Semiconductor nanoparticles have been intensively studied in recent times because of the dependence of their properties on nanoparticle size, an effect which has tremendous technological implications. In this study we focus on a specific set of properties - the modification of the bulk modulus with size. Studies on semiconductor nanocrystals have been found to have an enhanced
bulk modulus compared to values for the bulk. It is difficult to study the renormalization of the mechanical properties experimentally. One does not always have a homogeneous distribution of particles. Further their sizes vary over several percent. In this context theoretical calculations which can simulate the ideal situation would provide valuable insight into the modifications as a function of size.
We have examined within first principle calculations, the bulk modulus enhancement in the elemental group IV semiconductors as a function of size for particles with diameters upto $\sim$ 30 $\AA$. In the case of Si, a cross-over to almost bulk-like values for the bulk modulus is seen for particles sizes in the range 25-30 $\AA$. For particles with diameter larger than 15 $\AA$, we find a scaling of the bulk modulus which is in very good agreement with the scaling relation derived in general for bulk semiconductors. The results for other systems will be contrasted with "bulk-motivated" models in an
attempt to formulate a general picture for the modifications. |