Measurement and simulation results show good agreements in respect to value of forces and characteristics of the bond strength curves. The two distinguishable linearly increasing and decreasing regions observed in all measurement curves can be seen in the simulation curves as well (see Figure 55 - 58). In the term of bond strength value,
simulation results based on the VdW forces approach and the capillary force (with β = 0.2°) approach show better compatibility to the measured values in comparison to
the contact mechanics approach. Almost no mismatch in term of bond strength value is observed between simulations (based on all three models) and measurement results for samples from the needle-like surfaces 1 - 3. Only position of the maximum simulated bond strength in respect to bonding load for samples from the needle-like surface 2 is shifted a little bit in comparison to measured values; the maximum measured bond strength value is obtained at a bonding load of 8.33 kg, whereas the maximum simulated bond strength occurs at a bonding load of 10.33 kg (see Figure 56). However, for samples from the needle-like surface 4, two mismatches between measured and simulated bond strengths are observed. First, maximum simulated bond strength values and their positions (for all three models) are different from the measurement result. All maximum simulated bond strengths are obtained at a bonding load of 10.33 kg while the maximum measured value occurs at a bonding load of 8.33 kg, and the simulated bond strengths are almost 2 to 4 times greater than the measured bond strengths (see Figure 58). Second, the measured bond strength at the highest bonding load (12.33 kg) is almost 4 to 7 times lower than the simulated bond strengths.
In all measured bond strengths, bond strength is increased by increasing bonding load and reached to a maximum when the bond interface width between two surfaces (65.27 ± 10.26 μm in the needle-like surface 1, 32.08 ± 5.73 μm in the needle-like surface 2, 27.64 ± 5.59 µm in the needle-like surface 3, and 47.84 ± 2.14 µm in the needle-like surface 4 (see Figure 42 )) is very close to average height of needles (65.9 ± 6.7 μm in the needle-like surface 1, 24.6 ± 2.2 µm in the needle-like surface 2, 25.1 ± 1.9 µm in the needle-like surface 3, and 37.5 ± 3.2 µm in the needle-like surface 4 (see Table 3)). At this point, the maximum interlacing lengths between partner needles is occurred. The maximum interlacing length for the needle-like surface 1 is
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obtained at a bonding load of 10.33 kg, whereas for other needle-like surfaces, it occurs at a bonding load of 8.33 kg. After this point, increasing the bonding load by 2 kg and 4 kg, decreases the interlacing length of needles by forcing needles to compress and shorten. Consequently, it lowers the bond interface width below the mean value of height of needles and reduces the bond strength.
The difference between measurement and simulation results occurs at a point where needles start touching substrates due to high bonding loads (linearly decreasing region of the curves) since the proposed bonding model cannot properly predict compression and breaking of needles at this point. On the other hand, at any bond interface width (distance between two bonded needle-like substrate) lower than the average height of needles, the employed compression model considers presence of all needles in the adhesion mechanism with their heights equal to the bond interface width and neglects their breakings and exclusions.
The linearly increasing region of bond strength curves shows 5 - 20 % difference between simulated and measured bond strengths. This difference can be either due to errors in assumed parameters (e.g., closest distance of approach (0.3 nm), the Tabor parameter (0.1), and the filling angle (0.2°)) for each porposed adhesion model or due to errors in measured surface and bond properties (e.g., clustered needle densities, height of clustered needles, diameter of clustered needles, distance between adjacent clustered needles, and bond interface widths).
Among the surface and the bond properties, height of clustered needles and width of bond interface show a slight influence on simulated bond strengths. For all investigated needle-like surfaces, assuming all other parameters are held fixed, a 1 μm change in height of needles and the bond interface width will result in about 2.8 ± 0.5 % and 1.6 ± 0.3 % difference in total simulated bond strengths, respectively.
However, the distance between adjacent clustered needles and the diameter of clustered needles show more impacts on the total simulated bond strength. About 6.5 ± 0.8 % and 15.6 ± 3.2 % difference in total simulated bond strengths will obtain by a 1 μm change in the distance between adjacent clustered needles, and the diameter of clustered needles, respectively. Miscounting a needle on a SEM surface image will also result in around 1.8 % reduction in the needle density, and consequently around 2 % reduction in the total simulated bond strengths. Diameter of a needle exhibits the highest impact on the bond strength since it defines the
137 interacting area in the needle-substrate interaction, cooperative needle or needles for the needle-needle interaction, and the width of the line-interaction in the needle-needle interaction. Additionally, it defines stability of the needle during the bonding process;
a low aspect ratio needle is more stable or more resistive to a bonding load than a high aspect ratio needle. These impacts can be clearly observed through Figures 59 - 61. Only the average values of the simulation results for the generated needle-like surface 1 is shown in these figures; their spared values are not included in the graphs.
