Simultaneous measurement of charge carrier density, mobility, and their transients with four electrical contacts: Frequency-multiplexed Hall effect method

The frequency multiplexed Hall effect method (FMHM) simultaneously measures time-dependent Hall Rxy(t) and longitudinal resistance Rxx(t) in arbitrary shaped samples using only four electrical contacts. FMHM applies the Onsager reciprocity relations along with three independent current sources and three lock-in amplifiers at three different frequencies. Transient FMHM measures samples with time-dependent Rxx(t) and Rxy(t) in the Drude limit at fixed magnetic field B. Parametric FMHM measures Rxx[A(t)] and Rxy[A(t)], where A(t) is an time-dependent control parameter such as B(t) or temperature T(t). Transient FMHM is demonstrated in the Drude regime at fixed magnetic field B to measure photoconductivity transients n(t) and μ(t) in GaN/AlGaN two-dimensional electron systems and on Zn0.3In1.4Sn0.3O3 amorphous oxide thin films. Parametric FMHM is demonstrated both in the Drude regime to study the temperature dependence of persistent photoconductivity n(T) and μ(T) and in the quantum Hall regime to study the magnetic-field dependence of Rxx(B) and Rxy(B) in GaAs quantum wells.