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EE415/515 Fundamentals of Semiconductor Devices

Fall 2012

Lecture 10:MOS Capacitor

(Chapter 10.1, 10.2)

MOS capacitorAssume p-type substrate, i.e. N-channel device

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Capacitance/unit area

Charge/unit area

Metal ”gate”

MOS=metal-oxide-semiconductor

VCQ

tC

ox

ox

//

/

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Negative gate bias

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Positive gate bias

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Negative space charge region is depleted of holes → immobile negative acceptor ions

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Band-bending with applied bias:accumulation & depletion regions

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“Flat band” condition

Increased positive bias: “Inversion”

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“Inversion” layer:

EF>EFi → n-type → electrons

“N-channel”

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N-type substrate

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Accumulation, depletion, & p-channel inversion

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Surface potential φs, depletion width, & inversion

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i

aFFifp n

N

e

kT

e

EEln

voltagegate threshold thresholdInversion

2 when threshold"inversion " theDefine

2 :junctionpn sided-one Compare

layer charge space across potential

fps

a

ssd

s

eNx

incrdensity electron surface &

little changes

: thresholdbeyond bias Increase

ln44

th region widinversion :ldAt thresho

s

dT

i

a

a

s

a

fpsdT

x

n

N

e

kT

eNeNx

Ex 10.1 Find xdT for an oxide to p-type Si junction at 300K with Na=2x1015/cm3. Does xdT increase or decrease as Na increases?

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10

15

105.1

102ln0259.0ln

i

atfp

n

NV

3056.0 V

2/14

a

fpsdT eN

x

2/1

1519

14

102106.1

3056.01085.87.114

51029.6 dTx cm

or 629.0dTx m

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P-channel inversion threshold

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d

fnsdT

i

dfn eN

xn

N

e

kT

4 ln

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xdT variation with Na, Nd

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Surface charge density

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fpss

fpist

sst

sfpi

sfpis

FiFi

kt

enn

kt

en

kt

e

kt

en

kt

enn

kT

EEnn

2 and

ld,at threshoion concentratelectron

exp where

expexpexp

exp

density chargeinversion electron so

expion concentratElectron

Note ns incr rapidly with φs (gate voltage), so xdT approx constant

For ns=1016/cm3

at threshold

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Work function effects

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eχi ≈ 0.9eV for SiO2

Φm/ & χ/ “modified” for e- injection into oxide conduction band

Work function effects

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differencefunction tor work semiconduc-metal theis where

2 i.e.

2)()(

//00

0/

0/

ms

msfpg

msox

fpsg

ioxim

e

EV

eeE

eeeVee

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Ex 10.2 Find φms for Al-SiO2 φm/=3.20V and Si-SiO2 χ/=3.25eV.

Assume Eg=1.12eV and Na=1016/cm3.

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10

16

105.1

10ln0259.0ln

i

atfp

n

NV

347.0 V

fp

gmms e

E

2

347.056.025.320.3

957.0ms V

(Degenerate) polysilicon gates

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2

2

2

2

:npolysilicop :npolysilicon

E belowor E above 0.2eV-0.1possibly E practice,In or Degenerate

//ms

//ms

vcF

fpg

fpgg

fpg

fpg

vcF

e

E

e

E

e

E

e

E

e

E

EEE

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N-type substrate (negative bias)

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fn

gmms e

E

2 //

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Φms vs substrate doping for various gate materials

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Flat band voltage(=gate voltage for zero semiconductor band bending

i.e. for zero net space charge)

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mssox

ssoxox

soxG

mssox

V

VV

VV

V

)()(

voltagegateFor

: voltagegate zeroFor

00

00

Oxide chargeMay have Q/

ss/unit area trapped charge

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condition bandflat at the 0 since

and V i.e.

0VC i.e. , 0

:bandflat at charge oxidenet zeroFor

//

ox

/oxox

//

s

ox

ssmsFBG

ox

ss

ssssm

C

QVV

C

Q

QQQ

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Ex 10.3 Find VFB for a MOS capacitor with a n+ poly-Si gate and Na=2x1015/cm3, tox=4nm, Q/

ss=2x1010e/cm2. What is φms?

