Hybrid metrology for nanometric energy harvesting devices

The parametrization of the nanostructures covering the energy harvesting (EH) devices play an important role in maximizing the exploitation of light and so does the selection of the best suitable fabrication and measurement methods. The fabrication and optical inspection of periodic cylindrical nanostructures for EH devices is a challenging task for both manufacturers and metrologists. In this paper we present the fabrication process of nanowires (NWs) along with optical and non-optical measurement techniques which were used to measure the geometrical parameters of these periodic nanostructures. The paper explains the benefits of hybrid metrology that combine data from different metrology tools to obtain more accurate dimensional information about the measured NW samples than those which can be achieved by using only one metrology instrument and thereby improve the fabrication process. Measurement procedure and the determination of geometrical parameters achieved with uncertainties down to 2 nm are provided in the paper and discussed in detail.


Introduction
Energy harvesting (EH) from renewable sources (solar, heat and movement) is seen as a prominent solution to our world energy problems with the shift now from micro-to nano-scale devices. Nanowire (NW) based EH systems have achieved a big progress, but due to nm-dimensions and large device size (m 2 ) they also bring challenges for testing and characterization. Averaged properties of EH devices can be measured, * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. but a quantitative link and correlation between the performance of single NWs and that of the overall device is lacking. Over the past decade, multiple attempts have been made to develop EH devices and scale them down from the macroand microscales to the nanoscale [1][2][3]. Due to their extremely small physical size and high surface to volume ratio, NW based EH systems, including photovoltaic solar cells, thermoelectrical and electromechanical energy nanogenerators, have gained a great interest and achieved a progress. However, the challenge lies not only in the fabrication of these structures but also in the characterization of their geometry. The fast in-line optical metrology tools, such as confocal microscopy and scatterometry, have been developed for the semiconductor industry that manufactures high quality uniform structures and not the EH industry, where the high quality is not crucial for obtaining a good performance. However, in order to quantify the performance of EH device and manipulate the light-matter interaction, above mentioned methods are the best option when it comes to high accuracy non-destructive measurements. Certain sample conditions such as uniformity of the NWs have to be met for the best results. This condition is quite challenging when the fabricated NWs are approaching the 1 µm in length. Therefore, for this research it was decided to reduce the height of NWs to less than 400 nm and fabricate them as uniform and parallel to each other as possible while maintaining the fixed period in x and y axes.
In line scanning electron microscopy (SEM) is a possible solution for the measurement of the structures applied in EH, but is not widely used since it is very expensive, and the surface is affected by inspection. For this purpose the best way of getting as much information about the geometry of NWs as possible is to combine fast in-line optical metrology tools with off-line SEM and/or atomic force microscopy (AFM) tools to measure the NWs. Good agreement between the measured height by the metrology instruments scatterometry, confocal microscopy and AFM were reported in [4] for line gratings with varying heights and a pitch of 3.3 µm. In this paper we therefore focus on the development of the hybrid metrology for nanopillar measurement. Moreover, the paper shows the first steps towards handling the stochastic behavior of the NW's dimensions in scatterometry and thereby enlarging the application area of scatterometry to the samples with less perfect structures. In this novel approach for EH device characterization, we furthermore investigate how these techniques complement each other in order to achieve the most accurate results and how they may be used to improve the fabrication process.
Recently, 3D silicon nano-structures as vertically-aligned Si NW arrays (SiNWAs) with defined surface roughness were fabricated in large-scale and it has shown great potential for the next-generation energy-harvesting (photovoltaics, thermoelectrics, etc) [5,6] and storage devices (Li ion battery, supercapacitor, etc) [7,8]. Target values for NW diameter, height and density are in the range of 100 nm, tens of micrometers, and >10 8 cm −2 , respectively. Large-scale SiNWAs can be realized using metal-assisted chemical etching combined with nanosphere lithography or nanoimprint lithography [9]. In this case, the bending or breakage of the NWs and nonuniform height on larger scales may occur. Alternatively, ordered SiNWAs with high structure fidelity and purity can be fabricated on large-scale using deep reactive ion etching (DRIE) at cryogenic temperatures (cryo-DRIE), without scalloped sidewalls as in the Bosch process [10,11]. With electron beam lithography (EBL), nanostructures below 10 nm can be fabricated by maskless-exposing (direct-writing) a polymeric thin resist film under a highly focused electron beam [11]. Although it has a high resolution, the relatively high instrumentation costs, and long processing time, producing nanopatterns at low throughput, are limiting its application to low-volume production of semiconductor devices and space satellite applications. The advantage of generating defect-free and geometrically flexible nanopatterns makes it an attractive tool for prototyping and specialized processing.
