Self-Purification in Semiconductor Nanocrystals

Doping of nanocrystals is an important and very difficult task. “Self-purification” mechanisms are often claimed to make this task even more difficult, as the distance a defect or impurity must move to reach the surface of a nanocrystal is very small. We show that self-purification can be explained through energetic arguments and is an intrinsic property of defects in semiconductor nanocrystals. We find the formation energies of defects increases as the size of the nanocrystal decreases. We analyze the case of Mn-doped CdSe nanocrystals and compare our results to experimental findings.

Figure 1

Partial density of states projected into ${\mathrm{Mn}}_d$ orbitals for Mn-doped (a) bulk CdSe and nanocrystals with (b) 2.6 nm and (c) 1.4 nm diameter. Each figure is split into spin-up (above) and spin-down (below) channels. The dashes in (b) and (c) are the eigenvalues for the nanocrystals. The zero of energy is set to the highest occupied orbital.

Figure 2

Charge density plot of the impurity $d$ levels in a Mn-doped CdSe nanocrystal with 1.7 nm of diameter. (a) is for the level resonant in the valence band, and (b) is for the hybrid level.

Figure 3

Variation of the formation energy of a substitutional Mn impurity in a CdSe nanocrystal as a function of the nanocrystal diameter. The increase in the formation energy is important to explain self-purification in nanocrystals.