Forced Motion Activated Self-Alignment of Micro-CPV Solar Cells

In micro-concentrating photovoltaics (micro-CPV), the size of solar cells is reduced (<1x1 mm2) compared to conventional CPV. However, the quantity and requirement for placement accuracy of solar cells is increased. To be economically competitive, a promising possibility for the die assembly is a high throughput and relatively unprecise pick and place process combined with surface tension-driven self-alignment of the liquid solder. In this article, this approach is experimentally investigated, with a focus on the influences of solder volume, receiving pad layouts, and initial displacements of the cells on the self-alignment accuracy. Here, we show that an induced motion due to the initial displacement of the cells or due to solder flow along tracks leads to a more robust and accurate process. We found that less solder and rather smaller pads than cells (here by 92 μm or 10.4% of the cell length) are beneficial for self-alignment accuracy. However, for micro-CPV, conductor tracks connected to the pad are required for electrical interconnection and heat dissipation. Here, all cells are self-aligned and reach an accuracy between −15 and +15 μm, which is mainly due to the cell-to-pad size difference. Optical simulations show that this displacement would lead to an optical loss of 0.1%abs instead of 12.1%abs when displacing the cell by 150 μm. Thus, the self-alignment using the surface tension of the liquid solder leads to sufficient accuracy.

1 mm 2 , is one major trend in CPV [1], [2], [3].The reduction of the component sizes leads to a lower heat load per solar cell.Hence, otherwise required heat spreaders can be omitted and low-cost printed circuit board (PCB) technology can be applied.Typically, PCB on glass is used to match the coefficient of thermal expansion of the also glass-based lens plate; in addition, it yields good mechanical and long-term stability.
To assemble the increased number of solar cells, parallelized and/or high throughput processes from other industries, such as panel level packaging in micro-and optoelectronics, micro-/mini-light-emitting diode (LED) display technology and advanced PCB technologies (chip-on-board and chip-on-glass), can be adapted and promise cost-reduction for CPV.Various micro-CPV module approaches have been presented with micro-scale solar cells with edge lengths below 1 mm, e.g., [4], [5], [6], [7], [8], [9], [10].
Yet, the required precision regarding alignment of the solar cells with respect to the optics that comes with miniaturization poses a challenge: While offsets in the order of 50 μm may be irrelevant for 5 × 5 mm 2 devices, they are critical for 0.5 × 0.5 mm 2 devices.To assemble these small devices, in industry, the current standard for precise die bonding is pick-and-place.The assembly rate depends on the machine speed, distances between chips, the number of assembly heads, and the required accuracy.Fig. 1 shows a survey of data sheet information of state-of-the-art pick-and-place machines.As can be seen in the graph, higher accuracy implies fewer dies per hour and, thus, higher related manufacturing costs.High speeds (170 000 or ∼1 000 000 dies/hour [11]) and high accuracies (up to 2 μm [12] or 5 μm [11]) are achievable with micro transfer printing, which however requires accurate stamps and sophisticated equipment.Fluidic self-assembly [13], [14] on the other hand, promises high speeds with comparatively imprecise tools, as the placement is done via a continuous fluidic flow or batch-wise in a fluid container.While the accurate positioning is achieved through surface tension driven self-alignment.
A sketch of our micro-CPV module design, developed at Fraunhofer ISE, is shown in Fig. 2. It is based on a circuit board on glass.35 μm thick Cu tracks are used for electrical interconnection and heat dissipation.The cell temperatures during operation depends on the specific circuit board layout and has been estimated to be between 65 °C and 85 °C [15]; for solder layer thicknesses of 100 μm it has no significant influence on heat dissipation.Micro 5-junction (5j) concentrator solar cells [16] with an active area of 585 × 585 μm 2 and rectangular chip size of 885 × 685 μm 2 are used.The cells are soldered using a no-clean SnAgCu (SAC) paste and a reflow process.The front contact of the solar cell is wire bonded.All cells are equipped with spherical lenses with a diameter of 1.6 mm as secondary optical elements.The primary optical element is a silicone-on-glass plano-convex lens with an edge length of 18.5 × 18.5 mm 2 and a focal distance of 44 mm.The geometrical concentration is C geo = 1000 [15], [17].
The manufacturing process is described in [17].One module includes 690 cells, hence 2921 cells/m 2 .The required alignment accuracy was determined by using an in-house ray tracing tool Raytrace3D [18], developed at Fraunhofer ISE.We simulate the optical losses (light hitting the solar cell) of a micro-CPV cell lens unit, detailed description is shown in [17] and [18].An acceptable optical loss through the solar cell displacement is 0.1% abs , which leads to a required accuracy of ±16.6 μm.
For precise solar cell mounting, surface tension-driven selfalignment, also known as capillary self-alignment [19] is foreseen.During the heating process, the solder melts and the surface tension of the liquid solder pulls the die into perfect alignment with the underlying pad to minimize the surface energy.
It should be noted that this assembly process only requires one step of chip assembly (chip-on-board technology).This contrasts with other micro-CPV approaches based on a chip scale package approach, that require first the assembly of chip scale packages similar to LED fabrication, and second their respective assembly onto the baseplate [4], [8].
For our micro-CPV cell assembly, the receiving pad always needs a connected track for electrical connection.Moreover, polymer-based solder masks cannot be directly applied (e.g., by inkjet printing) to define the receiving pad, as they need to withstand concentrated sunlight in case of tracking errors.So far, there has been no experimental investigation of the self-alignment of a fully metalized die on a receiving pad with connected tracks and without a solder mask.
In this article, first, we investigate experimentally how manufacturing tolerances, i.e., size deviations in rectangular receiving pads, influence the accuracy of the alignment.Next, connected circuit tracks are added and the influence of solder volumes is studied for initial die to pad displacements up to 150 μm.Application limits regarding solder volume and initial displacement are evaluated in detail in the Appendix.

