Analysis of CV-measurement Microsoft PowerPoint - CV2.ppt Created Date: 12/13/2006 10:19:42 AM

download Analysis of CV-measurement 

Microsoft PowerPoint - CV2.ppt Created Date: 12/13/2006 10:19:42 AM

of 26

  • date post

    16-Jun-2020
  • Category

    Documents

  • view

    1
  • download

    0

Embed Size (px)

Transcript of Analysis of CV-measurement Microsoft PowerPoint - CV2.ppt Created Date: 12/13/2006 10:19:42 AM

  • 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

    1 0

    2''

    MSg

    BS

    I

    IHF

    MIS

    U q

    kT U

    nq

    C

    C C

    Depl

    +−+

    =

    εε

    With depletion approximation

    ( )

    g

    HF

    MIS

    HF

    MIS

    S

    B

    Ud

    dC

    C

    q n

    Depl

    Depl

    ''

    3''

    0

    1

    εε −=

    IMISS

    BS

    S

    SHF

    S

    CCC

    kT

    q

    nkT

    kT

    q

    d C

    depl

    111

    1

    2

    2 0

    00

    −=

    == ϕ

    εεεε ''

    )1( ''

    0

    ''

    0 −== MIS

    I

    I

    S

    HF

    S

    S S

    C

    C

    CC d

    Depl

    εεεε

    )()( SSBB dfdnn ==

    BS

    HF

    MIS

    I

    nq

    C

    C

    C

    Ugd

    d I

    Depl εε0

    2'' 2

    2 =

      

       

    )( 2

    1 0

    2'' 2

    MSg

    BS

    HF

    MIS

    I U q

    kT U

    nq

    C

    C

    C I

    Depl

    +−=−   

       

    εε

    0.0 0.5 1.0 1.5 2.0 0

    5

    10

    15

    20

    25

    245.8 mV

    25.8 mV

    depletion

    depletion with U MS

    (n-Si, Al -0.22 V)

    linear Fit

    linear Fit

    Si

    SiO 2 d

    i =100nm

    nb=10 15

    cm -3

    (C i"/

    C " M

    IS )2

    -1

    |U gideal

    | [V]

    Slide 3

  • 0.0 0.5 1.0 1.5 2.0 0

    5

    10

    15

    20

    25

    245.8 mV

    25.8 mV

    depletion

    depletion with U MS

    (n-Si, Al -0.22 V)

    linear Fit

    linear Fit

    Si

    SiO 2 d

    i =100nm

    nb=10 15

    cm -3

    (C i" /C

    " M IS

    )2 -1

    |U gideal

    | [V]

  • 0.0 0.5 1.0 1.5 0

    5

    10

    15

    20

    25

    0.2

    0.4

    0.6

    0.8

    1.0

    1.2

    d R

    L Z [

    µ m

    ]

    Si

    SiO 2 d

    i =100nm

    nb=10 15

    cm -3

    (C i" /C

    " M IS

    )2 -1

    |U gideal

    | [V]

  • Doping profile

    With inversion approximation

    nB Iteration

    i

    B

    BS

    i

    B

    BSHF

    S

    n

    n kT

    nq

    n

    n kT

    nq C

    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

  • dWnNqdWqnQ C

    F

    DD

    F

    V

    A

    W

    W

    itit

    W

    W

    itit ∫∫ −+−= )('' [ ] ( )itititit DeVmnNn DDA 2 1

    =,,

    acceptors donors

    dW d

    dn qdW

    d

    dn q

    G jC

    d

    dQ C

    V

    D

    F

    V

    A

    W

    W

    it

    W

    W

    itit it

    it ∫∫ −−=−−= 000 ϕϕωϕ

    )( ''

    DADA itititititit GGGCCC +=+=

    0=++ itSg QQQ

    MS

    I

    it

    I

    S g U

    C

    Q

    C

    Q U +−−= 0ϕ

      

       =+ ''it

    S S

    I I Q

    dx

    d

    dx

    d ρεεϕεε 00

    same influence of both types

    quantitative point of view

    G

    itSMIS MIS

    G

    G

    dU

    d

    d

    dQ

    d

    dQG jC

    dU

    dQ 0

    00

    ϕ ϕϕω

    )( +−=−=

    S S C

    d

    dQ −=

    GI

    it

    I

    S

    G dU

    d

    Cd

    dQ

    Cd

    dQ

    dU

    d 0

    00

    0 111 ϕ

    ϕϕ ϕ

    )( −−+=

    charge balance

    voltage balance

    ωϕ it

    it it GjC

    d

    dQ −=−

    0

    nit occupied

    Nit total

  • 22

    2

    22

    2

    )()(

    )()(

    )())((

    ω ωω

    ω

    ω

    it itSI

    IitMIS

    it itSI

    it IitSIitSI

    MIS

    G CCC

    CGG

    G CCC

    G CCCCCCC

    C

    +++ =

    +++

    ++++ =

    CMIS

    GMIS

    CS

    CI

    Cit

    Git

    Folie 13

  • Determination of Cit, Git

    Shockley-Read-Hall (SRH-model)

