Incomplete ionization of aluminum in silicon and its effect on accurate determination of doping profiles

We present a detailed study on incomplete ionization (i.i.) of aluminum acceptors in highly aluminum-doped p+ silicon formed by alloying from screen-printed Al pastes. We apply electrochemical capacitance-voltage (ECV) and secondary ion mass spectrometry (SIMS) measurements to detect the Al doping profiles and discuss key aspects necessary for a precise determination of the profiles. The excellent accordance of ECV- and SIMS-measured acceptor profile curves allows for the accurate investigation of Al acceptor ionization. We review the physics of i.i. and verify a simple quantitative model for incomplete Al acceptor ionization by comparing measured and calculated sheet-resistances of Al-doped p+ Si surfaces. We thus show that the electrically active Al doping concentration is nearly two times lower than the total Al concentration, so that i.i. of Al acceptors has to be considered for the correct description of highly Al-doped p+ Si regions. Therefore, our results allow for an improved quantitative analysis of n- and p-type silicon solar cells with Al-alloyed p+ rear emitter or back surface field, respectively.