Modeling thermoelectric effects in piezoelectric semiconductors: New fully coupled mechanisms for mechanically manipulated heat flux and refrigeration

We present a continuum theory for analyzing the interaction between the thermoelectric and mechanical fields in piezoelectric semiconductors. The balance laws and dissipation inequality are formulated in the reference configuration. Thermodynamically consistent constitutive equations are derived, including the drift-diffusion current, Fourier's law for thermal flux, Seebeck effect, and Peltier effect, by introducing a generalized Fick's law. The heat conduction equation and Joule heating generation with the semiconducting effect are derived by combing the energy balance and the second Gibbs relation. The framework is then geometrically linearized for applications in small deformation of crystal solids. Based on the newly developed framework, two new coupling mechanisms between thermoelectric and mechanical fields in crystals of class of 6mm are identified. 1) A mechanical load can block both electron and thermal fluxes in the loading area via the mechanically induced potential well. At a strain level of 1%, the current and heat flow can be reduced by as much as 80%. This effect facilitates the design of new switching devices. 2) The mechanical load can surprisingly act as a current amplifier through the induced potential barrier. Furthermore, making use of the new and unusual Joule heating generation, thermal dipoles can be created, indicating that mechanical loading can lead to local refrigeration. Via a simple numerical model, we demonstrate that the mechanical deformation can produce a temperature difference of 0.06 K at the strain level of around 1%. Based on this new and exciting cooling mechanism, we further propose a novel multi-stage pyramidal cascade device for refrigeration. The framework in this paper provides a foundation for analyzing multiple physics problems in semiconductor structures and also potential ideas for switching and refrigeration devices. Since it is based on finite deformation theory, the present framework would be helpful in analyzing the behavior of emerging flexible semiconductor materials or developing the corresponding computational methods.