一种由自由电子能带模型计算费米能级的方法

Fermi Level Calculation by Free Electronic Band Model

对面心立方 (fcc)、体心立方 (bcc)和六角密堆积 (hcp)三种不同结构的晶体 ,在假设它们的原胞中包含8个价电子并将价电子近似为自由电子的情况下 ,采用“自由电子气理论”和“自由电子能带模型” ,研究其根据费米球确定的费米能级EF 与根据自由电子能带模型计算的平均键能Em。研究结果表明 ,由自由电子能带模型计算所得 3种不同结构晶体 (因而电子密度也不一样 )的平均键能Em 等于各自自由电子系统的费米能级EF。平均键能Em 是我们在异质结带阶理论计算中建议的一种参考能级 ,研究结果在深化对平均键能Em 物理实质认识的同时 ,提供了一种借助于自由电子能带模型计算自由电子系统费米能级EF 的新方法。

Three different kinds of crystal structures,face centered cubic(fcc),body centered cubic(bcc),and hexagonal close packed(hcp) structures with eight valence electrons in each primitive unit cell were studied.In the framework of free electron approximation,their Fermi level E F were determined by Fermi sphere according to the theory of free electron gas,and the average bond energies E m were calculated by free electronic band model.The calculated results of E F and E m indicate that the average bond energies E m of three different crystal structures (therefore their electron densities are different) correspond to their Fermi levels E F respectively.In the semiconductor energy band,the average bond energy E m is defined as the mid point of the energy gap between E b (bonding orbital energy) which is the avergage valence band level of the four highest valence band levels,and E a (anti bonding orbital energy) which is the average conduction band level of the five lowest conduction band levels in the whole Brillouin zone eigenvalues.It is the reference energy level in our theoretical calculation of heterojunction band offset.Therefore,the relationship between E F and E m found here is helpful to understand the physical concept of average bond energy E m and the reason why it aligns at the two sides of the heterojunction interface.It also suggests a new method to calculate the Fermi level E F of free electron systems through free electronic band model.