This lecture discusses energy bands, bonds, and the differences between metals, insulators, and semiconductors. Insulators have a large band gap of 3.5-6eV, resulting in very few charge carriers at room temperature. Semiconductors have a smaller 1eV band gap, allowing their resistivity to be controlled over many orders of magnitude. The document also briefly introduces statistical mechanics and three probability distribution functions: Maxwell-Boltzmann for distinguishable particles, Bose-Einstein for indistinguishable particles with unlimited occupancy of states, and Fermi-Dirac for indistinguishable particles with single occupancy of states.
5. Metals, Insulators, and
Semiconductors
The band gap energy E, of an insulator is usually on the order of
3.5 to 6eV or larger, so that at room temperature, there are
essentially no electrons in the conduction band and the valence
band remains completely full. There are very few thermally
generated electrons and holes in an insulator.
6. Semiconductor
The bandgap energy may be on the order of 1 eV. This
energy-band diagram represents a semiconductor for T > 0 K.
The resistivity of a semiconductor, as we will see in the next
chapter, can be controlled and varied over many orders of
magnitude.
8. STATISTICAL MECHANICS
• In dealing with large numbers of particles, we
are interested only in the statistical behavior
of the group as a whole rather than in the
behavior of each individual particle.
9. Statistical Laws
• One distribution law is the Maxwell-
Boltzmann probability function. In this case,
the panicles are considered to be
distinguishable by being numbered, for
example, from I to N. with no limit to the
number of particles allowed in each energy
state. The behavior of gas molecules in a
container at Fairly low pressure is an example
of this distribution.
10. Bose-Einstein function
• The particles in this case are indistinguishable
and, again, there is no limit to the number of
particles permitted in each quantum state.
The behavior of photons, or black body
radiation, is an example of this law.
11. Fermi-Dirac probability function
• In this case, the particles are again
indistinguishable, but now only one particle is
permitted in each quantum state. Electrons in
a crystal obey this law. In each case, the
particles are assumed to be noninteracting.
