Peak current densities (I-p) as high as 1.3 x 10(5) A/cm(2) with peak-to-valley current ratios of 3.7 are reported for InAs/AlSb/GaSb/AlSb/InAs double-barrier resonant interband tunnelling diodes. The fact that 1-monolayer-thick AlSb barriers exist between the InAs and GaSb layers is essential in obtaining such a high value of I-p.