Introduction

The reaction of thin films consisting of nanolayer systems is widely known, specifically the Ni/Al system has been intensively investigated [1,2,3,4,5,6,7,8,9,10,11,12]. These are called reactive multilayer (RML) systems and consist of alternating materials with layer thicknesses in the nanometer range [7]. The working mechanism is based on the release of chemically stored energy from a metastable system in the form of heat, during which the reactants form an inter-metallic compound. The reaction is called self-propagating if more heat is released than lost, in the course of the process [13, 14]. For igniting the chain reaction, it is required to introduce energy into the RML system. To achieve it, different methods like spark, laser and mechanical ignition have been investigated [7, 15, 16]. Other material combinations apart from Ni and Al are also possible, such as Al/Ti, Al/Ru, Al/Pt and more [7, 14, 17, 18]. Additionally, ternary combinations like Ni/Al/Ru are under research [17].

Various investigations to tailor the RML systems for the purpose of bonding of different materials or ultrafast phase transformations were carried out so far [6, 10, 14, 19,20,21,22,23]. Bilayer thickness, total thickness, intermixing thickness and chemical composition are the most studied multilayer properties for tailoring the reaction [13, 24,25,26,27]. Further, the substrate was found to be a pre-dominant parameter which provides different thermal and surface properties [11, 28]. B. Liu et al. demonstrated the influence of different substrates such as, AlN, AlNi3, Si and Al2O3 on the growth behavior of RML and the reaction progression [28]. The variations in the surface topography of these substrates affected the interlayer roughness of the RML, which resulted in varying reaction velocities, energy releases and phase formations [13, 28]. Moreover, increasing the surface roughness by means of laser structuring on low temperature co-fired ceramics (LTCC) substrates improved the adhesion of the reacted multilayers. [11, 12, 29]. The formation of black Si by reactive ion etching (RIE) also changes the surface roughness, which influences the phase transformation during rapid thermal annealing processes [11]. This paper introduces a new approach to change the substrate surface with deep reactive ion etching (DRIE) to create higher structures, than the 1-µm-height black Si formations. These new structures change not only the substrate surface but also the thermal properties just below the RML. It can reduce the necessary total thickness of RML to initiate a self-propagating reaction, which is necessary for bonding applications. This is similar to the function of a thermal insulation layer, like SiO2 [14]. In a preliminary test, 5-µm-thick Al/Ni RML was deposited on a thermally oxidized Si 100 substrate. The oxide layer was around 1 µm thick. The RML configuration consisted of a bilayer thickness of 50 nm and an atomic ratio of 1:1. The deposited RML surface was flat without any visible defects under the light microscope. An electrical impulse was used to ignite the self-propagating reaction. During the reaction, a noticeable separation between the RML and the substrate surface becomes evident, primarily attributed to the volumetric changes occurring during the phase transformation. The resulting stress from the volume change is higher than the adhesion between the Al and the SiO2, thereby causing the separation of the RML from the substrate [30]. As a consequence of the strong adhesion between the RML and the substrate, it was observed that even the substrate surface underwent partial destruction down to the Si bulk substrate during the phase transformation, as illustrated in Fig. 1. This destruction was in the form of a conchoidal fracture and was caused by the volume change of the RML during the phase transformation, as well as due to the differences in the coefficient of thermal expansion between Si and SiO2. These two factors increased the stress on the substrate until it reached the breaking point [31, 32]. A sketch of the cross section of the formed conchoidal fracture is visible in Fig. 1.

Figure 1
figure 1

Top-optical microscope image of the surface after reaction with visible Si substrate due to the destruction of the surface; bottom-sketch of the cross section of the conchoidal fracture formed in the Si bulk substrate after the reaction

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Motivated by the need to enhance adhesion and control reaction propagation, we delve into the intricate relationship between surface structuring and the ensuing reaction phenomena [14]. To explore the influence of grass-like structures with different heights and densities, a comprehensive investigation was conducted to assess their impact on the growth and reaction behavior of Ni/Al RML. With a total thickness of 5 µm and a bilayer thickness of 50 nm, a self-propagating reaction on bulk Si would be prevented by the thermal properties of Si [13]. In contrast, a self-propagating reaction was successfully achieved and observed on the structured surface. As previously mentioned, the present study delves into the enabling factors behind the self-propagating reaction facilitated by the structured surface. Furthermore, the influence of diverse structure morphologies on both the propagation of the reaction and the growth of the RML is thoroughly discussed. Also, the experiments give insights on the significant role the substrates structuring can play in the interaction with the RML in determining the reaction kinetics, adhesion, and overall performance of the system. As a substrate, a Si (100) wafer was modified using DRIE process, to form structures with heights in the range of 8–13 µm. These structures will be further referred to as Si grass (SiG). The structure height and density were analyzed to determine their effect on the reaction parameters. The RML characterization was done using X-ray diffraction (XRD), scanning electron microscopy (SEM), focused ion beam (FIB), high-speed camera and high-speed pyrometer.

