1.1 Band structure and photoconductivity of semiconductors
1.1.1 Band structure of semiconductors
No matter how electrons and holes move, they must have many states of motion. When not stimulated by external energy, these motion states are stable, and they must have a certain amount of energy. Generally, energy is used to express these motion states, that is, “energy level” is used to indicate various motion states. When the carrier is affected by external energy, it will enter a high-energy state from a low-energy state of motion. It can also be said that the carrier transitions from a low-energy level to a high-energy level. Therefore, the state of electron movement in the atom can be expressed by energy level. The more moving electrons are on the periphery of the nucleus, the weaker the force of the nucleus, and the higher the energy on the usual energy coordinates. The more moving electrons in the inner circle of the nucleus, the stronger the force of the nucleus and the lower the energy.
In a crystal composed of a large number of atoms, the movement of electrons located in the inner circle of each atom is rarely affected by other atoms, and still maintains its original state of motion and energy. The movement of electrons located on the periphery of the nucleus, due to its high energy level and high energy content, changes the original power of the movement. Naturally, it is easier to change its state of movement when subjected to the action of other atoms. Originally it moved around the nucleus to which it belonged, but now it moves in the entire crystal and no longer belongs to any atom. Its movement energy is obviously different from the original movement energy. For example, when considering the moving electrons at the outermost periphery of an atom, in an independent atom, the energy of these electrons is the same for any atom. In order to illustrate the problem, only the case of a crystal with a volume of only 1cm3 is studied, if there are a total of M atoms in this 1cm3 crystal. These electrons are all moving in the whole crystal, the movement state is M, there are M energy levels. But the energy of each state of motion is not equal, they are evenly distributed between the highest energy and the lowest energy. Due to the large number of M, the difference between the highest energy and the lowest energy is not large, so these M energy levels actually form a band that can be considered continuous in energy, called the “energy band”.
Figure 1-1(a) shows the energy band of metallic copper crystal. The energy band theory believes that only two electrons are allowed in each energy level, that is, the energy level from 1 to F in the figure has two electrons at absolute zero, and the energy level from F to 2 is empty. . The energy band theory also believes that the motion states of the two electrons in each energy level are exactly opposite, and they do not have the effect of conducting current. But once subjected to the external thermal energy or the force of an external electric field, some electrons below the F energy level may be excited to the empty energy level above F.
Figure 1-1(b) shows the energy band of semiconductor silicon crystal. Take silicon crystal, the main material of solar cells, as an example to illustrate the “energy band” problem. Since only two electrons are allowed in each energy level, then four electrons (there are four valence electrons on the outermost periphery of a silicon atom) have two energy levels; if there are two energy levels, there should be two energy bands; therefore, two One energy band is exactly occupied by four valence electrons. The energy band from energy 1 to energy 2 in the figure is the higher one of the two energy bands, which has been occupied by electrons, so it is called “full band”.
Also known as the “price band”. There is no possible state of motion in a period of energy from 2 to 3, so it is called “forbidden band”. From 3 to 4, it is the possible movement state of electrons in the crystal. Under the condition of absolute zero, each energy level in the full band has two electrons, so there is no conductivity. When it rises to a certain temperature, the electrons in the full band are excited by heat, and get enough energy to enter the upper energy band called “conduction band”.
Figure 1-1 The energy band of a crystal
Carriers can also be generated by irradiating semiconductors with radiation. As long as the energy of the radiated photon is greater than the forbidden band width, the electron absorbing the photon is enough to transition to the conduction band, producing a free electron and a free hole. The electrons or holes excited by radiation also have mobility after entering the conduction band or the full band. Therefore, the effect of irradiation is to increase the carrier concentration in the semiconductor. The part of carriers that the specific thermal equilibrium carrier concentration increases are called “photo-generated carriers”. The resulting increase in conductivity is called “photoconductivity”.
In fact, after each electron absorbs a photon and enters the conduction band, it can move freely in the crystal. If there is an electric field, this electron participates in conduction. But after a period of time, this electron may disappear and no longer participate in conduction. In fact, any photo-generated carrier has only a period of time to participate in conduction. This period of time is long or short, and its average value is called “carrier lifetime”.