Mosfet Parameters
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Mosfet Parameters as PDF for free.
More details
- Words: 653
- Pages: 9
MOSFET parameters Body Effect, Early Effect Small signal parameters,
Other Effects • Parameters γ - Body effect parameter λ - Drain Modulation- Early Effect – b – Mobility ratio
Equations Again (1) • VGB = φMS + ΨS + Vox (2) • QG(x) + Qox + QB + Qch(x) = 0 • In MOSFET: • VGB = VGS + VSB = φMS + ΨS(x) + Vox (x) • Vox(x) = (QG(x)/Cox) = - (Qox + QB + Qch(x) )/Cox • ψS(x) = 2ψB + V(x) = 2ψB + VSB + Vch(x) • 2ψB + VSB = q NA wmax2/(2εS) • QB = qNAwmax = [2qNAεS(2ψB + VSB)]1/2 • VGB = φMS + 2ψB + VSB + Vch(x) - (Qox + QB + Qch(x) )/Cox
MOSFET Threshold Voltage • QB = qNAwmax = [2qNAεS(2ψB + VSB)]1/2 …………….. (1) • VGB = φMS + 2ψB + VSB + Vch(x) - (Qox + QB + Qch(x) )/Cox …… (2) •
VGB = [φMS – Qox/Cox] + [2ψB + VSB] + Vch(x) - (QB + Qch(x) )/Cox …(3)
• VGB = VGS + VSB • VGB = VFB + [2ψB + VSB] + Vch(x) - ( QB + Qch(x) )/Cox • Case 1: VSB = 0, x = 0, Qch(0) = 0; => VGS = VTh0 • VGB = VTh0 = VFB + 2ψB + [2qNAεS(2ψB)]1/2 /Cox ……………. (4) • Case 1a: VSB = 0, Qch(x) > 0; => VGS > VTh0 • VGS - VTh0 - Vch(x) = – Qch(x)/Cox
MOSFET CURRENT •
Case 1b: VSB = 0, Qch(x) > 0 for 0 < x < L; VGS > VTh0
•
Complete Channel • IDS = µCox(W/L)([VGS – VTh0] VDS - 1/2 VDS2) •
Case 1c: • VSB = 0, Qch(x) = 0 for x < L; VGS > VTh0
• Qch(x) = - Cox(VGS - VTh0 - Vch(x)) • At x = L' Qch(L' ) = 0 • Vch(L') = (VGS - VTh0) = VDSAT •
IDS = ½ µCox(W/L)([VGS – VTh0]2
Body Effect Parameter •
Case 2: VSB ≠ 0, x = 0, Qch(0) = 0; => VGS = VTh
•
VGB = VGS + VSB = VFB + [2ψB + VSB] + [2qNAεS(2ψB + VSB)]1/2 /Cox
•
VTh = VFB + [2ψB] + [2qNAεS(2ψB + VSB)]1/2 /Cox ……(5)
•
Δ VTh = [2qNAεS(2ψB + VSB)]1/2 /Cox - [2qNAεS(2ψB)]1/2 /Cox
•
VTh = VFB + [2ψB] + [2qNAεS(2ψB + VSB)]1/2 ……(5)
•
Δ VTh = [2qNAεS(2ψB + VSB)]1/2 - [2qNAεS(2ψB)]1/2
MOSFET CURRENT • Case 2b: VSB ≠ 0, Qch(x) > 0 for 0 < x < L; VGS > VTh • Complete Channel • IDS = Cox(W/L)([VGS – VTh] VDS - 1/2 VDS2) • Case 2c: • VSB ≠ 0, Qch(x) = 0 for x < L; VGS > VTh • Qch(x) = - Cox(VGS - VTh - Vch(x)) • Incomplete Channel • At x = L' Qch(L' ) = 0 • Vch(L') = (VGS - VTh) = VDSAT • IDS = ½ µCox(W/L)([VGS – VTh]2
Small Signal Parameters • In Saturation • IDS = ½ µCox(W/L)([VGS – VTh]2 • ΔIDS = gm ΔVGS + gmb ΔVSB + gds ΔVDS • gm = µCox(W/L) (VGS – VTh) • gmb = µCox(W/L) (VGS – VTh)[∂VTh/∂VSB] •
VTh = VFB + [2ψB] + [2qNAεS(2ψB + VSB)]1/2/Cox ……(5)
• [∂VTh/∂VSB] = ½ [2qNAεS ]1/2/Cox(2ψB + VSB)-1/2 • γ = [2qNAεS ]1/2/Cox •
gmb = ½ gm γ (2ψB + VSB)-1/2
Early Effect • Saturation • IDS = ½ µCox(W/ L') [VGS – VTh]2 • L' = L – ΔL = L ( 1 - ΔL/L) ≈ L ( 1 + ΔL/L)-1 • IDS = ½ µCox(W/ L)[VGS – VTh]2( 1 + ΔL/L) • ΔL/L ≈ λ VDS = VDS/VEA • VEA = Early Voltage => Point on –x axis where IDSAT converges for different V when extrapolated. • IDS = ½ µCox(W/ L)[VGS – VTh]2( 1 + λ VDS) • gds = ∂IDS/∂VDS ≈ IDS / VEA
