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Digital Integrated
Circuits
A Design Perspective
The Inverter
July 30, 2002
© 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
Two Inverters
Share power and ground
Abut cells
VDD
Connect in Metal
© Digital Integrated Circuits2nd
Inverter
CMOS Inverter: Transient Response
V DD
V DD
tpHL = f(R on.CL)
Rp
= 0.69 RonCL
V out
V out
CL
CL
Rn
V in 5 0
V in 5 V DD
(a) Low-to-high
(b) High-to-low
© Digital Integrated Circuits2nd
Inverter
Voltage Transfer
Characteristic
© Digital Integrated Circuits2nd
Inverter
CMOS Inverter Load Characteristics
ID n
PMOS
Vin = 0
Vin = 2.5
Vin = 0.5
Vin = 2
Vin = 1
Vin = 1.5
Vin = 1.5
Vin = 1
Vin = 1.5
Vin = 2
Vin = 2.5
NMOS
Vin = 1
Vin = 0.5
Vin = 0
Vout
© Digital Integrated Circuits2nd
Inverter
CMOS Inverter VTC
NMOS off
PMOS res
2.5
Vout
2
NMOS s at
PMOS res
1
1.5
NMOS sat
PMOS sat
0.5
NMOS res
PMOS sat
0.5
© Digital Integrated Circuits2nd
1
1.5
2
NMOS res
PMOS off
2.5
Vin
Inverter
Switching Threshold as a function
of Transistor Ratio
1.8
1.7
1.6
1.5
M
V (V)
1.4
1.3
1.2
1.1
1
0.9
0.8
10
0
10
W /W
© Digital Integrated
Circuits2nd
p
n
1
Inverter
Determining VIH and VIL
Vout
V OH
VM
V in
V OL
V IL
V IH
A simplified approach
© Digital Integrated Circuits2nd
Inverter
Gain as a function of VDD
0
2.5
-2
2
-4
-6
gain
Vout(V)
1.5
-8
-10
1
-12
-14
0.5
-16
0
0
-18
0.5
1.5
1
V (V)
in
© Digital Integrated Circuits2nd
2
2.5
0
0.5
1
1.5
2
2.5
V (V)
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
CMOS Inverter Propagation Delay
VDD
tpHL = f(Ron.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
Transient Response
3
2.5
?
Vout(V)
2
tp = 0.69 CL (Reqn+Reqp)/2
1.5
1
tpHL
tpLH
0.5
0
-0.5
0
0.5
1
1.5
t (sec)
© Digital Integrated Circuits2nd
2
2.5
-10
x 10
Inverter
Design for Performance
 Keep
capacitances small: Cload, Cgate, Cdiff
 Increase transistor sizes: W/L
 watch out for self-loading!
 Increase
© Digital Integrated Circuits2nd
VDD (????)
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
Device Sizing
-11
3.8
x 10
(for fixed load)
3.6
3.4
tp(sec)
3.2
3
2.8
Self-loading effect:
Intrinsic capacitances
dominate
2.6
2.4
2.2
2
2
4
6
© Digital Integrated Circuits2nd
8
S
10
12
14
Inverter
NMOS/PMOS ratio
-11
5
x 10
tpHL
tpLH
tp(sec)
4.5
b = Wp/Wn
tp
4
3.5
3
1
1.5
2
2.5
3
3.5
4
4.5
5
b
© Digital Integrated Circuits2nd
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=0.25mm
• 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 
1
 WN 

 Runit 
 Wunit 
Delay (D): 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
© Digital Integrated Circuits2nd
Wunit = 1
Inverter
Inverter with Load
CP = 2Cunit
Delay
2W
W
CN = Cunit
Cint
CL
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
CL= 8 C1
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
ln F
N
CL  F  Cin  f Cin with N 
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
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 = CL * Vdd2
Power = Energy/transition * f = CL * Vdd2 * f
Not a function of transistor sizes!
Need to reduce CL, Vdd, and f to reduce power.
© Digital Integrated Circuits2nd
Inverter
Node Transition Activity and Power
Consider switching a CMOS gate for N clock cycles
E N = CL  V dd2  n N 
EN : the energy consumed for N clock cycles
n(N ): the number of 0->1 transition in N clock cycles
EN
2
n N 
P avg = lim --------  fclk =  lim ----------- C  Vdd  f clk
N   N 
N N
L
0  1 =
n N 
lim -----------N N
P avg = 0 1  C  Vdd 2  f clk

L
© Digital Integrated Circuits2nd
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
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
Leakage Currents
Vd d
Vout
Drain Junction
Leakage
Sub-Threshold
Current
Sub-threshold current one of most compelling issues
Current
Dominant Factor
in Sub-Threshold
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 a 1.2
technology
mmpA/mm2
mm
= 10-100
at 25
degCMOS
C for 0.25mm
CMOS
JS doubles for every 9o deg C!
Js double with every 9 C increase in temperature
© Digital Integrated Circuits2nd
Inverter
Total Power Consumption
Ptot
= Pdyn + Pdp + Pstat
2
= (CLVDD + VDD Ipeak ts)f0-1 + VDD Ileak
Ipeak = Maximum short circuit current
Ts
= 0-100% transition time of Ipeak
Ileak = The current that flows between the supply rails in
the absence of switching activity.
© 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
© Digital Integrated Circuits2nd
Inverter
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]
2000
2001
2004
2008
2011
2014
130
90
60
40
30
0.6-0.9
0.5-0.6
0.3-0.6
8
9
9-10
10
3.5-2
7.1-2.5
11-3
14.9
-3.6
1.5-1.8 1.5-1.8 1.2-1.5 0.9-1.2
Wiring levels
6-7
6-7
7
Max frequency
[GHz],Local-Global
1.2
Max mP 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
1.6-1.4 2.1-1.6
Node years: 2007/65nm, 2010/45nm, 2013/33nm, 2016/23nm
© Digital Integrated Circuits2nd
Inverter
ITRS Technology Roadmap
© Digital Integrated Circuits2nd
Inverter
Terminology


ITRS: International Technology Roadmap for
Semiconductors. It is devised and intended for
technology assessment only and is without regard to
any commercial considerations pertaining to
individual products or equipment
DRAM Half-pitch: The common measure of the
technology generation of a chip. It is half the distance
between cells in a dynamic RAM memory chip. For
example, in 2002, the DRAM half pitch has been
reduced to 130 nm (.13 micron).
© Digital Integrated Circuits2nd
Inverter
Half Pitch
© Digital Integrated Circuits2nd
Inverter
Technology Scaling (1)
Minimum Feature Size (micron)
10
10
10
10
2
tp decreases by 13%/year
50% every 5 years!
1
0
-1
-2
10
1960
1970
1980
1990
2000
2010
Year
Minimum Feature Size
© Digital Integrated Circuits2nd
Propagation Delay
Inverter
Technology Scaling (2)
Number of components per chip
© Digital Integrated Circuits2nd
Inverter
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
© Digital Integrated Circuits2nd
Inverter
Transistor Scaling
(velocity-saturated devices)
© Digital Integrated Circuits2nd
Inverter
mProcessor Scaling
P.Gelsinger: mProcessors for the New Millenium, ISSCC 2001
© Digital Integrated Circuits2nd
Inverter
mProcessor Power
P.Gelsinger: mProcessors for the New Millenium, ISSCC 2001
© Digital Integrated Circuits2nd
Inverter
mProcessor Performance
P.Gelsinger: mProcessors for the New Millenium, ISSCC 2001
© Digital Integrated Circuits2nd
Inverter
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: mProcessors 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