Digital Integrated
Circuits
A Design Perspective
Jan M. Rabaey
Anantha Chandrakasan
Borivoje Nikolic
The Inverter
© Digital Integrated Circuits2nd
Inverter
DIGITAL GATES
Fundamental Parameters
Functionality
 Reliability, Robustness
 Area
 Performance

 DC Characteristics
 Speed (delay)
 Power Consumption
© Digital Integrated Circuits2nd
Inverter
Noise in Digital Integrated Circuits
v(t)
VDD
i(t)
(a) Inductive coupling
(b) Capacitive coupling
(c) Power and ground
noise
© Digital Integrated Circuits2nd
Inverter
The Ideal Gate
Vout
Ri = 
Ro = 0
g= 
Vin
© Digital Integrated Circuits2nd
Inverter
CMOS Inverter
First-Order DC Analysis
V DD
V DD
Rp
V out
V out
VOL = 0
VOH = VDD
VM = f(Rn, Rp)
Rn
V in = V DD
© Digital Integrated Circuits2nd
V in = 0
Inverter
Mapping between analog and digital signals
"1"
V
OH
V
IH
V(y)
V
Slope = -1
OH
Undefined
Region
"0"
V
IL
V
OL
© Digital Integrated Circuits2nd
Slope = -1
VOL
V
IL
V
IH
V(x)
Inverter
Definition of Noise Margins
"1"
V
OH
NMH
Noise Margin High
Noise Margin Low
NML
V
IH
Undefined
Region
V
IL
V
OL
"0"
Gate Output
© Digital Integrated Circuits2nd
Gate Input
Inverter
The Regenerative Property
...
v1
v0
v2
v3
v5
v4
v6
(a) A chain of inverters.
v1, v3, ...
v1, v3, ...
finv(v)
f(v)
finv(v)
v0, v2, ...
(b) Regenerative gate
© Digital Integrated Circuits2nd
f(v)
v0, v2, ...
(c) Non-regenerative gate
Inverter
Fan-in and Fan-out
(a) Fan-out N
M
N
© Digital Integrated Circuits2nd
(b) Fan-in M
Inverter
The CMOS Inverter: A First
Glance
V DD
V in
V out
CL
© Digital Integrated Circuits2nd
Inverter
CMOS Inverter
N Well
VDD
VDD
PMOS
2l
Contacts
PMOS
In
Out
In
Out
Metal 1
Polysilicon
NMOS
NMOS
GND
© Digital Integrated Circuits2nd
Inverter
VTC of Real Inverter
5.0
Vout (V)
4.0
NML
3.0
2.0
VM
NMH
1.0
0.0
1.0
© Digital Integrated Circuits2nd
2.0
3.0
Vin (V)
4.0
5.0
Inverter
CMOS Inverter: Transient Response
V DD
V DD
tpHL = f(R on .C L )
= 0.69 R on C L
Rp
V out
V out
CL
CL
Rn
V in = 0
V in = V DD
(a) Low-to-high
(b) High-to-low
© Digital Integrated Circuits2nd
Inverter
Delay Definitions
Vin
50%
t
Vout
t
pHL
t
pLH
90%
50%
10%
tf
© Digital Integrated Circuits2nd
t
tr
Inverter
Ring Oscillator
v1
v0
v0
v2
v1
v3
v4
v5
v5
T = 2  tp N
© Digital Integrated Circuits2nd
Inverter
Power Dissipation
© Digital Integrated Circuits2nd
Inverter
Voltage
Transfer
Characteristic
© Digital Integrated Circuits2nd
Inverter
CMOS Inverter
N Well
VDD
VDD
PMOS
2l
Contacts
PMOS
In
Out
In
Out
Metal 1
Polysilicon
NMOS
NMOS
GND
© Digital Integrated Circuits2nd
Inverter
DC Operation:
Voltage Transfer Characteristic
V(y)
V
dVo/dVi =-1
OH
f
V(x)
V(y)
V(y)=V(x)
NML
V
LT
Switching Logic Threshold
NMH
V OL
V OL
VIL VIH
V
OH
V(x)
Nominal Voltage Levels
© Digital Integrated Circuits2nd
Inverter
CMOS Inverter Load Characteristics
I n,p
V in = 0
V in = 5
NMOS
PMOS
V in = 4
V in = 1
V in = 4
V in = 3
V in = 2
V in = 3
V in = 4
V in = 3
V in = 2
Vin = 1
V in = 2
V in = 0
V in = 5
Vout
© Digital Integrated Circuits2nd
Inverter
CMOS Inverter VTC
NMOS off
PMOS lin
NMOS sat
PMOS lin
4
PMOS: linear if Vsg –Vtp > Vsd
•Vo > Vin +Vtp
Vou t
5
Vin < Vtn -NMOS Off
Vin > Vdd – Vtp -PMOS Off
3
2
VOH: PMOS(lin) & NMOS(off)
VOL: PMOS(off) & NMOS(lin)
VIH: PMOS(sat) & NMOS(lin)
VIL: PMOS(lin) & NMOS(sat)
VLT: PMOS(sat) & NMOS(sat)
NMOS sat
PMOS sat
NMOS lin
PMOS sat
1
NMOS: Linear if Vgs-Vtn > Vds
•Vo < Vin –Vtn
1
© Digital Integrated Circuits2nd
2
3
4
NMOS lin
PMOS off
5
Vin
Inverter
CMOS Inverter VTC
VOH: PMOS(lin) & NMOS(off) = Vdd
VOL: PMOS(off) & NMOS(lin) = Gnd
VIH: PMOS(sat) & NMOS(lin): Solve:
p
2
(Vdd  VIH  | Vtp |)2 
n
2
 p   p Cox
Wp
Lp
&  n   n Cox
Wn
Ln
[2(VIH  Vtn )Vo  Vo ]
2
p
p
dV0
 1  VIH (1  )  2V0  Vtn 
(Vdd  | Vtp |)
dVin
n
n
VIL: PMOS(lin) & NMOS(sat): Solve:
n
(VIL  Vtn ) 
2
p
[2(Vdd  VIL  | Vtp |)(Vdd  Vo )  (Vdd  Vo ) 2 ]
2
2
dV0


