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

Unified Channel Charge Density ExpressionQ= Qchsubs0 0Vgs−Vthexp( )nvt(3.1.1a)where Q 0 isQ0= qεsiNchVoffv t exp(2− )φsnvtQchs0 = Cox( Vgs −Vth)(3.1.1b)(3.1.2)In both Eqs. (3.1.1a) and (3.1.2), the parameters Q chsubs0 and Q chs0 are the channelcharge densities at the source for very small Vds. To form a unified expression, aneffective (V gs -V th ) function named V gsteff is introduced to describe the channelcharge characteristics from subthreshold to strong inversionVgsteff⎡ Vgs−Vth⎤2 nvtln⎢1+exp( ) ⎥nvt=⎣ 2 ⎦2ΦsVgs −Vth − 2Voff1+ 2 n COXexp( −)qεsiNch2 nvt(3.1.3)The unified channel charge density at the source end for both subthreshold andinversion region can therefore be written asQC Vchs0 = ox gsteff(3.1.4)Figures 3-1 and 3-2 show the smoothness of Eq. (3.1.4) from subthreshold tostrong inversion regions. The V gsteff expression will be used again in subsequentsections of this chapter to model the drain current.3-2 BSIM3v3.2.2 Manual Copyright © 1999 UC Berkeley