Self-alignment of whole wafers using patterning for capillary forces

3D packaging using multiple wafers is an important new direction in packaging, and some of the key early work and concepts were contributed by Gary McGuire and his collaborators.^1,2 It offers advantages in choice of substrate materials for each subassembly, reduced line lengths for speed and reliability, and more efficient use of area in sensor applications. Indeed, some simple wafer stacks have been made.^3,4 However, as the number of wafer layers grows or the circuitry either becomes complex enough or too opaque for high resolution IR through-imaging (as used in the prior work), other techniques are required. Two leading contenders, “SmartView” and “3Dalign,” have been developed to address this problem.⁵ Both rely on imaging both sides of the wafer stack, the primary difference being if they are done simultaneously, which requires a specialized microscope, or serially with a digital image of one side superimposed while aligning the second. The problem is that, with multiple wafers in a stack, the particular wafer to the next alignment accuracy depends upon more than one alignment so that it becomes inaccurate in addition to its costliness.⁶ In this paper, we investigate the use of fluidic self-assembly (FSA) in a process that can be combined with wafer-to-wafer bonding^7,8 and a via-last, through silicon via scenario. Submicrometer levels of alignment will soon be required.⁹ 

Self-alignment via capillary forces is not a new concept³ and is valid when the scale of the meniscus is less than the capillary length,¹⁰ as is the case for the liquid between our wafers. It has been applied to positioning millimeter-sized objects, particularly chips, to surfaces with success.^3,11–25 Models can predict the chip process and extend to different, uniformly coated geometries (small polygons).^23,25–34 Magnetic alignment of chips is another option.³⁵ Still, new ideas will be needed for reliable fan-out into more complex situations.^11,36 Further adaptation of this technique to a wafer scale process is nontrivial. Initial attempts have either to use only edges of the wafer to align even a few centimeter structures³⁷ or to provide a spacer to prevent wafer edge dragging.³⁸ Temperature changes during the alignment or bonding stages can misalign the wafers. Cycling of temperature over large ranges for multiple levels can exacerbate this problem.^5,39 As the alignment accuracy becomes more stringent, the temperature excursions must decrease. Whereas the old “low temperature” was 300–400  $°$C, the new low temperature is $∼200 °$C.^40–42 The alignment method proposed here is compatible with a low temperature, $<200 °$C, bonding scheme⁷ demonstrated at the end of the paper and using the bonding precursor as the capillary fluid.

The innovations and design rules for the wafer scale alignment that do not require a spacer and can align a pattern, not wafer edges, are described in this paper: (1) rather than simply applying a uniform coating or surface treatment to the chips and using the edge of the chip as the guiding surface, patterns must be applied to both surfaces, and we use a uniform vinyl-terminated self-assembled monolayer (SAM) layer, a lithographic process compatible with the SAMs, and a rapid process for conversion of exposed SAM from hydrophobic to hydrophilic;⁴³ (2) since the patterns may not be in the same position on both wafers, the edges of the wafers must not dominate or interfere with the alignment so that the pattern must have many pattern edges; (3) the patterns must not allow multiple energy minima that would result in a metastable misaligned system, which is guaranteed by using structures at many length scales as we show; (4) the capture range must be large with sufficient force to accurately position the wafer so that there must be some larger features; (5) the entire wafer must be kept floating on the alignment fluid until the alignment is complete (no edge drag) so that flow channels are used to engineer wafer drop and keep it level; (6) our model for the capillary edge forces predicts that these forces decrease linearly for small displacements⁴⁴ so that we use many fine-line features to compensate; (7) we use the model to calculate the alignment force of a complex pattern as a function of alignment fluid surface energy and experimentally show that it works, and (8) we show the integration of the alignment with bonding.⁷ 

In this paper, we investigate several methods based on surface-energy minimization. A method based upon capillary forces, which required several innovations, is shown to work well. SAMs are used to define the local surface energies to drive the capillary forces. We begin with a description of the production of self-assembled monolayers and a lithography process compatible with them. We then discuss sliding force measurements in a dry system and measure surface-energy differences. A capillary-force based system is described next, beginning with mask design, and ending with its successful implementation. Quantification is achieved by measurements and modeling of both the fluid profile and the alignment forces. Finally, the design rules that enabled success are summarized.

