The Physics of Electric Field Effect Thermoelectric Devices
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The Physics of Electric Field Effect Thermoelectric Devices V. Sandomirsky, A. V. Butenko, R. Levin1 and Y. Schlesinger Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel 1 The College of Judea & Samaria, Ariel 44837, Israel ABSTRACT We describe here a novel approach to the subject of thermoelectric devices. The current best thermoelectrics are based on heavily doped semiconductors or semimetal alloys. We show that utilization of electric field effect or ferroelectric field effect, not only provides a new route to this problem, bypassing the drawbacks of conventional doping, but also offers significantly improved thermoelectric characteristics. We present here model calculation of the thermoelectric figure of merit in thin films of Bi and PbTe, and also discuss several realistic device designs. INTRODUCTION Application of an electric field (Electric Field Effect - EFE) to a capacitor structure of the type Gate-Dielectric-Semimetal (or non-degenerate semiconductor), or Gate-FerroelectricSemimetal injects, into the semimetal or semiconductor sample, charge carriers which are distributed among the electron and hole bands. Depending on the field polarity, the number of carriers of the corresponding sign increases, while the number of carriers of the other sign diminishes. This is connected with the change of the electron (ηe) and the hole (ηh) Fermi levels with an applied electric field, i. e. ηe=ηe(E) and ηh=ηh(E). Increasing the electric field can result in zero concentration of the corresponding charge carrier type. A further increase of the electric field results in a further increase of the introduced carriers and hence of the conductivity. It follows from the above argument that all the thermoelectrical effects (the state-of-art of the field has been recently presented by Mahan [1]), such as Peltier, Seebeck, Nernst etc are strongly dependent on the magnitude of the electric field. Thus, the EFE offers a novel, controllable and more effective route to thermoelectricity. In the following we will term this sort of thermoelectrics by EFE-TE. In following we analyze in detail the electric field dependence of the Seebeck effect (see also [2]). One can show that the Seebeck effect is expressed by the formula S = S p − Sn ,
(1)
where Sp =
σ n sn kB σ p s p k ; Sn = B . e σ p +σn e σ p +σn
CC11.13.1
(1’)
Here σp and σn are the hole and the electron conductivities, sp and sn are the hole and the electrons related Seebeck coefficients, < > denotes averaging over the sample thickness. The later is needed because of the inhomogeneous electric field in sample (the larger the dielectic constant ε the larger the characteristic screening length Ls, determining the rate of the exponential decrease of the field in the sample). In absence of electric field (E=0), Sn and Sp are of comparable magnitude, therefore S is smaller than each of the above quantities. For a certain value of the mobilities, Sp could equal Sn and therefore S=0. It should be noted (Eq. 1’) that S depends on the electric field via the fiel
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