II. MECHANISMS OF SELF-ALIGNMENT
The self-alignment process includes three steps, as depicted in Fig. 3(a)-(c).First, the die is imperfectly placed on a receiving pad equipped with a solder paste depot [see Fig. 3(a)].The typical SAC paste is a mixture of beads of a tin-silver-copper alloy and flux and keeps the die temporarily in place.Next, during the heating process, the solder paste melts and wets the attached surfaces of receiving pad and rear side of the die.It forms a meniscus whose forced capillary action tends to align the die to the receiving pad [see Fig. 3(b)].The main force for the die movement is originating from the surface tension of the liquid solder.The die stops when the liquid reaches the minimal surface energy or if the friction force gets equal or larger as the restoring force [see Fig. 3(c)].If the receiving pad is larger or smaller than the die, then typically the self-alignment range is between the alignment on the left edges and on the right edges [19].Fig. 3(d) and (f) shows edge alignment for a larger and a smaller pad than die after initial displacement in x-direction.Fig. 3(e) and (g) shows center-to-center alignment.Edge alignment leads to an offset of half of the pad to cell length difference ±Δl/2.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The movement of the die can be equivalently described by either surface energy-or force-based models [19], [20], [21].
For a rectangular die with the die-liquid boundary area on the die rear side, the acting forces in lateral direction are the surface tension force F st and the dynamic friction force F v .In vertical direction pressure related force and gravity force are acting.For self-alignment the acting forces in lateral direction are relevant.
In a gaseous-solid-liquid (G-S-L) phase system, the balance between the surface tensions γ SG , γ LS, and γ LG and the contact angle θ can be described by Young´s equation (1).The resulting force acts on the contact line of the three-phase system and can be calculated by integrating along the contact lines (2).
A simplified case is shown in Fig. 4, here a rectangular die with the same shape as the pad with the length l and the width w is displaced in x direction.The solder depot with the height h is simplified with straight flanks and it is assumed perfect wetting of the rear side of the die and the surface of the pad.Thus, no surface tension gradients occur on the liquid-solid interface and can be neglected.The lateral restoring force along x can be described according to (3) [19] The force against self-alignment is the dynamic friction force F v between the liquid and the solid phases, which mainly originates from the viscosity η L of the liquid solder.This can be described by the Newton (4) [20].The speed of the molten solder v can be set equal to the speed of the die and as the die moves with the molten solder the surface of the die rear side A LS has to be taken into account [20] Klicken oder tippen Sie hier, um Text einzugeben.. Thus, the dynamic friction force in x-direction can be expressed as Thus, the self-alignment process is influenced by the wetting behavior of the receiving pad and die surface, the properties of the liquid, surface tension and viscosity, and the shape of dies and receiving pads, as well as the initial displacement [19].Previous studies have analyzed the influence of the liquid volume on the self-alignment process [22], [23].It is noted that the reflow conditions and alloy composition can have an additional influence [24].Regarding the solder volume, there exists an optimum amount between too less and too much volume [22].With insufficient volume, the receiving pad and die surfaces are not completely wetted.Therefore, the die can touch the substrate and resulting dry friction can prevent accurate alignment [22].On the contrary, too much solder volume increases the risk of a tilted and misaligned chip [22], [25].
The influence of the receiving pad layout on the die alignment accuracy was also investigated using water droplets [22], [23] and solder paste [20], [24].Conventional SMDs are typically mounted on two receiving pads [20], [24].There, for the electrical interconnection, one track is connected to one receiving pad, and is covered with solder mask.Härter [24] investigated different layouts of two receiving pads per die (SMD type 01005) like different circle sizes, rectangular sizes but also special shapes.In general, self-alignment worked for all layouts, but the highest accuracy with the most robust process was reached for two pads with a rectangular shape, matching with the shape of the device.Smaller or larger rectangular shapes than device size increased the scattering.
Other layouts like regular hexagons, squares, rectangles and circles, but also without in-plane rotational symmetry like semicircles and commas, were investigated with water droplets [23].The dies were rectangular with a pattern on the backside, corresponding to the receiving pad.Self-alignment worked for all in-plane rotational symmetric shapes, but approximately for 30-40% for pads without in-plane rotational symmetry.
If the die has the same shape as the receiving pad and just the size differs, it can lead to partial self-alignment, corner self-alignment or edge self-alignment [19].In summary, it is beneficial, if the layouts of the receiving pad and die are matching, size differences lead to higher scatterings [23], [24].

