Design, fabrication, and characterization of kinetic-inductive force sensors for scanning probe applications

• August K. Roos,
• Ermes Scarano,
• Elisabet K. Arvidsson,
• Erik Holmgren and
• David B. Haviland

Beilstein J. Nanotechnol. 2024, 15, 242–255, doi:10.3762/bjnano.15.23

• cryogenic amplifier for low-noise microwave reflection measurement, as shown in Figure 8. Low- and high-frequency signals are synchronously synthesized and measured with a digital multifrequency microwave measurement device (Vivace from Intermodulation Products AB) to measure phase-sensitive

• Swedish SSF Grant No. ITM17–0343 supported this work. Conflict of Interest DBH is a part owner of Intermodulation Products AB, which manufactures and sells the microwave measurement platform used in this experiment. AKR, ES, EKA, and EH declare no competing interests.

Dual-heterodyne Kelvin probe force microscopy

• Benjamin Grévin,
• Fatima Husainy,
• Dmitry Aldakov and
• Cyril Aumaître

Beilstein J. Nanotechnol. 2023, 14, 1068–1084, doi:10.3762/bjnano.14.88

• ; intermodulation; KPFM; nc-AFM; surface photovoltage; time-resolved measurements; Introduction Kelvin probe force microscopy (KPFM) is a well-known variant of AFM that allows probing at the nanoscale the electrostatic landscape on the surface of a sample by measuring the so-called contact potential difference

• measurements [16], which consists in analysing the intermodulation products between the mechanical oscillation of the cantilever and the photogenerated surface potential. In short, intermodulation spectroscopy allows working in the frequency domain (instead of the time domain) by extracting, during a single

• due to the enhanced quality factors under vacuum, which severely limits the frequency window available to increase the amplitude of the intermodulation products (for a more detailed discussion, see [14]). In this work, we propose to approach the measurement of intermodulation products with non-contact

Spatial mapping of photovoltage and light-induced displacement of on-chip coupled piezo/photodiodes by Kelvin probe force microscopy under modulated illumination

• Zeinab Eftekhari,
• Nasim Rezaei,
• Hidde Stokkel,
• Jian-Yao Zheng,
• Andrea Cerreta,
• Ilka Hermes,
• Minh Nguyen,
• Guus Rijnders and
• Rebecca Saive

Beilstein J. Nanotechnol. 2023, 14, 1059–1067, doi:10.3762/bjnano.14.87

• the cantilever resonance. Modulating the tip with VAC while the cantilever is oscillating near its resonance frequency leads to frequency mixing and intermodulation of the two frequencies (f0 ± fAC) [34]. The lock-in amplifiers 2 and 3 are fed with the vertical deflection signal of the cantilever to

Intermodal coupling spectroscopy of mechanical modes in microcantilevers

• Ioan Ignat,
• Bernhard Schuster,
• Jonas Hafner,
• MinHee Kwon,
• Daniel Platz and
• Ulrich Schmid

Beilstein J. Nanotechnol. 2023, 14, 123–132, doi:10.3762/bjnano.14.13

• field, where two eigenmodes are excited and read simultaneously [40]. Last, intermodulation products, created by two signals close to the fundamental cantilever mode, form a sea of evenly spaced tones to be measured [35][41][42]. All of these rely on the nonlinear tip–surface force to create these

• amplifier (Intermodulation Products MLA-3 [36]) is used to control the piezoshaker and measure multiple frequencies from the vibrometer. For each possible mode combination, we activated the anti-Stokes pump and used a smaller sweeping signal to amplify the sense mode. Results and Discussion Compared to a

• team for insightful and detailed discussions on the topic: D. Haviland, E. Arvidsson, A. Roos, E. Scarano, T. Glatzel, and M. Zutter. From Intermodulation Products, E. Tholén and D. Forchheimer provided us with outstanding support in programming the MLA-3 lock-in amplifier. Funding This project has

Comparing the performance of single and multifrequency Kelvin probe force microscopy techniques in air and water

• Jason I. Kilpatrick,
• Emrullah Kargin and
• Brian J. Rodriguez

Beilstein J. Nanotechnol. 2022, 13, 922–943, doi:10.3762/bjnano.13.82

• paper, including pump-probe KPFM [13][20][43], time-resolved KPFM [11][12][44][45][46][47], fast free force recovery KPFM (G-Mode) [14][48][49][50], intermodulation electrostatic force microscopy (EFM) [42][51], and PeakForce tapping KPFM [52]. The fundamental detection sensitivity to electrostatic

• ]. Furthermore, Het-KPFM can be extended using two electrical drive signals combined with a mechanical drive signal to aid in the positioning of the required harmonics on eigenmodes, enhancing both SNR and spatial resolution [91]. Examples include intermodulation AFM, which applies two electrical signals, ωe1

Open-loop amplitude-modulation Kelvin probe force microscopy operated in single-pass PeakForce tapping mode

