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Basic MOSFET Model Q = channel charge L = channel length Channel Current = Rate of Flow of Charge v = carrier velocity Ids = Q/τsd µ = carrier mobility Derive transit time τsd Eds = electric field τsd = channel length (L) / carrier velocity (v) Vds = drain - source voltage v = µEds Cg = gate - channel capac. Eds = Vds / L Tox = gate oxide thickness v = µVds / L єox = gate oxide permittivity Thus τsd = L2/ µVds W = channel width Vt = threshold voltage Channel charge: charge appears in channel when gate voltage exceeds threshold. p 240cm 2 / V sec( surface) Since gate and oxide form a capacitor: n 650cm 2 / V sec( surface) 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 єox / Tox Hence, drain current Ids = W L єox µVds (Vgs -Vt - Vds/2) / L2 x Tox EE213 VLSI Design S Daniels Basic MOSFET Model Vds2 W I ds K (Vgs Vt )Vds L 2 In the non - saturated region where Vds < Vgs - Vt K = єox µ/Tox = process transconductance parameter ß = KW/L = device transconductance parameter Saturation begins when Vds = Vgs - Vt I ds K W (Vgs Vt ) 2 L 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 EE213 VLSI Design S Daniels Threshold Voltage 1 Tox Vt Vt (0) 2 SiQN (VSB ) 2 ox VSB N Vt(0) = substrate bias voltage = impurity concentration in the substrate = the threshold voltage for VSB = 0 Increasing VSB causes the channel to be depleted of charge carriers and thus the threshold voltage is raised Vt VSB Change in Vt depends on VSB and a constant which depends on substrate doping EE213 VLSI Design S Daniels Transconductance I ds gm forVds const Vds Transconductance expresses the relationship between output current Ids and input voltage Vgs I ds I ds Qc ds QcVds In saturation Vds = Vgs -Vt L2 (Q CV ) CVgs Vds I ds L2 I ds CVds Vgs L2 An indication of frequency response can be given by: C oxWL gm Tox ox W Tox L (Vds V t) g m (Vgs Vt ) 0 gm (Vgs Vt ) C L2 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 EE213 VLSI Design S Daniels