Question

A semiconducting material has a band gap of 1 eV. Acceptor impurities are doped into it which create acceptor levels 1 meV above the valence band. Assume that the transition from one energy level to the other is almost forbidden if kT is less than 1/50 of the energy gap. Also if kT is more than twice the gap, the upper levels have maximum population. The temperature of the semiconductor is increased from 0 K. The concentration of the holes increases with temperature and after a certain temperature it becomes approximately constant. As the temperature is further increased, the hole concentration again starts increasing at a certain temperature. Find the order of the temperature range in which the hole concentration remains approximately constant.

Answer 1

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Explanation:

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Answer 2

Explanation:

It is given that

Gap of band = 1 eV

After doping,

Acceptor levels position = above the valence bond, 1 meV  

After doping, the net band gap = $\left(1-10^{-3}\right) \mathrm{eV}=0.999 \mathrm{eV}$

As per the question,

The transaction of energy from one level to the other level is almost prohibited if 1/50 of the energy gap is more than kT.

⇒kT1 = 0.99950  

⇒T1 = 231.78, which is 232.8 K.

No transaction is possible when the temperature is T1.

When kT is higher than double the gap, there will be maximum population in upper levels; that is, there will be no more transitions.

For the maximum limit,

$\mathrm{KT} 2=2 \times 10-3$

$\Rightarrow \mathrm{T} 2=28.62 \times 102=23.2 \mathrm{K}$

The temperature above which there will be no transition is T2.

Therefore, the range of temperature = 23.2 − 231.8 .