[MUSIC] Let's look at the silicon lattice. Silicon has 14 electrons occupying the lowest three energy levels, 1s, 2s, 2p, filled by the 10 electrons, and 3s, 3p filled by the four electrons. Therefore, silicon has four arms are neighbors of the 3s and 3p orbital. Structure of the silicon is the diamond lattice. Inside the unit cell of a silicon lattice there's a two fcc structures showing in this image It is kind of a little difficult to understand of why this is the two fcc inside. To understand more a little bit easier, let's look at the zinc blende structure below here. This is the gallium arsenide and zinc blende lattice. There is let's say the black is the gallium. Gallium has an fcc structure, they have a four, they have eight location of gallium. And each face they have a gallium also, there is a total six faces. Another fcc of arsen is located on upper level of two, this is arsen and lower level of arsen here and here. This is the two fcc intercalating each other. For silicon cases, same structure but only silicon. So this two fcc intercalated structure is called diamond lattice. Diamond, how many atom in per unit cell in silicon? So they have eight atoms At the end but each atom contribution to the unit cell is one-eighth. And they have all total eight of silicon. They have six silicon on the surface, so six on the each surface, their contribution to the union is only half, So one fcc has four atoms per fcc, how many fcc has in this silicon lattice? There's a two FCC, therefore four times two total eight atoms in per unit cell. This is important, we are talking about eight atom in unit cell later and germanium is also diamond structures. Other semiconductors such as gallium arsenide, aluminum arsenide, indium phosphide is zinc blende lattice. And gallium nitride and cadmium sulfide and zinc sulfide in the Wurtzite lattice which is related to the hexagonal structures of 120 angle. So crystal plane is this is silicon 100 direction, perpendicular to the 100 direction is crystal plain parenthesis 100. This means the crystal plane 100, which is perpendicular to the direction above 100. Direction, normally described by the 100. So crystal plane is perpendicular to the direction of 100. Same thing for the crystal plane, 110 is perpendicular to the direction of the 110 direction. If you have a direction in 111 direction, then perpendicular to the direction of 111, this triangle is crystal plane 111. So silicon wafer, if you buying silicon wafer, there's a two format of silicon wafer. One is the flat surface on top and the other one is there's a notch at the top of the silicon wafer. Let's say that you bought the silicon wafer 100 crystal plane. These are both silicon 100 crystal plane semiconductor and if you saw the flat surface on top Perpendicular to the top plat is 110 or 011 direction crystal is the symmetry. So 011 direction and 110 direction is identical. Another silicon wafer that has a notch on top, this is the silicon 100 silicon and then notches on top, this notch direction is 011 direction. Why this is important? If you look at the right side of the image, depending on the crystal plane of silicon, this is the 100 silicon wafer, this is the 110 crystal wafer, this is the 111 crystal wafer, depending on the crystal plane. Device mobility which is very important for the current and performance is different. Not only crystal plane, but for the same crystal plane, you can make a most source drain caught the direction in this direction or this direction. So, not only the crystal plane but also the direction of the current flowing, they have different mobility. These are the electron mobility and these are the whole mobility. Interestingly, whole mobility of silicon has highest of the crystal plane of the 110 and then direction to the perpendicular to the 100 direction. So that's why the crystal plane and direction is important to the semiconductor device. So calculate the maximum fraction of volume in simple cubic crystal occupy the atom. Assume that atoms are closely packed and they can be treated as a hard sphere. For simple cubic, the unit cell volume has acubic. That is in simple cubic, there is only one atoms because there is total eight atom at the corner but their contribution is one over eight, therefore one. So one atom is located at the simple cubic and volume of the one atom is four over three pi r cubic. Then are for the simple cubic because, Because atoms are closely packed. Is simple cubic, So two r equals to the lattice of the a, therefore r equal a pi 2. If you put this then this is the Pi over six packing density is the 52%. For example of the face center the cubic, there are four atom as I said in previous and face center in each face then 4r equals Root 2a because a a root 2, therefore, radius is becomes like This. Then packing density is 74.
