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The Physical Structure (NMOS)
Field Oxide
SiO2
Gate oxide
Field Oxide n+ n+
Al Al SiO2 SiO2
Polysilicon Gate
channel
L
P Substrate
D S
L
W
(D) (S)
Metal
n+ n+
(G)
Poly
contact
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Transistor Resistance
:
Two Components:
Drain/ Sources Resistance: RD(S) = Rsh x no. of squares+ contact resistance.
Channel Resistance:
Depends on the region of operation:
L
W
(D) (S) n+ n+
(G)
RS Rch RD
Linear
RCH2
K'W
L----- V
GSV
T– 2
----------------------------------------------------= Saturation
RCH1
K'W
L----- V
GSV
T– VDS–
---------------------------------------------------------------- '=
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Transistor Geometry
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Transistor Geometry- Detailed
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NMOS Operation-Linear
K Cox= Process Transconductance uA/V2 for 0.35u, K’ (Kp)=196uA/ V2
Cox
ox
tox
-------= Gate oxide capacitance per unit area
ox = 3.9 x o = 3.45 x 10-11 F/m
tox Oxide thickness
for 0.35 , tox=100Ao
Quick calculation of Cox: Cox= 0.345/tox (Ao) pf/um2
= mobility of electrons 550 cm2/V-sec for 0.35 process
VDS
IDS
VGS
IDS N KN VGSN VTN– VDSN1
2---VDSN
2–
= KN=K’. W/L
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NMOS Operation-Linear
Effect of W/L Effect of temperature
Rds W/L
W
temp
Rds
W
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Variations in Width and Length
Weff
Wdrawn WD WD
1. Width Oxide encroachment Weff= Wdrawn-2WD
2. Length Lateral diffusion LD = 0.7Xj Leff= Ldrawn-2LD
Ldrawn
LD Leff LD
polysilicon
polysilicon
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Large Transistors
Rchannel decrease with increase of W/L of the transistor
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Semiconductor Resistors
R= p(l /A) = (p/t). (l /w) = Rsh. (l /w) For 0.5u process: N+ diffusion : 70 / □ M1: 0.06 P+ diffusion : 140 /□ M2: 0.06 Polysilicon : 12 /□ M3: 0.03 Polycide:2-3 /□ P-well: 2.5K N-well: 1K
w
current
l t
(A)
1
n n q p p q +
------------------------------------------------=
Rsh values for 0.35u CMOS Process: Polysilicon 10 /□ Polycide 2 /□ Metal1 0.07 /□ Metal II 0.07 /□ Metal III 0.05 /□
Contact resistance: PolyI to MetalI 50
Via resistance: Metal I to Metal II 1.5 Via resistance: Metal II to metal III 1.
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Modelling: Resistance
1. Resistance: Rint= Rsh [l/w] Rsh values for 0.35u CMOS Process: Polysilicon 10 / Polycide 2 / Metal1 0.07 / Metal II 0.07 / Metal III 0.05 / Contact resistance: PolyI to MetalI 50 Via resistance: Metal I to Metal II 1.5 Via resistance: Metal II to metal III 1.