 1  VIL (1  n )  2V0  n Vtn  Vdd  | Vtp |
dVin
p
p
© Digital Integrated Circuits2nd
Inverter
CMOS Inverter VTC
VLT: PMOS(sat) & NMOS(sat):
p
2
(Vdd  VLT  | Vtp |) 2 
VLT 
Vtn 
n
2
(VLT  Vtn ) 2 
p
 n (Vdd  | Vtp |)
p
1
n
If Vtn = Vtp & p = n  VLT = Vdd/2: Gives a symmetric Inverter!
© Digital Integrated Circuits2nd
Inverter
Simulated VTC
Vout (V)
4.0
2.0
0.0
0.0
1.0
2.0
3.0
4.0
5.0
Vin (V)
© Digital Integrated Circuits2nd
Inverter
Gate Logic Switching Threshold
4.0
V LT
3.0
2.0
Vtn 
p
1.00.1
 n (Vdd  | Vtp |)
VLT 
p
1
n
© Digital Integrated Circuits2nd
0.3
1.0
p /n
3.2
10.0
Inverter
Inverter Gain
0
-2
-4
gain
-6
-8
-10
-12
-14
-16
-18
0
0.5
1.5
1
2
2.5
V (V)
© Digital Integrated
in
Circuits2nd
Inverter
Gain as a function of VDD
2.5
0.2
2
0.15
Vout(V)
Vout (V)
1.5
0.1
1
0.05
0.5
Gain=-1
0
0
0.5
1.5
1
V (V)
in
© Digital Integrated Circuits2nd
2
2.5
0
0
0.05
0.1
V (V)
0.15
0.2
in
Inverter
Impact of Process Variations
2.5
2
Good PMOS
Bad NMOS
Vout(V)
1.5
Nominal
1
Good NMOS
Bad PMOS
0.5
0
0
0.5
1
1.5
2
2.5
Vin (V)
© Digital Integrated Circuits2nd
Inverter
Propagation Delay
© Digital Integrated Circuits2nd
Inverter
Delay Definitions
Vin
50%
t
Vout
t
pHL
t
pLH
90%
50%
10%
tf
© Digital Integrated Circuits2nd
t
tr
Inverter
CMOS Inverter: Transient Response
VDD
tpHL = f(R on.CL)
= 0.69 RonCL
Vout
ln(0.5)
Vout
CL
Ron
1
VDD
0.5
0.36
Vin = V DD
RonCL
© Digital Integrated Circuits2nd
t
Inverter
CMOS Inverter Propagation Delay
V DD
tpHL = C
L
V swing /2
Iav
V out
Iav
CL
I (Vo  Vdd / 2)  I (Vo  0)
I av 
2
t pHL 
CL (Vdd / 2)
(  n / 2)(Vdd  Vtn ) 2
~
V in = V
DD
© Digital Integrated Circuits2nd
CL
k n V DD
Inverter
CMOS Inverter Propagation Delay
V DD
Vo
VH
NMOS(sat)
Vdd
Vdd-Vtn
NMOS(lin)
V out
VL
CL
to t1
t2
Time
VL Vdd / 2
t pHL  CL
V in = V
DD
© Digital Integrated Circuits2nd

