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 {Γ}X direction. The following critical points are obtained (relative to the valence-band maximum): For Ge, L3c=4.4 eV and L2c^'=7.8 eV; for Si, Γ15c=3.05 eV, Γ2c^'=4.1 eV, and X1c=1.25 eV; for GaAs, L3c=5.45 eV and L1c=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}.