We report a procedure to determine the frequency-dependent conductance of quantum Hall structures in a broad frequency domain. The procedure is based on the combination of two known probeless methods -- acoustic spectroscopy and microwave spectroscop
y. By using the acoustic spectroscopy, we study the low-frequency attenuation and phase shift of a surface acoustic wave in a piezoelectric crystal in the vicinity of the electron (hole) layer. The electronic contribution is resolved using its dependence on a transverse magnetic field. At high frequencies, we study the attenuation of an electromagnetic wave in a coplanar waveguide. To quantitatively calibrate these data, we use the fact that in the quantum-Hall-effect regime the conductance at the maxima of its magnetic field dependence is determined by extended states. Therefore, it should be frequency independent in a broad frequency domain. The procedure is verified by studies of a well-characterized $p$-SiGe/Ge/SiGe heterostructure.
Using acoustic methods we have measured nonlinear AC conductance in 2D arrays of Ge-in-Si quantum dots. The combination of experimental results and modeling of AC conductance of a dense lattice of localized states leads us to the conclusion that the
main mechanism of AC conduction in hopping systems with large localization length is due to the charge transfer within large clusters, while the main mechanism behind its non-Ohmic behavior is charge heating by absorbed power.