For this research, NWs with various aspect ratio were fabricated by EBL and measured by SEM, AFM, optical coherent and partially coherent Fourier scatterometry. These different types of measurement techniques were combined to determine the geometrical parameters such as the diameter, the height, and the pitch of the NWs. This paper addresses the challenges of incorporating both non-optical and optical techniques for the measurement of geometrical parameters using hybrid metrology. It also discusses the benefits of this hybrid metrology approach compared to the results that can be achieved by using only one metrology instrument.

EBL
For this work, a field-emission SEM (FE-SEM, Supra 40, Carl Zeiss AG, Germany) was used to form the pattern in the positive resist poly(methyl methacrylate) (PMMA, P 672.03 AR-P 672, Allresist GmbH, Germany), which is soluble after electron exposure due to chain breakage of long into smaller polymers. The FE-SEM is equipped with an E-beam writer (Raith, type EBPG 5200, 100 KeV, Raith GmbH, Germany) and can provide accurate exposure down to 10 nm. The nanopatterned resist was used as a negative mask for the metal deposition (figure 1(c)), where a Cr layer of 30 nm has been evaporated working as hard mask (figure 1(d)) for cryo-DRIE after a liftoff process. Fabrication of Si NWs arrays (figure 1(e)) was done by means of cryo-DRIE (PlasmaPro 100 RIE, Oxford). At last, the Cr masks have been removed (figure 1(f)) using mix solution of perchloric acid and ammonium cerium nitrate (Chrom etch n • 1, MicroChemicals, Germany), resulting in SiNWAs which have clean coating free surface.

Geometry of the fabricated samples
Cr masks with designed nanopatterns of 200 nm in diameter and 600 nm in pitch (tubs_ebl04) have been checked by SEM, as shown in figure 2(a) and the diameter were found to be approximately ∼224 ± 6 nm. Vertical Si NWAs obtained using anisotropic cryo-DRIE (following the recipe: −95 • C, ICP/HF power = 140/8 W, SF 6 /O 2 flux ratio = 120/15 sccm, reactor pressure = 1.0 Pa, process time t = 200 s) with the aforementioned masks are shown in figure 2(b), where the high fidelity and purity of the manufactured NWs can be observed. The NWs diameters and heights produced by this recipe have been measured, by SEM, to be ∼205 ± 3 nm and 362 ± 3 nm, respectively. Figure 2(b) indicates that the NWs have a low undercut of ∼10 nm under the circular mask (removed before SEM inspection). Similarly, vertical Si NWAs (ebl_tubs_vsl_03) with NW diameter of ∼108 ± 4 nm, pitch of ∼500 nm and the height of 156 ± 4 nm have been fabricated.

AFM
The atomic force microscope is part of the group of scanning probe microscopes where the interaction between a surface  and a small probe is controlled and measured while the probe is scanned over the area of interest. As shown in figure 3, the interaction is sensed by measuring the deflection of a laser beam that is reflected off the back side of the cantilever that is connected to the probe. By scanning over the surface in a raster scan, the shape of the surface is captured point by point and line by line with (sub)nanometer resolution.
The AFM measurements of NWs were performed with a Veeco Dimension 3100 AFM in tapping mode. The probe was a nunano scout 350R HAR type with a nominal tip radius curvature <10 nm. Since the Veeco 3100 is not traceable by itself, the lateral range and height range were calibrated using calibrated gratings and step height standards. Next to the lateral scale, also the residual non-linearity of the scan piezo for the lateral movement was established and used along with the scale calibration and height calibration coefficients to correct measurement data off-line. After this calibration phase, the data were processed to extract the pitch, the height, and the  diameter of NWAs. The histogram for the nearest neighbor distance between the NWs is shown in figure 4.
