MOS Transistor Theoryjmorizio/ece261/classlectures/MOS_theory.pdf · MOS Transistor Theory • So...

EE 261 James Morizio 1

MOS Transistor Theory

• So far, we have viewed a MOS transistor as an ideal switch (digital operation)– Reality: less than ideal


Introduction• So far, we have treated transistors as ideal

switches• An ON transistor passes a finite amount of current

– Depends on terminal voltages– Derive current-voltage (I-V) relationships

• Transistor gate, source, drain all have capacitance– I = C (∆V/∆t) -> ∆t = (C/I) ∆V– Capacitance and current determine speed

• Also explore what a “degraded level” really means


MOS Transistor Theory

• Study conducting channel between source and drain• Modulated by voltage applied to the gate (voltage-controlled device)• nMOS transistor: majority carriers are electrons (greater mobility), p-substrate doped (positively doped)• pMOS transistor: majority carriers are holes (less mobility), n-substrate (negatively doped)


Terminal Voltages• Mode of operation depends on Vg, Vd, Vs

– Vgs = Vg – Vs

– Vgd = Vg – Vd

– Vds = Vd – Vs = Vgs - Vgd

• Source and drain are symmetric diffusion terminals– By convention, source is terminal at lower voltage– Hence Vds ≥ 0

• nMOS body is grounded. First assume source is 0 too.• Three regions of operation

– Cutoff– Linear– Saturation

Vg

Vs Vd

VgdVgs

Vds+-

+

-

+

-


Gate Biasing

p-substrate

n+ n+

Source Gate Drain

Channel

+ -

E

SiO2

VSS (Gnd)

• Vgs=0: no current flows fromsource to drain (insulated by two reverse biased pn junctions

• Vgs>0: electric field created across substrate

• Electrons accumulate under gate: region changes from p-typeto n-type

• Conduction path between source and drain


nMOS Device Behavior

Vgs << Vt

Polysilicon gatep-substrate

Accumulationmode

• Enhancement-mode transistor: Conducts when gate biasVgs > Vt

• Depletion-mode transistor: Conducts when gate bias is zero

Vgs = Vt

Depletion mode

Depletion region

Oxide insulator

Vgs > Vt

Inversion mode

Depletion region

InversionRegion(n-type)


nMOS Cutoff

• No channel• Ids = 0

+-

Vgs = 0

n+ n+

+-

Vgd

p-type body

b

g

s d


nMOS Linear• Channel forms• Current flows from d to s

– e- from s to d

• Ids increases with Vds

• Similar to linear resistor

+-

Vgs > Vt

n+ n+

+-

Vgd = Vgs

+-

Vgs > Vt

n+ n+

+-

Vgs > Vgd > Vt

Vds = 0

0 < Vds < Vgs-Vt

p-type body

p-type body

b

g

s d

b

g

s d Ids


nMOS Saturation

• Channel pinches off• Ids independent of Vds

• We say current saturates• Similar to current source

+-

Vgs > Vt

n+ n+

+-

Vgd < Vt

Vds > Vgs-Vt

p-type body

b

g

s d Ids


I-V Characteristics

• In linear region, Ids depends on– How much charge is in the channel?– How fast is the charge moving?


Channel Charge

• MOS structure looks like parallel plate capacitor while operating in inversion– Gate – oxide – channel

• Qchannel =

n+ n+

p-type body

+

Vgd

gate

+ +source

-

Vgs

-drain

Vds

channel-

Vg

Vs Vd

Cg

n+ n+

p-type body

W

L

tox

SiO2 gate oxide(good insulator, εox = 3.9)

polysilicongate


Channel Charge

• MOS structure looks like parallel plate capacitor while operating in inversion– Gate – oxide – channel