Materials and methods

Materials

Si (100), n-doped-type wafers with 100 mm diameter and a thickness of 525 µm were used as substrates. The SiG was etched into the Si substrate using the inductively coupled plasma (ICP) multiplex Advanced Silicon Etch (ASE) (STS) DRIE system. SiG is formed by alternating the passivation and etching phase of the DRIE [33]. During the first process cycle, both passivation and etching steps are applied for 11 s each. A polymer layer, known as passivation layer, is formed during the passivation step when C4F8 gas reacts with the Si. SF6 and O2 gases are introduced into the vacuum chamber during the etching step. For the formation of SiG, it is necessary to physically etch the passivation layer with O2 ions. Afterward, the Si is chemically etched by the SF6 ions. The residual passivation layer is the starting point for the formation of the SiG. To ensure the further deep etching of the Si, the duration of the passivation step needs to be decreased by 1 s, until a time ratio of 9 s:11 s (passivation time:etching time) is achieved. The sidewalls of the SiG begin to get covered with the polymer, at the second passivation step. This prevents the deepening of undercuts caused by SF6 chemical etching. Due to the anisotropy of physical etching, the SiG are etched perpendicular to the substrate surface. In Table 1, the process parameters are listed for the etching and passivation steps, which were repeated 60 times to form SiG. A higher number of repetitions would subsequently increase the height of the SiG structures [34, 35]. The resulting wafer is referred to as SiG-Wafer.

Table 1 Process parameters of the DRIE process for the formation of SiG
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The DRIE plasma process is not uniform. Field inhomogeneities and the resulting non-uniform distribution of etch specimens in the vacuum chamber lead to different etching rates across the wafer. Figure 2a shows an overview of the two zones formed, the edge (E) and the center (C). The inner ring is the C zone, and the outer ring is the E zone, both of which contain SiG. The outermost ring is the support ring, which does not contain any SiG. The distance from the main flat is defined as x. In Fig. 2b, the overall process flow of the investigated samples is illustrated. Table 2 shows the abbreviations used for all the used samples.

Figure 2
figure 2

Illustration of the sample nomenclature: a defining the two zones E and C depending on their location on the structured Si wafer; b process flow of the sample preparation starting with the structuring until the reaction tests for the free-standing (flat wafer) and the SiG samples; the yellow star defines the point of ignition

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Table 2 Sample abbreviation and their respective description
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A direct current (DC) magnetron sputtering device was used for the deposition of the Ni/Al RML (CS400, Von Ardenne). The Al -5N (FHR) and Ni -3N8 (FHR) targets were located 105 mm away from the substrate. During the process, a pressure of 0.5 Pa, sputtering power of 200 W and an Ar gas (6N) flow of 30 sccm were applied. As a result of the sputter parameters, deposition rates of 0.317 nm s–1 and 0.336 nm s–1 for Al and Ni, respectively, were achieved. In order to keep the temperature as low as possible, heating was not applied. A total RML thickness of 5 µm was obtained by depositing 100 bilayers with a thickness of 50 nm each and atomic ratio of 1:1. Two wafers, one structured with SiG and one flat, not processed, were used as substrates for the deposition. After the deposition, the wafers were diced as depicted in Fig. 2b. A layer of AZ® 1518 photoresist (Microchemicals GmbH) was coated on top of the RML, to protect its surface from particle contamination during the dicing. Ultraviolet (UV) foil 1027R-9.05 (Ultron systems Inc.) was used as a additional protection layer. Dicing machine ProVectus7100 (ADT), equipped with an FTBR 46 45130 blade, was used to obtain chips in the dimensions of 13 mm × 18 mm. To remove the UV foil, it was illuminated with UV light for 10 min. Finally, the photoresist and other contaminants were removed from each chip surface using acetone, isopropanol and deionized water.

