In an ideal crystal there must be regular repeating

arrangement of the constituting particles and its entropy must be zero at absolute zero temperature. However, it is impossible to obtain an ideal crystal and it suffers from certain defects called imperfections, In pure crystal, these defects arise either due to disorder or dislocation of the constituting particles from their normal positions or to the movement of the particles even at absolute zero temperature. Such defects increase with rise in temperature. In addition to this, certain defects arise due to the presence of some impurities. Such defects not only modify the existing properties of the crystalline solids but also impart certain new characteristics to them.

In pure crystal, e.g. silicon or germanium at 0 K, the electrons are present in fully occupied lowest energy states and are not expected to conduct any electricity. However at temperature above 0 K, some electrons leave their bonds and become free to move in the crystal lattice, giving rise to electrical conductivity. The electron deficient bonds, called holes

(+ively charged) and thermally mobile electrons move in opposite directions under the electric field.

Stoichiometric point defects include

(1) Schottky defects, which arise due to missing of both cations and anions from their lattice sites without disturbing the stoichiometry and (2) Frenkel defects, which arise due to misplacement of certain ions in the crystal lattice. The former defect gives rise to decrease in density of the crystal and the latter leads to no change of density.

Another type of defects are non-stoichiometric defects where the cations and anions are not present in the stoichiometric ratio. In metal excess defect, metal ions or positive ions are in excess as compared to anions of non-metals stoichiometrically. On the other hand in metal deficient defect, the cations are in lesser proportion than stoichiometric value. Since the crystal is neutral electrically, the balance of charge is maintained by free electrons or extra positive charges. The metal excess defects give rise to conduction of electricity due to the presence of tree electrons. Also crystals having metal excess defects are paramagnetic and coloured due to the presence of electron in the anions vacancies.

Impurity defects arise when some foreign atom are present at the lattice sites in place of the host atoms or at the vacant interstitial sites,

When 15 group elements like P or As are doped into Si or Ge, the added impurity atoms occupy the lattice sites forming four covalent bonds with 4 Si/Ge atoms leaving an extra electro free to move. Such a crystal is said to be n-type

semi conductor because the conduction of electricity is due to the movement of extra unbonded electrons.

If doping of a covalent crystals of 14 group elements are caused by addition of small amounts of elements of group 13, e.g. Al or Ga with three valence electrons, one covalent bond formed will be electron deficient and acts as a positive hole. The presence of such holes in the crystal leads to electrical conductivity and the crystal is said to be p-type semiconductor.

(i) In the crystal of Fe 0.95 O, the percentage of Fe(III) will be –