This Lecture 3 is starting over the semiconductor device. In Lecture 2, you learned atom crystal and why semiconductor has a band gap based on the quantum mechanics and solid state physics. It is very difficult and very short overview. However, as long as you understand that silicon has a band gap, then you don't have to worry about learning the semiconductor device, which is starting from now. Semiconductor has a band gap that has the intrinsic semiconductor and extrinsic semiconductor. Intrinsic semiconductor is without dopant, that only silicon is located in silicon lattice. Intrinsic semiconductor, when T equals zero Kelvin, silicon is bonded to each other perfectly, and there is no electron and holes at T equals zero Kelvin. If you're increasing temperature, for example, T equal room temperature of 300 Kelvin, what happen is that the bonding between the silicon is disconnected at certain number of silicon lattice. They generating hole and electron. At equilibrium, the generation of electron-hole pair and the combination of electron hole is equal, so generation and recombination is equal. At room temperature, at T equals 300 Kelvin, there is intrinsic carriers of the electron and hole, number is in gallium arsenide, 2 times 10_16, silicon, 1.5 10_10, germanium is 2 times 10_13. For intrinsic semiconductor, there's a breaking of the silicon bonding generating exact same number of electron and hole. Therefore, intrinsic electron, intrinsic hole is equal to the n_i. You need to memorize this number of silicon in the intrinsic carriers, 1.5 10_10. As I said, in room temperature, bonding is break, the electron-hole pair generating by transforming electron in valence band to the conduction band. This becomes the electron free movement of electron and these becomes the hole. So question, what fraction of silicon atom contribute to intrinsic electron concentration at room temperature? Then first, let's calculate how much silicon atom located in unit cell in cubic centimeters. In unit cell, volume is a cubic and silicon is diamond structure, and there is total eight silicon atom in silicon unit cell. "A" of silicon lattice is 5.43 times 10_minus 8. Then here is the question, what fraction of the silicon atoms contribute to intrinsic electron concentration at room temperature? To know this, we need to know how many atom are existing at cubic centimeter. Then this number is equal to the, in one unit cell the volume is a cubic. In one unit cell there is eight silicon atoms. "A" is a silicon lattice, which is 5.43 times 10_minus 8 centimeters. If you insert this "a" to this equation, then answer is 5 times 10_ 22 silicon atoms are existing at one cubic centimeters. As we learned in previous, intrinsic carrier concentration is 1.5 times 10_10 per cubic centimeter, therefore, silicon atoms are in per cubic centimeter, which is 5 times 10_22, and fraction of the 1.5 10_10 is intrinsic carrier concentration, answer is 3 times 10_minus 13. So this is that one silicon atom out of 10_13 contribute intrinsic carrier concentration, which is very rare. Then extrinsic semiconductor. Another way to generate carrier is extrinsic semiconductor, where you doping of different atom, for example, of boron, three [inaudible] , and arsenic five [inaudible]. So boron has three [inaudible] , arsenic has five [inaudible]. Arsenic of the five [inaudible] has another [inaudible] of electron, then they can contribute extra electrons. For the boron case, there is only three [inaudible] , therefore, they can generate one hole. For donor, if you doped arsenic, there is a donor energy level between the band gap and these electron in donor level in excited to go to the conduction band becomes the electron carrier. If you doped boron, then this becomes the acceptor level, and electron in valence band jump to the acceptor energy level generating hole in valence band, becomes the hole. Maybe we can ask the one question. If n-type semiconductor has only electron, no hole? Answer is, no. There is also holes in n-type semiconductor which is contributed by the intrinsic carrier concentrations. So this graph shows that germanium, silicon, and gallium arsenide at room temperature, all the different temperature, intrinsic carrier concentration at room temperature, silicon is 1.5 10_10, germanium 2.5 10_13, and gallium arsenide is 2.2 times 10_6. If you're increasing the temperature, then intrinsic carrier concentration will be increasing. Another thing, doping versus resistivity. So if you want to buy a silicon wafer, you cannot say that I want to buy 10_16 n-type doped silicon. Vendor would not understand what kind of wafer they can provide. Instead, you need to say that 10_16 n-type semiconductor, resistivity is 0.8 ohm centimeter. So you need to ask them, I want to buy 0.8 ohm centimeter resistivity n-type silicon wafer. Consider this, intrinsic silicon has the resistivity 2 times 10_5, but 10_15 arsenic doped n-type semiconductor has five ohm centimeter. So huge difference in resistivity of almost 10 to the minus 5 by doping intrinsic dopant. This is ionization energy level. In silicone has a 1.1 electron volt, depending on the dopant of donor and acceptor, where they have energy level between the bandgap. To ionize this dopant, ionization energy is required to act like a dopant. The electron in p can contribute to the conduction band electron. One interesting point is that the energy to activate the arsenic, let's say the 0.054 electron volt, is lower than room temperature thermal energy, which is normally kT equals 0.026. In room temperature, thermal energy is 0.026, which is almost half of the ionization energy, then this arsenic cannot be ionized. How could this possible? Answer is that room temperature thermal energy, which is 0.026, is the average. The ideal thermal energy distribution is some kind of Gaussian [inaudible] that there's the thermal room temperature energy. The portion, which is higher than 0.05, can ionize the electron dopant. Same thing for the gallium arsenide. We know that semiconductor bandgap. To know that how much carrier concentration are located in a valence band or conduction band, we need to approach this with a statistical or probability. To define this probability and statistics, there is Fermi-Dirac distribution function, fE equals 1 over 1 plus exponential e minus Fermi energy per kT. This Fermi energy is probability of occupancy of available state at E by electron. Fermi energy is defined by here. Normally, this Fermi energy is located between the valence band and conduction band. Boltzmann constant is this constant. If you look at the Fermi energy, this is the symmetrical by the Fermi energy. T equals 0 energy above the Fermi energy, the probability is zero. Below the Fermi energy, probability is one. Up Fermi energy, probability is 0.5. If you're increasing temperature term, then height becomes this graph, and more higher temperature becomes like this. This is the Fermi-Dirac function. Next class we're going to learn how much carrier concentration predicted by this Fermi-Dirac function.
