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Two-dimensional electron and hole gases separated by a few nm from each otherare produced in p-i-n diodes based upon MBE-grown GaAs/AlGaAs heterostructures.At such interlayer distances, the exciton formation and possibly Bose-Einsteincondensation (BEC) is expected. We measure the capacitance between the layersand find it to oscillate as a function of the bias voltage. The peak valuesexceed the geometric capacitance by up to a factor of two. The surprisinglyregular periods of the oscillations are of the order of 10 to 30 mV and scalelinearly with the inverse of the thickness, between 60 and 150 nm, of the GaAslayer placed between the barrier and the p-doped AlGaAs. The oscillations arerelated to the resonant electron tunneling into high energy levels of this GaAslayer acting as a quantum well. We suggest that long lifetimes of the electronsin these levels are the origin of the large peak values of the capacitance. Thepossible relation of the capacitance oscillations with BEC is discussed.

Capacitance and conductance oscillations from electron tunneling into high energy levels of a quantum well in a p-i-n diode