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7/30/2019 Capacitance s
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CapacitancesCapacitances
Alpana AgarwalAssistant Professor
Email: [email protected], [email protected]
Electronics & Communication Engineering Department
Thapar University, Patiala
Alpana Agarwal, Thapar University 210/13/2007
CapacitanceCapacitance
Any two conductors separated by an insulatorhave capacitance
Essential for transient and ac responses
Most of them are distributed & not lumped
On-chip capacitances, used for hand estimation
Gate to channel capacitor is very important Creates channel charge necessary for operation
Source and drain have capacitance to body Across reverse-biased diodes
Called diffusion capacitance because it is associatedwith source/drain diffusion
More parasitic capacitances
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Alpana Agarwal, Thapar University 310/13/2007
CMOS Inverter: DynamicCMOS Inverter: Dynamic
VDD
Rn
Vout = 0
Vin = V DD
CL tpHL = f(Rn, CL)
Todays focus
Covered earlier
Transient, or dynamic, response determines the maximumspeed at which a device can be operated.
Alpana Agarwal, Thapar University 410/13/2007
Sources of CapacitanceSources of Capacitance
Cw
CDB2
CDB1
CGD12
CG4
CG3
wiring (interconnect) capacitance
intrinsic MOS transistor capacitances
Vout2Vin
extrinsic MOS transistor (fanout) capacitances
Vout
VoutVin
M2
M1
M4
M3
Vout2
CL
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Alpana Agarwal, Thapar University 510/13/2007
MOS Intrinsic CapacitancesMOS Intrinsic Capacitances
Structure capacitances
Channel capacitances
Depletion regions of the reverse-biased pn-junctions of the drainand source
Alpana Agarwal, Thapar University 610/13/2007
MOS Structure CapacitancesMOS Structure Capacitances
LDSource
n+Drain
n+W
Ldrawn
Poly Gate
n+n+
tox
Leff
Top view
lateral diffusion
CGSO = CGDO = Cox LD W = Co W
Overlap capacitance (linear)
LD
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Alpana Agarwal, Thapar University 710/13/2007
MOS Channel CapacitancesMOS Channel Capacitances
S D
p substrate
B
GVGS +
-
n+n+
depletionregion
n channel
CGS = CGCS + CGSO CGD = CGCD + CGDO
CGB = CGCB
The gate-to-bulk capacitance depends upon theoperating region and the terminal voltages
Alpana Agarwal, Thapar University 810/13/2007
Average Distribution of ChannelAverage Distribution of ChannelCapacitanceCapacitance
(2/3)CoxWL +2CoW
(2/3)CoxWL0(2/3)CoxWL0Saturation
CoxWL + 2CoWCoxWLCoxWL/2CoxWL/20Resistive
CoxWL + 2CoWCoxWL00CoxWLCutoff
CGCGCCGCDCGCSCGCBOperationRegion
Channel capacitance components are nonlinear and varywith operating voltage
Most important regions are cutoff and saturation since thatis where the device spends most of its time
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Alpana Agarwal, Thapar University 910/13/2007
MOS Diffusion CapacitancesMOS Diffusion Capacitances
S D
p substrate
B
GVGS +
-
n+n+
depletionregion
n channel
CSB
= CSdiff
CDB
= CDdiff
The junction (or diffusion) capacitance is from the reverse-biased source-body and drain-body pn-junctions.
