基于晶格动力学的硅单晶热学性质研究(II)——晶格非和谐势能和格律纳森参数

Study on Thermal Properties of Silicon Single Crystal Based on Lattice Dynamics (II)—Lattice Anharmonic Potential and Gruneisen Parameter

为用晶格动力学方法研究硅单晶的热膨胀性质,必须首先计算作为微扰哈密顿的硅单晶晶格的三阶非和谐势能,而三阶非和谐势能的计算又可以建立在已知不同晶格常数所对应的晶格和谐势能的基础上,因此本文运用他人计算得到的最近邻和次近邻原子间的相互作用力常数,推导了的硅单晶的晶格和谐势能公式,并在此基础上根据不同晶格常数下的晶格和谐势能推导了三阶非和谐势能公式,为后续硅单晶的热膨胀系数计算公式的推导做了必要准备。最后还运用本文提出的三阶非和谐势能模型,计算了不同温度下硅单晶的格律纳森参数,发现其与他人的实验结果吻合,从而验证了本文所提出的三阶非和谐势能模型的正确性。

Abstract: In order to study the thermal expansion properties of silicon single crystal by lattice dynamics, the third order anharmonic potential of silicon single crystal lattice should be calculated as the perturbation Hamiltonian first, and the calculation of the third order anharmonic potential can be based on the lattice harmonic potential corresponding to different lattice constants. Therefore, the formula for lattice harmonic potential energy of silicon single crystal is derived first by using the interaction force constants between the nearest neighbor atoms and the next-nearest neighbor atoms calculated by others, and then the formula for the third order anharmonic potential is derived based on the lattice harmonic potential with different lattice constants. It is a necessary preparation for the subsequent derivations of formula for thermal expansion coefficient. Finally, with the third-order anharmonic potential energy model proposed in this paper, the Gruneisen parameters of silicon single crystal at different temperature are calculated, and it coincides with the experimental results of others. Thus the correctness of the third-order anharmonic potential energy model proposed in this paper is verified.