MOSFET I-V characteristics: general mosfet i-v and c-v.pdf¢  MOSFET capacitance-voltage...

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Transcript of MOSFET I-V characteristics: general mosfet i-v and c-v.pdf¢  MOSFET capacitance-voltage...

  • 1

    The channel current is: I = V (q nS μ W) /L = V q μ W (ci/q) × (VGS – VT) /L

    MOSFET I-V characteristics: general consideration

    The current through the channel is VI

    R =

    where V is the DRAIN – SOURCE voltage

    Here, we are assuming that V

  • 2

    Key factors affecting FET performance (for any FET type):

    In most MOSFET applications, an input signal is the gate voltage VG and the output is the drain current Id. The ability of MOSFET to amplify the signal is given by the output/input ratio: the transconductance, gm = dI/dVGS.

    MOSFET transconductance

    L I and gm

    High carrier mobility μ and short gate length L are the key features of FETs

    I = μ W ci × (VGS – VT) V /L

    gm = V μ W ci /L

    (V is the Drain – Source voltage)

    From this:

    μ I and gm

  • 3

    Modern submicron gate FET

    V-groove quantum wire transistor

    Source Drain

    Gate

    Operating frequency – up to 300 GHz

    2 μm

  • 4

    When no drain voltage V is applied, the entire channel has the same potential as the Source, i.e. VCH = 0. In this case, as we have seen, nS = (ci/q) × (VGS – VT)

    Drain current saturation in MOSFET

    - + G

    Semiconductor

    The gate length L

    DS

    + -

    V

    VGS

    where VGS is the gate – source voltage and VT is the threshold voltage

    When the drain voltage V is applied, the channel potential changes from VCH = 0 on the Source side to VCH= V on the drain side. In this case, the induced concentration in the channel also depends on the position.

  • 5

    Drain current saturation in MOSFET

    - + G

    Semiconductor

    The gate length L

    DS

    + -

    V

    VGS

    With the drain voltage V is applied, the actual induced concentration in any point x of the channel depends on the potential difference between the gate and the channel potential V(x) at this point. This is because this local potential difference defines the voltage that charges the elementary gate – channel capacitor. On the source end of the channel (x=0, VCH=0): nS(0) = (ci/q) × (VGS – VT). On the drain end of the channel (x=L, VCH= V): nS(L) = (ci/q) × (VGS – VT - V) < nS(0) At any point between source and drain,

    nS(L) < nS(x) = (ci/q) × [VGS – VT – V(x)] < nS(0)

  • 6

    L

    nS

    V=0

    VGS > VT

    x

    Drain current saturation in MOSFET

    V1 > 0

    V2 > V1

    V3 = VGS-VT

    G

    Semiconductor

    DS

    VVGS

    Id

    V

  • 7

    MOSFET Modeling

    1. Constant mobility model

    Assuming a constant electron mobility, μn, using the simple charge control model the absolute value of the electron velocity is given by,

    vn = μnF = μn dV dx

    With the gate voltage above the threshold, the drain current, Id, is given by

    Id = Wqμn dV dx

    ns Where W is the device width

    Rewriting, Where VGT = VGS – VT.

    d

    n i GT

    I dV dx

    W c V V( )μ =

    dV vs dx dependence represents a series connection of the elementary parts of MOSFET channel (for the series connection, voltages add up whereas current is the same).

  • 8

    Integrating along the channel, from x=0 (V=0) to x=L (V=VDS), we obtain:

    Id = W μn ci

    L VGT VDS

    Id = Wμnci

    L VGT −

    VDS 2

    ⎛ ⎝ ⎜

    ⎞ ⎠ ⎟ VDS

    For, VDS

  • 9

    Channel pinch off and current saturation Pinch off occurs when VG – VCH = VT at the drain end;

    nS (L) =0; the current Id saturates

    When,

    VDS = VSAT = VGS − VT

    where VSAT is the saturation voltage.

    The saturation (pinch off) current,

    Id = Isat = Wμnci

    2L VGT

    2

    Id = Wμnci

    L VGT −

    VDS 2

    ⎛ ⎝ ⎜

    ⎞ ⎠ ⎟ VDS

    From the Id – V dependence, at VDS=VSAT = VGT,

  • 10

    Transconductance

    Defined as

    gm = dId

    dVGS VDS From the equations for the drain current, Id, derived above, we find that

    gm = βVDS , for VDS VSAT

    ⎧ ⎨ ⎩ β = μnci

    W Lwhere

    High transconductance is obtained with high values of the low field electron mobility, thin gate insulator layers (i.e., larger gate insulator capacitance ci = εi/di), and large W/L ratios.

