Estimate the proportion of boron impurity which will increase the conductivity of a pure silicon sample by a factor of 100. Assume that each boron atom creates a hole and the concentration of holes in pure silicon at the same temperature is $$7 \times 10^{15}$$ holes per cubic metre. Density of silicon is $$5 \times 10^{25}$$ atoms per cubic metre.
Total no.of charge carriers initially $$= 2 \times 7 \times 10^{15} = 14 \times 10^{15}/Cubic\, meter$$
Finally the total no. of charge carriers $$= 14 \times 10^{17} / m^3$$
We know :
The product of the concentrations of holes and conduction electrons remains, almost the same.
Let x be the no.of holes.
So, $$(7\times 10^{15})\times (7\times 10^{15}) = X \times (14 \times 10^{17}-X)$$
$$\Rightarrow 14 X \times 10^{17}- x^2 = 79 \times 10^{30}$$
$$X^2 - 14 X \times 10^{17}- 49 \times 10^{30}=0$$
$$X =\dfrac {14 \times 10^{17}\pm 14^2 \times \sqrt{10^{34}+4 \times 49 \times 10^{30}}}{2}= 14.00035 \times 10^{17}$$
= Increased in no.of holes or the no.of atoms of Boron added.
$$\Rightarrow 1$$ atom of Boron is added per $$\dfrac {5\times 10^{28}}{1386.035 \times 10^{15}}= 3.607 \times 10^{-3} \times 10^{13}= 3.607\times 10^{10}$$
When a semiconducting material is doped with an impurity, new acceptor levels are created. In a particular thermal collision, a valence electron receives an energy equal to 2kT and just reaches one of the acceptor levels. Assuming that the energy of the electron was at the top edge of the valence band and that the temperature T is equal to 300 K, find the energy of the acceptor levels above the valence band.
Which of the statements given is true for p-type semiconductors (a) Electrons are majority carriers and trivalent atoms are the dopants. (b) Electrons are minority carriers and pentavalent atoms are the dopants. (c) Holes are minority carriers and pentavalent atoms are the dopants. (d) Holes are majority carriers and trivalent atoms are the dopants.
An n-type and p-type silicon can be obtained by doping pure silicon with :
Indium impurity in germanium makes
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In a $$p$$-type semiconductor germanium is doped with :
The energy band diagrams for three semiconductor sample of silicon are shown. It follows that.
To obtain $$P-$$ type $$Si$$ semiconductor, we need to dope pure $$Si$$ with
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