This is the Lecture 2. We are going to learn the crystal property of a semiconductor. This is related with the semiconductor crystallography and quantum mechanics, solid state physics, which is depicting what kind of silicon crystal structure and why semiconductor is a band gap and what kind of electrical and mechanical property they have. So as I said, Lecture 2 is not directly related with the semiconductor device, and then you probably learn previous lecture to this semiconductor device. So I will not go over this lecture detailedly. Please, if you're interested in this field, please learn in quantum mechanics, solid state physics. Crystal lattice is the periodic arrangement of atoms. Depending on the crystal lattice, it can be amorphous, there is no order, or polycrystalline. In domain, they are crystal but entirely they are not single crystal. Final one is silicon cases, everything is crystalline. Depending on the crystal structure, they have a different semiconductor property, such as mobility, band gap, etc. Crystal lattice is a repeated unit cell and which is the stopping atom in the unit cell. Example of a semiconductor material, normally, has a four arms semiconductor is silicon and germanium. Carbon is also semiconductor. They can be CNT, carbon nanotube. Grepping is consisted with the carbon. Another way to making a semiconductor is mixing three to five, such as gallium nitride, gallium arsenide, indium nitride, indium phosphide. Two, six semiconductor is zinc sulfide, zinc selenide, or zinc oxide. Those can become a semiconductor material. Depending on the crystal lattice and semiconductor material, they have a different property, such as the band gap. For silicon is 1.1 electron volt, germanium 0.67. For blue LED semiconductor, gallium nitride is 3.4 electron volt. Red LED device, gallium arsenide is 1.4. Also, gallium nitride has a very high melting point, which is 2,500 Celsius. They can be used very high temperature semiconductor application, such as power electronics, of electric car, etc. One of the most important electrical property is the mobility. Mobility defines, if higher mobility has high current is flowing, which means the high-performance. Depending on the semiconductor material mobility is changing, for silicon, electron mobility is 1,300, unit is centimeter squared for voltage sec. For organic semiconductor, mobility normally is 1. Then comparing to the organic and silicon, current flowing at same condition is 1,000 different. So silicon is very high-performance semiconductor. There will be gallium arsenide and then other material too. But if you look at it, silicon has very high mobility, electron mobility, and hole mobility. Another reason that we are using silicon instead of other semiconductor, silicon, we can get material very easily. Then after the silicon, what semiconductor is next generation semiconductor? There is various candidate, but I believe, I think another very probable semiconductor can be a germanium. Germanium has very high electron mobility and hole mobility. Current semiconductor device using a CMOS, which is the complimentary metal-oxide-semiconductor, using both electron, MOSFET and hole MOSFET. So both electron and hole MOSFET has to be high mobility. Silicone has very high mobility of electron, but relatively low mobility of hole. So you need to compensate those mobility difference, maybe you can make much wider with the MOSFET of the hole so that more current can flow in. If you're using germanium, we have a very high electron mobility and very high hole mobility. But how can we solve the deficiency of germanium compared to the silicon? Maybe we can grow germanium epitaxy, single crystal epitaxy germanium on top of the silicon. Then we can make germanium semiconductor relatively cheap. But actually, realizing the germanium MOSFET is a little difficult issues that involves a lot of semiconductor technology. Crystal structure, this is, basically, based on the material science of the crystallography. In the material scientist, you probably learned this in sophomore year. Then unit cell is the most simplest structure. Each semiconductor material atom can be arranged that is shown in here. Unit cell is the most basic structure shown in here. This is called a unit cell. The periodic lattice can be drawn as shown in this graph and can be defined a and b, and some vector shown in here. Semiconductor material can be located each endpoint of the structure, and these lattice can be defined by the a, and corresponding angle of alpha, and b, corresponding angle of the beta c and corresponding angle of a gamma. Fundamental geometry of any lattice can be defined by the seven crystal system. Those are the cubic, tetragonal, orthogonal, rhombohedral, hexagonal, monoclinic, triclinic. You can define them in the axis of a equal b equal c. Alpha, beta, gamma equal 90 Celsius, which is the cubic. Same thing for the tetragonal, orthorhombic, rhombohedral, hexagonal, where the gamma is 120 angle, monoclinic and triclinic. Every silicon geometry can fall into these four system. Then depending on the atom locating the seven system, we can divide the 14 Bravais' Lattice. For example of the cubic, there's a simple cubic and another atom located in the center, that is the body-centered cubic. Atoms are located at each faces, then there's the six faces. Then this is the face-centered cubic. Same thing for the other structure, simple tetragonal, body-centered tetragonal, full orthorhombic structures, rhombohedral, hexagonal, monoclinic, and triclinic. Other structure that seems a little different than this 14 Bravais' Lattice, if you rotate them, they are falling to one of this 14 Bravais' Lattice. This is all material science class which is learned previously. I will not go over the detail. The lattice with a semiconducting device, this is not so much important in semiconductor devices operations.