Alpana Agarwal, Thapar University 1010/13/2007
Source Junction ViewSource Junction View
side walls
channel
W
xj
channel-stopimplant (NA+)
source
bottom plate(ND)
LSource
substrate (NA)
Cdiff = Cbp + Csw = Cj AREA + Cjsw PERIMETER
= Cj LSource W + Cjsw (2LSource + W)
junctiondepth
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Alpana Agarwal, Thapar University 1110/13/2007
Review: Reverse Bias DiodeReview: Reverse Bias Diode
All diodes in MOS digital circuits are reverse biased;
the dynamic response of the diode is determined by depletion-region charge or junction capacitance
Cj = Cj0/((1 VD)/0)m
where Cj0 is the capacitance under zero-bias conditions (afunction of physical parameters), 0 is the built-in potential (afunction of physical parameters and temperature) and m is thegrading coefficient
m = for an abruptjunction (transition from n to p-material is instantaneous)
m = 1/3 for a linear (or graded) junction (transition is gradual)
Nonlinear dependence (that decreases with increasing reverse
bias)
+
-VD
Alpana Agarwal, Thapar University 1210/13/2007
MOS Capacitance ModelMOS Capacitance Model
CGS
CSB CDB
CGD
CGB
S
G
B
D
CGS = CGCS + CGSO CGD = CGCD + CGDO
CGB = CGCB
CSB = CSdiff CDB = CDdiff
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Alpana Agarwal, Thapar University 1310/13/2007
Transistor Capacitance ValuesTransistor Capacitance Valuesfor 0.25for 0.25
0.90.320.220.90.481.90.276PMOS
0.90.440.280.90.520.316NMOS
bsw(V)
mjswCjsw(fF/m)
b(V)
mjCj(fF/m2)
Co(fF/m)
Cox(fF/m2)
Example: For an NMOS with L = 0.24 m, W = 0.36 m,
Ldrain = Lsource = 0.625 m
CGC = Cox WL =
CGSO = CGDO = Cox LD W = Co W =
so Cgate_cap = CoxWL + 2CoW =
Cbp = Cj LSource W =
Csw = Cjsw (2LSource + W) =
so Cdiffusion_cap =
Alpana Agarwal, Thapar University 1410/13/2007
Transistor Capacitance ValuesTransistor Capacitance Valuesfor 0.25for 0.25
0.90.320.220.90.481.90.276PMOS
0.90.440.280.90.520.316NMOS
bsw(V)
mjswCjsw(fF/m)
b(V)
mjCj(fF/m2)
Co(fF/m)
Cox(fF/m2)
Example: For an NMOS with L = 0.24 m, W = 0.36 m,Ldrain = Lsource = 0.625 m
CGC = Cox WL =
CGSO = CGDO = Cox LD W = Co W =
so Cgate_cap = CoxWL + 2CoW =
Cbp = Cj LSource W =
Csw = Cjsw (2LSource + W) =
so Cdiffusion_cap =
0.11 fF
0.52 fF
0.74 fF
0.45 fF
0.45 fF
0.90 fF
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Alpana Agarwal, Thapar University 1510/13/2007
Review: Sources of CapacitanceReview: Sources of Capacitance
Vout
Cw
Vin
CDB2
CDB1
CGD12
M2
M1
M4
M3
Vout2
CG4
CG3
wiring (interconnect) capacitance
intrinsic MOS transistor capacitances
Vout2Vin
extrinsic MOS transistor (fanout) capacitances
Vout
CL
ndrain
pdrain
Alpana Agarwal, Thapar University 1610/13/2007
Extrinsic (FanExtrinsic (Fan--Out) CapacitanceOut) Capacitance
The extrinsic, or fan-out, capacitance is the total gatecapacitance of the loading gates M3 and M4.
Cfan-out = Cgate (NMOS) + Cgate (PMOS)
= (CGSOn+ CGDOn+ WnLnCox) + (CGSOp+ CGDOp+WpLpCox)
Simplification of the actual situation
Assumes all the components of Cgate are between Vout and GND (or VDD)
Assumes the channel capacitances of the loading gates are constant
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Alpana Agarwal, Thapar University 1710/13/2007
Layout of Two Chained InvertersLayout of Two Chained Inverters
InOut
Metal1
VDD
GND
1.2m=2
1.125/0.25
0.375/0.25
PMOS
NMOS
Polysilicon
2.3750.72.3750.71.125/0.25PMOS
1.8750.31.8750.30.375/0.25NMOSPS (m)AS (m
2
)PD (m)AD (m2
)W/L
0.125 0.5
Alpana Agarwal, Thapar University 1810/13/2007
Components of CComponents of CLL (0.25(0.25mm))
6.06.1CL
0.120.12from extractionCw
2.282.28(2 Cop)Wp + CoxWpLpCG4
0.760.76(2 Con)Wn + CoxWnLnCG3
1.151.5KeqbppADpCj + KeqswpPDpCjswCDB2
0.900.66KeqbpnADnCj + KeqswnPDnCjswCDB1
0.610.612 Cop WpCGD2
0.230.232 Con WnCGD1
Value (fF)LH
Value (fF)HL
Expression
C Term
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Alpana Agarwal, Thapar University 1910/13/2007
Wiring CapacitanceWiring Capacitance
The wiring capacitance depends upon the lengthand width of the connecting wires and is a function of the fan-out from the driving gate and thenumber of fan-out gates.
