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MOSFET Characteristics

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					            Qualitative Description
IDS as a function of VDS and VGS
                MOSFET Symbols




          MOSFET Characteristics


                         Dr DC Hendry




                        September 2007




                    Dr DC Hendry      MOSFET Characteristics
                          Qualitative Description
              IDS as a function of VDS and VGS
                              MOSFET Symbols


Outline I
  1   Qualitative Description

        Effect of VG on the Channel


  2   IDS as a function of VDS and VGS

        Resistive Mode

        Saturation Mode or Triode Mode

        Summary of MOSFET Equations


  3   MOSFET Symbols

                                  Dr DC Hendry      MOSFET Characteristics
                        Qualitative Description
            IDS as a function of VDS and VGS      Effect of VG on the Channel
                            MOSFET Symbols


Definition of W and L

  The variation of IDS versus VGS and VDS is a basic property of a
  MOS device. The values of L and W, the length and width, of the
  transistor channel directly affect IDS .




                                Dr DC Hendry      MOSFET Characteristics
                        Qualitative Description
            IDS as a function of VDS and VGS      Effect of VG on the Channel
                            MOSFET Symbols


Definition of W and L

  The variation of IDS versus VGS and VDS is a basic property of a
  MOS device. The values of L and W, the length and width, of the
  transistor channel directly affect IDS .



            W
        S           G               D




                    L


                                Dr DC Hendry      MOSFET Characteristics
                        Qualitative Description
            IDS as a function of VDS and VGS      Effect of VG on the Channel
                            MOSFET Symbols


Definition of W and L

  The variation of IDS versus VGS and VDS is a basic property of a
  MOS device. The values of L and W, the length and width, of the
  transistor channel directly affect IDS .



            W
        S           G               D




                    L


                                Dr DC Hendry      MOSFET Characteristics
                        Qualitative Description
            IDS as a function of VDS and VGS      Effect of VG on the Channel
                            MOSFET Symbols


Effect of VG on the Channel

  Suppose that both the source and the drain of an n-channel
  MOSFET are at ground, that is, 0V. Now consider the effect of
  varying the gate voltage VG .




                                Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS      Effect of VG on the Channel
                             MOSFET Symbols


Effect of VG on the Channel

  Suppose that both the source and the drain of an n-channel
  MOSFET are at ground, that is, 0V. Now consider the effect of
  varying the gate voltage VG .

  Suppose first that the gate voltage is negative, VG < 0.

                                 VG < 0
                   + + + + + + + +

       Source                                                 Drain




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS      Effect of VG on the Channel
                             MOSFET Symbols


Effect of VG on the Channel

  Suppose that both the source and the drain of an n-channel
  MOSFET are at ground, that is, 0V. Now consider the effect of
  varying the gate voltage VG .

  Suppose first that the gate voltage is negative, VG < 0.

                                 VG < 0
                   + + + + + + + +

       Source                                                 Drain

  The negative voltage on the gate attracts the positively charged
  holes causing then to collect beneath the thinox - this is referred to
  as accumulation.
                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS      Effect of VG on the Channel
                             MOSFET Symbols


VG > 0 but small

  The positive gate voltage now repels the majority holes from the
  area beneath the thinox.




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS      Effect of VG on the Channel
                             MOSFET Symbols


VG > 0 but small

  The positive gate voltage now repels the majority holes from the
  area beneath the thinox.


                                             VG > 0
                                - - - - - - - -

             Source               +         +      +         +           Drain




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS      Effect of VG on the Channel
                             MOSFET Symbols


VG > 0 but small

  The positive gate voltage now repels the majority holes from the
  area beneath the thinox.


                                             VG > 0
                                - - - - - - - -

             Source               +         +      +         +           Drain


  As holes are repelled from beneath the gate the negative acceptors
  of the p-type material are exposed. Essentially this is a depletion
  zone.

                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS      Effect of VG on the Channel
                             MOSFET Symbols


VG > VT 0 Inversion

  If VG is made sufficiently positive then enough electrons are drawn
  up to the thinox to give n-type semiconductor - this is inversion.




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS      Effect of VG on the Channel
                             MOSFET Symbols


VG > VT 0 Inversion

  If VG is made sufficiently positive then enough electrons are drawn
  up to the thinox to give n-type semiconductor - this is inversion.