Silicon wafers of 10, 30, 70, and 400  $μ$m thicknesses were obtained from Wafer World, Inc. or Virginia Semiconductor. All were of 1-0-0 orientation. Isopropanol of HPLC grade was obtained from Fisher. ACS grade chloroform and dichloromethane were obtained from Fisher. Anhydrous hexadecane $>99$% purity was obtained from Aldrich Chemical. Technical grade hexadecyltrichlorosilane was obtained from Aldrich. Microposit MF319—developer (organic developer designed for S1800 line photo resists) and Microposit Remover 1165 were from Rohm & Haas.

The sample preparation procedure and the lithography process were developed to be compatible with the SAM layers. Standard lithography processes cannot be used with SAMs because the developers are strong bases. These destroy the SAM layers. We, thus, use an organic developer with a compatible photoresist. The effect of a remnant photoresist on the SAM contact angle is also investigated. We show that commercial photoresist remover is the best choice for maintaining proper contact angles through the lithography process.

Silicon wafers are cleaned in a piranha solution of 2:1 H $2$SO $4$ (⁠ $∼34 N$⁠) and 30% H $2$O $2$ (both obtained from Fisher) for 1 h. The H $2$SO $4$ is added last, slowly. Agitation of the samples in an ultrasonic bath during cleaning was not possible for the thin wafers without breaking. After cleaning, samples are rinsed twice with de-ionized water. The surface of the silicon wafer after cleaning displayed high interfacial free energy as verified through surface wetting by water. Finally, the wafer is spun dry on a spin coater at 3000 rpm while spraying with isopropyl alcohol (HPLC grade from Fisher). It is then spun for an additional 30 s to completely dry the surface. A very clean surface is required for ellipsometry, surface chemistry, and unimpeded water sliding.

Wafers for self-alignment were prepared in one of two ways, which we briefly describe before elaborating the details. For type 1 wafers, a layer of aluminum patterned onto a surface using lift-off, then a hydrophobic, methyl-terminated (-CH $3$⁠) SAM layer is grown from hexadecyltrichlorosilane, and the aluminum etched away with concentrated HCl to form clean, hydrophilic regions. The properly patterned hydrophilic and hydrophobic regions drive the capillary action. An example is shown in Fig. 1. For type 2 wafers, the entire wafer is coated with a hydrophobic vinyl-terminated (-C=CH $2$⁠) layer grown from 10-undecenyltrichlorosilane. Photoresist was then applied and patterned, leaving the regions to be hydrophobic covered with a photoresist (as above). The initial vinyl layer has a value typical of clean layers. After exposure to resist and its removal, it is not quite as hydrophobic as it was, but sufficiently so for alignment purposes. The contact angle recovery (to $72 °$⁠) is better with the Microposit resist remover than with acetone (to $68 °$⁠) or exposure and development (to $52 °$⁠). A solution-based oxidation method is not complete, and a fairly large contact angle remains. This is too large for good wafer self-alignment, as the wetting of the hydrophilic region is important to successful capillary action and subsequent alignment. Thus, we developed an ozonation method that is very effective and leaves a surface close to wetting but with a SAM layer intact.⁴³ Ozonation is followed by resist removal and water rinsing to clean the samples and hydrolyze the ozone-treated areas to finish the conversion of the SAM termination to carboxyl (wetting).

