KAHIBARO
Table of Contents
Basic Picture
In a semiconductor detector, radiation is detected because it gives energy to the material and creates mobile electric charges. These charges are not usually free electrons in the same way as in a metal. Instead, the radiation promotes electrons from a bound state into a conducting state. When this happens, two charge carriers appear together, an electron and a hole.
An electron is the excited particle that can move through the conduction band. A hole is the empty place left behind in the valence band, and it behaves like a positive charge carrier. The creation of this electron-hole pair is the fundamental microscopic step that allows semiconductor detectors to measure radiation.
Energy Bands and the Band Gap
To understand pair creation, it is useful to think of semiconductor electrons as occupying allowed energy bands. The lower band, called the valence band, is mostly filled. The higher band, called the conduction band, is mostly empty. Between them is an energy gap called the band gap, usually written as $E_g$.
If a particle or photon transfers enough energy to an electron, the electron can cross this gap and enter the conduction band. The vacancy left in the valence band is the hole.
The band gap is important because it sets the minimum energy needed for pair creation. However, the actual average energy required to produce one electron-hole pair is larger than just $E_g$, because some deposited energy goes into other processes inside the crystal, such as lattice vibrations.
How Radiation Produces Pairs
When radiation enters a semiconductor, it can lose energy by interacting with the atoms and electrons of the crystal. If enough energy is transferred locally, many electrons can be lifted into the conduction band. Each such event creates an electron-hole pair.
For example, if an incoming particle deposits energy $E$ in the detector, the approximate number of created pairs is
$$
N \approx \frac{E}{w},
$$
where $w$ is the average energy needed to create one electron-hole pair.
In common detector materials, $w$ is only a few electron volts. This is much smaller than the energy needed to create an ion pair in a gas detector. Because of this, semiconductor detectors can produce a large number of charge carriers from a small deposited energy, which is one reason they can achieve very good energy resolution.
Important relation:
$$
N \approx \frac{E}{w}
$$
Here, $N$ is the number of electron-hole pairs, $E$ is the deposited energy, and $w$ is the mean pair creation energy.
A larger deposited energy creates more pairs, and therefore usually a larger measurable signal.
Why the Pair Creation Energy Exceeds the Band Gap
A beginner might expect that one pair needs exactly the band gap energy $E_g$. In practice, the average required energy $w$ is larger than $E_g$. The reason is that not all deposited energy goes directly into lifting electrons across the gap.
Part of the energy is lost to the crystal as vibrational energy, often called phonons. Also, the interaction process can involve complicated cascades of secondary excitations before the energy finally appears as separated charge carriers.
So, although the band gap sets the threshold, the mean energy per produced pair is higher than that threshold.
Typical Values
Different semiconductor materials have different band gaps and different pair creation energies. Two very important detector materials are silicon and germanium.
| Material | Approximate band gap $E_g$ | Mean pair creation energy $w$ |
|---|---|---|
| Silicon | about $1.1 \, \text{eV}$ | about $3.6 \, \text{eV}$ |
| Germanium | about $0.67 \, \text{eV}$ | about $2.9 \, \text{eV}$ |
These numbers show clearly that $w > E_g$.
From Pair Creation to Signal
Once electron-hole pairs are created, they can be separated by an electric field inside the detector. The electrons drift one way and the holes drift the other way. Their motion induces a measurable electrical signal at the electrodes.
The present chapter focuses only on the creation step, but it is important to remember that pair creation alone is not enough. The charges must also survive long enough and be collected efficiently to produce a useful detector pulse.
Signal Size and Deposited Energy
Because the number of pairs is roughly proportional to deposited energy, the total collected charge is also proportional to deposited energy.
If $N$ pairs are created, then the total charge magnitude collected at one side is approximately
$$
Q = Ne,
$$
where $e$ is the elementary charge.
Combining this with the pair creation relation gives
$$
Q \approx \frac{E}{w} e.
$$
This proportionality is what makes semiconductor detectors especially useful for spectroscopy, where one wants to determine the energy of incoming radiation from the pulse size.
Key proportionality:
$$
Q \approx \frac{E}{w} e
$$
The collected charge is approximately proportional to the energy deposited in the detector.
Statistical Fluctuations
Electron-hole pair creation is a statistical process. Even if two particles deposit the same energy, the exact number of created pairs is not always identical. There are fluctuations.
These fluctuations are usually smaller than one would expect from completely random independent production. This reduced fluctuation is one reason semiconductor detectors often have excellent energy resolution. A full treatment of energy resolution belongs elsewhere, but the main point here is that stable and efficient pair creation helps produce sharp energy measurements.
Threshold for Detection
If the deposited energy is very small, only a few pairs may be created. Then the signal may be too weak compared with electronic noise. This means there is a practical lower limit to the detectable energy.
Because the pair creation energy is small, semiconductors can detect relatively low energies very effectively. This is one major advantage over some other detector types.
Summary Relation
Electron-hole pair creation is the central microscopic process in semiconductor radiation detectors. Radiation deposits energy in the crystal, electrons are excited across the band gap, and electron-hole pairs are produced. The average number of pairs is proportional to the deposited energy, with
$$
N \approx \frac{E}{w}.
$$
The pair creation energy $w$ is larger than the band gap $E_g$ because some energy is lost to other internal processes, especially lattice vibrations. Once created, the electron and hole can be separated by the detector electric field and collected as a measurable signal.
Essential facts to remember:
Electron-hole pairs are created when radiation gives enough energy to lift electrons into the conduction band.
One created pair consists of one free electron and one hole.
The mean number of pairs is
$$
N \approx \frac{E}{w}.
$$
The mean pair creation energy $w$ is greater than the band gap $E_g$.
Good semiconductor detection depends on creating many pairs from a small deposited energy.