The thickness dependence of the optical absorption spectrum of thin single crystals of W${\mathrm{Se}}_2$ (500 Å to a unit-cell layer) was studied in the wavelength region 8000-5000 Å at 77°K. A significant shift (0.15 eV) to higher energies in the position of the exciton absorption peaks was observed with decreasing thickness. Such a shift is shown to follow a $\frac{1}{t^2}$ dependence on the thickness ($t$) down to 40 Å. This fact suggests the presence of a quantum size effect. A deviation from the $\frac{1}{t^2}$ law has been observed for crystals less than 40 Å thick.

• Received 17 August 1970

DOI:https://doi.org/10.1103/PhysRevB.2.4893