Bias-dependent Peltier coefficient and internal cooling in bipolar devices

The work described here is an investigation of thermoelectric phenomena in bipolar semiconductors and $p-n$ junctions. In contrast to majority-carrier semiconductors in which a constant material-dependent Peltier coefficient is defined for a given temperature, bipolar devices can be modeled by introducing a bias-dependent Peltier coefficient at interfaces that takes into account the variation of the carriers’ average transport energy. It is shown that this effective Peltier coefficient can vary by orders of magnitude as a function of applied bias, and can give rise to interfacial thermoelectric cooling or heating depending on device parameters. The bias-dependent bipolar Peltier coefficient is modeled analytically for short-length and long-length diodes, and the different regimes of bias for which cooling is achieved are described, as well as the effects of recombination, length, and doping. Analytical expressions to optimize the thermoelectric effect inside an idealized diode cooler are presented with numerical results for several common semiconductors, a figure of merit for internal diode cooling is introduced, and extensions of the model are given for applications such as the internal cooling of a semiconductor laser diode.