Fast Multifrequency Measurement of Nonlinear Conductance

Abstract

We describe a phase-coherent multifrequency lock-in measurement technique that uses the inverse Fourier transform to reconstruct the nonlinear current-voltage characteristic (IVC) of a nanoscale junction. The method provides for a separation of the galvanic and displacement currents in the junction, and easy cancellation of the parasitic displacement current from the measurement leads. These two features allow us to overcome traditional limitations imposed by the low conductance of the junction and high capacitance of the leads, thus providing an increase in measurement speed of several orders of magnitude. We demonstrate the method in the context of conductive atomic force microscopy, acquiring IVCs at every pixel while scanning at standard imaging speed.The sensitive measurement of small currents in nanometer-scale junctions is a central problem in modern experimental physics. Characterization of numerous novel materials and devices, in applications ranging from topological quantum computers [1, 2] to energy harvesting and energy conversion [3][4][5][6][7][8][9][10], struggles with the same basic limitations imposed by the small measurement current and the large stray capacitance of the macroscopic leads. We describe how to circumvent these limitations using phase-coherent multifrequency lock-in measurement and inverse Fourier transform to achieve a dramatic improvement in the speed of measurement, or alternatively, in the signal-to-noise ratio at the same measurement speed. In addition, our frequency-domain approach allows for active cancellation of parasitic current due to the lead capacitance and it provides for unambiguous separation of the galvanic and displacement currents flowing in the nanoscale junction.One area where this improvement is particularly useful is scanning probe microscopy (SPM), where a measurement of the nonlinear current-voltage characteristic (IVC) is desired at each tip location. In scanning tunneling microscopy (STM) the IVC allows for mapping energy dependence of the local density of electronic states [11]. In conducting atomic force microscopy (AFM) it can be used to map energy-conversion efficiency in photoactive nanocomposite materials [12]. Due to the aforementioned limitations, present-day SPM has two basic modes of operation. In imaging mode the current is measured while scanning the surface with a constant tip-sample voltage, quickly generating an image but with only limited information. Multiple scans at different bias are required to get the full IVC, greatly increasing measurement time and introducing problems due to instrument drift and tip wear. In spectroscopic mode the IVC is recorded at each tip position, but the voltage must be swept slowly so as to minimize displacement current in the parallel capacitance of the measurement leads. This large background current puts a limit on the achievable gain and sensitivity of current measurement, and the slow sweep greatly limits the speed of the scan, or equivalently spatial resolution in a given measurement time. We demonstra...

Nanoscale characterization of an all-oxide core–shell nanorod heterojunction using intermodulation atomic force microscopy (AFM) methods

“…The important advantage of ImCFM method over standard CAFM and pcAFM is that every pixel in the current distribution maps already contains current-voltage curves, and map data capturing is very fast. The measured current magnitude at increasing bias is similar to some other PV systems studied with CAFM methods 27,32,33,35 11 . A slight increase in both applied forward and reverse bias voltage facilitated increasing photogenerated current.…”

“…The spatially-resolved I-V curves and corresponding currentdistribution maps at the nanometer scale under dark and illumination conditions were measured utilizing the newly developed ImCFM method 27 . ImCFM applies a full cycle of a sinusoidal oscillating voltage at every pixel of the scan.…”

“…The voltage was then sampled by the MLA. A more detailed procedure is described in the method introduction paper 27 . A frequency, df, of 100 Hz was used during the scanning.…”

“…Recently, Borgani et.al. introduced a novel fast multifrequency nonlinear conductance AFM (ImCFM) 27 . This new intermodulation method offers capturing the full IV curve at every pixel and reconstructing a set of current-voltage maps with great improved scanning times, which was not achieved before with other CAFM methods.…”

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

“…Fourier analysis has also been implemented for AFM force reconstructions within the so-called intermodulation AFM method, developed by Haviland and co-workers, where the cantilever is typically excited simultaneously at two different frequencies, while various intermodulation products are recorded with a collection of lock-in amplifiers [30,31]. More recently, Borgani et al used Fourier analysis to investigate non-linear conductance in C-AFM measurements, acquiring current-voltage responses at every scan point without sacrificing scanning speed [32].…”