Lec_23 Effect of Substrate Bias VB and Channel Bias VC

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Transcript of Lec_23 Effect of Substrate Bias VB and Channel Bias VC

  • 1Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    ( ) SioxFBBG VVVVV ++=

    net bias across MOS

    MO

    p-Si

    VVG

    C

    inversionelectrons

    depletionregion

    VB

    n+n+

    Effect of Substrate Bias VB and Channel Bias VC

  • 2Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    ( )

    ( )s

    da

    OX

    daFBBG

    BCpSi

    XqNCXqNVVV

    VVV

    max2

    max

    21

    2

    ++=

    +=

    M O SiEiEfs

    q(VC-VB)

    Efn

    pq

    pq

    s

    daSi

    XqNV

    max2

    21

    =

    At the onset of strong inversion, where VG is defined as the threshold voltage

  • 3Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    At threshold: VG VB = VFB+Vox+VSi But VSi = 2|p| + (VC - VB ) => xdmax is different from no-bias case

    B

    SiSid qN

    Vx 2=max

    VT -VB = VFB + 2sqNB(2|F| + VC-VB)

    Cox + 2|F| + VC - VB

    Vox VSi

  • 4Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    Flat Band Voltage with Oxide charges

    VFB is the Gate voltage required to create no charge in the Si

    dxx

    xxCC

    QV

    oxx

    ox

    ox

    oxox

    fSMFB

    0

    )(1

    x = 0 x = xox

    M O S

    ox (x) Qf

    ox (x) due to alkaline contaminants or trapped charge

    Qf due to broken bonds at Si-SiO2 interface

  • 5Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    VT Tailoring with Ion Implantation

    Nsub

    Shallow implanted dopant profile at Si-SiO2interface (approximated asa delta function)

    Acceptor implant gives positive shift (+ VT) Donor implant gives negative shift - VTAlgebraic sign of VT shift is independent of n or p substrate !

    OX

    iT C

    QV =

    Qi = q implant dose in Si

  • 6Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    p-Si

    implanted acceptors

    NaSiO2

    Doping Profile After Implantation

    SiO2

    xdmax

    Q

    Qd

    d

    Qn

    p-Si

    (due to implanted acceptors)

    Charge Distribution for V G > VT

    * Valid if thickness of implanted dopants

  • 7Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    Summary : Parameters Affecting VT

    6

    7

    n+

    Na

    VB

    5

    1

    2

    4

    3

    Dopant implant near Si/SiO2 interface

    fOX Q& M

    xox

    VCQn n+

  • 8Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    + Qf or Qox

    B threshold implant

    As or P threshold implant

    Xox increases

    Xox increases

    M increases

    M decreases

    |VCB| increases

    |VCB| increases

  • 9Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    Summary of MOS Threshold Voltage (NMOS, p-substrate)

    Threshold voltage of MOS capacitor:

    Threshold voltage of MOS transistor:

    Note 1: At the onset of strong inversion, inversion charge is negligible and is often ignored in the VT expressionNote 2: VT of a MOSFET is taken as the VT value at source ( i.e., VC =VS)Note 3 : Qi = (q implant dose ) is the charge due to the ionized donorsor acceptors implanted at the Si surface. Qi is negative for acceptors and is positive for donors

    VT = VFB + 2sqNB(2|F|)

    Cox + 2|F| -

    QiCox

    VT = VFB + 2sqNB(2|F| + VC-VB)

    Cox + 2|F| + VC -

    QiCox

  • 10Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    Summary of MOS Threshold Voltage (PMOS, n-substrate)

    Threshold voltage of MOS capacitor:

    Threshold voltage of MOS transistor:

    * Yes, + sign for VC term but VC (

  • 11Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    Negligible electron concentration underneath Gate region; Source-Drain is electrically open

    High electron concentration underneath Gate region; Source-Drain is electrically connected

    VG < Vthreshold VG > Vthreshold

    Metal -Oxide-Semiconductor Transistor [ n-channel]

  • 12Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    MOSFET I-V Analysis

    n+ n+

    VS VGW

    VB=0

    VDID

    L

    Qn

    N-MOSFET

    In general, inversion charge Qn ( [VG-VT]) decreases from Source towardDrain because channel potential VC increases.