Other Effects • Parameters γ - Body effect parameter λ - Drain Modulation- Early Effect – b – Mobility ratio
Equations Again (1) • VGB = φMS + ΨS + Vox (2) • QG(x) + Qox + QB + Qch(x) = 0 • In MOSFET: • VGB = VGS + VSB = φMS + ΨS(x) + Vox (x) • Vox(x) = (QG(x)/Cox) = - (Qox + QB + Qch(x) )/Cox • ψS(x) = 2ψB + V(x) = 2ψB + VSB + Vch(x) • 2ψB + VSB = q NA wmax2/(2εS) • QB = qNAwmax = [2qNAεS(2ψB + VSB)]1/2 • VGB = φMS + 2ψB + VSB + Vch(x) - (Qox + QB + Qch(x) )/Cox
MOSFET Threshold Voltage • QB = qNAwmax = [2qNAεS(2ψB + VSB)]1/2 …………….. (1) • VGB = φMS + 2ψB + VSB + Vch(x) - (Qox + QB + Qch(x) )/Cox …… (2) •
VGB = [φMS – Qox/Cox] + [2ψB + VSB] + Vch(x) - (QB + Qch(x) )/Cox …(3)
• VGB = VGS + VSB • VGB = VFB + [2ψB + VSB] + Vch(x) - ( QB + Qch(x) )/Cox • Case 1: VSB = 0, x = 0, Qch(0) = 0; => VGS = VTh0 • VGB = VTh0 = VFB + 2ψB + [2qNAεS(2ψB)]1/2 /Cox ……………. (4) • Case 1a: VSB = 0, Qch(x) > 0; => VGS > VTh0 • VGS - VTh0 - Vch(x) = – Qch(x)/Cox
MOSFET CURRENT •
Case 1b: VSB = 0, Qch(x) > 0 for 0 < x < L; VGS > VTh0
•
Complete Channel • IDS = µCox(W/L)([VGS – VTh0] VDS - 1/2 VDS2) •
Case 1c: • VSB = 0, Qch(x) = 0 for x < L; VGS > VTh0
• Qch(x) = - Cox(VGS - VTh0 - Vch(x)) • At x = L' Qch(L' ) = 0 • Vch(L') = (VGS - VTh0) = VDSAT •
IDS = ½ µCox(W/L)([VGS – VTh0]2
Body Effect Parameter •
Case 2: VSB ≠ 0, x = 0, Qch(0) = 0; => VGS = VTh
•
VGB = VGS + VSB = VFB + [2ψB + VSB] + [2qNAεS(2ψB + VSB)]1/2 /Cox
•
VTh = VFB + [2ψB] + [2qNAεS(2ψB + VSB)]1/2 /Cox ……(5)
•
Δ VTh = [2qNAεS(2ψB + VSB)]1/2 /Cox - [2qNAεS(2ψB)]1/2 /Cox
•
VTh = VFB + [2ψB] + [2qNAεS(2ψB + VSB)]1/2 ……(5)
•
Δ VTh = [2qNAεS(2ψB + VSB)]1/2 - [2qNAεS(2ψB)]1/2
MOSFET CURRENT • Case 2b: VSB ≠ 0, Qch(x) > 0 for 0 < x < L; VGS > VTh • Complete Channel • IDS = Cox(W/L)([VGS – VTh] VDS - 1/2 VDS2) • Case 2c: • VSB ≠ 0, Qch(x) = 0 for x < L; VGS > VTh • Qch(x) = - Cox(VGS - VTh - Vch(x)) • Incomplete Channel • At x = L' Qch(L' ) = 0 • Vch(L') = (VGS - VTh) = VDSAT • IDS = ½ µCox(W/L)([VGS – VTh]2
Small Signal Parameters • In Saturation • IDS = ½ µCox(W/L)([VGS – VTh]2 • ΔIDS = gm ΔVGS + gmb ΔVSB + gds ΔVDS • gm = µCox(W/L) (VGS – VTh) • gmb = µCox(W/L) (VGS – VTh)[∂VTh/∂VSB] •
VTh = VFB + [2ψB] + [2qNAεS(2ψB + VSB)]1/2/Cox ……(5)
• [∂VTh/∂VSB] = ½ [2qNAεS ]1/2/Cox(2ψB + VSB)-1/2 • γ = [2qNAεS ]1/2/Cox •
gmb = ½ gm γ (2ψB + VSB)-1/2
Early Effect • Saturation • IDS = ½ µCox(W/ L') [VGS – VTh]2 • L' = L – ΔL = L ( 1 - ΔL/L) ≈ L ( 1 + ΔL/L)-1 • IDS = ½ µCox(W/ L)[VGS – VTh]2( 1 + ΔL/L) • ΔL/L ≈ λ VDS = VDS/VEA • VEA = Early Voltage => Point on –x axis where IDSAT converges for different V when extrapolated. • IDS = ½ µCox(W/ L)[VGS – VTh]2( 1 + λ VDS) • gds = ∂IDS/∂VDS ≈ IDS / VEA