Methods

SiG density and height depends on the observed position on the wafer [33]. For the analysis, the wafer was broken near the center and characterized using scanning electron microscope (SEM) (Hitachi S4800). The top view images provided data for the calculation of the structure density, while the height was obtained from cross-sections. The first measurement point for both images was at a distance of 50 µm from the main flat. MountainsMap (MM) version 7.4 (Digital Surf) software was used for the analysis of the structure density. The contrast between SiG tips and the etched areas was adjusted for the following image processing steps. An example of the captured image is shown in Fig. 3a. In the next processing step, the image was divided into sections of 15 µm × 15 µm. Thereafter, the watershed segmentation method was used to obtain the ‘number of SiG tips’, as shown in Fig. 3b. Cropped structures at the edge of the image were excluded in order to prevent overcounting effects. For example, a structure with a crescent-shape, where only the ends are visible, would be counted as two separate SiG tips. The top view images were captured every 10 mm, and for the height measurement, the cross-sectional images were captured every 5 mm. In every cross-sectional image, at least five SiG structures were measured, as depicted in Fig. 3c. For each position, an average height was calculated, including a standard deviation. The determination of the Si to air ratio from top-view images was accomplished through a comprehensive analysis of the binary-transformed images, focusing on the grain size of the air occupied region (represented in black). This analysis was conducted on SEM images, obtained at distances of 10 mm and 60 mm from the main flat. Furthermore, the same image analysis technique was employed using SEM top view images to examine the presence of voids and boundaries at the surface of the RML. By employing grain analysis within a 40 µm2 area, the extent of black areas, representing defects in the RML, could be quantified. Four images were analyzed for each zone, and the average values were calculated. Figure 4 illustrates an exemplar top-view image of the deposited RML, alongside the results obtained after conducting the grain analysis.

Figure 3
figure 3

a SEM image of the top view of SiG showing the SiG tips; b watershed analysis of (a) along with the resulting number of SiG tips; c SEM image of the SiG cross-section including the formula to calculate the average height

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Figure 4
figure 4

Exemplary results of the defects analysis in the deposited RML using MM and grains analysis on a sample from the wafer edge. Left side is a SEM top view image of the RML after deposition on the SiG and on the right side is the results of the grain analysis

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To enable a self-propagating reaction of the RML deposited on flat Si, separation of the RML was required [13]. A 5-µm-thick foil was obtained by peeling the RML from the substrate with tweezers, which will be referred to as FS. For the SiG samples, the RML was not separated from the substrate. To trigger a reaction, a voltage of 5 V was applied to the RML. Videos of the reactions were recorded using a high-speed camera FASTCAM SA-X2 type 480k (Photron) with a Navitar 12 × zoom lens. The reaction velocity was measured and analyzed using FASTCAM Viewer 4 (Photron) software. Additionally, temperature curves were recorded with high-speed pyrometer KGA series 840 (Kleiber) with 25-S1 optic, a time resolution of 10 µs, a wavelength of 2.2 µm and a temperature range of 350–3500 °C. For every measurement, the emission coefficient was adjusted to ε = 1.

X-ray diffraction (XRD) (Theta-Theta X- ray diffractometer, Siemens D5000) measurement provided information about the phases in the RML before and after the reaction. The 2θ range was between 20° and 100° with 0.02° step size using gracing incidence method, with an incidence angle of 5°. Anode material of Cu with Kα (λ = 0.15418 nm), an acceleration voltage of 40 kV and a current of 40 mA were applied for all measurements. Further, the analysis was done using the software DIFFRAC.EVA 5.1 (Bruker). Focused ion beam (FIB) (Auriga 60, Zeiss), with a Ga ion source, was used to observe the growth of the Ni/Al RML. To protect the sample during the FIB preparation, carbon and tungsten layers were deposited on top of the RML.

Results

Structure analysis

The plot in Fig. 5 depicts the data acquired from the analysis of the SiG. Average heights and densities data, including standard deviations, are shown over the distance from the main flat x. The attained data showed a tendency of decreasing height with increasing x. The average height was higher in the E zone than in the C zone and vice versa in case of the structure density. In the C zone, the average height was roughly constant, at a value of 9 µm. The density in the C zone was in the range of 3.0–3.5 structures per µm2, while in the E zone it reduced to values less than 2.5 structures per µm2. At x = 20 mm, height data could not be obtained due to destroyed SiG, caused by the breaking of the sample.

