BSIM3v3.2.2 MOSFET Model - The University of Texas at Dallas

Non-Uniform Doping and Small Channel Effects on Threshold VoltageThe right hand side of Eq. (2.1.23) represents the additional voltageincrease. This change in V th is modeled by Eq. (2.1.24a). This formulationincludes but is not limited to the inverse of channel width due to the factthat the overall narrow width effect is dependent on process (i.e. isolationtechnology) as well. Hence, parameters K 3 , K 3b , and W 0 are introduced asox( K3+ K3V ) ΦsbbsWeffT' + W0(2.1.24a)W eff ’ is the effective channel width (with no bias dependencies), whichwill be defined in Section 2.8. In addition, we must consider the narrowwidth effect for small channel lengths. To do this we introduce thefollowing:(2.1.24b)D''⎛WeffLeffWeffLeff⎞⎜exp( − DVT w ) + 2exp( −DVT w ) ⎟( Vbi− Φs)⎝2ltwltw⎠VT 0w1 1When all of the above considerations for non-uniform doping, short andnarrow channel effects on threshold voltage are considered, the finalcomplete V th expression implemented in SPICE is as follows:BSIM3v3.2.2 Manual Copyright © 1999 UC Berkeley 2-13