Off-Center N and O in Silicon
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OFF-CENTER N AND 0 IN SILICON HAROLD P. HJALMARSON*, DWIGHT R. JENNISON*, *Sandia National Laboratories Albuquerque, New Mexico 87185 **Sandia National Laboratories Livermore, California 94550
AND J. S. BINKLEY**
ABSTRACT The pseudo Jahn-Teller effect and chemical rebonding are both considered as mechanisms that drive substitutional atoms, such as N in Si, off-center. By use of an effective Hamiltonian technique, impurities forming very deep levels, such as Si:N, are found to be susceptible to offcenter displacement by the pseudo Jahn-Teller effect. Using a Hartree-Fock technique, we find two classes of N displacements which depend on the For outward relaxation relaxation of the nearest-neighbor Si atom "cage". of the four nearest neighbors, the N displaces by 0.05 A in the [111] direction and retains sp bonding; this mechanism appears equivalent to the pseudo Jahn-Teller effect. For inward relaxation of the "cage" by 0.45 the N displaces by 0.75 A in the [111] direction and forms a trigonal sp bond; this is a chemical rebonding mechanism. Additional cluster calculations suggest that inward relaxation of the "cage" is likely. Similar calculations for 0 revealed a displacement of approximately 1.1A. INTRODUCTION The work of Brower [1,2] on substitutional N in Si showed that an EPR active center can be associated with N and that this center has C symmetry. On the basis of symmetry and other considerations, he Rnferred that N is substitutional but is distorted off-center along a direction. By analogy to the Jahn-Teller effect [3] proposed for the off-center displacement of N in diamond [4], Brower conjectured that substitutional N in Si is also driven off-center by a Jahn-Teller effect [1]. In this model [3], the paramagnetic electron residing in a threefold degenerate T state drives the atom off-center by coupling to a C^ distortion wgich breaks the Td-symmetry and lowers the total energy. However, Green's function calculations for substitutional impurities have found that the electron should be localized in an A -symmetric state Subsequently, a because A states have lower energy than T states [5]. pseudo Jahn-Teller mechanism was proposed io explain the distortion in diamond [6]. This mechanism was also adopted to explain total energy MNDO Si:N cluster calculations [7]. Later, however, an alternative explanation in terms of chemical rebonding was advanced by workers doing Hartree-Fock cluster calculations [8] and other workers doing valence bond cluster calculations [9]. In this *paper we consider both the pseudo Jahn-Teller and the chemical rebonding mechanisms.
Mat. Res. Soc. Symp. Proc. Vol. 59. @1986 Materials Research Society
554
THEORY The focus of this work is on the total energy E(d) as a function of displacement d. For small displacements from the substitutional lattice site the total energy can be written as: (1)
E(d) - E0 + fd + (k/2)d2 + ....
If the force constant f is nonzero, such a point would not be at equilibrium and the impurity would distort off-center; furthermore, for k In the case of a
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