Figure 5
figure 5

Plot showing the variation of structure density (red squares) and height (black squares) of SiG over two different zones E and C across the wafer. The x axis shows the distance from the main flat; note that the error bars of the structure density is in some cases too small to be visible

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Moreover, by utilizing top view images, a comprehensive analysis of the black/white areas was conducted, providing valuable insights into the estimation of the Si and air content at different positions on the wafer. The corresponding values are presented in Table 3. Notably, an increase in SiG structure density correlates with a rise in the measured Si content between the E and the C zone, from 19.11% to 23.56%. Concurrently, there is a reduction in the air content by approximately 4%, decreasing from 80.89% to 76.44%. These ratios form the basis for calculating the effective thermal diffusivity keff of the Si/air layer. In our calculations, we employ the following Eq. (1):

$$k_{{\text{eff}}} = {\text{amount}}\,{\text{of}}\,{\text{air}}* k_{{\text{air}}} + {\text{amount}}\,{\text{of}}\,{\text{Si}}*k_{{\text{Si}}}$$
(1)
Table 3 This table presents a summary of the obtained results from the multiple MM analyses. It includes the measured ratio between Si and air in the different zones, the calculated effective diffusivity (keff), and the average area covered with defects of the RML surface
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The values for the thermal diffusivity were kair = 20 mm2*s−1 and kSi = 87 mm2*s−1, respectfully [13]. The similarity in material ratios between the E zone and C zone leads to a difference of 3 mm2*s−1 in their effective thermal diffusivity keff, with the E zone exhibiting a lower value. Table 3 additionally presents the results of the defect analysis conducted on various zones of the deposited RML. Notably, the E zone samples exhibited a defect coverage of 2.67% within the RML surface, whereas the C zone samples displayed a significantly lower coverage of only 0.87%. In comparison, the C zone has a higher effective diffusivity keff, but the RML surface is covered three times lower in defects than the E zone.

Reaction analysis

Figure 6a illustrates the average velocity and the maximum temperature of the RML reactions. The CR samples had higher values for both velocity and maximum temperature than the ER samples. The highest propagation velocity of a sample with SiG was measured in CR3, with a value of 3.1 m s−1. In comparison with ER2, which is the fastest sample from the wafer edge, CR3 is faster by 1 m s−1. The CR samples had an average reaction propagation of 2.7 m s−1, while the reacted FS sample reached a velocity of 11.8 m s−1 with identical RML properties.

Figure 6
figure 6

Results of the reaction experiments; a comparison of average velocity (black squares) and maximum temperature (red squares) of SiG and FS samples; b temperature curves of SiG and FS samples; c reaction propagation on the example of sample CR3 between ignition frame (0 ms) until 6 ms afterward; the yellow star defines the point of ignition

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The highest maximum temperature of a SiG sample was 608 °C, measured on sample CR2. ER2 had the highest temperature for samples from the E zone, reaching 573.8 °C. With a temperature of approximately 1300 °C, the reacted FS had more than twice the temperature of the CR2 sample. In Fig. 6b, the temperature curves of the high-speed pyrometer measurements are shown. CR samples demonstrated a shorter but steadier temperature progression, than the ER samples. The samples from the E zone did not reach temperatures over 600 °C, but the measured temperature stayed up to 250 µs longer over 350 °C. The reacted FS reached a maximum temperature of 1296 °C in 370 ms. From the graphs in Fig. 6b, it can be deduced that the reacted FS had higher heating rates and a longer cooling down phase, while the SiG samples showed a parabolic behavior during the temperature measurements.

In Fig. 6c, the reaction of the CR3 sample is depicted in frames taken from the high-speed camera video, with time differences of 1.5 ms between them. The starting frame is the ignition of the samples with 5 V impulse. Since the reaction started on both electrode tips, two reaction fronts can be observed, with the upper one being faster. It is due to an earlier start of the upper reaction front combined with a defect in the RML. This defect is caused by a scratch, located in the pathway of the lower reaction front. Contrary to the separation of RML and substrate shown in Fig. 1, the RML in this case stayed on the SiG samples.

Phase identification

To identify possible macroscopic phase transformation, prior to the reaction ignition, XRD analysis was performed. In Fig. 7, the obtained XRD pattern of unreacted SiG sample (UR) and reacted samples from the E zone (ER) and C zone (CR) are depicted. The UR data showed pure Al (PDF-2 2003 65-2869) and Ni (PDF-2 2003 65-2865) peaks after the deposition process, with the highest intensity from Ni (111) and Al (111). A peak at 56° is a possible signal from the Si substrate, because it matches with the occurrence area of Si (311). No peaks or signs of an AlxNiy alloy could be found in XRD data of the UR sample; however, in the ER and CR samples these peaks were detected. In the blue graph representing the ER sample and the red graph representing the CR sample, Al0.9Ni1.1 (PDF-2 2003 44-1185) peaks are visible with (110) with the highest intensity. Pure Al or Ni were not detected in the investigated CR or ER samples. Among these two samples, the CR sample displayed higher intensities.

