Download - ECE 124a/256c MOS Gate Models
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ECE 124a/256cMOS Gate Models
Forrest BrewerDisplays: W. Burleson, K. Bernstein,
P. Gronoski
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Basics (MOS Electrical Model)
Nonlinear model with 3 conduction modes: Linear Mode (Vds < Vgs-VT) and (Vds < Vsat): VF =
Vds Saturation (Vds > Vgs-VT) and (Vds < Vsat): VF = Vgs-
VT Velocity Saturation (Vds > Vsat): VF = Vsat
VF = Min(Vgs-VT, Vsat, Vds )
)1)(2
)((2
dsF
FTgsds VVVVVL
kWI
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Body Effect Threshold is function of back potential
Increases difficulty of turn on for junction reverse bias increase
ox
aSi
i
af
fSBfTT
CNq
nN
qkT
VVV
2
ln
220
0.18 f
N-type
0.4 (V) 0.32
P-type
0.4 (V) -0.42
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Velocity Saturation Carrier Velocity Saturates at about 1.7x107cm/s For short channel (small L) this occurs at Vsat Mobility () is a function of doping and temperature
)/()()/107.1(
2
7
VscmcmLscmVsat
2/3)300/)(300()( TKT
0.18 Vsat
N-type
400 (cm2/Vs)
0.8V
P-type
150 (cm2/Vs)
2.2V
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MOS Capacitors Gate (assume constant) = Si WL/tox Source/Drain
Bottom (Area) CJ mJ SideWall (Perimeter) CJSW mJSW
Equivalent Capacitance (Swing Vlow to Vhigh)
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Transient Capacitor Parasitics
Only capacitors which change potential over the swing are included.
Cgs and Cgd are often modeled as Cg and Cgso, Cgdo. Cgdo models the feed though (input to output) capacitance
For low swing rates, double Cgdo For high swing rates, start the
output swing from the offset output voltage
Cgdo and Cload produce a capacitive voltage divider.
DS
G
B
CGDCGS
CSB CDBCGB
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Static Complementary CMOS
VDD
F(In1,In2,…InN)
In1In2InN
In1In2InN
PUN
PDN
PMOS only
NMOS only
PUN and PDN are logically dual logic networks…
…
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Inverter Threshold vs. N/P Ratio
100
101
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
MV
(V)
Wp
/Wn
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Inverter Gain
0 0.5 1 1.5 2 2.5-18
-16
-14
-12
-10
-8
-6
-4
-2
0
gain
))(2/(1
)(1
)(
)()(
pnnDSATTnM
pn
pDSATpnDSATn
MD
VVVr
VkVkVI
gain
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CMOS Inverter Propagation Delay
VDD
Vout
Vin = VDD
CLIav
tpHL = CL Vswing/2Iav
2)()( finalIinitII dsds
AV
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Approximating Iavg
Prescription from Hodges and Jackson Assume input rise is instantaneous: ignore rise-time effects
Average charging current at endpoints of swing Initial point is usually a supply rail, final point is threshold of next
gate
Ich
Vout
Ifinal (@Vout = Vfinal)
Iinitial (@ Vout = Vinit) ActualCurrent
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Hodges-Jackson Current Averaging
FET’s act as a current source Simple model for full-swing current:
I1 is initial current at start of swing I2 is current at threshold of next stage Iavg is approximated by (I1+I2)/2
Delay eqeffavg
CRCRI
VCt 69.0
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Transient Response
0 0.5 1 1.5 2 2.5
x 10-10
-0.5
0
0.5
1
1.5
2
2.5
3
t (sec)
V out(V
) tpHL tpLH
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Constructing a Complex Gate Logic Dual need not be Series/Parallel Dual In general, many logical dual exist, need to
choose one with best characteristics Use Karnaugh-Map to find good duals
Goal: find 0-cover and 1-cover with best parasitic or layout properties
Maximize connections to power/ground Place critical transistors closest to output node Know the order of arrival of signals! – order the
transitions if possible
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Example: Carry Gate F = (ab+bc+ac)’ Carry ‘c’ is critical Factor c out: (Why c?) F=(ab+c(a+b))’ 0-cover is n-pull up 1-cover is p-pull down
C C’
AB 0 0
AB’ 0 1
A’B’ 1 1
A’B 0 1
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Example: Carry Gate (2) Pull Down is easy Order by maximizing
connections to ground and critical transistors
For pull up – Might guess series parallel graph dual– but would guess wrong
a
b
c
a b
f'
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Example: Carry Gate (3) Series/Parallel Dual 3-series transistors 2 connections to Vdd 7 floating capacitors
a b
c a
b
f'
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Example: Carry Gate (4) Pull Up from 1 cover of
Kmap Get a’b’+a’c’+b’c’ Factor c’ out
3 connections to Vdd 2 series transistors Co-Euler path layout Moral: Use Kmap!
c
a ba
bf'
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Euler Path For CMOS standard cell, and Euler path often helps
to organize the transsistor order so that a faster, more dense cell can be constructed.
Ideally, the p-fet and n-fet sub-circuits can be traversed in identical transistor orders to create a layout without diffusion (thinox) gaps.
Euler Path: Traversal of entire schematic (every transistor) without
traversing any transistor twice. Possible only if 0 or 2 odd nodes in schematics. Node count
is the number of transistors incident on a common point. If 0, any point can be start (will also be end) of path, for 2,
one of the odd nodes is the start and the other is the end.
