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Abstract
Physical unclonable functions (PUFs) are receiving significant attention with the rise of cryptography and the drive towards creating unique structures for security applications and anti-counterfeiting. Specifically, nanoparticle based PUFs can produce a high degree of randomness through their size, shape, spatial distribution, chemistry, and optical properties, rendering them very difficult to replicate. However, nanoparticle PUFs typically rely on complex preparation procedures involving chemical synthesis in solution, therefore requiring dispersion, and embedding within a host medium for application. We propose laser machining of surfaces as a one-step process for the creation of complex nanoparticle based PUFs by machining 600 nm thick copper films on a silicon substrate to yield a complex spatial and chemical distribution of redeposited copper, silicon, and oxide species. The approaches and material system investigated have potential applications in silicon chip authentication.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Physical unclonable functions (PUFs) are physical sources of inherent randomness on a device or structure, which can be readily interrogated using a series of challenges to produce a repeatable and unique response, while being impractical or essentially impossible to duplicate [1,2]. Many optical PUFs have been proposed in literature, such as randomly-dispersed particles suspended in transparent substrates or rough surfaces, which under laser interrogation, create unique images or speckle patterns [3–5]. Other optical PUFs include laser generated holographic features [6], plasmonic enhanced resonators [7], or nanoparticles of different composition and geometry deposited onto substrates to generate random distributions [8–13]. Many other types of non-optical PUFs exist as well, including electrodes [14], memories [15–18] acoustic devices [19], and MEMS devices [20,21]. This vast array of techniques enable different challenges and responses which can be advantageous, depending on the application the end user will require.
However, the use of laser-machining to create random particle distributions for PUFs has only very recently been discussed in literature. For instance, work on laser-induced forward transfer to create Mie-resonant silicon nanoparticles on a transparent donor substrate has been reported [22]. Femtosecond lasers have also been used to create hybrid gold/graphene random color patterns for covert structural features [23], as well as in studies of the breakdown of gold films on silicon to generate non-linear white-light luminescence [24]. Here we report the use of laser irradiation of thin Cu films on Si wafers to generate distributions of mixed Cu and Si particles on the smooth Cu surface surrounding the ablated region. These particles yield distinct signatures in both optical brightfield and darkfield microscopy, as well as distinct Raman scattering and fluorescence signals, all of which can be used to uniquely identify a laser machined structure. Laser-written structures can be easily generated in vast numbers and can be integrated into workflow with minimal disturbance given the prevalence of lasers in many industrial processes. In general, plasmonic systems are commonly used in varieties of optical applications including PUFs [25–30] and the theory behind these types of devices has been described in detail elsewhere [31]. Laser induced surfaces structures have also generated a great deal of attention [32]. Previous work has also shown laser machining of copper and other metals can generate complex colorimetric responses that result from the interplay of plasmonic resonances, the presence of oxide layers, and diffractive effects [33,34].
Optical microscopy provides a rapid and relatively cheap method of authentication while Raman and fluorescence imaging provide access to additional security features but require more complex equipment and additional time to authenticate. The process can be readily scaled down using tightly focused laser light with higher magnification optics to interrogate and validate features at the microscale. A variety of pulsed and continuous lasers of different wavelengths can be used, as the process relies only on the ability to ablate the material(s) to produce a random distribution of nanoparticles. The process for examination of the structures uses a combination of darkfield analysis for spatial coordinate maps, and chemical analysis of Raman features, while proposing a simple laser machining method for generating the structures and the addition of fluorescence mapping. The approach could be applied to silicon chip authentication given the relevance of the material system investigated, where methods of fingerprinting manufactured devices are becoming increasingly important in a world where counterfeit electronics are on the rise [35].
2. Methodology
2.1 Wafer processing
Double side polished Si p-type (boron) wafers, < 100 > orientation, 550 µm thick were used as the primary substrate. These wafers were cleaved into 4 × 4 cm2 pieces. Using an Angstrom Nexdep evaporator, 10 nm of titanium was first applied as an adhesion layer, followed by 600 nm of Cu. The actual thickness was measured using a DektakXT profilometer and was found to be 600 nm.