A. Materials: Solar Cells and Receiving Pad Layouts
Micro-solar cells with a footprint of 885 × 685 μm 2 and thickness of 190 μm are placed on different solder depots on receiving pads with different layouts [see Fig. 5(a)].
The receiving pads are fabricated by a subtractive PCB process and consist of 30 μm copper with a chemical nickel/ gold finish on a 3 mm thick glass substrate.Three rectangular pads ("R"), i.e., freestanding pads without connected tracks [see Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.I.

B. Assembly Process
The assembly process including stencil printing and die assembly took place at CEA-Leti.First, the pads are cleaned with first acetone and then ethanol to create a comparable surface condition and increase the surface energy, especially the dispersive part.Afterwards, Sn 96.5 Ag 3.0 Cu 0.5 solder paste with a flux content of 11.5±1.0%and particle sizes between 20 and 45 μm is applied using stencil printing.Due to the flux and the particles, a reduction of solder volume is expected after melting.To control the solder volume, the rectangular openings of a 200 μm thick stencil mask are varied from 615 × 454 μm 2 to 765 × 565 μm 2 (see Table II).The layout was designed according to IPC-7525B stencil design guidelines to achieve solder thicknesses between 40 and 85 μm, assuming 50% shrinkage.The cells are assembled with pick-and-place tool with a <5 μm accuracy.Here, the cells are intentionally ideally placed (Δx initial = 0 μm) or displaced with respect to the receiving pad position, with center-to-center displacements of Δx initial = 50, 100, and 150 μm.Reflow solder melting is performed with a comparatively slow heating ramp up to 255 °C, resulting in 2.5 min above the liquidus temperature of 217 °C.The resulting thickness of the solder depends on the pad sizes: for layout R B the resulting solid solder thickness is between 28.1 and 50.9 μm and for layout I between 5.3 and 15.4 μm.The solder volume is calculated based on the solder thickness on the pads R B and are between 16 and 29 nl.Note, that these volumes are the solid volumes and are assumed to be slightly larger in the liquid state.For each variation, 20 samples are prepared.After assembly, all solar cells are performing electrically as expected.
The offset of the cell center to receiving pad center Δx offset after the assembly process is determined by measuring accurate x,y positions of cells and pads before and after the process (coordinate measurement device accuracy <2 μm).

