The lateral dimensions of resonant tunneling AlGaAs‐GaAs double barrier heterostructures have been restricted by hydrogen plasma exposure. Ohmic contacts to the submicron diodes have been made by solid phase epitaxial growth of Ge on GaAs. The current‐voltage characteristics show a fine structure splitting that is inversely proportional to the lateral size of the diode. The results are interpreted as resonant tunneling through zero‐dimensional states in the quantum box confined by the AlGaAs barriers and a harmonic lateral confining potential.