The pitch and the pitch uncertainty were determined as the mean value and standard deviation of a normal distribution fit to the measured histogram distribution. Similarly, the height was determined from a fit to the height distribution provided by all NWs in the scanned field. The measured samples had some material residual, from the manufacturing process, in the areas between the NWs, resulting in an uneven background plane. The zero level of the background plane must therefore be chosen carefully in this process as this affects the determination of the height of the NWs.
For the samples in this paper, the histogram of the data representing the zero level shows a normal distribution. The reference level is therefore set to the height represented by the maximum of the fitted distribution. The background usually contains some noise, either due to actual surface texture or instrumental noise, figure 5. In our case, the noise was dominated by surface texture with a normal height distribution. The zero level was therefore set at the height associated with the maximum value of the histogram peak representing the background data. The (effective) diameter was determined from the cross-sectional area of each NW. The height of slice to determine the cross-sectional area was set to 10 nm below the maximum height of the wires. However, the probe shape has a profound influence on the fidelity of AFM diameter measurements. The shapes acquired by AFM are a geometrical  convolution of the actual shape of the surface under study and the probe shape as shown in figure 6. Accurate determination of the diameter of the NWs therefore requires correction for the diameter of the probe [12].
The profile measured with an AFM is a combination of the surface profile and the shape of the probe itself. Height and pitch are not affected but the diameter of the wires cannot be determined accurately from the measured profile without correcting for the probe shape. One method to determine the probe diameter is based on performing an AFM measurement on spherical nanoparticles with the same probe [13,14], figure 7. Because of the sphericity of the particles, the resulting nonsphericity of the acquired shapes is due to the probe shape. Since the height of the acquired shapes is not influenced by the probe shape, the height of each shape represents the diameter of the underlying spherical particle. The probe shape can therefore be reconstructed by subtracting a spherical shape with a diameter equal to the measured height from the raw data. Finally, since the probe diameter varies along the length of the probe, the diameter is evaluated at a certain distance from the very end. Since the diameter of the NWs was calculated at a position of 10 nm below the maximum height, the probe diameter was evaluated at the same position along the reconstructed probe shape.
The probe shape corrected NW diameter was evaluated for sample ebl_tubs_vsl_03 for a sequence of nine consecutive measurements, figure 8. Since the probe diameter was only determined after the final measurement, a single value for the probe correction was used for the sequence in the figure. The Probe shape reconstruction procedure. The upper row represents the process of obtaining a measured profile resulting from the unknown probe shape and a spherical nanoparticle. Lower row: by subtracting a spherical shape determined by the height of the profile, the probe shape can be reconstructed. trend in the figure shows an apparent change in the NW diameter as the measurement sequence continues. Since it does not seem likely that the NW diameters would actually change during the measurement sequence, the apparent change in the diameter most likely shows the wear of the probe, resulting in an increase of the probe diameter. The probe shape measurements were performed right after the final measurements on sample ebl_tubs_vsl_03. The diameter determination for the final measurement is therefore most accurate while the earlier measurements are corrected with a probe diameter that is increasingly too large.
Due to aforementioned AFM probe and geometry convolution and the small interspace between the structure on the substrate, the measurement of certain shapes can become very complex. Therefore, optical measurement techniques were used for the further investigation.

Coherent and partially coherent Fourier scatterometry
Among other optical measurement techniques, scatterometry is very widely used for the precise characterization of the geometry of periodic nanostructures. After the light-sample interaction, the scattered light creates a unique diffraction signature which can be observed in the back focal plane of the microscope objective. For the NW measurement at VSL a Coherent Fourier scatterometer with confocal detection was used. The NWs were placed under the confocal microscope objective. After shining on the reflective sample, the light travelled back through the microscope objective to its back focal plane. The schematic render of the focused light and the diffraction orders forming the pattern is shown in figure 9.
