Effect of incomplete ionization of gate impurity and band-gap narrowing on tunneling current from the gate

摘要

Incomplete ionization of impurities highly doped in gate poly-Si and band-gap narrowing (BGN) due to many-body interactions between carriers and ionized impurities are shown to affect direct tunneling current from the gate to the substrate Si. It is hardly possible in theory to self-consistently calculate the ionization rate of the impurities and the BGN, since the BGN is described in terms of a scattering state whereas the ionization is described in terms of a bound state. Thus, a phenomenological scheme is proposed to self-consistently calculate the ionization rate and the BGN. As a result, the incomplete ionization assumption is found to fit the calculated I-V curve to the measured one, which could not be done by the complete ionization assumption.