Wiring capacitance is growing in importance with the scaling of technology.
Alpana Agarwal, Thapar University 2010/13/2007
Parallel Plate Wiring CapacitanceParallel Plate Wiring Capacitance
electrical field linesW
H
tdi dielectric (SiO2)
substrate
Cpp = (di/tdi) WL
current flow
permittivity
constant(SiO2= 3.9)
L
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Alpana Agarwal, Thapar University 2110/13/2007
Permittivity Values of Some DielectrPermittivity Values of Some Dielectricsics
3.2 4.0Fluorosilicate glass (FSG)
2.6 2.8Aromatic thermosets (SiLK)
11.7Silicon
9.5Alumina (package)
7.5Silicon nitride
5Glass epoxy (PCBs)
3.9 4.5Silicon dioxide
3.1 3.4Polyimides (organic)
2.1Teflon AF
1Free spacediMaterial
Alpana Agarwal, Thapar University 2210/13/2007
Sources ofSources ofInterwireInterwire CapacitanceCapacitance
interwire
fringe
pp
Cwire = Cpp + Cfringe + Cinterwire= (di/tdi)WL
+ (2di)/log(tdi/H)
+ (di/tdi)HL
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Alpana Agarwal, Thapar University 2310/13/2007
Impact ofImpact ofInterwireInterwire CapacitanceCapacitance
(from [Bakoglu89])
Alpana Agarwal, Thapar University 2410/13/2007
InsightsInsights
For W/H < 1.5, the fringe component dominates the parallel-plate component. Fringing capacitance can increase the overall capacitance by a factor of 10 or more.
When W < 1.75H interwire capacitance starts to dominate
Interwire capacitance is more pronounced for wires in the higher interconnect layers (further from the substrate)
Rules of thumb
Never run wires in diffusion
Use poly only for short runs Shorter wires lower R and C
Thinner wires lower C but higher R
Wire delay nearly proportional to L2
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Alpana Agarwal, Thapar University 2510/13/2007
Wiring CapacitancesWiring Capacitances
52271914121212
38149.16.65.45.45.2Al5
452718151514
35158.976.86.5Al4
4927201918
4115109.48.9Al3
45292725
36171513Al2
544740
574130Al1
5488Poly
Al4Al3Al2Al1PolyActiveField
fringe in aF/mpp in aF/m2
1158585859540Interwire Cap
Al5Al4Al3Al2Al1Poly
per unit wire length in aF/m for minimally-spaced wires
Alpana Agarwal, Thapar University 2610/13/2007
Dealing with CapacitanceDealing with Capacitance
Low capacitance (low-k) dielectrics (insulators)such as polymide or even air instead of SiO2 family of materials that are low-k dielectrics
must also be suitable thermally and mechanically and
compatible with (copper) interconnect
Copper interconnect allows wires to be thinnerwithout increasing their resistance, thereby decreasing interwire capacitance
SOI (silicon on insulator) to reduce junction capacitance
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Alpana Agarwal, Thapar University 2710/13/2007
Gate CapacitanceGate 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= 3.9
0)
polysilicongate
Alpana Agarwal, Thapar University 2810/13/2007
Diffusion CapacitanceDiffusion Capacitance
Csb, Cdb Undesirable, called parasitic capacitance
Capacitance depends on area and perimeter
Use small diffusion nodes
Comparable to Cgfor contacted diff
Cg for uncontacted
Varies with process
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Questions, if any?Questions, if any?Questions, if any?Questions, if any?Questions, if any?Questions, if any?Questions, if any?Questions, if any?