MOSFETs -An Introduction

MOSFETs - An Introduction

Sung June Kim

[email protected]

http://helios.snu.ac.kr

Chapter 17.

CONTENTS

• Qualitative Theory of Operation

• Quantitative I

D - V

D Relationships

• Subthreshold Swing

• ac Response

Qualitative Theory of Operation

• Assumption

– Ideal Structure

– Long Channel Enhancement-Mode

– MOSFET=MOS-Capacitor + 2 pn junctions

– n - channel (p-type substrate)

V D = 0 Case

• When V

G £ V

T , very few electrons in the channel.

an open circuit between the n+ region

• When V

G > V

T ,

– Inversion layer is formed

– The conducting channel (induced “n-type” region, inversion layer) connects the D & S

– V

­ the pile up of electrons­ conductance ­

\ V

determines the maximum conductance – Thermal equilibrium prevails, and I

D

=0

• The V

D is increased in small steps starting from V

= 0 D

– The channel acts like a simple resistor – I

µ V

– The reverse bias junction current is negligible

– voltage drop from the drain to the source starts to negate the inverting effect of the gate

– V

­ Depletion of the channel­ # of carriers¯ conductance¯ slope-

over in the IV

• Pinch - off (V

D = V

Dsat )

– Disappearance of the channel adjacent to the drain

• The slope of the I

D

-V

D

becomes approximately zero(Point B)

• Post-pinch-off (V

D > V

Dsat )

– The pinched-off portion widens from just a point into a depleted channel section

D ^L

– The pinched-off section absorbs most of the voltage drop in excess of V

Dsat

– For D L << L, the shape of the conducting region and the potential across the region do not change Constant I

D

– For D ^{L ~ L, I}

D

will increase with V

D

> V

Dsat

• General form of the I

D - V

D ( D L << L )

– For V

G

£ V

T

, I

D

» 0 – For V

G

>V

T

, transistor action: I

D

is modulated by V

G

– V

> V

Dsat

: saturation region – V

< V

Dsat

: linear(triode) region

I D - V

D Characteristics

The slope increases with

V

V

increases with V

Quantitative I

D - V

D Relationships

• Effective Mobility

: Impurity Scattering

+ Lattice Scattering

+ Surface Scattering

• Effective Mobility

( )

ò ò

(y) x

y x

n

n

c

n(x,y)dx

)dx (x,y)n(x,y

=

0

0 m

m

¯

®

­

® surface scattering m

G

­®

– V more carriers closer to the interface higher

electric field

dy V d

V C

W

E WQ

I V

V C

Q

T G

o n

n N

D T

G o

N

f f m

m f

) (

(y) (y)

) (

(y)

- -

= -

=

® -

- -

@

• Square - Law Theory

– VD < V

• A drift current is dominant

At an arbitrary point y

) ( _{G T}

o N

N semi

gate

V V

C Q

Q Q

Q

- -

@

-

@ -

=

Integrating

ú û ù ê

ë

é - -

=

® ( ) 2

2 D D

T G

o n D

V V V

L V C I W m

f f

m _ò - -

ò ₀ ^L I _D dy = W _n C _{o 0} ^V

( V _G V _T ) d

– V

³ V

Dsat

• I D is approximately constant

( ) ²

2

2

0 )

( )

(

) 2 (

T G

o n Dsat

T G

Dsat

Dsat T

G o

N

Dsat Dsat

T G

o n Dsat

V L V

C I W

V V

V

V V

V C

L Q

V V V

L V C I W

-

=

-

=

= -

- -

=

ú û ù ê

ë

é - -

=

m

m

• Subthreshold transfer characteristics

– At weak inversion, diffusion current dominates

– In long channel MOSFETS the subthreshold current varies exponentially with V

G

and is independent of V

D

provided V

D

> a few kT/q

G

S

V

Q is exponentia l function of

where

exp

where

) exp(

1

÷ ø ç ö

è æ

ú û ù ê ë

é - -

µ µ

»

kT - qV

=Q Q

kT qV L

Q L

-Q I Q

I

D S

D

D S

D S diff

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 10

10

10

10

10

10

10

D ra in C u rr e n t [A ]

Gate Voltage [V]

Subthreshold swing

[ ]

D G

G t D

I V

mV/dec dV

I S d

in change

decade a

for

in change

=

= log 1

S

slope 1

=

17.3 a.c. Response(skip)

• C

(C

gd

): The interaction between G and the channel charge near S(D)

• C

,C

gdp

: parasitic or overlap capacitances

• Small-signal equivalent circuit

G S

D S

in MOSFET out

G

S

D

S v

+

- v

+

-

g

v

g

G

S

D

S v

+

- v

+

-

g

v

g

C

C

•A capacitor behaves like an open circuit at low frequencies.

• I

(V

,V

) + i

= I

(V

+ v

, V

+v

)

• i

= I

(V

+ v

, V

+v

) - I

(V

,V

)

( ) ^{( )}

g G V

D d

D V D d

g G V

D d

D V D G

D D g

G d D

D

V v v I

V i I

V v v I

V V I

V I v

V v V

I

D G

D G

¶ + ¶

¶

= ¶

\

¶ + ¶

¶ + ¶

= +

+ , ,

ce conduc

mutual or

ce c

transcondu V

g I

ce conduc

channel or

drain V the

g I

t cons G V

D m

t cons D V

D d

D G

tan tan

tan

tan tan

L L

=

=

¶

= ¶

¶

= ¶

g m d

d

d g v g v

i = +

\

G

S

D

S v

+

- v

+

-

g

v

g

i

• Table 17.1

) (

O n

d

V V V

L C

g = Z m - -

Below pinch-off (V

≤V

) Above pinch-off (V

>V

)

0

d

= g

D O n

m

V

L C g Z m

=

( V

V

)

L C

g = Z m -

• At the higher operational frequencies encountered in practical applications, the circuit must be modified to take into account capacitive coupling between the device terminals.

• The overlap capacitance is minimized by forming a thicker oxide in the overlap region or preferably through the use of self aligned gate procedures. è C

is typically negligible.

G

S

D

S v

+

- v

+

-

g

v

g

C

C

• 17.3.2. Cutoff Frequency

The f

be defined as the frequency where the MOSFET is no longer amplifying the input signal under optimum conditions.

à Value of the output current to input current ratio is unity

Dsat D

D n o

m T

in out

g m out

g o g

gd gs

in

V V

L if V C

f g i i

v g i

v C f

j v

C C

jw i

£

=

=

\

=

»

@ +

=

2 2

2 1

) 2

( )

(

p m p

p

Small Signal Characteristics

• g d vs. V

G (V

D =0)

– Extrapolating the linear portion of the g

d

- V

characteristics into the V

axis and equating the voltage intercept to V

T

– Deduce the effective mobility from the slope

)

= ) (V -V

L (V C

= W

g _d m ^{n o} _{G T D} 0

– Diagnostic purposes in much the same manner as the MOS-C C-V

G

characteristics – Unlike the MOS-C , a low-frequency

characteristics is observed even for frequencies exceeding 1MHz

• Because the source and drain islands supply the minority carries

· Gate Capacitance vs. V _G (V _D =0)