Quantum size effects and temperature dependence of low-energy electronic excitations in thin Bi crystals

The quantum size effect (QSE) and temperature dependence of the low-energy electronic properties of thin bismuth crystals are studied by means of the high-resolution electron-energy-loss spectroscopy (HREELS) technique. Electronic interband transitions, taking place at the points L and T of the bismuth Brillouin zone (BZ), are distinctly brought into evidence at 47 and ∼200 meV, and the corresponding complex dielectric function in this energy region is determined. This provides direct experimental determination of the electronic transition from the Fermi level (EF) to the point T6+. The quantum size effect in thin Bi crystals is studied following the evolution of these electronic excitations as a function of the crystal thickness (110-2500). A downshift (upshift) of the transition at the point (T) of the BZ is measured by HREELS, and shown to be related to the Fermi-level modification as a function of thickness. This experimental finding is consistent with the theoretical predictions for the QSE-induced Fermi-level shift. In addition, the same experiment is performed as a function of temperature for crystals 750 thick, for which QSE's are not expected, and for crystals 200 thick which exhibit QSE's. A redshift by ∼12 meV of the lower-lying electronic excitation is measured on decreasing the temperature from 298 to 155 K. The energy shift is mainly due to the temperature dependence of the gap energy (Eg) in L. However, the temperature evolution of the occupancy of the filled and empty levels involved in the transition (through the width of the Fermi-Dirac distribution function around EF) cannot be neglected in fully determining the observed temperature dependence. These two causes are still determinant when the crystal is in a QSE regime.