Analytical model for threshold voltage shift due to impurity penetration through a thin gate oxide

We derived an analytical model for the threshold voltage shift due to impurity penetration through gate oxide and evaluated the thermal budget for pMOS devices with a thin gate oxide. The threshold voltage shift decreases as the channel doping concentration increases, but the decrease is quite small. The allowable surface concentration of the penetrated impurity increases as the gate oxide thickness decreases if the allowable threshold voltage shift is constant. Therefore, the allowable diffusion length normalized by the gate oxide thickness d_ox increases with decreasing d_ox