Energy Band View of Semiconductors

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Energy Band View of Semiconductors
Conductors, semiconductors, insulators Why is
it that when individual atoms get close together
to form a solid such as copper, silicon, or
quartz they form materials that have a high,
variable, or low ability to conduct
current? Understand in terms of allowed, empty,
and occupied electronic energy levels and
electronic energy bands. Fig. 1 shows the
calculated allowed energy levels for electrons
(vertical axis) versus distance between atoms
(horizontal axis) for materials like silicon.
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Fig. 1. Calculated energy levels in the diamond
structure as a function of assumed atomic spacing
at T 0o K. (From Introduction to
Semiconductor Physics, Wiley, 1964)
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In Fig. 1, at right atoms are essentially
isolated at left atomic separations are just a
few tenths of a nanometer, characteristic of
atoms in a silicon crystal.

• If we start with N atoms of silicon at the
  right, which have 14 electrons each, there must
  be 14N allowed energy levels for the electrons.
  (You learned about this in physics in connection
  with the Bohr atom, the Pauli Exclusion
  principle, etc.)
• If the atoms are pushed together to form a
  solid chunk of silicon, the electrons of
  neighboring atoms will interact and the allowed
  energy levels will broaden into energy bands.

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• When the actual spacing is reached, the
  quantum-mechanical calculation results are that
• at lowest energies very narrow ranges of energy
  are allowed for inner electrons (these are core
  electrons, near the nuclei)
• a higher band of 4N allowed states exists that,
  at 0oK, is filled with 4N electrons
• then an energy gap, EG, appears with no
  allowed states (no electrons permitted!) and
• at highest energies a band of allowed states
  appears that is entirely empty at 0oK.
• Can this crystal conduct electricity?

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NO, it cannot conductor electricity at 0o K
because that involves moving charges and
therefore an increase of electron energy but we
have only two bands of states separated by a
forbidden energy gap, EG. The (lower) valence
band is entirely filled, and the (upper)
conduction band states are entirely empty. To
conduct electricity we need to have a band that
has some filled states (some electrons!) and some
empty states that can be occupied by electrons
whose energies increase.
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Metals, pure silicon at 0K and 300K, and doped
silicon

• A. Conductors such as aluminum and gold can
  conduct at low
• temperatures because the highest energy band is
  only partly
• filled there are electrons and there are empty
  states they can
• move into when caused to move by an applied
  electric field.
• B. Silicon at 0K cant conduct because the
  highest band containing
• electrons is filled.
• Pure silicon at room temp. is slightly conductive
  since thermal
• energy can raise some electrons to the mostly
  empty conduction
• band.
• Silicon doped with donors (like P or As) can
  conduct (and become
• n-type) better than pure silicon at room temp.
  since it doesnt take
• much energy to free a valence electron so it can
  enter the conduction
• band.
• Silicon doped with acceptors (like B) can conduct
  (and become
• p-type) at room temp. since it doesnt take much
  energy to free a
• valence electron and create a hole in the valence
  band.

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A. Metal B. Pure Si 0K C. Pure Si at 300K D.
n-type Si E. p-type Si
Conduction band



Donor level
Forbidden energy band (energy gap)
Acceptor level
-
-
-
Valence band