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Directed self-assembly of mesoscopic electronic components into sparse arrays with controlled orientation using diamagnetic levitation
Journal of Magnetism and Magnetic Materials 385 (2015) 286–291
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Directed self-assembly of mesoscopic electronic components into sparse arrays with controlled orientation using diamagnetic levitation Anton Tkachenko n, James J.-Q. Lu NSF Smart Lighting Engineering Research Center, Rensselaer Polytechnic Institute, 110 8th Street CII 7015, Troy, NY 12180, USA
ar t ic l e i nf o
a b s t r a c t
Article history: Received 4 December 2014 Received in revised form 3 March 2015 Accepted 6 March 2015 Available online 9 March 2015
This paper presents a directed self-assembly (DSA) approach for assembling small electronic components, such as semiconductor dies, into sparse 2D arrays using diamagnetic levitation. The dies attached to a diamagnetic layer can be levitated at a room temperature over a stage made of magnets arranged in a checkerboard pattern. By selecting a proper die design, levitation height, and vibration pattern of the magnetic stage we assemble the dies into a regular 2D array with a specific lateral and vertical orientation of the dies. The assembled dies are transferred to a receiving substrate using capillary force. & 2015 Elsevier B.V. All rights reserved.
Keywords: Directed self-assembly Mesoscopic Diamagnetic levitation
1. Introduction Diamagnetic materials are repelled and can be levitated by magnetic fields. Diamagnetic repulsion was first observed in bismuth more than 230 years ago by Brugmans [1], though the term diamagnetism was coined by Faraday in 1845 [2]. However, roomtemperature diamagnetic levitation became more accessible much later, only after the discovery of neodymium magnets and light, strongly diamagnetic materials, such as pyrolytic graphite (PG). This paper presents a novel application of diamagnetic levitation – directed self-assembly of mesoscopic electronic components. Currently, assembly of electronic components is done using pick-and-place robots. However, a number of macroelectronic applications require much higher speed and lower cost to assemble a large amount of meso- or microscopic devices on large substrates with desired lateral and vertical orientations for forming permanent electrical and mechanical connections to the substrate. Such applications may include fabrication of large-area LED luminaires or displays, electronic skin or textiles, or photovoltaics [3]. Several alternatives to pick-and-place assembly are under development, such as laser-assisted transfer [4], transfer printing [5], or directed self-assembly (DSA). The latter term refers to approaches utilizing a variety of forces such as electrostatic [6], magnetic [7], capillary [8], or their combinations [9] to assemble the components in a parallel fashion without individually manipulating each component [10]. The DSA process may take place n
Corresponding author. E-mail address: [email protected] (A. Tkachenko).
http://dx.doi.org/10.1016/j.jmmm.2015.03.022 0304-8853/& 2015 Elsevier B.V. All rights reserved.
in air [11] or liquid [12,13]. The use of diamagnetic levitation as a means for parallel and scalable handling of multiple components remains largely unexplored, even though it was proposed as a potential way for creating sensors [14,15], energy harvesting [16], vertically stacking multiple objects in liquid [17], and assembly of floating spheres into small clusters [18]. Permanent magnets can levitate a mesoscopic sample made of strongly diamagnetic material, such as PG with χz ¼ 6 10 4 [19], or microscopic amounts of weakly diamagnetic material such as water [20,21]. In order for diamagnetic levitation at an equili→ brium point r to be stable, the potential energy must increase in all directions from this point [22], leading to: →
∂ 2z B 2 (r ) > 0
→
∂ 2x B2 (r ) > 0
→
∂ 2y B2 (r ) > 0
(1)
Stable diamagnetic levitation can be achieved by arranging the magnets in a checkerboard pattern with alternating north and south poles, a 2D Hallbach array or other configurations [23].
2. Diamagnetic levitation of mesoscopic components We demonstrated the use of diamagnetic levitation for DSA, where levitation serves three functions. First, it provides a lowfriction assembly environment. Second, a combination of gravitational and periodic magnetic potentials creates a 2D array of potential wells, which trap the levitating objects. Third, it allows the vertical orientation of the objects to be controlled. The objects we used are unpackaged Si dies (1.6 1.6 0.15 mm3) and GaN LEDs (1.4 1.4 0.17 mm3) bonded to a PG sheet (from GraphiteStore).
