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 2f).
 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(2qSiNA/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