• Gheorghe Stan and
• Pradeep Namboodiri

Beilstein J. Nanotechnol. 2021, 12, 1115–1126, doi:10.3762/bjnano.12.83

• -excitation OL BE-KPFM [37][38][39], intermodulation electrostatic force microscopy [40], and dual-harmonic KPFM (DH-KPFM) [34][41][42]. In DH-KPFM, the CPD is obtained from the ratio of the amplitudes of the first two harmonics of the cantilever response to an AC bias modulation and requires a prior

Bulk chemical composition contrast from attractive forces in AFM force spectroscopy

• Dorothee Silbernagl,
• Media Ghasem Zadeh Khorasani,
• Natalia Cano Murillo,
• Anna Maria Elert and
• Heinz Sturm

Beilstein J. Nanotechnol. 2021, 12, 58–71, doi:10.3762/bjnano.12.5

• of atomic force microscopy (AFM) is the measurement of physical properties at sub-micrometer resolution. Methods such as force–distance curves (FDCs) or dynamic variants (such as intermodulation AFM (ImAFM)) are able to measure mechanical properties (such as the local stiffness, kr) of nanoscopic

• methods. This has resulted in methods such as force modulation [4], bimodal mode [5], pulsed-force mode [6] or peak force [7], and intermodulation AFM (ImAFM) with amplitude-dependent force spectroscopy (ADFS) [8][9][10]. Dynamic methods record local mechanical properties with a resolution in the range of

• for this task, a high-resolution method of AFM force spectroscopy was used, which is called intermodulation AFM. This dynamic method is able to scan the sample with a resolution comparable to the tapping-mode images, producing the equivalent of a FDC at each pixel. A 2 × 2 µm topography scan of the

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

• Berkin Uluutku and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 453–465, doi:10.3762/bjnano.11.37

• 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

• developed, such as for the intermodulation AFM method, which uses a battery of lock-in amplifiers [30][31], but the amplification in that case is much smaller than what would be required for ICM-AFM. In addition to the above challenges, which may not represent an exhaustive list, there are challenges that

A review of demodulation techniques for multifrequency atomic force microscopy

• David M. Harcombe,
• Michael G. Ruppert and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2020, 11, 76–91, doi:10.3762/bjnano.11.8

• within dynamic mode AFM. It involves studying multiple frequency components in the cantilever oscillation during tip–sample interactions [13]. Observing higher eigenmodes of the cantilever [14], higher harmonics of the fundamental resonance [15] and intermodulation products [16] have been shown to

• theoretical foundations for determining secondary sample properties such as Young’s modulus [13][22]. Applications include the imaging of secondary properties of proteins [23] and polymers [24]. Intermodulation AFM actively drives the cantilever slightly below and above resonance with a two-tone drive

• . Compared to higher-harmonic AFM, this technique has more enhanced non-linear interactions [25]. Intermodulation products present in the cantilevers motion have been shown to be sensitive to material and chemical contrast [16][26], leading to enhanced nanomechanical insights [27]. Regardless of which MF-AFM

Review of time-resolved non-contact electrostatic force microscopy techniques with applications to ionic transport measurements

• Aaron Mascaro,
• Yoichi Miyahara,
• Tyler Enright,
• Omur E. Dagdeviren and
• Peter Grütter

Beilstein J. Nanotechnol. 2019, 10, 617–633, doi:10.3762/bjnano.10.62

• limitations, we then introduce a new technique we refer to as voltage-pulse averaging EFM, and then continue to explain and examine three other techniques with applications to ionic transport measurements, specifically fast free time-resolved EFM [22], phase-kick EFM [23], and intermodulation spectroscopy [20

• . Intermodulation spectroscopy Background and implementation Significant progress has clearly been made in measuring electrostatic force microscopy signals in the time domain. The main challenges of the techniques discussed thus far have been the detection methods (specifically, bandwidth limitations) and various

• assumptions and approximations that have been made, which limit the useful parameter space of some experiments. Looking instead in the frequency domain, one very recent method of extracting fast sample dynamics appears to be a promising alternative to many of these challenges. Intermodulation spectroscopy

Lyapunov estimation for high-speed demodulation in multifrequency atomic force microscopy

• David M. Harcombe,
• Michael G. Ruppert,
• Michael R. P. Ragazzon and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2018, 9, 490–498, doi:10.3762/bjnano.9.47

• stiffness, elasticity and adhesiveness [10]. The acquisition of these observables requires tracking the amplitude and phase of additional frequencies of interest. These include higher harmonics of the fundamental frequency [11], higher flexural eigenmodes [12] and intermodulation products [13]. Higher

• harmonic methods have demonstrated the ability to image relatively large biological objects, such as cells [14][15], while bimodal AFM has successfully imaged properties of protein complexes [16]. Intermodulation AFM is a novel extension to the bimodal method that focuses on the mixing products of a

