CV-measurement

basics

MIS-capacitor

CMIS

GMIS

CV measurement

measurement of differential C

by small ac modulation of the

bias voltage (dc)

ω

MISMIS

G

G GjC

dU

dQ

−=

MISMISMIS GCjY += ω

qualitative point of view

Band diagram in general (here n-type!!!)

LFssaffIAM UUUUUU +++=−

Ideal:

•no work function difference

•no oxide charges

•no interface charges

•no current through insulator

•no tunnelingp-type!!!

band diagram

with no bias

Φm->Φm’

Φs-> Φs’

just for simplification of band diagrams

accumulation (Ug<0, p-type)

Small LDebey maxCCC IMIS =≅

depletion (Ug>0, p-type)

SI

SIMIS

CC

CCC

+

=

Series of CI and CD (=CS)

SI

SIMIS

CC

CCC

+

=

Inversion (Ug>>0, p-type)

definition:

IFFS UUU 22 ==

Carrier concentration of surface

=(inverted) carrier concentration

of substrate

Threshold voltage:

IF

I

SIFInThr U

C

QUUU 22

''

''

+=+=

Ug´>UThr

strong inversion

min

HF

MISMIS CC <

HF (typical 100kHz, 1MHz)

NF (typical <100Hz), quasi static

Minority carriers can follow the NF-signal

Inversion layer (small dimension)

maxCCC IInv

NF

MIS =≅

Minority carriers can not follow the HF-signal

further expansion of space charge region is screened by inversion layer

Pulsed CV (HF )

Pulsed increasing of bias voltage from accumulation to inversion. Formation of

inversion layer is inhibited.slide 20

slide 23

min

min

min CCC

CCC

SI

SI

Inv

HF

MIS =

+

=

HF/NF-CV for p and n-type semiconductor (n-channel, p-channel !!!)

Pulsed CV

slide 29

Charge distribution

Real world•difference in work function between semiconductor and metal, φMS

•fixed oxide charges Qf

unsaturated Si- or O-valences, result in positive Si-O-Complexes

•moveable ionic charges in the insulator Qm

impurities, should be avoided

•interface states Qit

dangling bonds, tension in the interface

centers of recombination can avoid in extreme a built-up of the inversion layer

00 >++= itmf QQQQmostly:

Band bending without any bias: ''

''

0

I

effgr

K

I

MSFBC

QU

C

QU −=−= φ

''

''

0

I

effgr

K

I

MSFBC

QU

C

QU −=−= φ

IF

I

SFBnThr U

C

QUU 2

''

''

++=

quantitative point of view

(of ideal MIS)

Voltage balanceindex

German L

english C

USUCF

x=0 x=dI

MSIg UUU ++= 0ϕ

Charge balance

0

0

=+++

���tiISg QQQQ

ideal

0

,

)()(

)(

ϕϕϕϕ

ϕχ

===

=−−Φ

dixx

orUalsoqUE

SSS

MSKMSCFSfafM

CFSSaffIgM

CFssaffIAM

EqqUqU

UUUUUU+−+−=−Φ

+++=−

ϕχ ,

“strenge Energieschreibweise”

Sg QQ −=

Poisson equation in the insulator

idealx I

II 00

2

2

=−=

∂∂

εερϕ

21 *)( cxcxI +=ϕ

I

S

I

SI

C

Q

C

QU −=−=

''

''

idealQdx

d

dx

dit

SS

II 0''

00 ==+

ρεεϕεε

dx

dc Iϕ

=1

''

SS

S Qdx

d

=ρεε 0

0

"

1 εε I

SQc −=

Poisson equation in the semiconductor

0

2

2

εερϕ

S

SS

x

−=

∂∂

)( DAS NnNpq +−−=ρ

)exp(kT

WWNn FC

C−

−=

)exp(kT

WWNp VF

V

−

−=

00 =∞= )()( SIS d ϕϕϕ)()( xqWxW SCC ϕ−= ∞

)()( xqWxW SVV ϕ−= ∞

)exp(kT

WWNn FC

CB

−

−= ∞

ABDBBulk NpNnn ===

)exp(kT

WWNp VF

VB

∞−

−=

)exp(kT

qnn S

B

ϕ

= )exp(kT

qpp S

Bϕ

−=2

iBB npnnp ==

−−−−=

∂∂

))(exp())(exp( 112

0

2

2

kT

q

n

n

kT

qn

q

x

S

B

iSB

S

S ϕϕ

εε

ϕ

Poisson equation in the semiconductor

charge in the semiconductor

))(exp()()exp(

*''

11

2

00200

0

00

−+−+−−

−=

kT

q

kT

q

n

n

kT

q

kT

q

nkTQ

B

i

BSS

ϕϕϕϕ

ϕϕεε

MS

I

Sg U

C

QU +−= 0ϕ

Differential capacity

MS

I

Sg U

C

QU +−= 0ϕ

ω

MISMIS

G

G GjC

dU

dQ

−=

SS C

d

dQ

−=

0ϕ

I

S

I

Sg

C

C

Cd

dQ

d

dU

+=−= 11

100 ϕϕ

Sg QQ −=

MIS

IS

IS

g

S

g

gC

CC

CC

dU

d

d

dQ

dU

dQ

=

+

=−= 0

0

ϕ

ϕ

0=MISGideal

CMIS

GMIS

CMIS

CSCI

HF-CV (n-type)

1

1

22

00

0

0

−−−

=

kT

q

kT

q

kT

q

nkTkT

qC BS

HF

S ϕϕϕ

εε

)exp(

)exp(''

MS

I

Sg U

C

QU +−= 0ϕ

Back view slide 9

HF ∞→ω

0

0

=−=

BpSHF

Sd

dQC |

ϕ

DC-Voltage with minorities!!!