VH
dVo
I n (V0 )
Inverter
CMOS Inverter Propagation Delay
VL Vdd / 2
t pHL  CL

VH
dVo
 CL
I n (V0 )
VOH Vtn

VOH
n
2
t pHL 
CL
 n (VOH
dVo
(VOH  Vtn )
 CL
2
Vdd / 2

VOH Vtn
n
2
dVo
[2(VOH  Vtn )Vo  Vo ]
2
 2Vtn
 4(VOH  Vtn )  
 ln 
 1 

 Vtn )  (VOH  Vtn )
(
V

V
)
OL
 OH
 
Similarly:
t pLH
 2 | Vtp |
 4(VOH  | Vtp |)  
CL

 ln 
 1 

 p (VOH  | Vtp |)  (VOH  | Vtp |)
 (VOH  VOL )
 
© Digital Integrated Circuits2nd
Inverter
CMOS Inverter Rise & Fall Time
Similarly, Fall Time:
t HL
 2Vtn
 2(VH  Vtn )  
CL

 ln 
 1 

 n (VH  Vtn )  (VH  Vtn )
VL

 
Similarly, Rise Time:
t LH
 2 | Vtp |
 2(VH  | Vtp |)  
CL

 ln 
 1 

 p (VH  | Vtp |)  (VH  | Vtp |)
VL

 
© Digital Integrated Circuits2nd
Inverter
Computing the Capacitances
VDD
VDD
M2
Vin
Cg4
Cdb2
Cgd12
M4
Vout
Cdb1
Cw
M1
Vout2
Cg3
M3
Interconnect
Fanout
Simplified
Model
© Digital Integrated Circuits2nd
Vin
Vout
CL
Inverter
The Miller Effect
Cgd1
V
Vout
Vout
V
Vin
M1
V
2Cgd1
M1
V
Vin
“A capacitor experiencing identical but opposite voltage swings
at both its terminals can be replaced by a capacitor to ground,
whose value is two times the original value.”
© Digital Integrated Circuits2nd
Inverter
Computing the Capacitances
© Digital Integrated Circuits2nd
Inverter
Impact of Rise Time on Delay
0.35
tpHL(nsec)
0.3
0.25
0.2
0.15
0
© Digital Integrated Circuits2nd
0.2
0.6
0.4
trise (nsec)
0.8
1
Inverter
Delay as a function of VDD
5.5
5
tp(normalized)
4.5
4
3.5
3
2.5
2
1.5
1
0.8
1
1.2
1.4
1.6
V
1.8
2
2.2
2.4
(V)
DD
© Digital Integrated Circuits2nd
Inverter
NMOS/PMOS ratio
-11
5
x 10
4.5
tpHL
tpLH
 = Wp/Wn
tp(sec)
tp
4
3.5
3
1
1.5
2
2.5
3
3.5
4
4.5
5

