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. Assumed 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 0K. The concentration of the holes increase 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.

Originally the band gap was 1eV. After doping, the band gap will become =(1eV-1meV)

= (1-0.001) eV


=0.999 eV


It is given that the transition is almost forbidden at 1/50 of 0.999eV. Let the upper limit for temperature be T1 over which the transition becomes a forbidden transition.


• kT1=0.999/50


• T1=231.78K≈231.8K


Let the lower limit for temperature be T2 for which the transitions are most feasible or for which the upper levels have maximum population.


• kT2=2(0.999)


• T2=23.2K


Therefore, the required temperature range=(23.2K-231.8K)


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