Fast Hall™: A High Speed Hall Measurement for Material Characterization

The Hall effect is the primary method to measure carrier density, mobility and carrier type in materials. The most common method for measuring the Hall effect in semiconductors uses a DC magnetic field. This method depends are reversing the direction of the magnetic field. This method breaks down for materials with mobility < ~ 10 cm² /(V s). We present a measurement protocol based on the reverse-field reciprocity theorem. The reverse-field reciprocity theorem considers a four-port network with current inputs and voltage measurements and an applied magnetic field. If a current is applied to two of the inputs (say 1 and 3) and a positive field B a voltage (V) is measured on terminals 2 and 4. If the current and voltage leads are interchanged, current on terminals 2 and 4, voltage measured between 1 and 3, V₂(B). The theorem states that V₂(B) = V₁(-B). This is a very general result; the only requirement of the material is that it is electrically linear. This means that thermoelectric voltages require special treatment. The method presented here has been extended for material characterization, in particular the measurement of low mobility materials based of the reverse-field reciprocity theorem.