Simultaneous Measurement of Carrier Density, Mobility, and their Transients with Four Electrical Contacts: The Frequency-multiplexed Hall Effect Method

A frequency multiplexed Hall effect method (FMHM) is introduced which requires only 4 contacts to simultaneously measure carrier density and mobility in arbitrarily shaped semiconducting samples. By multi-purposing contacts as both current and voltage contacts at different frequencies, one longitudinal resistance measurement and two complementary Hall resistance measurements can be made at the same time. The two Hall resistance measurements are Onsager reciprocals of each other, so that their difference-average is a geometry-independent pure Hall signal. Three independent current sources at three different frequencies are synchronized with three respective lock-in voltage measurements to conduct the necessary measurements. The FMHM method allows transient relaxations of mobility and density to be simultaneously characterized. Such transients are measured in photoconductivity excitation and relaxation in GaN/AlGaN two-dimensional electron systems and in Zn_0.3In_1.4Sn_0.3O₃ amorphous oxide thin films. Parametric FMHM can also be implemented whereby a control variable is varied with time and an instantaneous system response recorded. Magnetic field-dependent parameteric FMHM is demonstrated by measuring the quantum Hall effect in a GaAs/AlGaAs quantum well sample, as is a temperature-dependent parametric FMHM for measuring persistent photoconductivity activation and relaxation. This technique allows full transport characterization with a minimal number of contacts and promises to reduce hours-long magnet sweep times for by a factor of 3 or more by allowing simultaneous collection of different measurements with the multi-purposed contacts.