Low-temperature and high magnetic field dynamic scanning capacitance microscope

Abstract

We demonstrate a dynamic scanning capacitance microscope (DSCM) that operates at large bandwidths, cryogenic temperatures, and high magnetic fields. The setup is based on a noncontact atomic force microscope (AFM) with a quartz tuning fork sensor for the nonoptical excitation and readout in topography, force, and dissipation measurements. The metallic AFM tip forms part of a rf resonator with a transmission characteristics modulated by the sample properties and the tip-sample capacitance. The tip motion gives rise to a modulation of the capacitance at the frequency of the AFM sensor and its harmonics, which can be recorded simultaneously with the AFM data. We use an intuitive model to describe and analyze the resonator transmission and show that for most experimental conditions it is proportional to the complex tip-sample conductance, which depends on both the tip-sample capacitance and the sample resistivity. We demonstrate the performance of the DSCM on metal disks buried under a polymer layer and we discuss images recorded on a two-dimensional electron gas in the quantum Hall effect regime, i.e. at cryogenic temperatures and in high magnetic fields, where we directly image the formation of compressible stripes at the physical edge of the sample.

Scanning capacitance imaging of compressible and incompressible quantum Hall effect edge strips

“…We use a home-built dynamic scanning capacitance microscope [22] (DSCM) that operates between 1.9 K and room temperature and magnetic fields perpendicular to the sample surface of up to 12 T. The microscope is based on a non-contact atomic force microscope (AFM) in a low pressure (2 mbar) He atmosphere. A quartz tuning fork sensor and a phase-locked loop allow non-optical sensor excitation and readout of the topography and the average force.…”

“…An analysis of the tip-sample interaction in terms of lumped-circuit elements is possible since the wavelength of the excitation is much larger than the relevant geometrical dimensions. One can show [22] that for reasonably sharp tips U out is proportional to the complex conductance between the tip and ground, G ts , independent of the details of the tip-sample interaction:…”

“…The voltage amplitude on the AFM tip we estimate to be 24 mV, a compromise between a sufficient signal-to-noise ratio and useful scan rates and minimal charging of the sample surface. The perturbation of the rf resonator due to the sample is exceedingly small and a direct measurement is very slow and not suitable for scanning [22]. We operate the AFM in the dynamic mode where the tip oscillates perpendicular to the sample surface.…”

“…The coupling between the tip and the 2DEG can be described by three capacitances in series; the tip-surface capacitance, C ts (t); the capacitance of the GaAs cap layer, C cap , and the self or quantum capacitance C 2DEG of the 2DEG. The current path to ground is closed by the capacitance of the substrate, C sub , in parallel with the resistance through the 2DEG, R. We estimate R from the homogeneous zero-field bulk conductivity and a circular-symmetric current density to the tip [22,27]. Simple modelling indicates that except for very large R the substrate capacitance can be neglected.…”

“…Here we present dynamic scanning capacitance microscopy (DSCM) [22] images recorded at the edge of a 2DEG in the QHE regime at zero bias as well as in the QHE breakdown regime at finite currents. A related method was used recently to image square areas of a 2DEG around the average bulk filling factor ν ≈ 2 [23].…”