Electronic structure of bismuth telluride nanowires with the growth directions [110] and [015] is studied in the framework of the anisotropic effective mass method using the parabolic band approximation. The components of the electron and hole effective mass tensors for six valleys are calculated for both growth directions. For a square nanowire, in the temperature range from 77 K to 500 K, the dependence of the Seebeck coefficient S, the thermal κ and electrical conductivity σ as well as the figure of merit ZT on the nanowire thickness and on the excess hole concentration pex are investigated in the constant-relaxation-time approximation. The carrier confinement is shown to play essential role for nanowires with cross section less than 30 × 30 nm 2 . In contrast to the excess holes (impurities), the confinement decreases both the carrier concentration and the thermal conductivity but increases the maximum value of the Seebeck coefficient. The confinement effect is stronger for the direction [015] than for the direction [110] due to the carrier mass difference for these directions. In the restricted temperature range, the size quantum limit is valid when the p−type nanowire cross section is smaller than 8 × 10 nm 2 (6 × 7 nm 2 and 5 × 5 nm 2 ) at the excess hole concentration pex = 2 × 10 18 cm −3 (pex = 5 × 10 18 cm −3 and pex = 1 × 10 19 cm −3 correspondingly). The carrier confinement increases the maximum value of ZT and shifts it towards high temperatures. For the growth direction [110], the maximum value of the figure of merit for the p−type nanowire is equal to 1.4, 1.6, and 2.8, correspondingly, at temperatures 310 K, 390 K, and 480 K and the cross sections 30 × 30 nm 2 , 15 × 15 nm 2 , and 7 × 7 nm 2 (pex = 5 × 10 18 cm −3 ). At the room temperature, the figure of merit equals 1.2, 1.3, and 1.7, respectively.

A method to calculate a smooth electrical conductivity versus mobility plot ("mobility spectrum") from the classical magnetoconductivity tensor in heterogeneous structures with the help of a "maximum entropy principle" has been developed. In this approach the closeness of the fit and the entropy of the mobility spectrum are optimized. The spectrum is then the most probable one with the least influence of the personal bias of the investigator for any given set of experimental data and is maximally noncommittal with regard to the unmeasured data. The advantages of the maximum entropy mobility spectrum analysis as compared to the conventional mobility spectrum analysis are demonstrated using a synthetic dataset.

We theoretically studied the effect of the perpendicular electric field on the thermoelectric properties of the intrinsic, n−type and p−type bismuth telluride nanowires with the growth direction [110]. The electronic structure and the wave functions were calculated by solving self-consistently the system of the Schrödinger and Poisson equations using the spectral method. The Poisson equation was solved in terms of the Newton -Raphson method within the predictor-corrector approach. The electron -electron exchange -correlation interactions were taken into account in our analysis. In the temperature range from 77 to 500 K, the dependences of the Seebeck coefficient, thermal conductivity, electron (hole) concentration, and thermoelectric figure of merit on the nanowire thickness, gate voltage, and excess hole (electron) concentration were investigated in the constant relaxation-time approximation. The results of our calculations indicate that the external perpendicular electric field can increase the Seebeck coefficient of the bismuth telluride nanowires with thicknesses of 7 -15 nm by nearly a factor of 2 and enhance ZT by an order of magnitude. At room temperature, ZT can reach a value as high as 3.4 under the action of the external perpendicular electric field for realistic widths of the nanowires. The obtain results may open up a completely new way for a drastic enhancement of the thermoelectric figure of merit in a wide temperature range.

A variational procedure for the solution of the Boltzmann equation with a n arbitrary number of variational parameters is developed. In the frame of the method it is possible to carry out t h e optimization of trial function, as well as to check the convergence of the solution. It is shown that. in semimetals the probability matrix of charge carrier scattering on acoustic phonons entering the expression for the collision operator has a non-diagonal form in the coordinate system of the effective mass tensor. General expressions are obtained for the transport coefficients allowing to determine their numerical values.PaapaBo~ntra BapHaqnoman npouenypa pelrremn KHtIeTwIec~oro ypani~eiiuc! Gontu-