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.
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)
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.
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?
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.
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.
Fig. 2. Electronic energy bands for (a) metallic conductor
at T = 0o K; (b) insulator or intrinsic semiconductor at 0o K.
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 =
Boltzmann’s 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
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.
Fig. 3a. Electronic energy band for n-type semiconductor
(Ge) with donors only.
Fig. 3b. Electronic energy band for p-type semiconductor
(Ge) with acceptors only.