The Schottky barrier on a contact of a magnetic 3$d$ metal with a semiconductor

Analytical expressions for the charge (electron or hole) transfer between a metal and a semiconductor and for the Schottky barrier height are obtained using the Friedel model for the $d$ band of a transition metal and the local defect model for a semiconductor. It is shown that taking into account the metal magnetization enhances the charge transfer and the related contribution to the Schottky barrier height. Numerical estimates are presented for Co and Ni contacts with 6$H$ and 4$H$ SiC polytypes.