Analysis of CV-measurement

From CV-measurements

Determination of

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

• CI dI or εεI

• estimation of threshold voltage

• doping profile

• density of interface states

• fixed oxide charge

• life time of minority charge carriers

Doping profile

)(2

10

2''

MSg

BS

I

IHF

MIS

Uq

kTU

nq

C

CC

Depl

+−+

=

εε

With depletion approximation

( )

g

HF

MIS

HF

MIS

S

B

Ud

dC

C

qn

Depl

Depl

''

3''

0

1

εε−=

IMISS

BS

S

SHF

S

CCC

kT

q

nkT

kT

q

dC

depl

111

1

2

20

00

−=

−

==ϕ

εεεε''

)1(''

0

''

0 −==MIS

I

I

S

HF

S

SS

C

C

CCd

Depl

εεεε

)()( SSBB dfdnn ==

BS

HF

MIS

I

nq

C

C

C

Ugd

dI

Deplεε0

2''2

2=

)(2

10

2''2

MSg

BS

HF

MIS

I Uq

kTU

nq

C

C

CI

Depl

+−=−

εε

0.0 0.5 1.0 1.5 2.00

5

10

15

20

25

245.8 mV

25.8 mV

depletion

depletion with UMS

(n-Si, Al -0.22 V)

linear Fit

linear Fit

Si

SiO2 d

i=100nm

nb=1015

cm-3

(Ci"/

C" M

IS)2

-1

|Ugideal

| [V]

Slide 3

0.0 0.5 1.0 1.5 2.00

5

10

15

20

25

245.8 mV

25.8 mV

depletion

depletion with UMS

(n-Si, Al -0.22 V)

linear Fit

linear Fit

Si

SiO2 d

i=100nm

nb=1015

cm-3

(Ci"/

C" M

IS)2

-1

|Ugideal

| [V]

0.0 0.5 1.0 1.50

5

10

15

20

25

0.2

0.4

0.6

0.8

1.0

1.2

dR

LZ [

µm

]

Si

SiO2 d

i=100nm

nb=1015

cm-3

(Ci"/

C" M

IS)2

-1

|Ugideal

| [V]

Doping profile

With inversion approximation

nB Iteration

i

B

BS

i

B

BSHF

S

n

nkT

nq

n

nkT

nqC

Inv

ln)ln(

''

4122

0

2

0

2 εεεε≈

−=

Pulsed CV

Influence of interface charges

Donor type occupied with electrons neutral

unoccupied positive

Acceptor type occupied with electrons negative

unoccupied neutral

FD-Statistic (Fermi-Dirac)

W>WF unoccupied

W<WF occupied

''

''

0

I

effgr

K

I

MSFBC

QU

C

QU −=−= φ

dWnNqdWqnQC

F

DD

F

V

A

W

W

itit

W

W

itit ∫∫ −+−= )('' [ ] ( )itititit DeVm

nNnDDA 2

1=,,

acceptors donors

dWd

dnqdW

d

dnq

GjC

d

dQ C

V

D

F

V

A

W

W

it

W

W

ititit

it ∫∫ −−=−−=000 ϕϕωϕ

)(''

DADA itititititit GGGCCC +=+=

0=++ itSg QQQ

MS

I

it

I

Sg U

C

Q

C

QU +−−= 0ϕ

=+ ''

itS

SI

I Qdx

d

dx

d ρεεϕεε 00

same influence of both types

quantitative point of view

G

itSMISMIS

G

G

dU

d

d

dQ

d

dQGjC

dU

dQ 0

00

ϕϕϕω

)( +−=−=

SS C

d

dQ−=

0ϕ

GI

it

I

S

G dU

d

Cd

dQ

Cd

dQ

dU

d 0

00

0 111

ϕϕϕ

ϕ)( −−+=

charge balance

voltage balance

ωϕit

itit G

jCd

dQ−=−

0

nit occupied

Nit total

22

2

22

2

)()(

)()(

)())((

ωωω

ω

ω

ititSI

IitMIS

ititSI

itIitSIitSI

MIS

GCCC

CGG

GCCC

GCCCCCCC

C

+++=

+++

++++=

CMIS

GMIS

CS

CI

Cit

Git

Folie 13

Determination of Cit, Git

Shockley-Read-Hall (SRH-model)

)()( ttptptnttnt nNpcpncnncnNnc

dt

dn−+−−−= 11

1 2 3 4nt occupied

Nt total

cn, cp catching coefficient for electrons and holes, respectively

)exp(kT

WWNn tC

C∞∞ −

−=1

)exp(kT

WWNp Vt

V∞∞ −

−=1ACDC

ttt

sss

ACDC

ACDC

nnn

nnn

ϕϕϕ +=

+=

+=AC

AC

t

tt njdt

dn

dt

dn ω==

wc

wt

wv

nt

SRH-model leads to

[ ]( )

[ ][ ]( ) t

gpgn

itgpititgn

W

W

it

t

gpgn

itgpititgn

W

W

it

dWppcnnc

npcnNnc

kt

qG

dWppcnnc

npcnNnc

kt

qC

it

it

it

it

2

11

2

2

11

2

1

1

2

1

2

1

)()()(

))(

)()()(

)(

''

''

ωτωτ

ω

ωτ

+++++−

=

+++++−

=

∫

∫

)exp()(kT

qndxnn BIg

0ϕ===

)exp(kT

qpp Bg

0ϕ−=

)()( 11

1

ppcnnc gpgn +++=τ

characteristic trap time constant

[ ] ( )ititit DeVm

nN2

1=,

n-type semiconductor (interaction with conduction band)

