Utilizing three-terminal tunnel emission of ballistic electrons and holes, we have developed a method to self-consistently measure the bandgap of semiconductors and band discontinuities at semiconductor heterojunctions without any prerequisite material parameter. Measurements are performed on lattice-matched GaAs/AlxGa1−xAs and GaAs/(AlxGa1−x)0.51In0.49P single-barrier heterostructures. The bandgaps of AlGaAs and AlGaInP are measured with a resolution of several meV at 4.2 K. For the GaAs/AlGaAs interface, the measured Γ band offset ratio is 60.4:39.6 (±2%). For the GaAs/AlGaInP interface, this ratio varies with the Al mole fraction and is distributed more in the valence band. A non-monotonic Al composition dependence of the conduction band offset at the GaAs/AlGaInP interface is observed in the indirect-gap regime. 73.23.Ad, 73.40.Kp Among the most important properties of semiconductor materials are their energy gaps and the relative alignment of the energy band edges at the heterojunction (HJ) interface between two dissimilar semiconductors, i.e. the way in which the total bandgap difference distributes between the conduction band discontinuity ∆E C and the valence band discontinuity ∆E V . An accurate knowledge of such properties is crucial for the design of heterostructure devices widely used in high-speed and power electronics, photonics, and energy conversion.Numerous efforts have been devoted to measure the bandgap and band offsets. Bandgaps are measured mostly with optical spectroscopies such as absorption, photoluminescence (PL), photoluminescence excitation (PLE), and ellipsometry [1]. Band offset measurements can be divided into three categories: electrical techniques such as thermionic emission and capacitance-voltage (C-V); optical techniques such as absorption, PL, and PLE; and photoelectron techniques such as x-ray photoelectron spectroscopy (XPS) and ultraviolet photoelectron spectroscopy (UPS) [2]. However, each of these methods has certain limitations or weakness. Absorption requires values of effective masses and parabolic band structure to measure the band offset [3]. PL and PLE are often subject to interference from competing optical transitions due to strain splitting, phonon replicas, and impurities [4]. Thermionic emission requires currentvoltage (I-V) measurements at different temperatures to extract the activation energies over barriers, and it does not work at low temperatures [5]. In C-V measurements, detailed device simulations are needed to consider the effect of deep levels in the barrier layer [6]. * Electronic address: weiyi@seas.harvard.edu XPS and UPS are limited to measuring the valence band offests [2]. With a three-terminal device configuration, Ballistic Electron Emission Microscopy (BEEM) and Spectroscopy (BEES) utilize ballistic injection of electrons/holes to probe the band offsets of HJs buried beneath a metal-semiconductor (m-s) interface [7]. To measure the genuine barrier heights, a delta-doping is needed to reach a flat-band condition in the heterostructure, whic...