A photoresist is applied so that areas can be masked off into hydrophobic and hydrophilic zones. Shipley 1818 (a G line photoresist obtained from Rohm & Haas) is added and spun at 3000 rpm for 30 s leaving a layer approximately 2.3  $μ$m thick. The wafer is then baked on a hotplate at $115 °$C for 3 min. UV exposure with a contact mask took 11 s for type 1 samples and 7.5 s for type 2 samples. It is developed in Microposit MF 319 developer for 1–1.5 min at room temperature. The UV exposure was adjusted so that the exposed zones are distinguishable from unexposed zones during the development process. The development is stopped with water.

For removal of the remaining photoresist after the patterning has been used, the sample is submerged in a 1165 photoresist stripper and heated to $80 °$C. For type 2 samples, the photoresist was just a patterned protective layer from the oxidation. For type 1 samples, some of the aluminum coating is removed by lift-off. The sample needs to be agitated occasionally to help the aluminum removal process.

For deposition of the SAM layer, the wafers were inserted into a drybox with a nitrogen atmosphere. The chemicals used during deposition are all hygroscopic or reactive with water. All reagent bottles are opened and used within this drybox. The substrate is first submerged in isopropyl alcohol (100%). Next, it is submerged in dichloromethane. Then, it is submerged in chloroform. Finally, it is rinsed by submersion in hexadecane. Then, deposition begins by submersion in the deposition solution, which consists of 2%/V trichlorosilane (precursor noted above) solution in hexadecane. Although the majority of the SAM is formed within 15 min, deposition was done over 24 h to achieve maximum density of the SAM. Afterward, the substrate was washed in hexadecane, dichloromethane, and chloroform and then in isopropyl alcohol to remove any remainder of the precursor before removal from the drybox. The silicon wafer sample stays in one beaker with the top surface down throughout the whole washing, rising, and deposition. The wafer stays in the beaker by capillary force. We are concerned with the top surface only. However, during washing or rinsing, the beaker must be agitated sufficiently to circulate the solvent under the wafer.

Approximately 30 nm of aluminum is deposited onto a type 1 patterned sample. The vacuum chamber is pumped down with a diffusion pump to less than $1× 10 − 6$ Torr. Aluminum is thermally evaporated onto the sample, which is held at its edges with aluminum squares secured to the aluminum stage. When thin wafers are used (⁠ $<70μ$m), a small piece of paper is inserted behind the sample to keep it from breaking due to thermal and vacuum welding effects. The Al layer is deposited at 1–2 Å/s. Afterward, the chamber is vented with pure oxygen to approximately 500 Torr and allowed to sit for a minute. This allows growth of a clean oxide layer on the aluminum.⁴⁵ 

Ozonation is used to oxidize the vinyl group for type 2 samples. We had poor (⁠ $∼20$%) yield when using wet chemical oxidation with organic acids,⁴⁶ presumably due to the reduced mobility from geometric constraints induced by the vinyl being bound to the surface via the SAM molecule. Yield is measured with the Cassie equation $cos θ m=β cos θ 1+(1−β) cos θ 2$⁠, where $θ m$ is the measured contact angle, $θ 1$ is the contact angle for layer one, and $θ 2$ is the contact angle for layer two.⁴⁷ Ozone preferentially attacks the carbon-carbon double bond and forms a precursor to a carboxyl group after reaction. For our particular ozonator strength and geometry, we subjected the surface to ozone for 11.5 min. There is a narrow ozonation window, as too little will yield a surface that is not wetting, but too much will remove the entire SAM layer.⁴³ We optimized the process with ellipsometry and contact angle measurements. A further rinse in water is required to hydrolyze the surface and complete the conversion to carboxyl termination with high yield (essentially wetting).

