Inverse-photoemission study of Ge(100), Si(100), and GaAs(100): Bulk bands and surface states

We present momentum-resolved inverse-photoemission data from Ge(100)2×1, Si(100)2×1, and GaAs(100)4×2 surfaces. The bulk conduction bands of these three semiconductors are mapped along the ΓX direction. The following critical points are obtained (relative to the valence-band maximum): For Ge, ${\mathrm{L}}_{3\mathrm{c}}$=4.4 eV and ${\mathrm{L}}_{2\mathrm{c}}^{\prime }$=7.8 eV; for Si, ${\mathrm{\Gamma }}_{15\mathrm{c}}$=3.05 eV, ${\mathrm{\Gamma }}_{2\mathrm{c}}^{\prime }$=4.1 eV, and ${\mathrm{X}}_{1\mathrm{c}}$=1.25 eV; for GaAs, ${\mathrm{L}}_{3\mathrm{c}}$=5.45 eV and ${\mathrm{L}}_{1\mathrm{c}}$=8.6 eV. The L points are reached via surface umklapp processes. The experimental band dispersions and the critical points are consistent with state-of-the-art quasiparticle calculations. The empty π* surface state is seen in Si and Ge. Its cross section changes significantly with the photon energy, reflecting a wave-function character derived from that of the bulk states near Γ.