Since all surface properties were optically measured or extracted using SEM images, a 1 μm measuring error or 1 miscounting needle can be a very reasonable and optimistic assumption for all obtained data.
Among assumed parameters for proposed adhesion models, the closest distance of approach (CDA) shows a significant impact on simulated bond strengths based on the VdW force model. Decreasing the CDA from 0.3 nm to 0.2 nm will result in about 275 % increase in the total bond strength. Whereas, increasing the CDA from 0.3 nm to 0.4 nm will result in about 49 % decrease in the total bond strength. For the proposed contact mechanics model, the Tabor parameter (𝜇𝑇) shows a moderate effect on simulated bond strengths. About 29 % decrease in the total bond strength will obtain by decreasing the 𝜇𝑇 from 0.1 to 0.05. However, increasing the 𝜇𝑇 from 0.1 to 0.15 will result in about 22 % increase in the total bond strength. For the proposed capillary force model, the total simulated bond strength is strongly dependent on the filling angle (𝛽). Changing the 𝛽 by ± 0.1° will result in about ± 48 % difference in total simulated bond strengths. These influences can be clearly observed through Figure 62. Only the average value of simulation results for the generated needle-like surface 1 is shown in this figure; their spared values are not included in the graphs.
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+1 um change in height of clustered needles -1 um change in height of clustered needles
0
+1 um change in distance between adjacent clustered needles -1 um change in distance between adjacent clustered needles
0
+1 um change in diameter of clustered needles -1 um change in diameter of clustered needles
0 simulated bond strengths based on the VdW force model for the generated needle-like surface 1: a) height of clustered needles, b) bond interface width, c) distance between clustered needles, d) diameter of clustered needles, and e) clustered needle density.
Original data with CDA = 0.3 nm means simulation results based on measured data and assuming 0.3 nm as closest distance of approach between interacting bodies.
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+1 um change in height of clustered needles -1 um change in height of clustered needles
0
+1 um change in distance between adjacent clustered needles -1 um change in distance between adjacent clustered needles
0
+1 um change in diameter of clustered needles -1 um change in diameter of clustered needles
0
-1 needle misscounting Figure 60. Impact of mismeasuring of the
surface and the bond properties on simulated bond strengths based on the contact mechanics model for the generated needle-like surface 1: a) height of clustered needles, b) bond interface width, c) distance between clustered needles, d) diameter of clustered needles, and e) clustered needle density. Original data with uT = 0.1 means simulation results based on measured data and assuming 0.1 as Tabor parameter for contacting bodies.
a) b)
c) d)
e)
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+1 um change in height of clustered needles -1 um change in height of clustered needles
0
+1 um change in distance between adjacent clustered needles -1 um change in distance between adjacent clustered needles
0
+1 um change in diameter of clustered needles -1 um change in diameter of clustered needles
0 surface 1: a) height of clustered needles, b) bond interface width, c) distance between clustered needles, d) diameter of clustered needles, and e) clustered needle density.
Original data with β = 0.2 means simulation results based on measured data and
141 Although from the structural point of view, the proposed model (ideal needle) using a cylinder and a hemisphere to describe a needle differs from the experimentally observed clustered needle, they are very similar in terms of shape, volume, and the number of atoms or molecules per unit volume. The volume difference between a clustered needle (truncated conical needle) and a cylindrical needle is only
1
3𝜋ℎ(𝑟𝑏2+ 𝑟𝑏𝑅 − 2𝑅2). Since the difference between 𝑟𝑏 and 𝑅 in clustered needles is only a few micrometers, the volume difference between a clustered needle and its corresponding ideal needle, and consequently their generated attractive force, will be also very small and can be neglected. Additionally, by optimizing the surface fabrication process, needle-like surfaces with less clustered needles or even standalone needles can be generated in which generated clustered needles are much closer to the proposed ideal needles.
c) Figure 62. Impact of assumed parameters in
the proposed adhesion models on simulated bond strengths for the generated needle-like surface 1: a) closest distance of approach (CDA) for the VdW force model, b) Tabor parameter (uT) for the contact mechanics model, and c) filling angle (β) for the capillary force model.
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Although all proposed adhesion models can predict the adhesion between two needle-like surfaces quite well, they have their specific advantages and disadvantages. The VdW force model is only valid in dry environments or when the distance between interacting surfaces is less than or equal to the interatomic spacing (≤ 0.3 nm). In humid environments, capillary forces dominate VdW forces, and the capillary force model becomes valid. In contrast to the VdW force model and the capillary force model, the contact mechanics model is valid in both dry and humid environments only if there is a contact between interacting bodies (zero separation).
