lecture 17

Lecture 17

OUTLINE• The MOS Capacitor (cont’d)– Small-signal capacitance

(C-V characteristics)

Reading: Pierret 16.4; Hu 5.6

S and W vs. VG (p-type Si)

)(for 1)(2

12

22

2 TGFBsiA

FBGox

ox

siAs VVV

qN

VVC

C

qN

VFB VT

VG

2FS:

)(for 1)(2

12 2

TGFBsiA

FBGox

ox

Si

A

SSi VVVqN

VVC

CqNW

accumulation depletion inversion0

VGaccumulation depletion inversion0

A

FSiT

)(2

qN

2εW

W:

VFB VT

EE130/230M Spring 2013 Lecture 17, Slide 2

Total Charge Density in Si, Qs(p-type Si)

invdepaccs QQQQ

VG


VFB VT

WqN AdepQ

VG


VFB VT

)( TGox VVC invQ

VGaccumulation

depletion inversion0

VFB VT

)( FBGox VVC accQ

VG

accumulation depletion inversion

0 VFB VT

Qinv

slope = -Cox


MOS Capacitance Measurement

G

s

G

GATE

dV

dQ

dV

dQC

vac

iac

C-V Meter

GATE

MOS Capacitor• VG is scanned slowly• Capacitive current due to vac is measured

dt

dvCi ac

ac

Semiconductor


MOS C-V Characteristics (p-type Si)

G

s

dV

dQC VG


VFB VT

Qinv

slope = -Cox

VG


VFB VT

C

Cox

Ideal C-V curve:


Capacitance in Accumulation (p-type Si)

oxG

acc CdV

dQC

• As the gate voltage is varied, incremental charge is added (or subtracted) to (or from) the gate and substrate. The incremental charges are separated by the gate oxide.

M O SQ

Q

Q

-Q

Cox


Flat-Band Capacitance(p-type Si)

• At the flat-band condition, variations in VG give rise to the addition/subtraction of incremental charge in the substrate, at a depth LD

– LD is the “extrinsic Debye Length,” a characteristic screening distance, or the distance where the electric field emanating from a perturbing charge falls off by a factor of 1/e

Si

D

oxFB

L

CC

11

A

SiD Nq

kTL

2

Cox CDebye


Capacitance in Depletion (p-type Si)

Sioxdepox

W

CCCC

1

111

• As the gate voltage is varied, the depletion width varies. Incremental charge is effectively added/subtracted at a depth

W in the substrate.

M O SQ

Q

Q-Q

Cox

W

Cdep

SiA

FBG

oxG

dep

qN

VV

CdV

dQC

)(21

2


Capacitance in Inversion (p-type Si)

CASE 1: Inversion-layer charge can be supplied/removed quickly enough to respond to changes in gate voltage.

Incremental charge is effectively added/subtracted at the

surface of the substrate.

M O SQ

Q

Cox

WT

oxG

inv CdV

dQC

Time required to build inversion-layercharge = 2NAo/ni , where o = minority-carrier lifetime at surface


Capacitance in Inversion (p-type Si)

CASE 2: Inversion-layer charge cannot be supplied/removed quickly enough to respond to changes in gate voltage.

Incremental charge is effectively added/subtracted at a depth WT in the substrate.

M O SQ

Q

WT

min

1)2(21

1

111

CqNC

W

C

CCC

SiA

F

ox

Si

T

ox

depox

Cox Cdep


Supply of Substrate Charge (p-type Si)

Accumulation: Depletion:

Inversion: Case 1 Case 2


MOS Capacitor vs. MOS Transistor C-V(p-type Si)

VGaccumulation depletion inversion

VFB VT

C MOS transistor at any f,MOS capacitor at low f, orquasi-static C-V

MOS capacitor at high fCmin

Cmax=Cox

CFB


Quasi-Static C-V Measurement(p-type Si)

The quasi-static C-V characteristic is obtained by slowly ramping the gate voltage (< 0.1V/s), while measuring the gate current IG with a very sensitive DC ammeter. C is calculated from IG = C·(dVG/dt)


VFB VT

C

Cmax=Cox

Cmin

CFB


Deep Depletion(p-type Si)

• If VG is scanned quickly, Qinv cannot respond to the change in VG. Then the increase in substrate charge density Qs must come from an increase in depletion charge density Qdep

depletion depth W increases as VG increases

C decreases as VG increases

VG

VFBVT

CCox

Cmin


MOS C-V Characteristic for n-type Si



VT VFB

CMOS transistor at any f,MOS capacitor at low f, orquasi-static C-V

MOS capacitor at high fCmin

Cmax=Cox

CFB

Examples: C-V Characteristics

Does the QS or the HF-capacitor C-V characteristic apply?

(1) MOS capacitor, f=10kHz

(2) MOS transistor, i=1MHz

(3) MOS capacitor, slow VG ramp

(4) MOS transistor, slow VG ramp

VG

VFBVT

C

Cox

QS

HF-Capacitor


Example: Effect of Doping• How would the normalized C-V characteristic below change if

the substrate doping NA were increased?

– VFB

– VT

– Cmin

VFBVT

C/Cox

1


Example: Effect of Oxide Thickness• How would the normalized C-V characteristic below change if

the oxide thickness xo were decreased?

– VFB

– VT

– Cmin


VFBVT

C/Cox

1

lecture 17

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