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.

我们提出了一种连续统理论，用于分析压电半导体中热电场和机械场之间的相互作用。平衡定律和耗散不等式在参考配置中制定。通过引入广义菲克定律，推导出了热力学一致的本构方程，包括漂移扩散电流、傅里叶热通量定律、塞贝克效应和珀尔帖效应。结合能量平衡和第二吉布斯关系，推导出具有半导体效应的热传导方程和焦耳发热。然后对该框架进行几何线性化，以用于晶体固体的小变形。基于新开发的框架，1)机械负载可以通过机械感应势阱阻挡负载区域中的电子和热通量。在 1% 的应变水平下，电流和热流可减少多达 80%。这种效应有助于设计新的开关器件。2)机械负载可以通过感应势垒出人意料地充当电流放大器。此外，利用新的和不寻常的焦耳热产生，可以产生热偶极子，这表明机械负载可以导致局部制冷。通过一个简单的数值模型，我们证明了机械变形可以在大约 1% 的应变水平下产生 0.06 K 的温差。基于这种新的令人兴奋的冷却机制，我们进一步提出了一种新颖的多级金字塔形叶栅制冷装置。本文中的框架为分析半导体结构中的多个物理问题以及开关和制冷设备的潜在想法提供了基础。由于它基于有限变形理论，