bubble is the absence of fluid. The motion of the bubble can be described more

concretely as a movement of the fluid around it. When the bubble moves one way, there

is a flow of fluid in the other direction. However, the “movement” of the bubble is much

more noticeable than the motion of the fluid itself. Semiconductor engineers and

physicists treat holes as though they were particles as real as electrons.

Holes resemble bubbles

Holes move

36.13 - Doping

Doping: Increasing the availability of

conducting electrons or holes by adding

impurities to a material like silicon.

Commercial semiconductors are doped. This is thoroughly frowned upon in the

Olympics, but quite a desirable thing to do in a semiconductor foundry. Adding

impurities to a substance like silicon allows engineers to tailor its electrical properties

and makes it more useful in building devices like diodes and transistors.

We start with the diagram in Concept 1 showing silicon atoms in an ideal or equilibrium

state, perhaps at a temperature near absolute zero. The atoms fill their valence bands

by sharing electrons.

Now let’s consider the same pure silicon, but at room temperature. The average thermal

energy of the atoms has increased. This increase in energy means some electrons will

have enough energy to spontaneously make the energy jump from the valence to the

conducting band.

In fact, in absolute terms, a large number of electrons will make the jump. A cubic

centimeter of silicon contains 5×10^22 atoms, and 2×10^23 valence electrons. At room

temperature ( 293 K), you will find about 1×10^10 electrons in the conducting band in this

volume of silicon. Since they have left the valence band, you will find an identical

number of holes. On the one hand, this is a vast number (10,000,000,000 electrons

and an equal number of holes). On the other hand, it is extremely small compared to

the total number of electrons: About one electron out of every 1013 valence electrons

has become a conducting electron.

One out of 1013 is a small fraction, less than semiconductor engineers desire. To

increase the number of conducting electrons and holes, the silicon is doped. In doping,

impurities are added to the silicon to increase its ability to conduct current. Arsenic and

phosphorus are common elements that are added to increase the number of available

conducting electrons, while hole-increasing elements include gallium and boron.

Arsenic and phosphorus atoms both have five valence electrons, one more than silicon

has. When an arsenic atom takes the place of a silicon atom in the atomic lattice, four of

its valence electrons fit easily into the covalent bonds and in essence become members

of the valence band of the adjacent silicon atoms. The fifth electron, however, enters

the conduction band since there is no room for it in the valence band.

In Concept 2, you see an arsenic (As) atom and its “fifth” electron. When it is doped with

an element like arsenic, the semiconductor is called an n-type semiconductor. The “n”

stands for negative, since the charge carriers supplied by the dopant are negative. The

“extra” electrons are called donor electrons.

To facilitate the flow of current, an engineer may want a material with holes: places for

those electrons to flow to. She would use an element like gallium or boron whose atoms

have just three valence electrons. When such an element replaces silicon in the atomic

lattice, it is one electron short. The result is a hole, as shown in Concept 3.

When it is doped with an element like gallium (Ga), the semiconductor is called a p-type

semiconductor. The “p” stands for positive, representing the fact that holes act like

positive charges when they move.

Arsenic is used to supply carrier electrons and gallium is used to supply holes. In

quantitative terms, the band gap separating the “fifth” arsenic valence electron from the

Pure silicon

Doping

Adding a different material to silicon

n-type: inserts extra electron

“Extra” electron readily moves to

conduction band

Creating holes with doping

p-type: an electron “short”

Provides destination for mobile

electrons

(^674) Copyright 2007 Kinetic Books Co. Chapter 36