Lecture 7

ETE411

Dr. Mashiur Rahman

The Energy Band and the Bond Model

Concept of the Hole

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.

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.

Metal

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.

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.

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.

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.

The Fermi-Dirac Probability Function

EXAMPLE 3.4

EXAMPLE 3.5