Figure 7
figure 7

XRD plot of Ni/Al RML on unreacted (UR) and reacted (ER and CR) SiG samples; the phases are represented as following: orange triangle is Al0.9Ni1.1, brown circle is Ni and green square is Al

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SEM study of RML—before and after reaction

Figure 8a shows an SEM top view image of the deposited RML on the SiG-wafer before dicing. The color variation in the SEM image is according to the topographic characteristic of the surface. The highest regions are represented by the gray color, while the white areas are lower in height. Additionally, black areas are voids in the deposited layers, where no RML can be seen. Figure 8b shows a top view image of the sample after the reaction. The appearance of cracks, as well as a decrease in the number of black voids, are visible. FIB cross-sectional results of the samples before and after the reaction can be seen in Fig. 8c, d, respectively. The discernable materials are in order from top to bottom, starting with tungsten followed by carbon and Ni/Al RML and lastly the SiG. The tungsten and carbon layers were deposited for the protection of the sample during the FIB nano-milling. In Fig. 8c, the growth of the RML in form of inverse cones can be seen. These cones start from the tip of the SiG, with some tips having only a small number of RML deposited. The width of the cones increased visibly after reaching an RML thickness of 1.3 µm. Some of these cones connect together, as illustrated in the red boxes in Fig. 8c, while some other cones remain separated. Some cones only connected near the surface of the RML, where the cone base is in the shape of a hemisphere. These hemispheres are seen to have uneven surface. In the top 400 nm part of the RML cone, the Ni and Al layers diffused into each other, whereas these layers could be distinguished in the rest of the RML cone.

Figure 8
figure 8

SEM images of deposited Ni/Al RML before and after reaction; a Top view before reaction of sample UR; b top view of sample CR1 after reaction, with visible cracks; c cross-section of inverse cone-shaped RML from sample UR; d cross-section of reacted RML from the sample CR1

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After the reaction, any distinguishable Al or Ni layers could not be seen (Fig. 8d). Furthermore, in the cross-sectional view of Fig. 8d, the unevenness of the hemispherical surface disappeared, and the base of the inverse cones appear smoother. The cones are now connected with each other, with a few small holes and spacings in between them. Figure 9a shows that the SiG structures and the RML are perpendicular to the Si substrate. After the reaction, the SiG and the first Ni/Al layers are bending or partially breaking, as seen in Fig. 9b. Additionally, the deformations of the SiG structures are oriented in the opposite direction of the reaction propagation.

Figure 9
figure 9

SEM images of a SiG tips with deposited Ni/Al RML before reaction; b SiG tips and reacted RML cones bent in the opposite direction of the propagation, pointed out by the orange arrow

