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BAND THEORY :written by GENESIS TUTORIALS

BAND THEORY
→An atomic orbital on one atom combines with an atomic orbital on the anther atom to form equal number of molecular orbitals.
→These molecular orbitals are of two types Bonding molecular orbital having lower energy Anti-bonding molecular orbital having higher energy
→With increasing number of atoms of atoms, the separation between the anti-bonding and bonding orbitals becomes smaller and smaller
→These anti bonding and bonding orbitals collectively represent continuous band
→The gap between these Band is called band-gaps



Eq Na→1S2, 2S2, 2P6, 3S1
The first two shells of the sodium are held close to nucleus and do not interact with the orbitals of the atoms on neighboring lattice points. The 3S (practically filled) and 3P (empty) orbitals are sufficiently large enough in size to overlap with the corresponding orbitals on neighboring atoms to produce a band.
→ Band containing electrons is called valence band and band containing no electrons (or empty) above the valence band is called conduction band.
→ The separation between the valence and conduction bands dictates the overall electronic properties.
→ The separation of the bands depends on the original sparation of the atomic orbitals. If the original atomic orbitals were very close in energy, the bands will also be very in energy.
The change in conductivity with temperature for conductor, semiconductor and Insulator can be explained as follows__
→ For conduction to occur. The electrons must have enough energy to move to a vacancy in another energy level.
       
→An insulating material would have a band gap of much greater than 3eV (e.g. for diamond, the band gap is 6eV). There is not enough energy to jump this gap at practical temperatures which would allow the material to be used as semiconductor.        
Typical band gaps (eV) of insulators
B.T (D) 1eV = 1.60217733×10-19J molecule-1
= 96.485 KJ     mol-1
Insulators                    Energy
Semiconductors                energy/eV
C (diamond)                       6
NaCI                                   9
NaBr                                  8
KF                                     11
KCI                                    9
Si                                   1
Ge                                  0.7
Sn                                  0.1
GaAs                              1.4
Inp                                 1.3



→Materials which naturally have a small band gap, like silicon and germanium, are called intrinsic semiconductors
→Elements and compounds which are not semiconducting in the pure. State can be made semiconducting by doping. These materials are called extrinsic semi conducting (eq. n- type semi cond. and p-type semi cond.)
→ doping involves replacing a very small amount of the element with either lesser or more electrons per atom. The doping silicon, having elec. Configuration 1S2 2S2 2P6 3S2 3P2 can be done with aluminum (one less electron) and phosphorous (one more electron)
→The donor band is formed when silicon is doped with phosphorous (having one more than)
→The donor band is closer in energy to the conduction band of silicon than the silicon valence band. Hence promotion of an electron from donor band to the conduction band in the doped material required less energy and will occur at lower temperature than in the pure material. This process creates an ‘n-type extrinsic semiconductor, where n stands for negative.
→The opposite is true for addition of aluminum. Addition of very small amounts of aluminum creates a conduction band lower in energy than the lost silicon lattice for each aluminum, a hole is formed. These hole can accept an electron from the energy barrier for conduction. This types of extrinsic semiconductor is called ‘p-types semiconductor’ where p stand is positive.
Ques The band structure in an n-type semiconductor is-
Ques consider a n-type semiconductor whose Ev = 0 Ec = 2.0eV And Ed = 1.98 eV. The correct statement among the following is-
(a) Ef = 1 eV and is independent of T
(b) Ef = 1.99 eV and remains independent of T
(c) Ef = 1.99 eV and increases towards 2.0eV with increase of T

(d) Ef = 1.99eV and decrease with increase of T
author

DESH DEEPAK A P S CHAUHAN

M.Sc. CHEMISTRY!

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