    VT increases

  • 13Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    Let VT defined to be threshold voltage at Source

    ( )

    =

    =

    +

    2VVVC

    )average(VVC)average(Q2

    VV~)average(V

    DSTGOX

    TGOXn

    DSTT [ This is an approximation ]

    ID = Wt (-q n vdrift)= W Qn vdrift

    Inversion layer thickness Inversion layer concentration

    Approximate Analysis

    Note: ID is constant for all positionsalong channel

  • 14Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    LVEvWith DSnndrift

    =

    DSDS

    TGOXD V2VVVC

    LWI

    =

    VDS

    ID

    Linear with VDSQuadratic with VDS

  • 15Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    VD saturation

    n+ n+

    VS=0

    VD

    Qn=0 at the drain

    Lateral E-field Electrons moves

    saturation velocity

    VDsat is defined to be the value of VDwith Qn=0 at drain.

    From Qn = Cox (VG -VT -VD), we get VDsat =VG-VT

  • 16Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

  • 17Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    VD

    ID

  • 18Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    DSDS

    TGOXn

    D VVVVC

    LWI

    =

    2

    MOSFET I-V Characteristics Summary

    For VD < VDsat

    ( )22 TGOXn

    DsatD VVCLWII ==

    For VD > VDsat

    Note: VDsat = VG - VT

  • 19Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    Ex

    SiO2inversionlayer

    Mobility of inversion charge carriers

    *Carrier will experience additional scattering at theSi/SiO2 interface

    *Channel mobility is lower than bulk mobility

    * (effective) is extracted from MOSFET I-V characteristics* Typically ~0.5 of (bulk)

  • 20Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    Parameter Extraction from MOSFET I-V

    (A) VT VDIDD

    S

    ( )

    .

    0

    221

    2

    '

    '

    modesaturationinisMOSFEToffpinchatisDrain

    VV

    VqNC

    VV

    drainatV

    VVVFor

    TG

    DpasOX

    pDFB

    T

    TGD

    =

  • 21Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    ( )2TDDsatD VVLWkII ==

    VDVT

    DI

    LkWslope=

    VG

    nCOX

  • 22Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    Alternative way to extract VT

    Measure ID versus VG for a fixed small VDS (say

  • 23Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    VDID

    VB(varies)

    VD

    VB =0 VB1 VB2

    VT0 VT1 VT2

    DI

    ( ) ( )

    OX

    as

    pSBp

    SBTSBT

    CqN

    V

    VwithVVwithV

    2

    22

    00

    =

    +

    =

    (B) Body Coefficient

  • 24Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    ID

    VD

    VG2

    VG1

    (C)

    VD

    ( ) DTGOXnD

    D

    DD

    TGOXnD

    VsmallforVVL

    WCVI

    VVVVCL

    WI

    =

    =

    2

    IDVG slope

    LWCOXn

  • 25Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    (D) Transconductance gm

    (a) For VDS VDsat

    DVfixedG

    Dm V

    Ig

    DSOXnG

    D

    DSDS

    TGOXn

    D

    VL

    WCVI

    VVVVCLWI

    =

    =

    2

    ( )

    ( )TGOXnG

    D

    TGOXn

    DsatD

    VVCLW

    VI

    VVCLWII

    =

    ==

    22

    ID

    VDS

    VG1+VG

    VG1

    VDsat

    [gm varies with VDS]

    [gmsat varies with VG]

  • 26Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    ID

    VDVDsat

    real

    ideal

    n+ n+Qn

    ( ) ( )1

    2

    )(01.01.0~

    12

    +=

    volttoTypically

    VVVkI DSTGDsat

    (E) Channel Modulation Parameter

  • 27Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    Short Channel Effect on VTVT

    idealanalysis

    Ldepletionchargecontrolledby gate.

    n+ n+

    VG

    pdepletion layer

    L

  • 28Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    n+ n+

    VS=0 VD=0

    Wo

    x

    WoXj+Wo

    Xj

    Xj

    Xj

    L

    L

    ( )[ ]

    +=

    +=

    =

    1212

    2

    2'22

    j

    oj

    jooj

    XWXL

    XWWXL

    xLL Note: Wo is xdmax

    Sameelectric potentialbecause of heavily doped n+

  • 29Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    fXW

    LX

    QQ

    WWLLNq

    j

    oj

    ideal

    actual

    oa

    +=

    =

    +

    =

    1211

    21

    Area of gate charge distribution

    Yau Model for short-channel effect.

  • 30Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    Implantation at low energySmall Dt.Minimize channeling and transient enhance diffusion

    To make f 1

    Xj

    Wo Increase Na

    L large

    S/D S/D

    L small

    S/DS/D

  • 31Professor N Cheung, U.C. Berkeley

    Lecture 23EE143 S06

    VT

    L

    Large VDS

    VDS ~ 0

    Effect of VDS on VT Lowering

    Large VDS Larger S/D depletion charge at the drain side Smaller depletion