Scanning probe microscopy (SPM)

Scanning probe microscopy (SPM)

CHAPTER 2.1.3 Scanning probe microscopy (SPM) ea, Nicolas Feltina, Sebastien Ducourtieuxa, Loic Crouziera, Alexandra Delvalle b b Kai Dirscherl , Gu...

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CHAPTER 2.1.3

Scanning probe microscopy (SPM) ea, Nicolas Feltina, Sebastien Ducourtieuxa, Loic Crouziera, Alexandra Delvalle b b Kai Dirscherl , Guanghong Zeng a French National Laboratory for Metrology and Testing, Paris, France Danish National Metrological Institute (DFM A/S), Hørsholm, Denmark

b

Introduction to NP measurements by AFM The generic term scanning probe microscopy (SPM), coined in the 1980s, applies to microscopy-based techniques implementing a very small physical probe interacting with a sample to analyze its surface properties (e.g. topographic, magnetic, and electrical). A feedback loop is added to regulate the distance between the tip (probe) and the sample surface. The first SPM was the Russell Young’s ‘topografiner’ in 1972 [1], precursor of the famous Binnig and Rohrer’s scanning tunnelling microscope (STM), developed in 1981 [2]. But, the emergence of the atomic force microscopy (AFM) [3] in 1986 paved the way to nanoscale measurements with the development of many applications in imaging, metrology, and nano-manipulation. AFM has an advantage compared with other SPM because it may be used for analyzing various types of materials (conductive or nonconductive) in different environments (air, vacuum, and liquid). The operation principle of AFM is based on the force that appears when the atoms constituting the end of the probe/tip interact with the atoms of the sample surface. The tip is made of silicon or silicon nitride fabricated to present an apex (Fig. 1) with a radius of curvature of about 10 nm. The tip is attached to a cantilever characterized by a spring constant, k, whose objective is to convert the tip/sample interaction force into a deflection that is sometimes negative when forces are attractive or sometimes positive when forces are repulsive. The nature of the forces involved depends on the tip/sample distance, which is often described by the Lennard-Jones potential [4]. The cantilever deflection is measured by the optical beam deflection method. It uses a laser beam that is reflected on the top of the cantilever and directed on a four-quadrant photodiode that analyses the beam displacement and converts it in electrical signal. The tip is scanned on the surface with XY piezoelectric actuators while a Z actuator maintains the tip/sample distance constant during the scan. Three operating modes are commonly used. (i) In ‘contact mode’, the sample is scanned while the tip is maintained in contact with the surface, usually in the repulsive regime. (ii) In the ‘noncontact mode’ implemented in ambient air, the tip oscillates at its resonance frequency in the attractive regime, and sample surface topography is detected

Characterization of Nanoparticles https://doi.org/10.1016/B978-0-12-814182-3.00005-5

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through changes of resonance frequency. (iii) ‘Tapping mode’ is an advanced mode that forces the cantilever to oscillate with high amplitude (roughly 20 nm) near its resonance frequency. In this mode, also called intermittent contact mode, the tip intermittently contacts the surface and pass from attractive regime to repulsive regime. Changes in the oscillation amplitude due to energy loss are detected by a lock-in amplifier and used to control the tip–sample distance and measure the sample surface topography. Since AFM is capable of measuring force after proper calibration, it is well suited for nanomechanical measurements. Compared to conventional instrumented indentation (IIT), AFM works with smaller forces and allows high-resolution inspection of the sample before and after nanomechanical tests. For nano-objects, as mechanical properties are inevitably coupled with surface topography, the capability of obtaining topographical information together with mechanical properties is therefore essential. This makes AFM a unique tool for characterizing mechanical properties of nanomaterials [5]. Accurate measurement of mechanical properties of nanoparticles with force spectroscopy is particularly challenging. Typically, the deformation has to be limited to several nanometres or even smaller to avoid possible measurement artefacts due to substrate stiffness. The dimensions of nanoparticles are comparable or smaller to that of the tip, which makes it sometimes impossible to determine the contact area accurately. Locating the nanoparticles and keeping them immobilized during measurement can be yet another challenge.