In general, VdW forces are highly dependent on the separation distance between two bodies and are drastically reduced by increasing the separation distance. For instance, the VdW interaction forces between two interlaced needles based on the VdW force model (see Eq. 50) depends on 𝑑′, as 1
𝑑′5/2 [108]. Increasing 𝑑′ from 0.3 nm to 0.6 nm, will result in ~ 80 % reduction in the adhesion force. However, capillary forces do not significantly depend on 𝑑′ if the meniscus is formed between two interlaced needles.
For instance, considering all other parameters are held fixed, only 1 % reduction in the adhesion force will be obtained by changing 𝑑′ between two interlaced needles from 0.3 nm to 0.7 nm at a constant relative humidity of 30 % and a filling angle of 0.2°. In contrast to VdW forces, capillary forces show more dependency on the meridional radius (𝑟𝑟) (radius of curvature of the meniscus) defined by the relative humidity (see Eq. 65), as (1
𝑟𝑟). At a constant filling angle (0.2°), increasing relative humidity from 30 % to 50 % will vary 𝑟𝑟 from 0.43 nm to 0.75 nm, and consequently will reduce the adhesion force up to 43 %. However, increasing the humidity from 30 % to 50 % will extend the existing range of attractive capillary forces from 0.7 nm to 1.4 nm with only
~ 1 % reduction in the adhesion force. In comparison to the VdW force model and the capillary force model, the contact mechanics model is extremely dependent on 𝑑′; even a very small separation distance between interacting needles drops the adhesion force to zero.
Even though needles in generated needle-likes surfaces are in the range of micrometer size, their surfaces may include pores in the range of nanometer, and consequently waviness and roughness in the same order of the magnitude [272, 273], which can increase their actual contact distances above zero or the interatomic spacing. Therefore, assuming zero and 0.3 nm (the interatomic spacing), as the
143 separation distance between two interlaced needles or between needles and substrates at their contacts, may not be a proper and a valid assumption in the contact mechanic model and the VdW force model, respectively. Additionally, while bonding of two silicon needle-like surfaces carries on at a normal clean-room condition, it is not possible to ignore the influence of condensed vapors on needles’ surfaces resulting from condensation of water vapors into their nano-pores [274], which dominate capillary forces over VdW forces at any distance greater than the interatomic spacing.
Therefore, the adhesion model based on capillary forces can be more appropriate to describe the adhesion between two silicon needle-like surfaces at room temperature.
Additionally, the capillary force model does not significantly depend on the distance between two interacting bodies as long as a capillary meniscus is formed. However, the model is sensitive to the filling angle (𝛽) parameter, which is difficult to obtain and confirm experimentally.
6.5 Summary
The bonding mechanism between two similar silicon needle-like surfaces is modelled by considering both deformation and interaction mechanisms of needles.
The proposed bonding model is then demonstrated by comparison with experimental results.
A clustered needle (bundle of several needles) is represented as an ideal needle (a cylinder with a hemisphere head in which the cylindrical body and the hemispherical head have the same radius). The cantilever beam approach is used to describe the deformation of needles. The interaction of needles is modelled based on the uncoupled multi-asperity approach in which the interaction of each needle is considered locally and separately from others, and the total interaction force is obtained by summing up all individual contributed needles. Intermolecular forces, such as VdW forces and capillary forces are considered as the basis of the interaction. The interaction force (adhesion) between two needle-like surfaces is then obtained based on three different approaches or models: i) the VdW force model which considers only VdW forces, ii) the capillary force model which considers only capillary forces due to condensed vapor, and iii) the contact mechanic model which considers only near range VdW forces in term of surface tension.
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Irrespective of considered interaction approaches or models, the bonding model agrees quite well with experimental data in respect to characteristics of curves and value of bond strengths. The bonding model fails only at a point where width of a bond interface is lower than the mean value of height of needles (resulting from a high bonding load) since the employed compression model cannot properly predict the compression and breaking behaviors of needles at the point where needles start to touch substrates.
Around 5 - 20 % difference between simulated and measured bond strengths have been observed. This difference can be either due to errors in assumed parameters (e.g., the closest distance of approach, the Tabor parameter, and the filling angle) for each proposed adhesion model or due to errors in the measured surface and bond interface properties (e.g., clustered needle densities, height of clustered needles, diameter of clustered needles, distance between adjacent clustered needles, and bond interface widths). It is found that errors in the assumed parameters for the adhesion models have higher impact on simulated bond strengths compared to errors in the measured surface and bond interface properties.
