1. (a). Given that silicon crystallizes in the diamond cubic structure, atoms are tetrahedrally co-ordinated, and bonds are along the <111> directions, calculate the bond length and the lattice parameter of silicon; assume that the covalent tetrahedral radius of the silicon atom is 0.117 nm.
(b). If a silicon atom is replaced by a boron atom whose covalent tetrahedral radius is 0.08, calculate the change in bond length and the local strain.
(c). Common n- and p-type dopants in silicon are, respectively, P, As, and B; justify their choices using the local strain considerations; the respective radii are 0.110 and 0.117 nm
2. (a) Using dimensionality as the criterion, discuss the classification of defects in crystalline solids and explain their thermodynamic stability.
(b). Explain the concept of anti-site defects in the zinc-blende structure.
(c). Two types of anti-site defects are possible in GaN; will their energies be equal or different? Give reasons.
3. Given that two edge dislocations of opposite in sign are gliding on two parallel (111) planes in an FCC crystal; the vertical separation between the planes is one micron.
(a). Sketch the extra-half plane of the edge dislocation.
(b) Calculate the number of point defects that will be required for the dislocations to annihilate each other; assume that the dislocation lengths are one micron in each case and the lattice parameter is 0.5 nm.
4. If an FCC single crystal is pulled in tension along the [12-3] direction, determine the slip system along which deformation will occur.