Electronic structure, carrier generation and recombination

There are three popular ways to describe the electronic structure of a crystal. The first starts from single atoms. An atom has discrete energy levels. When two atoms come close each energy level splits into an upper and a lower level, whereby they delocalize across the two atoms. With more atoms the number of levels increases and groups of levels form bands. Semiconductors contain many bands. If there is a large distance between the highest occupied state and the lowest unoccupied space, then a gap will likely remain between occupied and unoccupied bands even after band formation.

A second way starts with free electrons waves. When fading in an electrostatic potential due to the cores, due to Bragg reflection some waves are reflected and cannot penetrate the bulk, that is a band gap opens. In this description it is not clear, while the number of electrons fills up exactly all states below the gap.

A third description starts with two atoms. The split states form a covalent bond where two electrons with spin up and spin down are mostly in between the two atoms. Adding more atoms now is supposed not to lead to splitting, but to more bonds. This is the way silicon is typically drawn. The band gap is now formed by lifting one electron from the lower electron level into the upper level. This level is known to be anti-bonding, but bulk silicon has not been seen to lose atoms as easy as electrons are wandering through it. Also this model is most unsuitable to explain how in graded hetero-junction the band gap can vary smoothly.

When ionizing radiation strikes a semiconductor, it may excite an electron out of its energy level and consequently leave a hole. This process is known as electron–hole pair generation. Electron-hole pairs are constantly generated from thermal energy as well, in the absence of any external energy source.

Electron-hole pairs are also apt to recombine. Conservation of energy demands that these recombination events, in which an electron loses an amount of energy larger than the band gap, be accompanied by the emission of thermal energy (in the form of phonons) or radiation (in the form of photons).

In some states, the generation and recombination of electron–hole pairs are in equipoise. The number of electron-hole pairs in the steady state at a given temperature is determined by quantum statistical mechanics. The precise quantum mechanical mechanisms of generation and recombination are governed by conservation of energy and conservation of momentum.

As the probability that electrons and holes meet together is proportional to the product of their amounts, the product is in steady state nearly constant at a given temperature, providing that there is no significant electric field (which might move carriers of both types from neighbour regions containing more of them to meet together) or externally driven pair generation. The product is a function of the temperature, as the probability of getting enough thermal energy to produce a pair increases with temperature.

The probability of meeting is increased by carrier traps—impurities or dislocations which can trap an electron or hole and hold it until a pair is completed. Such carrier traps are sometimes purposely added to reduce the time needed to reach the steady state.

Ex 1. Answer the following questions.

1. How many ways to describe the electronic structure of a crystal are there? Describe them.

2. What do semiconductors contain?

3. What model is the most unsuitable to explain how in graded hetero-junction the band gap can vary smoothly?

4. What is known as electron-hole pair generation?

5. What is apt to recombine?

6. What is determined by quantum statistical mechanics?

7. Is the product a function of the temperature or size?

8. What are impurities or dislocations which can trap an electron or hole and hold it until a pair is completed?

9. Why is such carrier traps sometimes purposely added?

10. What is electron-hole pairs constantly generated from?

Words to be memorized.