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

Non-Uniform Doping and Small Channel Effects on Threshold Voltage2.1.3 Short Channel EffectThe threshold voltage of a long channel device is independent of the channellength and the drain voltage. Its dependence on the body bias is given byEq. (2.1.4). However, as the channel length becomes shorter, the thresholdvoltage shows a greater dependence on the channel length and the drainvoltage. The dependence of the threshold voltage on the body bias becomesweaker as channel length becomes shorter, because the body bias has lesscontrol of the depletion region. The short-channel effect is included in theV th model as:Vth= Vth0⎛+ K ⎜1⎜⎝+ K11+( Φ −V− Φ )NlxLeffs⎞−1⎟⎟⎠bsΦss− ∆V− K Vth2bs(2.1.12)where ∆V th is the threshold voltage reduction due to the short channeleffect. Many models have been developed to calculate ∆V th . They usedeither numerical solutions [4], a two-dimensional charge sharing approach[5,6], or a simplified Poisson's equation in the depletion region [7-9]. Asimple, accurate, and physical model was developed by Z. H. Liu et al.[10]. This model was derived by solving the quasi 2D Poisson equationalong the channel. This quasi-2D model concluded that:thth( L) ( ( V − Φ ) V )∆V = θ 2 +bisds(2.1.13)where V bi is the built-in voltage of the PN junction between the source andthe substrate and is given byBSIM3v3.2.2 Manual Copyright © 1999 UC Berkeley 2-7