2.2 Laser machining
Samples were machined at a wavelength of 1030 nm using a Light Conversion PHAROS femtosecond laser, which outputs 320 fs pulses at a repetition rate of 10 kHz. The position of the laser on the samples was controlled using an Aerotech AGV-10HPO galvo scanner mounted on an Aerotech ANT130-L-ZS nano-positioning lift stage with z-axis control. The laser was focused using a telecentric ƒ-Theta lens with a 50 mm focal length resulting in an ablation spot size of approximately 15 µm. Starting at a peak pulse energy of approximately 200 µJ, the deposited energy was adjusted by rotating the polarization with a half waveplate followed by a Glan-laser calcite polarizer which allows horizontal polarization to pass through while vertical polarization is rejected. The machining speed was set to 100 mm/s with acceleration (from 0 mm/s) and deceleration (to 0 mm/s) towards the start and end of the line, respectively, resulting in more energy deposited at the end of the lines producing a crater (cf. Figure 1). A peak fluence of approximately 190 J/cm2 was achieved at maximum speed. Ten identical lines of length 3 mm spaced apart by 1 mm were machined using five different incident average power settings: 125, 60, 30, 20 and 15 mW, as measured using an Ophir VEGA digital multimeter and thermal sensor (Ophir 3A-P-Quad).
Fig. 1. Brightfield (left) and darkfield (right) optical microscope images of laser machined lines at 50x magnification. Lines were machined with average incident powers of (a) 125 mW, (b) 60 mW, (c) 30 mW, (d) 20 mW and (e) 15 mW.
2.3 Optical and dark field microscopy
Bright and darkfield images were captured using a Zeiss Axio Imager M2.M microscope equipped with an EC Epiplan-Apochromat 50×/095 H objective lens and collected using an Axiocam 512 camera with a theoretical 0.062 µm/pixel ratio and Zeiss Zen microscopy software. The gamma correction factor on the camera was fixed to 1.0, and the integration time was varied between brightfield (1 ms) and darkfield (1000 ms) measurements to account for lower total collected light in the latter case. A second optical microscope was also used for comparison, an Olympus BX 51TRF equipped with an MPlanFL N 50x/0.8BD ∞/0/FN26.5 objective lens. Images were collected using a PixelLINK PL-D685CU digital camera and the µScope microscopy software. The Olympus microscope is equipped with a 50 W 12 V Halogen display lamp type 64610 HLX.
2.4 Scanning electron microscopy (SEM) and energy dispersive x-ray (EDX) spectroscopy
Images of the machined lines were acquired on a Zeiss Gemini SEM 500 field emission microscope at an acceleration voltage of 5.00 kV, a working distance of approximately 7.4 mm, and at 1000x magnification. Topographic scans were collected using the secondary electron detector positioned at 30° relative to the sample surface. EDX scans were obtained with a Bruker XFlash 61|60 detector positioned at 30° relative to the sample surface. Signals for Cu’s Lα peak at 0.93 keV, Si’s Kα peak at 1.739 keV, and oxygen’s Kα peak at 0.525 were detected across the machined lines and plotted such that the color of each pixel was determined by the standard color mixing feature of the Bruker Esprit 2.1 software using automatic filtering.
2.5 Raman spectroscopy
A WiTec Alpha a300 system in the backscattering configuration equipped with a 12 mW 532 nm pump laser and a 600 grooves/mm grating blazed at 500 nm was used to record Raman spectra. Raman maps were generated over a field area of 150 × 100 µm2 at a spectral point density of 90 × 60 pixels (5400 spectra total) and an integration time of 0.01 s to limit scan time to 5 minutes. The pump laser was focused using a 20× 0.4 NA objective such that the minimum spot size was achieved on the Cu surface. Post processing of Raman data was done using WiTec ProjectFour and Origin software suites. The distribution of Si was mapped using the integrated area under the main Si Raman peak appearing at 521 cm-1 (integrated area between 482.5 cm-1 and 557.5 cm-1). Fluorescence maps were generated using the same setup and map the integrated emission between 800 cm-1 and 3600 cm-1.
