Chemical trend of the formation energies of the group-III and group-V dopants in Si quantum dots

Abstract

Doping behavior in quantum dots (QDs) differs from that in the bulk. Despite many efforts, the doping properties are still not fully understood. Using first-principles methods, we have calculated the formation energies of various group-III acceptors and group-V donors doping at all non-equivalent sites in a Si QD (Si147H100). To analyze the trend of the formation energy, we decompose it into two terms: the unrelaxed formation energy (chemical energy) and the relaxation energy. We find that the unrelaxed formation energy generally increases as the dopant moves from the center of the QD to the surface. The variation of the unrelaxed formation energy in the surface region is explained by the variation of the local potential of the QD and the size effect. The relaxation energy gain increases as the size mismatch between the dopant and Si atom increases. Generally, the relaxation effect becomes more significant as the dopant moves toward the surface of the QD. The trend of the formation energy is determined by the two terms discussed above. If the size mismatch between the dopant and Si atom is small, the trend of the formation energy generally follows that of the unrelaxed formation energy, increasing as the dopant moves from the center to the surface; thus, these dopants have a better chance of staying in the core region. On the other hand, if the size mismatch is large, the relaxation effect dominates and the formation energy decreases, which indicates these dopants cannot enter the core region under equilibrium growth conditions.

Ab-initio study of the segregation and electronic properties of neutral and charged B and P dopants in Si and Si/SiO2 nanowires

“…A similar trend for the neutral B and P dopants in small Si nanoclusters has been explained in the literature 13 as follows: confinement tends to shift both valence and conduction bands away from the bulk gap when approaching the edge of the system. Therefore, acceptor levels created near the top of the valence band (as in the case of B impurities) will be lower in energy near the surface.…”

“…5(a)). This suggests that the mechanism driving the formation energy of impurity dopants in H-passivated Si nanoclusters, 13 which we discussed in the Introduction, can also be extended to the case of H-passivated nanowires.…”

“…To understand the various influences of the impurities on the dopant formation energy, we try to isolate the different contributing effects of the substitutional atoms. Following the results of Ma and Wei 13 for doping in Si nanoclusters, we distinguish the environmental (or chemical) and relaxation effects. The environmental effect is defined as the changes in the properties of the wire that follow from substituting a silicon atom with a dopant one without allowing a relaxation of the structure.…”

“…A second observation that can be made is that the relaxation at the edge is larger than at the center. 3,13 In other words, the relaxation effect favors the edge over the center of the nanowire. Interestingly, the observed trend in the formation energy can again be understood in terms of the average bond lengths of the dopants with the surrounding atoms.…”

“…The origin of the segregation process of neutral dopants in H-passivated Si nanoclusters (quantum dots) has recently been discussed. Ma and Wei argued that two effects determine the preferential positions of the dopants: 13 their chemical environment and their structural relaxation. The chemical environment favors the center of the dots, while the structural relaxation favors the edge as the most preferable position for dopants.…”