                                            VG > VT 0
                                - - - - - - - -

             Source             -       -     -    -       -   -         Drain
                                    +        +         +       +




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS      Effect of VG on the Channel
                             MOSFET Symbols


VG > VT 0 Inversion

  If VG is made sufficiently positive then enough electrons are drawn
  up to the thinox to give n-type semiconductor - this is inversion.



                                            VG > VT 0
                                - - - - - - - -

              Source            -       -     -    -       -   -         Drain
                                    +        +         +       +


  The voltage VT 0 is referred to as the threshold voltage. There is
  now a conducting channel from source to drain of the MOSFET.

                                 Dr DC Hendry      MOSFET Characteristics
                        Qualitative Description   Resistive Mode
            IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                            MOSFET Symbols        Summary of MOSFET Equations


Modes of Operation


  The MOSFET, whether n-channel or p-channel, has three modes
  of operation, these are:




                                Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Modes of Operation


  The MOSFET, whether n-channel or p-channel, has three modes
  of operation, these are:

   1   Cutoff For VGS < VT 0 no conducting channel is formed and
       there is no current from source to drain. IDS = 0.




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Modes of Operation


  The MOSFET, whether n-channel or p-channel, has three modes
  of operation, these are:

   1   Cutoff For VGS < VT 0 no conducting channel is formed and
       there is no current from source to drain. IDS = 0.
   2   Resistive or Linear For VGS >= VT 0 and VDS < VGS − VT 0
       the current through the device is dependent, initially linearly,
       on VDS , and on VGS .




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Modes of Operation


  The MOSFET, whether n-channel or p-channel, has three modes
  of operation, these are:

   1   Cutoff For VGS < VT 0 no conducting channel is formed and
       there is no current from source to drain. IDS = 0.
   2   Resistive or Linear For VGS >= VT 0 and VDS < VGS − VT 0
       the current through the device is dependent, initially linearly,
       on VDS , and on VGS .
   3   Saturation or Triode For VGS >= VT 0 and
       VDS >= VGS − VT 0 the current through the device is
       dependent only on VGS .



                                 Dr DC Hendry      MOSFET Characteristics
                        Qualitative Description   Resistive Mode
            IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                            MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 1
  Assume that VGS >= VT 0 and that VDS < VGS − VT 0 . Since
  VGS >= VT 0 a conducting inversion layer is formed from the
  source to the drain.




                                Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description       Resistive Mode
             IDS as a function of VDS and VGS          Saturation Mode or Triode Mode
                             MOSFET Symbols            Summary of MOSFET Equations


Resistive Mode - 1
  Assume that VGS >= VT 0 and that VDS < VGS − VT 0 . Since
  VGS >= VT 0 a conducting inversion layer is formed from the
  source to the drain. Define the Channel Support Voltage as:


                          VCS = (VGS − VT 0 ) − V (x)                                   (1)

  where V (x) is the channel voltage at a distance x along the
  channel.

                                                   L



                                                   x
                                 Dr DC Hendry          MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 2


  Now assume that V (x) is linear in x (this is not actually true but
  for long channels is not too far off),




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 2


  Now assume that V (x) is linear in x (this is not actually true but
  for long channels is not too far off), so that V (x) can be written as
                                                   x
                                      V (x) =        VDS                            (2)
                                                   L




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 2


  Now assume that V (x) is linear in x (this is not actually true but
  for long channels is not too far off), so that V (x) can be written as
                                                   x
                                      V (x) =        VDS                            (2)
                                                   L
  The average value of the channel support voltage is then:
                                                              VDS
                           VCS = (VGS − VT 0 ) −                                    (3)
                                                               2




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 2


  Now assume that V (x) is linear in x (this is not actually true but
  for long channels is not too far off), so that V (x) can be written as
                                                   x
                                      V (x) =        VDS                            (2)
                                                   L
  The average value of the channel support voltage is then:
                                                              VDS
                           VCS = (VGS − VT 0 ) −                                    (3)
                                                               2
  Due to the assumption that VDS < VGS − VT 0 the channel
  support voltage is never zero.



