Physically sound parameterization of incomplete ionization in aluminum-doped silicon

Incomplete ionization is an important issue when modeling silicon devices featuring aluminum-doped p+ (Al-p+) regions. Aluminum has a rather deep state in the band gap compared to boron or phosphorus, causing strong incomplete ionization. In this paper, we considerably improve our recent parameterization [Steinkemper et al., J. Appl. Phys. 117, 074504 (2015)]. On the one hand, we found a fundamental criterion to further reduce the number of free parameters in our fitting procedure. And on the other hand, we address a mistake in the original publication of the incomplete ionization formalism in Altermatt et al., J. Appl. Phys. 100, 113715 (2006).