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-en ergy electronic properties of thin bismuth crystals are studied by mea ns of the high-resolution electron-energy-loss spectroscopy (HREELS) t echnique. Electronic interband transitions, taking place at the points L and T of the bismuth Brillouin zone (BZ), are distinctly brought in to evidence at 47 and approximately 200 meV, and the corresponding com plex dielectric function in this energy region is determined. This pro vides direct experimental determination of the electronic transition f rom the Fermi level (E(F)) to the point T6+. The quantum size effect i n thin Bi crystals is studied following the evolution of these electro nic excitations as a function of the crystal thickness (110-2500 angst rom). A downshift (upshift) of the transition at the point L (T) of th e 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 funct ion of temperature for crystals 750 angstrom thick, for which QSE's ar e not expected, and for crystals 200 angstrom thick which exhibit QSE' s. A redshift by approximately 12 meV of the lower-lying electronic ex citation is measured on decreasing the temperature from 298 to 155 K. The energy shift is mainly due to the temperature dependence of the ga p energy (E(g)) in L. However, the temperature evolution of the occupa ncy of the filled and empty levels involved in the transition (through the width of the Fermi-Dirac distribution function around E(F)) canno t be neglected in fully determining the observed temperature dependenc e. These two causes are still determinant when the crystal is in a QSE regime.