Incomplete activation and ionization of dopants in Si at room temperature

A new model for incomplete ionization of dopants in Si is presented, where the Fermi level of free carriers may displace with respect to the case of full activation of dopants. The curves of the ratio of free-carrier density and active-dopants density vs doping, which are calculated at partial activation of dopants with the new model, overlap exactly with the curves of the same quantity calculated at full activation of dopants with a reported model. Calculations are performed with and without reported parameterizations of the density of states and occupancy probability of the dopant band simulating incomplete ionization around the Mott concentration. With parameterizations, comparisons with Hall-mobility data show that the curves of free-carrier density calculated at partial dopant activation with the new model are more accurate than the curves of the same quantity calculated at full dopant activation with the reported model. Without parameterizations, the new model allows calculating for the same carrier species curves of majority-carrier mobility that fit measured data of minority-carrier mobility at high dopings and agree with the Klaassen mobility model for minority carriers. The consistency with the band theory of the new and reported models is discussed, and the new model is found to be the most appropriate in this respect. The free-carrier density calculated with the new model without parameterizations overlaps at high dopings with free-carrier density calculated with reported models for band-gap narrowing and allows calculating curves of Auger lifetime of majority carriers that fit measured lifetime data of minority carriers.