① Band structure of P-N junction
Due to the diffusion and drift of carriers, a space charge region and a built-in electric field appear in the semiconductor, causing the potential U and related hole potential energy (eV) or electron potential energy (one eV) of this part to change with the position, and finally change the PN Band structure at the junction (Figure 1). The built-in electric field is directed from the N-type semiconductor to the P-type semiconductor. Therefore, along the direction of the electric field, the potential gradually decreases from N-type semiconductor to P-type semiconductor. The potential energy of the electrons gradually rises. In other words, the potential energy of holes is high in N-type semiconductors and low in P-type semiconductors. If holes move from an N-type semiconductor to a P-type semiconductor, they need to overcome a “potential barrier” formed by a built-in electric field; on the contrary, for electrons, the potential energy in the N-type semiconductor is low, and the potential energy in the P-type semiconductor High, if you move from N-type semiconductor to P-type semiconductor, you need to overcome a “barrier.”
When the N-type semiconductor and P-type semiconductor material form a PN junction, the energy band at the PN junction is distorted due to the electric field caused by the space charge region. At this time, the energy band at the bottom of the conduction band, the top energy level of the valence band, and the intrinsic Fermi energy Both the energy level and the defect energy level have the same magnitude of bending. However, in equilibrium, the Fermi levels of N-type semiconductors and P-type semiconductors are the same. Therefore, the potential difference U at both ends of the space charge region of the balanced P-N junction is equal to the Fermi level difference between the original N-type semiconductor and the P-type semiconductor. It can be seen from the above that the higher the doping concentration of the N-type semiconductor and the P-type semiconductor of the P-N junction, the greater the Fermi level difference between the two, the wider the band gap, and the greater the contact potential difference U of the P-N junction.
② P-N junction energy band and contact potential difference
Under thermal equilibrium conditions, the junction zone has a uniform Fermi level EF. The position far away from the junction zone is the same as the state before the junction is formed. When N-type and P-type semiconductors exist alone, there is a certain difference between EFN and EFP. When the N-type and house-type semiconductors are in close contact, electrons will flow from the end with the higher Fermi energy level to the end with the lower Fermi energy level, and the holes flow in the opposite direction. Under the action of the built-in electric field, EFN will move down along with the energy band of the entire N region, and EFP will move up together with the energy band of the entire P region until the Fermi level is leveled to EFN = EFP and the carriers stop flowing. At this time in the junction region, the conduction band and the valence band are bent correspondingly, forming a potential barrier, and the full height of the potential is equal to the difference between the time-consuming energy levels of the N-type and P-type semiconductors alone:
In the formula, q is the electric quantity of electrons: UD is the contact potential difference or the built-in potential.
For states outside the depletion zone:
In the formula, NA, ND, ni are acceptor, donor, and intrinsic carrier concentration respectively; K is Boltzmann’s constant: T is temperature.
It can be seen that UD is related to the doping concentration. At a certain temperature, the higher the doping concentration on both sides of the P-N junction, the greater the UD. For materials with forbidden bandwidth, ni is small, so UD is also large.
③P-N junction under light
When the P-N junction is exposed to light, both the intrinsic absorption and extrinsic absorption of the photon by the sample will produce photo-generated carriers, but only the minority carriers excited by the intrinsic absorption can cause the photovoltaic effect. Because of the photo-generated holes generated in the P region, the photo-generated electrons generated in the N region are many sons, and they are all blocked by the barrier and cannot pass through the junction. Only the photogenerated electrons in the P region and the photogenerated holes in the N region and the “electron-hole pairs” (minority carriers) in the junction region can drift through the junction under the action of the built-in electric field when they diffuse to the junction electric field (Figure 2). The photo-generated electrons are drawn to the N area, and the photo-generated holes are drawn to the P area, that is, the “electron-hole pairs” are separated by the built-in electric field. This leads to the accumulation of photogenerated electrons near the boundary of the N zone and the accumulation of photogenerated holes near the boundary of the P zone. They generate a photogenerated electric field that is opposite to the built-in electric field of the thermally balanced P-N junction, and its direction is from the P zone to the N zone. This electric field lowers the potential barrier, and the reduction is the photo-generated potential difference. The P terminal is positive and the N terminal is negative. Therefore, the junction current flows from the P area to the N area, and its direction is opposite to the photogenerated current.