Measurements of nanoparticles by AFM Size measurements A simple method for determining the nanoparticle size consists of measuring their main characteristic dimensions from profiles obtained by AFM, as shown in Fig. 1 [6–8]. However, the tip/nano-object convolution leads to measurement artefacts in lateral dimensions due to the tip shape (apex is typically 10 nm diameter), which is of the same order of magnitude as the nanoparticle to be analyzed. By contrast, this convolution is null at the top of the nanoparticle (noted ‘A’ in Fig. 1). The AFM technique is thus particularly well suitable for measuring the height of a nanoparticle deposited on a clean and flat substrate. Nevertheless, the ‘B’ point, diametrically opposed to A, is not accessible by any probe. Height is then approximated by the distance between the top of the nanoparticle and the reference plane corresponding to the plane of mean surface roughness (Fig. 1). With this assumption, the substrate on which the nanoparticles are deposited must be chosen to have a roughness as low as possible to not perturb the measurement. Above all, the sample preparation is a key step in the measuring process of the size of nanoparticle population by AFM. Indeed, the mean diameter is estimated from a statistically representative set of nanoparticles measured one by one. The height measuring principle detailed earlier requires that each nanoparticle remains in contact with the defined

Scanning probe microscopy (SPM)

reference plane in order to minimize the measurement errors. But, during the drying of a colloidal suspension droplet, nanoparticles tend to agglomerate in larger clusters. Consequently, the height of a nanoparticle embedded within agglomerate can be biased (see, in insert, Fig. 1). The measurement is reliable if the nanoparticles are well dispersed on the substrate surface and isolated. Then, an optimized sample preparation leads to a good dispersion of nanoparticles on the substrate and requires taking into account several parameters: (i) stability of the colloidal suspension before deposition, (ii) nanoparticle surface charge, (iii) substrate surface charge, and (iv) hydrophilic/phobic nature of the substrate. Two kinds of substrate are commonly used in AFM: mica sheet and silicon wafer [6]. For instance, muscovite mica has the advantage of presenting a clean and defect-free surface after cleaving. Silicon is an electrically conductive substrate allowing a combined observation of the surface by AFM and scanning electron microscopy (SEM). The roughness (Sq) measured by AFM is typically found to be 0.08 and 0.28 nm, for mica and silicon, respectively [6]. There is a need to work with substrate roughness as low as possible in order to minimize the measuring error due to the gap between the position of the ‘B’ point and the reference plane (see Fig. 1). Deposition of the nanoparticles on the substrate must be controlled with care to avoid the formation of nanoparticle agglomerates. Several methods are proposed implementing spin coater [6] or a fluid cell [9]. However, the quality of the deposition depends also on the electrostatic charge of nanoparticles compared to the substrate. It must be kept in

Fig. 1 Schematic illustration of particle measurement with the AFM tip.

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mind that most of metallic or oxide nanoparticles are negatively charged as are many substrates, such as silicon wafer. The behaviour of mica is more complex. Its surface is naturally negative, but electrostatic properties tend to change in contact with aqueous solutions [10]. In any case, repulsive interactions between substrate surface and nanoparticles can promote the agglomeration process. Then, two methods can be implemented to enhance the adhesion of nanoparticles on the substrate and improve their dispersion. Firstly, the substrate charge can be modified by functionalizing the surface with various molecules [9,11]. However in this case, the surface roughness can be dramatically impacted. A second way to improve the adhesion is to make the nanoparticle positively charged. To this end, the colloidal suspension must be acidified to obtain a positive zeta potential. Fig. 2 shows two depositions of FD-304 silica nanoparticles on silicon substrate at initial pH (pH  7, left) and acid medium (pH < 2, right). With the initial pH-neutral suspension, very few nanoparticles are present on the surface and are essentially agglomerated on localized areas. In contrast, upon using an acidic solution, the substrate is fully covered by well-dispersed nanoparticles. The last determining step of the measuring process is the image processing and data analysis. The measurement result is determined from heights measured, one by one, from a population of 250 to 500 nanoparticles. The number of nanoparticles to be counted depends mainly on the population polydispersity and the required measurement uncertainty. The height measurements can be facilitated by using software. Various software packages exist on the market (SPIP or Moutains Map) or are available as open access such as Gwyddion, ImageJ, or WSxM. The image processing operates following three steps: (1) image levelling, (2) identification and labelling of each nano-object present on the

Fig. 2 Two depositions of FD-304 silica nanoparticles on silicon wafer following the protocol detailed in Ref. [6], (A) at initial neutral pH and (B) after adding acidic solution (pH < 2).