Advantages and disadvantages of each proposed adhesion model are also studied.
The VdW force model and the contact mechanics model show extreme dependence on the distance between interacting bodies. However, the capillary force model does not significantly depend on the distance between interacting bodies if a meniscus between the interacting bodies is formed.
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7 | Conclusion and outlook
Although plenty of different bonding techniques have been developed to adhere silicon wafers or substrates together, they follow mostly the same three steps consisting of surface preparation, surface contacting, and annealing. In all approaches, an ultra-cleaning process is required prior to the bonding, and many voids may generate during the annealing process. In addition, obtained bonds are mostly permanent irrespective of the technique used. However, miniaturization of microsystems and microelectronic devices towards “smart dust” requires new bonding techniques with adequate bond strengths and pick and place capabilities at room temperature. This thesis offers and demonstrates a Si-Si bonding technique using needle-like surfaces to overcome these issues. The proposed bonding technique does not require any ultra-cleaning and annealing process and is even capable of multiple bonding and debonding of the same substrates with adequate bond strengths through a simple pick and place approach similar to gecko or Velcro adhesion concept.
A bond strength (pull-off force) in a range of 10 - 1032 kPa and up to 10 rebonds for similar substrates are obtained from the investigated needle-like surfaces. The bond strength reduces after every attachment and detachment process due to an increase in number of broken and shortened needles. However, more than 40 % of the bond strength is still available after the third rebond for half of the investigated needle-like surfaces. The obtained bond strengths are almost three times higher than the bond strengths reported by Han et. al [81] using micromechanical Velcro structures and are almost two times lower than the ones obtained by Stubenrauch et. al [17]
using the black silicon. The obtained bond strengths are not directly comparable with the ones reported by Jonnalagadda et. al [16] since different bond strength evaluations are employed; Jonnalagadda et. al measured shear bond strength.
Anodic etching of silicon in a HF based solution is used to generate needle-like surfaces due to its cost-effective production. Although generation of needle-like surfaces by this technique has been presented by some other researchers [16, 104, 105], here, a detailed study about impacts of anodization parameters and substrate materials on morphology of needle-like surfaces, and formation mechanisms of needles are presented. A suitable working condition to generate needle-like surfaces
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is obtained and presented. A needle-like silicon surface can be simply fabricated by anodic etching of <100> lowly doped (10 - 20 Ωcm) p-type silicon wafers with a constant current density in a range of 40 - 75 mA/cm² in a 7.2 wt.% aqueous HF solution. Due to stochastic nature of pores’ geometries and morphologies and clustering behavior of needles due to their fabrication process, clustered needles with inhomogeneous height, diameter, and separation are obtained. However, specific morphology of clustered needles with this process condition is sensitively dependent on the current density and the crystal growth method of the wafer. For this specific condition, clustered needle density and height of clustered needles increase by increasing current density, whereas diameter of clustered needles and distance between adjacent clustered needles decrease by increasing current density. CZ grown wafers result in much denser needle-like surfaces with longer needles compared to FZ grown wafers, and consequently higher bond strengths between similar surfaces.
However, more homogenous needle-like surfaces in terms of distribution, height, and diameter of clustered needles are obtained from FZ grown wafers compared to CZ grown wafers. In CZ wafers, inhomogeneities in height, diameter, and distribution of clustered needles are increasing from middle of the wafer towards its rime. However, in FZ wafers, these inhomogeneities are randomly distributed on different areas of the wafer. These inhomogeneities can be due to the different axial and radial resistivity variations in CZ and FZ wafers due to their production methods. Formation mechanisms of needles is investigated through SEM surfaces images taken after different etch times during anodization of <100> p-type (12 -17 Ωcm) silicon wafers with a constant current density of 50 mA/cm² in a 7.2 wt.% aqueous HF solution. A
However, more homogenous needle-like surfaces in terms of distribution, height, and diameter of clustered needles are obtained from FZ grown wafers compared to CZ grown wafers. In CZ wafers, inhomogeneities in height, diameter, and distribution of clustered needles are increasing from middle of the wafer towards its rime. However, in FZ wafers, these inhomogeneities are randomly distributed on different areas of the wafer. These inhomogeneities can be due to the different axial and radial resistivity variations in CZ and FZ wafers due to their production methods. Formation mechanisms of needles is investigated through SEM surfaces images taken after different etch times during anodization of <100> p-type (12 -17 Ωcm) silicon wafers with a constant current density of 50 mA/cm² in a 7.2 wt.% aqueous HF solution. A