Welcome to this short video about doping of semiconductors and the PN junction. So far, you have got a fairly in-depth explanation of the intrinsic semiconductors and how photon can generate electron-hole pairs via the band structure in the semiconductor material. You have also learned how electrons and holes can recombine via four mechanisms and how current can run in the semiconductor via diffusion and drift. In this video, you will learn the fundamental concepts of charge separation, where electron and holes can be extracted from the solar cell. This is done through the PN junction. In the following video, we will use the basic concepts to go further into details on balancing the concepts to maximize efficiency. The content of this video is doping of semiconductors and the PN junction. By adding the right impurity atoms into the semiconductor crystal lattice, the conductivity and the Fermi levels can be manipulated by either adding more electrons called n-doping or more holes called p-doping. This manipulation can be used to create a p-n junction diode, which is one of the simplest semiconductor devices, even though not really simple, used for solar cells and integrated circuits. The p-n junction creates an internal electrical field which can be used for charge separation. The overall concept of the ideal solar cell is illustrated in the figure where the electron hole pairs are generated in the absorber material and the electrons are extracted via an electron selective layer and similar for the holes. n-doping is the result of adding more electrons in the conduction band of the semiconductor, it can be done replacing and very little fraction of silicon atoms with group five elements which have five valence electrons. The band structure will remain the same, but each group five element add an additional electron, which will be in the conduction band at room temperature, and these electrons will be free charge carriers. We call these atoms donor items since they donate an electron. The number of free electrons in the conduction band corresponds to the number of donor atoms for group five elements. The most commonly used donor atoms are phosphorus, arsenic, and antimony. For solar cells, phosphorus doping is used for n-type doping in industrial solar cells. Since the donor atoms populates the conduction band with more electrons, the Fermi level is displaced towards the conduction band, which is illustrated in the figure. The change and Fermi level is a key to make successful charge separation and solar cells using p-n junctions. p-doping is the result of adding more holes in the valence band of a semiconductor. Replacing a very little fraction of silicon atoms with group three elements which have three valence electrons, the band structure will remain the same, but each group three element adds an additional hole, which would be in the valence band at room temperature. These holes will be free charge carriers. We call these atoms acceptor atoms since they accept or rather absorb an electron. The number of free holes in the conduction band corresponds to the number of acceptor atoms for group three elements. The most commonly used acceptor atoms is boron, aluminum, gallium, and indium. For solar cells, boron is used for the p-type doping of industrial solar cells. Since the acceptor atoms populate the valence band with more holes, the Fermi level is displaced towards the valence band, which is illustrated in the figure. The change in Fermi level is a key to make successful charge separation in solar cells. Doping is measured in doping concentration, which is the number of doping atoms per cubic centimeter. N-type concentrations are denoted N_D, for donors, or N_e, for electrons. Similar p-type doping is denoted N_A, for acceptors, or N_h, for holes. Sometimes doping concentrations are also called doping densities. For the dopings to be active, the doping atoms needs to be placed in the crystal lattice. When they are placed in the crystal lattice, the electrons contribute to filling the band and the atoms are fully ionized. Full ionization is assumed, and in general, this is a good assumption. Doping concentration range is typically from 10^12-10^19, per cubic centimeter, which should be compared to pure silicon, which have 5 times 10^22 atoms per cubic centimeter, and therefore, the impurity concentration is much below 0.1 percent. The upper limit for doping is called the solid solubility. If the doping is increased beyond the solid solubility of the semiconductor, the material goes from being a heavily doped semiconductor to an alloy, being a mixture of the dopant material and the host material. This material have different material properties. The solid solubility is dependent on the dopant. For silicon, most commonly used dopants, have solid solubilities in silicon of around 10^20 per cubic centimeter. Doping also decreases the resistivity of the semiconductor. The higher doping concentration, the lower resistivity. Recall from the previous video that the conductivity, which is the inverse of the resistivity, is proportional to the product of the charge carrier concentration and the mobility. In the equation here, only the majority carriers contribute since its concentration are several orders of magnitude higher than the minority carriers. Doping around the solid solubility gives you a typical resistivity of around 10 to the minus four ohms centimeter, still two orders of magnitude higher than the one of copper. So a doped piece of silicon is still a bad conductor at room temperature compared to copper, but the conductivity is as for all other semiconductor properties, strongly temperature dependent. As the last part of the doping, we need to review the charge carrier statistics. The changes in the Fermi level can be calculated as the thermal energy multiplied by the natural logarithm to the ratio between the density of states at the conduction or valence band and the doping concentration. The number of free electrons and holes follows the Boltzmann statistics using the relevant Fermi levels. The Boltzmann statistics is a simplification of the Fermi-Dirac statistics, valid when the energy difference is much larger than kT. The distance from the conduction or valence band to the Fermi level is plotted on the graph as a black solid line. The higher p- or n-doping, the closer the Fermi level is to the valence or conduction band respectively. For the intrinsic semiconductors, the number of electrons and holes was always equal. However, for doped semiconductors in equilibrium, this is no longer the case. Instead, the product of free electrons and holes is always equal to the intrinsic carrier concentration squared. As you saw in the previous lecture, there were three types of bulk recombination mechanisms. A silicon with an indirect band gap or Auger recombination as limiting the lifetime of minority carriers. Auger recombination is a free particle process, where the recombination