A. Cell Alignment Accuracies on Rectangular Pads
In the following the influence of pad size, solder volume, and initial displacement on the self-alignment of dies on the rectangular pads is described.
Fig. 6(a) shows the offset of the cell center to the receiving pad center Δx offset after the melting process as a function of the solder volume.The top graph shows the case of perfect placement of die to receiving pad, i.e., Δx initial = 0 μm, whereas the bottom graph shows the data for a case of significant initial displacement of Δx initial = 150 μm.Here, the pad R B is smaller by 27 μm than the cell.The cell is expected to stop when the cell is fully placed above the smaller or larger pad.Thus, several alignments are possible, from the left edge to right edge alignment.When the cell to pad offset is within this range ±Δl/2, shown in yellow in Fig. 6, then the self-alignment is seen to be successful.As a first observation, with ideal initial alignment, the cells move somewhat during the process, but show no preferred direction: The median offset (black) is close to the abscissa.The dark gray area represents the 25-75 percentiles (P25-P75), the light gray area the 10-90 percentiles (P10-P90).The scattering within 25-75 percentiles increases by around 82% with increased solder volume from 16 to 29 nl, which is from −1 -+3 μm for 16 nl to −22 -+2 μm for 29 nl.For initial displacements of 150 μm the median line follows the upper border of the self-alignment range ±Δl B /2, hence, cell edge to pad edge alignment.For the case with initial displacement also a noticeable reduction in the scattering is observed.For example, for 20 nl and no initial displacement the P25-P75 offsets are between −11 and 7 μm, whereas for x initial = 150 μm between 13 and 22 μm.
2) Rectangular Pad Size: The second part of the study investigates the influence of pad size.Here, for one solder volume, three different rectangular pad sizes (R A , R B , R C ) are evaluated (see Table I).
Fig. 6(b) shows for the three different pad sizes (R A , R B , R C ) the offsets of cells to pads Δx offset as a function of initial displacements Δx initial for the solder volume of 20 nl.For the smallest pad R A , which is 92 μm smaller than the cell, independent of the initial displacement all data scatters around a median offset close to zero with offsets Δx offset < = 7.5 μm.When the pad size is closer to the size of the die, R B 27 μm smaller than the die (middle) and R C 41 μm larger than the die (bottom) the data shows a different picture: The scattering of the data is significantly larger with offsets up to 31.1 μm.Interestingly, for small initial displacements the scattering is rather isotropic and the median close to zero.However, for displacement above 100 μm the data shifts upward and scatters around a median at the upper border of the self-alignment range ±Δl/2, again shown in yellow.At the same time, with increasing initial displacement, the scattering reduces, namely the P25-P75 range by 49.6% for pad layout R B and by 78.3% for pad layout R C over the investigated range.

B. Cell Alignment Accuracies on Pads With Connected Circuit Tracks
In micro-CPV, the electrical interconnection requires that the receiving pads need at least on one side a track connected to them.In this article, we investigate the influence of the connected tracks for the interconnected pad design I, four different solder volumes between 16 and 29 nl (see Table II) and different initial displacements up to 150 μm.
For all four volumes, solder flows along the circuit tracks (see Fig. 7).Therefore, the solder layer thickness reduces to between 5 and 15 μm, and therefore is significantly lower than on the rectangular pads.
Fig. 8 plots the measured offsets in x-and y-direction, (a) Δx offset and (b) Δy offset , against solder volume for different initial displacement between 0 μm and 150 μm (top to bottom).The x-direction is defined as perpendicular to the connected circuit track, whereas the y-direction is along it.Note that the cells here are also initially displaced in the two different directions, i.e., (a) shows data with varying Δx offset but for Δy offset = 0, whereas for (b) it is vice versa.The range of the percentiles P10-P90 and P25-P75 as well as the self-alignment range are illustrated in the graphs analogous with Fig. 6.
In general, for displacements in x-direction [see Fig. 8(a)] the median is close to zero for all cases and no clear trends are observed, expect for a slight reduction in the scattering when the initial displacement is introduced (i.e., for Δx initial > 0).
In contrast, for cell to pad displacements in y-direction, increasing solder volume leads to increased scattering in the cell position after self-alignment.However, with increasing initial displacement Δy initial this effect reduces.The median offsets do not follow a clear trend.Finally, the scattering in y-direction is observed to be higher by 46% on average than in x-direction for the same initial displacement and the same volume.