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Fig. 1. Stable diamagnetic levitation of small dies. (a) Stable levitation points for large (Die 1, Lmag/Ldie E 0.8) and small (Die 2, Lmag/Ldie E 3) diamagnetic dies. Die 3 consists of a PG layer attached to a white 1.4 mm LED die with a thin ferromagnetic layer, which shifts the stable levitation point to the edge between the magnets. (b) Total magnetic field produced by the magnetic stage at 0.5 mm above the stage surface. (c) Potential energy of a diamagnetic die (Ldie ¼ 1.6 mm) located at the corner between the magnets as a function of levitation height. The minimum corresponds to the equilibrium levitation height. (d) Dies with “PG-on-bottom” (left) and “PG-on-top” (right) vertical orientations exhibiting different levitation height.
The PG thickness is chosen between 300 and 1000 mm depending on the desired levitation height [24]. In this work a magnetic stage for levitation is built using 6.35 mm cubic NdFeB magnets (N52 grade, from K&J Magnetics) in a checkerboard orientation (Fig. 1(a), north poles are marked with black dots). When a square die with PG is placed on the “checkerboard” magnetic stage, its preferred levitation location is determined by the ratio between the lateral die size (Ldie) and the lateral magnet size (Lmag), and magnetic properties of the die. Three stable levitation locations are shown in Fig. 1(a). For a given Lmag/Ldie ratio, these stable levitation points form a 2D square lattice. When a sufficiently strong vibration is applied to the stage, the dies start jumping from one node of the lattice to another as shown in movie S1. Supplementary material related to this article can be found online at
Magnetostatic simulation [24] was used to determine the magnetic field (Fig. 1(b)) and forces acting on a die at and near the stable levitation points. A small square die experiences a minimum vertical magnetic field at the corner between magnets, rotated by 45° relative to the magnet orientation (die 2 in Fig. 1(a)). For a diamagnetic die with a thin ferromagnetic layer (e.g. Ni), the stable levitation location is at the edge between the magnets (die 3 in Fig. 1(a)) because of the combination of a strong total magnetic field (Fig. 1(b)) and a weak vertical field at this spot. The equilibrium levitation height with the zero net vertical (magnetic þ gravitational) force corresponds to the minimum total potential energy of the die (Fig. 1(c)). The levitation height, i.e., the gap between the die bottom surface and the magnet surface, depends on the vertical orientation of the die (Fig. 1(d)).
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3. Self-assembly of levitating components into a square array
4. Vertical self-alignment
The Lmag/Ldie ratio also affects the strength of the “magnetic trap” at each node of the lattice. A larger ratio (Lmag/Ldie 41) results in a stronger die trapping than smaller ratios. If more than one die is present at a node, the magnetic trapping is weaker for extra dies that are not centered at a node and they can escape from the node easier. Therefore, when proper vibration strength is selected, the extra dies escape, leaving only one die per each node. The extra dies eventually reach the edges of the magnetic stage and fall off. As a result, the dies are assembled into a 2D array, as shown in movie S2. In order to ensure that each of the nodes is occupied by a die, the initial number of dies should be higher than the number of nodes (Fig. 2(a)). Supplementary material related to this article can be found online at The lateral orientation of the dies is defined by 4-fold rotational symmetry of the dies and the magnets. Most electronic components, which require high-speed, low-cost assembly on large substrates (e.g., LEDs), either have 2- or 4-fold rotational symmetry or can be designed so. Complex electronic components (such as ICs) can include an orientation circuit allowing them to function regardless of the lateral orientation [25].
VSA is done after the dies are assembled into a 2D array. The assembled dies levitate either with the PG layer on the bottom or upside down (Fig. 2(b)). Therefore, it is necessary to change the vertical orientation of the dies without allowing them to escape from their nodes in this array. The vertical self-alignment process uses a series of short vibration pulses separated by longer pauses (Fig. 3) to flip all the dies to the same vertical orientation, with PG on the bottom (Fig. 2 (c)). This process utilizes the dependence of levitation height on die vertical orientation (Fig. 1(d)) by selecting the vibration amplitude, which flips only the dies with “PG-on-top” orientation. The dies with “PG-on-bottom” orientation remain unaffected due to the absence of mechanical contact between the die and the stage. Pulse duration is kept long enough to allow the dies to flip between two vertical orientations, but short enough to prevent them from leaving their nodes in the 2D lattice, as shown in movie S3. Short pulse duration limits the maximum distance a die can travel during each pulse. As long as the distance the dies travel during a single pulse is less than half of the lateral magnet size, Lmag, the dies always return to their nodes, i.e. corner regions between the magnets. Supplementary material related to this article can be found online at The amplitude of each pulse is selected so that vibration affects
Fig. 2. Self-assembly of levitating dies using a vibrating magnetic stage. (a) Dies dispersed on a magnetic stage. (b) Dies after being assembled into a 2D square array. Vertical orientation of the dies is still random at this point. (c) A 2D array of dies after the vertical self-alignment in “PG-on-bottom” orientation.
