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What is the energy band of semiconductors?

admin on August 3, 2021 0 Comments • Tags: #electronorbit #electronicenergylevel #semiconductorcrystal

Interpreted from the energy band point of view, the reason why the conductivity of a semiconductor is between a conductor and an insulator lies in the band gap of the semiconductor energy band. The energy value that the electrons in free space can obtain is basically continuous, but in semiconductors, due to quantum effects, the electrons in isolated atoms occupy a very fixed set of separate energy lines. When the isolated atoms are close to each other, the rules are neat In the arranged crystals, due to the interaction of the electrons outside the nucleus of each atom, the originally isolated and separated atoms overlap each other and become bands, called energy bands.

Specifically, the shell model of an atom believes that the center of the atom is a positively charged nucleus, and there is a series of discontinuous shells composed of electron trajectories outside the nucleus. The electrons can only go around the nucleus in the shell. sports. In the steady state, the electrons moving in each shell have a certain energy state, so a shell is equivalent to an energy level, called an energy level. An energy level also represents a state of movement of electrons.

The distribution of electrons in the shell should satisfy the following two basic principles: ① Pauli’s incompatibility principle, that is, two or more electrons in an atom cannot be in the same state of motion with equal quantum numbers; ② The principle of minimum energy, that is, each electron in an atom has a tendency to occupy the empty energy level with the lowest energy first.

The chemical and physical properties of an element are determined by its atomic structure, in which the number of outer electrons plays the most important role. The combination of atoms and atoms mainly depends on the interaction of the outer layer and the changes in the movement of valence electrons. When electrons move around the nucleus, the electrons in each orbit have a certain energy. The innermost orbit corresponds to the lowest energy. The second orbit has a larger energy. The more the outer electrons are affected by the nucleus. The weaker the bond, the greater the energy. The electron does not have an energy state in the middle of two layers of orbits. For the sake of visualization, a series of different levels of horizontal lines can be used to represent the energy value that an electron can obtain when moving in two-layer orbits. These horizontal lines are the electronic energy levels that mark the energy levels of the electrons.

In an isolated atom, electrons can only move on different allowed orbits, and the energy of electrons in different orbits is different. In crystals, the distance between atoms is very close, the electron orbits of neighboring atoms overlap and influence each other, and the electric fields of each atom are superimposed on each other. In this way, the energy level corresponding to the orbit is not a single electronic energy level, but is split into many electronic energy levels with very close energies but different sizes. These regions, which are composed of many electron energy levels with very small energy differences, look like a band, so they are called energy bands. Each track has a corresponding energy band, as shown in Figure 1. Because the outer layer of electrons is more affected by neighboring atoms, its corresponding energy band is wider; the inner layer of electrons is less affected by neighboring atoms, and its corresponding energy band is narrower. The distribution of electrons in each energy band is generally to fill the lower energy level first, and then gradually fill the energy level with higher energy, and each energy level is only allowed to be filled with two electrons with the same energy, as shown in Figure 2. Shown.

Figure 1 Energy band corresponding to electron orbit
Figure 2 The distribution of electrons on the energy band

The energy band corresponding to the inner electron energy level is filled with electrons. The energy band corresponding to the energy level of the outermost valence electron is filled with electrons and some not filled, which mainly depends on the type of crystal. For example, the valence electron energy bands of metal crystals such as copper and silver are empty with half of the energy level, while the valence electron energy bands of semiconductor crystals such as silicon and germanium are all filled with electrons.

The highest filling energy level occupied by electrons in the energy band at 0K (thermodynamic temperature) is called the Feilai energy level. The electrons in the energy band occupy energy levels in order of energy from low to high. The energy band corresponding to the energy level of the outermost valence electron is called the valence band. Above the valence band is the empty energy band not occupied by electrons. Valence electrons will be able to participate in conduction after reaching the empty band, which is also called conduction band. The way the energy band is occupied by the valence band determines the conductivity of the medium. There is a conduction band in the conductor that is partially occupied by electrons and can participate in conduction. The energy required for the transition of electrons in the conduction band in this band is very small, which makes the momentum of the electrons continuously change, thus forming a macroscopic movement: the image body There are only bands and vacant bands, and the transfer of electrons can only be carried out between different energy bands. This requires a lot of energy and is generally not easy to occur: although the energy bands in semiconductors are also full bands, they are full and empty. The energy gap between the bands is very small or overlaps, and it is easy to form a conduction band under the influence of the outside (such as light, heating, etc.), but its conductivity is far less than that of a conductor.

The energy bands with the highest energy of semiconductors are the conduction band and the valence band. The electron is in the conduction band, usually near the bottom of the conduction band. The bottom of the conduction band is equivalent to the potential energy of the electron: the hole is in the valence band, generally near the top of the valence band, and the top of the valence band is equivalent to the hole. Potential energy. The energy range where there is no energy level between the valence band and the conduction band is called the band gap. The energy width of the band gap is called the band gap, as shown in Figure 3.

Figure 3 Energy band and band gap

Since the band gap reflects the energy required for the bound electrons in the outermost layer of a solid atom to become free electrons, the band element determines the electrical conductivity of the solid. So what is the difference between the band gap of semiconductors and the band gaps of insulators and metals? The band gap of insulators is wide, and electrons can hardly transition from the valence band to the conduction band, so it has a high resistivity, that is, it is almost non-conductive: metal The band gap is zero, and the valence band electrons are all free electrons, so the conductivity is very strong. For semiconductors, the band gap is narrow. When the temperature rises, or is exposed to light, or after doping, the semiconductor valence band The electrons can easily transition from the valence band to the conduction band. At this time, the number of carriers in the semiconductor greatly increases, and its conductivity is greatly increased.

Figure 4 Energy band diagrams of metals, semiconductors and insulators

Figure 4 shows the energy band diagrams of metals, semiconductors and insulators. As shown in Figure 4(b), in order for valence electrons to jump from the valence band to the conduction band to participate in the conduction movement, they must obtain an additional energy at least equal to Eg from the outside world. The size of Eg is the energy difference between the bottom of the conduction band and the top of the valence band, which is called the forbidden band width or band gap, and its unit is electron volts (eV). For example, the band gap of silicon is an energy of 1.119 eV at room temperature. If the outside gives the electrons in the valence band an energy of 1.119eV, the electrons may jump over the forbidden band and jump into the conduction band, and the crystal will conduct electricity.

The difference between metal and semiconductor is that it has good conductivity under all conditions. Its conduction band and valence band overlap, and there is no forbidden band. Even if it is close to 0K, electrons can still participate in conductive motion under the action of an external electric field. The semiconductor has a band gap of a few tenths of electron volts to 4eV. At 0K, electrons are full of the valence band and the conduction band is empty. At this time, it cannot conduct electricity like an insulator. When the temperature is higher than 0K, thermal motion occurs inside the crystal, so that a small amount of electrons in the valence band gain enough energy to jump to the conduction band. This process is called excitation. At this time, the semiconductor has a certain conductivity. The number of electrons excited to the conduction band is determined by the temperature and the forbidden band width of the crystal. The higher the temperature, the more the number of electrons excited to the conduction band, and the better the conductivity; the same temperature, the smaller the forbidden band width of the crystal, the more the number of electrons excited to the conduction band, the better the conductivity. The difference between semiconductors and insulators lies in the band gap width. The forbidden band width of insulators is relatively large, generally 5~10eV, the number of electrons excited to the conduction band at room temperature is very small, so its conductivity is very small; the forbidden band width of semiconductors is smaller than that of insulators, so it has a considerable amount at room temperature. A large number of electrons will jump to the conduction band.

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