The Fermi level position is dependent on the QD size; specifically, the smallest bandgap QD have the Fermi level near the conduction band minimum and the Fermi level moves away from the conduction band for larger bandgap QD.
Say for a Bulk material(semi metal) fermi level is at conduction band minimum at 0K. How can I calculate the shift in this fermi enegy when that material is scaled down to nanocrystal size or Quantum Dots in case of semiconductors? Is there any means to calculate fermi energy level variation with size of Quantum Dots.