Compact Modeling of Qunatum Effects in Undoped Long- Channel Cylindrical Surrounding-Gate MOSFETs

Quantum effects have been incorporated in the analytic potential model for cylindrical surrounding-gate or gate-all-around metal oxide semiconductor field effect transistors (MOSFETs). By extracting some constants parameter from the self-consistent Schrodinger and Poisson equations, two physical parameters, threshold voltage shift and inversion layer centroid, are expressed as closed form function of device radius and charge density. The quantum version of inversion charge density is obtained by incorporating of those parameters into the classical procedure as modifications for gate work function and inversion layer capacitance. The model represented here has been able to reproduce simulation data obtained from self-consistent calculation. The calculated results show that the model fits well with the self-consistent calculation.