A. Cell Alignment Accuracies on Rectangular Receiving Pads 1) Solder Volume:
In general, we observed for all rectangular receiving pads that the scattering of the cell to pad offsets increases with increased solder volume.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Larger solder volume implies larger solder layer thickness h, which according to (3), reduces the restoring force (∼x/ √ x 2 + h 2 ).However, the dynamic friction force, acting against the restoring force, also decreases with a higher cell to pad distance (∼Δv/h), see (4).The dynamic friction force is constant over all displacements given under the assumption of constant velocity.To evaluate the magnitude of the dynamic friction force we can estimate a velocity of 0.1 m/s and for the case of the lowest solder layer thickness we get a dynamic friction force of 0.004 mN.In comparison, the restoring force is higher for larger displacements and gets closer to zero with smaller displacements.Fig. 9 shows the curve for the four investigated solder layer thicknesses of the pad layout R B dependent on the displacement of the die.The restoring force is equal to 0.004 mN for x < 0.3 μm.Thus, in the investigated case, the restoring force is dominating for nearly all displacements.
In more detail, for large offsets (x>>h) the influence of the solder thickness on the restoring force diminishes (∼1/x), whereas for small offsets (x<<h) the thickness is important ∼x/h.Here, the initial displacements are up to 150 μm and the solder thicknesses h between 28 and 56 μm.Thus, they differ by only half an order of magnitude at the maximum.However, the dependency of the restoring force on the solder volume is valid.For example, for a displacement of 30 μm the restoring force differs between the minimal and maximal solder layer thickness by 29.6% whereas for a displacement of 100 μm the restoring force differs by 7%.The increased dependency on the solder thickness for small offsets fits to the observed behavior, as for all performed experiments offsets remained below 30 μm, despite initial displacements between 50 and 150 μm.
2) Rectangular Pad Size: Our study showed that for the case of rectangular receiving pads which are significantly smaller than the dies (R A ), typically cell center to pad center alignment occurs.This was observed independent of the initial displacement [see Fig. 6(b)].For rectangular pads only slightly smaller (R B ) or larger (R C ) than the die, for small displacements the dies scatter rather isotropic around zero but tend to edge alignment for larger initial displacements.
For dies on smaller or larger pads, center to center or edge alignment occurs depending on the balancing forces.The motion of the die stops when the restoring force either becomes zero or equal or lower to an opposed friction force.According to (3), the restoring force depends on the cell edge to pad edge distance.In the case of edge alignment, the restoring force on the side where the die aligns at the edge is zero, whereas on the opposite side it still depends on the cell edge to pad edge distance.If the pad is significantly smaller than the cell, the restoring force is higher than for slightly smaller or larger pads.Fig. 3(d) and (f) illustrates the dimensions to scale for the pads R C and R A .It has to be noted that (3) is a simplification and to explain the self-alignment behavior more accurate, numerical simulations are required, which is in preparation [27].
Furthermore, for the slightly smaller and larger rectangular pads R B and R C , for no initial displacement the median offsets are close to 0 μm whereas for higher initial displacement the median offsets are close to the border of the self-alignment range ±Δl/2 and thus edge aligned.Additionally, for the case of ideal placement with no initial offset the scattering is higher than for the cases of nonzero initial displacements.When the cell is accurately placed, there is no force which induces a motion.When the cell is initially displaced, the initial restoring force increase with increasing offset.It seems that at the edge of the pad the restoring force is as high as the friction force and the cell stops.It should be noted, that even for the case of ideal initial placement some scattering is observed.To some extend the cause for this scattering could simply be machine precision and measurement uncertainty.Yet, some deviations are larger than those which suggests that additional effects can have a minor impact.These could possibly be from nonideal surface wetting, the transport from the pick and place tool to the reflow oven or vibration of the conveyor belt during the reflow process.
It is important to emphasize that the solder volume for all pad sizes were constant.Hence, the solder layer thickness differs, namely for a solder volume of 20 nl by 12.8 μm between the smallest (R A ) and the largest (R B ) pad.Still, the previous finding that a thinner solder layer is beneficial does not apply here, because presumably the influence of the pad size dominates the behavior.
3) Receiving Pad Layout With Connected Tracks: Receiving pads with connected tracks showed a different behavior regarding the influence of initial displacements and solder volumes compared to rectangular receiving pads with no connected tracks.
The receiving pad with connected tracks allows solder flowing along the tracks.Therefore, the solder layer thinned down by a factor between 3.3 and 5.3, compared with the rectangular pad R B .This leads to two different effects: First, the solder layer thickness varies between 5.3 and 15.4 μm.Thus, the dependency on the solder layer thickness decreases and an even scattering of the offsets is to be expected.For classification, for the rectangular pad R B the difference in the offset scattering between the two lowest thicknesses, 28 and 35 μm, was in the P10-P90 range between 6 to 14% dependent on the initial displacement.Hence, dependencies below this range are expected for lower thicknesses.Second, the solder flow along the tracks, even for the case of ideal placement, causes a stronger motion than with the isolated rectangular pad.This motion leads to overcoming the static friction force and thus, all cell to pad offsets are similar independently of the initial displacement.
Regarding the direction of the self-alignment, initial displacement in y-direction lead to slightly higher scattering than for initial displacements in x-direction.This is understood as a result of the tracks which partially cover the backside of the cell and thereby reduce the restoring force.Yet, it is noted that despite this reduction of the restoring force, self-alignment still occurs for all cells.

