  We present measurements of trapped-ion motional-state heating rates in
niobium and gold surface-electrode ion traps over a range of trap-electrode
temperatures from approximately 4 K to room temperature (295 K) in a single
apparatus. Using the sideband-ratio technique after resolved-sideband cooling
of single ions to the motional ground state, we find low-temperature heating
rates more than two orders of magnitude below the room-temperature values and
approximately equal to the lowest measured heating rates in similarly-sized
cryogenic traps. We find similar behavior in the two very different electrode
materials, suggesting that the anomalous heating process is dominated by
non-material-specific surface contaminants. Through precise control of the
temperature of cryopumping surfaces, we also identify conditions under which
elastic collisions with the background gas can lead to an apparent steady
heating rate, despite rare collisions.
