Electronic structure of Si nanocrystals codoped with boron and phosphorus

The electronic structure of Si nanocrystals (NCs) doped with B(acceptor) and P (donor) impurities is calculated. A tight-binding approach is employed, allowing us to investigate NCs of up to 10 nm diameter and to compare directly with recent experiments on colloidal Si NCs. The calculations show that the experimental data of optical and electrical spectroscopy are consistent with configurations of full compensation between donors and acceptors. The NC energy gap is narrowed in the presence of codopants and can be even smaller than in bulk Si, but at the same time it varies with NC size under the effect of quantum confinement. Measured energy gaps are compatible with NCs containing a small number (similar to 2-5) of B-P pairs if we assume a random placement of the dopants in the NC core. B-P clusters in which the B and P atoms are nearest neighbors have a marginal influence on the NC energy gap. In the case of Si NCs doped with a single P impurity, the theory predicts the hyperfine splitting of electron spin resonance as a function of the NC size, in excellent agreement with experiments if the dopant is placed at random positions.