Assumption of complete ionization of donors in a semiconductor

exercise 3_4965

Calculate the Fermi level (chemical potential) position relative to the conduction band minimum and intrinsic Fermi level of Si doped with ( i ) 10 15 , ( ii ) 10 17 , and ( iii ) 10 19 phosphorus atoms/cm 3 at room temperature ( T = 300 K), assuming complete ionization. Verify that the intrinsic Fermi level position is close to mid-gap for each of these cases. From the calculated Fermi level , (chemical potential), check if the assumption of complete ionization is justified for each doping concentration. The donor ionization energy of phosphorous is 45 meV and the bandgap of Si is 1.12 eV at room temperature.