In fact, not all photo-generated carriers produced contribute to the photo-generated current. Suppose that the diffusion distance of holes in the N zone during the lifetime τp is Lp, and the diffusion distance of the electrons in the P zone during the lifetime τn is Ln. Ln+Lp=L is much larger than the width of the P-N junction itself, so it can be considered that the photogenerated carriers generated within the average diffusion distance L near the junction all contribute to the photogenerated current. The “electron-hole pairs” whose positions are more than L from the junction area will be recombined during the diffusion process and will not contribute to the photoelectric effect of the P-N junction.
In order to understand the above process, we briefly introduce the concepts of download stream life, mobility, and diffusion length.
Carrier lifetime refers to the average survival time of non-equilibrium carriers before recombination. In the case of thermal equilibrium, the generation rate of electrons and holes is equal to the recombination rate, and the concentration of the two maintains a balance. Under the action of external conditions (such as light), additional non-equilibrium carriers will be produced, that is, “electron-hole pairs”: after the external conditions are dissipated, because the recombination rate is greater than the generation rate, the non-equilibrium carriers will gradually recombine and disappear Drop and return to thermal equilibrium. The decay law of non-equilibrium carrier concentration with time generally obeys an exponential relationship. In semiconductor devices, the non-equilibrium minority carrier lifetime is referred to as the minority carrier lifetime.
The recombination process can be roughly divided into two types: the electron directly transitions between the conduction band and the valence band, causing the disappearance of a pair of electrons and holes, which is called direct recombination: “electron-hole pairs” may also pass through the forbidden band. The energy level (recombination center) is recombined, which is called indirect recombination. The minority carrier lifetime of each semiconductor is not a fixed value, it will vary greatly depending on the chemical composition and crystal structure. Mobility refers to the average drift speed of carriers (electrons and holes) under the action of a unit electric field, that is, a measure of how fast the carriers move under the action of an electric field. The faster the movement, the greater the mobility; The slower, the lower the mobility. In the same semiconductor material, different types of carriers have different mobility, generally the mobility of electrons is higher than that of holes. Under the action of a constant electric field, the average drift speed of carriers can only take a certain value, which means that the carriers in the semiconductor are not free from any resistance and are continuously accelerated. In fact, in the process of thermal movement, carriers continuously collide with crystal lattices, impurities, defects, etc., and change their moving direction irregularly, that is, scattering occurs. Inorganic crystals are not ideal crystals, while organic semiconductors are essentially amorphous, so there are phenomena such as lattice scattering and ionized impurities scattering.
Because the minority carrier has a certain lifetime, that is, the minority carrier lifetime. Therefore, in the process of diffusion, the minority carriers must recombine while diffusing. After a certain distance, the minority carriers will disappear, and the distance covered is the so-called diffusion length.
The absorption of light by a semiconductor is mainly determined by the forbidden band width of the semiconductor material. For a semiconductor with a certain band gap, low-energy photons with a small frequency will absorb light from the semiconductor to a small extent, and most of the light can penetrate; as the frequency becomes higher, the ability to absorb light increases sharply. In fact, the light absorption of semiconductors is determined by various factors. Here, only the transition between electronic energy bands used in solar cells is considered. Generally, the wider the band gap, the smaller the absorption coefficient for a certain wavelength. In addition, the absorption of light also depends on the density of states of the conduction band and valence band. Light provides energy for electrons in the valence band and directly makes it transition to the conduction band. During the transition, energy and momentum are conserved, and the transition without the participation of phonons, that is, the transition without a change in momentum is called a direct transition. Conversely, the transition accompanied by a phonon is called an indirect transition. Therefore, when manufacturing solar cells, direct transition materials can fully absorb sunlight even if the thickness is very thin, while indirect transition materials, without a certain thickness, cannot guarantee full light absorption. However, the required thickness of solar cells is not determined only by the absorption coefficient, but also has a relationship with the lifetime of minority carriers. When semiconductors are doped, the absorption coefficient will shift to the higher energy side.