Local Electrodynamics of a Disordered Conductor Model System Measured with a Microwave Impedance Microscope
Holger Thierschmann (Kavli institute of nanoscience Delft, TU Delft - QN/Klapwijk Lab)
Hale Cetinay (TU Delft - Electrical Engineering, Mathematics and Computer Science, Universiteit Leiden)
Matvey Finkel (Kavli institute of nanoscience Delft, TU Delft - QN/Klapwijk Lab)
Allard J. Katan (TU Delft - Applied Sciences, Kavli institute of nanoscience Delft)
Marc P. Westig (Kavli institute of nanoscience Delft, TU Delft - QN/Klapwijk Lab)
Piet Van Mieghem (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Teun M. Klapwijk (TU Delft - QN/Klapwijk Lab, Moscow State Pedagogical University)
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Abstract
We study the electrodynamic impedance of percolating conductors with a predefined network topology using a scanning microwave impedance microscope at gigahertz frequencies. For a given percolation number we observe strong spatial variations across a sample that correlate with the connected regions (clusters) in the network when the resistivity is low such as in aluminum. For the more-resistive material (Nb,Ti)N, the impedance becomes dominated by the local structure of the percolating network (connectivity). The results can be qualitatively understood and reproduced with a network current-spreading model based on the pseudoinverse Laplacian of the underlying network graph.