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 (${\mathit{E}}_{\mathit{F}}$) to the point ${\mathit{T}}_6^{+}$. 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 Å). 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 Å thick, for which QSE’s are not expected, and for crystals 200 Å 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 (${\mathit{E}}_{\mathit{g}}$) 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 ${\mathit{E}}_{\mathit{F}}$) cannot be neglected in fully determining the observed temperature dependence. These two causes are still determinant when the crystal is in a QSE regime.