Scanning probe microscopy (SPM)

image and (3) height measurement. But, such software is often a black box from a metrological point of view and must be carefully operated to obtain reliable results. For instance, the inability of the automatic option to discriminate isolated nanoparticles, agglomerates, or artefacts must be kept in mind. One study has proposed a semiautomatic approach to ensure that histogram of size distribution includes only isolated nanoparticles [7]. The method outlined here, consisting of determining the nanoparticle size through their height measurements, is well suited for spherical-like particles but not for more complex shapes. Other alternative methods have been developed by metrology institutes to accurately determine the mean diameter of spheroidal NP. For instance, the diameter can be deduced from the lateral spacing between adjacent nanoparticles touching each other and self-assembled in a 2D-ordered array [8,12,13] or from specific image analysis by fitting the upper part of the nanoparticle topographical image with a spherical cap [14].

Mechanical measurements To do mechanical measurement, force spectroscopy is performed. As illustrated in Fig. 3A, the AFM probe is approached towards the sample, contact is made, and approach continues until predefined maximum load is reached. The probe is then retracted. Most of the time, adhesion was observed when the tip snaps off the surface before the probe is fully retracted. During this process, the photodiode sensor deflection (PSD) versus scanner displacement is recorded as raw data. After calibration of cantilever spring constant and sensitivity, this curve can be converted to force versus tip–sample separation curve (Fig. 3B).

Fig. 3 Illustration of AFM force spectroscopy and data analysis. (A) Deflection versus displacement curve as the raw data. (B) Force versus separation curve after calibration and conversion, sometimes also called force–distance curve (F-D curve). Retraction part of the curves is shifted for illustration. In principle, the flat part of approach and retraction part should overlap.

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Selecting the best probe is crucial. A probe is selected so that it will cause enough deformation of the sample, but it should not be too stiff to damage the sample. If the intention is to measure the mechanical properties of titanium dioxide nanoparticles, the Young’s modulus of bulk TiO2 is around 259 GPa, which gives a first indication of the order of magnitude. A probe with spring constant higher than 200 N/m is required. At this stiffness range, it is highly recommended to use diamond or diamond-coated probes, which are more durable than conventional silicon probes. The diamond tip has the shape of a cubic corner. The nominal tip radius is 40 nm and can be confirmed by scanning a tip ‘characterizer’ sample. An even sharper tip can be beneficial for visualizing small particles. Ideally, deformation should be within 10% of the total thickness of the sample (empirical rule of B€ uckle) [15]. For TiO2 nanoparticles with a diameter of several nanometres, this can be difficult to achieve, as the small deformation makes it difficult to obtain meaningful result. The peak force should be set so that deformation is at least 1.5 nm.

Traceability routes at the nanometre scale Dimensional traceability Calibration of the instrument and determination of the measurement uncertainty are the two most important steps to make the nanoparticle height measurements traceable to the metre as defined by the International System of Units (SI) and improve measurements reliability (trueness, repeatability, and comparability to other measurements provided by other AFM). As the measurements concern nanoparticle heights, the AFM scanner only has to be calibrated along the Z-axis. Various sample standards are available on the market. Most of the time, the standard consists of a 2D grating whose pitch and height mean values are specified in a certificate of calibration and associated to a measurement uncertainty that reflects the confidence level with which these values are estimated. In the particular case of the standard presented on Fig. 4, the mean height of the structure is established at 60 nm and is provided with an associated measurement uncertainty of 0.5 nm. In practice, to calibrate the scanner Z-axis, the grating is imaged with the AFM and then processed to determine its height. For such operations, an image processing software like SPIP from Image Metrology can be very useful to accurately determine the grating height according to ISO 5436-1 standard based on profile analysis. Once this operation is done and if significant deviations from the value indicated in the certificate of calibration are observed, then a correction factor must be applied to the controller of the instrument in order to recalibrate the Z-axis. This operation must be performed periodically to avoid any drift of the instrument calibration: this period depending on the instrument, its environment, the user, and the level of accuracy required.

