使用等价轨道法计算AB型晶体的倍频系数

在忽略电子-声子相互作用的基础上,本文探讨了从能带波函数出发计算AB型晶体倍频系数的可能性。采用计算AB型晶体能带的近似方法——等价轨道法。计算了k=0点的倍频系数,然后通过带宽的修正,使k=0点的倍频系数近似地表为不同k点倍频系数的平均,这一平均值乘以第一布里渊区内k点的总数就是晶体的宏观倍频系数。计算了十七种闪锌矿型和纤维锌矿型晶体的倍频系数,计算值和实验值的吻合相当满意。从中得出几点有用的结论:(1)倍频系数的双能级跃迁模型对闪锌矿型结构是适用的;但对纤维锌矿型结构并不适用。(2)纤维锌矿型晶体的X₃₃₃^2ω系数可表示成两项之和:单重态(Γ₁,Γ₃)的贡献和双重态(Γ₅,Γ₆)的贡献。其中单重态对倍频系数贡献正值,双重态贡献负值。(3)使用Pauling的离子性标度f_i来表征A—B键的离子性是适宜的。关键词：

THE CALCULATION OF SHG COEFFICIENTS FOR CRYSTALS WITH ZINC BLENDE AND WURTZITE STRUCTURES BY USING THE EQUIVALENT ORBITAL METHOD

The calculation of SHG coefficients for crystals with zinc blende and wurtzite structures (AB-type crystals) has been carried out by using the equivalent orbital method. Upon neglect of the electron-phonon interactions, the possibility of adopting the energy bands functions for calculation of these coefficients has been considered. The equivalent orbital method, originally an approximate one in the calculation of the band structures of AB-type crystals, is then used to calculate SHG coefficients for those crystals at K = 0. With some modifications of the band width, the SHG coefficients at K = 0 can be represented approximately as the average of the SHG coefficients for various K vectors. Multiplied by the total number of K vactors in the first Brillouin zone, this gives the macroscopic SHG coefficients for these crystals.Attempts have been made to calculate SHG coefficients for 17 species of crystals with zinc blende and wurtzite structures systematically. It is interesting to note that the values thus obtained agree satisfactorily with the experimental data. Hence the following conclusions can be drawn:1. The one-gap model has been found to be appropriate to zinc blende structures, but it is not the case for wurtzite. 2. It is shown that the coefficients x₅₃₃^(2ω) for the wurtzite structure are the sum of two terms, i.e., contributions from the single state (Γ₁,Γ₃) as well as from the doublet state (Γ₅,Γ₆). The former is found to be negative, whereas the latter is positive.3. It is appropriate to use Pauling ionicity as a measure of the ionicity of the A-B bond.