VI. CONCLUSION
We have experimentally investigated the influence of three different rectangular receiving pad layouts, one receiving pad with connected circuit tracks, four different solder volumes, and different initial cell displacements on the self-alignment accuracy of micro-solar cells.For isolated rectangular receiving pads without connected circuit tracks, a significantly smaller pad than cell, here R A , smaller by 92 μm than the die, compared to slightly smaller (R B by −27 μm) or larger (R C by +41 μm) pads, leads to best results.Depending on the initial displacement the scattering of the offsets of R A , compared to R B and R C is reduced between 47.2 and 88.8%.As a consequence, we recommend significantly smaller receiving pads than die to reach a more robust process.Most important, initial displacements of the dies lead to higher alignment accuracies and reduced scattering on rectangular pads.The reason is the motion induced by the surface tension force, i.e., the friction force is overcome.The investigated solder volumes; between 16 and 29 nl, are all sufficient for self-alignment, although lower volume results in less scattering and is, thus, recommended.For pads with connected tracks, molten solder flows along the tracks, which leads to low thicknesses and decreases the sensitivity on solder volume.Furthermore, initial displacements like for rectangular pads, are not required to reach higher alignment accuracies.Here, the motion is induced by the solder flow along the tracks, which leads already to overcoming the friction force.With self-alignment, placement accuracies for the pad I between −15 μm and +15 μm were reached.According to raytracing simulations, this results in optical losses below 0.1% abs and fulfills the required accuracy for our micro-CPV module.

A. Limits of Self-Alignment
The purpose of this article was to test the limits of the self-alignment.Therefore, solder volume was largely decreased and increased as well as the initial displacement were shifted to extremes.
For initial displacement up to 500 μm, which is more than half of the die width, we found that mostly self-alignment still works, but sometimes major failure modes occur, which are depicted in Fig. 10.Failure can occur due to solder flowing along the rear side of the cell to the opposite circuit track [see Fig. 10(b)].Then, an additional surface tension force pulls in the other direction and the die is balanced between the receiving pad and the opposite track.In principle this failure mode can occur only if the die is initially displaced farther than the gap width between pad and circuit track, here 200 μm, and at the same time a large solder volume is applied.If the solder volume is too low, the backside of the cell as well as the pad fail to be wetted completely [see Fig. 10(c)].In this case, the restoring force is smaller than the friction force and the self-alignment of the die fails.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.For asymmetric cells like the rectangular cells in this article, also the in-plane rotation of the dies is important, as illustrated in Fig. 11.For rotations below 45°the cell rotates in the preferred direction during reflow soldering, whereas for larger initial rotations, the cell rotates in the other direction.This can be relevant for self-assembly processes which are based on random motion, for example like in an automated reel-to reel fluidic self-assembly machine [14].In this case, symmetric squared chips would be beneficial.This is in line with the finding of Srinivasan et al. [23].

