  We determined the interface state density ($D_{\rm it}$) distributions in the
vicinity of the conduction band edge in silicon carbide (SiC)
metal-oxide-semiconductor (MOS) structures by reproducing the experimental
current-voltage characteristics of MOS field effect transistors (MOSFETs) with
numerical calculations. In the calculation, potential distributions and energy
sub-bands in the inversion layer were calculated by solving Poisson and
Schr\"{o}dinger equations, respectively. We demonstrate that gate
characteristics of the MOSFETs are well described by considering that the
interface states are caused by fluctuation of free-electron density of states
in a two-dimensional system. The $D_{\rm it}$ distributions are almost uniquely
determined by the oxide formation process (as oxidation or interface
nitridation) and independent of the acceptor concentration
($3\times10^{15}-1\times10^{18}\ {\rm cm^{-3}}$).
