MOSFET Transistor Basics

AVLSI Workgroup

Paul Hasler

Diffusion of Charge over Barrier

Ec

Ec

Ef

Ec

A B

P(E) =

~ e-(E-Ef)/kT

1

1 + e-(E-Ef)/kT

10-4

10-3

10-2

10-1

100

-2

-1

0

1

2

3

4

5

6

7

8

Probability

Ene

rgy

(eV

)

Case I: P(E) ~ exp( - E0 /kT)

qV

E0

Case II: P(E) ~ exp( - ( E0 - qV)/kT)

Ratio of Case II to Case I = exp( V / UT )

UT = kT/q

P-N Junctions

N-typeN

D

P-typeN

A

Depletion Layer or Region

ChargeDensity

qND

-qNA

BandDiagram

P-N Junctions --- Diodes

N-typeN

D

P-typeN

A

First-Principles Model

A MOSFET Transistor

Gate

Source

Drain

Source

Substrate

Gate

Drain

Self-Aligned Process

How do we make a basic transistor element?

We create a silicon-oxide “stencil” (or mask)

We get highly repeatable gates because the gate acts as a stencil as well

CMOS Process Cross Section

n nn pp

(n-well)

all p-n junction must be reversed bias

p

CMOS Process = nFETs and pFETs are available

MOS Transistor Operation

• Use subthreshold operation as the fundamental case

• Allows intuition across sub-VT and above-VT operation

• Sub-VT operation simplifies this 2D problem to 2 1D problems

Water Analogy of a MOSFET

Channel Current Dependence on Gate Voltage

In linear scale, we have a quadraticdependence

In log-scale, wehave an exponentialdependence

MOSFET Channel Picture

MOS Capacitor Picture

MOSFET Channel Picture

Calculation of Drain Current

No recombination 02

2

dx

ndDn

ndx

dnqDJ

l

nnqD drainsource

n

ddC

SSC

V

V

0 l varies as VG

TSC usource en /

TdC udrain en /

n = Ax + B

RGdx

ndD

dt

dnn

2

20 0 0

(qDn / l) (e-( - Vs)/UT - e-( - Vd)/UT)

eeIIuVVuVV TdgTSg / /

0

MOSFET Current-Voltage Curves

1

/)(0

//)(0

///0

TSG

TdSTSG

TDTSTG

uVKV

uVuVKV

uVuVuKVDS

eI

eeI

eeeII

Saturation

4 TdS uV

eeIIuVVuVV TdgTSg //

0

1 //0

TSdTSg uVVuVVeeI

Channel Current Dependence on Gate Voltage

In linear scale, we have a quadraticdependence

In log-scale, wehave an exponentialdependence

Channel Current Dependence on Gate Voltage

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.910

-11

10-10

10-9

10-8

10-7

10-6

Gate voltage (V)

Dra

in c

urr

en

t (A

)

= 0.58680 Io = 1.2104fA

In linear scale, we have a quadraticdependence

In log-scale, wehave an exponentialdependence

Determination of Threshold Voltage

0.4 0.5 0.6 0.7 0.8 0.9 10.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Gate voltage (V)

Dra

in c

urre

nt /

sub

thre

shol

d fit

VT = 0.86

Drain Current --- Source Voltage

0.6 0.65 0.7 0.75 0.8 0.85 0.9

10-12

10-11

10-10

10-9

10-8

10-7

Gate voltage (V)

Dra

in c

urre

nt (

A)

UT = 25.84mV

= 0.545

Origin of Drain Dependencies

Increasing Vd effects the drain-to-channel region:

• increases depletion width

• increases barrier height

Cause of DIBL

Drain Characteristics

Current versus Drain Voltage

Current versus Drain Voltage

Current versus Drain Voltage

Not flat due to Early effect (channel length modulation)

Current versus Drain Voltage

Not flat due to Early effect (channel length modulation)

In BJTs --- Base Modulation Effects

Current versus Drain Voltage

Not flat due to Early effect (channel length modulation)

Id = Id(sat) (1 + (Vd/VA) )

or

Id = Id(sat) eVd/VA

In BJTs --- Base Modulation Effects

Drain Induced Barrier Lowering

Data taken from a popular 1.2m MOSIS process

Data taken from a popular 2.0m MOSIS process

MOSFET Operating Regions

End on mobilecharges in channel

End on fixedions in bulk

Field Lines fromgate charges

Below Threshold Above Threshold

Channelcurrent flows Diffusion Drift

Charge boundarycondition at source

Set by FermiDistribution

Cox((Vg-VT)-Vs)

= ln( 1 + e )((Vg - VT) - Vs)/UT

Qs = e( - Vs)/UT

Approximatesurface potential Vg ln(Qs)

(EKV modeling)

MOS-Capacitor Regions

Qs = ln( 1 + e )((Vg - VT) - Vs)/UTQs = e

( - Vs)/UT

Depletion ((Vg - VT) - Vs < 0)

Qs = e ((Vg - VT) - Vs)/UT

Inversion ((Vg - VT) - Vs > 0)

Qs = ((Vg - VT) - Vs)/UT

Surface potentialmoving from depletionto inversion

Band-Diagram MOSFET Picture

Band-diagrampicture moving from subthreshold toabove-threshold

Conduction band bends due to electrostatic force of the electrons moving through the channel

Physics Based Models: Channels

Utilizing the physics of physical medium (Si) to efficiently implement computation

n +

p-substrate

n +

l = Channel LengthDe pl e tion Lay er

Vds

Ec

Ec

What if Hodgkin and Huxley had known / understood MOSFET transistors when developing the original modeling…..

+ -

V

Out

side

Insi

de

+

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

+

+ +

+ +

+ +++

+ +

+ +

+ +

GateDrainSource

E K

E Na

C

Vme m

M Na

M K

[Farquhar and Hasler, 2004]