esign and Implementation of VLSI System (EN0160) Prof. Sherief Reda Division of Engineering, Brown University Spring 2007 [sources: Weste/Addison Wesley – Rabaey/Pearson]
Dec 19, 2015
Design and Implementation of VLSI Systems(EN0160)
Prof. Sherief RedaDivision of Engineering, Brown University
Spring 2007
[sources: Weste/Addison Wesley – Rabaey/Pearson]
pn-junction reminder
• Depletion region has associated capacitance
• When the diode is reversed biased (supposedly cutoff), tiny current based on the minority carries still flows
• Transistor has two p-n diodes
n
p
A
B
Al
One-dimensionalrepresentation
fixed ionsdepletion region(almost no mobile carriers)
Gate Capacitance
• Approximate channel as connected to source
• Cgs = oxWL/tox = CoxWL = CpermicronW
• Cpermicron is typically about 2 fF/m
n+ n+
p-type body
W
L
tox
SiO2 gate oxide(good insulator, ox = 3.90)
polysilicongate
Source/Drain diffusion capacitance
• Csb, Cdb
• Undesirable, called parasitic capacitance
• Capacitance depends on area and perimeter– Use small diffusion nodes
– Comparable to Cg
– Varies with process
Bottom
Side wall
Side wallChannel
SourceND
Channel-stop implant NA1
SubstrateNA
W
xj
LS
Transistor resistance
In the linear region
• Not accurate, but at least shows that the resistance is proportional to L/W and decreases with Vgs
• If R/C are for a unit size transistor then a transistor of K unit width has KC capacitance and R/K resistance
• The resistance of a PMOS transistor = 2× resistance of NMOS transistor of the same size
Switch-level RC models
• Use equivalent circuits for MOS transistors– Ideal switch + capacitance and ON resistance– Unit nMOS has resistance R, capacitance C– Unit pMOS has resistance 2R, capacitance C
• Capacitance proportional to width• Resistance inversely proportional to width
kg
s
d
g
s
d
kCkC
kCR/k
kg
s
d
g
s
d
kC
kC
kC
2R/k
Inverter RC delay estimate
• Estimate the delay of a fanout-of-1 inverter
C
CR
2C
2C
R
2
1A
Y
C
2C
C
2C
C
2C
RY
2
1
d = 6RC
Fallacies
1. Increasing Vds does not increase the saturation current
2. The transistor does not conduct in cutoff 3. The saturation current increases
quadratically for linear increases in Vgs
4. Transistor temperature can be ignored
Channel length modulation
• The reverse-bias p-n junction between drain and body forms a depletion region with a width Ld that increases with Vdb
• Increasing Vds increases depletion width decreases channel length increases current
Channel length modulation factor (empirical factor)
n+
p
GateSource Drain
bulk Si
n+
VDDGND VDD
GND
LLeff
Depletion RegionWidth: Ld
Leakage current
n+ n+
p-type body
W
L
tox
polysilicon
gate
Subthreshold conduction
Tunnel current
Junction leakage
Subthreshold leakage is the biggest source in modern transistors 180nm process
0e 1 egs t ds
T T
V V V
nv vds dsI I
2 1.80 eds TI v n = 1.4-15
Velocity saturation
(V/µm)c = 1.5
n
(m
/s)
sat = 105
Constant mobility (slope = µ)
Constant velocity
At high electric field, drift velocity rolls of due to carrier scattering
Empirically:
With channel length modulation