2.6 Image authentication
Image authentication was completed using open-source Fiji software based on ImageJ [36,37]. The images were first converted to 8-bit greyscale, and then thresholding of the optical bright and dark field images was done using the Color Threshold function with a pass filter for brightness greater than background signal intensity. Using pixel brightness, the dark particles were isolated in the brightfield images, and the bright particles were isolated in the darkfield images. Thresholding of the Raman and fluorescence maps was done using the Auto Local Threshold function. Different thresholding methods were used for optical and chemical maps due to the high background signal present in the chemical scans making color thresholding an ineffective solution in that case. Local contrast would not work for brightfield images due to changes in the Cu background being detected thus yielding erroneous results. After thresholding, the Particle Analysis function from ImageJ was used to isolate the redeposited particles from the machined line by filtering out the largest deposits across optical and Raman images, yielding only the unique distributions and eliminating large repeatable elements such as the machined line itself, which is used for rough alignment. Images of the same surface were aligned using the plugin Register Virtual Stack Slices described in literature by Arganda-Carreras et al. [38]. Translational movements were used to align the structures prior to pixel-by-pixel comparisons. This step could not be completed for aligning non-identical surfaces as the software failed to find sufficient correlation to align them, however the laser line and crater itself act as alignment features during the acquisition of scans. All images were correlated using the Image Correlator plugin created by Wayne Rasband and Kevin Baler [36]. The plugin works by separating the images into 4 bins, (0,0), (255,255), (0,255) and (255,0). These represent matching off pixels (0,0) where no element is present in either image, mismatched (0,255) and (255,0) where a pixel is on in one image and off in the other, and matching on pixels (255,255) where an element is present in both images. A correlation factor is obtained between 0 and 1 where 1.0 is a perfect match and 0.0 is a complete mismatch by comparing the percentage of pixels in the (255,255) bin with the sum of mismatched pixels in both (0,255) and (255,0) bins. In this process, matching off pixels (0,0) are ignored such that a blank image would yield a correlation factor of 0.0.
3. Results and discussion
Random particle distributions were generated by laser irradiation of a 600 nm thick Cu film on a Si wafer over a series of five different average incident laser powers: 125, 60, 30, 20 and 15 mW. Incident powers above 125 mW yielded large, agglomerated particles which were sensitive to the incident Raman pump beam causing damage that wasn’t seen at 125 mW and below. In addition, the particle density grew such that resolving individual particles became problematic with brightfield and darkfield imaging. On the low end, 15 mW is the minimum power required to eject enough silicon for the particle density to become noticeable. The laser powers depend on the thickness of the Cu film, which was 600 nm for these trials, the thickest layer obtainable with the given evaporator system without causing undo thermal effects due to sample heating from the evaporation. A thinner layer would require lower power and vice-versa. The laser machined lines terminate with a crater, where increased ablation occurs due to the decelerating raster scan speed of the laser. This process yields a repeatable laser marked line-crater combination feature surrounded by a random distribution of particles with a variety of sizes. The line and crater are used as an alignment feature for repeated imaging of the associated particle distribution, with the crater serving as the central focus and the line extending out is used to adjust for rotation. Ten lines were generated for each incident machining power.
Representative optical brightfield and darkfield images for each machining power are shown in Fig. 1 and highlight the decrease in density and brightness of the redeposited particles as the laser intensity decreases. A rainbow ring surrounding the machined line is observed in the darkfield images of Figs. 1(a)–1(c). It is known that redeposited silver [39] and Cu [34] nanoparticles exhibit plasmonic resonances generating colors in the visible under darkfield illumination [40–42]. The ability of laser-machined Cu to generate plasmonic and oxide based colors has also been reported [33]. A mixture of plasmonic Cu nanoparticle resonances, Mie Si nanoparticle resonances, as well as Cu oxides and Si compounds in the ring surrounding the machine structures is likely driving the rainbow of colors observed in Fig. 1. This region contains a high density of redeposited particles and glows under darkfield illumination, bounded by a small barren region directly adjacent to the machined line where much less redeposition occurred. This barren region is likely caused by a shock wave as the laser decelerates, pushing particles away from the machined line, and becomes prominent for machining at higher laser powers. Additional brightfield and darkfield images, consisting of five repeated images of the same two lines (L1 and L2) are given in Supplement 1, Figs. S1 (brightfield) and S2 (darkfield) – each of these images was manually misaligned and then realigned and refocused on the surface to simulate an end-user re-imaging the same feature.
Optical darkfield imaging is commonly used in the examination of nanoparticle distributions due to the high contrast that is provided between the bright scattering of nanoparticles and the dark background [5,8,14]. This is most easily seen when particle densities are low, as in the cases of Figs. 1(c)–1(e) in the region directly beside the machined line. However, even the higher density regions seen in Figs. 1(a)–1(b) show discernible particles, especially farther from the machined line. Brightfield images have less overall contrast but allow better particle identification in the regions closest to the machined feature, whereas the darkfield images have regions where the optical scattering of particles overlap decreasing the resolution. Both optical brightfield and darkfield imaging techniques are readily accessible, with microscopes capable of imaging such surfaces already widespread, thereby decreasing the economic hurdle of integrating the challenge-response pair into industrial processes.
