Using Quantized Breakdown Voltage Signals to Determine the Maximum Electric-Fields in A Quantum Hall-Effect Sample

Abstract

We estimate the maximum values of the electric field across the width of a GaAs/AlGaAs heterostructure quantum Hall effect sample at several currents when the sample is in the breakdown regime. This estimate is accomplished by measuring the quantized longitudinal voltage drops along a length of the sample and then employing a quasielastic inter-Landau level scattering (QUILLS) model to calculate the electric field. We also present a pictorial description of how QUILLS transitions occurring between states distributed across the sample width can be detected as voltage signals along the sample length.

Potential and Current Distributions Calculated Across A Quantum Hall-Effect Sample atLow and High Currents

“…Therefore the positive z axis points downward for a right-handed coordinate system. The magnetic field B also points downward, simply to be consistent with results from the breakdown experiment [ 11 ] that will be used in Secs. 4 and 5.…”

“…1 . For convenience in writing the equations, the origin is located at the source S and is halfway across the sample width w. The sample labeling is chosen to be consistent with previous work [ 11 ]. Potential probes 1 and 2, and the drain D, are not shown.…”

“…Figure 2(a) shows a schematic of the charge distribution in the GaAs/AlGaAs interface region near one side of the mesa when there is no applied magnetic field. The GaAs layer of our sample [ 11 ] has a residual donor density of about 1 × 10 14 /cm 3 , while the donor concentration in the AlGaAs layer is about 1 × 10 18 /cm 3 and n s = 5.94 × 10 11 /cm 2 . There is an ionized donor atom in the AlGaAs layer for every electron in the 2DEG but, unlike Choi, Tsui, and Alavi [ 9 ], we assume the ionized donor atoms are distributed over a volume rather than in a surface sheet with density n s .…”

“…In this paper we calculate the potential distributions across the sample for applied currents I SD between 0 μA and 225 μA by: (a) assuming a parabolic confining potential for the charge carriers and using parameters of the parabola obtained experimentally by Choi, Tsui, and Alavi [ 9 ]; (b) assuming an applied current-induced logarithmic charge-redistribution potential for the charge carriers that is similar to that of Balaban, Meirav, and Shtrikman [ 10 ], but with very different cut-off values for the spatial extent of the potential; (c) assuming that the width of the conducting region varies with applied current because a Lorentz force deflects the conducting electrons slightly towards one side of the sample; (d) using the maximum electric field deduced by Cage and Lavine [ 11 ] from a breakdown experiment at high currents to determine the cut-off value for the spatial extent on one side of the sample; and (e) using the quantum Hall voltage to determine the cut-off value of the spatial extent on the other side of the sample. The calculated potential distributions are in excellent agreement with the measurements of Fontein et al [ 8 ].…”

Dependence of contact resistance on current for ohmic contacts to quantized Hall resistors

“…Cage et al [11] have proposed that when the current through an ideal contact is increased, the Hall voltage increases, and eventually becomes high enough to cause the electric field in certain regions of the sample to reach a critical value that permits electrons to tunnel from the highest occupied Landau level to the lowest unoccupied Landau level, a process called quasi-elastic inter-Landau level scattering. Under these conditions, breakdown of the QHE occurs, and the contact resistances increase sharply.…”