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Reconstruction of surface potential from Kelvin probe force microscopy images
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2013 Nanotechnology 24 295702
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IOP PUBLISHING |
NANOTECHNOLOGY |
Nanotechnology 24 (2013) 295702 (13pp) |
doi:10.1088/0957-4484/24/29/295702 |
Reconstruction of surface potential from Kelvin probe force microscopy images
G Cohen1, E Halpern1, S U Nanayakkara2, J M Luther2, C Held3,
R Bennewitz3, A Boag1 and Y Rosenwaks1
1 School of Electrical Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel
2 National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, CO, USA
3 INM–Leibniz-Institute for New Materials, Campus D2 2, D-66123 Saarbrucken,¨ Germany
E-mail: yossir@eng.tau.ac.il
Received 27 March 2013, in final form 16 May 2013
Published 27 June 2013
Online at stacks.iop.org/Nano/24/295702
Abstract
We present an algorithm for reconstructing a sample surface potential from its Kelvin probe force microscopy (KPFM) image. The measured KPFM image is a weighted average of the surface potential underneath the tip apex due to the long-range electrostatic forces. We model the KPFM measurement by a linear shift-invariant system where the impulse response is the point spread function (PSF). By calculating the PSF of the KPFM probe (tip C cantilever) and using the measured noise statistics, we deconvolve the measured KPFM image to obtain the surface potential of the sample.The reconstruction algorithm is applied to measurements of CdS-PbS nanorods measured in amplitude modulation KPFM (AM-KPFM) and to graphene layers measured in frequency modulation KPFM (FM-KPFM). We show that in the AM-KPFM measurements the averaging effect is substantial, whereas in the FM-KPFM measurements the averaging effect is negligible.
(Some figures may appear in colour only in the online journal)
1. Introduction
It is well known that the finite tip size in scanning probe-microscopes has a profound effect on the measured image. In Kelvin probe force microscopy (KPFM), the effect of the measuring tip is enhanced due to the long-range electrostatic force [1]. KPFM applies a bias voltage to a conductive atomic force microscope (AFM) probe to compensate for the electrostatic forces between the probe and the sample [2]. Ideally, the magnitude of this bias should be equal to the contact potential difference (CPD) between the probe and the sample surface in the close vicinity of the probe’s tip. However for non-uniform samples, due to the long-range nature of the electrostatic force, the measuring probe (composed of the tip and cantilever) significantly affects the measured KPFM signal [3–6]. Figure 1 shows a schematic KPFM setup consisting of a scanning probe above a sample with a non-uniform surface divided into m areas of constant CPD, 8i; i D 1; : : : ; m. Ideally, the KPFM should measure a CPD of 81, but since the entire sample contributes to the electrostatic force on the probe, the KPFM measures a
weighted average of the sample CPD. The total surface charge on the probe is affected both by the sample inhomogeneous potential CPD (red capacitors) and homogeneously by the interaction between the probe and the grounded surface (blue capacitor). Therefore, in order to obtain a quantitative CPD image the probe averaging effect must be taken into account.
Several models have analyzed the tip–sample electrostatic interaction in KPFM measurements. Jacobs et al [7] presented a model which correlates the measured KPFM signal with the actual sample CPD distribution. They treated the sample similarly to figure 1 and showed that the KPFM signal on smooth surfaces is a two-dimensional convolution of the CPD on the surface with the system point spread function (PSF). However they did not include the cantilever in their analysis and ignored the non-uniform charge distribution on the tip. Gil et al [8] analyzed the contribution of the entire probe to the electrostatic force by dividing the probe into sub-domains, calculating the contributed force for each domain, and comparing the results to experimental data. They showed that the total electrostatic force is dominated by the cantilever and not by the tip. Machleidt et al [9] considered
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