The machined structures were examined with a scanning electron microscope (SEM) equipped with an energy dispersive X-ray (EDX) detector, as shown in Fig. 2. As expected, a trend of decreasing exposure of the underlying Si wafer as the laser power decreases and a concomitant decrease in redeposited Si particles compared to Cu is observed. The bright rainbow regions observed under optical darkfield imaging (Fig. 1) are accompanied by oxygen as observed under EDX spectroscopy (Fig. 2), particularly around the crater and at higher machining powers. These scans highlight that redeposited Cu and Si particles ejected from the machined line can react with oxygen species in the laser plume before redepositing as oxides on the surface. The rainbow effect is likely due to oxide vanishing away from the crater, as explained by the steady decrease in oxide moving away from the machined line, observed under EDX. The SEM images of Figs. 2(a) and 2(b) suggest that the oxide regions form as a film, as a step appears between the oxide-rich and oxide-free regions immediately beside the machined line.
Fig. 2. SEM (left) and EDX (right) maps of laser machined lines at (a) 125 mW, (b) 60 mW, (c) 30 mW, (d) 20 mW and (e) 15 mW. EDX map colors, yellow: Cu, magenta: Si and cyan: O.
As seen in Fig. 2, laser machining breeches the thin Cu layer and ejects both types of material (Cu and Si) which make up the underlying structure. This naturally leads to the redeposition of particle mixtures as well as oxide compounds generated as the ejected material interacts with the plume. Exploiting the well-defined Raman scattering signal of Si, spectral maps were generated of the region surrounding the machined area, revealing a unique distribution of the Si Raman scattering signal. The integrated area of the main Raman scattering peak of Si appearing at 521 cm-1 is mapped out in Figs. 3(a)–3(e). Example spectra obtained in the brightest regions are shown in Fig. 3(f). These maps were scaled such that the peak signal was used as the upper limit and the lower value of the color-bar was leveled such that background signals were eliminated where possible. The Si signal decreases steadily from sample to sample as the machining power decreases, coinciding with less ejected Si from the underlying structure, a trend which was also confirmed in the EDX measurements appearing in Fig. 2. Despite this decrease, Raman scattering from Si was still detected in resolvable amounts for all but the 15 mW sample shown in Fig. 3(e), where less than 15 counts were detected and no obvious concentration of Si was detectable beyond the system noise at our collection parameters. The crater itself is not obvious, likely due to the change in z height in that region yielding a lesser focus of the Raman pump beam, and therefore less counts in the area than would be expected. This effect can also be seen in Figs. 3(a) and 3(b) where an obvious decrease in the detected Si signal can be noted in the center of the craters. Thus, challenging the surface at different z-heights would naturally yield another set of unique responses.
Fig. 3. Intensity maps of the primary Si peak (∼520 cm-1) of laser machined lines at (a) 125 mW, (b) 60 mW, (c) 30 mW, (d) 20 mW and (e) 15 mW. (f) Example spectra from hotspots for all five incident laser powers from top (125 mW, (a)) to bottom (15 mW (e)); the area under the curves bounded by the two vertical lines in (f) is plotted in Parts (a)-(e).
The surfaces machined at powers above 15 mW reveal denser distributions of Si particles with increasing machining power. The distributions are not as finely defined as in the optical darkfield case (Fig. 1), however the distributions for lines machined with the same parameters remain unique, while repeat measurements of the same line yields a repeatable distribution, as can be appreciated from the Raman scattering images of the Si peak appearing in Supplement 1, Fig. S3. Care must be exercised in setting the power used during Raman collection of the surface response due to the potential of surface damage from the focused pump laser. This can be detrimental, but also represents a tamper detection mechanism. In attempting to record the signal originating from the surface one can overshoot or undershoot and drastically alter the resulting Si Raman scattering maps. Without tampering of the surface, the Si trace will remain constant over long periods of time and will not react in ambient conditions, leading to a stable Raman signal readout which is important in PUF applications where the system will be challenged at some later date [1,2]. This long term stability also applies to optical imaging of the surfaces, and also assumes that no wear or tear has taken place. For application to microchips or other electronic devices, PUFs would be machined on die and subsequently packaged, thereby ensuring longevity of the structures.