• Qchannel = CV• C =

n+ n+

p-type body

+

Vgd

gate

+ +source

-

Vgs

-drain

Vds

channel-

Vg

Vs Vd

Cg

n+ n+

p-type body

W

L

tox


polysilicongate


Channel Charge• MOS structure looks like parallel plate capacitor

while operating in inversion– Gate – oxide – channel

• Qchannel = CV• C = Cg = εoxWL/tox = CoxWL• V =

n+ n+

p-type body

+

Vgd

gate

+ +source

-

Vgs

-drain

Vds

channel-

Vg

Vs Vd

Cg

n+ n+

p-type body

W

L

tox


polysilicongate

Cox = εox / tox


Channel Charge• MOS structure looks like parallel plate capacitor while

operating in inversion– Gate – oxide – channel

• Qchannel = CV• C = Cg = εoxWL/tox = CoxWL• V = Vgc – Vt = (Vgs – Vds/2) – Vt

n+ n+

p-type body

+

Vgd

gate

+ +source

-

Vgs

-drain

Vds

channel-

Vg

Vs Vd

Cg

n+ n+

p-type body

W

L

tox


polysilicongate

Cox = εox / tox


Carrier velocity

• Charge is carried by e-• Carrier velocity v proportional to lateral E-field

between source and drain• v =


Carrier velocity


between source and drain• v = µE µ called mobility• E =


Carrier velocity


between source and drain• v = µE µ called mobility• E = Vds/L• Time for carrier to cross channel:

– t =


Carrier velocity


between source and drain• v = µE µ called mobility• E = Vds/L• Time for carrier to cross channel:

– t = L / v


nMOS Linear I-V

• Now we know– How much charge Qchannel is in the channel– How much time t each carrier takes to cross

dsI =


nMOS Linear I-V

• Now we know– How much charge Qchannel is in the channel– How much time t each carrier takes to cross

channelds

QI

t=

=


nMOS Linear I-V• Now we know

– How much charge Qchannel is in the channel– How much time t each carrier takes to cross

channel

ox 2

2

ds

dsgs t ds

dsgs t ds

QI

tW VC V V VL

VV V V

µ

β

=

= − −

= − −

ox = W

CL

β µ


nMOS Saturation I-V

• If Vgd < Vt, channel pinches off near drain– When Vds > Vdsat = Vgs – Vt

• Now drain voltage no longer increases current

dsI =


nMOS Saturation I-V



2dsat

ds gs t dsatVI V V Vβ = − −


nMOS Saturation I-V



( )2

2

2

dsatds gs t dsat

gs t

VI V V V

V V

β

β

= − −

= −


nMOS I-V Summary

( )2

cutoff

linear

saturatio

0

2

2n

gs t

dsds gs t ds ds dsat

gs t ds dsat

V V

VI V V V V V

V V V V

β

β

< = − − <

− >

• Shockley 1st order transistor models


Current-Voltage Relations


Current-Voltage Relationsk n: transconductance of transistorW : width-to-length ratioL

• As W increases, more carriers available to conduct current

• As L increases, Vds diminishes in effect (more voltage drop). Takes longer to push carriers across the transistor, reducing current flow


Example• For a 0.6 µm process

– From AMI Semiconductor– tox = 100 Å– µ = 350 cm2/V*s– Vt = 0.7 V

• Plot Ids vs. Vds– Vgs = 0, 1, 2, 3, 4, 5– Use W/L = 4/2 λ

( )14

28

3.9 8.85 10350 120 /

100 10ox

W W WC A V

L L Lβ µ µ

−

−

• ⋅ = = = ⋅

0 1 2 3 4 50

0.5

1

1.5

2

2.5

Vds

I ds (m

A)

Vgs = 5

Vgs = 4

Vgs = 3

Vgs = 2Vgs = 1


pMOS I-V

• All dopings and voltages are inverted for pMOS• Mobility µp is determined by holes

– Typically 2-3x lower than that of electrons µn

– 120 cm2/V*s in AMI 0.6 µm process

• Thus pMOS must be wider to provide same current– In this class, assume µn / µp = 2 to 3


Capacitance

• Any two conductors separated by an insulator have capacitance

• 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 associated

with source/drain diffusion


Gate Capacitance• Approximate channel as connected to source• Cgs = εoxWL/tox = CoxWL = CpermicronW• Cpermicron is typically about 2 fF/µm

n+ n+

p-type body

W

L

tox

SiO2 gate oxide(good insulator, εox = 3.9ε0)

polysilicongate


The Gate Capacitance


Diffusion Capacitance• Csb, Cdb

• Undesirable, called parasitic capacitance• Capacitance depends on area and perimeter