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Euler Path II Eg. Carry Gate
Path: b-a-c-b-a or a-b-c-a-b or …
Can sometimes also minimize the routing by careful choice of order
b
a
c
a b
f'c
a ba
b
Xb a c b a
XXXXX
X X X X
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Static Logic: Rules of Thumb
1. Step-up (alpha) ratio of 4 produces minimum power-delay product
2. P vs. N (beta) ratio of 2 balances pull-up and pull-down times and noise margins.
3. Approximately 75% of static logic are NAND stacks (limit stack to 3-4, use ordering and tapering for speed)
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More Rules of Thumb
1. Glitches consume approximately 15% of overall chip power.
2. Crossover (short-circuit) current consumes ~ 10% of a static chip’s total power (but is a function of input/output slews, ie sizing)
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Ratio Logic
VDD
VSS
PDNIn1In2In3
F
RLLoad
VDD
VSS
In1In2In3
F
VDD
VSS
PDNIn1In2In3
FVSS
PDN
Resistive DepletionLoad
PMOSLoad
(a) resistive load (b) depletion load NMOS (c) pseudo-NMOS
VT < 0
Goal: to reduce the number of devices over complementary CMOSas a means to reduce parasitics (usually for performance).
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Pseudo NMOSVDD
A B C D
FCL
VOH = VDD (similar to complementary CMOS)
kn VDD VTn– VOLVOL
2
2-------------–
kp
2------ VDD VTp– 2=
VOL VDD VT– 1 1kpkn------–– (assuming that VT VTn VTp )= = =
SMALLER AREA & LOAD BUT STATIC POWER DISSIPATION!!!
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Even Better Noise Immunity/DensityVDD
VSS
PDN1
Out
VDD
VSS
PDN2
Out
AABB
M1 M2
Differential Cascode Voltage Switch Logic (DCVSL)
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DCVSL Example
B
A A
B B B
Out
Out
XOR-NXOR gate
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DCVSL Transient Response
0 0.2 0.4 0.6 0.8 1.0-0.5
0.5
1.5
2.5
Time [ns]
Vol
tage
[V] A B
A B
A,BA,B
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Complementary Pass Gate Logic (CPL)
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Pass-gate Logic issues Limited fan-in Excessive fan-out Noise vulnerability (not restoring) Supply voltage offset/bias vulnerability Decode exclusivity (else short-circuit!) Poor high voltage levels if NMOS-only Body effect
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Pass-Gate Logic Rules of Thumb
Pass-logic may consume half the power of static logic. But be careful of Vt drop resulting in static leakage.
Pass-gate logic is not appropriate when long interconnects separate logic stages or when circuits have high fan-out load (use buffering).
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Dynamic Logic Idea – use the low leakage of FETs to store
charge instead of moving current. Provides higher density, faster operation at the cost of reduced noise immunity and tricky design…
Domino is by far the most common style in CMOS
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Domino logic (single and dual-rail)
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Dynamic Logic Rules of Thumb
Dynamic logic is best for wide OR/NOR structure (e.g. bit-lines), providing 50% delay improvement over static CMOS.
Dynamic logic consumes 2x power due to its phase activity (unconditional pre-charging), not counting clock power.
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Domino Rules of Thumb
Typical domino keepers have W/L = 5-20% of effective width of evaluate tree.
Typical domino output buffers have a beta ratio of ~ 6:1 to push the switch point higher for fast rise-time but reduced noise margin.
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Conventional and Delay-precharge domino
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Advanced Domino Logic forms
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Concerns in Dynamic Logic Charge-sharing Charge-leakage Interconnect coupling Back-gate coupling Supply noise and variation
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Back-gate coupling
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Manchester Carry Chain
P0
Ci,0
P1
G0
P2
G1
P3
G2
P4
G3 G4
VDD
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Sizing the Manchester Carry Chain
R1
C1
R2
C2
R3
C3
R4
C4
R5
C5
R6
C6
Out
M0 M1 M2 M3 M4MC
Discharge Transistor
1 2 3 4 5 6
1 1.5 2.0 2.5 3.0k
5
10
15
20
25
Spe
ed
1 1.5 2.0 2.5 3.0k
0
100
200
300
400A
rea
Speed (normalized by 0.69 RC) Area (in minimum size devices)
npeq
N
i
N
ijji kCCCkRRCRt
,,69.01
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Domino Nor16 (zero-detect)
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Flip-flops/latches/state elements Flip-flops occupy a special place in
conventional digital design Always Dynamic Behavior Allow time coherence across large parts of the
circuit Preserve data across synchronization
boundaries --Inherently asynchrnous design
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Level-sensitive latch pair
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Modified Svensson Latch of 21064
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Tri-state based static latch
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Master-slave (Dynamic) FF
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Sense Amplifier-Based Flip-Flop
Courtesy of IEEE Press, New York. 2000
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Sense Amplifier-Based Flip-Flop
The first stage is unchanged sense amplifierSecond stage is sized to provide maximum switching speed
Driver transistors are large
Keeper transistors are small and disengaged during transitions
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On-chip Memory
Typically largest fraction of chip area Nearly always topologically organized (low
Rent parameter <0.6) Simple wire/area planning rules
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Generic memory block diagram
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SRAM read operation
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SRAM cell sized to avoid read-disturbance
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Realistic layout issues in SRAM cell
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Asymmetric Read/Write Ports
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Multi-porting
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Split Row Decoder
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Column mux and sense-amp
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21264 Integer Unit floorplan
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21264 Integer Register File cells
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21264 L1 Dcache
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21164 L2 Cache