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The energy levels of the ideal divacancy states in band gap for more than 10 cubic semiconductors are invesgated by using the basic equations given in ref. [1] and the tight binding Hamiltonian given by vogl et al. A simple physical model is used to describe the basic physics of the divacancy problem.

By using Koster-Slater Green's function method and on-site defect potential approximation, a systematic method of A1 symmetric deep level wavefunction calculation of substitutional defect pairs is worked out. The method is applied to the spectator-oxygen pairs in GaP successfully. The Zn-O and Cd-O pair wavefunctions are obtained for the first time. The wavefunction is mainly concentrated on four bonds which locate at four nearest neighbour sites of oxygen center and point toward the oxygen. Nevertheless, the four bonds are not in the equal weight. The component of the bond which links spectator with oxygen is reduced in comparison with other three and it is more reduced for more electropositive spectator. The rest part of the wavefunction extends diversely over a wide range of space.

A complete set of equations for determining the energy levels and the wavefunc-tions with different symmetry of electronic states of the ideal divacancy in cubic semiconductors is obtained using the Koster-Slater Green's function method. Using an empirical tight binding Hamiltonian for the band structure of the host and the on-site pertubation approximation for the defect, only the on-site and the off-site Green's functions of the host and their derivatives with respect to energy E are involved in these equations.

A systematic investigation and numerical results of calculation of T2 symmetric deep level wave function induced by short range defect potential in Si are described, based on a recently developement on site defect potential Green's function method. [5,6] Such a complete information of T2 symmetric wave functions in Si is presented for the first time. The occupation probability P1 of the wave function located around four nearest neighbour sites of the defect center has a peak exceeding 50%. This part of wave function could be described by T2 symmetric combination of four hybrid orbital quasi dangling bonds located at four nearest neighbour sites and pointing toward the defect center. The total occupation probability of wave function located on the 0,1,2 shells arround the defect center is about 70%. The rest part of the wave function extends diversely over a wide range of space. The characteristics of the wave function are insensitive to the defect energy over most part of the energy range in the gap. Only when the defect energy level approaches very closely to the band edge of either conduction (Ec) or valence (Ev) band, the aforementioned peak P1 disappears and the wave function extends smoothly all over the space. A T2 symmetric deep level due to ideal vacancy is found at 0.51 eV up to the Ev.

New criterion for symmetric properties of defect potential in semiconductors is presented. For a degenerate energy level Es, we introduce the average Es of energy splitling under stress. Es is invariant under symmetry operation of Hamiltonian. Therefore, it is straight foward to reduce the stress coefficient tensor of Es by group theoretical method. For instance, for cubic semiconductors, if the defect level ET is withdefect potential of T group symmetry, the uniaxial stress coefficient of (?(Ec-ET))/(?F) or (?(ET-Ev))/(?F) is isotropic and equal to one third of corresponding hydrostatic pressurecoefficient. The case of defect potential with C3v symmetry is also discussed.The electron (or hole) emission and capture processes of defect levels under energy splitting are analysed. The weighted average of emission rate en and capture rate cn satisfy the following relation: en=gTgc-1cnN′ce(-(Bc-BT)/kT) By measuring the stress dependence of en., various schemes for determining the symmetry property of defect potential are discussed. The transient processes under defect level splitting are also discussed. When transitions are al lowed between the splitting states, the transient is exporential with single decay time constant en-1. When transitions between different states are forbidden, the transient is decay with multi-exponential time constants. en is determined by the initial transient slope.

The behavior of deep level wavefunctions induced by short range defect potential is investigated when the energy difference e between the defect state and the band edge is very small. When e→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 e is very small. For the case of A1 symmetric defect states near the bottom of the conduction band, for Si, when e 2 meV, the wavefunctions tend to concentrate rapidly in k space; for GaAs, the wavefunctio'ns do not concentrate in k space until e is as small as 0.1 meV. The critical e 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.

A simple method in the framework of Koster-Slater Green's function calculation and central cell defect potential (CGDP) approximation is used to calculate the distribution of deep level wavefunctions in Bloch space for Si, GaAs and GaP for the first time. Convergence properties are discussed. It is shown that for definite number of energy bands in the host crystal model, the convergence of deep level wavefunction calculations is faster than that of deep energy calculations.

The wavefunctions of the Eu, state and the Eg state are evaluated for the ideal divacancy in Si, using the basic equations given in [1] and the tight binding Hamiltonian given by P. Vogl et al. Comparison between the culculated results and the ESR and ENDOR spectra of V2+ and V2- in Si is discussed.

The hydrostatic pressure coefficient of gold acceptor levels Er in Silicon was measured by transient capacitance method. Under the pressure range of 0-8 Kbar, thepressure coefficient (?(Ec-ET))/(?P) =-1.9 meV/kbar. The electron capture cross section of gold acceptor centers does not depend on pressure within the experimental accuracy. By comparing the present result of hydrostatic pressure coefficient with the uniaxial pressure coefficient reported in [13], we conclude that the defect potential is lack of Td symmetry. Therefore, the gold acceptor levels are not originated by simple gold substitutional or interstitial configuration in Si crystals.

The wavefunctions of the A1 and E states of the ideal divacancy in GaAs, GaP are calculated using the basic equations given in ref. [1] and the tight-binding Hamiltonian given by P. Vogl et al. It is shown that the largest part of the wavefunctions of divacancy states is on the three nearest Ga atoms of the As or P vacancy, the rest part of the wavefunction decreases slowly and non-monotonically as the distance from the defect increases.