Scanning probe microscopy (SPM)

Fig. 4 (Left) Traceability chain associated to the measurement of nanoparticles height by AFM. (Right) Example of 2D grating standard used for the AFM calibration.

To ensure traceability of the measurement, the 2D grating must also be calibrated periodically. For such operation, the standard must be sent to a National Metrology Institute that provides such calibration services. Many possess a so-called metrological AFM, a reference instrument [15a] whose specific purpose is to calibrate standards or provide dimensional measurements with a low and known measurement uncertainty. About 30 metrological AFM are available in the world. Their designs have been optimized for metrological applications and to ensure the reliability of the measurement. In most cases, they use interferometers to measure the displacement of the scanner that images the surface. The measured displacements are then directly traceable to SI metre definition as long as the wavelength of the laser source used for interferometer has been calibrated against a frequency-stabilized laser. This long chain of calibration ensures the traceability to the SI of the nanoparticles height measurements realized by an AFM.

Mechanical traceability A number of factors affect the accuracy of mechanical measurements by AFM. Leaving topographic effects aside, as they are arbitrary and highly variable, some of the major factors dominating uncertainty on the determination of elastic modulus include cantilever sensitivity, cantilever spring constant, piezo scanner nonlinearity and drift, tip geometry and other model parameters [16]. In nanoparticle measurements, small indentation depth coupled with the fact that tip geometry is less ideal at the very apex means that it is challenging to get accurate and reliable tip geometry parameters at this scale. Moreover, as

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pointed out in Ref. [16], the dominating factor in measurement uncertainty at small indentations is cantilever sensitivity, which accounts for 93% of the total uncertainty in elastic modulus. Measurement on, for example, TiO2 nanoparticles requires stiff cantilevers to effectively deform the sample, yet the determination of the spring constant of stiff cantilevers is only possible with sophisticated techniques [17–19]. To overcome these limitations, a relative method could be implemented, which does not require determination of all parameters to calculate the Young’s modulus. First measurement is carried out on a reference material with known modulus. One parameter, typically tip radius, is adjusted so that the fitted modulus matches the expected value. Using the updated tip radius, measurement is then performed on the unknown sample to achieve the same sample deformation (in order to minimize effect of deviation from spherical tip geometry), which leads to the measured modulus of the sample. The advantage of the relative method is that it avoids the accumulation of errors from different parameters. It also eliminates the need for tedious and often unreliable tip geometry characterization as well as the sometimes inaccessible spring constant determination. The drawback is that a reference sample with similar modulus to the unknown sample is not always available, reference values may not be accurate, and the reference sample can be subject to variation due to ageing. For mechanical property analysis, deflection versus displacement curves need to be converted into force versus separation curves. Deflection sensitivity of the cantilever is firstly calibrated by recording curves on nondeformable hard surface. In this case, the displacement of piezo equals the deflection of the cantilever, that is, Zp ¼ Zc. The deflection of the cantilever is related to deflection on the photosensitive detector (VPSD) by defining the sensitivity, S: S¼

Zp Zc ¼ VPSD VPSD

(1)

Now consider measurements on the sample, where the tip deforms the sample after contact. The displacement of the piezo scanner is a combination of cantilever deflection (upward) and sample deformation (downward). To get the tip–sample separation D, the cantilever deflection Zc is subtracted from the piezo displacement Zp: d ¼ Zp  Zc ¼ Zp  SV PSD

(2)

Assuming that the cantilever acts as a spring with spring constant k, the force F is given by Hook’s law: F ¼ kZc ¼ kSVPSD

(3)

From the force versus separation curve, which is abbreviated to the ‘force curve’, the deformation (indentation depth) can be determined from the distance to the contact point.