• higher harmonics and minor intermodulation products are present. These are due to non-linear atomic forces exciting the cantilever during contact. Amplitude imaging results are shown in Figure 9. As the sixth and seventh harmonics are closely spaced to the second resonance frequency of the cantilever

Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions

• Santiago D. Solares

Beilstein J. Nanotechnol. 2016, 7, 554–571, doi:10.3762/bjnano.7.49

• frequencies well below the cantilever resonance frequency [21]. Novel spectroscopy methods have also been recently developed for intermittent-contact imaging. For example, it is now possible to extract tip–sample force curves using dual-eigenmode frequency-modulation AFM [10] and intermodulation AFM [11][12

Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments

• Horacio V. Guzman,
• Pablo D. Garcia and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2015, 6, 369–379, doi:10.3762/bjnano.6.36

• spatial resolution and contrast of different dynamic AFM methods has also been studied by simulations [28][30][31]. Finally, the emergence of multifrequency AFM [32] in particular bimodal [33][34], trimodal [35], intermodulation [36] or torsional harmonics [37] has been supported by simulations [38]. In

Dynamic calibration of higher eigenmode parameters of a cantilever in atomic force microscopy by using tip–surface interactions

• Stanislav S. Borysov,
• Daniel Forchheimer and
• David B. Haviland

Beilstein J. Nanotechnol. 2014, 5, 1899–1904, doi:10.3762/bjnano.5.200

• , knowledge of the geometry of cantilever is not required to reconstruct the tip–surface force. The framework proposed harnesses a force reconstruction technique inspired by the Intermodulation AFM [27] (ImAFM), which was recently generalized to the multimodal case [28]. It is worth noting that the proposed

• to the unknown kn and αn. Intermodulation AFM Assuming that α1 and k1 are calibrated by using one of the methods mentioned in the Introduction, the resulting system contains 2(N − 1) + P unknown variables. Use of the equipartition theorem (Equation 3) for each eigenmode gives us N − 1 equations and

• force behaves in a nonlinear way (P > 1), as is usually the case, more measurable response components in the frequency domain are needed. The core idea of ImAFM relies on the ability of a nonlinear force to create intermodulation of discrete drive tones in a frequency comb. Driving an eigenmode subject

Polynomial force approximations and multifrequency atomic force microscopy

• Daniel Platz,
• Daniel Forchheimer,
• Erik A. Tholén and
• David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 352–360, doi:10.3762/bjnano.4.41

• Daniel Platz Daniel Forchheimer Erik A. Tholen David B. Haviland KTH Royal Institute of Technology, Section for Nanostructure Physics, Albanova University Center, SE-106 91 Stockholm, Sweden Intermodulation Products AB, Vasavägen 29, SE-169 58 Solna, Sweden 10.3762/bjnano.4.41 Abstract We present

• polynomial force reconstruction from experimental intermodulation atomic force microscopy (ImAFM) data. We study the tip–surface force during a slow surface approach and compare the results with amplitude-dependence force spectroscopy (ADFS). Based on polynomial force reconstruction we generate high

• to spectral data, and we demonstrate how it can be adapted to a force quadrature picture. Keywords: AFM; atomic force microscopy; force spectroscopy; multifrequency; intermodulation; polynomial; Introduction The combination of high-resolution imaging [1][2][3][4] and high-accuracy force

Interpreting motion and force for narrow-band intermodulation atomic force microscopy

• Daniel Platz,
• Daniel Forchheimer,
• Erik A. Tholén and
• David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 45–56, doi:10.3762/bjnano.4.5

• Daniel Platz Daniel Forchheimer Erik A. Tholen David B. Haviland Royal Institute of Technology (KTH), Section for Nanostructure Physics, Albanova University Center, SE-106 91 Stockholm, Sweden Intermodulation Products AB, Vasavägen 29, SE-169 58 Solna, Sweden 10.3762/bjnano.4.5 Abstract

• Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip–surface force by measurement of the mixing of multiple modes in a frequency comb. A high-quality factor cantilever resonance and a suitable drive comb will result in tip motion described by a

• , providing deeper insight into the tip–surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface. Keywords: atomic force microscopy; AFM; frequency combs; force spectroscopy; high-quality-factor resonators; intermodulation; multifrequency

Repulsive bimodal atomic force microscopy on polymers

• Alexander M. Gigler,
• Christian Dietz,
• Maximilian Baumann,
• Nicolás F. Martinez,
• Ricardo García and
• Robert W. Stark

Beilstein J. Nanotechnol. 2012, 3, 456–463, doi:10.3762/bjnano.3.52

• contrast, we calculated a two-dimensional Fourier transformation as presented in Figure 5b with a maximum at a spatial frequency of 29 µm−1. This frequency corresponds to a pitch between the cylinders of polystyrene of 33.5 nm. Intermodulation effects can occur when an oscillating nonlinear system is