See the supplementary material for a schematic diagram of the lithography process, and some of the contact angles observed at the various stages are shown in Fig. S1.⁵⁰ 

Contact angle measurement by the sessile drop technique is a simple, but useful, technique to characterize surface energies. SAMs have interfacial surface energy with either ambient or the chemicals in contact with them. Liquids placed on the SAM surface will arrange themselves to minimize the total system energy. A de-ionized water interaction with these surfaces is of particular interest in this experiment. Surfaces that water adheres to are hydrophilic, while areas that do not attract water are hydrophobic. Using images taken from a 5 MP camera with a +10 D auxiliary lens, contact angles between the horizontal surface and the edges of the water droplets were measured. We used few microliter water droplets that were dropped from about 1 cm above the surface. The resulting droplets will have a contact angle between the advancing and receding angles as constrained by the hysteresis of the system. See the supplementary material for an example in Fig. S2.⁵⁰ The angle between the surface and droplet is measured in photoshop or the gnu image manipulation program. The visible reflection of the droplet helps to pinpoint the contact point in the image and, therefore, improves the angle accuracy.

Ellipsometry is used to measure layer thickness. It can detect the presence of a SAM layer or multiple layers rather than one. It is also used to detect changes in the layer thickness during oxidation. A Rodolph AutoEl II null ellipsometer was used to measure the ellipsometric parameters $Δ$ and $Ψ$⁠, the phase change between, and the arctangent of, the amplitude ratio of p to s polarized plane wave light, respectively. The incident angle was set at $70 °$ and the measurement was performed with 632.8 nm light from an He-Ne laser. Assuming an index of refraction of 1.456 for the SAM and a flat, uniform coating, single layer thicknesses were calculated. The precision of this instrument translates to better than $±0.1$ nm. Six measurements per sample at different locations were performed before and after deposition. Since the index of refraction of this SAM is very similar to the top oxide layer coating of the silicon wafer, the difference between pre- and postdepositions will represent the thickness of the SAM layer. Water monolayers are removed by spin cleaning in HPLC grade isopropanol or methanol before measurements with the ellipsometer.

Sliding force measurements are used to measure relative surface energies and to test the alignment force models. A cantilever force sensor, Fig. 2, deflects upon application of a force to the free end. A voltage proportional to the deflection is produced and measured in a bridge configuration. Calibrations are performed by hanging masses with the cantilever mounted horizontally. When measuring force vs displacement, as done here, an “erosion” correction needs to be applied to the displacement to account for the motion of the cantilever end, which is applying the force. For stage motion $t$ and cantilever motion $x=F/k$ for measured force $F$ and cantilever spring constant $k$⁠, the actual displacement $d=t−x=t−F/k$⁠. The value of $k$ was measured using an object that does not slide; therefore, $d=0$ and $kt=F$⁠; i.e., $k$ is the slope of the straight line $F$ vs $t$ data. We will note when the data have been corrected by this method.

In the above discussions, several constraints for a full-wafer alignment become evident, which were not relevant for aligning small objects as has been done before. In particular, during the initial stages of alignment, too much fluid is present. The thickness of the fluid required to support a wafer is constrained by the fluid curvature on the side (pressure) and edge angles to both surfaces,⁴⁴ so has a fixed value for a particular pressure (weight of upper wafer/area of fluid). Excess fluid must leak out first from the pattern as a whole and then from the hydrophobic regions as the proper water layer thickness is established. If the fluid does not flow out evenly, then the top wafer will tilt, and one edge will touch the other wafer, drag, and prevent proper alignment. Thus, fluid channels in the hydrophobic regions must be supplied and designed so that the fluid level decreases uniformly across the wafer. These fluid channels should be long, fairly narrow, and contain corners so as to ensure a slow loss of fluid and, hence, allow time for alignment to complete. The channels need to lead to the outer edge of the wafer from near the center. Second, the alignment force decreases as alignment is approached (below); therefore, many small regions are required to increase the number of edges present and, hence, retain sufficient alignment force as the final alignment position approaches. These are best located near the edge of the wafer to provide more torque for rotational alignment. Finally, edges must be present in a variety of directions so that the alignment is robust under translations in either lateral direction or wafer rotation.

