs across the energy gap at elevated temperatures. Rather, it is necessary to include the carriers generated by defect formation at elevated temperatures. Both Schottky-Wagner and Frenkel defects are present, the activation energies for formation of the two types of defects being related by the equation EF=!Es+0.55 ev~0.7 ev.

Anharmonic effects in the thermoelectric properties of PbTe

“…(18) by fitting the constant D ¼ 0.794 X cm. 40 There is very good agreement between the computed extrinsic contribution and the experimental data at temperatures above 700 K. On the whole, we regard the agreement between our theoretical results and the experimental data as reasonable.…”

Temperature dependent band gap in PbX (X = S, Se, Te)

“…Our results, shown in Figures 2(b) and 2(c) (and others [45][46][47][48] ), show that the gap continues to increase for temperatures greater than 673 K, albeit at a lower rate above 500 K. Experimental and AIMD results in this work suggest that the band convergence temperature is much higher, closer to 700 K. The temperature dependence of electronic transport properties (resistivity, Hall effect, and Seebeck) can also be used to estimate the band gap. While early results from resistivity and Hall effect measurements 28,49 showed large values of the thermal band gap (>1 eV), photoconductivity measurements by Moss showed a near unity quantum efficiency above 0.4 eV for PbS which was concluded as evidence that the gap must be much smaller 50 and more consistent with the optical measurements of Gibson, Devyatkova, and Saakyan et al 22,51 (also shown in Figure 2(b)) measured both n and p-type samples in the bipolar regime to estimate the temperature dependent gap using an extrapolation technique for the single parabolic band model. They obtained a constant gap for temperatures greater than 550 K in PbTe and one that increased continuously until 800 K in PbSe.…”

Doping-dependent thermopower of PbTe from Boltzmann transport calculations

“…Electrical measurements indicate a band gap of ϳ0.3 eV, 38 while optical experiments indicate a band gap with a strong nearly linear T dependence below 400 K, and constant above. 36 This is an unusual and difficult to understand form.…”

“…An important issue is the fact that PbTe tends to form with substantial defect concentrations and it is very difficult to obtain undoped, intrinsic PbTe. 10,38 One possibility is that the smaller, low-temperature value of the band gap of ϳ0.2 eV quoted from T-dependent optical experiments is an artifact of the fits of the optical spectra in a material with doping, Urbach tails, and a highly nonparabolic band structure. Here we assume that the observed T dependencies come from Fermi broadening and a conventional weakly T dependent but highly nonparabolic band structure rather than a strongly T dependent band structure.…”