Molecular-Orbital Treatment for Deep Levels in Semiconductors: Substitutional Nitrogen and the Lattice Vacancy in Diamond

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Abstract
A deep-defect level in a semiconductor is simulated by a cluster of host atoms surrounding the defect. The system is then treated as a "large molecule," the energy levels and wave functions for the entire cluster being obtained using molecular-orbital techniques. As examples, the substitutional nitrogen-atom impurity and the lattice vacancy in diamond are treated in some detail. The molecular-orbital technique used in these examples is extended Huckel theory (EHT) and clusters of up to 70 atoms are considered. The results of an EHT treatment of bulk diamond are shown to provide an adequate description of the bands. Lattice relaxations are investigated and shown to be an important part of the deep-level problem. Wave functions are obtained and compared to EPR results for nitrogen in diamond. The agreement between theory and experiment is found to be very good. For the vacancy, the theoretical results are compared to experimental work on the vacancy in silicon. A comparison to the Coulson—Kearsley—Yamaguchi "defect-molecule" treatment of the vacancy is also provided. It is concluded that this cluster approach is a highly promising one for the deep-level problem. Throughout, the physical insight provided by the calculations in understanding the features of the defect centers is stressed.