Spectroscopic properties of semiconductor crystals with direct forbidden energy gap
Spectroscopic properties of semiconductor crystals with direct forbidden energy gap
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DOI：
10.1002/pssa.2210430102
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发表时间：
1977-09
期刊：
影响因子：
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通讯作者：
V. T. Agekyan
中科院分区：
文献类型：
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作者：
V. T. Agekyan
激子效应与电子-电子相互作用有关，因此不能在单电子近似下考虑。已经证明[2]，在有效质量近似下，激子态由电子-空穴库仑吸引的波动方程描述。该方程的解给出了具有球形带的立方晶体的大半径激子的能谱，其中p是约化质量，M是激子总质量，k是激子波矢，n是主量子数，x是介电磁化率。光激子的波矢很小，因此，如果x是常数，谱（2）应是里德伯常数R= p~ e~/2A~的类氢吸收线系列，考虑带间跃迁和库仑相互作用，在cg-hv< R的范围内给出了离散和准连续能级。激子效应（2）强烈地改变了hw-E~> 0的区域。在这种情况下，当能量接近带边缘时，K近似为常数，并且仅当hw-zg>> R时与（1）中的K一致。
The exciton effect is connected with electron-electron interaction and for this reason it cannot be considered in the one-electron approximation. It has been shown [2] that in an effective-mass approximation the exciton state is described by the wave equation for electron-hole Coulomb attraction. The solution of this equation gives the energy spectra of the large-radius exciton of a cubic crystal with spherical bands as where p is the reduced mass, M the total exciton mass, k the exciton wave vector, n the main quantum number, and x the dielectric susceptibility. The wave vector of the optical exciton is small and therefore the spectra (2) should forin hydrogenlike series of absorption lines with the Rydberg constant R= p~ e~/2A~~~, if x is supposed to be constant.The consideration of the interband transition, the Coulomb interaction being taken into account, gives discrete and quasicontinuous levels in the region cg-hv< R. The exciton effect (2) transforms strongly the region where hw-E~> 0. I n this case K is approximately constant when the energy is close to the band edge and coincides with K in (1) only for hw-zg>> R.