Transistors and Layout 2
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Transcript Transistors and Layout 2
Topics
Derivation of transistor characteristics.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
MOSFET gate as capacitor
Basic structure of gate is parallel-plate
capacitor:
gate
+
Vg
SiO2
xox
-
substrate
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Parallel plate capacitance
Formula for parallel plate capacitance:
Cox = ox / xox
Permittivity of silicon:
ox = 3.46 x 10-13 F/cm2
Gate capacitance helps determine charge in
channel which forms inversion region.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Threshold voltage
Components of threshold voltage Vt:
Vfb = flatband voltage; depends on
difference in work function between gate
and substrate and on fixed surface charge.
s = surface potential (about 2f).
Voltage on paralell plate capacitor.
Additional ion implantation.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Body effect
Reorganize threshold voltage equation:
Vt = Vt0 + Vt
Threshold voltage is a function of
source/substrate voltage Vsb.
Body effect is the coefficienct for the Vsb
dependence factor.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Example: threshold voltage of a
transistor
Vt0 = Vfb + s + Qb/Cox + VII
= -0.83 V + 0.58 V + (1.4E-8/8.6E-7) +
0.93 V
= 0.7 V
Body effect n = sqrt(2qSiNA/Cox) = 0.1
Vt = n[sqrt(s + Vsb) - sqrt(Vs)]
= 0.05 V
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
More device parameters
Process transconductance k’ = Cox.
Device transconductance = k’W/L.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Channel length modulation
length parameter
describes small dependence of drain
corrent on Vds in saturation.
Factor is measured empirically.
New drain current equation:
– Id = 0.5k’ (W/L)(Vgs - Vt) 2(l - Vds)
Equation has a discontinuity between linear
and saturation regions---small enough to be
ignored.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Gate voltage and the channel
gate
source
current
drain
Vds < Vgs - Vt
Id
gate
source
current
drain
Vds = Vgs - Vt
drain
Vds > Vgs - Vt
Id
gate
source
Id
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Leakage and subthreshold current
A variety of leakage currents draw current
away from the main logic path.
The subthreshold current is one particularly
important type of leakage current.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Types of leakage current.
Weak inversion current (a.k.a. subthreshold
current).
Reverse-biased pn junctions.
Drain-induced barrier lowering.
Gate-induced drain leakage;
Punchthrough currents.
Gate oxide tunneling.
Hot carriers.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Subthreshold current
Subthreshold current:
– Isub = ke[(Vgs - Vt)/(S/ln 10)][1-e-qVds/kT]
Subthreshold slope S characterizes weak
inversion current.
Subthreshold current is a function of Vt.
– Can adjust Vt by changing the substrate bias to
control leakage.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Thermal effects
Vicious cycle:
– Leakage current causes heating.
– Heating increases leakage current.
Thermal runaway: chip overheats due to
leakage.
Subthreshold leakage current is most
important temperature-dependent current.
– 8x-12x per 100°C.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Circuit simulation
Circuit simulators like Spice numerically
solve device models and Kirchoff’s laws to
determine time-domain circuit behavior.
Numerical solution allows more
sophisticated models, non-functional (tabledriven) models, etc.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR
Some (by no means all) Spice
model parameters
L, W: transistor length width.
KP: transconductance.
GAMMA: body bias factor.
AS, AD: source/drain areas.
CJSW: zero-bias sidewall capacitance.
CGBO: zero-bias gate/bulk overlap
capacitance.
Modern VLSI Design 4e: Chapter 2
Copyright 2009 Prentice Hall PTR