In addition to the Raman scattering signal from Si at 521 cm-1, these machined surfaces also yield broad fluorescence features that appear in the 800-3600 cm-1 range as shown in Fig. 4. The Raman spectrum of bulk crystalline silicon has been studied and is well understood, possessing only one active first-order phonon centered in the Brillouin zone, with an optical phonon energy of 520 -521 cm−1 [43,44]. A general emission map was generated by mapping the integrated intensity over the 800-3600 cm-1 spectral range. Although the fluorescence signals are quite broad and not strong, unique distributions like those generated by mapping the Si Raman peak can be obtained. Good distributions are shown in Figs. 4(a) and 4(b), where a very distinct set of bright spots that are well-resolved from the background can be observed and coincide with the increased signals in the 2800-3600 cm-1 spectral range in Fig. 4(f) (125 and 60 mW cases). The spectra from the other three samples show only one peak at ∼1900cm-1 which can be detected even on the surface of unmachined Cu but with lower intensity. This 1900cm-1 fluorescence signal is likely associated with the surface oxides of Cu, with more Cu oxides being formed as ejected Cu reacts with oxygen species within the plume before redepositing on the surface. This signal is present on all of the machined structures, as well as in very small amounts on bare unmachined copper which naturally oxidizes. These Cu oxides are likely combined with redeposited Si species which can also yield broad Raman fluorescence in the 3000-5000 cm-1 region as confirmed in Supplement 1, Fig. S5. At lower laser machining powers, 30, 20 and 15 mW samples shown in Figs. 4(c)–4(e), a more uniform signal across pixels is seen, likely due to a decrease in the aforementioned Cu and Si species, as confirmed by EDX measurements in Fig. 2, and leads to a decreasing signal to background ratio. Repeated fluorescence measurements of the same line yielded a repeatable distribution and are presented in Supplement 1, Fig. S4.
Fig. 4. Fluorescence maps obtained using a Raman microscope of laser machined lines at (a) 125 mW, (b) 60 mW, (c) 30 mW, (d) 20 mW and (e) 15 mW. (f) Example spectra from select hotspots for all five incident laser powers from top (125 mW, (a)) to bottom (15 mW (e)); the area under the curve beyond the vertical line at 800 cm-1 is plotted in Parts (a)-(e).
It has been noted in literature that Si nanoparticles redeposited next to machined lines can fluoresce. [45] To determine whether this could be the origin of the additional fluorescence signal observed in the case of the 120 and 60 mW samples (Fig. 4(f)), machined lines were generated on an un-coated Si wafer, and the results are shown in Supplement 1, Fig. S5. From these measurements (Fig. S5(b)) fluorescence bands with peaks around 3600 cm-1 are observed, thus it is highly likely that Si nanoparticles are responsible for the fluorescence shoulders appearing in the 2800-3600 cm-1 range in Fig. 4(f) for 125 and 60 mW cases, and thus the unique distributions observed in Figs. 4(a) and 4(b). A representative spectrum of machined pure Cu is shown in Supplement 1, Fig. S5(a). By comparison, the 30, 20 and 15 mW samples, only show fluorescence from Cu and Cu oxides. Additionally, it should be noted that the asymmetric broadening of the Si peaks seen in Fig. 3(f) has also been noted in literature as being associated with the presence of Si nanoparticles on the surface [46,47]. This broadening is only obvious for the 125 and 60 mW cases which further reinforces the assignment of this fluorescence to the redeposited Si species as these surfaces have Si in greater amounts compared to the other samples. Although not obvious, samples that were machined using powers of 125 and 60 mW also exhibit a broad feature centered near 480 cm-1 which indicates the presence of amorphous Si species. Further investigation is required to determine the exact interplay between the formation of microcrystalline Si, nano-Si, and amorphous Si while laser machining since all these effects will result in asymmetric broadening of the main Raman scattering peak in crystalline Si.
Optical brightfield and darkfield microscopy can be realistically implemented at a point of challenge by an end user given the economic accessibility of these techniques. Raman microscopy, although more involved in terms of the required equipment, can be cost-reduced sufficiently to become accessible to an end user. However, SEM and EDX analysis will likely remain cost-prohibitive to implement. We thus consider optical and Raman microscopy as viable methods to interrogate PUFs.
