Utilizing three-terminal tunnel emission of ballistic electrons and holes in a planar tunnel transistor with a Mott-barrier collector, we have developed a method to self-consistently determine the energy gap of a semiconductor and band discontinuities at a semiconductor heterojunction without using a priori material parameters. Measurements are performed on lattice-matched $\text{GaAs}/{\text{Al}}_x{\text{Ga}}_{1-x}\text{As}$ (100) single-barrier double heterostructures with ${\text{Al}}_x{\text{Ga}}_{1-x}\text{As}$ as the model ternary III–V compounds. Electronic band gaps of the AlGaAs alloys and band offsets at the GaAs/AlGaAs (100) interfaces are measured with a resolution of several meV at 4.2 K. The direct-gap $\Gamma$ band offset ratio for the GaAs/AlGaAs (100) interface is found to be 59:41 $\left(\pm 3\mathrm{\%}\right)$. Reexamination of our previous experiment [W. Yi et al., Appl. Phys. Lett. 95, 112102 (2009)] revealed that, in the indirect-gap regime, ballistic electrons from direct tunnel emissions probe the X valley in the conduction band, while those from Auger-like scattering processes in the metal base film probe the higher-lying L valley. Such selective electron collection may be explained by their different momentum distributions and parallel momentum conservation at the quasiepitaxial Al/GaAs (100) interface. We argue that the present method is in principle applicable to arbitrary type-I semiconductor heterostructures.

• Received 6 May 2010

DOI:https://doi.org/10.1103/PhysRevB.81.235325