Binding energy, vapor pressure, and melting point of semiconductor nanoparticles

Abstract

Current models for the cohesive energy of nanoparticles generally predict a linear dependence on the inverse particle diameter for spherical clusters, or, equivalently, on the inverse of the cube root of the number of atoms in the cluster. Although this is generally true for metals, the authors find that for the group IV semiconductors, C, Si, and Ge, this linear dependence does not hold. Instead, using first principles, density functional theory calculations to calculate the binding energy of these materials, they find a quadratic dependence on the inverse of the particle size. Similar results have also been obtained for the metallic group IV elements Sn and Pb. This is in direct contradiction to current assumptions. Further, as a consequence of this quadratic behavior, the vapor pressure of semiconductor nanoparticles rises more slowly with decreasing size than would be expected. In addition, the melting point of these nanoparticles will experience less suppression than experienced by metal nanoparticles with comparable bulk binding energies. This nonlinearity also affects sintering or Ostwald ripening behavior of these nanoparticles as well as other physical properties that depend on the nanoparticle binding energy. The reason for this variation in size dependence involves the covalent nature of the bonding in semiconductors, and even in the “poor” metals. Therefore, it is expected that this result will hold for compound semiconductors as well as the elemental semiconductors.