The dynamic behavior of single bistable Si dopants in the GaAs (110) surface, which switch between a positive and a negative charge configuration, was investigated using a scanning tunneling icroscope (STM) and noise analysis electronics. The dopant atom switching frequency shows a clear dependence on the bias voltage and tunneling current, because these parameters influence the escape and capture processes of electrons. Our physical model for these processes, taking into account the relevant tunneling barriers, matches well with the experimental data. By choosing the appropriate tunneling conditions, we show that a single dopant can be employed as a memory element. The STM tip serves both as an electrical gate to write and as a probe to read the information stored on a single Si atom.