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The observed heavy-hole, light-hole and split-off band edges of a semiconductor are the well known consequence of two physical processes: atomic spin–orbital interaction and solid-state band–band anticrossing. In this work, we examined the four band-edge-like bands in great detail within the Ge space–charge layer with either Pb/Ge(111)- $\sqrt{3}\times \sqrt{3}$ R30° or a 2 ML Pb film on Ge(111). Our results reveal that the conventional picture of band edges for a semiconductor is actually crude. In addition, momentum-dependent Rashba splitting effect can be included to explain the observed non-split-off band, indicating the Rashba effect as an intrinsic property near a semiconductor surface.