The experimental intensity values are captured by the charge-coupled device-CCD camera. Scatterometry is not a direct geometry measurement method. Therefore, an inversion method is needed to determine the geometrical parameters of the nanostructures, a mathematical model of the NWs structure, a first principal numerical Maxwell solver [15,16] is used for calculating theoretical intensities and a least square method is used for selecting the theoretical intensities with the smallest difference from the experimental intensities. For generating numerical simulations, we used one of the most frequently applied tools to solve Maxwell's equations in scatterometryrigorous coupled wave analysis (RCWA). To generate the diffraction pattern, we insert apriori information about the NWs, such as the geometrical shape (the periodicity, the height, the diameter of the structure, etc.), into the mathematical model of the NWs. The RCWA algorithm uses the mathematical NW model for generating the electrical field scattered from the NW structure. The collection of the scattered field and the propagation to the back focal plane is done as described in [17]. The more structure parameters there are in the mathematical NW model, the more advanced geometrical shapes can be simulated. The principles of scatterometry are explained in more detailed in these publications [18][19][20].
Nominal parameters are usually provided by the manufacturer, unfortunately it is not necessarily always the case. If unavailable, one may obtain the nominal parameters from confocal microscopy, AFM or SEM measurements. If reliable nominal parameters with uncertainties exist, they may be used in a chi square merit function for hybrid metrology [21] to limit the parameters range that must be evaluated to create, a database library of back focal plane diffraction signatures. In the final step, all the solutions within the database library are tested for a minimum in the chi square merit function, the simulation matching the measurement result is selected and the geometric parameters are retrieved from the knowledge of the best matching simulation. Putting it all together we have the following procedure. Measure the back focal plane intensity on the NWs, I sample , on a flat piece of Si(100), I ref, and a dark measurement, I dark , obtained by blocking the light source. The diffraction efficiency, η, is calculated from these three parameters in the following way where N is the number of pixels, λ is the incident wavelength and R(λ,i) are the reflection coefficient for the ith pixel of the reference sample. Assuming that the measured back focal plane intensities are independent, the experimental uncertainty may be found using the law of propagation in equation (2) where δI sample , δI ref and δI dark are the experimentaluncertainties for the sample, the reference and the darkmeasurements of each pixel, respectively. Under the assumption that no systematic errors are present, random errors can be estimated from the noise in the measurements. The noise is assumed to be normally distributed as we detect many photons, and thus the measurement uncertainty is given by the standard deviation of the measured data in each pixel. The σ η uncertainties (equation (2)) for the sample ebl_tubs_vsl_03 are shown in figure 10.
Measurement uncertainties were calculated for each pixel of obtained data within the numerical aperture. As shown in figure 10 the uncertainties are evenly distributed with the values below 0.025 nm.
The hybrid chi-square merit function can now be written as: Here p c is shorthand notation for all the calculated geometrical parameters in the mathematical model, σ AFM is the AFM height uncertainties, σ SEM is the SEM width uncertainties and σ η (i) is the scatterometry uncertainties for the ith pixel.
Two different aspect ratio NW samples were investigated using coherent Fourier scatterometry. The sample tubs_ebl_04 was provided with these nominal parameters: NW pitch of 600 nm, NW height of 360 nm, NW diameter of 200 nm and the sidewall angle of 90 • . Sample ebl_tubs_vsl_03 had the  Figure 11 shows the diffraction signature obtained in the Fourier plane (on the left). The numerical simulations were created based on apriori knowledge provided by the manufacturer (in the middle). The setup also has an imaging camera which provides the image of the sample (on the right).
As preliminary results obtained by coherent Fourier scatterometer showed, for such aspect ratio subwavelength NW samples the higher contrast is required, and the simulated pattern is not very characteristic in comparison with normalized numerical simulations. The measured structure had a periodicity smaller than the wavelength and contained slight nonuniformity in geometrical parameters. These aspects together with surface roughness might have affected the signal to noise ratio.
