Space-charge-induced Seebeck effect in solid dielectrics

We show theoretically that, in the presence of space charge, the Seebeck coefficient of a homogeneous plane-parallel capacitor could go beyond corresponding limits of the linear-response regime. In this study, we consider the coexistence of p-type and n-type carriers and interrelate the carrier concentrations via the mass-action law. If only Ohmic conductivity is considered or if the distribution of space charge is taken to be uniform, the Seebeck coefficient, which is the same as that given by Onsager’s reciprocal relations, takes on a magnitude between $0$ and $kB/q$⁠, where $kB$ is the Boltzmann constant and $q$ is the electronic charge. But in the nonlinear-response regime which corresponds to any space-charge-limited scenario with a nonuniform distribution of space charge, Onsager’s reciprocal relations break down and the magnitude of the Seebeck coefficient takes on a value between $kB/q$ and $2kB/q$⁠, exceeding the limit of the linear-response regime.