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Semiconductor Resistors
Al Al
n+
Diffusion n+
Field oxide
polysilicon
Polysilicon Resistor Diffusion Resistor
SiO2
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Delay Definitions
tpHL
tpLH
t
t
Vin
Vout
50%
50%
tr
10%
90%
tf
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Semiconductor Capacitors
1. Poly Capacitor: a. Poly to substrate b. Poly1 to Poly2 2. Diffusion Capacitor
n+ (ND)
depletion region
substrate (NA)
bottomwall
capacitance
sidewall
capacitances
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Dynamic Behavior of MOS Transistor
DS
G
B
CGDCGS
CSB CDBCGB
Prentice Hall/Rabaey
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SPICE Parameters for Parasitics
Prentice Hall/Rabaey
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SPICE Transistors Parameters
Prentice Hall/Rabaey
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Computing the Capacitances
V DD V DD
V in V out
M 1
M 2
M 3
M 4 C db 2
C db 1
C gd 12
C w
C g 4
C g 3
V out 2
Fanout
Interconnect
V out V in
C L
Simplified
Model
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Computing the Capacitances
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CMOS Inverter: Steady State Response
V DD V DD
V out V out
V in = V DD V in = 0
R on
R on
V OH = V DD
V OL = 0
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Switching Characteristics of Inverters
VDD
Vout
Vin = VDD
Ron
CL
tpHL = f(Ron.CL)
= 0.69 RonCL
t
Vout
VDD
RonCL
1
0.5
ln(0.5)
0.36
Transient Response
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Step Response
Fall Delay Time: TPHL
Vin
IDN V in = 5
V in = 4
V in = 3
VDD=5V
Vin
G
S
D
D
G
S
Vo
GND
MP
MN
CL
VDD
VDD Vo VDD-VT
MN OFF Saturation Linear
(VDSAT)
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Step Response- Fall time, tf
tr
CL
KPVDD 1 p+( )
---------------------------------------2–( ) 1 p+( )
1 p+( )---------------------------- 19 20p+( )ln+=
DDn
L
V
Ck
.
.
DDp
L
V
Ck
.
.
vin
vo 1-n
td1 td2
1
0.1
0.9
tf
CL
KN
VDD 1 n–( )---------------------------------------
2 n 0.1–( )
1 n–( )------------------------ 19 20n–( )ln+=
tf=~ k is a constant
tr=~ k is a constant
0.1
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Step Response-tPHL
Vin
Vo VDD-VTN
Vx
td1 td2
vin
vo 1-n
td1 td2
VDD
1
0.5
VDD/ 2
Assume normalized voltages vin= Vin/ VDD vo= Vo/ VDD n = VTN/ VDD p = VTP/ VDD tPHL=td1+td2
tPHL
CL
KN
VDD 1 n–( )---------------------------------------
2n
1 n–( )---------------- 3 4n–( )ln+=
tPHL
CL
A'N
KN
VDD----------------------=
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Step Response Rise Delay tPLH and Rise Time tr
VDD
Vin
G
S
D
D
G
S
Vo
GND
MP
MN
CL
VDD
tPLH
CL
KP
VDD 1 p+( )---------------------------------------
2p–
1 p+( )----------------- 3 4p+( )ln+=
tPLH
CL
A'P
KP
VDD---------------------=
tr
CL
KPVDD 1 p+( )
---------------------------------------2–( ) 1 p+( )
1 p+( )---------------------------- 19 20p+( )ln+=
tr
4CL
A'P
KP
VDD---------------------= (P= - 0.2)
0.1
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Factors Influence Delay
Inverter Delay,td = (tPHL+tPLH)/2 The following factors influence the delay of the inverter: • Load Capacitance • Supply Voltage • Transistor Sizes • Junction Temperature • Input Transition Time
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Delay as a function of VDD
0
4
8
12
16
20
24
28
2.00 4.001.00 5.003.00
No
rm
ali
zed
Dela
y
VDD (V)
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Delay as a function of Transistor Size
tPHL and tf decrease with the increase of W/L of the NMOS tPLH and tr decrease with the increase of W/L of the PMOS
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Temperature Effect
Temperature ranges: commercial : 0 to700C industrial: -40 to 850C military: -55 to 1250C Calculation of the junction temperature tj= ta + ja X Pd Effect of temperature on mobility Delay and speed implications
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Effect of Input Transition Times
r Vin Vo
The delay of the inverter increases with the increase of the input transition times r and f
tPHL = (tPHL) step + (r /6).(1-2p) tPLH = (tPLH) step + (f/6).(1+2n)
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Define = (W/L)p/(W/L)n For Equal Fall and Rise Delay KN=KP
= n/ p For Minimum Delay dtD/d = 0
opt = Sqrt (n/ p)
Transistor Sizing
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Power Dissipation in CMOS
Two Components contribute to the power dissipation:
» Static Power Dissipation
– Leakage current
– Sub-threshold current
» Dynamic Power Dissipation
– Short circuit power dissipation
– Charging and discharging power dissipation
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Static Power Dissipation
G
S
D
D
G
S
Vo
VDD
GND
B
B
MP
MN
Leakage Current: • P-N junction reverse biased current: io= is(e
qV/kT-1) • Typical value 0.1nA to 0.5nA @room temp. • Total Power dissipation:
Psl= i0.VDD
Sub-threshold Current • Relatively high in low threshold devices
Vin
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Analysis of CMOS circuit power dissipation
The power dissipation in a CMOS logic gate can be
expressed as
P = Pstatic + Pdynamic
= (VDD · Ileakage) + (p · f · Edynamic)
Where p is the switching probability or activity factor
at the output node (i.e. the average number of output
switching events per clock cycle).