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Discussion

Influence of structure morphology on RML

The growth behavior of the RML is intricately influenced by the surface structuring process, wherein the deposition of RML is confined to the SiG tip regions. Each SiG tip acts as a nucleation site, initiating and serving as a seed for the subsequent growth of the RML. This phenomenon bears resemblance to the growth of RML on black Si. In-depth analysis employing transmission electron microscopy (TEM) has unveiled that the RML exclusively coated the tip of the black Si structure [11, 29]. The same behavior was observed in the case of the SiG in Fig. 9a. Furthermore, it was observed that an increase in the number of deposited layers correlated with an augmentation in curvature. [11]. In case of the SiG structures, this phenomenon led to the formation of the RML cone shape and the hemispheric structure at the RML surface. This shape is consistent with the findings of Fritz et al. 2011 and Arlington et al. 2020 when they deposited RML on a fiber mesh to either ignite as powder or on substrate [36, 37]. Another common feature between the RML growth on black Si, fiber and SiG is the formation of small gaps in between the RML cones, as depicted in the FIB cross-section in Fig. 8c. Two potential explanations for the variation in connectivity between cones were identified. The first one is an inaccurate presentation of the real circumstances, caused by the FIB cross-sectional preparation. In Fig. 8c, it is possible that the cones were initially connected; however, due to preparation procedures, that specific area was damaged and is no longer discernible. The other reason is the growth behavior of the RML, which looks like the growth defect mentioned in Thornton 1977 [38]. The RML cones show growth behavior of the Zone 1, in which the effects of shadowing are stronger than the adatom diffusion on the RML surface [39]. Zone 1 structures also widen with increasing height, like the RML on the SiG in Fig. 8c. Due to the existence of defects, like the structured surface in the form of SiG, the occurrence of the Zone 1 growth is enhanced. The deposition rate exhibits an elevation-dependent trend on the structure, with the highest point experiencing a greater deposition rate. Consequently, the shadowing effect leads to the formation of open boundaries between the cones. These boundaries are the cause for the cones to grow closer to each other but then keeping them from forming connections [38]. Due to appearance of the open boundaries in other studies, these gaps are most likely caused by the growth behavior of the RML [11, 31, 38]. Additionally to the open boundaries, voids are visible in the RML in the form of black holes in the SEM top view image in Fig. 8a. One cause for voids in the RML is the random distribution of the SiG structures itself [33]. Certain areas lack SiG structures, impeding the growth of RML cones, particularly within the E zone, where lower structure density is more prevalent. The limited lateral growth of the RML impeded the cones from spanning the distance to the neighboring cone, resulting in the formation of voids. Another reason for the void formation is the height difference between neighboring SiG structures. The RML is growing in width with increased number of layers on both structures. This trend continued until the widening cone of the larger SiG structure reached a size that interfered with the growth on the smaller SiG structure, effectively halting its growth. This occurrence can be attributed to the shadowing effect observed during the process of sputtering deposition [38]. In order to elucidate the variations in RML growth behavior among the different zones, the ratio between the RML and the defects within the RML is quantitatively analyzed and presented in Table 3. The observed disparities in the defect area can be attributed to differences in structure density. As mentioned previously, the lower density of SiG structures in the E zone results in a reduction in the number of available RML nucleation sites. Consequently, the connections between the RML are limited and more voids appear, which caused the area of measured defects to be increased.

Reaction propagation in SiG

The cross-sectional view depicted in Figs. 8c and 9a offers an overview of the layered structure of the observed system. At the top, we have the RML, responsible for releasing heat through the exothermic reactions. Adjacent to the RML layer is the SiG layer characterized by varying thermal properties depending on the position on the wafer. This SiG layer serves as a conduit for heat conduction from the RML phase transformation. Notably, the SiG layer exhibits alterations in material composition attributable to the diverse structure morphology observed in different regions, leading to changes in the ratio between air and Si [33]. Finally, the bulk silicon layer is functioning as a heat sink to dissipate the generated heat [13]. In order to elucidate the influence of the differences in material ratios, the heat equation was calculated using the fundamental solution. The equation for the fundamental solution is as follows:

$$H\left(t,x\right)= \frac{{e}^{-{x}^{2}/4kt}}{\sqrt{4\pi kt}}$$
(2)

where t is time in s, x is the average height of the SiG structures and k is the diffusivity of the analyzed material. The values for the average SiG heights are taken from the measured data from Fig. 5 for the two different zones. The fundamental solution is only applicable if the heat release is regarded as a dirac-impulse. Due to the high velocity of the reaction, it is a valid assumption for this observation. Additionally, the calculation is just to validate the influence of the material ratio qualitatively, without providing a quantitative analysis. The results of the calculations for the different position from Table 3 are depicted in Fig. 10, as well as the calculation if there is only air or Si beneath the RML. The heat equation demonstrates that air, possessing the lowest thermal diffusivity, exhibits the highest values. Following air, the thermal diffusivity values gradually decrease for the ER samples, then the CR samples, and ultimately reach the lowest position if pure Si is considered. For pure materials, the values for x = 11 µm, equivalent to the average SiG height in the E zone, are always lower, because of the higher distance to the heat source. The higher distance x as well as the lower keff is decreasing the heat flow from the heat source to the bulk Si. Consequently, the ER samples should show higher temperatures as well as higher energy compared to the CR samples in the reaction tests. It is noteworthy that the heat loss over the SiG is still lower than the heat release; otherwise, the reaction would be stopped from the Si bulk heat sink. The observed variations in temperature across different regions can be attributed to differences in heat dissipation. Theoretical estimates based on the fundamental solution of the heat equation indicated lower heat loss in the E zone compared to the C zone. However, the experimental data presented in Fig. 6 showed the opposite trend. It was determined that the larger defect area in the E zone had a more pronounced impact on heat generation. This can be attributed to the reduced amount of RML material available for heat generation due to the presence of defects. Moreover, these defects serve as pathways for heat dissipation, requiring additional energy to overcome and sustain the self-propagating reaction. Consequently, the lower heat generation observed in the E zone can be attributed to a combination of reduced RML material and increased heat loss through the defects.