© Digital Integrated Circuits2nd
Inverter
Device Sizing
-11
3.8
x 10
(for fixed load)
3.6
3.4
tp(sec)
3.2
3
Self-loading effect:
Intrinsic capacitances
dominate
2.8
2.6
2.4
2.2
2
2
4
6
© Digital Integrated Circuits2nd
8
S
10
12
14
Inverter
Design for Performance
 Keep capacitances
small
 Increase transistor sizes
 watch out for self-loading!
 Increase
VDD (????)
© Digital Integrated Circuits2nd
Inverter
Impact of Rise Time on Delay
0.35
tpHL(nsec)
0.3
0.25
0.2
0.15
0
© Digital Integrated Circuits2nd
0.2
0.4
0.6
trise (nsec)
0.8
1
Inverter
Inverter Sizing
© Digital Integrated Circuits2nd
Inverter
Inverter Chain
In
Out
CL
If CL is given:
- How many stages are needed to minimize the delay?
- How to size the inverters?
May need some additional constraints.
© Digital Integrated Circuits2nd
Inverter
Inverter Delay
• Minimum length devices, L=0.7m
• Assume that for WP = 2WN =2W
• same pull-up and pull-down currents
• approx. equal resistances RN = RP
• approx. equal rise tpLH and fall tpHL delays
• Analyze as an RC network
 WP 

RP  Runit 
 Wunit 
Delay (D):
1
 WN 

 Runit 
 Wunit 
tpHL = (ln 2) RNCL
Load for the next stage:
© Digital Integrated Circuits2nd
2W
W
1
 RN  RW
tpLH = (ln 2) RPCL
W
C gin  3
Cunit
Wunit
Inverter
Inverter with Load
Delay
RW
CL
RW
Load (CL)
tp = k RWCL
k is a constant, equal to 0.69
Assumptions: no load -> zero delay
Wunit = 1
© Digital Integrated Circuits2nd
Inverter
Inverter with Load
CP = 2Cunit
Delay
2W
W
Cint
CL
CN = Cunit
Load
Delay = kRW(Cint + CL) = kRWCint + kRWCL = kRW Cint(1+ CL /Cint)
= Delay (Internal) + Delay (Load)
© Digital Integrated Circuits2nd
Inverter
Delay Formula
Delay ~ RW Cint  C L 
t p  kRW Cint 1  C L / Cint   t p 0 1  f /  
Cint = Cgin with   1
f = CL/Cgin - effective fanout
R = Runit/W ; Cint =WCunit
tp0 = 0.69RunitCunit
© Digital Integrated Circuits2nd
Inverter
Apply to Inverter Chain
In
Out
1
2
N
CL
tp = tp1 + tp2 + …+ tpN
 C gin, j 1 

t pj ~ RunitCunit 1 
 C

gin
,
j


N
N 
C gin, j 1 
, C gin, N 1  C L
t p   t p , j  t p 0  1 
 C

j 1
i 1 
gin, j 
© Digital Integrated Circuits2nd
Inverter
Optimal Tapering for Given N
Delay equation has N - 1 unknowns, Cgin,2 – Cgin,N
Minimize the delay, find N - 1 partial derivatives
Result: Cgin,j+1/Cgin,j = Cgin,j/Cgin,j-1
Size of each stage is the geometric mean of two neighbors
C gin, j  C gin, j 1C gin, j 1
- each stage has the same effective fanout (Cout/Cin)
- each stage has the same delay
© Digital Integrated Circuits2nd
Inverter
Optimum Delay and Number of Stages
When each stage is sized by f and has same eff. fanout f:
f N  F  CL / Cgin,1
Effective fanout of each stage:
f NF
Minimum path delay

t p  Nt p 0 1  N F / 
© Digital Integrated Circuits2nd

Inverter
Example
In
C1
Out
1
f
f2
C L= 8 C 1
CL/C1 has to be evenly distributed across N = 3 stages:
f 38 2
© Digital Integrated Circuits2nd
Inverter
Optimum Number of Stages
For a given load, CL and given input capacitance Cin
Find optimal sizing f
CL  F  Cin  f N Cin with N 
ln F
ln f
t p 0 ln F  f


t p  Nt p 0 F /   1 

  ln f ln f
t p t p 0 ln F ln f  1   f


0
2
f

ln f

1/ N
For  = 0, f = e, N = lnF
© Digital Integrated Circuits2nd




f  exp 1   f 
Inverter
Optimum Effective Fanout f
Optimum f for given process defined by 
f  exp 1   f 
fopt = 3.6
for =1
© Digital Integrated Circuits2nd
Inverter
Impact of Self-Loading on tp
No Self-Loading, =0
With Self-Loading =1
u/ln(u)
60.0
40.0
x=10,000
x=1000
20.0
x=100
x=10
0.0
1.0
3.0
5.0
7.0
u
© Digital Integrated Circuits2nd
Inverter
Normalized delay function of F

