An analytic model for threshold voltage shift due to quantum confinement in surrounding gate MOSFETs with anisotropic effective mass

Threshold voltage shift due to quantum confinement in surrounding gate MOSFETs with anisotropic effective mass is calculated from the solution of 2D Schrödinger equation in elliptic coordinates. The solutions are of the Mathieu function type. It is shown that for some intermediate range of radius in silicon, several subbands need be taken into account to obtain accurate threshold voltage shifts. However, for small radius, only the lowest subband need be considered, and even anisotropic effective mass can be replaced by reduced isotropic effective mass, for which Bessel function is sufficient.