Figure 10
figure 10

Results of the calculation of the heat equation for the different zones as well as for air and bulk Si. The x values were the average height of the SiG structures in the respective zones

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A previous study shows that the RML with a total thickness of 5 µm is not self-propagating on Si substrates [13]. Similar observations were made for the reaction on black Si structures, where the reaction was achieved locally only [11, 29]. In case of the SiG, a self-propagating reaction was enabled on Si due to two reasons. The first reason is the cone shape growth of the RML and their connections to each other. The shape of the RML results in a substantial portion of its surface being surrounded by air both above and below, with the exception of the regions occupied by the SiG tip and other RML cones. The thermal insulator air causes a reduction in the heat loss to the surrounding, when compared with a heat sink material like a Si substrate structured with black Si [7, 11, 29]. In the case of the SiG structures, the reaction propagation was supported by the existence of interconnected RML cones and close proximity of the interconnections to the RML surface. Distance measurements conducted in Figs. 8c and 11 showed on average a smaller distance between two RML cones compared to the total thickness of the RML (5 µm). The smaller distance between cones enabled a rapid energy transfer from one cone to another before the reaction reached the SiG tips. Therefore, the released energy during the phase transformation is firstly transferred to the surrounding RML as well as the air above the RML. Only after the reaction reaches the SiG, the heat conductively dissipates into the substrate similar to the data shown in Fig. 10 [13, 14]. Additionally to the heat loss to the SiG structures, the voids and the open boundaries are functioning as a thermal diffusion barrier, obstructing the reaction propagation [29, 40]. In Fig. 6a, the measurements results show lower reaction velocities in the ER samples. This phenomenon can be attributed to the already mentioned lower structure densities, leading to a decreased occurrence of multilayer cones and an increased probability of disconnected cone formations as well as a higher likelihood of void formation, as shown in Table 3. As previously indicated, either the reaction propagates from cone to cone, increasing the reaction path or has to progress over the open boundary losing energy, which causes a reduction in reaction velocity and in temperature [40]. The presence of voids further introduces an extended reaction pathway, resulting in a decrease in measured reaction velocity [41]. The variation between the two ER samples can be related to the random characteristic of the production process of the SiG structures and due to the varying structure density between the samples, as depicted in Fig. 5.

Figure 11
figure 11

FIB cross-section of a different sample showing no signs of diffusion close to the RML surface

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Another parameter affecting the reaction propagation could be the diffused zone depicted in Fig. 8c, which would reduce the overall released heat during the reaction [27, 42]. The cause of the diffusion in the layers close to the surface in Fig. 8c was identified to be related to the separation process during the sample preparation from Fig. 2. Due to the application of UV light to remove the dicing foil, the RML absorbed the light and heat was produced on the RML surface. Furthermore, the photoresist as well as the dicing foil worked as thermal insulator and trapped the heat in RML which caused the diffusion [11, 27, 29]. To elucidate the occurrence of the diffusion zone, another FIB cross-section was prepared. The newly prepared cross-section of a different sample, depicted in Fig. 11, showed no signs of diffusion between the RML. With different intermixing, the reaction parameters between the samples would also vary, but due to the consistency of the reaction data shown in Fig. 6a, b it is more likely that the reaction behavior stems from the differences in the area covered by defects [27]. This claim is supported by the detection of only pure Al and Ni in the XRD data depicted in Fig. 7.

After the reacted RML is cooled down, the cracks in Fig. 7b are formed, due to the volume change during the phase transformation and the cooling down phase afterward [21, 32]. This volume reduction induces stress in the structured substrate and when it is too high, the SiG structures broke. This is happening on a smaller scale than observed in Fig. 1 from the reaction on SiO2 substrate. Due to the shrunken Al0.9Ni1.1 compound, the reacted material areas are then separated in island by the visible cracks in Fig. 7b [43]. Looking at this phenomenon in a mechanical way, the SiG can be regarded as a Euler–Bernoulli beam with one fixed end at the Si bulk substrate, resembling a cantilever [44]. The free end of the beam is the SiG tip with deposited RML on top. Due to the volume reduction during the phase transformation, a force is applied on the free end, which bended the Si beam. While the reaction progressed further, the applied force also increased, until it is either breaking the SiG beam or it is pulling of the RML from the SiG structure. Respectively, both cases are depicted in Fig. 12a, b, which are showing a higher magnification SEM image of a crack. In order to enhance the visibility of the underlying phenomena, an SEM image was captured at an inclination angle of 15°.