t p  Nt p 0 1  N F / 
© Digital Integrated Circuits2nd

Inverter
Buffer Design
1
f
tp
1
64
65
2
8
18
64
3
4
15
64
4
2.8
15.3
64
1
8
1
4
16
2.8
8
1
N
64
© Digital Integrated Circuits2nd
22.6
Inverter
Power
Dissipation
© Digital Integrated Circuits2nd
Inverter
Where Does Power Go in CMOS?
• Dynamic Power Consumption
Charging and Discharging Capacitors
• Short Circuit Currents
Short Circuit Path between Supply Rails during Switching
• Leakage
Leaking diodes and transistors
© Digital Integrated Circuits2nd
Inverter
Dynamic Power Dissipation
Vdd
Vin
Vout
CL
Energy/transition = C
L
* V dd2
Power = Energy/transition * f = C L * V dd2 * f
Not a function of transistor sizes!
Need to reduce C L , V dd, and f to reduce power.
© Digital Integrated Circuits2nd
Inverter
Modification for Circuits with Reduced Swing
Vdd
Vdd
Vdd -Vt
CL
E 0  1 = CL  Vdd   Vdd – Vt 
Can exploit reduced sw ing to low er power
(e.g., reduced bit-line swing in memory)
© Digital Integrated Circuits2nd
Inverter
Node Transition Activity and Power
Consider switching a CMOS gate for N clock cycles
E
= C  V 2  n N 
N
L
dd
EN : the energ y consumed for N clock cycles
n(N ): the number o f 0->1 transition in N clock cycles
EN
2
n N 
P
= lim --------  f
=  lim ------------   C  V
 f clk
a vg N
clk
dd


N
N
N

L
0
P
av g
© Digital Integrated Circuits2nd
1
=
n N 
lim -----------N N
= 
C
V 2 f
0  1  L  dd  clk
Inverter
Short Circuit Currents
Vd d
Vin
Vout
CL
IVDD (mA)
0.15
0.10
0.05
0.0
© Digital Integrated Circuits2nd
1.0
2.0
3.0
Vin (V)
4.0
5.0
Inverter
How to keep Short-Circuit Currents Low?
Short circuit current goes to zero if tfall >> trise,
but can’t do this for cascade logic, so ...
© Digital Integrated Circuits2nd
Inverter
Minimizing Short-Circuit Power
8
7
6
Vdd =3.3
Pnorm
5
4
Vdd =2.5
3
2
1
Vdd =1.5
0
0
1
2
3
4
5
t /t
sin sout
© Digital Integrated Circuits2nd
Inverter
Leakage
Vd d
Vout
Drain Junction
Leakage
Sub-Threshold
Current
Sub-threshold current one of most compelling issues
Sub-Threshold
Current Dominant Factor
in low-energy
circuit design!
© Digital Integrated Circuits2nd
Inverter
Reverse-Biased Diode Leakage
GATE
p+
p+
N
Reverse Leakage Current
+
V
- dd
IDL = JS  A
2
JS = JS
1-5pA/
for aat1.2
m CCMOS
technology
= 10-100
pA/m2
25deg
for 0.25m
CMOS
m
JS doubles for every 9 deg C!
Js double with every 9oC increase in temperature
© Digital Integrated Circuits2nd
Inverter
Subthreshold Leakage Component
© Digital Integrated Circuits2nd
Inverter
Static Power Consumption
Vd d
Istat
Vout
Vin =5V
CL
Pstat = P(In=1).Vdd . Istat
Wasted•energy
… over dynamic consumption
Dominates
Should be avoided in almost all cases,
• Not a function of switching frequency
but could
help reducing energy in others (e.g. sense amps)
© Digital Integrated Circuits2nd
Inverter
Principles for Power Reduction
 Prime
choice: Reduce voltage!
 Recent years have seen an acceleration in
supply voltage reduction
 Design at very low voltages still open question
(0.6 … 0.9 V by 2010!)
 Reduce
switching activity
 Reduce physical capacitance
 Device Sizing: for F=20
– fopt(energy)=3.53, fopt(performance)=4.47
© Digital Integrated Circuits2nd
Inverter
Impact of
Technology
Scaling
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Goals of Technology Scaling
 Make
things cheaper:
 Want to sell more functions (transistors) per
chip for the same money
 Build same products cheaper, sell the same
part for less money
 Price of a transistor has to be reduced
 But
also want to be faster, smaller, lower
power
© Digital Integrated Circuits2nd
Inverter
Technology Scaling

