In this article, we have investigated the effects of rapid thermal annealing on the electrical and structural properties of Ru/Cu Schottky contacts on n-InP by current density–voltage (J–V), capacitance–voltage (C–V), Secondary ion mass spectrometer (SIMS) and X-ray diffraction (XRD) measurements. The Schottky barrier height (SBH) of the as-deposited Ru/Cu Schottky contact is found to be 0.65 eV (I–V) and 0.84 eV (C–V), respectively. The obtained barrier height values 0.81 eV (I–V), 0.95 eV (C–V) at 100 °C, 0.85 eV (I–V), 1.02 eV (C–V) at 200 °C, 0.80 eV (I–V), 0.90 eV (C–V) at 300 °C and 0.75 eV (I–V), 0.88 eV (C–V) at 400 °C. It is observed that the SBH increases with annealing temperature up to 200 °C. Further, increase in the annealing temperature up to 400 °C, SBH decreases compared to the one at 200 °C annealed samples. Norde method is also used to calculate the barrier height of Ru/Cu Schottky contact. Based on the above results, the optimum annealing temperature for the Ru/Cu Schottky contact is 200 °C. According to SIMS and XRD results, the formation of indium phases at the interface may be the reason for the increase of barrier height after annealing at 200 °C. The AFM results showed that the overall surface morphology of Ru/Cu Schottky contact is fairly smooth even after annealing at 400 °C.