Figure 12
figure 12

Closer look into the cracks appearing after the reaction using the SEM with an inclination angle of 15°; a shows an area where the SiG structures broke after the reaction; b depicts an area, where the SiG just bend due to the volume reduction in the RML

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The difference in reaction parameters between the SiG samples and the FS sample was primarily caused by the presence of substrate material. The absence of a substrate results in higher maximum temperature and velocity values for the FS samples, as depicted in Fig. 6a. In addition to the substrate, the influence of the SiG morphology is further decreasing the reaction velocity of the SiG samples due to the increase in reaction path from cone to cone. Thus, the average velocity difference is 9 m s−1 between the reacted FS and the SiG samples. The differences in the temperature curves between ER and CR samples in Fig. 6b can be explained by the lower number of interconnections due to the lower structure density. With a more complex reaction path, the reaction stays longer in the observation spot of the pyrometer, which results in a widening of the temperature curve. The structure density is established as a parameter to control the reaction velocity and the heat release of the RML. These are valuable revelations for the application for bonding, where some materials need lower reaction velocities to achieve a successful bond [23].

Phase analysis

In the XRD data analysis shown in Fig. 7, the 400 nm diffused Ni/Al layers were not observed, only pure Al and Ni peaks were detected. As already mentioned, the diffusion zone was neither found in an additional cross-section in Fig. 11 nor was it detected in the XRD data.

The goal was to deposit Ni and Al in a 50:50 atomic ratio, which transforms to AlNi during reaction [7]. In the SiG samples, a phase richer in Ni, Al0.9Ni1.1, was formed. This could have been caused by a deviation in the planned deposition of the RML materials [45]. Another possible reason for the formation of Al0.9Ni1.1 is the changes in the interlayer roughness caused by the SiG [28]. The inconsistency in the material distributions generated by the cone formation could also play a role; however, it needs further investigation. The XRD data of the reacted RML showed complete transformation of pure Ni/Al phases to Al0.9Ni1.1 B2 phase. Also, cross-sectional images in Fig. 8d and 9 confirmed that the RML reacted completely. The highest intensity peak in the reacted samples was on SiG (110) the same as in previous studies on flat surfaces [46, 47].

Conclusion

By introducing a surface structuring process for Si substrates, we successfully achieved a self-propagating reaction using a reduced total thickness of RML. This achievement was made possible by the cone-shaped growth of the RML on the SiG structure tips, effectively creating a predominantly air-surrounded environment that acts as a thermal insulator. The only significant heat loss occurred through conduction between the RML cones and the SiG structures. To evaluate the heat sink capabilities of the SiG structures, a comprehensive numerical analysis of the heat equation was conducted for the different zones. Surprisingly, the results indicated higher heat loss in the C zone compared to the E zone, contradicting the measured reaction data. Consequently, we concluded that the area of defects had a greater influence on the reaction dynamics than the heat loss to the SiG structures. These defects manifested as voids in the RML, a consequence of the inherent randomness in the DRIE structuring process, which left certain areas on the Si substrate without SiG structures for RML deposition. Additionally, gaps between RML cones, identified as Zone 1 of the Thornton model, also contributed to the formation of defects. Notably, the E zone exhibited a higher density of defects due to its lower structure density within that specific region of the wafer. These defects significantly impacted the propagation of the reaction by reducing the released energy, owing to the lower amount of reactive material available, and increasing energy loss as the reaction had to traverse the boundaries between the cones. Remarkably, after the reaction, the reacted compound remained attached to the substrate due to the behavior of the produced SiG structures, which functioned as Euler–Bernoulli beams, effectively absorbing the stress resulting from the volume change during the phase transformation. While some SiG structures may have experienced bending or breakage, the adhesion of the RML was not compromised. This highlights the potential of surface structuring as a means to prevent RML detachment during the reaction without the need for additional solder materials. In order to further explore the area between the SiG tips and the RML, future experiments involving TEM analysis will be conducted. At present, it can be tentatively assumed that the SiG structures do not induce any diffusion at the boundary between the SiG and RML, as suggested by previous studies with black Si structures, although confirmation is still pending. Nonetheless, this study provides valuable initial insights into an additional parameter for controlling the phase transformation process, enabling the reduction in the total thickness of deposited RML while establishing a strong adhesion between the substrate and the reacted compound. Our findings underscore the significance of defect coverage and structure density in influencing the reaction dynamics of the RML system, contributing to a comprehensive understanding of the underlying mechanisms and highlighting the intricate interplay between structural factors and reaction properties within the studied system.