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    Ee 212 HMW 5

    Uploaded by

    Ekin Karaca
    This document contains a homework assignment on semiconductor devices and MOS modeling for an electrical engineering course. It includes 6 problems: [1] Filling in boxes in a diagram, [2] Drawing energy band diagrams and charge distributions for different bias conditions of a MOS capacitor, [3] Drawing an energy band diagram of an inversion layer in a MOS capacitor, [4] Providing information about an enhancement-type MOSFET characteristic curve, [5] Deriving expressions related to resistance, charge density, potential, and current in a MOSFET, and [6] Drawing the structure of a p-channel MOSFET and determining biasing voltage ranges for linear operation.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Ee 212 HMW 5

    Uploaded by

    Ekin Karaca
    112 views5 pages
    This document contains a homework assignment on semiconductor devices and MOS modeling for an electrical engineering course. It includes 6 problems: [1] Filling in boxes in a diagram, [2] Drawing energy band diagrams and charge distributions for different bias conditions of a MOS capacitor, [3] Drawing an energy band diagram of an inversion layer in a MOS capacitor, [4] Providing information about an enhancement-type MOSFET characteristic curve, [5] Deriving expressions related to resistance, charge density, potential, and current in a MOSFET, and [6] Drawing the structure of a p-channel MOSFET and determining biasing voltage ranges for linear operation.

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    EE_212_HMW_5

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    This document contains a homework assignment on semiconductor devices and MOS modeling for an electrical engineering course. It includes 6 problems: [1] Filling in boxes in a diagram, [2] Drawing energy band diagrams and charge distributions for different bias conditions of a MOS capacitor, [3] Drawing an energy band diagram of an inversion layer in a MOS capacitor, [4] Providing information about an enhancement-type MOSFET characteristic curve, [5] Deriving expressions related to resistance, charge density, potential, and current in a MOSFET, and [6] Drawing the structure of a p-channel MOSFET and determining biasing voltage ranges for linear operation.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    112 views5 pages

    Ee 212 HMW 5

    Uploaded by

    Ekin Karaca
    This document contains a homework assignment on semiconductor devices and MOS modeling for an electrical engineering course. It includes 6 problems: [1] Filling in boxes in a diagram, [2] Drawing energy band diagrams and charge distributions for different bias conditions of a MOS capacitor, [3] Drawing an energy band diagram of an inversion layer in a MOS capacitor, [4] Providing information about an enhancement-type MOSFET characteristic curve, [5] Deriving expressions related to resistance, charge density, potential, and current in a MOSFET, and [6] Drawing the structure of a p-channel MOSFET and determining biasing voltage ranges for linear operation.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 5

    1

    Middle East Technical University


    Electrical and Electronics Engineering Department
    EE 212-Semiconductor Devices and Modeling
    Homework (not to be collected)
    Due May 21, 2014

    1. Fill in the boxes given in the figure.



    2. Consider the following MOS capacitor Draw the energy band diagram (only on the
    semiconductor side) and charge distribution (on the metal and semiconductor sides)
    under the following conditions. Show Ei and EF on the energy band diagram and define
    the sources of semiconductor side charge on the charge distribution diagram.








    2




    Condition Energy Band Diagram Charge Distribution




    VG<0





    VT >VG>0
    (no inversion layer)





    VG >VT













    3
    3. Draw the energy band diagram of a MOS capacitor on n-type substrate at the onset of strong
    inversion under an applied bias of V. Include and label in your diagram the following:

    Metal Fermi Level: E
    FM

    Semiconductor (Bulk) Fermi Level: E
    FS

    Intrinsic Level: E
    i

    E
    C
    and E
    V

    Surface Potential:
    S
    Provide all the other necessary labels.
    The dashed lines below show the boundaries between metal-oxide and oxide-semiconductor.
















    Metal Oxide Semiconductor

    4. The following figure shows the characteristics of an enhancement type MOSFET. Provide the
    required information.


    MOSFET Type (n or p-channel):

    Threshold Voltage:

    Transconductance Parameter:
    4

    5. Consider the following MOSFET. Assume that VD is small enough to operate the device
    in the linear region.

    a) Write the expression for the resistance (R) of the elemental volume (with length x) in
    terms of x, electron mobility in the inversion layer (i), inversion charge per unit area (Q (x))
    and the other necessary parameters.






    b) Express the inversion layer charge per unit area at location x (Q(x)) in terms of oxide
    permittivity(),oxide thickness(tox),channel potential (V(x)), VGS and other necessary
    parameters.





    c) Express the potential drop (V) on the channel elemental volume (with length x) in terms
    of channel current (ID), tox , , V(x), VGS, i , x and the other necessary parameters.






    d) Derive the expression for the drain current (ID) in terms of tox , , VDS=VD, VGS, i , x and the
    other necessary parameters. You must use your result in part (c).









    R=
    R=
    R=
    V=
    V(x)=V
    D
    =V
    DS
    at x=L
    V(x)=V
    S
    =0 at x=0
    Threshold voltage=V
    T

    Channel thickness (depth) at x=h(x)
    R=
    Q(x)=
    5
    6. Draw the internal structure of a p-channel enhancement type MOSFET operating in linear region on
    the figure given below. Determine the range of the biasing voltage values (V
    GS
    and V
    DS
    ) to operate the
    transistor in linear region and fill in the boxes accordingly.

    V
    GS
    V
    DS
    D
    S
    G
    B
    v(0)=
    v
    ox
    (0)=
    v(L)=
    v
    ox
    (L)=
    v(x)=Potential at
    point x with respect
    to source
    v
    ox
    = Potential
    across the oxide
    layer
    V
    TP
    0


    a) The parameters of the transistor are: length of the channel (L), width of the channel (W), and the
    capacitance per unit area (C
    ox
    ). Express the average charge stored per unit length in the channel in terms
    of the transistor parameters and biasing voltages. Clearly show each step of your derivation. (Hint:
    Assume v(x) changes linearly across the channel and use its average value).

    b) Express the average drift velocity of the holes in the channel in terms of
    p
    , transistor parameters and
    biasing voltages. Clearly show each step of your derivation and use the hint given in part (a).

    c) Express I
    SD
    in terms of transistor parameters and biasing voltages.

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