Magneto-capacitance-voltage measurements of electrons in wide parabolic quantum wells

Abstract

We report here on the properties of quasi 3-dimensional electron gases (3DEGs) probed via magneto-capacitance-voltage (MCV) measurements. The 3DEGs are realized in wide parabolic quantum wells grown by molecular beam epitaxy of precisely graded Al xGa 1−xAs, into which electrons are introduced by modulation doping. This technique results in a good approximation of a high-quality uniform 3-dimensional electron gas or jellium. Predictions of electrical and optical properties for jellium can therefore be tested. The system furthermore has implications for the case of quantum wires and boxes where the electron-confining potential, in most cases, is approximately parabolic. A number of these 3DEGs with 3D densities ranging from ≈4×10 15 cm −3 to ≈ 8×10 16 cm −3 have been grown and studied. The measurements have been done at T = 4.2 K, and in perpendicular and parallel magnetic fields up to 8T. With a front gate electrode on the top surface of the sample we are abletto deplete the electrons in the parabolic well by squeezing the width of the 3DEG while retaining a constant 3D density. We also simultaneously depopulate the electrical subbands in this multi-subband system. In contrast to a 2DEG at a single interface we observe a monotonic decrease in the measured capacitance with increasing negative bias at all magnetic fields, and for all samples. A self-consistent solution of the Poisson-Schrödinger equation for our system explains this decreasing capacitance very well, but not the weak oscillations that appear at the points of subband depopulation. The MCV trace for electrons in a very narrow (≈ 750Å-wide) parabolic quantum well shows pronounced minima corresponding to different subband filling factors at different magnetic fields with one high filling factor appearing earlier than filling factors 2 and 4. Multiple-subband occupancy causes the Shubnikov-de-Haas oscillations in the longitudinal resistance to exhibit non-periodic structure due to a beating in the density of states at the Fermi energy. The measured mobility vs sheet density behaves differently than for a 2DEG.