energy is transferred to a third electron or hole. From the previous video, the rates of the recombination processes were presented. The Auger recombination lifetime is inversely proportional to the square of the free charge carriers, and it is therefore decreasing with increasing doping concentration. Therefore, also the diffusion length is inversely proportional to the doping concentration, and thus, greatly reduced at high doping. Since the Auger rate constant is almost the same for holes and electrons, these figures are valid for both. The diffusion length is plotted as a function of doping concentration using the low n-type dopant diffusion constant in blue, and using the high doping diffusion constant for holes as the red line. In real life, the diffusion lengths are between these two lines. At low doping level, the electron diffusion length is closer to the blue, and at high doping levels, the hole diffusion lengths is closer to the red. We will, in the next video, see the diffusion length sets an important upper limit for the doping concentration. Now, we have looked in greater details of the properties of both p and n-doped semiconductors, and have seen that by doping semiconductors, especially the Fermi level, can be manipulated. Now, it's time to use this knowledge and apply it in order to create a charge separation. Let's create a PN junction simply by contacting an N-type semiconductor with a P-type semiconductor. The Fermi level must be constant throughout the junction, which is required by thermal equilibrium. The conduction and valence bands bends and creates a built in potential. A so-called space charge region is created. In the N-region of the space charge region, there are more electrons than in the P-region, and therefore, electrons diffuses to the P-region and recombine with the holes. A similar but opposite concentration difference exists for holes while the hole diffuses to the N-region, where they recombine with the electrons. From the excess charges electrical fields are created, creating a drift current that cancels the diffusion currents and enables charge neutrality. The differences in Fermi levels relative to the valence or conduction band creates a so-called Build in potential. The build in potential helps separating the charges. and is also the upper limit for the voltage of a solar cell. The build in potential can be calculated from the Fermi level displacement that arises from the doping. What happens if we forward bias a P-N junction? If the applied voltage goes below the built-in voltage, the built-in voltage prevent excess electrons moving to the p-region. The space charge region is reduced, and there is a very small current in the diode. On the other hand, if the voltage is above build-in voltage, the built-in voltage is almost neutralized and the space charge region almost disappears. In this case, the diode becomes a conductor with a large current. Obviously, if we reverse bias the junction, the space charge region enlarges and only a minimal reverse current flows. If the P-N junction is severely reverse biased, the breakdown voltage is reached and the P-N junction starts reverse flow of current. Actually, similar to a diode since the P-N junction is basically a diode. Let's take a closer look at the space charge region. The charges from the fixed uncompensated atoms, which arises due to the electron and hole diffusion creates an electrical field. This electrical field is zero outside the space charge region and increases numerically linearly towards the N and P region. Exactly at the junction, the field has its maximum numerical value. By integrating the field over the space charge region, the built-in potential can also be determined. We will later see that the width of the space charge region is important as this field separates the charges and is decreasing with increasing doping concentrations. Further, charge neutrality requires that the product of the doping concentration and the width of the respective regions must be equal. Now the most important physics has been presented, which is laying a solid foundation for understanding the physics of the solar cell. Before we end this video, we'll take a brief look at the current -voltage relationship. In the dark condition the current voltage relationship can be derived knowing that at the zero bias that diffusion current cancels the drift current. Further using that the drift current is generated by the electric field in the junction. The solution to the obtained differential equation after applying appropriate boundary conditions, is the exponential current voltage relationship, as stated in the equation. This equation is called the Shockley equation and its describing the behavior that we saw on the forward and reverse bias in the dark. With a small so-called saturation current below the threshold voltage and otherwise conduction. If the junction is illuminated, electron-hole pairs are generated and a photo current is running in the opposite direction of the saturation current. An expression for the reverse saturation current is given. As you can see, it decreases with increasing doping densities. The temperature dependence, especially through the intrinsic carrier concentration, makes the reverse saturation current increase with temperature. Let's conclude this video. In this video, we have introduced N and P doping, where excess electrons and holes can be added to the conduction and valence band by replacing a few silicon atoms with group 5 and 3 elements. The additional charge carriers moves the Fermi-level toward the band edges and increases the conductivity. We also saw that Auger recombination is limiting diffusion length, which is decreasing with increasing doping concentration. We also created the P-N junction, where an n-type semiconductor is connected with a p-type semiconductor. Since the Fermi-level must be constant throughout the junction, a built-in potential is created. Further concentration gradients makes electron diffused to the p-region and vice versa. The uncompensated charges create an electric field that generates an opposite current. In equilibrium, these cancel. The electric field is in the so called space charge region and outside the space charge region, there in no field. When applying a small forward bias, a small current is flowing, which is the reverse saturation current. When the applied voltage is higher than the built-in voltage, the junction starts to conduct current. For a reverse bias, the junction general prevents flow of current until the breakdown voltage is exceeded generally at high reverse voltages. When the junction is illuminated, a photo-current is created in the opposite direction as a reverse saturation current. This current is facilitated by the charge separation from the P-N junctions built-in electric field. Now we have finished semiconductor physics and will in the next video look at how these principles are applied in a simple solar cell.