Initially without any processing, these images share similar features, even among different lines, due to the repeatability of the machining process. To isolate the nanoparticle distribution from the machined line (which serves as a targeting feature for imaging only), a method to convert the raw images obtained by optical and Raman microscopy into what would be stored in a PUF database was developed. Image processing techniques were implemented with the workflow depicted in Fig. 5, starting with a conversion to greyscale (Figs. 5(a), 5(d), 5(g), 5(j)), followed by thresholding (Figs. 5(b), 5(e), 5(h), 5(k)), and lastly particle analysis (Figs. 5(c), 5(f), 5(i), 5(l)). The details of this process are further described in the methods section. This workflow was applied to optical brightfield images (Figs. 5(a)–5(c)), optical darkfield images (Figs. 5(d)–5(f)), Si Raman maps (Figs. 5(g)–5(i)), and fluorescence maps (Figs. 5(j)–5(l)) obtained from a line machined at 60 mW. Additional images obtained from 10 different lines machined with the same parameters at 60 mW are provided in Fig. S6 for optical microscopy and Supplement 1, Fig. S7 for Raman microscopy.
Fig. 5. Sample of workflow applied to a 60 mW machined line. First raw images are converted to 8 bit greyscale (a, d, g, j), followed by thresholding (b, e, h, k) and lastly particle analysis (c, f, i, l) which is used in PUF validation. From top to bottom: optical brightfield (a-c), optical darkfield (d-f), Raman Si shift (g-i) and Raman fluorescence (j-l). Color thresholding is used in (b) and (e) to filter for the dark regions of the brightfield (b), and the bright regions of the darkfield (e). Local contrast thresholding is used in (h) and (k) due to the higher background signal near the machined lines. Particle analysis (c, f, i, l) limits the size of accepted regions to isolate redeposited particles from the large, machined regions.
A different method was used for thresholding the optical and Raman images due to the incompatibility of a single technique for all four types of images. A pure brightness thresholding was used in the optical case whereas a local contrast thresholding method was implemented for the Raman and fluorescence maps. Local contrast proved ineffective in the case of the brightfield measurements while brightness thresholding failed to isolate particles on the brighter backgrounds seen in the Si Raman maps as well as the fluorescence maps without removing features which were much less intense. These thresholding techniques referred to as ‘binary encoding’ due to the restriction of the colors to either white or black for on and off are common in PUF literature [8–10], though more advanced ‘quaternary’ thresholding has been used as well [9]. Others have used the individual colors of particles in dark field to obtain multiple PUF readouts for color channels such as red, green and blue [12]. This could also be applied in this work, though this approach would work best with the less dense distributions produced at lower machining powers (Fig. 1).
Issues arise in isolating the specific RGB response of individual particles due to glowing halos around some particles, particularly in the higher density distributions, due to the varying response from scan to scan because of sensitivity to the illumination conditions. An RGB implementation was demonstrated by Kustov et al. using Mie-resonant silicon particles forward-ejected onto a transparent donor substrate [22], where they focus on specific nanoparticles within the distribution, and obtain their color coordinates (X and Y in the CIE 1931 color space) combined with a measure of the crystallinity of the silicon particles via Raman scattering. This same process could be applied to the surfaces generated in this work provided additional algorithms are developed to directly link the gathered chemical data to the bright and darkfield images. A drawback of the color association method is that under varying illumination the color rendition can be vastly different despite particle locations and brightness remaining consistent. This is shown in Supplement 1, Fig. S8, where images from two different microscopes are compared. However, despite their differences, using binary encoding yielded correlations for ‘like’ scans of approximately 70% for brightfield and 65% for darkfield with ‘dislike’ scan correlations below 5%. These results were also taken over different days to highlight the time independence of the surfaces. This effect plays a significantly smaller role in the case of the Raman microscopy where the output should be nearly identical between hardware.
Rather than combining multiple methods into a single highly robust PUF our work seeks to compare the robustness of individual methods and to create a simple and flexible authentication method using free open-source software. Our analysis also allows a great number of particles to be examined rapidly, which allows the encoding capacity to be increased without a large increase in processing time. Encoding capacity is expressed as $EC = {V^n}$ where V is the number of responses and n is the number of elements being examined, and it has been proposed that EC = 10300 is sufficient to generate a PUF [9,22]. Gu et al. specify that even using a pixel density of 50 × 50 and binary encoding, similar to the encoding method used here, will yield EC = 22500 as the encoding capacity [9]. In our case, using brightfield and darkfield images with a pixel resolution of roughly 4200 × 2800 yields EC = 24200 × 2800, and using Raman maps with a pixel resolution of 150 × 100 yields EC = 3150 × 100, both well exceeding the limits proposed to generate a PUF. The Raman maps are a power of 3 because the wavelength used to obtain the scans represents another variable as the fluorescence depends on wavelength (the scattered silicon signal remains largely independent of wavelength). However, in the case of brightfield and darkfield measurements, the encoding capacity is limited by the density of the particles on the images, which can vary substantially depending on the magnification used for imaging and the laser power used during machining. Combining several features together could yield a higher encoding capacity over larger areas. A more conservative estimate would put the encoding capacity closer to the number of separate particles in the region of interrogation, after processing, which in the case of the 125 mW sample, is roughly 16000 particles. This translates to roughly EC = 2160 × 100 which far exceeds the requirements [9,22].
