An Analytical Model for the Threshold Voltage Shift Caused by Two-Dimensional Quantum Confinement in Undoped Multiple-Gate MOSFETs

An analytical model describing the effects of 2-D quantum-mechanical carrier confinement on the threshold voltage V th of multiple-gate MOSFETs with rectangular cross section is developed. The model is verified by a comparison with self-consistent solutions of 1-D and 2-D Schroumldinger and Poisson equations. It is shown that: 1) the model results asymptotically approach the case of 1-D confinement in single-gate silicon-on-insulator or double-gate MOSFETs if one body dimension becomes larger than 20 nm and 2) the effect of 2-D confinement is remarkably stronger than a simple combination of two 1-D quantization effects.