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Threshold voltage of MOS transistor

By Barbara Hill,2014-03-21 15:05
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Threshold voltage of MOS transistorof,mos,MOS

Threshold voltage of MOS transistor:

~ The threshold voltage of a MOS transistor (Vth is V required to GS

    strongly invert the surface of the substrate under the gate.) is calculated

    like that of a MOS structure with one slight modification in Q B .

     2 q N |2 V|QsubsubFSB B

Where V is the source to bulk voltage. SB

~ For circuit analysis:

    VV;((|2V||2|) thT0FSBF

    qN2subsub(Where is called body effect coefficient = Cox

V = the threshold voltage with V =0 i.e. with out the body effect. T0SB

Depletion mode Versus Enhancement mode MOSFET:

    ~ If a MOSFET is on (i.e. in strong inversion) at zero bias then it is a

    depletion Mode MOSFET (it is normally ON).

    o We actually have to apply a V < V to turn off the NMOS GSth

     or a V > V for PMOS . GSth

    ~ If a MOSFET is normally off it is enhancement mode

    o Then for NMOS we have to apply a V > V to turn it ON GSth

    or a V < V to turn a PMOS ON. GSth

    Depletion NMOS Vth 0 Enhancement NMOS Vth >0

    Depletion PMOS Vth 0 Enhancement PMOS Vth < 0

Poly Gate MOSFET:

The gate of MOS transistors is usually made with polycrystalline Si, that is

    heavily doped (either P or N type).

    ~ In this case G depends on the type of poly Si

    ~ For N-type poly ; the Fermi level is in the conduction band ;

    = E E = G O FS EO

     = G SE E FC

    The flat-band voltage V: E FBV

    EgV[;]FBGSssF ; q2

    EgV;FBF q2

    ~ For P-type poly; the Fermi level is in the Valence band ;

    = E E = + Eg G O FS EO S E C

     E g G

    Hence:

    E E FV

    EEggV;[]FBssF ; qq22

    EgV;FBF q2

    16-3Ex1) An MOS transistor is made with a P-type substrate (Na = 10 cm)

    and a heavily doped P-type poly Si gate. 2Cox = 2 fF/µm . Calculate Vth and specify the type of the transistor

Sol:

    This is an NMOS transistor, since the type of substrate is p-type .

     0

    QQBOXVV;2thFBF CCOXOX

    16Na10

    Vln0.025ln0.345FT10 n10i

    EgVEg;[;]FBGSssF q2

     = - 0.345 + 0.55 = 0.19 v

     1916142 q N |2 |1.6102108.851012 QsubsubFB

    -82 = - 4.8 × 10 c/cm

    -8Vth = 0.19 + 0.69 + 4.8 × 10 = 1.12 V

the type is enhancement NMOS

Ex2) For the same transistor in [Ex1], if the Gate poly is N-type &

    -82 Q = 5x 10 c/cmCalculate Vth and specify the type of the transistor ox

    Sol:

= -.345 v , F

    EgV[;]FBssF q2

     = - 0.89 V , Q is the same. VBFB

    -884.8 10510

    Vth -0.89 ;0.69 ; ?0.21v -7-72 102 10

the type is Depletion NMOS

Ex3)

    For example 2, what is the type of the doping and its concentration

    required to make Vth = + 0.8v?

Sol.:

We want to increase Vth by about 1v ( i.e. make it harder to invert

     we need to make it more P-type => i.e. increase Na

    ~ By how much should we increase Na?

    Na affects : | | ln Na FF

    V:VlnNaNa also affects FBFB

    QNaNa affects . This is a bigger dependency B

    Ignore effects of Na on and => FVFB

     QBwe need to increase by 1 volt

    COX

    QB was?0.23v

    C OX

    we need it to be = 1.23 v ;

-72 Q = 1.23 Cox = 2.46 x 10 c/cm B

1722 q N |2 |Na2.58x10c/cm Fsubsub

16171616-3we alreadyhave 10 => we need to add 2.58x 10 10 = 2.48x 10 cm more acceptors.

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