The different scans were compared using a pixel-by-pixel image correlation technique which indicates the percentage of pixels that have the same value in both images. Further details on this technique are given in the methods section. Initial raw scans show near perfect correlation between repeated scans of the same surface of greater than 90%, however the correlations between other lines with the same parameters were also high. The implementation of thresholding and particle analysis still yields good agreement between ‘like’ scans, while having a correlation factor usually below 10% for scans of different lines, thereby greatly improving the pass/fail criteria of the PUF. Tests were also performed comparing brightfield and darkfield images generated by two different microscope systems with results shown in Supplement 1, Fig. S8. Overall, though correlations were not as high (∼55-75%) as with the same imaging system (∼90%), they remained substantially higher for repeat measurements of the same surface compared to dislike surfaces (∼10% or lower), for both brightfield and darkfield measurements.
The statistical analysis of the four different methods, comparing repeated scans of the same line (‘like’ surfaces), and comparing scans of different lines machined with the same parameters (‘dislike’ surfaces) are summarized in Fig. 6. Statistics used a total of 45 ‘dislike’ and 12 ‘like’ data points for brightfield and 45 ‘dislike’ and 30 ‘like’ scans for darkfield for each power. Both Raman and fluorescence maps had 10 ‘dislike’ scans and 14 ‘like’ scans per power. The images being compared for statistics are the final ones after all image processing is complete of the kind shown in Figs. 5(c), 5(f), 5(i) and 5(l). It is clear from Fig. 6, with results summarized in Table 1 and Table 2, that the largest split between ‘like’ and ‘dislike’ correlations over our five sets of machining parameters and four imaging techniques occurs for the optical darkfield scans (Fig. 6(b)). This technique is commonly used to image nanoparticle distributions in literature and its effectiveness is also noted here. Brightfield scans have similar ‘dislike’ correlations, but darkfield yields ‘like’ correlations roughly 10% higher. It is also notable that the best performing laser machining power is 60 mW. This incident power produces sufficiently large ejection to have recognizable and unique structures using all interrogation techniques, without producing an overly dense background as in the case of the 125 mW samples. The increased particle density produced by machining at 125 mW makes image processing more difficult as individual particles become harder to discern from one another, resulting in a slight decrease in correlation of ‘like’ scans for all four methods compared to the 60 mW sample. Overall, optical interrogation of the surface provides a fast, easy, and highly repeatable method of identifying the fingerprint of these unique particle distributions (Figs. 6(a) and 6(b)). Under these optical interrogation techniques, the performance of the machined lines as PUFs is excellent for all of the machining powers tested, making it easy to adjust the PUF to conditions the end user may require.
Fig. 6. Statistical analysis of the pixel-by-pixel correlation factors of brightfield (a), darkfield (b), Raman Si map (c) and fluorescence images (d). Statistics used a total of 24 data points per power for Raman and Fluorescence maps, 57 data points per power for brightfield and 75 data points per power for darkfield.
When looking at the results for the Raman maps and fluorescence images (Figs. 6(c) and 6(d)), the correlation factors are significantly lower, on the order of 65% for the 60 and 125 mW samples, compared to the 85–95% for the optical images. However, the ‘dislike’ and ‘like’ images are still widely separated, enough to yield an easily identifiable pass/fail condition. This outcome is limited to samples machined with sufficiently high power to cause enough ejection of Si from the underlying substrate to be easily identifiable in a short timeframe. For these Raman scans low integration time and low pixel density were used to limit the scan time to five minutes. This yields a low signal to noise ratio in some cases, such as the line machined at 20 mW, where the correlation factors of ‘like’ Si images plunges below 50% (Figs. 6(c)). The lines machined at 15 mW failed as PUFs when interrogated using this technique. Higher integration would lead to unnecessarily long scans. This limits the machining powers that can be used to generate PUFs interrogated via low-integration time Raman and fluorescence spectroscopy to the upper range of the study. In theory, a balance between measurement time and signal to noise ratio can be achieved for different applications.
