Nitrogen and Phosphorous Impurities in Diamond
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NITROGEN AND PHOSPHOROUS IMPURITIES IN DIAMOND
Koblar Jackson+, Mark R. Pederson and Joseph G. Harrison*, Complex Systems Theory Branch, Naval Research Laboratory, Washington D.C. 20375-5000. +NRCNRL Research Associate. University of Alabama-Birmingham, Birmingham, AL 35294.
ABSTRACT In this paper we use a first-principles local density approximation-based approach to study the properties of the n-type impurities nitrogen and We determine impurity donor level positions of 0.90 phosphorous in diamond. eV and 1.09 eV, respectively for C:N and C:P, measured relative to the bottom of the conduction band. We also study the energetics of impurity atom relaxation along the direction in the diamond lattice. While experimental observations indicate a trigonal distortion about the impurity site, we find the on-center position for both impurity atoms to be stable against the simple relaxation.
INTRODUCTION Substitutional nitrogen and phosphorous, with five valence electrons, are prototype n-type impurities in diamond. In this paper we study the properties of C:N and C:P using a first-principles quantum mechanical approach based on the local density approximation (LDA), performing self-consistent LDA calculations on finite clusters of atoms. In these calculations we seek first to determine the positions of the impurity donor levels relative to the host conduction band (CB). A second issue of interest is the position of the impurity atom in the diamond lattice. Experimental evidence clearly shows[l] a trigonal distortion at the impurity site. A simple model for this distortion has the the nitrogen atom moving off-center in the direction as a result of a Jahn-Teller effect. Four equivalent anti-bonding orbitals centered on the C-N bonds are available to the donor electron. Stretching one of the bonds lowers the energy of the corresponding anti-bonding orbital, and placing the donor electron in this state gives a non-degenerate ground state for the C:N system. From the point of view of a one-electron theory such as LDA, however, such a picture is problemmatic. The lowest one-electron state available to the donor electron is a symmetric combination of the four anti-bonding orbitals. Any off-center relaxation in LDA must then be due to higher order effects. We investigate the off-center relaxation of the impurity atom in the diamond lattice by performing LDA total energy calculations as the impurity atom is systematically moved off-center.
COMPUTATIONAL METHOD The local density approximation[2] is the starting point for most current first-principles condensed-matter calculations, and detailed expositions of the theory are abundant in the literature. In our calculations we employ the Kohn-Sham exchange functional, with Ceperly-Alder correlation as parametrized by Perdew and Zunger. (3 We solve the LDA one-electron Schroedinger equations in a Gaussian-orbital based, linear combinations of atomic orbitals framework, using a recently developed[4] variational mesh to evaluate the Hamiltonian matrix elements numerically. We investiga
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