The designs assume that the initial placement of the upper wafer is within a certain precision to start the self-alignment process. A large capture area of two millimeters was the goal. Larger features present in the center of the mask help provide this capture effect. We make a simple model to test the details that is similar to that of Böhringer et al.²⁶ We have considered several possible geometric patterns of hydrophilic (hl) and hydrophobic (hb) regions. The pattern is the same on both layers. The system energy is minimized when the layers are aligned. An indication of the force is determined by the rate of change of the hb/hl (unmatched) area. It does not account for the decrease in the magnitude of the force as alignment is approached but offers a relatively simple to calculate model that will give important insights. The design process involves identification of a pattern that will converge to the aligned state with a significant force at a range of misalignments; see Fig. 3. Since we have not measured the energies yet, the force plots are qualitative. The trends and variation of the capture range with a frictional force should be qualitatively correct. Since the force curves peak sharply near the aligned state, it appears that alignment will proceed even with the linear decrease in the actual force magnitude for small $x$⁠, as found above.

In the progression of the leftmost three patterns in Fig. 3, the addition of nonperiodic features along possible displacements is shown to prevent local minimum trapping where features in the pattern might line up before the patterns have come into alignment. The rest of the design needs to overcome these local minima. If not, the alignment process will get stuck. It also shows that the addition of smaller features improves the capture force near alignment. The comparison of the rightmost two patterns in Fig. 3 shows that the capture range is decreased unless there are large areas of a hydrophobic pattern. Thus, two additional criteria are discovered in this exercise: nonperiodic features and large hydrophobic regions are both required for full-wafer alignment.

We can combine these requirements with the criterion above that the loss of fluid must be controlled to prevent an imbalance of the upper wafer, which can cause one side of it to touch the lower wafer, often before alignment was achieved, and, therefore, allow the drag force of that corner to exceed the alignment force and prevent good alignment from being achieved. This is done by inserting channels to slowly but controllably allow excess fluid to escape, while the wafer is supported uniformly for long enough that alignment is good. Two such designs are shown in Figs. 4(a) and 3(c) with 4(b) magnifying the channel regions (gaps).

Initially, the patterns were tested with soft masks, while hard masks were in the planning stage. The soft masks were generated from the inkjet on transparencies. The transparency was coated with a nonacetone based vinyl spray to prevent scratching. The feature size of the smallest resolvable triangles is approximately 265  $μ$m, Fig. 4(b). More important is the edge roughness, which is of the order of a few tens of micrometers. Line resolution of the hard mask is better than 1  $μ$m. The smallest triangle used was 8  $μ$m. These chrome on quartz masks were fabricated by Photo Science, Inc. using laser pattern generators. The best mask pattern of Fig. 3(c) is repeated throughout the mask to cover a 4 in. wafer.

Initial indications of the relative surface energies can be obtained by measuring the forces needed to slide the wafers across each other. Although the friction forces are too large to permit dry alignment, variations in the forces are observed. These can be understood by consideration of the surface tension or the surface energy of the various regions within the sample. Figure 5 shows a diagram of the sample used. It consists of a larger wafer with an A- (hydrophobic vinyl or hydrophilic carboxyl) terminated coating in the rectangle and a B- (opposite) terminated coating over the rest of the wafer. There are four different surface energies: $U 1$ of A/air, $U 2$ of A/top wafer, $U 3$ of B/top wafer, and $U 4$ of B/air. For sliding forces, only the interactions with the top wafer are important.