Another optical measurement technique suitable for NW characterization is partially coherent Fourier scatterometry. Since the data obtained by both AFM and coherent Fourier scatterometry showed better results on sample ebl_tubs_vsl_03, it was decided to measure this sample with partially coherent unpolarized light.
The system, sketched in figure 12, is developed at DFM and is based on a Navitar optical microscope equipped with a 5 W light emitting diode light source, and a monochrome 1.3 MPx CCD camera. An interchangeable lens system enables it to work as a regular microscope as well as a Fourier microscope For this research the microscope was equipped with infinity corrected microscope objective Mitutoyo NA = 0.90, magnification 100x and a 405 ± 5 nm filter.
The focus can be adjusted by moving the sample stage. The sample is brought into focus by monitoring it on the CCD detector. The diffraction signature as a measurement result was taken by the CCD camera.
The results provided in figure 13 show that by applying smaller wavelength (405 nm) than the period (500 nm)  of the measured structure, the diffraction pattern is more characteristic due to the higher number of diffraction orders enhancing the signal within the numerical aperture. As figure 13 shows, the diffraction efficiencies obtained by partially coherent Fourier scatterometry agree with AFM measurement results. Numerical simulation in figure 13 (middle) was generated with parameters: pitch 500 nm, height 210 nm and diameter 115 nm and it is a best match for the measurement data (figure 13 left). Numerical simulation in figure 13 (right) was generated with nominal parameter (pitch 500 nm, height 150 nm, diameter 100 nm).
A summary of the pitch, height and diameter measurement by the individual metrology tools and the hybrid approach is shown in table 1. In the hybrid metrology analysis, we use the optimal measurement parameters for each metrology tool e.g. height from AFM, width from SEM and diffraction efficiencies from partially coherent scatterometry. Data analysis and chi-square calculation (equation (3)) revealed that the best match for the hybrid approach is with the height of NWs being 205 nm and the width 110 nm, which is identical to the combination AFM and Scatterometry as well as AFM and SEM. Therefore, we recommend to use one of these combinations for process validation.
The table 1 lists the measurement results for the individual metrology tools and for hybrid metrology. The AFM diameter values outside the brackets are the values obtained after the final tip deconvolution approach whereas the values inside the brackets are for the initial tip deconvolution approach.

Conclusions
Contact and non-contact measurement techniques were used to analyze the geometrical parameters of silicon NWs fabricated by DRIE at cryo-DRIE using Cr masks nanopatterned with EBL. The study and the findings presented in the paper confirm that hybrid metrology gives the best height and diameter estimate of the NWs. This is achieved by using the best individual metrology tools for measuring of each measurands and thereby avoiding correlation between multi parameters measured with the same metrology tool. In this research coherent Fourier scatterometry for subwavelength gratings was limited by the excessive noise most likely generated by the sample roughness. The numerical simulations were generated based on provided nominal sample parameters. AFM is an excellent technique for height measurement but has limitations depending on the type and shape of NWs [12]. Although, in this case, the AFM was limited by its probe shape for the determination of the diameter and the sidewall angle of NWs, the measurement results showed that the measured height was in good agreement with the hybrid result. SEM is widely used for measuring the width of structures and to a less degree for measuring height. In our case the measured width matched well with the result of the hybrid analysis. The NWs were also measured by partially coherent Fourier scatterometry which provided diffraction efficiencies and the characteristic diffraction signature in the Fourier plane. A library of diffraction efficiencies with height and diameter values around the measured AFM height and SEM width values were simulated. The data analysis gave a fair height and diameter estimation using only scatterometry and good parameter estimation together with AFM. Indicating that the technique is more sensitive to width than height. This study is a good example of obtaining high-quality measurement using complimentary measurement techniques if the nominal parameters are provided with the big uncertainty or if the fabrication error might be expected. Scatterometry requires numerical simulations of many diffraction images to create a huge library that may be used to find the best match. The computation of one diffraction images took 4 h in this work. Computational time for a library might therefore become very long if one does not have a way to limit the parameter range. AFM and SEM plays a big role in providing the height and diameter parameters. However, shape beyond height and diameter can be reconstructed by the optical scatterometry techniques [21].

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).