Scanning probe microscopy (SPM)

The adhesion force can be determined from the lowest force in the force curve. The hysteresis between approach and retraction part of the curves provides the energy dissipated during the indentation and is an indication of plastic deformation. This is calculated as the difference between force integrated over separation for the approach and retraction force curves. The retraction part of force versus deformation is particularly useful: Assuming full elastic recovery during retraction, this part of the curve can be fitted to classical contact mechanic models such as Hertz model to give an estimation of the elastic modulus of the sample (Fig. 3B). Performing these mechanical measurements at defined locations on the sample enables the ability to map height, adhesion, dissipation, deformation, and Young’s modulus (see Fig. 5). Young’s modulus is calculated by fitting the retraction curve to the Derjaguin–Muller–Toporov (DMT) model: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 F  Fadh ¼ E∗ Rðd  d0 Þ3 (4) 3 Where F  Fadh is the total force subtracted by adhesion force (effective loading force on sample), R is the tip radius of curvature at apex, and d  d0 is deformation. The DMT model is a modified version of the older Hertz model and specifically takes adhesion force into account. This model assumes that sample deformation is fully plastic, which holds when deformation is small and the retraction part of the force curve is analyzed. It also assumes spherical tip geometry with radius, R. This could be problematic as tip tends to deviate from sphere at very small indentations. It is therefore important that calibration of tip geometry is performed at the same deformation as the measurement. The obtained modulus from the DMT model fit is the reduced modulus E∗, which is related to sample modulus by: " # 2 1 1  vs2 1  vtip E∗ ¼ + (5) Es Etip νs and νtip are the Poisson’s ratio of sample and tip, and Es and Etip are the elastic modulus of sample and tip, respectively. For consistency of the test, it is strongly suggested that calibrations on sapphire and a reference sample (such as fused silica) are done immediately before the measurement of sample due to potential drift of the system over time. While the relative method, if implemented correctly, is able to correct errors from other parameters, it still needs to be validated to make sure that the measurement and data analyses are carried out correctly. One way of validation is to compare the effective tip radius with measured tip radius from SEM or tip characterization samples. The effective tip radius should at least be comparable with measured tip radius.

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Fig. 5 Images of nanoparticulate structures in a TiO2 film (created using physical vapour deposition): (A) height, (B) adhesion, (C) energy dissipation, (D) deformation, (E) DMT Young’s modulus, and (F) histogram of Young’s modulus. Red and blue bins (dark grey and light grey in print version) are excluded for data analysis. (G–I) Force curves from typical points on the modulus map: 1, average modulus from the particle; 2, high modulus from the particle; 3, low modulus from between the particles. Grey curves in (G) and (I) are fit to DMT model.

Uncertainty assessment Uncertainty for size measurement Once the measurements have been completed, the estimation of the measurement uncertainty of the NP heights can be carried out. For this specific purpose, the Guide to the Expression of Uncertainty in Measurement (GUM, developed by the Joint Committee for Guides in Metrology) is a helpful document on which the reader can rely on. It specifies two approaches to evaluate measurement uncertainties, a type A evaluation in the case where statistical studies are available and a type B evaluation for assessing systematic errors [20].

Scanning probe microscopy (SPM)

Type A (statistics) evaluation of uncertainty is defined in Section 2.3 of GUM as the ‘method of evaluation of uncertainty by the statistical analysis of series of observations’. By definition, the repeatability assesses the agreement between the results of successive measurements of the same measure and carried out under the same conditions of measurements. But, it is often more relevant to evaluate the repeatability of the measurement method rather than the instrument reproducibility and to perform the measurements exactly on the same population. This implies to restart the measuring process from initial state of instrument and carry out again the approach of the tip, the settings, etc. For instance, a same set of 50 FD-304 silica nanoparticles has been imaged four times. Between each images, the AFM tip was withdrawn. The mean height has been found to be equal to 25.4 nm, and the type A uncertainty has been estimated to be 0.4 nm. Type B (systematic) evaluation of uncertainty is defined in Section 2.3 of GUM as the ‘method of evaluation of uncertainty by means other than the statistical analysis of series of observations’. Evaluation of uncertainties is then determined by investigating all error sources impacting the measuring process in a systematic way. In this section, we propose to list and rank the main error sources encountered in the case of the nanoparticle height measurements performed by AFM and detailed in Ref. [7]: Z calibration: Calibration of the instrument is performed using 2D grating with its certificate including the traceable values of the measured quantity. In our case, the relevant data is the mean step height of the grating with an associated measurement uncertainty reflecting the confidence level of the measured value. This uncertainty affects directly all the measurements carried out after the calibration process and is equal to 1 nm. Z noise level: This component of the uncertainty budget can be evaluated by holding the tip at a fixed XY position on a substrate. Thus, the resulting ‘image’ (1024  1024 pixels, scan rate ¼ 0.4 Hz) corresponds to the variation during the measurement. In our case, the root mean square (RMS) noise was estimated at 0.15 nm. Roughness and shape of the substrate: As described in the measurement principle, roughness and shape of the substrate have a direct impact on NP height measurement. As mentioned in the section above called ‘size measurements’, NP height is expressed as the difference between the top of the NP and a reference plane corresponding to the mean surface roughness. Even if the flatness can be corrected by levelling the image, the roughness must be listed as a possible uncertainty source. For a mica substrate, the impact on the measurement is 0.08 nm. Sensor resolution limit along the Z-axis: The sensor resolution limit along the Z-axis is calculated as 1.5  LSB where LSB is the least significant bit in the displacement range. For a displacement range of 7620 nm, the sensor resolution limit is equal to 0.17 nm. As the distribution of the resolution is uniform, the uncertainty associated with the height measurement is equal to 0.05 nm. Scan speed influence along the scan axis: This component is evaluated by imaging the same NP population with different scanning speed. For a direct comparison between all measurements, the proportional–integral (PI) gain is kept constant for all the experiments. Images were recorded in real time by varying the scan speed from 1 to