– Use small diffusion nodes– Comparable to Cg

for contacted diff– ½ Cg for uncontacted– Varies with process


Diffusion Capacitance


Parasitic Resistances

W

LD

Drain

Draincontact

Polysilicon gate

DS

G

RS RD

VGS,eff

RS = (LS/W)R + RC

RD = (LD/W)R + RC

RC: contact resistanceR : sheet resistance per square

of drain-source diffusion


Body Effect• Many MOS devices on a common substrate

– Substrate voltage of all devices are normally equal

• But several devices may be connected in series– Increase in source-to-substrate voltage as we proceed vertically

along the chain

d1

d2

s1

s2

V12

V11

g1

g2

Vsb1 = 0

Vsb2 = 0• Net effect: slight increasein threshold voltage Vt,Vt2>Vt1


Pass Transistors

• We have assumed source is grounded• What if source > 0?

– e.g. pass transistor passing VDD

VDDVDD


Pass Transistors

• We have assumed source is grounded• What if source > 0?

– e.g. pass transistor passing VDD

• Vg = VDD– If Vs > VDD-Vt, Vgs < Vt

– Hence transistor would turn itself off

• nMOS pass transistors pull no higher than VDD-Vtn– Called a degraded “1”– Approach degraded value slowly (low Ids)

• pMOS pass transistors pull no lower than Vtp

VDDVDD


Pass Transistor Ckts

VDDVDD

VSS

VDD

VDD

VDD VDD VDD

VDD


Pass Transistor Ckts

VDDVDD Vs = VDD-Vtn

VSS

Vs = |Vtp|

VDD

VDD-Vtn VDD-VtnVDD-Vtn

VDD

VDD VDD VDD

VDD

VDD-Vtn

VDD-2Vtn


Effective Resistance

• Shockley models have limited value– Not accurate enough for modern transistors– Too complicated for much hand analysis

• Simplification: treat transistor as resistor– Replace Ids(Vds, Vgs) with effective resistance R

• Ids = Vds/R– R averaged across switching of digital gate

• Too inaccurate to predict current at any given time– But good enough to predict RC delay


RC Delay Model• Use equivalent circuits for MOS transistors

– Ideal switch + capacitance and ON resistance– Unit nMOS has resistance R, capacitance C– Unit pMOS has resistance 2R, capacitance C

• Capacitance proportional to width• Resistance inversely proportional to width

kgs

d

g

s

d

kCkC

kCR/k

kgs

d

g

s

d

kC

kC

kC

2R/k


RC Values

• Capacitance– C = Cg = Cs = Cd = 2 fF/µm of gate width– Values similar across many processes

• Resistance– R ≈ 6 KΩ in 0.6um process– Improves with shorter channel lengths

• Unit transistors– May refer to minimum contacted device (4/2 λ)– Or maybe 1 µm wide device– Doesn’t matter as long as you are consistent


Activity1) If the width of a transistor increases, the current willincrease decrease not change

2) If the length of a transistor increases, the current willincrease decrease not change

3) If the supply voltage of a chip increases, the maximum transistor current will

increase decrease not change4) If the width of a transistor increases, its gate capacitance willincrease decrease not change

5) If the length of a transistor increases, its gate capacitance willincrease decrease not change

6) If the supply voltage of a chip increases, the gate capacitance of each transistor will

increase decrease not change


DC Response

• DC Response: Vout vs. Vin for a gate• Ex: Inverter

– When Vin = 0 -> Vout = VDD

– When Vin = VDD -> Vout = 0– In between, Vout depends on

transistor size and current– By KCL, must settle such that

Idsn = |Idsp|– We could solve equations– But graphical solution gives more insight

Idsn

Idsp Vout

VDD

Vin


Transistor Operation

• Current depends on region of transistor behavior• For what Vin and Vout are nMOS and pMOS in

– Cutoff?– Linear?– Saturation?