Fig. 1 .
Fig. 1.Die placement accuracy dependent on speed for different commercial pick-and-place machines.

Fig. 2 .
Fig. 2. Sketch of the micro-CPV module and its components.

Fig. 3 .
Fig. 3. (a)-(c) Process steps of self-alignment of a die on a receiving pad using the surface tension of liquid solder for the case of shape matching.(d)-(g) Illustrations of different scenarios: edge-and center-aligned dies on a larger or smaller pad (sizes to scale with respect to the experiments performed in this article).(a) Inaccurate die placement.(b) Liquid solder wets pad and die surface, surface tension forces act on the die.(c) Cooling down and solder freezing after self-alignment.(d) Pad>die: Edge alignment.(e) Pad>die: Center alignment.(f) Pad<die: Edge alignment.(g) Pad<die: Center alignment.

Fig. 4 .
Fig. 4. Simplified sketch, sizes not to scale.The die (S) is displaced by the distance x on a liquid depot (L) with the height h.A LS is the contact area of die rear side.α is the angle between the gaseous (G) and liquid (L) phase.The die moves with the velocity v.

Fig. 5 .
Fig. 5. Microscope pictures of the different materials.All sizes are in μm.(a) Solar cell.(b) Rectangular pad R B .(c) Interconnected rectangular pad I.

Fig. 5 (
Fig.5(b)], of different sizes as well as one interconnected pad ("I") with connected tracks [see Fig.5(c)] are investigated.The nominal pad sizes were designed to be equal and 65 μm smaller and larger than the cell edge lengths.However, the subtractive PCB process yielded approximately 30 μm smaller.The actual pad to cell deviations are given in TableI.

Fig. 6 .Fig. 7 .
Fig. 6.Offset in x-direction of the cell to a rectangular pad Δx offset as a function of (a) solder volume with pad layout R B for the cases of ideal alignment (Δx initial = 0, a-top) and for an initial displacement of Δx initial = 150 μm (a-bottom).The second graph (b) plots Δx offset as function of the initial displacement Δx initial for the case of a solder volume of 20 nl.From top to bottom the pad size, difference pad to cell length, is varied from Δl A = −92 μm to Δl B = −27 μm to Δl C = +41 μm.The yellow area visualizes the self-alignment range ±Δl/2, the dark gray area the offsets within 25−75 percentiles, light gray 10-90 percentiles and the thick black line the median offset.(a) Pad layout R B Δl B = −27 μm.(b) Solder volume 20.1 nl.

Fig. 8 .
Fig. 8. (a) and (b) Offset of the cell to receiving pad I dependent on solder volume for initial displacement (a) in x-direction and (b) in y-direction.From top to bottom: Initial displacement x initial or y initial is increased from 0 to 150 μm.The median offset (black line) is for nearly all cases in the self-alignment range ±Δl I /2 or ±Δw I /2 (yellow).Note, that the solder volume is given as the volume applied to the pad.Here, the solder layer thickness is significantly reduced by solder leaving the target pad area.Note, the y-scale differs compared to Fig. 6.(a) Pad layout I Δl I = −15 μm.(b) Pad layout I Δ WI =−16 μm.

Fig. 9 .
Fig. 9. Calculated restoring force according to (3) as function of the displacement of a die on the pad layout R B and for different solder layer thicknesses.Surface tension of the molten solder Sn 96.5 Ag 3.0 Cu 0.5 is set to 0.54 N•m [26].

Fig. 10 .
Fig. 10.Microscope images after reflow soldering.Dies placed on receiving pads with connected circuit tracks with initial displacements in x-direction of 500 μm.(a) Successful self-alignment (b) Failure: Too much solder (c) Failure: Too much solder