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40.7 μm s1. The evolution of NP height measurement with scan speed is reported in Fig. 6. The average height has been found to be 20.3 nm with a standard deviation of 0.25 nm on the stable part of the curve corresponding to the scan speeds ranged from 1 to 15.3 μm s1. This limit value of 15.3 μm s1 corresponds to a threshold value beyond which the measurement results increase dramatically, and the height reaches 25.3 nm for 40.7 μm s1. Dragging effects also appear on images beyond this threshold. Thermal drift along the Z-axis: Thermal drifts can disturb the measurements in the first few hours of an experiment. Temperature measurements were performed by fixing a thermal sensor near the AFM head, all thermally protected from the outside. Firstly, the controller was switched off, and the acoustic insulation enclosure was kept open in order to stabilize both the whole instrument and the sample at room temperature (20  0.05°C). Then, the temperature was recorded as soon as the enclosure was closed while the controller was switched on. A continuous series of images was performed and recorded on silica nanoparticle population on 2 μm  2 μm scan range (256  256 pixels). The Z drift has been evaluated by measuring the maximal point of one pattern acquired during the experiment. As observed in Fig. 7, the temperature stabilizes after 25 h. But, regarding basic measuring principle detailed earlier, the measured height will be only affected by eventual drift along the Z-axis. During the thermal stability period (plateau in Fig. 7) from 25 to 47 h, the slope corresponding to the drift along the Z-axis has been found to be equal to 0.31 nm min1. Therefore, a line-to-line correction of the image will make this effect negligible.

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Fig. 6 Height measurements performed on a single silica nanoparticle (FD-304) as a function of scan speed.

Scanning probe microscopy (SPM)

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Drift (nm)

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Z-axis drift –200

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Fig. 7 Time variation of temperature and height measured on reference silica nanoparticles (FD-304).

Uncertainty for mechanical measurements With the relative method where the properties of the unknown sample are immediately determined after measuring a known reference sample, uncertainties of Young’s modulus measurement come from two major sources: measurement error and the reference sample. The measurement error comes from many sources, including, but not limited to, drift of scanner (xyz), noise of electric components such as photodetector and controller, noise and vibration from the environment, fluctuation of temperature, and deviation from modelling. A comprehensive analysis of measurement uncertainty has been conducted in Ref. [16]. These errors can be roughly evaluated by analyzing the variation of measurement on the reference sample (e.g. fused silica). The sample is clean and flat, which minimizes errors from sample topography and contamination. Force mapping errors on fused silica are therefore mainly attributed to measurement system errors. For uncertainty analysis, the modulus mapping on fused silica with the same probe should be analyzed. Another source comes from uncertainty of the properties of the reference sample. As there is no available certified standard for fused silica, we propose to compile Young’s modulus data from different resources and estimate measurement uncertainty based on the data. For the calculation of the measurement uncertainties associated to the Young’s modulus, we assume a simple model, where the uncertainties of the measurements of the reference sample (fused silica) are added to the standard uncertainty of the mean of the particle measurements. Typical expanded uncertainties are in the order of a few percent of the measured value (see Table 1). The measured Young’s modulus of TiO2 nanostructures in Fig. 5 is 93.9 GPa with an expanded uncertainty of 1.2 GPa.

