Vertical hall effect in GaAs quantum wells

Applying orthogonal in-plane electric and magnetic fields in a 2D system leads to the development of a Hall voltage across the width of the quantum well when the cyclotron orbit is greater than the well width. Tang and Butcher [1] have calculated the developed Hall voltage for a parabolic quantum well where they find that the Hall voltage is dependent on the frequency associated with the harmonic potential in the well. The limitation of this model is that it does not enable one to determine the well width dependence of the Hall Voltage, nor is it a particularly good model for a quantum well. It is also difficult to compare their model with the bulk result which would apply at large well widths. In this work we present a model calculation which considers a square quantum well and hence is able to predict the well width dependence of the Hall Voltage and compare the large well width case to the bulk result. An electro-optic probing method previously used to measure bulk Hall voltages [2] is shown to be capable of measuring the Hall ’voltage across a quantum well, and therefore can be used to confirm the prediction of the model presented here. © 1994 Academic Press. All rights reserved.