The band gap in germanium is  ΔE=0.68eV. Assuming that the number of hole – electron pairs is proportional to  e−ΔE2kT, find the percentage increase in the number of charge carriers in pure germanium as the temperature is increased from 300 K to 320 K

The number of charge carriers in an intrinsic semiconductor is double the number of hole – electron pairs (No of holes = No of electrons). If N1 be the number of charge carriers at temperature   T1and  N2 at   T2, we have N1=N0e−∆E/2kT1                                                 N2=N0e−∆E/2kT2The percentage increase as the temperature is raised from  T1 to T2 isf=N2−N1N1×100=[N2N1−1]100                                              =100[eΔE2k[1T1−1T2]−1]Now; ΔE2k[1T1−1T2]=0.68×1.6×10−192×1.38×10-23[1300−1320]=0.82Thus,            f=100×[e0.82−1]≃127∵e0.82=2.27 ∴The number of charge carriers increases by  about 127 %.