Electronic properties of $\ensuremath{\delta}$-doped Si:P and Ge:P layers in the high-density limit using a Thomas-Fermi method

Electronic properties of $δ$ -doped Si:P and Ge:P layers in the high-density limit using a Thomas-Fermi method

J. S. Smith, J. H. Cole, and S. P. Russo

Phys. Rev. B 89, 035306 – Published 13 January 2014

Abstract

We present a scalable method for calculating the electronic properties of a $δ$ -doped phosphorus layer in silicon and germanium. Our calculations are based on an $s p^{3} d^{5} s^{*}$ tight-binding model and the Thomas-Fermi-Dirac approximation. The energy shift in the lowest conduction band states of the Ge band structure is characterized and a comparison is made to a $δ$ -doped P layer in Si. The results for the $δ$ -doped Si:P layer themselves compare well to the predictions of more “resource intensive” computational models. The Thomas-Fermi method presented herein scales easily to large system sizes. Efficient scaling is important for the calculation of quantum transport properties in $δ$ -doped semiconductors that are currently of experimental interest.