( )

( ) t

g

ititg

W

W

it

t

g

ititg

W

W

it

dWnn

nNn

kt

qG

dWnn

nNn

kt

qC

it

it

it

it

2

1

2

2

1

2

1

1

2

1

2

1

)()(

)(

)()(

)(

''

''

ωτωτ

ω

ωτ

++−

=

++−

=

∫

∫

[ ] ( )ititit DeVm

nN2

1=,

?1nn

n

g

g

+

itgit

g

g

it NfNnn

nn =

+=

1

0)( 1 =−−= itnititgnit nncnNnc

dt

dnACDC ititit nnn +=

fg Fermi Dirac occupation function

kT

WW

n

nnn

nf

Ft

g

g

g

g −+

=+

=+

=exp1

1

1

1

11

)exp(kT

WWNn tC

C∞∞ −

−=1

)exp(kT

qnn Bg

0ϕ=

)exp(kT

WWNn FC

CB

−−= ∞

0ϕqWW tt −= ∞

)( gititit fNnN −=− 1

borderline cases

HF ∞→ω

NF 0→ω

00 →→ω

itit

GC

)()()(

)()(''

Ftit

W

W

FtFtit

Ftit

W

W

tggit

W

W

NF

it

WWNqdWWWWWNq

dWWWkTNkt

qdWffN

kt

qC

it

it

it

it

it

it

==−==

−=−=

∫

∫∫

2

1

2

22

2

1

2

1

2

1

1

�� ���

δ

δ

[ ] ( )itit DeVm

N2

1=

)(''

Ftit

NF

it WWDqC == 2[ ]

[ ]2

2

1

1

mN

eVmD

it

it

=

=

.0 neglGit →ω

Folie 9

Discrete traps

2

2

2

2

1

1

1

1

)(

)(

)(

)(

''

''

ωτωτ

ω

ωτ

+−

=

+−

=

ggitit

ggit

it

ffN

kt

qG

ffN

kt

qC [ ]

2

1

mNit =

frequency dependent transformation

itSI

SI

gg

MIS

itSI

itSINF

MIS

SI

SIHF

MIS

CCC

CC

nc

fg

CCC

CCCC

CC

CCC

n++

+=

+++

=

+=

τ

)(( )( )

( )2

2

1

1

MIS

MIS

HF

MIS

NF

MISMIS

MIS

HF

MIS

NF

MISHF

MISMIS

CCG

CCCC

τωτω

ωω

τωω

+−

=

+−

+=

)(

)(

MIS

Max τωω 1

==

))(()(

)(

max

max

itSISI

itI

HF

MIS

NF

MISMIS

HF

MIS

NF

MISMIS

CCCCC

CCCCG

CCC

+++=

−=

+=

2

2

2

ωω

ω

maxωMIS

MIS

G

stepC

itMIS D

G~)( maxω

ωGV measurements at different frequencies

MS

I

it

I

Sg U

C

Q

C

QU +−−= 0ϕ

Determination of Dit,, Nit, from CV measurement

calculation of ideal curve

measurement of real curve

I

Sg

C

QU

ideal−= 0ϕ

MS

I

itgg U

C

QUUU

ideal+−=−=∆

''

2

''

''

00

)(1

I

Ftit

I

itit

I C

WWDq

C

C

d

dQ

Cd

Ud ===−=

∆ϕϕ

0

2 ϕd

Ud

q

CWWD I

Ftit

∆==

''

)(

axis to energy axis0ϕ

Flat band

B

CFC

FCCBg

n

NkTWW

kT

WWNnn

ln

)exp(

=−

−−==

∞

∞

00 =ϕ

Determination of Dit,, Nit, from CV measurement

MS

I

itgg U

C

QUUU

ideal+−=−=∆ neglect of UMS, (=konst)

''

''''''

''

I

git

I

git

I

it

I

it

I

it

C

fqNU

C

fqN

C

qn

C

Q

C

QU

=∆

−=−=−=−=∆

[ ]2

1

mNit =

Determination of fixed oxide charge

''

''

(I

oxiFMG

I

oxFB

C

qNWWU

C

qNU

==∆

=∆ Literature (but here Qinterchangeable included)

Only fixed charges

itSI

itSINF

MISCCC

CCCC

+++

=)(

NF-CV

S

NF

MIS

I

Iit C

C

C

CC −

−=

1

theoretically known

measurement

itit DC →

Berglund-Integral 000 )1( ϕϕ +−= ∫ g

I

NF

MIS dUC

CaxisWaxis −→−0ϕ

or from HF-CV

I

HF

MISS CCC

111−=

11

1111−−

−−

−=

I

HF

MISI

NF

MIS

itCCCC

C

So called

High-Low-Method

Problem: high leakage, RB-influence

RB in accumulation (Nicollian)

Substitution of RB: two frequency measurement (Yang)

222

2

)(1

MM

M

M

M

M

M

M

BGC

G

GC

G

C

G

R+

=

+

=ω

ω

ω

In Accumulation

But not valid for high leakage

( ) ( )

( )( ) ( )22

222

22

1

1

BMMB

MMBMMIS

BMMB

MMIS

RCGR

CGRGG

RCGR

CC

ωω

ω

+−+−

=

+−=

Measure

at two f

GMISCMIS

RB