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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Fig. 2 shows the situation at 0o K for (left) a
metallic solid such as copper, and (right) a
semiconductor such as silicon. The metal can
conduct at 0o K because the uppermost band
contains some electrons and some empty available
energy states. The semiconductor cannot conduct
it is an insulator. If we raise the
temperature of the semiconductor, some electrons
in the filled valence band may pick up enough
energy to jump up into an unoccupied state in the
conduction band. Thus, at a finite temperature,
a pure (intrinsic) semiconductor has a finite
electrical conductivity.
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Fig. 2. Electronic energy bands for (a) metallic
conductor at T 0o K (b) insulator or intrinsic
semiconductor at 0o K.
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How much conductivity can a pure (intrinsic)
semiconductor exhibit? This depends on how much
thermal energy there is and the size of the
energy gap, EG

• Mean thermal energy is kT, where k
  Boltzmanns constant 1.38 x 10-23 J/K and T is
  the absolute temperature.
• In electron volts this is kT/qe, or 26
  millivolts for room temperature (300o K)
• For silicon, EG 1.12 eV at 300o K
• This leads in pure (intrinsic) Si to a carrier
  concentration ni 1010 carriers/cm3 at 300o K

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Adding Impurities (Doping) to Adjust
Carrier Concentrations

• Adjust carrier concentrations locally in
  semiconductor by adding easily ionized impurities
  to produce mobile electrons and/or holes
• To make silicon N-type
• Add valence 5 phosphorous (P) atoms to valence
  4 silicon. Fifth electron is easily freed from
  the atom by a
• little thermal energy (0.045 eV for phosphorous)
  to create (donate) a mobile electron. Fig. 3a
  shows the donor energy level just below bottom of
  conduction band.
• To make silicon P-type
• Add valence 3 boron (B) to silicon. An
  electron at the top of the valence band can pick
  up enough thermal energy to release it from the
  silicon so it attaches to a boron atom,
  completing its outer ring of electrons. In the
  band picture, Fig. 3b, this is represented by an
  acceptor. energy level 0.045 eV above the top of
  the valence band.

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Fig. 3a. Electronic energy band for n-type
semiconductor
(Ge) with donors only.
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Fig. 3b. Electronic energy band for p-type
semiconductor (Ge) with acceptors only.