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only the dies levitating at a lower height (in a “PG-on-top” orientation). However, this difference in levitation heights, Δhlev, is noticeable only when the dies are stationary. Once a levitating die is hit by the magnetic stage and starts vibrating, the surface of the vibrating die is no longer parallel to the surface of the stage. This effect, as well as the amplitude of die vibration in the vertical direction, overshadows Δhlev, and makes it impossible to differentiate between the dies levitating in two different vertical orientations. Once the levitating die comes into the contact with the vibrating stage at least once, it is affected by all the following vibration pulses and it starts flipping continuously between two possible vertical orientations. In order to make the dies stay in one preferred orientation it is necessary to bring the dies close to equilibrium after each pulse so that Δhlev becomes relevant again. This is accomplished by controlling the duration of the pauses, Tp, between the pulses for vibrational energy relaxation [24].
Die pick-up from the top is accomplished by wetting the whole surface of the receiving substrate with isopropanol and lowering the substrate until it touches the dies. Die pick-up from the bottom is done by passing the receiving substrate between the levitating dies and the magnets. An array of liquid droplets is applied to the receiving substrate using hydrophilic/hydrophobic patterning, stencil printing, inkjet printing, or other techniques. Before the dies come into contact with droplets, their position is determined by the magnetic force and the dies remain stationary as the substrate moves. However, once the dies touch the droplets, they are attached to the receiving substrate by the capillary force, thus leaving their nodes on the magnetic stage In this study the first approach was preferred because it enables easier formation of permanent connections between the dies and the substrate. After vertical self-alignment the dies have a “PG-on-bottom” vertical orientation so, if the substrate picks up the dies from the top, it comes into contact with the semiconductor die instead of the PG. Consequently, a solder reflow step can follow immediately afterwards to form permanent solder interconnects. If pick-up from the bottom is used, either an additional transfer step would be necessary, or the dies have to have a “PG-on-top” vertical orientation. The demonstrated approach enables DSA of mesoscopic components into regular 2D arrays. If the components need to be assembled in a shape different from a regular array, magnetic DSA is used as a re-distribution step, after which only some of the dies from the newly formed array are selectively picked up using the die transfer process. A selectively wetted substrate or template can be used to achieve this goal. After the transfer, a solder reflow step is used to form permanent connections to the substrate. The PG layer is removed by dissolving the bonding adhesive used to attach it to the semiconductor die.
5. Die transfer to receiving substrate
6. Scaling of assembly time with array size
Transfer of dies to the receiving substrate is a final step of the DSA process. A fast drying and residue-free liquid, such as isopropyl alcohol, can be used for picking up the dies in a parallel fashion. Residue-free evaporation is essential in order to allow the formation of permanent solder interconnects between the dies and the substrate. There are two possible variants of this process: die pick up from the top (Fig. 4(a)) or from the bottom (Fig. 4(b)).
For real-world applications, the assembly speed has to be high. Therefore, it is important to understand how the time required for this DSA process scales with the size of the array. The whole assembly process involves three steps (Fig. 5(a)), each of them scales differently with the array size. Assembly of the dies into a 2D square lattice process can be approximated by a discrete random walk in a 2D square lattice
Fig. 3. Waveform used for the stage vibration during the vertical self-alignment. Each pulse contains several periods of a sine wave with a period, T1, separated by a pause with duration, Tp. Here T1 is 7.7 ms, Tp is 550 ms, the duration of each pulse, T2, is 70 ms.
Fig. 4. Transfer of levitating dies to the receiving substrate. (a) The substrate is above the dies and is lowered until it comes into contact with the die surface. (b) The substrate is between the levitating dies and the magnetic stage. An array of droplets is used to anchor the dies to the desired locations.
