半导体短程势深能级在浅能区的波函数行为

本文对短程缺陷势深能级在能量趋向禁带边缘时波函数的行为作了研究。当深能级能量与禁带边能量差ε很小时,在一定的能量和对称性条件满足下,波函数在k空间向极值收缩而在实空间扩展。本文发展了一种方法可有效地用于ε很小时的波函数数值计算。对于靠近导带的A₁态波函数,对于出Si,当ε小于2meV时,开始显著地在k空间收缩;对于GaAs,直至ε=0.1meV还未发生显著收缩。发生显著收缩对应的ε值与有效质量以及缺陷态和能带边波函数对称性匹配度有灵敏的关系。对于靠近价带顶的A₁态,由于与价带顶对称性不匹配,不发生k空间收缩现象。 关键词：

THE BEHAVIOR OF DEEP LEVEL WAVEFUNCTIONS IN SHALLOW ENERGY REGION

The behavior of deep level wavefunctions induced by short range defect potential is investigated when the energy difference ε between the defect state and the band edge is very small. When ε→0, the wavefunctions tend to expand in real space and concentrate in k space when some symmetric matching condition is satisfied. A specific scheme is developed for efficient and reliable numerical calculations of the deep level wavefunctions when ε is very small. For the case of A₁ symmetric defect states near the bottom of the conduction band, for Si, when ε<2 meV, the wavefunctions tend to concentrate rapidly in k space; for GaAs, the wavefunctio'ns do not concentrate in k space until ε is as small as 0.1 meV. The critical ε value corresponding to obvious concentration in k space is sensitive to the magnitude of the effective mass and the degree of matching of symmetry between the defect state and Bloch states at the band edge. For A₁ defect states near the top of the valance band, no concentration in k space occur since the A₁ defect states mismatch to the Block states at valance band maxima.