Q.9. Derive an expression for the conductivity of
semiconductor containing both free electrons and holes in terms of the
concentration n and p and the mobility me and mh. (AKTU. 2014 - 15)
Ans. There is a simple relation between mobility and
electrical conductivity. Let n be the number density (concentration) of
electrons, and let me be their mobility. In the electric field E,
each of these electrons will move with the velocity vector -meE, for a total current density of nemeE (where e is the elementary charge). Therefore, the
electrical conductivity s satisfies:
s = neme
This formula is valid
when the conductivity is due entirely to electrons. In a p-type semiconductor,
the conductivity is due to holes instead, but the formula is essentially the
same: If p is the concentration of holes and mh is the hole
mobility, the the conductivity is
s = pemh
If a semiconductor has
both electrons and holes, the total conductivity is
s =
e(nme + pmh)
Q.10. Show that a Fermi level in an intrinsic
semiconductor lies half way between the top of valence band and bottom of
conduction band. (2014 - 15)
Ans. Fermi
level in an intrinsic semiconductor: -
To classify conductors, semiconductors and insulators
we make use of the reference energy level called Fermi level. In case of an
intrinsic semiconductor, Fermi level (EF) lies in the middle of energy gap or mid way between
the conduction and valance bands.
Let (at any temperature T0K)
nv = number of
electrons in the valance band
ne = number of
electrons in the conduction band, and
N = Number of electrons in both
bands.
Assumptions: -
(i) In valance band
energy of all levels is zero.
(ii) In conduction
band, energy of all levels is equal to Eg (energy at gap)
(iii) As compared to
forbidden energy gap between two bands, the widths of energy bands are small.
(iv) All levels in a
band consist of same energy due to small width of band.
Let the zero energy reference level
is arbitrarily taken at the top of valence band.
\ No. of
electrons in the conduction band, ne = N.P (Eg)
Where P (Eg) = probability of an electron having energy Eg
Fermi-Dirac probability
distribution function gives its value given below:
Q.11. How the temperature affects the critical
field of a superconductor? (2015 - 16)
Ans. Superconductivity
is characterized both by perfect conductivity (zero resistance) and by the
expulsion of magnetic fields (the Meissner effect). Changes in either
temperature or magnetic field can cause the phase transition between normal and
superconducting states. For a given temperature, the highest magnetic field
under which a material remains superconducting is known as the critical field.
The highest temperature under which the superconducting state is seen is known
as the critical temperature. At that temperature even the smallest external
magnetic field will destroy the superconducting state, so the critical field is
zero. As temperature decreases, the critical field increases generally to a
maximum at absolute zero.
