Predicting the behaviors of thermoelectric material, such as the Seebeck coefficient, using first-principle material properties will accelerate material design and selection to optimize the performance of thermoelectric generator. This paper presents an analytic framework for the Seebeck coefficient. Particularly, it elucidates the important contribution of chemical potential to the overall Seebeck coefficient. This factor, however, is often neglected when Seebeck coefficient is defined based on only electrostatic potential or when methods based on the Boltzmann transportation equation is used to derive the expression of the Seebeck coefficient. (The diffusion component due to chemical potential gradient is generally ignored.) In this paper, methods based on local equilibrium assumption and Fermi–Dirac distribution are utilized to derive the expressions for the Seebeck coefficients using the first-principle parameters. The analytic expression of both the total Seebeck coefficient and the contribution from chemical potential component is derived, which is solved using numerical methods. A case study on a popular thermoelectric material bismuth telluride (both n-type and p-type) is conducted based on the derived expressions. Results of numerical calculations prove that chemical potential contributes significantly to the total Seebeck coefficient of bismuth telluride (76% for n-type and 88% for p-type materials, respectively, at room temperature if the materials are doped with shallow energy level impurities) when working under optimal Seebeck coefficient conditions.

利用第一性原理的材料特性预测热电材料的行为，例如塞贝克系数，将加速材料设计和选择，从而优化热电发电机的性能。本文提出了塞贝克系数的解析框架。特别是，它阐明了化学势对整个塞贝克系数的重要贡献。但是，当仅基于静电势定义塞贝克系数时，或者使用基于玻尔兹曼输运方程的方法推导塞贝克系数的表达式时，通常会忽略此因素。（由于化学势梯度而引起的扩散分量通常被忽略。）在本文中，基于局部平衡假设和费米-狄拉克分布的方法被用于使用第一原理参数推导塞贝克系数的表达式。导出了总塞贝克系数和化学势成分贡献的解析表达式，使用数值方法求解。基于导出的表达式，对一种流行的热电材料碲化铋（n型和p型）进行了案例研究。数值计算结果表明，化学势显着影响了碲化铋的总塞贝克系数（如果室温下掺入浅能级杂质，则n型和p型材料的塞贝克系数分别为76％和88％）。在最佳塞贝克系数条件下工作时。