Most of the alignment studies used a $2.5×2.5$ cm $2$ pattern similar to Fig. 3(c) or 4(a), which was repeated on larger samples. We tested alignment on sample sizes ranging from just one 2.5 cm square to full 10 cm diameter (4 in.) wafers top and bottom. Performance was similar, although wafer edge sliding limits were more common when using full wafers with the repeated patterns. This would be reduced by nonrepeating patterns with longer flow channels, but even an initial water distribution also suffices in this work. For simplicity, most of the results shown here use a 2.5 cm square top wafer on one of the patterns on a 10 cm diameter bottom wafer. It allowed verification that wafer edge effects were not important and provided easier repeated top wafer removal and linear and rotation displacement of the top wafer on the larger bottom wafer. Different thickness upper wafers (see Sec. II A) were used for the upper wafer to further demonstrate generality of the process. The primary effect of thinner wafers is less mass for the fluid to support. The upper wafer is held by the fluid forces along the edges perpendicular to the misalignment; therefore, only second order effects to the force are expected due to contact angle constraints at the top and bottom. We did not notice any significant change to the alignment.

The soft mask trial used type 1 samples. Once the pattern was transferred to the wafers as described above, one surface was coated by a light spray of water and the second wafer was lowered onto it with an offset of $∼1$–2 mm from the aligned position. Air bubbles were observed to expand into the regions with hydrophobic coating, filling the larger areas in less than 10 s and the smaller zones within a minute.⁴⁴ The alignment proceeded quickly and reliably without any need for tinkering after placement. Figures 7–9 show alignment events of various misalignments using the soft masks. Using an infrared light source and a CCD camera, the water and air trapped between the two substrates form a visible boundary. When the wafers are pushed out of alignment, this boundary is observed to increase in breadth. When released, they return to alignment. Alignment marks were not present on these soft masks; therefore, the alignment precision was estimated from the water edge width in the images to be better than the resolution limitation of the imaging system. Higher precision on the soft masks was not pursued, and concentration was placed on the higher resolution hard masks and alignment marks.

In the images shown in these figures, the large triangle centered in the bottom half of the image is a hydrophilic region, as are channels along its bottom and up the sides. There is a smaller hydrophilic triangle in the upper right. These areas appear slightly darker than other regions of the image. Surrounding these objects, in the slightly lighter gray, are hydrophobic regions. The length of the base of the larger triangle is one third of an inch (8.5 mm). The maximum displacements are $∼1$–2 mm. In all cases, Figs. 7–9, the period for the realignment process was less than or about 1 s; the realignment occurred as the tweezers driving the offset were removed.

In Fig. 7, the top wafer was displaced to the right in the picture. Part (a) shows partial misalignment with the tweezers holding the misalignment. The water is still attached as when aligned, but is stretched. A further held misalignment (tenths of a mm, about the thickness of the water layer) in (b) is sufficient to break the water contact to the lower wafer along the left edge everywhere except at the top tip of the triangle. This unpinning is anticipated and modeled in Ref. 30. The top wafer is released and is moving back in (c), bringing the water junction closer to where it was on the lower wafer, but not yet exactly there. The wafer is almost aligned again in (d), although the water edge has not yet reformed properly. The other side is presumably pushing the wafer. A “wave” of edge reforming is visible in (e). It started at the top corner where it was never broken and proceeds quickly down the edge. It has nearly completed reforming the edge by (f) and is completely realigned as before displacement in image (g). We have not modeled this “wave” phenomenon.

The edge does not always break, even for a similar displacement level. In Fig. 8(a), which involves a vertical downward displacement of the top wafer, the water remains attached throughout, and alignment is rapid. An interesting feature here is that a channel on the right is opened during the displacement in Fig. 8(a) but quickly closes by Fig. 8(b) before realignment, Fig. 8(c).

Rotational misalignments were also tested, Fig. 9. The wafer is twisted clockwise, around a center point just beyond the upper left of the image. The wafer is rotated some in (a), more in (b), but the edge remains attached, and realignment follows in (c).