An alternative method presented in literature [10,14,17] to determine the uniqueness of a PUF is to calculate the intra chip (“like”) and inter chip (“dislike”) Hamming distance, which consists of the sum of all the mismatched entries in a data string. This number can be divided by the total length of the string to obtain a Hamming percentage. These results were calculated in supplementary Fig. S9 for the case of the 125 mW incident laser power, and show the same trends as the correlation factors plotted in Fig. 6, with darkfield having the largest separation between “like” (intra) and “dislike” (inter) images, followed by brightfield, and finally, the Si Raman and fluorescence maps. All Hamming percentages are below 50% due to the presence of whitespace. Brightfield images have a total of 12 million pixels and a Hamming distance of close to 106, giving a percentage of ∼8% for inter class on average and ∼1.7% for intra class. Comparatively the Raman maps yield a higher percentage overall. For example, the Si maps have 7 × 105 pixels, an average interclass percentage of ∼25% and an average intraclass percentage ∼10%. The Raman maps have less white space than the corresponding optical maps which leads to this increase in the Hamming percentage. In terms of the difference factors, this yields a factor of ∼5× between inter and intra class for brightfield images, a factor of ∼7× for darkfield images, and ∼2.5× for the Raman Si and fluorescence maps. The white space in the bright and darkfield cases can be reduced by zooming in on specific regions of the distribution closer to the machined line which have a higher density of redeposited material.
Table 1. Summary of Brightfield and Darkfield Results from Fig. 6
Table 2. Summary of Raman Si and Fluorescence Results from Fig. 6
A significant advantage of Raman spectroscopy is that it yields chemical information in the form of very specific Raman signatures, such as the characteristic 521 cm-1 Raman peak of Si (Fig. 3), or the sample may emit a specific fluorescence spectrum (Fig. 4). This adds a layer of complexity to any attempt at counterfeiting since an attempt to mimic only the spatial distribution of particles over the surface is insufficient for authentication, which now also depends on the chemical composition of the particles (Cu and Si here).
Also worth noting, although the surface remains stable under ambient conditions, a passivation layer could provide protection against environmental hazards such as scratches, contamination by foreign particles, and aggressive atmospheric conditions as discussed by Smith et al. [8] Using an optically transparent layer that is also Raman compatible would allow protection of the surfaces while largely maintaining the effectiveness of the structures as PUFs interrogated using multiple methods. In addition, if the PUF is used to authenticate a silicon chip then it will be isolated from environmental or physical damage by packaging, so its longevity is ensured. Our method also allows the use of more complex structures that can be tailored to the needs of a specific application, using a substrate other than silicon, bearing traceable elements other than copper, producing distributions dependent on the chemical composition of the starting materials.
4. Conclusion
Laser machining to generate nanoparticle distributions as a technique to create PUFs was proposed and demonstrated on samples consisting of a thin Cu layer (600 nm) on a Si substrate. Four methods of generating challenge/response pairs were applied to PUFs formed by laser machining at different power levels. Optical darkfield microscope images produced the most reliable pass/fail challenge followed closely by optical brightfield images although of lower contrast. Two additional methods consist of imaging the Raman spectral peak of redeposited Si on the Cu film, and spectral mapping of the fluorescence emitted by redeposited Cu and Si compounds. Both methods provide sufficient pass/fail conditions when enough Si has redeposited to yield a sufficient Raman signal or fluorescence in a short scan time. Both methods yield images that depend on the chemical composition of the substrate, and thus provide an additional layer of protection against counterfeiting in applications where the bright/darkfield results alone may not provide the level of security that is needed. The laser machined surfaces are stable over time but could benefit from the addition of a passivation layer as a barrier against potential mechanical or chemical contamination of the surface. As a one-step process, laser machining to create PUFs is fast, easy, and relatively inexpensive to integrate into various manufacturing environments. The PUFs generated can be interrogated using various challenge/response methods based on optical and Spectro-microscopy methods, making them adaptable to the needs of the end user. Although demonstrated for samples of a specific construction (Cu on Si), which would lend themselves to silicon chip authentication, the technique is expected to be broadly applicable across a wide range of sample compositions.
Funding
Ministère de la Défense Nationale (CFPMN1-040-Carleton University).
Acknowledgments
The authors acknowledge funding from the Department of National Defence’s Innovation for Defence Excellence and Security (IDEaS) Program in support of this work. We would also like to thank Peter Banzer and Jörg Eismann from the University of Graz, Austria, for useful discussions.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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