MOSFET Transistors

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MOSFET Transistors

• Wk 11

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MOSFET Energy Band Diagram

• The MOSFET energy band diagram combines the work
  function of the metal and the semiconductor work
  function and a gate voltage that must be applied
  for no electric field in the SiO2 Silicon Dioxide
  gate insulator. This voltage is referred to as
  the Flat band voltage.
• If there is surface charge /cm2 in the oxide
  silicon interface an addition term is present in
  VFB.

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MOSFET Energy Band Diagram 2

• Expressing the semiconductor work function ?s in
  terms of the electron affinity ?, Eg/2, and the
  doping for an p well the flat band voltage is
• For a n well the flat band voltage is

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MOSFET Oxide Capacitance COX n channel surface
inversion condition

• COX the oxide capacitance per unit area is
• The surface is considered inverted forming a n
  channel in an p well if the Fermi level goes from
  Ei-EF to Fn-Ei where Ei-EF Fn-Ei ?F the
  inversion potential is then 2 ?F where ?F is

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n channel depletion region for 2?F

• To invert the surface to form an n channel in a p
  well we start from the flat band voltage and
  apply the needed 2?F. This implies a depletion
  region from Poissons equation of W
• Associated with the depletion region is a total
  immobile negative charge per unit area Qd

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n channel VG at inversion

• Starting from the flat band voltage VFB to invert
  the surface requires 2?F creating a depletion W
  with charge QD that creates an Electric Field in
  the Silicon dioxide requiring additional gate
  voltage given by
• The gate voltage, the threshold voltage to invert
  the surface of a p well to create a n channel is

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p channel VG at inversion

• For a p channel in an n well inversion requires
  -2?F where ?F is
• Associated with the depletion region is a total
  immobile positive charge ND resulting in the VG
  threshold equation

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CGate capacitance two terminal model gate to
substrate contact

• The gate to substrate capacitance is often
  monitored in MOS production for process control.
  Monitors have large area to allow capacitance
  meter measurement.
• The gate to substrate capacitance for strong
  inversion at low frequency or the opposite
  condition of accumulation is just COX and allows
  TOX measurement for a given area capacitor.

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CGate capacitance two terminal model gate to
substrate contact 2

• For gate voltages in the transition range where
  the device is between accumulation and strong
  inversion and for strong inversion at high
  frequency (no thermally generated mobile
  accumulation charge available) the gate to
  substrate capacitance is the depletion
  capacitance in series with the oxide capacitance

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The gate to substrate capacitance when VG VFB
is the flat band capacitance CFB

• When the gate voltage is equal to the flat band
  voltage the majority charge variation has
  associated with if a length called the extrinsic
  (doped) Debye length
• Associated with the Debye length is a Debye
  capacitance CDebye. The flat band capacitance CFB
  is CDebye in series with COX