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  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    (impurity) - .

    - (Diffusion); (deep junction) .

    - (Ion Implantation); (shallow junction) .

    Main topics

    - (lattice) .

    - (diffusivity)

    (Impurity profiles).

    - (lateral diffusion) (device) .

    - SUPREM .

  • Semiconductor Materials Lab. Hanyang University

    Figure 6.1 (p. 105) Comparison of (a) diffusion and (b) ion-implantation techniques for the selective introduction of

    dopants into the semiconductor substrate.

    -

    (Diffusion)

    -

    ; / oxide source

    -

    (Ion Implantation)

    -

    ; Ion Beam

    -

    ,

    Chapter 6 Diffusion

  • Semiconductor Materials Lab. Hanyang University

    6.1

    Figure 6.2 (p. 106) Schematic diagram of a typical open-tube diffusion system.

    (quartz-tube furnace) - Dopant .

    - Si ; 800 1200 / GaAs ; 600 1000

    dopant .

    Si - P ; (B) .

    i i - N ; (As) (P) .

    (source)- (BN, As2O3, P2O5), (B2H6, AsH3, PH3 ),

    (BBr3, AsCl3, POCl3)- .

    Chapter 6 Diffusion

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    - / (P) .

    4POCl3 + 3O2 2P2O5 + 6Cl2 (1)

    2P2O5 + 5Si 4P + 5SiO2 (2)

    P2O5 glass-on-Si wafer , Si P .

    P Si , Cl2 .

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    GaAs .

    As (decomposition) (evaporation)

    As .

    - As (overpressure)

    - oxide capping layer(SiN) open-tube furnace

    GaAs dopant (Se) (Te) .

    P-type dopant: Zn (sealed-ampule) Zn-Ga-As ZnAs2

    , (open-tube) ZnO-SiO2 (Zn) .

    N-type dopant in GaAs: Se,Te

    Note

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    6.1.1

    Figure 6.3 (p. 107) Atomic diffusion mechanisms for a two-dimensional lattice.

    (a) Vacancy mechanism. (b) Interstitial mechanism.

    - (Vacancy Mechanism)

    - (Interstitial Mechanism) (: interstitialcy, crowdian mechanisms)

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    (3)

    F : dopant C : dopant .

    xCDF

    =

    Driving force of diffusion process is the conc. grad (C/x)

    F (C/x) , dopant

    () .

    Note

    D : (Diffusion coefficient / Diffusivity)

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    (host) (3) (1-D continuity eq.) ,

    (4)

    Dopant ,

    (5) : Ficks diffusion equation / Ficks law

    =

    =

    xCD

    xxF

    tC

    (5)

    =

    2

    2

    xCD

    tC

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    Figure 6.4 (p. 108) Diffusion coefficient (also called diffusivity)

    as a function of the reciprocal of temperature for (a) silicon and (b) gallium arsenide.

    Dopant .

    .

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    6.4 ,

    (6)

    D0 : cm2/s

    Ea : eV

    Ea dopant . Si GaAs 0.5~2 eV .

    Ea . Si GaAs 3~5 eV .

    Note

    =

    kTEDD aexp0

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    Ea Ea 2 eV .

    .

    ) Si GaAs Cu ( 6.4a b ).

    Ea Ea 3 eV .

    .

    ) Si GaAs As ( 6.4a b ).

    Note

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    6.1.2

    Dopant : (initial) (boundary) .

    (Constant Surface Concentration).

    - ,

    .

    - .

    dopant (Constant Total Dopant).

    - dopant ,

    .

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    (Constant Surface Concentration).

    t=0

    (7)

    dopant 0 (zero) ,

    (8a)

    C(x,0)=0

    C(x,t)=Cs

    (8b) C(,t)=0

    and,

    8(a) Cs : x=0 . . 8(b) .

  • Semiconductor Materials Lab. Hanyang University

    CONSTANT SOURCE DIFFUSION C (0, t ) = Cs C (x, 0) = 0 C (, t) = 0

    SOLUTION :

    erfc(x) = COMPLEMENTARY ERROR FUNCTION = 1 - erf(x)

    erf (0) = 0

    0

    erfc (x) dx =

    1

    dxd erf (x) =

    2 e-x

    2

    erf () = 1

    erf (x) = 2 e-a2da

    0

    --Fixed Concentration at Surface: Constant Source

    C(x,t) = Cs erfc[ ] x

    2 Dt

  • Semiconductor Materials Lab. Hanyang University

    ERROR FUNCTION PROFILES JUNCTION DEPTH

    TOTAL DOPANT IN Si

    C

    x

    Csub

    0 0

    C(x,t) dx = CS erfc 2 Dt

    x dx

    0

    2 CS Dt

    2 Dt CS

    erfc 2 Dt

    x d

    2 Dt

    x =

    =

    t) CSUBSTRATE = C (xj,

    xj = 2 D t erfc-1

    CS

    CSUB

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    Ficks ,( )

    (9) C(x,t)=Cs erfc

    Dt

    x2

    efrc : (complementary error function; 6.1 )

    Dt : (diffusion length)

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    Figure 6.5 (p. 111) Diffusion profiles.

    (a) Normalized complementary error function () versus distance for successive diffusion times.

    (b) Normalized Gaussian function ( dopant ) versus distance.

    . D

    .

    : . : .

    dopant .

    Note

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    dopant ,

    (10)

    (9) (10) ,( )

    ( ) ( )dxtxCtQ ,0

    =

    (11) ( ) DtCDtCtQ ss 13.12

    =

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    Q(t) 6.5a (). 2 , Cs .

    , Q(t) Cs

    Note

    Dt

    Dt

    C / x (gradient). (9) .

    (12) Dtxs

    tx

    eDt

    CxC 4/

    ,

    2=

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    dopant (Constant Total Dopant).

    (13b) C(,t)=0

    and,

    () dopant , dopant .

    (7) . ,

    (13a) ( ) StxC =

    ,0

    S : dopant .

    C(x,0)=0

  • Semiconductor Materials Lab. Hanyang University

    FINITE SOURCE DIFFUSION

    SOLUTION : GAUSSIAN PROFILE

    VARIES WITH TIME

    C (0, t ) = QT C (x, 0) = 0 C (, t) = 0

    0

    Csurface = C(0, t) = QT

    Dt

    QT

    Dt C(x, t) = exp( ) -x2 4Dt

  • Semiconductor Materials Lab. Hanyang University

    DIFFUSION PROFILES Erfc GAUSSIAN (constant source) (finite source)

    from S.K. Ghandhi, VLSI Fabrication Principles, Wiley Interscience 1983, P.142-4

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    ,( )

    (14) ( )

    =

    Dtx

    DtStxC

    4exp,

    2

    (Gaussian distribution).

    Dopant , dopant S .

    , x=0 (14) .

    (15) ( )Dt

    StxC

    =,

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    6.5b : dopant .

    .

    .

    Note

    (14) .

    (16) ),(2)(2 23,txC

    Dtx

    DtxS

    xC

    tx

    ==

    () x=0 x= 0(zero).

    : Dtx 2=

  • Semiconductor Materials Lab. Hanyang University

    Chapter 6 Diffusion

    (two-step) .