I

HF

S

I

HF

SHF

MISCC

CCC

+

=

)(

)(

0

0

ϕϕ

-5 -4 -3 -2 -1 0 1 2 3 4 55.0x10

-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

3.5x10-4

Si nb=10

15 cm

-3

SiO2 d

i=100nm

C" M

IS [

F/m

2]

Ugideal

[V]

NF

HF

Approximations HF-CV (n-type)

Debye

SBSHF

SLkT

nqC

FB

εεεε 00

2'' ==Flat band

)( B

HF

FB nfC == 00ϕ

I

HF

S

I

HF

SHF

MISCC

CCC

FB

FB

FB +

=

)(2

10

2''

MSg

BS

I

IHF

MIS

Uq

kTU

nq

C

CC

Depl

+−+

=

εε

Depletion 100 −<

kT

q

kT

q ϕϕ

exp

Inversion

)ln(

''

122

0

2

−

=i

B

BSHF

S

n

nkT

nqC

Inv

εε

const

CC

CCC

I

HF

S

I

HF

SHF

MIS

Inv

Inv

Inv

=

+

=

)ln(

)(

i

B

iF

n

nkTq

WWq

Inv

Inv

2

2

0

0

=−

−=− ∞

ϕϕ

)( MSg

IHF

MIS

UUq

kT

CC

Acc

−−

+=

0

21

ϕ

Accumulation 100 −>>

kT

q

kT

q ϕϕexp

IMIS CCUg =↑↑

NF-CV (n-type)

−+−+−−

−−−−

=

11

11

22

00200

020

0

kT

q

kT

q

n

n

kT

q

kT

q

kT

q

n

n

kT

q

nkTkT

qC

B

i

B

i

BS

NF

S

ϕϕϕϕ

ϕϕ

εε

)exp()()exp(

)exp()()exp(''

MS

I

Sg U

C

QU +−= 0ϕ

Back view slide 9

NF 0→ω

0ϕd

dQC SNF

S −=

DC-Voltage with minorities!!!

I

NF

S

I

NF

SNF

MISCC

CCC

+

=

)(

)(

0

0

ϕϕ

with minorities!!!

-5 -4 -3 -2 -1 0 1 2 3 4 55.0x10

-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

3.5x10-4

Si nb=10

15 cm

-3

SiO2 d

i=100nm

C" M

IS [

F/m

2]

Ugideal

[V]

NF

HF

Approximations NF-CV (n-type)

NF

MIS

NF

MIS

NF

MIS deplFBAccCCC ,,

Accumulation, Flat band, Depletion

Inversionnp >

Somehow similar to HF

)exp(''

kT

q

n

n

kT

nqC

B

iBSNF

SInv 22

00

2 ϕεε

−=

)( MSg

INF

MIS

UUq

kT

CC

Inv

−−

+=

0

21

ϕ

IMIS CCUg =↑↑

-4 -2 0 25.0x10

-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

3.5x10-4

Si nb=10

15 cm

-3

SiO2 d

i=100nm

C" M

IS [

F/m

2]

Ugideal [V]

HF

HF accumulation

HF depletion

HF inversion

NF

NF inversion

-5 -4 -3 -2 -1 0 1 2 3 4 55.0x10

-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

3.5x10-4

Si: nb=10

15 cm

-3 (n-type) p

b=10

15 cm

-3 (p-type)

SiO2: d

i=100nm

C" M

IS [

F/m

2]

Ugideal

[V]

n-type semiconductor

NF

HF

p-type semiconductor

NF

HF

-10 -8 -6 -4 -2 0 2 45.0x10

-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

3.5x10-4

nb=10

17 cm

-3

nb=10

16 cm

-3

nb=10

15 cm

-3

Si

SiO2 d

i=100nm

C" M

IS [

F/m

2]

Ugideal

[V]

NF

HF

-10 -8 -6 -4 -2 0 2 4

5.0x10-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

3.5x10-4

di=300nm

di=200nm

di=100nm

di=300nm

di=200nm

di=100nm

Si nb=10

15 cm

-3

SiO2

C" M

IS [

F/m

2]

Ugideal

[V]

NF

HF

From CV-measurements

Determination of

• type of semiconductor in the substrate (p or n)

• CI dI or εεI

• estimation of threshold voltage slide 9

• doping profile

• density of interface states

• fixed oxide charge

• life time of minorities