With the increase in temperature, the mobility of electrons and holes in a semiconductor actually decreases like the decrease in mobility of electrons in metals. But, there is a large increase in the charge carrier concentration due to more breakage of covalent bonds with the increasing temperature. It is so large that conductivity increasing temperature and the decrease in mobility has no influence.
According to the equation of the drift velocity
(v = eE/m ×ζ ), v ∝ E
But v cannot be increased indefinitely by increasing E and the relation does not hold good at high values of E. it is so because, at high temperature, the increase in drift velocity of free electrons will bring more collisions and hence average time between two successive collisions (i.e. ζ) starts decreasing. As a result of it, the drift velocity saturates at thermal velocity and becomes almost independent of electric field at higher values of E.
The exact value of E where drift velocity saturates depends on the nature of semiconductor, doping and other defects in the semiconducting crystal.
In intrinsic semiconductor the fraction (ƒ) of the number of electrons raised from valence based to conduction band at temperature TK is given by
ƒ € e –Eg/kT
Where Eg is the value of energy band gap. The above relation shows that as T increases ƒ also increases. It means with the increase in temperature the number of electrons in conduction band increases. Due to which the conductivity of semiconductor increases with increase in temperature.
Conductivity of p-type semiconductor: in this case nh >> ne and nh = Na, where Na is the number density of acceptor atoms. Therefore, conductivity of p-type semiconductor is
σp = e Naµh
Intrinsic conduction: the number density of intrinsic current carriers (ni) of a semiconductor varies with temperature T, according to relation
ni = A0 T3/2e-Eg/kT
A0 = constant, independent of temperature
k = Boltzmann constant,
Eg = energy gap at 0 K
The energy gap: the forbidden energy gap Eg in a semiconductor is a function of temperature. It has been found that
Eg (T) = 0.785 – 2.23 × 10-4 T
For silicon, Eg (T) = 1.21 – 3.60 × 10-4 T.
At room temperature (300 K),
For Ge, Eg = 0.72 eV
And for Si, Eg = 1.1 eV.
The mobility of charge carriers varies as T-m over a temperature range of 100 to 400 K.
i.e. u ∝ T-m
In case of germanium, m = 1.66 for electron and 2.33 for hole.
In case of silicon, m = 2.5 for electron and 2.7 for hole.
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