Peak current densities of InAs/AlSb/GaSb/AlSb/InAs resonant interband tunneling diodes ͑RITD͒ grown by molecular beam epitaxy have been measured as a function of the growth temperature. The growth procedures were designed to produce nominally identical AlSb tunneling barriers. The variations observed in the peak current for positive bias are consistent with the barrier on the substrate side of the RITD becoming effectively thicker for diodes grown at high temperatures. Plan-view in situ scanning tunneling microscopy ͑STM͒ measurements indicate that smoother AlSb barriers are grown at high temperature. The growth temperature dependence of the peak current density and STM results are consistent, because tunneling is highly dependent on barrier thickness. While the high and low temperature growths were designed to have the same barrier thickness, the large current flowing through the thin areas of a rough barrier result in an effectively thinner barrier compared to the smooth one.