1. EE213 VLSI Design S Daniels Channel Current = Rate of Flow of Charge I ds = Q/τ sd Derive transit time τ sd τ sd = channel length (L) / carrier velocity (v) v = µE ds E ds = V ds / L v = µV ds / L Thus τ sd = L 2 / µV ds Channel charge: charge appears in channel when gate voltage exceeds threshold. Since gate and oxide form a capacitor: Q = C x ( Vgc - Vt ) Q = C x ( Vgs - Vt ) source end Q = C x ( Vgs - Vds -Vt) drain end So, average channel charge Q = C x (Vgs -Vt - Vds/2) Gate - channel capacitance is a parallel plate capacitor Cg = W L є ox / T ox Hence, drain current Ids = W L є ox µV ds (Vgs -Vt - Vds/2) / L 2 x T ox Basic MOSFET Model Q = channel charge L = channel length v = carrier velocity µ = carrier mobility Eds = electric field Vds = drain - source voltage Cg = gate - channel capac. Tox = gate oxide thickness є ox = gate oxide permittivity W = channel width Vt = threshold voltage

2. EE213 VLSI Design S Daniels K = є ox µ/Tox = process transconductance parameter ß = KW/L= device transconductance parameter In the non - saturated region where Vds < Vgs - Vt Saturation begins when Vds = Vgs - Vt In the saturated region where Vds = Vgs - Vt These expressions are based on a very simple model. Real transistors will behave slightly differently These expressions hold for both enhancement mode and depletion mode devices Basic MOSFET Model

3. EE213 VLSI Design S Daniels Threshold Voltage V SB = substrate bias voltage N = impurity concentration in the substrate V t (0) = the threshold voltage for V SB = 0 Increasing V SB causes the channel to be depleted of charge carriers and thus the threshold voltage is raised Change in Vt depends on V SB and a constant which depends on substrate doping

4. EE213 VLSI Design S Daniels Transconductance expresses the relationship between output current I ds and input voltage V gs Transconductance In saturation V ds = V gs -V t An indication of frequency response can be given by: This shows that switching speed is proportional to gate voltage above threshold and carrier mobility. Speed is inversely proportional to the square of the length of the channel Both gm and Vt are important FET characteristics which need to be tightly controlled