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Fig. 5. Scaling of the assembly time with the number of dies. (a) Diagram of a 3-step self-assembly process. (b) A simulation of the required time for die assembly into a square array using a modified 2D random walk model. The numbers in red squares shows the number of dies trapped at the corresponding node of the stage. (c) Scaling of the assembly time for the first step with array size for different numbers of extra dies. (d) Scaling of the assembly time for the first step with the number of extra dies for a stage with 16 nodes. (e) The time needed for vertical self-alignment assuming all dies start in the wrong orientation.
with certain modifications [24]. A simulation (Fig. 5(b)) is used to estimate the scaling of assembly time with the number of nodes in a magnetic stage. Fig. 5(c) shows that when the initial number of dies is several times larger than the number of nodes, the assembly time scales almost as a square of the array size in each dimension, i.e., linearly with the total number of nodes in the array. For a fixed stage size, the assembly time increases logarithmically as more extra dies are added (Fig. 5(d)). During vertical self-alignment, only the dies in the “wrong” vertical orientation respond to vibration pulses of the magnetic stage. After m pulses a die can remain in the wrong orientation only if it keeps its orientation after each of the pulses. Assuming all
dies start in the wrong orientation and the probability of a die changing its vertical orientation is 0.5, for N dies after m pulses the probability of a die having the correct orientation can be expressed by Eq. 2:
Pcorr N dies = (1 − 0.5m ) Ndies
(2)
The minimum required number of pulses mmin to flip all N dies to the correct orientation with a Pcorr N dies probability is:
mmin = ceiling(
ln (1 − Pcorr N dies1/ Ndies ) ln (0.5)
)
(3)
A. Tkachenko, J.J.-Q. Lu / Journal of Magnetism and Magnetic Materials 385 (2015) 286–291
The number of pulses calculated using Eq. 3 is below 20 even for several thousands of dies. (Fig. 5(e)). The time required for the third assembly step, i.e. transfer to the receiving substrate, can be assumed to be independent of the number of dies and, thus, constant. Both the required number of time steps from Fig. 5(c) and the required number of pulses from Fig. 5(e) are directly proportional to the time needed for the DSA process to complete. Considering that the first two parts of this DSA scale linearly and logarithmically with Ndies, we can estimate the total assembly time as:
t = a1Ndies + a2 + b1 ln(Ndies) + b2 + DSA into a 2D array
VSA
c ⏟ transfer
291
Acknowledgments This work was supported primarily by the Engineering Research Centers Program (ERC) of the National Science Foundation under NSF Cooperative Agreement no. EEC-0812056 and in part by New York State under NYSTAR contract C090145.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jmmm.2015.03.022.
(4)
where ai, bi and c are constants. The assembly time is dominated by the first term for large Ndies. The assembly speed can also be increased by dividing the total number of dies into several subsets, i.e., reducing Ndies in Eq. 4 for each subset. This can be achieved by splitting one large magnetic stage into a number of small ones with a small gap in-between to allow extra dies to fall off. Considering that the assembly time is proportional to the square of the stage size in each dimension, dividing each dimension of the stage into two, i.e. splitting it into four smaller stages, can reduce the assembly time by up to 4 times for the same total number of dies. Assuming that the “standard” assembly speed is around 1 die per second, as shown in movie S2, assembly time of 1600 dies can be decreased from 1600 s to approximately 100 seconds by using 16 smaller stages. For comparison, the time estimate for vertical self-alignment of the same amount of dies based on Eq. 3 is close to 10 seconds, assuming the period of the signal, i.e. the sum of pulse and pause durations, is 0.5 s. Another way to increase the assembly speed is to add a directional force acting on the dies (air flow, tilt of the stage, centrifugal force) or by altering the trajectory of some dies by selectively heating an edge of their PG layer using a laser beam [26]. In this case the movement of the dies is not random anymore and they will reach one or several edges of the stage faster than predicted by Eq. 4. The simulation results shown in Fig. 5 explore the parameter window, in which the initial number of dies is 3 or more times larger than the number of nodes in the array. Such a large number of dies was selected to ensure a high probability of filling all the nodes of the magnetic stage with dies during the assembly process. If a certain amount of empty nodes after the assembly is acceptable, it is possible to reduce the assembly time by using a smaller number of extra dies.
7. Conclusions Diamagnetic levitation provides unique advantages compared to DSA directly on a solid surface or in a liquid medium. With diamagnetic levitation, low friction allows the levitating objects to be moved fast even with very weak forces, leading to high assembly speed. Steep magnetic field gradients facilitate the attraction of the levitating objects to the correct assembly locations, while reliably rejecting all the extra ones. Levitation height depends on the vertical orientation of levitating objects, resulting in vertical self-alignment in the desired orientation when a proper pattern of vibration pulses is applied to the magnetic stage. This approach can be utilized for placement of a large variety of thin electronic components from diodes to small ICs, enabling fast and parallel assembly of large-area heterogeneous systems, which can benefit a wide range of applications from LED lighting to robotics.
