It was well known that the effective mass approximation cannot be used to calculate the deep impurity levels in semiconductors. Starting from the band wave functions and making use of the idea of pseudo-potential, we proved that, the impurity states are the approximate solutions of an equivalent Schr?dinger equation, which contains not only the usual term of the long range Coulomb potential, but also a short range one. For the shallow level impurities this short range force gives rise to the so called "valley-orbit" splitting, while for deep level impurities it cannot be taken as perturbation. It is essentially different for different impurities.The effect of this short range force on the bond states was discussed. It was shown that, when this part is so strong that it alone can give rise to resonance scattering or bond state of electron, the bond energy does strongly depend on it, and rapidly increases as it increases. At the same time the wave function also shrinks largely. It was proved that the matrix elements between valence and conduction bands of this part of potential can be replaced approximately by an equivalent intraband repulsive interaction and the influence of interband interaction is important when the bond energy is nearly equal to the forbidden band width. It also may be the cause of the fact that many impurities can capture electron and hole simultaneously.Furthermore, we carried out numerical calculation for a simple model and analysed in detail all the above mentioned effects. Finally the energy levels of Cu, Ag, Au in Ge were discussed with the help of this simple model.
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