    )()( ttptptnttn t nNpcpncnncnNnc

    dt

    dn −+−−−= 11

    1 2 3 4 nt occupied

    Nt total

    cn, cp catching coefficient for electrons and holes, respectively

    )exp( kT

    WW Nn tCC

    ∞∞ −−=1

    )exp( kT

    WW Np VtV

    ∞∞ −−=1 ACDC

    ttt

    sss

    ACDC

    ACDC

    nnn

    nnn

    ϕϕϕ +=

    +=

    += AC

    AC

    t

    tt nj dt

    dn

    dt

    dn ω==

    wc

    wt

    wv

    nt

  • SRH-model leads to

    [ ]( )

    [ ] [ ]( ) t

    gpgn

    itgpititgn

    W

    W

    it

    t

    gpgn

    itgpititgn

    W

    W

    it

    dW ppcnnc

    npcnNnc

    kt

    qG

    dW ppcnnc

    npcnNnc

    kt

    q C

    it

    it

    it

    it

    2

    11

    2

    2

    11

    2

    1

    1

    2

    1

    2

    1

    )()()(

    ))(

    )()()(

    )(

    ''

    ''

    ωτ ωτ

    ω

    ωτ

    ++++ +−

    =

    ++++ +−

    =

    )exp()( kT

    q ndxnn BIg

    0ϕ===

    )exp( kT

    q pp Bg

    0ϕ−= )()( 11

    1

    ppcnnc gpgn +++ =τ

    characteristic trap time constant

    [ ] ( )ititit D eVm

    nN 2

    1 =,

  • n-type semiconductor (interaction with conduction band)

    ( )

    ( ) t g

    ititg

    W

    W

    it

    t

    g

    ititg

    W

    W

    it

    dW nn

    nNn

    kt

    qG

    dW nn

    nNn

    kt

    q C

    it

    it

    it

    it

    2

    1

    2

    2

    1

    2

    1

    1

    2

    1

    2

    1

    )()(

    )(

    )()(

    )(

    ''

    ''

    ωτ ωτ

    ω

    ωτ

    ++ −

    =

    ++ −

    =

    [ ] ( )ititit D eVm

    nN 2

    1 =,

    ? 1nn

    n

    g

    g

    +

    itgit

    g

    g

    it NfN nn

    n n =

    + =

    1

    0)( 1 =−−= itnititgn it nncnNnc

    dt

    dn ACDC ititit

    nnn +=

    f g Fermi Dirac occupation function

    kT

    WW

    n

    nnn

    n f

    Ft

    g

    g

    g

    g − +

    = +

    = +

    = exp1

    1

    1

    1

    11

    )exp( kT

    WW Nn tCC

    ∞∞ −−=1

    )exp( kT

    q nn Bg

    0ϕ=

    )exp( kT

    WW Nn FCCB

    − −= ∞

    0ϕqWW tt −= ∞

    )( gititit fNnN −=− 1

  • borderline cases

    HF ∞→ω

    NF 0→ω

    00 →→ ω

    it it

    G C

    )()()(

    )()(''

    Ftit

    W

    W

    FtFtit

    Ftit

    W

    W

    tggit

    W

    W

    NF

    it

    WWNqdWWWWWNq

    dWWWkTN kt

    q dWffN

    kt

    q C

    it

    it

    it

    it

    it

    it

    ==−==

    −=−=

    ∫∫

    2

    1

    2

    22

    2

    1

    2

    1

    2

    1

    1

    �� ���

    δ

    δ

    [ ] ( )itit D eVm

    N 2

    1 =

    )( ''

    Ftit

    NF

    it WWDqC == 2

    [ ]

    [ ] 2

    2

    1

    1

    m N

    eVm D

    it

    it

    =

    =

    .0 negl Git → ω

    Folie 9

  • Discrete traps

    2

    2

    2

    2

    1

    1

    1

    1

    )(

    )(

    )(

    )(

    ''

    ''

    ωτ ωτ

    ω

    ωτ

    + −

    =

    + −

    =

    ggitit

    ggit

    it

    ffN

    kt

    qG

    ffN

    kt

    q C [ ] 2