Quantum Confinement

A priori, there is no reason to expect any particular variation in the structure parameters due simply to a reduction in the volume of the nanocrystal. However, for very small dimensions, of the order of a few nanometers, a quantum confinement effect occurs, leading among other things to a change in the electronic structure. This change is accompanied by a shortening of the atomic bonds within the nanocrystal. This effect is relatively small and difficult to demonstrate experimentally. However, although this variation is small, it has been obtained in simulations for Ge nanoparticles (see Fig.1). The surfaces, passivated by hydrogen, have little influence in this case, and the bond contraction observed does indeed arise as a consequence of quantum confinement. The effect nevertheless remains very slight, even for very small nanocrystals with diameters of the order of 2 nm.

Fig.1. Calculated variation of the atomic volume and the associated pressure as a function of the size of Ge nanocrystals. Two types of structure are considered: diamond cubic (black symbols) and ST12 (white symbols); and two surface states: hydrogen passivated (circles) and with reconstructed layers (squares)