Origin of the Residual Acceptor Ground-State Splitting in Silicon

The residual ground-state splitting of acceptors in high-quality silicon has been studied intensely by different experimental techniques for several decades. Recently, photoluminescence studies of isotopically pure silicon revealed the ground-state splitting to result from the random distribution of isotopes in natural silicon. Here we present a new model that explains these surprising experimental results, and discuss the implications for acceptor ground-state splittings observed in other isotopically mixed semiconductors, as well as for the acceptor ground state in semiconductor alloys.

Figure 1

The calculated statistical distribution of the ground-state splittings for 40 000 configurations of random distributions of the isotopes around the acceptor site. The most frequent values for each acceptor (the most probable value for the ground-state splitting) are listed in Table .

Figure 2

(a) The statistical distribution of the calculated eigenvalues for Al. (b) After removing 75% of the broadening, the doublet splitting is observable. The inset shows the doublet splitting observed in the PL spectra, on the same energy scale.

Figure 3

Schematic of the photoluminescence transition. (Left) The electron and hole in the bound exciton (initial state) recombine leaving behind the neutral acceptor in its ground state (final state). In an isotopically pure crystal the ground state is fourfold degenerate, and as a result, the transitions would be singlets [right ($a$)], while the perturbation caused by the isotopic impurities lifts the degeneracy of the ground state [right ($b$)]. It also causes an energy shift of the ground state, which leads to additional broadening of the transitions. The initial state bound exciton two-hole state is also shifted, but by a smaller amount than the ground state.