KAHIBARO
Table of Contents
Between conductors and insulators
Semiconductors are materials whose electrical behavior lies between that of conductors and insulators. In a conductor, electric charges move easily. In an insulator, they hardly move at all. In a semiconductor, charge motion is possible, but it depends strongly on conditions such as temperature, light, and the presence of impurities.
This special middle behavior makes semiconductors extremely useful. They are the basic materials of modern electronics, including diodes, transistors, solar cells, and computer chips.
Why semiconductors are special
The key idea is that electrons in a solid are not free to have just any energy. Instead, allowed energies form bands. In semiconductors, the most important bands are the valence band and the conduction band.
The valence band is usually filled or nearly filled with electrons. The conduction band is higher in energy and is usually nearly empty. Between them is an energy gap called the band gap.
If the band gap is small enough, some electrons can gain enough energy to move from the valence band into the conduction band. Once in the conduction band, they can help carry electric current.
A semiconductor has a small but nonzero band gap.
If the band gap is too small or absent, the material behaves like a conductor.
If the band gap is very large, the material behaves like an insulator.
The band gap
The band gap is usually written as $E_g$. It is the energy difference between the top of the valence band and the bottom of the conduction band.
$$
E_g = E_{\text{conduction}} - E_{\text{valence}}
$$
For semiconductors, $E_g$ is typically of the order of about $1 \, \text{eV}$, though values vary from material to material.
A small band gap means that thermal energy at ordinary temperatures can excite some electrons into the conduction band. This creates mobile charge carriers.
Electrons and holes
When an electron leaves the valence band and moves into the conduction band, it leaves behind an empty state. This empty state is called a hole.
A hole behaves like a positive charge carrier. Even though it is not a real particle by itself, it acts like one in the solid. As neighboring electrons move to fill the empty place, the hole appears to move in the opposite direction.
So in a semiconductor, electric current can be carried by two kinds of carriers. These are conduction electrons and holes.
In semiconductors, current can be carried by both electrons and holes.
Intrinsic semiconductors
A pure semiconductor, with no intentional impurities, is called an intrinsic semiconductor. In such a material, electrons and holes are created in pairs. Every electron promoted to the conduction band leaves one hole in the valence band.
This means that in an intrinsic semiconductor, the number of conduction electrons equals the number of holes.
If we call these numbers $n$ and $p$, then for an intrinsic semiconductor,
$$
n = p
$$
The conductivity of an intrinsic semiconductor is usually not very large, but it increases strongly with temperature because more electrons gain enough energy to cross the band gap.
Temperature dependence
Semiconductors behave differently from metals when temperature changes. In a metal, increasing temperature usually makes it harder for electrons to move, so resistance increases. In a semiconductor, increasing temperature usually creates more charge carriers, so conductivity increases.
This happens because thermal energy helps electrons jump across the band gap.
For many semiconductors, higher temperature means higher conductivity.
This is opposite to the usual behavior of metals.
Comparison with conductors and insulators
The difference among conductors, semiconductors, and insulators can be understood mainly through the band gap.
| Material type | Band structure idea | Electrical behavior |
|---|---|---|
| Conductor | Valence and conduction bands overlap, or conduction band partly filled | Charges move easily |
| Semiconductor | Small band gap | Moderate conductivity, sensitive to temperature and light |
| Insulator | Large band gap | Very low conductivity |
Common semiconductor materials
Some important semiconductor materials are silicon and germanium. Silicon is the most widely used semiconductor in electronics because it is abundant, stable, and suitable for manufacturing.
Compound semiconductors also exist, such as gallium arsenide. These materials are especially important in optoelectronics and high speed devices.
| Material | Typical use |
|---|---|
| Silicon, Si | Computer chips, solar cells, transistors |
| Germanium, Ge | Early electronics, some detectors |
| Gallium arsenide, GaAs | LEDs, lasers, fast electronic devices |
Effect of light and energy input
Semiconductors are very sensitive to external energy. Light can excite electrons from the valence band to the conduction band if the photon energy is at least as large as the band gap.
If a photon has energy $E = hf$, then excitation can occur when
$$
hf \ge E_g
$$
This is why semiconductors are useful in light detectors and solar cells. Light creates electron hole pairs, and these carriers can then produce current.
A simple band picture
A useful mental picture is to imagine a lower filled band and an upper nearly empty band, separated by a small gap.
Conductivity in semiconductors
Electrical conductivity depends on both the number of charge carriers and how easily they move. In semiconductors, the conductivity can be written in a simplified form as
$$
\sigma = q \left( n \mu_n + p \mu_p \right)
$$
where $q$ is the magnitude of the electron charge, $n$ is the electron concentration, $p$ is the hole concentration, and $\mu_n$, $\mu_p$ are the mobilities of electrons and holes.
This formula shows that both types of carriers matter.
A basic conductivity formula for semiconductors is
$$
\sigma = q \left( n \mu_n + p \mu_p \right)
$$
Both electron concentration and hole concentration contribute to conduction.
Intrinsic excitation picture
In a pure semiconductor at low temperature, very few electrons are in the conduction band. As temperature rises, more electron hole pairs are created.
Relation to later topics
Semiconductors become even more useful when their properties are changed by adding small amounts of impurity atoms. That process is called doping, and it leads to p-type and n-type materials and to p-n junctions. Those topics are treated separately.
Here, the main point is that a semiconductor is a material with a small energy gap, capable of conducting through electrons and holes, and highly sensitive to temperature and light.
Key facts about semiconductors:
A semiconductor has a small band gap $E_g$.
Electrons can move to the conduction band and leave behind holes.
Current is carried by both electrons and holes.
Pure semiconductors have equal electron and hole concentrations, $n = p$.
Their conductivity usually increases with temperature.