Download PHYS1070 PhysicsPHYS1070 PhysicsPHYS1070 Physics and more Lecture notes Physics in PDF only on Docsity!
PHYSICS 1070
SEMICONDUCTOR PHYSICS
CRYSTAL STRUCTURE – Planes and Direction Vectors
Crystal directions, planes and the position of atoms can be easily described, particularly for cubic crystals since the coordinate system is orthogonal. Consider a plane as shown below which intercepts the axes of a Cartesian coordinate system at (p,q,s). Figs. 1.6 An Introduction to Semiconductor Devices, D. Neamen Planes can be identified by Miller Indices. To determine the Miller Indices for a plane; find intercepts, then their reciprocals (1/p,1/q,1/s) and finally multiply by the lowest common denominator to obtain the Miller indices for the plane (hkl). eg. Find the Miller indices of the planes shown below, where a = b = c = 1; Fig. 1.7 An Introduction to Semiconductor Devices, D. Neamen
Consider the following three planes in a simple cubic crystal. The length of the cube side is a, the lattice constant. In cubic crystals, the direction of the plane is given by a vector perpendicular to the plane, [hkl]. The planes shown are given by (100), (110) and (111) while the direction of the planes is [100], [110] and [111] respectively. In cubic crystals the distance between adjacent parallel planes is given by d = a/(h^2 + k^2 + l^2 )1/^. Fig. 1. 8 Semiconductor Physics and Devices, Donald A. Neamen
CRYSTAL STRUCTURE – Characteristics of Cubic Lattices
In the cubic system there are three lattices; simple cubic (sc), face-centered cubic (fcc) and body-centered cubic (bcc) with characteristics given in the following table; Fig. 1.5 Semiconductor Physics and Devices, Donald A. Neamen
Copper, silver and gold form face-centered cubic structures. Sodium Chloride is composed of two face-centered cubic lattices, the Na lattice and the Cl lattice are offset by ½ of a body diagonal. NaCl is an example of an ionic crystal. Na has 11 electrons with ground state electron configuration of 1s^2 2s^2 2p^6 3s^1 and is easily ionized. Cl has 17 electrons 1s^2 2s^2 2p^6 3s^2 3p^5 and easily gains an electron. The lattice constant for NaCl is a = 5.63 Å. Elements can occur in more than one crystal structure and a transformation from one type to another can occur when the temperature changes or under pressure eg. Iron becomes a solid at 1538° C and forms a bcc crystal, as it cools the crystal becomes fcc at 1394 °C and finally below 912 °C it becomes bcc again. These different forms are called allotropes. In some material more than one crystal structure can occur at the same temperature. eg. C has many allotropes including diamond, graphite, amorphous and hexagonal diamond. Hexagonal diamond is formed from graphite in meteorites due to the heat and pressure in impact with the earth. EXAMPLE PROBLEMS
- Find the number of atoms and the maximum packing fraction in a conventional unit cell of a bcc crystal.
