Mosfet

MOSFET I-V Characteristics

MOSFET Structure • MOS Capacitor – Inversion forms channel

• Reverse Biased Junctions – Source fills channel – Drain empties channel – Current of inversion charge by drift!

I-V Characteristics • Regions of operation – Regions of operation • Triode and Linear region

– Pinch-off • Saturation • Channel Shortening • Early Effect

– Body Effect

Equivalent Circuit • gm • gmb • Leakage currents • RC constants • Capacitances

Recap of MOS-C relations • • • • • • • • • •

Beyond strong Inversion VGB = φMS + ΨS + Vox (1) QG + Qox + QB + Qinv = 0 (2) For ΨS = 0 : VGB = VFB QB = 0; Qinv = 0 QG = CoxVox = - Qox VFB = φMS - Qox/Cox For ΨS = 2ΨB : VGB = VT; Qinv = 0 QB(2ΨB) = [ 2 εSi q NA(2ΨB)]1/2 VT = VFB + 2ΨB + [ 2 εSi q NA(2ΨB)]1/2/Cox

Assumptions in Derivation of I-V Characteristics • VGS = VGB = φMS + Vox(x) + ψS(x) • ψS(x) = 2ψB + V(x) – Gradual Channel Approximation

• V(x) = Vch(x) + VSB – Vch(x) = voltage with respect to source

• 2ψB = qNAwmax2/ 2εS – Strong Inversion Approximation

• Vox = Eox tox – Charge free oxide

Threshold Voltage • For MOS capacitor

– Voltage required at gate with respect to bulk silicon VGB = VT for inversion charge to form at the oxidesilicon interface i.e. ψS = 2ψB – VT = VFB + 2ΨB + [ 2 εSi q NA(2ΨB) / Cox]1/2

• For MOSFET

– Voltage required at gate with respect to source VGS = VTh to form inversion channel at the source end i.e. ψS = 2ψB – VGS = VTh0 if VSB ≠ 0 – VTh0 = VFB + 2ΨB + [ 2 εSi q NA(2ΨB) / Cox]1/2 – Note inversion channel need not extend from source to drain; inversion charge Qinv(x) is channel charge Qch(x); it must exist at least at source end.

Derivation of I-V Characteristics • Assume: – VSB = 0 => VGS = VGB – Channel complete – Qch(x) ≠ 0 for any x

• VGS = VGB = φMS + Vox(x) + ψS(x) • ψS(x) = 2ψB + V(x) = 2ψB + Vch(x) • Cox Vox = εox Eox tox/tox = εox Eox = Dox • Cox Vox = - (Qox+ Qch(x)+ QB) • VGS – V(x) = φMS - (Qox+ Qch(x)+ QB)/Cox + 2ψB

Channel Charge • VGS – V(x) = φMS - (Qox+ Qch(x)+ QB)/Cox + 2ψB • VTh0 = [φMS - (Qox+ QB)/Cox + 2ψB] • VGS – V(x) – VTh0 = - Qch(x)/Cox • Qch(x) => Mobile charge per unit area – Qch(x). W. dx = q nch(x) tch(x) W dx – Qch(x) = q nch(x) tch(x)

Current in Device • • • • •

Consider dx length of channel at x J(x) = - q nch(x) µ (dV/dx) IDS = - J(x)W tch(x) IDS = q nch(x) µ (dV/dx)W tch(x) Qch(x) = q nch(x) tch(x) ; V = f(x)

• VGS – V(x) – VTh0 = - Qmob(x)/Cox • Qch(V) = Cox [VGS – V(x) – VTh0] • IDS = Qch(x) µ (dV/dx)W • IDS dx = Qch(V) µ W dV

I-V Characteristics - II • IDS dx = Qch(V) µ W dV • IDS dx = Cox [VGS – V(x) – VTh0] µ W dV • Integrating : – x -> 0 – L, – V(0) = 0, V(L) = VDS

• IDS L = µ W Cox ([VGS – VTh0] VDS - 1/2 VDS2) • IDS = µCox(W/L)([VGS – VTh0] VDS - 1/2 VDS2)

Saturation region • IDS = µ Cox (W/L) ([VGS –VTh0 ] VDS - 1/2 VDS2)

• Maxima at VDS = [VGS –VTh0 ] • At Maxima: • IDS = 1/2 µ Cox (W/L) [VGS –VTh0]2 • Point of pinch-off • Increase in voltage does not cause increase in current

Operation • VT referred to source – VGS = VGB – VSB

• Operation – VSB = 0, VDS => small – IDS = µnCox [W/L] (VGS – VTh) VDS • TECHNOLOGY parameters - µnCox • Aspect ratio – Design Parameters - [W/L] • Circuit parameters-(VGS – VTh) VDS