In this video, we will discuss extrinsic semiconductors. When impurities contributes significantly to the carrier concentration in a semiconductor, we call it an extrinsic semiconductor or doped semiconductor. Extrinsic semiconductors, have their electron concentrations and hole concentrations determined primarily by the number of impurities that are present in the semiconductor and also the type of those impurities. When impurities supply additional electrons to the conduction then, those impurities are called donor impurities. When the impurities provide additional holes, those impurities are called the acceptor impurities. So, what are these donors and acceptors? Let's go back and take a look at the periodic table. So, once again, thise right side of the periodic table represents the non-metal species where many elements that make up semiconductors belong. So, if we zoom on it, then we have this group four elements, particularly silicon and germanium that make the elemental semiconductors. So, let's look at silicon, which is a semiconductor that is predominantly used in semiconductor devices. It is a group four element, so it has four valence electrons. It therefore bonds with four neighboring silicon atoms in a crystal, in a diamond crystal structure. Now, let's say that we add deliberately some impurities into the silicon crystal. This process is called doping. Let's say, we add phosphorous atom into a crystalline silicon crystal. Now, phosphorus is a group five element, so it has five valence electrons; one more than silicon. So, when phosphorus is doped inside a silicon crystal, four of the valence electrons will form covalent bonding with the neighboring silicon atoms, but there's one left. This one electron, x-ray electron is then donated to the conduction band and it will increase the electron number or electron concentration in the conduction band. Phosphorus impurity in silicon is therefore a donor. Similarly, if you add boron atom onto silicon, boron is a group three element, it has three valence electrons. So, when boron goes into silicon crystal, it tries to form covalent bonding with the four neighboring silicon atoms but it only has three valence electrons. So, one bonding will remain broken. Has one deficiency of electron. The deficiency of electron, is the hole. So, boron introduces a hole in the valence band of silicon. So, boron is an acceptor impurity in silicon. So, the donor impurity as I said in an example of phosphorous atom inside the silicon has one extra electron. They are typically loosely bound. At room temperature, this bonding between the phosphorus atom and the extra electron can be easily broken. When this binding between extra electron and phosphorus is broken, then this electron is free to move inside the crystal. They are the conduction band electron here shown in the energy band diagram. So, this electron, x-ray electron, bound to the phosphorus atom, okay? This energy level, it is state of the electrons is depicted by this donor energy level situated slightly below the conduction band. When the electron is broken free, these guys are the conduction band electron. The energy required to do that. Energy required to liberate this electron from phosphorus atom is the binding energy, and that's the energy difference between the Ec, bottom of the conduction band and the donor energy level. It will depend on the type of the donor. Likewise, acceptor impurities are shown here, boron atom for example in silicon has one less valence electrons so there is a deficiency of broken electron, and that's a hole. When this hole is bound to the boron, that is the electron in this acceptor energy level, when this hole is broken free, then that represents a hole in the valence band which can freely move around. So, the energy difference between the acceptor energy level and the valence band edge Ev represents the binding energy for this extra hole that this boron brings in. Now, how do we quantitatively describe the energy level belonging to this impurity atom? To our first approximation, you can treat the impurity as one extra charge at the core and one extra electron. So, this is an example of donor. So, phosphorous atom for example, in a silicon crystal has one extra electron. Its atomic core has one extra positive charges as well. So, we can describe this situation like a hydrogen atom, which has one unit of positive charge in the atom and one extra electron. So, this is like a hydrogen atom. Now, if you look at the undergrad textbook of quantum mechanics, the ground state energy of hydrogen atom is given by this equation here. If you plug in all these numbers, the electron's mass, vacuum permittivity and the Planck's Constants, et cetera, then you get 13.6 electron volt for the ground state energy. What does that mean? That means you have to supply 13.6 electron volt to the electron in the ground state in order to ionize hydrogen atom, in order to liberate the electron from the hydrogen atom. This is a huge energy and that's very difficult to occur. So, that's why hydrogen atoms is very stable. Now, if you apply this hydrogen atom like model for a donor, you basically have the same equation. There is no reason we should have a different equation, it's the same system. One proton, one unit of positive charge and one unit of negative charge form the hydrogen atom, equation is the same except that there are two key differences from the true hydrogen atom case and that is; one, the mass of electron is different inside the semiconductor. We have to replace the electron mass with the effective mass of the electron. Also, the permittivity here is the permittivity of vacuum. But a lot of semiconductors are dielectric material. It has its own permittivity or dielectric constant. So we need to take that into consideration. So, because of these two factors, the binding energy of the electron in a donor is dramatically modified from that of the hydrogen atom. So, the effect of this permittivity here is called the dielectric screening, and the effective mass, of course, for the reduces the binding energy. So, these two effect contributes to orders of magnitude reduction in the binding energy, so in germanium, the binding energy of donor is only 0.006 eV, and silicon 0.0025 eV, and gallium arsenide 0.007 eV. Now, compare that with the thermal energy at room temperature. Twenty six, 27, 29 electron volt, and these energies are easily overcomed by the thermal energy at room temperature. So, at room temperature you can imagine these donors are all ionized producing electrons in the conduction band. Likewise, for holes in the valence band. So, here is some examples of the donor and acceptor energy levels. The phosphorus atom, arsenic atom, antimony atom, they're all group five elements and they all have one one extra electron when they are introduced into silicon crystal producing electrons into the conduction band. So, these guys are donors. Boron, aluminum, gallium, indium all of these guys are group three elements. So they have one less electron then. So, they cancel and they're doped into silicon crystal, then they produce holes in the valence band. The binding energies are a little different depending on the atoms. Obviously, the hydrogen atom model will predict the roughly where these energy levels should be. Rigorous calculations will give you the exact position. There are slightly different but they're pretty close to what the simple hydrogen model predicts. So, these impurities that have very small binding energies, the donors and acceptors, they have very small binding energy. How small is small? Small compared to the thermal energy at room temperature. These guys are called the shallow impurities and these are good impurities with which we can control the carrier concentration in the conduction and valence bands. There are some impurities that goes deep inside of an Ga. The binding energy here, energy difference from conduction band to the centers level or energy difference from the valence band to this impurity level is very large. Much, much greater than the thermal energy and the thermal energy is not going to ionize these guys, and these impurities are called deep impurities. These are generally bad impurities and those are not usually intentionally introduced impurities on intentionally introduce impurities these guys are, and they are to be avoided. So, the shallow impurities are something we deliberately introduced to control carrier concentration, deep impurities, something to be avoided.