References [1] A. Brugmans, Magnetismus, Seu De Affinitatibus Magneticis Observationes Academicae, Apud Luzac & Van Damme, Lugduni Batavorum, 1778. [2] M. Faraday, Experimental researches in electricity. Twentieth series, Philos. Trans. R. Soc. Lond. 136 (1846) 21–40. [3] H. Reuss, et al., Macroelectronics: perspectives on technology and applications, Proc. IEEE 93 (7) (2005) 1239–1256. [4] N.S. Karlitskaya, J. Meijer, D.F. de Lange, H. Kettelarij, Laser propulsion of microelectronic components: releasing mechanism investigation, Proc. SPIE (2006) 62612P. [5] S.-I. Park, et al., Printed Assemblies of inorganic light-emitting diodes for deformable and semitransparent displays, Science 325 (5943) (2009) 977–981. [6] J. Tien, A. Terfort, G.M. Whitesides, Microfabrication through electrostatic selfassembly, Langmuir 13 (20) (1997) 5349–5355. [7] S.B. Shetye, I. Eskinazi, D.P. Arnold, Magnetic self-assembly of millimeter-scale components with angular orientation, IEEE J. Microelectromech. Syst 19 (3) (2010) 599–609. [8] W. Zheng, P. Buhlmann, H.O. Jacobs, Sequential shape-and-solder-directed self-assembly of functional microsystems, Proc. Natl. Acad. Sci. U.S.A 101 (35) (2004) 12814–12817. [9] S.A. Stauth, B.A. Parviz, Self-assembled single-crystal silicon circuits on plastic, Proc. Natl. Acad. Sci. U.S.A. 103 (38) (2006) 13922–13927. [10] M. Mastrangeli, S. Abbasi, Ç. Varel, C. van Hoof, C.P. Celis, K.F. Böhringer, Selfassembly from milli to nanoscales: methods and applications, J. Micromech. Microeng. 19 (8) (2009) 083001. [11] Q. Ramadan, Y.S. Uk, K. Vaidyanathan, Large scale microcomponents assembly using an external magnetic array, Appl. Phys. Lett. 90 (17) (2007) 172502. [12] A. Tkachenko, R.F. Karlicek Jr., James J.-Q. Lu, Evaluation of directed self-assembly process for LED assembly on flexible substrates, in: Proceedings of the IEEE Electronic Components and Technology Conference, ECTC, Las Vegas, NV, 2013. [13] A. Tkachenko, R.F. Karlicek Jr., James J.-Q. Lu, Directed self-assembly of mesoscopic dies using magnetic force and shape recognition, in: Proceedings of the IEEE Electronic Components and Technology Conference, ECTC, Orlando, FL, 2014. [14] D. Garmire et al., Diamagnetically levitated MEMS accelerometers, in: Proceedings of the International Solid-State Sensors, Actuators and Microsystems Conference, 2007, pp. 1203–1206. [15] L. Jiao, M. Winistoerfer, Diamagnetic levitation for passive tilt sensors, Mater. Res. Soc. Symp. Proc. 998 (2007) 133–139. [16] G. De Pasquale, S. Iamoni, A. Som, Modeling and experimental validation of levitating systems for energy harvesting applications, in: Proceedings of the Symposium on Design, Test, Integration and Packaging of MEMS/MOEMS, DTIP, 2011, pp. 97–102. [17] A.B. Subramaniam, et al., Noncontact orientation of objects in three dimensional space using magnetic levitation, Proc. Natl. Acad. Sci. U.S.A. 111 (36) (2014) 12980–12985. [18] F. Ilievski, K.A. Mirica, A. Ellerbee, G.M. Whitesides, Templated self-assembly in three dimensions using magnetic levitation, Soft Matter 7 (19) (2011) 9113–9118. [19] N. Ganguli, K.S. Krishnan, The magnetic and other properties of the free electrons in graphite, Proc. R. Soc. Lond. A 177 (969) (1941) 168–182. [20] H. Chetouani, C. Jeandey, V. Haguet, H. Rostaing, C. Dieppedale, G. Reyne, Diamagnetic levitation with permanent magnets for contactless guiding and trapping of microdroplets and particles in air and liquids, IEEE Trans. Magn. 42 (10) (2006) 3557–3559. [21] I.F. Lyuksyutov, D.G. Naugle, K.D.D. Rathnayaka, On-chip manipulation of levitated femtodroplets, Appl. Phys. Lett. 85 (10) (2004) 1817–1819. [22] M.V. Berry, A.K. Geim, Of flying frogs and levitrons, Eur. J. Phys. 18 (1997) 307–313. [23] R. Moser, F. Barrot, H. Bleuler., Optimization of two-dimensional permanent magnet arrays for diamagnetic levitation, in: Proceedings of the MAGLEV, 2002, pp. 2–4. [24] Refer to Web version for Supplementary Material. [25] P. Drzaic, et al., Plastic-film displays with NanoBlock IC drivers integrated by a fluidic self-assembly process, J. Soc. Inf. Disp. 11 (1) (2002) 726–729. [26] M. Kobayashi, J. Abe, Optical motion control of maglev graphite, J. Am. Chem. Soc. 134 (51) (2012) 20593–20596.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Directed self-assembly of mesoscopic electronic components into sparse arrays with controlled orientation using diamagnetic levitation Anton Tkachenko n, James J.-Q. Lu NSF Smart Lighting Engineering Research Center, Rensselaer Polytechnic Institute, 110 8th Street CII 7015, Troy, NY 12180, USA
