To solve the crucial power dissipation issue at the end of the conventional CMOS roadmap, there has been intense interest in tunneling field-effect transistors (TFETs), which are expected to offer superior subthreshold slope and high current drivability. The material system based on AlGaSb/InAs and related compounds is promising for the implementation of TFETs, since it can provide a staggered heterojunction band lineup, with a controllable, small energy gap E_cv between the valence band of the AlGaSb and the conduction band of InGaAs or InAlAs, which can enhance the junction tunneling probability. In this work we have fabricated and studied tunnel diodes in this material system, in order to allow device characterization with 2 terminal structures rather than the more complex FETs. We designed heterostructures with different compositions, which provide a set of band alignment values (heterojunction band-gaps E_cv) of 0.1eV and 0.2eV by adjusting mol-fractions in the III-V compounds. The carrier injector was AlGaSb, while the carrier collector (channel material in the corresponding FET) was InAlAs. Compositions were selected to maintain small lattice mismatch to allow high quality pseudomorphic growth. The AlGaSb/InAlAs heterojunctions were grown on InAs substrates by molecular beam epitaxy. The MBE growth used Si as the dopant species for n InAlAs and Be for p AlGaSb and p+ GaSb cap layers. AFM measurements showed RMS roughness smaller than 0.20nm. The carrier injector, AlGaSb was found to be chemically stable in air for weeks, even as its Aluminum mol-fraction approached 60%. Tunnel diodes in mesa-shape were fabricated by citric chemistry and Ohmic contacts formation, followed by Benzocyclobutene sidewall coverage. Four-probe Kelvin I-V characterization proved that the currents in both forward and reverse bias scale with the mesa area, which suggested no leakage current from the sidewall. The reverse and forward bias characteristics are believed to be dominated by tunneling of carriers and recombination of carriers respectively through Synopsis Sentaurus modeling. Both samples exhibited I-V slopes in reverse bias almost invariant with temperature (over the range 150K to 400K), which is a significant sign of tunneling behavior. For the sample with the 0.1eV heterojunction band-gap, the reverse biased I-V slope was sharper than kT/q at 400K (as needed for applications). By extrapolation from the measurements, we estimate the tunneling diodes could reach current density of 10^6A/cm2 at a low bias of 0.4V, without considering series resistance. This makes the system promising for achieving a 0.5mA/um on-current in future III-V tunneling MOSFETs. The sample with 0.1eV heterojunction band-gap showed higher current in forward bias than the 0.2eV sample, due to rapid recombination of carriers at the AlGaSb/InAlAs heterojunction. This implies that in tunneling MOSFETs design, generation-recombination leakage must be controlled while pursuing high tunneling current with small heterojunction band-gap.