Goals of scaling the dimensions by 30%:
 Reduce gate delay by 30% (increase operating
frequency by 43%)
 Double transistor density
 Reduce energy per transition by 65% (50% power
savings @ 43% increase in frequency
Die size used to increase by 14% per generation
 Technology generation spans 2-3 years

© Digital Integrated Circuits2nd
Inverter
Technology Evolution (2000 data)
International Technology Roadmap for Semiconductors
Year of Introduction
1999
Technology node
[nm]
180
Supply [V]
1.5-1.8
Wiring levels
2000
2001
2004
2008
2011
2014
130
90
60
40
30
1.5-1.8
1.2-1.5
0.9-1.2
0.6-0.9
0.5-0.6
0.3-0.6
6-7
6-7
7
8
9
9-10
10
Max frequency
[GHz],Local-Global
1.2
1.6-1.4
2.1-1.6
3.5-2
7.1-2.5
11-3
14.9
-3.6
Max P power [W]
90
106
130
160
171
177
186
Bat. power [W]
1.4
1.7
2.0
2.4
2.1
2.3
2.5
Node years: 2007/65nm, 2010/45nm, 2013/33nm, 2016/23nm
© Digital Integrated Circuits2nd
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ITRS Technology Roadmap
Acceleration Continues
© Digital Integrated Circuits2nd
Inverter
Technology Scaling (1)
Minimum Feature Size (micron)
10
10
10
10
2
1
0
-1
-2
10
1960
1970
1980
1990
2000
2010
Year
Minimum Feature Size
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Inverter
Technology Scaling (2)
Number of components per chip
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Technology Scaling (3)
tp decreases by 13%/year
50% every 5 years!
Propagation Delay
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Technology Scaling (4)
/
4
x
3
1
0.1
0.01
80
MPU
DSP
85
90
Year
(a) Power dissipation vs. year.
95
1000

3
10
ars
e
y
0.7

100

Power Dissipation (W)
100
rs
Power Density (mW/mm2 )
ea
x 1.4 / 3 y
10
1
1
Scaling Factor 
（normalized by 4 m design rule ）
(b) Power density vs. scaling factor.
From Kuroda
© Digital Integrated Circuits2nd
Inverter
10
Technology Scaling Models
• Full Scaling (Constant Electrical Field)
ideal model — dimensions and voltage scale
together by the same factor S
• Fixed Voltage Scaling
most common model until recently —
only dimensions scale, voltages remain constant
• General Scaling
most realistic for todays situation —
voltages and dimensions scale with different factors
© Digital Integrated Circuits2nd
Inverter
Scaling Relationships for Long Channel Devices
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Transistor Scaling
(velocity-saturated devices)
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Processor Scaling
P.Gelsinger: Processors for the New Millenium, ISSCC 2001
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Processor Power
P. Gelsinger: Processors for the New Millenium, ISSCC 2001
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Processor Performance
P. Gelsinger: Processors for the New Millenium, ISSCC 2001
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2010 Outlook

Performance 2X/16 months
 1 TIP (terra instructions/s)
 30 GHz clock

Size
 No of transistors: 2 Billion
 Die: 40*40 mm

Power
 10kW!!
 Leakage: 1/3 active Power
P.Gelsinger: Processors for the New Millenium, ISSCC 2001
© Digital Integrated Circuits2nd
Inverter
Some interesting questions
 What
will cause this model to break?
 When will it break?
 Will the model gradually slow down?
 Power and power density
 Leakage
 Process Variation
© Digital Integrated Circuits2nd
Inverter