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Data points from Fig. 7 were analyzed, excluding outliers. Average modulus is calculated as follows: Y ¼ X1 +X2 +X3.

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Characterization of nanoparticles

Table 1 Measurement uncertainty analysis of Young’s modulus of a TiO2 film

Scanning probe microscopy (SPM)

For data analysis and measurement uncertainty analysis of TiO2 nanoparticles, substrate has to be subtracted. This can be done by thresholding or manual area-of-interest selection in data analysis software; see the example in Fig. 5F, where blue and red (light grey and dark grey in print version) areas are excluded from the analysis.

References [1] [2] [3] [4] [5]

R. Young, J. Ward, F. Scire, Rev. Sci. Instrum. 43 (1972) 999. G. Binnig, H. Rohrer, C. Gerber, E. Weibel, Phys. Rev. Lett. 49 (1982) 57. G. Binning, C.F. Quate, C. Gerber, Phys. Rev. Lett. 56 (1986) 930. J.E. Jones, Proc. Royal Soc. A Math. Phys. Eng. Sci. 106 (1924) 463. N. Burnham, Measuring the nanomechanical properties and surface forces of materials using an atomic force microscope, J. Vac. Sci. Technol. A 7 (4) (1989) 2906. [6] A. Delvallee, N. Feltin, S. Ducourtieux, M. Trabelsi, J. Hochepied, Meas. Sci. Technol. 26 (2015) 85601. [7] A. Delvallee, N. Feltin, S. Ducourtieux, M. Trabelsi, J.-F. Hochepied, Metrologia 53 (2016) 41. [8] G. Wilkening, L. Koenders, Nanoscale Calibration Standards and Methods: Dimensional and Related Measurements in the Micro- and Nanometer Range, Wiley-VCH, 2005, 542. ISBN 3-527-40502-X. [9] C.M. Hoo, T. Doan, N. Starostin, P.E. West, M.L. Mecartney, J. Nanopart. Res. 12 (2010) 939. [10] O.J. Rojas, Encyclopedia of Surface and Colloid Science, vol. 1. CRC Press, 2002, p. 517. [11] R.D. Boyd, A. Cuenat, J. Nanopart. Res. 13 (2011) 105. [12] J. Garnaes, Meas. Sci. Tech. 22 (2011) 904001. [13] I. Misumi, et al., Proc. of SPIE, vol. 8378, 2012. [14] O. Couteau, G. Roebben, Meas. Sci. Technol. 22 (2011) 65101. [15] H. B€ uckle, The Science of Hardness Testing and Its Research Applications, American Society for Metals, Metals Park, Ohio, 1973. [15a] S. Ducourtieux, B. Poyet, Meas. Sci. Technol. 22 (2011) 094010 (15pp). [16] R. Wagner, Uncertainty quantification in nanomechanical measurements using the atomic force microscope, Nanotechnology 22 (45) (2011) 455703. [17] M.-S. Kim, Accurate determination of spring constant of atomic force microscope cantilevers and comparison with other methods, Measurement 43 (4) (2010) 520–526. [18] M.S.C.A. Clifford, The determination of atomic force microscope cantilever spring constants via dimensional methods for nanomechanical analysis, Nanotechnology 16 (2005) 1666–1680. [19] M.S.C.A. Clifford, Improved methods and uncertainty analysis in the calibration of the spring constant of an atomic force microscope cantilever using static experimental methods, Meas. Sci. Technol. 20 (12) (2009) 125501. [20] J. 100, Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement, https://www.bipm.org/utils/common/dcuments/jcgm/JCGM_100_2008_E.pdf, 2008.

Further reading [21] J. Sepp€a, Traceable measurement of mechanical properties of nano-objects, 24 05 2017, [En ligne]. Available from: http://www.ptb.de/emrp/fileadmin/documents/tmompon/2015_Guide_MechProp_ real_NP_AFM.pdf. Accessed 21 March 2018.

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