ELECTRICAL PROPERTIES AND BAND STRUCTURE IN Pb1-xSnxTe

Strong evidence for the existence of two valence bands in Pb0.7Sn0.3Te and Pbo.sSno.sTe is inferred from the observation of a kink in the variation of the Hall ratio R ~ O O ~ K I R ~ ~ O O K , as a function of hole concentration. This existence is also supported by the fact that the variation of the Seebeck coefficient as a function of hole concentration exhibits a minimum. Moreover, non parabolic bands are expected from our Hall mobility data, which indicate p-1 instead of p~ p-113 for a parabolic band. According to the existence of two valence bands, the thermal energy gap behavior in Pb-rich alloys (x < 0.3) is discussed. From electrical results in the intrinsic regions, the thermal energy gaps for different compositions ranging from PbTe to x = 0.3 were found to be of the same order. Taking into account the interpretation for PbTe, and in correlation with the observed behavior of the energy gap E,, the energy separation E, between the two valence bands Vl and VZ is expected to increase with increasing Sn content and to decrease with increasing temperature. Data on Sn-rich alloys would lead to a better appreciation of a possible shift of Vz relatively to VI and to the conduction band with increasing Sn content. Rbsumb. I1 existe de fortes presomptions pour l'existence de deux bandes de valence dans Pb0,7Sno,sTe et Pbo,sSno,sTe d'aprks l'observation d'un maximum dans la variation du rapport de Hall R300 oK/RIoo~~ en fonction de la concentration de trous. Cette existence est confirmee par le fait que la variation du coefficient de Seebeck en fonction de la concentration de trous possede un minimum. De plus, des bandes non paraboliques sont presumks d'aprks nos mesures de mobilite de Hall qui indiquent : p~ p-1 au lieu de p~ p-113 pour une bande parabolique. Nous discutons le comportement de la bande interdite thermique dans des alliages riches en plomb ( x < 0,3) dans l'hypothkse de deux bandes de valence. D'apres les resultats des mesures electriques dans les regions intrinseques, les bandes interdites thermiques pour diffkrentes compositions allant de PbTe a x = 0,3 se sont rkvelkes Stre du mgme ordre. En tenant compte de l'interprttation donnee pour PbTe et en correlation avec le comportement observe de la bande interdite Eg, la separation energktique Ev entre les deux bandes de valence VI et V2 devrait augmenter avec le pourcentage d'etain et decroitre quand la tempkrature augmente. Des mesures sur des alliages riches en etain conduiraient a une meilleure comprehension d'un deplacement possible de VZ par rapport & VI et la bande de conduction quand la quantitk d'etain croit, We report in this-paper some recent results on the electrical properties of Pbl-,Sn,Te. These data concern particularly the variation of Hall and Seebeck coefficients, and electrical resistivity as a function of hole concentration in two alloys Pbo.,Sno.,Te and Pbo.,Sno.,Te. The existence of two valence bands is inferred from the observed electrical behavior. Previous thermal energy gap results in Pb-rich alloys are discussed, and comparison with reported data on SnTe and PbTe yields information about the band structure in these solutions. An increase of the valence band energy separation E,, in Pb-rich alloys is suggested in correlation with the recent results [I ] [2] on the behavior of the energy gap E, in these alloys. Na-doped polycrystals of Pbo.,Sno.,Te and Pbo.,Sn0.,Te, with room-temperature hole concentrations between 10'' and loz1 ~ r n ~ were investigated in the temperature range SO0-600 OK. For all the samples, the Hall coefficient R increases with increasing temperature. This behavior was observed in a great number of extrinsic semiconductors. It was discussed by Aukerman and Willardson [3] in the case of classical statistics, and was extended by Allgaier [4] to higher carrier concentrations. The possibility of complex single band to explain the temperature dependence of R could not be ruled out. However, strong evidence for the existence of two valence bands could be obtained from the observation of a sharp kink [4] [5] in the carrier concentration dependence of the Hall ration RH/R,, where RH and RL are the Hall Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1968417 C 4 126 H. 3. ALBANY AND M. OCIO FIG. 1. Variation of the Hall ratio R ~ O O ~IC/RIOO as a function of apparent hole concentration p?oo 1 in Pbo,-~Sno.~Te and Pb~.sSno.sTe. ratio R,,, oK/R,oo as a function of apparent hole concentrationp~oo measured at 100 OK C 100" K O Pb0,7 Te 300% L9 a V) 2 -3