Electromagnetic model for near-field microwave microscope with atomic resolution: Determination of tunnel junction impedance

Abstract

An electrodynamic model is proposed for the tunneling microwave microscope with subnanometer space resolution as developed by Lee et al. [Appl. Phys. Lett. 97, 183111 (2010)]. Tip-sample impedance Za was introduced and studied in the tunneling and non-tunneling regimes. At tunneling breakdown, the microwave current between probe and sample flows along two parallel channels characterized by impedances Zp and Zt that add up to form overall impedance Za. Quantity Zp is the capacitive impedance determined by the near field of the probe and Zt is the impedance of the tunnel junction. By taking into account the distance dependences of effective tip radius r0(z) and tunnel resistance Rt(z) = Re[Zt(z)], we were able to explain the experimentally observed dependences of resonance frequency fr(z) and quality factor QL(z) of the microscope. The obtained microwave resistance Rt(z) and direct current tunnel resistance Rtdc(z) exhibit qualitatively similar behavior, although being largely different in both magnitude and the characteristic scale of height dependence. Interpretation of the microwave images of the atomic structure of test samples proved possible by taking into account the inductive component of tunnel impedance ImZt = ωLt. Relation ωLt/Rt ≈ 0.235 was obtained.