                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 3


  The charge stored within the inversion layer is:

                                        Q = VCS Cg                                  (4)

  where Cg is the gate capacitance, which is:




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description       Resistive Mode
             IDS as a function of VDS and VGS          Saturation Mode or Triode Mode
                             MOSFET Symbols            Summary of MOSFET Equations


Resistive Mode - 3


  The charge stored within the inversion layer is:

                                        Q = VCS Cg                                      (4)

  where Cg is the gate capacitance, which is:

                                                   A   0 SiO2
                                      Cg =                                              (5)
                                                       tox
  where A is the area of the gate (= WL), 0 is the permittivity of
  free space, SiO2 is the relative permittivity of silicon dioxide and
  tox is the thickness of the thinox.



                                 Dr DC Hendry          MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 4

  The charge stored within the channel is driven by the electric field
  from the source to the drain.




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 4

  The charge stored within the channel is driven by the electric field
  from the source to the drain. The magnitude of that electric field
  is:
                                   VDS
                               E=                                  (6)
                                    L




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 4

  The charge stored within the channel is driven by the electric field
  from the source to the drain. The magnitude of that electric field
  is:
                                     VDS
                                E=                                 (6)
                                       L
  The resulting velocity of the electrons is then:

                                          ve = µe E                                 (7)




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 4

  The charge stored within the channel is driven by the electric field
  from the source to the drain. The magnitude of that electric field
  is:
                                     VDS
                                E=                                 (6)
                                       L
  The resulting velocity of the electrons is then:

                                          ve = µe E                                 (7)

  and so the time to cross from source to drain is:
                                                   L
                                             t=                                     (8)
                                                   ve



                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 5


  The current IDS is therefore:
                             Q
             IDS     =       t




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 5


  The current IDS is therefore:
                             Q
             IDS     =       t
                             Q   VDS
                     =       L µe L




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 5


  The current IDS is therefore:
                             Q
             IDS     =       t
                             Q   VDS
                     =       L µe L
                                                    VDS      A   0 SiO2   µe VDS
                     =         VGS − VT 0 −          2           tox        L2




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Resistive Mode - 5


  The current IDS is therefore:
                             Q
             IDS     =       t
                             Q   VDS
                     =       L µe L
                                                    VDS      A   µe VDS
                                                                 0 SiO2             (9)
                     =         VGS − VT 0 −          2             L2
                                                                 tox
                                                                      2
                                                                    VDS
                                    W
                     = Kp           L        (VGS −    VT 0 )VDS − 2




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description     Resistive Mode
             IDS as a function of VDS and VGS        Saturation Mode or Triode Mode
                             MOSFET Symbols          Summary of MOSFET Equations


Resistive Mode - 5


  The current IDS is therefore:
                             Q
             IDS     =       t
                             Q   VDS
                     =       L µe L
                                                      VDS      A     µe VDS
                                                                   0 SiO2              (9)
                     =         VGS − VT 0 −            2           tox L2
                                                                          2
                                                                        VDS
                                    W
                     = Kp           L        (VGS −        VT 0 )VDS − 2

  where
                                                   0 SiO2 µe
                                     Kp =                                             (10)
                                                     tox




                                 Dr DC Hendry        MOSFET Characteristics
                        Qualitative Description   Resistive Mode
            IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                            MOSFET Symbols        Summary of MOSFET Equations


Saturation Mode


  When VDS is increased above VGS − VT 0 the end of the channel
  near the drain is no longer inverted.




                                Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Saturation Mode


  When VDS is increased above VGS − VT 0 the end of the channel
  near the drain is no longer inverted. No further increase in current
  occurs. Setting VDS = VGS − VT 0 then gives:

                                               W (VGS − VT 0 )2
                        IDS(sat) = Kp                                               (11)
                                               L      2




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Saturation Mode


  When VDS is increased above VGS − VT 0 the end of the channel
  near the drain is no longer inverted. No further increase in current
  occurs. Setting VDS = VGS − VT 0 then gives:

                                               W (VGS − VT 0 )2
                        IDS(sat) = Kp                                               (11)
                                               L      2
  The current IDS is, in this approximation, independent of VDS .
  Amplifier circuits normally use FETs in saturation mode (also
  called triode mode for historical reasons)




                                 Dr DC Hendry      MOSFET Characteristics
                            Qualitative Description   Resistive Mode
                IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                                MOSFET Symbols        Summary of MOSFET Equations


Summary of MOSFET Equations




           0                                                       VGS < VT 0
          
          
          
          
          
          
  IDS =
          
          
          
          
          
          




                                    Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Summary of MOSFET Equations




           0                                                    VGS < VT 0
          
          
          
          
          