  • 11

    2. Velocity saturation model

    In semiconductors, electric field F accelerates electrons, i.e. the drift velocity of electron increases: v=μF

    However, at high electric fields this velocity saturates

    In modern short channel devices with channel length of the order of 1 µm or less, the electric field in the channel can easily exceed the characteristic electric, Fs field of the velocity saturation

    Fs = vs μ n

  • 12

    Electric field in the channel

    the electric field in the channel in the direction parallel to the semiconductor- insulator interface

    F = Id

    qμ nns V( )W

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    0 1 2 3 4 5

    P ot

    en tia

    l ( V

    )

    Distance (µm)

    1

    1.2

    0

    2

    4

    6

    8

    10

    12

    14

    16

    18

    0 1 2 3 4 5

    E le

    ct ric

    F ie

    ld (k

    V /c

    m )

    Distance (µm)

    1

    1.2

    0 1 2 3 4 5S ur

    fa ce

    C on

    ce nt

    ra tio

    n (1

    01 2

    1/ cm

    2 )

    Distance (µm)

    1

    1.2

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    1.4

    Potential, electric field, and surface electron concentration in the channel of a Si MOSFET for VDS = 1 and 1.2 V. L = 5 µm, di = 200 Å, µn = 800 cm2/Vs, VGS = 2 V, VT = 1 V.

    vn = μnF = μn dV dx

  • 13

    Once the electric field at the drain side of the channel (where the electric field is the highest) exceeds Fs, the electron velocity saturates, leading to the current saturation. In short-channel MOSFETs, this occurs at the drain bias smaller than the pinch-off voltage VDS = VGT.

    Field at drain

    Saturation condition, Fs = ISAT

    μ nci VGT − VSAT( )W

    d

    n i GT

    I dV dx

    W c V V( )μ =

    d x L

    n i GT DS

    IdVF L dx W c V V

    ( ) ( )μ=

    = = −

  • 14

    Saturation current versus gate-to-source voltage for 0.5 µm gate and 5 µm gate MOSFETs. Dashed lines: constant mobility model, solid lines: velocity saturation model.

  • 15

    MOSFET saturation current accounting for velocity saturation:

    Isat = gchVGT

    1 + 1 + VGT VL

    ⎝ ⎜

    ⎠ ⎟

    2

    where VL = FsL and the channel conductance gch = q µn ns W / L, where ns=ci VGT/q

    When FS L >> VGT (MOSFET with long gate or no velocity saturation):

    Isat = gchVGT

    1 + 1 + VGT VL

    ⎝ ⎜

    ⎠ ⎟

    2 2 ch

    sat GT g

    I V≈ Id = Isat = Wμnci

    2L VGT

    2

    (Expression obtained before on slide 9)

    When FS L

  • 16

    Source and drain series resistances. Source and drain parasitic series resistances, Rs and Rd, play an important role, especially in short channel devices where the channel resistance is smaller.

    Gate

    DrainSource

    I R s I Rd+ V +DS

    R s R

    d

    ddV =ds

    VGS = Vgs − Id Rs

    VDS = Vds − Id Rs + Rd( )

  • 17

    The measured transconductance (extrinsic)

    gm = dId dVgs Vds =const

    The intrinsic transconductance (VGS and VDS being intrinsic voltages)

    gmo = dId

    dVGS VDS=const

    Where gd0 is the drain conductance gdo = dId

    dVDS VGS =const

    These parameters are related as gm = gmo

    1 + gmo Rs + gdo R s + Rd( )

    Similarly, extrinsic drain conductance can be written as,

    gd = gdo

    1 + gmo Rs + gdo Rs + Rd( )

    In the current saturation region (VDS > VSAT), gd0 ≈ 0

  • 18

    The saturation current in MOSFET with parasitic resistances:

    Isat = gchoVgt

    1 + gchoRs + 1 + 2gchoRs + Vgt / VL( )2

    0

    20

    40

    60

    80

    100

    120

    140

    160

    0 0.5 1 1.5 2 2.5

    D ra

    in C

    ur re

    nt (m

    A )

    Drain-to-Source Voltage (V)

    0

    20

    40

    60

    80

    100

    120

    140

    160

    0 0.5 1 1.5 2 2.5

    D ra

    in C

    ur re

    nt (m

    A )

    Drain-to-Source Voltage (V)

    MOSFET output characteristics calculated for zero parasitic resistances and parasitic resistances of 5 Ω. Gate length is 1 µm

    where VL = FsL and gcho = ciVgtµnW/L.

  • 19

    MOSFET capacitance-voltage characteristics

    To simulate MOSFETs in electronic circuits, we need to have models for both the current-voltage and the capacitance-voltage characteristics. As MOSFETs is a three terminal device, we need three ca