A physically based analytical model for the threshold voltage of strained-Si n-MOSFETs

A physically based analytic model for the threshold voltage V_t of long-channel strained-Si--Si_1-xGe_x n-MOSFETs is presented and confirmed using numerical simulations for a wide range of channel doping concentration, gate-oxide thicknesses, and strained-Si layer thicknesses. The threshold voltage is sensitive to both the electron affinity and bandgap of the strained-Si cap material and the relaxed-Si_1-xGe_x substrate. It is shown that the threshold voltage difference between strained- and unstrained-Si devices increases with channel doping, but that the increase is mitigated by gate oxide thickness reduction. Strained Si devices with constant, high channel doping have a threshold voltage difference that is sensitive to Si cap thickness, for thicknesses below the equilibrium critical thickness for strain relaxation.