Question

a) Is it possible to examine the crystal structure using visible light (wavelength between 300 and 700 nm). Why?
b) Briefly describe the meaning of the word “optics" in the optical phonon expression.
c) What is the effective mass, explain.
d) As doped Si:As semiconductor, n, p, and N_p means electron, hole and doped (As) respectfully. Use the charge neutrality to determine n/N_d in terms of n_i/N_d,for the determination of intrinsic carrier concentration for n_i Si semiconductor.

Answer 1

(a) No. atoms in a crystal are separated from each other by a distance which is of the order of few angstrom. But visible light has a wavelength of 390 - 760 nm. Hence, visible light can not probe between two adjacent atoms. Since, X ray has a wave length of the order of angstrom generally x-ray diffraction is used to understand the structure of a crystal.

(b) Optical phonon modes are those states of lattice vibration in which two neighboring atom in a lattice move out of phase to each other. The term 'optical' in the name of these phonon modes comes as these phonon modes in ionic crystal are excited by infrared. The electric field associated with infrared moves the positive ions in one directions and the alternate negative ions in other direction for a ionic crystal.

(c) In condensed matter physics effective mass of any particle is the mass assigned to it when responding to general forces in the system, or the mass that it seems to have when interacting with the lattice. Effective mass in different context can take different form. Most common use of effective mass is for the electrons and holes moving in the conductance band and valance band respectively. For a particular band dispersion, effective mass is related to the curvature of the band.

(d)