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From Figure 10.16, 03.1ms V

8

14

1040

1085.89.3

ox

oxox

tC

710629.8 F/cm 2 Then

ox

ssmsFB C

QV

7

1910

10629.8

106.110203.1

034.1FBV V

Threshold voltage=gate voltage for the inversion threshold

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) thresholdat the

0density electron inversion

:(Assumes

(max)

on conservati Charge

2or 2 :Threshold

///

dTaSDssmT

fpfns

xeNQQQ

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Threshold voltage

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fpox

SD

FB

msfpssSDox

ox

msfpox

ss

ox

SD

msfpox

mT

msfpoxTTN

mssoxsoxG

C

QV

QQt

C

Q

C

Q

C

Q

VV

VVV

2(max)

2(max)

2(max)

2

2

/

//

//

/

Ex 10.4 Find φms & VTN for Si MOS device at 300K with a p+

polysilicon gate, Na=2x1016/cm3, tox=8nm, Q/ss=2x1010/cm2.

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From Figure 10.16, 28.0ms V

We find

10

16

105.1

102ln0259.0ln

i

atfp n

NV

3653.0 V

2/14

a

fpsdT

eNx

2/1

1619

14

102106.1

3653.01085.87.114

510174.2 cm

dTaSD xeNQ max

51619 101744.2102106.1

810958.6 C/cm 2 Then

fpmsox

oxssSDTN

tQQV 2max

14

810198

1085.89.3

1080102106.110958.6

3653.0228.0

3653.0228.01539.0 TNV

16.1 V

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Depletion/enhancement modes

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Enhancement(heavy doping necessary)

Depletion

P-type substrate

N-type substrate

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Depletion

Enhancement

i

dfn

d

fnsdT

dTdSD

fng

mms

msfnssSDox

oxTP

n

N

e

kT

eNx

xeNQ

E

QQt

V

ln

4

(max)

2

2(max)

/

//

//

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Ex 10.5 Find VTN for n-type Si/SiO2 MOS capacitor at 300K for: p+ poly-Si gate, Nd=2x1016/cm3, tox=20nm, Q/

ss=5x1010/cm2. Determine the threshold voltage.Is it a depletion or enhancement mode device?

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From Figure 10.16, 06.1ms V

We find

10

16

105.1

102ln0259.0ln

i

dtfn n

NV

3653.0 V

2/14

d

fnsdT

eNx

2/1

1619

14

102106.1

3653.01085.87.114

510174.2 cm

fndSD eNQ max

51619 101744.2102106.1

810958.6 C/cm 2 Now

fnmsox

oxssSDTP

tQQV 2max

14

819108

1085.89.3

10200106.110510958.6

3653.0206.1

3653.0206.14495.0 TPV

or 12.0TPV V

Capacitance-Voltage Characteristics:Accumulation, depletion, & inversion modes

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ox

oxox t

CaccumulC

)(/

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C-V Depletion mode

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d

sSD

ox

oxox

ds

oxox

ox

SD

ox

ox

SDox

SDox

SDox

xC

tC

xtC

CC

CC

CCdeplC

CCdeplC

/

/

/

//

//

& since 1

)(

11

)(

1

C-V Inversion mode

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ox

ox

dTs

oxox

ox

tinvC

xtC

)( and changenot does xxinversion strongat and

minimum a reaches C(depl) and maximum, its reaches x inversion,At

/dTd

/min

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C-V characteristics

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a

s

s

oxox

oxFB

eNe

kTt

C

.

/

Ex 10.6 MOS capacitor: n+ poly-Si gate, Na=3x1016/cm3, tox=8nm, Q/

ss=2x1010/cm2. Find C/min/Cox & C/

FB/Cox.

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8

14

1080

1085.89.3

ox

oxox

tC

710314.4 F/cm 2

3758.0105.1

103ln0259.0

10

16

fp V

2/1

1619

14

103106.1

3758.01085.87.114

dTx

51080.1 cm Now

dTs

oxox

ox

xt

C

min

58

14

1080.17.11

9.31080

1085.89.3

810076.5 F/cm 2

We find

1177.010314.4

10076.57

8min

oxC

C

Now

a

st

s

oxox

oxFB

eN

Vt

C

1619

148

14

103106.1

1085.87.110259.0

7.11

9.31080

1085.89.3

710174.2 FBC F/cm 2

We find

504.010314.4

10174.27

7

ox

FB

C

C

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C-V for n-type substrate (p-channel)

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Low/high frequency

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At high frequencies, inversion electrons cannot respond, so C→Cmin(Inversion electrons come from minority carrier diffusion from p-type or EHP generation)

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Effect of fixed oxide charges Q/ss

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/ssFBB

/

Q with move )(V Curves

ox

ssmsFB C

QV

Interface charge effects

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Interface states:Negative charge on acceptor states if E<EF

Positive charge on donor states if E>EF

Charge can flow between substrate and states

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Effect of interface states on C-V

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Assignment #5

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9.4 10.79.15 10.179.27 10.249.29 10.30