The Effect of Multivalley Bandstructure on Thermoelectric Properties of Al x Ga1−x As

Abstract

We present the theoretical modeling of the thermoelectric properties of Alx Ga1−xAs. It was shown that, contrary to the known good thermoelectric materials, the optimum composition happens far from the point at which the multiple bands meet. This unexpected optimum material composition is related to the detrimental effect of multivalley bandstructure. A semi-empirical model was employed to predict the thermoelectric properties versus alloy composition, temperature, and doping concentration. The electrical conductivity, Seebeck coefficient and figure-of-merit (ZT) were calculated with consideration of the energy-dependent relaxation time and multivalley band structure for AlxGa1−xAs. The theoretical model was verified by comparison with different sets of experimental data on both electrical and thermal transport properties. It was shown that the multivalley bandstructure in AlxGa1−xAs affects the Seebeck coefficient in two counteracting processes; however, it always reduces the electrical conductivity and the electronic thermal conductivity. It was shown that the multivalley bandstructure also affects the lattice thermal conductivity. In contrast to several good thermoelectric materials in which their multivalley band structure enhances the ZT, in AlxGa1−xAs, the ZT reduces at the composition x at which the three bands of Γ, X, and L meet each other. Therefore, the maximum ZT happens far from this point. The optimum x also depends on temperature and reduces with temperature. Therefore, the Al concentration must decrease across the thermoelectric leg from the cold to the hot side. At the optimum composition, the ZT of AlxGa1−xAs is predicted to be comparable to that of good thermoelectric materials at high temperatures.