nMOS Operation

Vgsn >

Vdsn >

Vgsn >

Vdsn <

Vgsn <SaturatedLinearCutoff

Idsn

Idsp Vout

VDD

Vin


nMOS Operation

Vgsn > Vtn

Vdsn > Vgsn – Vtn

Vgsn > Vtn

Vdsn < Vgsn – Vtn

Vgsn < Vtn

SaturatedLinearCutoff

Idsn

Idsp Vout

VDD

Vin


nMOS Operation

Vgsn > Vtn

Vdsn > Vgsn – Vtn

Vgsn > Vtn

Vdsn < Vgsn – Vtn

Vgsn < Vtn


Idsn

Idsp Vout

VDD

Vin

Vgsn = Vin

Vdsn = Vout


nMOS Operation

Vgsn > Vtn

Vin > Vtn

Vdsn > Vgsn – Vtn

Vout > Vin - Vtn

Vgsn > Vtn

Vin > Vtn

Vdsn < Vgsn – Vtn

Vout < Vin - Vtn

Vgsn < Vtn

Vin < Vtn


Idsn

Idsp Vout

VDD

Vin

Vgsn = Vin

Vdsn = Vout


pMOS Operation

Vgsp <

Vdsp <

Vgsp <

Vdsp >

Vgsp >SaturatedLinearCutoff

Idsn

Idsp Vout

VDD

Vin


pMOS Operation

Vgsp < Vtp

Vdsp < Vgsp – Vtp

Vgsp < Vtp

Vdsp > Vgsp – Vtp

Vgsp > Vtp


Idsn

Idsp Vout

VDD

Vin


pMOS Operation

Vgsp < Vtp

Vdsp < Vgsp – Vtp

Vgsp < Vtp

Vdsp > Vgsp – Vtp

Vgsp > Vtp


Idsn

Idsp Vout

VDD

Vin

Vgsp = Vin - VDD

Vdsp = Vout - VDD

Vtp < 0


pMOS Operation

Vgsp < Vtp

Vin < VDD + Vtp

Vdsp < Vgsp – Vtp

Vout < Vin - Vtp

Vgsp < Vtp

Vin < VDD + Vtp

Vdsp > Vgsp – Vtp

Vout > Vin - Vtp

Vgsp > Vtp

Vin > VDD + Vtp


Idsn

Idsp Vout

VDD

Vin

Vgsp = Vin - VDD

Vdsp = Vout - VDD

Vtp < 0


I-V Characteristics• Make pMOS wider than nMOS such that βn = βp

Vgsn5

Vgsn4

Vgsn3

Vgsn2Vgsn1

Vgsp5

Vgsp4

Vgsp3

Vgsp2

Vgsp1

VDD

-VDD

Vdsn

-Vdsp

-Idsp

Idsn

0


DC Transfer Curve

• Transcribe points onto Vin vs. Vout plot

CVout

0

Vin

VDD

VDD

A B

DE

Vtn VDD/2 VDD+Vtp


Operating Regions

• Revisit transistor operating regions

CVout

0

Vin

VDD

VDD

A B

DE

Vtn VDD/2 VDD+VtpEDCBA

pMOSnMOSRegion


Operating Regions

• Revisit transistor operating regions

CVout

0

Vin

VDD

VDD

A B

DE

Vtn VDD/2 VDD+VtpCutoffLinearE

SaturationLinearD

SaturationSaturationC

LinearSaturationB

LinearCutoffA

pMOSnMOSRegion


Beta Ratio• If βp / βn ≠ 1, switching point will move from VDD/2• Called skewed gate• Other gates: collapse into equivalent inverter

Vout

0

Vin

VDD

VDD

0.51

2

10p

n

ββ

=

0.1p

n

ββ

=


Noise Margins• How much noise can a gate input see before it

does not recognize the input?

IndeterminateRegion

NML

NMH

Input CharacteristicsOutput Characteristics

VOH

VDD

VOL

GND

VIH

VIL

Logical HighInput Range

Logical LowInput Range

Logical HighOutput Range

Logical LowOutput Range


Logic Levels

• To maximize noise margins, select logic levels at

VDD

Vin

Vout

VDD

βp/βn > 1

Vin Vout

0


Logic Levels• To maximize noise margins, select logic levels at

– unity gain point of DC transfer characteristic

VDD

Vin

Vout

VOH

VDD

VOL

VIL VIHVtn

Unity Gain PointsSlope = -1

VDD-|Vtp|

βp/βn > 1

Vin Vout

0

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