                                                      2
                                                      VDS
  IDS   =   Kp W
               L      (VGS − VT 0 )VDS −               2         VGS > VT 0 , VDS < VGS − V
          
          
          
          
          
          




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Summary of MOSFET Equations




           0                                                    VGS < VT 0
          
          
          
          
          
                                                      2
                                                      VDS
  IDS   =   Kp W
               L      (VGS − VT 0 )VDS −               2         VGS > VT 0 , VDS < VGS − V
          
          
          
          
                   (VGS −VT 0 )2
          
            Kp W
          
               L        2                                        VGS > VT 0 , VDS >= VGS −




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description   Resistive Mode
             IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                             MOSFET Symbols        Summary of MOSFET Equations


Summary of MOSFET Equations




           0                                                    VGS < VT 0
          
          
          
          
          
                                                      2
                                                      VDS
  IDS   =   Kp W
               L      (VGS − VT 0 )VDS −               2         VGS > VT 0 , VDS < VGS − V
          
          
          
          
                   (VGS −VT 0 )2
          
            Kp W
          
               L        2                                        VGS > VT 0 , VDS >= VGS −

  A similar set of equations apply to p-channel devices, but with the
  polarity of voltages reversed, and µe replaced by µh .




                                 Dr DC Hendry      MOSFET Characteristics
                       Qualitative Description   Resistive Mode
           IDS as a function of VDS and VGS      Saturation Mode or Triode Mode
                           MOSFET Symbols        Summary of MOSFET Equations


MOSFET Curves
 For an n-channel device with VT 0 = 0.8V the above curves are as
 follows:




                               Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS
                             MOSFET Symbols


nMOS Enhancement Devices
  There are a variety of symbols in use for these devices, the two
  most commonly found are:

               d

    g                    b

               s




                                 Dr DC Hendry      MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS
                             MOSFET Symbols


nMOS Enhancement Devices
  There are a variety of symbols in use for these devices, the two
  most commonly found are:

               d                    g     -        gate
                                    d     -        drain
                                    s     -        source
    g                    b          b     -        bulk (substrate)

               s




                                 Dr DC Hendry         MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS
                             MOSFET Symbols


nMOS Enhancement Devices
  There are a variety of symbols in use for these devices, the two
  most commonly found are:

               d                    g     -        gate
                                    d     -        drain
                                    s     -        source
    g                    b          b     -        bulk (substrate)

               s

                    d

        g


                    s            Dr DC Hendry         MOSFET Characteristics
                         Qualitative Description
             IDS as a function of VDS and VGS
                             MOSFET Symbols


nMOS Enhancement Devices
  There are a variety of symbols in use for these devices, the two
  most commonly found are:

               d                    g     -        gate
                                    d     -        drain
                                    s     -        source
    g                    b          b     -        bulk (substrate)

               s

                    d            This symbol is most com-
                                 monly used for digital cir-
        g                        cuits.


                    s            Dr DC Hendry         MOSFET Characteristics
                        Qualitative Description
            IDS as a function of VDS and VGS
                            MOSFET Symbols


pMOS Enhancement Devices
  Again two symbols are in common usage:

              d

   g                    b

              s




                                Dr DC Hendry      MOSFET Characteristics
                        Qualitative Description
            IDS as a function of VDS and VGS
                            MOSFET Symbols


pMOS Enhancement Devices
  Again two symbols are in common usage:

              d                    g     -        gate
                                   d     -        drain
                                   s     -        source
   g                    b          b     -        bulk (substrate)

              s




                                Dr DC Hendry         MOSFET Characteristics
                        Qualitative Description
            IDS as a function of VDS and VGS
                            MOSFET Symbols


pMOS Enhancement Devices
  Again two symbols are in common usage:

              d                    g     -        gate
                                   d     -        drain
                                   s     -        source
   g                    b          b     -        bulk (substrate)

              s


              d

   g


              s
                                Dr DC Hendry         MOSFET Characteristics
                        Qualitative Description
            IDS as a function of VDS and VGS
                            MOSFET Symbols


pMOS Enhancement Devices
  Again two symbols are in common usage:

              d                    g     -        gate
                                   d     -        drain
                                   s     -        source
   g                    b          b     -        bulk (substrate)

              s


              d       This symbol is most com-
                      monly used for digital cir-
   g                  cuits.


              s
                                Dr DC Hendry         MOSFET Characteristics

				
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