Hard masks were fabricated according to the design criteria presented above, similar to the pattern shown in Fig. 4(a). Type 2 samples were used. These all-SAM surfaces can be incorporated into a covalent nanoglue,⁷ which will allow bonding once alignment is achieved. Thus, although the degree of wetting achieved is not as high, we show that it is still sufficient to align the wafers and moves the idea to the realm of practicality. A reference point was used on the upper wafer while it was viewed with a Nikon TE-2000 microscope at 200 $×$ magnification. The resolution of the optical and camera system was better than 1  $μ$m. The pattern showed a strong alignment tendency for a few seconds, and then, as intended, the liquid escaped through flow channels until the top wafer came to rest on the bottom wafer. If dried and rewetted (with a small drop of DI water in the center $∼0.05$ ml), the alignment forces came into play again. The nylon 6-6 bonding solution showed an even stronger alignment tendency than plain DI water alone, and the alignment pattern could be seen more clearly with the nylon 6–6 solution. The use of the nylon solution, however, destroyed the pattern, as diamine molecules bonded with the exposed carboxylic acid functional groups.

After initial alignment was achieved, the wafer was deliberately pushed or rotated out of alignment by $∼1$ mm and then allowed to return to the aligned position. The displacement of the reference point from the initial alignment point was used as an indicator of the alignment accuracy. This was repeated many times. The alignment accuracy, given by averaging several trials, was 3–5  $μ$m, showing that there is some variation between different wafer sets.

The alignment accuracy is less for whole wafers than for chips. The primary limit does not appear to be the pattern edge roughness or the smallest lithographic feature; our alignment accuracy exceeds those limits, especially when using soft masks. The reduced force at small misalignments also does not appear to dominate. The list of key wafer-level effects at the end of Sec. I does not offer insights. Rather, we noticed in these trials that the variations in the alignment accuracy are not uniform, which leads us to suggest that the wafer-level limits (assuming no wafer edge sliding and the other mask design suggestions are followed) are set by large scale mask distortion (pattern sizes not perfectly matched wafer edge to wafer edge on both top and bottom wafers). This would give different alignment accuracy at different points of the wafer and may produce overall flatness in the force profile at small misalignment separated from the theoretical one given in Sec. IV. We are limited by our mask fabrication machine and, therefore, do not further investigate this factor.

The size of the vias determines the required alignment precision in 3d wafer stacks. The results shown here are compatible with the via size less than 10  $μ$m, a reasonable level.⁴⁸ Interestingly, they are larger than the expected error of the line straightness. This suggests that improvements will be obtained by improving the precision in the mask fabrication and the design transfer tools so as to reduce distortion between the patterns. There is the possibility of error in the photolithography process, such as nonuniform/under exposure of the photoresist before the oxidation process or, most likely, mask distortion. We do not perform this optimization in the proof of principle study, although they would be ameliorated in a practical process.

During the course of the above and other alignment studies, we observed several important considerations required for our novel ability to align whole wafers rather than just few mm-sized units. Using these design rules, the size or thickness of the wafer should not be a limiting factor for the process: (1) Large patterns at the mask center for large capture ranges. (2) Finer patterns progressively away from the center to provide greater rotational and lateral capillary forces necessary for critical alignment of large wafers. In practice, we use this up to a 1 in. square and repeat that pattern as many times as is needed to cover the surface. (3) Nonperiodic features are present to prevent local minima trapping. (4) Large enough hydrophilic zones are needed to maintain the water necessary to suspend the top wafer. (5) Internal hydrophilic flow channels for displacement of water throughout the mask design keep the wafer level throughout the alignment process. (6) External hydrophilic flow channels designed for uniform drainage across the wafer removes water and lowers the wafer as the final placement is reached. (7) Basic solution to increase the alignment effect as indicated by decreased contact angles with carboxyl and hydroxyl terminated SAMs. SAMs used include methyl, vinyl, carboxyl, and hydroxyl terminated SAMS: hexadecyltrichlorosilane, 10-unidecenyltrichlorosilane (with its termination modified). (8) The overall mask distortion must be small for the capillary forces to work together throughout alignment. Points (4) and (5) deserve further comment. The mask used has its regions of the hydrophilic surface connected (Fig. 1). This allows the water to slowly leak out from the internal regions, pushed by the weight of the wafer. We observe this process, which takes seconds to minutes. If the pattern does not have these channels, self-alignment is very difficult to obtain—just the right amount and distribution of water must be used, and the wafer still tends to drift slightly during drying. When one side of the upper wafer touches the lower wafer before the other side, the wafer tends to pivot around that point, ruining the alignment elsewhere. Thus, the channels must be balanced so that the wafer evenly settles to the surface of the lower wafer.

