Low-temperature scanning tunneling spectroscopy measurements on semiconductor surface are described. We consider both surface which do not possess surface states within the bulk bandgap, such as GaAs(110), and surfaces which do have states within the gap, such as Ge(111)2x1 and Ge(111)c(2x8). Band bending in the semiconductor due to the electric field in the vacuum penetrating the semiconductor is found to be a substantial effect in the former case. Transport limitations in the semiconductor give rise to additional voltage drops, which can be observed by making measurements over a wide range of tunnel current magnitudes.