Welcome to the course module on the physics of solar cells. The main learning objective is for you to understand the working principles of a solar cell and how standard the art silicon solar cells are designed and fabricated. In the previous module, we learned about the solar resource and geometry to determine the radiant received in the plane of a solar panel. The next step would be to convert this radiant energy into electrical energy. This is mainly done by exploiting the electronic band structure of a class of solid materials we know as semiconductors. Therefore, in this video, we will be looking into how solid materials are formed, as well as the concept of electronic bandstructures. First, we consider the single atom, which consists of a positively charged nucleus and negatively charged electrons in discrete electronic states. Bohr's model of the atom introduces circular orbits corresponding to these states in which the electrons move around the nucleus. The electronic states are also often plotted on an energy scale which is very practical in terms of visualizing the energy difference between the different states. An electron may be excited from a lower energy to a higher energy state by absorbing energy, for instance, from a photon. But this photon energy must correspond to the exact energy difference between the two states, not any higher or any lower. In a similar way, the electron may be relaxed down to the lower energy state again, by emitting this amount of energy, for instance, as a photon. However, each orbit does not have an infinite amount of electron states and only one electron is allowed in a single state. Therefore, for an electron to transition from one orbit to another, there must be an unoccupied state available in the final orbit. This symbol play on model of the atom goes a long way in describing the working principles of solar cells. But more complicated models do exist where the orbits are described as three-dimensional orbitals and the position of the electron is not a single point in space but is rather spread out by what is called a wave function. We will not dive into the field of quantum mechanics in this course, but we need to use a few results to explain certain phenomena. Now that we are acquainted with news Bohr's model of the atom, we need to look at the periodic table of elements. Here are all the known single atoms are listed. We need to pay special attention to the atomic number. Because the atomic number corresponds to the number of electrons orbiting the nucleus. I have highlighted the atom silicon, which is the atom that we will be studying throughout this module. Using those Bohr's model, we're now going to construct a silicon atom. The first thing we need to know is the number of electrons we need to place on the orbits. Looking at the atomic number of silicon, we need a total of 14 electrons orbiting the nucleus. Electrons fill up the electronic states closest to the nucleus first, as these states have the lowest energies. However, the orbits only have a limited amount of states. The first orbit has two states, and the second one has eight. Now, the third one has eight states as well, but we have already placed 10 out of 14 electrons. So the remaining four electrons fail to completely fill up the third shell. These outermost electrons in an atom are known as valence electrons and they are extremely important as they are responsible for chemical bonding and electrical conductivity in crystals. The lowest energy configuration is always the most stable one. Which is achieved with either completely filled or a completely empty shells. Not a partially filled outer shell, as in the case of a single silicon atom. Therefore, silicon will make covalent bonds with neighboring silicon atoms. A covalent bond is simply the sharing of electron pairs between two atoms. After having made this chemical bond with four neighboring silicon atoms, the center atom now has eight electrons in its outer shell. That is a completely filled shell. The neighboring silicon atoms prefer fully occupied or empty shells as well. Therefore, all silicon atoms want to make covalent bonds to four silicon atoms. Such a periodic arrangement of atoms is known as a crystal lattice. The crystal structure of silicon is known as the diamond structure, and it looks like this and three-dimensions. However, no crystal can continue this bonding infinitely, which brings us to the surface of a solid. We usually distinguish between three types of solid materials that is amorphous, where there's no periodic arrangement of the atoms, polycrystalline, where we do have these regions with a high degree of ordered. Such a region is called a crystal grain, and the interface between two crystal grains is known as a grain boundary. Finally, we could have a single crystal material with a highly ordered and periodic arrangement of the atoms throughout the volume of the material. Now, let us take a look at what happens to the discrete electronic states. The circular orbits from Bohr's model of the atom gives the position at which we have the highest probability of finding an electron. But quantum mechanics states that this position is actually a bit uncertain, and we therefore use a probability function to describe the probability of finding an electron. Now as we bring two atoms close together, the probability functions of the two electrons you see here, may start to overlap. As a result, the two electrons start to fuel each other and start to interact. As no two electrons are allowed to occupy the same electronic state at the same energy level, the identical energy states of the two atoms must split up into two slightly perturbed states. The two states are still discrete, but they may be very closely separated in electron energies. Now, let us bring together a large collection of isolated atoms. The discrete electron states now split up many times and become very closely separated in energy. Depending on the conditions such as temperature, pressure, but also the material that we're trying to make, the atoms will settle at a certain inter-atomic distance. If we from this point on the graph, extracted all the allowed electron states, we arrive a two quasi-continuous energy bands. I called them quasi-continuous because if we zoom in, we can still see all the discrete states, but the energy difference between each state is now negligibly small. We therefore say that the energy bands are continuous. The valence electrons, that is the outermost electrons, reside in the valence band. We can still excite them into the conduction band, for instance, using a photon. However, in this specific case, the two energy bands are separated by a band gap where there are no allowed electron states. Therefore, the excitation energy of the photon should be at least that of the energy band gap. One thing we have not considered yet is temperature. The solid material we have just formed with a valence band and a conduction band separated by an energy band gap could for instance be a silicon crystal. As the valence electrons have not been given any energy to be excited, they will remain fixed in their bonds. Therefore, the electrons cannot move around in the crystal to conduct an electric current. If we now turn up the heat from zero Kelvin, a few electrons may be able to overcome the band gap energy. These electrons have been loosened from their bonds and are free to conduct an electric current. Finally, we have to get acquainted with this red dashed line that I have drawn, called the Fermi level. The Fermi-level is defined as the hypothetical energy level with a 50 percent probability of being occupied by an electron. Because the Fermi level is hypothetical, it may be located inside the energy band gap where there are no allowed energy states. If we look at the energy bands at zero Kelvin, we see that all the states at the top of the valence band are occupied and no states are occupied at the bottom of the conduction band. In this example, the Fermi level must therefore be in the center of the band gap. Solid materials on not only classified by crystallinity, but also by energy band structures. Here the position of the Fermi level is super important. Second metal, for instance, where the Fermi level is located within an energy band. One way of thinking about the Fermi-level is that it is the water level of electrons and I said only takes a very small amount of thermal energy to excite the electrons above the Fermi level. Metals are good conductors even at low temperatures. In a semiconductor such as silicon, the Fermi level is located in the energy bandgap that is not too large. This means that it takes a bit more thermal energy to excite an electron above the water level where it can conduct a current. Semiconductors are therefore poor conductors at low temperatures, but good conductors at high temperatures. Finally, an insulator is similar to a semiconductor, but the band gap is very large. Therefore, only very few electrons are excited into the conduction band, even at high temperatures, and insulators are therefore generally very poor conductors. In this video, we have learned that the single atom consists of a positively charged nucleus, a negatively charged electrons in discrete energy states. The outermost electrons, also known as the valence electrons, are super important because they are responsible for the chemical bonding of atoms and the electrical conductivity in a crystal. Based on crystallinity, we differentiated between amorphous, polycrystalline and single-crystal solids. A crystal is simply a collection of atoms that have been periodically arranged in a crystal lattice. As we brought atoms together to form a solid material, we saw that the discrete energy states split up into energy bands. Sometimes these energy bands are separated by an energy band gap, where there are no allowed electronic states. Finally, based on conductivity, we differentiated between metals, semiconductors, and insulators. Now this classification, we needed to consider both the position of the Fermi level, that is the water level of electrons, and the width of the energy band gap.