The dynamic energy consumed per output switching event is defined as
Edynamic = eventswitching
DDDD dtVi__1
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Analysis of CMOS circuit power dissipation
SCDDMDDLdynamic EVCVCE 22 2
SCDDgdpgdndbndbpDDload EVCCCCVC 22 )](2[
The first term —— the energy dissipation due to the
Charging/discharging of the effective load capacitance CL.
The second term —— the energy dissipation due to the input-to-
output coupling capacitance. A rising input results in a VDD-
VDD transition of the voltage across CM and so doubles the
charge of CM.
CL = Cload + Cdbp +Cdbn
CM = Cgdn + Cgdp
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• distributed,
• voltage-dependent, and
• nonlinear.
So their exact modeling is quite complex.
The MOSFET parasitic capacitances
Even ESC can be modeled, it is also difficult to calculate the
Edynamic.
On the other hand, if the short-circuit current iSC can be Modeled,
the power-supply current iDD may be modeled with the same
method.
So there is a possibility to directly model iDD instead of iSC.
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Schematic of the Inverter
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The short-circuit energy dissipation ESC is due to the rail-
to-rail current when both the PMOS and NMOS devices
are simultaneously on.
ESC = ESC_C + ESC_n
Where
and
DDVv
nDDcSC dtiVE0
_
0
0
_
0 DDVv
pDDdSC dtiVE
Analysis of short-circuit current
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Charging and discharging currents
Discharging Inverter Charging Inverter
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Factors that affect the short-circuit current
TVV
VI TDD
DD
mean
3)2(12
1
For a long-channel device, assuming that the inverter is
symmetrical (n = p = and VTn = -VTp = VT) and with zero load
capacitance, and input signal has equal rise and fall times (r = f
= ), the average short-circuit current [Veendrick, 1994] is
From the above equation, some fundamental factors that
affect short-circuit current are:
, VDD, VT, and T. )(L
W
tox
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Parameters affecting short cct current
For a short-channel device, and VT are no longer
constants, but affected by a large number of
parameters (i.e. circuit conditions, hspice
parameters and process parameters).
CL also affects short-circuit current.
Imean is a function of the following parameters (tox is process-
dependent):
CL, , T (or /T), VDD, Wn,p, Ln,p (or Wn,p/ Ln,p ), tox, …
The above argument is validated by the means of simulation in
the case of discharging inverter,
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The effect of CL on Short CCt Current
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Effect of tr on short cct Current
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Effect of Wp on Short cct Current
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Effect of timestep setting on simulation results
Tr (ps) Timestep (ps) MaxStep (ps) iMax (uA) iaverage_inT/2 (uA)
2 10 802.6 1.258
4 10 413.8 1.264
5 10 336.4 1.24
6 10 284.9 1.234
8 10 221 1.245
0
10 20 183 1.231
2 10 73.09 1.202
4 10 64.4 1.213
5 10 58.69 1.21
6 10 65.64 1.208
8 10 76.13 1.207
100
10 20 63.1 1.217
2 10 50.96 1.311
5 10 49.78 1.295
5 20 50.46 1.313
8 10 50.72 1.311
8 20 52.08 1.311
200
10 20 51.25 1.311
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Thank you !