ar t ic l e i nf o
a b s t r a c t
Article history: Received 4 December 2014 Received in revised form 3 March 2015 Accepted 6 March 2015 Available online 9 March 2015
This paper presents a directed self-assembly (DSA) approach for assembling small electronic components, such as semiconductor dies, into sparse 2D arrays using diamagnetic levitation. The dies attached to a diamagnetic layer can be levitated at a room temperature over a stage made of magnets arranged in a checkerboard pattern. By selecting a proper die design, levitation height, and vibration pattern of the magnetic stage we assemble the dies into a regular 2D array with a specific lateral and vertical orientation of the dies. The assembled dies are transferred to a receiving substrate using capillary force. & 2015 Elsevier B.V. All rights reserved.
Keywords: Directed self-assembly Mesoscopic Diamagnetic levitation
1. Introduction Diamagnetic materials are repelled and can be levitated by magnetic fields. Diamagnetic repulsion was first observed in bismuth more than 230 years ago by Brugmans [1], though the term diamagnetism was coined by Faraday in 1845 [2]. However, roomtemperature diamagnetic levitation became more accessible much later, only after the discovery of neodymium magnets and light, strongly diamagnetic materials, such as pyrolytic graphite (PG). This paper presents a novel application of diamagnetic levitation – directed self-assembly of mesoscopic electronic components. Currently, assembly of electronic components is done using pick-and-place robots. However, a number of macroelectronic applications require much higher speed and lower cost to assemble a large amount of meso- or microscopic devices on large substrates with desired lateral and vertical orientations for forming permanent electrical and mechanical connections to the substrate. Such applications may include fabrication of large-area LED luminaires or displays, electronic skin or textiles, or photovoltaics [3]. Several alternatives to pick-and-place assembly are under development, such as laser-assisted transfer [4], transfer printing [5], or directed self-assembly (DSA). The latter term refers to approaches utilizing a variety of forces such as electrostatic [6], magnetic [7], capillary [8], or their combinations [9] to assemble the components in a parallel fashion without individually manipulating each component [10]. The DSA process may take place n
Corresponding author. E-mail address: [email protected] (A. Tkachenko).
http://dx.doi.org/10.1016/j.jmmm.2015.03.022 0304-8853/& 2015 Elsevier B.V. All rights reserved.
in air [11] or liquid [12,13]. The use of diamagnetic levitation as a means for parallel and scalable handling of multiple components remains largely unexplored, even though it was proposed as a potential way for creating sensors [14,15], energy harvesting [16], vertically stacking multiple objects in liquid [17], and assembly of floating spheres into small clusters [18]. Permanent magnets can levitate a mesoscopic sample made of strongly diamagnetic material, such as PG with χz ¼ 6 10 4 [19], or microscopic amounts of weakly diamagnetic material such as water [20,21]. In order for diamagnetic levitation at an equili→ brium point r to be stable, the potential energy must increase in all directions from this point [22], leading to: →
∂ 2z B 2 (r ) > 0
→
∂ 2x B2 (r ) > 0
→
∂ 2y B2 (r ) > 0
(1)
Stable diamagnetic levitation can be achieved by arranging the magnets in a checkerboard pattern with alternating north and south poles, a 2D Hallbach array or other configurations [23].
