New Ionic Model Potential for Semiconductors with Application to Si

Teiji Kobayasi^a and Hisashi Nara^b

^aGeneral Education, College of Medical Sciences, Tohoku University; ^bDepartment of Systems and Information, Hachinohe Institute of Technology (kobayasi@cms42.cms.tohoku.ac.jp)

A new ionic model potential for semiconductors is proposed, which consists of a set of continuous exponential functions. Introduced damping and amplitude parameters into the model potential are to be treated as adjustable. Unlike the ionic model potentials of the Heine-Abarenkov and Topp-Hopfield types, the proposed model potential has no artificial sharp cut-off parameter for the repulsive core-orthogonality condition and has continuous derivatives of arbitrary orders. The reasons of the proposition are discussed in relation with light metals where the ionic model potentials with the cut-off parameter work successfully. In particular, an unphysical and artificial oscillation of the potential form factor in high momentum region, which is introduced by the potential discontinuity, will be discussed. The proposed model potential is applied to constructing crystal potential of Si semiconductor and the adjustable parameters are determined so as to be consistent with the Si crystal pseudo potential of high quality by taking a valence electron dielectric screening effect into account. The effectiveness of the proposed model potential is discussed by (1) comparing the calculated ionic energy levels of Si with experiments, (2) checking the consistency between the ionic and crystal potentials for Si, and so on.