We demonstrate the possibility to tune the tunneling probability between an array of self- assembled quantum dots and a two-dimensional electron gas (2DEG) by changing the energy imbalance between the dot states and the 2DEG. Contrary to the expectation from Fowler-Nordheim tunneling, the tunneling rate decreases with increasing injection energy. This can be explained by an increasing momentum mismatch between the dot states and the Fermi-circle in the 2DEG. Our findings demonstrate momentum matching as a useful mechanism (in addition to energy conservation, density of states, and transmission probability) to electrically control the charge transfer between quantum dots and an electron reservoir.
We use the variational principle to obtain the wave functions of elliptical quantum dots under the influence of an external magnetic field. For the first excited states, whose wave functions have recently been mapped experimentally, we find a simple expression, based on a linear combination of the wave functions in the absence of a magnetic field. The results illustrate how a magnetic field breaks the x-y symmetry and mixes the corresponding eigenstates. The obtained eigenenergies agree well with those obtained by more involved analytical and numerical methods.
We investigate the tunneling rates from a 2-dimensional electron gas (2DEG) into the ground state of self-assembled InGaAs quantum dots. These rates are strongly affected by a magnetic field perpendicular to the tunneling direction. Surprisingly, we find an increase in the rates for fields up to 4 T before they decrease again. This can be explained by a mismatch between the characteristic momentum of the quantum dot ground state and the Fermi momentum kF of the 2DEG. Calculations of the tunneling probability can account for the experimental data and allow us to determine the dot geometry as well as kF.
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