To test the force calculation, we use fluids with different surface tensions on the mask design shown in Fig. 4(a). The surface tension of a water/alcohol mixture decreases with additional alcohol, which we measure from the contact angle to be 73.1, 67.5, 58.5, 53.8, 50.6, 48.7, and 47.4 mN/m or obtain from the literature as 72.75, 47.53, 37.97, 32.98, 30.16, 27.96, and 26.23 mN/m⁴⁹ for concentrations of ethanol of 0, 10, 20, 30, 40, 50, and 60%volume,⁴⁴ respectively. The alignment force as a function of displacement begins as a linear rise and then levels off, as expected from the calculations above. A further linear rise followed by additional plateaus is also observed during larger motions,⁴⁴ suggesting interacting water surfaces on nearby alignment features—these effects are not included in the model. When identifying the first plateau, care must be taken so that it is reasonable (compared to the distance between the wafers and the distance between nearby features), as misidentification yields forces that are too high. We take all the line segments in Fig. 4(a) and sum their cosine-weighted contributions⁴⁴ for the various alcohol concentrations for both sets of surface tensions and plot them in Fig. 10(b) along with the measured data. There are no adjustable parameters. The agreement is quite good when the measured contact angles are used to determine surface energies, indicating that surface preparation is important. The Vasquez surface tensions are also based on mass concentrations rather than volume concentrations, and the density of ethanol is less than that of water, so are somewhat biased. Note that the edges of the wafer do not align, while the pattern does, in tests, such as Fig. 10(a). This, again, means that we have met another of our suggested design criteria. For use in practical 3D alignment of wafers, the process must be integrated with a bonding agent. The novel covalent nanoglue described in Ref. 7 can be used as the alignment fluid. It is based upon nylonlike bonding between the SAM surfaces with nylon intermediate bonds to span the gaps between nonflat wafers. Successful alignment and bonding have been demonstrated. The strong interaction between the nylon precursor solution and the SAMs that it bonds to act to give a stronger alignment force than observed with the water/alcohol mix used here. The wafers in Fig. 10(a) were bonded by this process, including self-alignment.

Although capillary force alignment has been done before, it has only been accomplished for mm-sized chips. The extension to the wafer level is not trivial and is shown here along with a description of the requirements, or design rules for defining hydrophobic/ hydrophilic zones on wafers, to allow self-alignment of whole wafers. Processes for making the patterns after deposition of a single SAM layer on each surface have been described, including key aspects related to contact angles. The pattern design criteria go far beyond that used for chips (using the edges of the chip) and must include large features for a large capture range and small features for an alignment force decrease as full alignment approaches. The handling of excess alignment fluid and a uniform fluid release as alignment is approached and the wafers are to be bonded is shown to be a crucial issue. Two working designs are provided. We demonstrated alignment of whole wafers to the patterned features rather than the wafer edges. The capture range is several millimeters or several degrees, and the alignment is within a few micrometers. Finally, we showed that the process can be integrated with previously published bonding techniques.

This work was supported by the AFRL-WPAFB (Grant No. FA8650-04-2-1619).

The authors have no conflicts to disclose.

Ernest M. Walker III, Ako Emanuel, and Hans D. Hallen contributed equally to this paper.

Ernest M. Walker III: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal). Ako Emanuel: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal). Hans D. Hallen: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

Ernest M. Walker: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal). Ako Emanuel: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal). Hans D. Hallen: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.