Question

(1) how Bragg diffraction occurs in a crystal with electrons inside

(2) what caused the energy levels to break into a “gap”,

(3) what is the different between a conductor such as Cu and a semiconductor such as Si?

Answer 1

1) the bragg condition for constructive interference is given by

when a beam of electrons was reflected from a single crystal fomed interference patterns . the solid horizotal lines form one set of reflecting planes.

2) A gap consists of an arrangement of two conducting energy levels seperated by a gap asusually filled with a gap, energy bands consisting of a large number of closely spaced energy levels exist.

the bands can be thought of as collection of the individual energy levels of electrons surrounding each atom. the wave functions of the individual electrons, however overlap those of electorons confined to neighboring atoms.

As the lattice constant reduced, there is an overlap of electron wavefunctions occupying adjacent atoms. this leads to break into a gap of energy levels consisting with pauli's exclusion principle.

In order to find the filled and empty bands we must find out howmany electorns can be placed in each band and how many electrons are available. each band is formed due to break into gap of one or more atomic energy levels. hence, the minimum number of states in a band equals twice the number of atoms in the material.

3) the important difference between conductors and semiconductors lies in the number of free electrons present in the material.

according to band theory of solids,

for conductors, there is no band gap between conduction band and valence band

for semiconductors, the band gap between conduction band and valence band is 1.1eV.

for example ,

charactristics	Cu as conductor	Si as semiconductor
electron availabilty	more number of electrons in conduction band	less number of electrons in conduction band
temperature coeffiecient of resistance	-0.07 per degree C	+0.004041 per degree C
forbidden gap in eV at 300K	1.11	0