Moore’s law and the silicon revolution - The Computing Universe: A Journey through a Revolution - page 121

materials have their constituent atoms arranged in a regular array, like bricks
in a wall but in three dimensions. This regular pattern of atoms is called a
crystal lattice , and substances with such a structure are called crystalline solids .
Arranging all the atoms in a regular array has a dramatic effect on the allowed
energy levels for the atomic electrons. The way to understand the energy levels
of such crystalline materials was discovered by a Swiss physicist named Felix
Bloch. To find the allowed electron energy levels for any quantum mechanical
system, you need to solve the Schrödinger equation - a mathematical formula
as fundamental for the behavior of quantum objects as Newton's laws are for
classical objects. Solving this equation for an electron in the potential of a pos-
itively charged nucleus leads to definite, isolated energy levels. For electrons in
a potential corresponding to a regular lattice of positive ions, Bloch found that
instead of isolated energy levels, the allowed energy levels merged into several
“bands” of allowed energies. The discovery of such energy band structures pro-
vides the foundation for our understanding of the difference between metals,
semiconductor, and insulators. Figure 7.3 shows typical allowed energy band
structures for these three types of materials.
In a metal such as copper, the lowest energy band has many unfilled levels
and the conduction electrons can move freely into empty levels, gaining energy
when a voltage is applied and generating an electric current ( Fig. 7.3a ). At abso-
lute zero, the coldest possible temperature (-273.15 °C), the energy levels in the
bands would be filled up one electron at a time, according to the Pauli Principle
to give the minimum energy state (see the quantum theory primer at the end of
this chapter for more details). At room temperatures, the lattice ions have some

Fig. 7.2. A Landsat photograph of Silicon
Valley and San Francisco Bay. In 1971
journalist Don Hoefler ran a series of
articles in Electronic News under the
title “Silicon Valley USA” and the name
caught on.

Conduction
band

3P

Conduction
electrons

Large
energy gap

Small energy gap

Conduction
holes

Valence
band

3S

Energy levels
below this filled
at zero tempera-
ture

(a) (b) (c)

Fig. 7.3. Band structures of metals, insulators, and semiconductors. (a) Band structure of a typical
metal like sodium. There are many unfilled energy levels in the “3S” valence band for the conduction
electrons to occupy. At normal temperatures, only a few electrons will be excited into the almost
empty “3P” band. (b) In an insulator, the valence band is full and the gap between the valence and
conduction bands is too large for any significant number of electrons to jump across the gap with
normal thermal energy distributions. As a result, an insulator conducts electricity very poorly, if
at all. (c) In a semiconductor, the valence is almost full but there is only a small energy gap to the
mostly empty energy levels in the conduction band. At normal temperatures, some of the electrons
have enough thermal energy to be able to jump across this energy gap.