Pressure Theory of the Thermoelectric and Photovoltaic Effects

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Abstract
The theory is based upon the hypothesis that free charge carriers—electrons and holes—and phonons exert pressures inside a solid. Gradients of such pressures exert motive forces on the carriers. On this basis, the hole current density Ip, in the absence of a magnetic field, is assumed to be Ip=σpE−μpgrad Pp−μp[open phi]gradP[open phi],where σp, μp, and Pp are, respectively, the conductivity, mobility, and pressure of holes; μpφ is the interaction mobility between holes and phonons; Pφ is phonon pressure; and E is the electrostatic field. A similar expression is obtained for electrons by exchanging the subscript p for n. (The two mobilities associated with electrons, however, are negative.) The theory is applied to the nondegenerate semiconductor, with the assumption that the equation of the ideal gas law applies. (Thus, Pp=pkT, Pn=nkT, where k is the Boltzmann constant, T is temperature Kelvin, and p and n are concentrations of holes and electrons, respectively.) It is also assumed— for small currents—that deviation from the equilibrium pressures can be neglected. Assumptions concerning the phonon effect are quite general; the contribution from this source to the hole current density Ip is given by Ip[open phi]=−σp(kT/e)δp grad ln T,where e is magnitude of electronic charge. The dimensionless quantity δp, the phonon-dragging coefficient for holes (a temperature- and material-dependent parameter), is not amenable to calculation by the theory, in its present form, and must be determined experimentally. Again, a similar expression exists for electrons.