Possible Violation of the Kelvin Relation in the Thermoelectric Coefficients of Silicon pn Junction Diodes

The Kelvin relation (KR), π/α = T, where π and α are the Peltier and Seebeck coefficients and T is the temperature, describes the coupling between thermoelectric effects in an electrical conductor. The KR is a specific case of an Onsager reciprocal relation (ORR) among transport coefficients in generalized force-flow problems. The ORR assumes linear relationships and a local equilibrium approximation (LEA). Modern derivations of the ORR disagree on what corrections may be required if these assumptions are violated. We report measurements of π/α in thermopiles composed of nonlinear silicon pn diodes where a temperature difference ∆T can be maintained between p- and n-sides. π and α were measured independently. For diode thermopiles, α was found to be ~30 smaller than in control thermopiles without pn junctions. Additionally, π was found to two decades larger than in control thermopiles. This leads to an apparent divergent violation of the KR where π/α exceeds T by several decades. This suggests that in this diode system the KR, and thus the ORR, fails even as an approximation. Because diode transport can be linearized for small voltage and ∆T, it might be expected that the KR is a good leading approximation. However, modeling of pn junctions shows that when ∆T ≠ 0, electrons, holes, and lattice in the depletion region maintain finitely different local temperatures. Consequently, we speculate the observed breakdown of the KR is rooted in a failure of the LEA.