EE 60556: Fundamentals of Semiconductors Lecture Note

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EE 60556 Fundamentals of SemiconductorsLecture
Note 20 (11/11/09)Fermi level, carrier
distribution and band diagram

• Outline
• Last class determination of Ef.
• see Pierret Ch.4.2 and Ch.4.4.4 for the
  statistical derivation of Fermi-Dirac
  distribution for Fermions and why gD and gA are
  introduced.
• What else can we learn from electron distribution
  function (or a given Fermi level)? Pretty much
  everything else!
• Band diagram basics (you will learn all the rest
  about band diagram in the Device class next
  semester!)

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Organization of Fundamentals of Semiconductors
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T-dependence of n or p
Freeze out region N? lt ND (nltND) Extrinsic
region N? gt ND gt ni (nND) Intrinsic region
ND lt ni (nni)

• - A Hall effect measurement in the freeze out
  region ? ED or EA
• A Hall effect measurement in the intrinsic
  T-region ? Eg
• A Hall effect measurement in the extrinsic
  T-region ? dopant concentration

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Ef determination its T-dependence
Intrinsic
Freeze-out/extrinsic T-region
Extrinsic T-region
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Distribution function and DOS ? system properties
The electron distribution function n(E) as a
function of energy (energy on the vertical
axis). Figure 2.17
Homework Question
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The most essential fundamentals in electrical
engineering Q, e, V, E
DP on parallel plate capacitors
Variation on parallel plate capacitors
integration
Differentiation
Q
Q
E-field
E-field
V
V
(electron) Energy
(electron) Energy
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Energy band diagram (Energy real space)
Superpose E-K on energy band diagram
For non-degenerate semiconductors, the whole
conduction band collapse to one energy level EC
with NC states (the effective conduction band
density of states) and the whole valence band
collapse to one energy level EV with NV states,
as shown in class. ? It makes sense to draw EC
and EV only in the band diagram
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How do I understand the superposition of E-K
diagram onto E-r band diagram? Real space and
momentum space (velocity space in classical
mechanics) are entirely two different spaces. We
can understand using the following example my
maximum running speed is 10 m/second (I am fast!
?), this maximum speed is the same no matter
where I am, in New York, South Bend, or Sydney!
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Recall when an object falls due to gravity (no
friction), its total energy does not change,
instead, its potential energy decreases and
converts to its kinetic energy. It is the same
here. Electric field does not change the total
energy of electrons, magnetic field does not
either, and other forces are negligible. The
most important way to lose energy for electrons
is to scatter with phonons or atom vibration.
EF
At thermal equilibrium the Fermi level in the
system is flat! Sketch potential V (volt), total
energy Etotal (eV), kinetic energy K.E. (eV),
potential energy P.E. (eV), electrical field E
(V/cm), charge distribution, carrier
concentration n p (cm-3), degenerately doped or
not?
This is the net charge!
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• Connect a piece of uniformly non-degenerately
  doped n-type semiconductor to a battery, as
  shown.
• Sketch its band diagram, indicating EC,EV, EF
• Sketch the carrier concentration
• What is the direction of electron flow?
• Sketch the electron total energy assuming the
  electron does not suffer any scattering event
  from one end to the other end of the
  semiconductor (this is call ballistic transport!)
• Sketch the kinetic energy of a ballistic
  electron.
• What happens if the electron scatters with
  impurities, phonons, defects and etc? (next
  class!)