From measurements of the dispersion of the lowest two conduction bands in silicon by $k$-resolved inverse photoemission the energies of the $L_1^c$ and $L_3^c$ critical points were determined as 2.40±0.15 and 4.15±0.10 eV relative to the valence-band edge, respectively. A comparison with energies derived from photoemission and optical data reveals a large excitonic lowering of the $E_1$ transition by 0.5±0.2 eV. The lowest unoccupied surface state on the Si(111) 2×1 surface at $\overline{\Gamma }$ is identified at 1.2±0.1 eV.

• Received 19 October 1984

DOI:https://doi.org/10.1103/PhysRevLett.54.142