The local density of states (LDOS) at the epitaxially grown InAs surface on a GaAs(111) A substrate were characterized using low-temperature scanning tunneling microscopy. Using dI/dV signal mapping, LDOS standing waves were clearly imaged at point defects and within nanostructures. Measurement of the wavelength as a function of bias voltage showed a nonparabolic dispersion relation for the conduction band. The observed wave features originate from the Friedel oscillations of the two-dimensional electron gas in the semiconductor surface accumulation layer.