2. Diamagnetic levitation of mesoscopic components We demonstrated the use of diamagnetic levitation for DSA, where levitation serves three functions. First, it provides a lowfriction assembly environment. Second, a combination of gravitational and periodic magnetic potentials creates a 2D array of potential wells, which trap the levitating objects. Third, it allows the vertical orientation of the objects to be controlled. The objects we used are unpackaged Si dies (1.6 1.6 0.15 mm3) and GaN LEDs (1.4 1.4 0.17 mm3) bonded to a PG sheet (from GraphiteStore).
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Fig. 1. Stable diamagnetic levitation of small dies. (a) Stable levitation points for large (Die 1, Lmag/Ldie E 0.8) and small (Die 2, Lmag/Ldie E 3) diamagnetic dies. Die 3 consists of a PG layer attached to a white 1.4 mm LED die with a thin ferromagnetic layer, which shifts the stable levitation point to the edge between the magnets. (b) Total magnetic field produced by the magnetic stage at 0.5 mm above the stage surface. (c) Potential energy of a diamagnetic die (Ldie ¼ 1.6 mm) located at the corner between the magnets as a function of levitation height. The minimum corresponds to the equilibrium levitation height. (d) Dies with “PG-on-bottom” (left) and “PG-on-top” (right) vertical orientations exhibiting different levitation height.
The PG thickness is chosen between 300 and 1000 mm depending on the desired levitation height [24]. In this work a magnetic stage for levitation is built using 6.35 mm cubic NdFeB magnets (N52 grade, from K&J Magnetics) in a checkerboard orientation (Fig. 1(a), north poles are marked with black dots). When a square die with PG is placed on the “checkerboard” magnetic stage, its preferred levitation location is determined by the ratio between the lateral die size (Ldie) and the lateral magnet size (Lmag), and magnetic properties of the die. Three stable levitation locations are shown in Fig. 1(a). For a given Lmag/Ldie ratio, these stable levitation points form a 2D square lattice. When a sufficiently strong vibration is applied to the stage, the dies start jumping from one node of the lattice to another as shown in movie S1. Supplementary material related to this article can be found online at
Magnetostatic simulation [24] was used to determine the magnetic field (Fig. 1(b)) and forces acting on a die at and near the stable levitation points. A small square die experiences a minimum vertical magnetic field at the corner between magnets, rotated by 45° relative to the magnet orientation (die 2 in Fig. 1(a)). For a diamagnetic die with a thin ferromagnetic layer (e.g. Ni), the stable levitation location is at the edge between the magnets (die 3 in Fig. 1(a)) because of the combination of a strong total magnetic field (Fig. 1(b)) and a weak vertical field at this spot. The equilibrium levitation height with the zero net vertical (magnetic þ gravitational) force corresponds to the minimum total potential energy of the die (Fig. 1(c)). The levitation height, i.e., the gap between the die bottom surface and the magnet surface, depends on the vertical orientation of the die (Fig. 1(d)).
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3. Self-assembly of levitating components into a square array
4. Vertical self-alignment
The Lmag/Ldie ratio also affects the strength of the “magnetic trap” at each node of the lattice. A larger ratio (Lmag/Ldie 41) results in a stronger die trapping than smaller ratios. If more than one die is present at a node, the magnetic trapping is weaker for extra dies that are not centered at a node and they can escape from the node easier. Therefore, when proper vibration strength is selected, the extra dies escape, leaving only one die per each node. The extra dies eventually reach the edges of the magnetic stage and fall off. As a result, the dies are assembled into a 2D array, as shown in movie S2. In order to ensure that each of the nodes is occupied by a die, the initial number of dies should be higher than the number of nodes (Fig. 2(a)). Supplementary material related to this article can be found online at The lateral orientation of the dies is defined by 4-fold rotational symmetry of the dies and the magnets. Most electronic components, which require high-speed, low-cost assembly on large substrates (e.g., LEDs), either have 2- or 4-fold rotational symmetry or can be designed so. Complex electronic components (such as ICs) can include an orientation circuit allowing them to function regardless of the lateral orientation [25].
