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The Physical Structure (NMOS)

Field Oxide

SiO2

Gate oxide

Field Oxiden+n+

AlAlSiO2SiO2

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' WL----- V

GSVT– 2

----------------------------------------------------= Saturation

RCH1

K'WL----- VGS VT– 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 VG SN VTN– VD SN12---VD SN

2–

= KN=K’.

W/L

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NMOS Operation-Linear

Effect of W/L

Effect of temperature

RdsW/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

Resistance

R= p(l /A) = (p/t). (l /w) = Rsh. (l /w)

Rsh = Sheet resistance /

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 + ------------------------------------------------=

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Semiconductor Resistors

AlAl

n+

Diffusionn+

Field oxide

polysilicon

Polysilicon Resistor Diffusion Resistor

SiO2

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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)bottomwallcapacitance

sidewallcapacitances

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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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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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CMOS Inverter: Steady State Response

VDD VDD

VoutVout

Vin = VDD Vin = 0

Ron

Ron

VOH = VDD

VOL= 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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Computing the Capacitances

VDD VDD

Vin Vout

M1

M2

M3

M4Cdb 2

Cdb 1

Cgd 12

Cw

Cg4

Cg3

Vout2

Fanout

Interconnect

VoutVin

CLSimplified

Model

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Computing the Capacitances

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Delay Definitions

tpHL

tpLH

t

t

Vin

Vout

50%

50%

tr

10%

90%

tf

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Step Response

Fall Delay Time: TPHL

Vin

IDN Vin = 5

Vin = 4

Vin = 3

VDD=5V

Vin

G

S

D

D

G

S

Vo

GND

MP

MN

CL

VDD

VDDVoVDD-VT

MN OFF Saturation Linear

(VDSAT)

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Step Response- Fall time, tf

trCL

KPVDD 1 p+( )--------------------------------------- 2–( ) 1 p+( )

1 p+( )---------------------------- 19 20p+( )ln+=

DDn

L

V

Ck

.

.

DDp

L

V

Ck

.

.

vin

vo1-n

td1 td2

1

0.1

0.9

tfCL

KNVDD 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

VoVDD-VTN

Vx

td1 td2

vin

vo1-n

td1 td2

VDD

1

0.5

VDD/ 2

Assume normalized voltagesvin= Vin/ VDDvo= Vo/ VDDn = VTN/ VDDp = VTP/ VDD

tPHL=td1+td2

tPHLCL

KNVDD 1 n–( )--------------------------------------- 2n

1 n–( )---------------- 3 4n–( )ln+=

tPHLCLA'N

KNVDD----------------------=

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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

tPLHCL

KPVDD 1 p+( )--------------------------------------- 2p–

1 p+( )----------------- 3 4p+( )ln+=

tPLHCLA'P

KPVDD---------------------=

trCL

KPVDD 1 p+( )--------------------------------------- 2–( ) 1 p+( )

1 p+( )---------------------------- 19 20p+( )ln+=

tr4C LA'PKPVDD---------------------= (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

Nor

mal

ized

Del

ay

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

rVinVo

The delay of the inverter increaseswith 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(eqV/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 theCharging/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

DDmean

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 !