VSA is done after the dies are assembled into a 2D array. The assembled dies levitate either with the PG layer on the bottom or upside down (Fig. 2(b)). Therefore, it is necessary to change the vertical orientation of the dies without allowing them to escape from their nodes in this array. The vertical self-alignment process uses a series of short vibration pulses separated by longer pauses (Fig. 3) to flip all the dies to the same vertical orientation, with PG on the bottom (Fig. 2 (c)). This process utilizes the dependence of levitation height on die vertical orientation (Fig. 1(d)) by selecting the vibration amplitude, which flips only the dies with “PG-on-top” orientation. The dies with “PG-on-bottom” orientation remain unaffected due to the absence of mechanical contact between the die and the stage. Pulse duration is kept long enough to allow the dies to flip between two vertical orientations, but short enough to prevent them from leaving their nodes in the 2D lattice, as shown in movie S3. Short pulse duration limits the maximum distance a die can travel during each pulse. As long as the distance the dies travel during a single pulse is less than half of the lateral magnet size, Lmag, the dies always return to their nodes, i.e. corner regions between the magnets. Supplementary material related to this article can be found online at The amplitude of each pulse is selected so that vibration affects
Fig. 2. Self-assembly of levitating dies using a vibrating magnetic stage. (a) Dies dispersed on a magnetic stage. (b) Dies after being assembled into a 2D square array. Vertical orientation of the dies is still random at this point. (c) A 2D array of dies after the vertical self-alignment in “PG-on-bottom” orientation.
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only the dies levitating at a lower height (in a “PG-on-top” orientation). However, this difference in levitation heights, Δhlev, is noticeable only when the dies are stationary. Once a levitating die is hit by the magnetic stage and starts vibrating, the surface of the vibrating die is no longer parallel to the surface of the stage. This effect, as well as the amplitude of die vibration in the vertical direction, overshadows Δhlev, and makes it impossible to differentiate between the dies levitating in two different vertical orientations. Once the levitating die comes into the contact with the vibrating stage at least once, it is affected by all the following vibration pulses and it starts flipping continuously between two possible vertical orientations. In order to make the dies stay in one preferred orientation it is necessary to bring the dies close to equilibrium after each pulse so that Δhlev becomes relevant again. This is accomplished by controlling the duration of the pauses, Tp, between the pulses for vibrational energy relaxation [24].
Die pick-up from the top is accomplished by wetting the whole surface of the receiving substrate with isopropanol and lowering the substrate until it touches the dies. Die pick-up from the bottom is done by passing the receiving substrate between the levitating dies and the magnets. An array of liquid droplets is applied to the receiving substrate using hydrophilic/hydrophobic patterning, stencil printing, inkjet printing, or other techniques. Before the dies come into contact with droplets, their position is determined by the magnetic force and the dies remain stationary as the substrate moves. However, once the dies touch the droplets, they are attached to the receiving substrate by the capillary force, thus leaving their nodes on the magnetic stage In this study the first approach was preferred because it enables easier formation of permanent connections between the dies and the substrate. After vertical self-alignment the dies have a “PG-on-bottom” vertical orientation so, if the substrate picks up the dies from the top, it comes into contact with the semiconductor die instead of the PG. Consequently, a solder reflow step can follow immediately afterwards to form permanent solder interconnects. If pick-up from the bottom is used, either an additional transfer step would be necessary, or the dies have to have a “PG-on-top” vertical orientation. The demonstrated approach enables DSA of mesoscopic components into regular 2D arrays. If the components need to be assembled in a shape different from a regular array, magnetic DSA is used as a re-distribution step, after which only some of the dies from the newly formed array are selectively picked up using the die transfer process. A selectively wetted substrate or template can be used to achieve this goal. After the transfer, a solder reflow step is used to form permanent connections to the substrate. The PG layer is removed by dissolving the bonding adhesive used to attach it to the semiconductor die.
5. Die transfer to receiving substrate
6. Scaling of assembly time with array size
Transfer of dies to the receiving substrate is a final step of the DSA process. A fast drying and residue-free liquid, such as isopropyl alcohol, can be used for picking up the dies in a parallel fashion. Residue-free evaporation is essential in order to allow the formation of permanent solder interconnects between the dies and the substrate. There are two possible variants of this process: die pick up from the top (Fig. 4(a)) or from the bottom (Fig. 4(b)).
For real-world applications, the assembly speed has to be high. Therefore, it is important to understand how the time required for this DSA process scales with the size of the array. The whole assembly process involves three steps (Fig. 5(a)), each of them scales differently with the array size. Assembly of the dies into a 2D square lattice process can be approximated by a discrete random walk in a 2D square lattice
Fig. 3. Waveform used for the stage vibration during the vertical self-alignment. Each pulse contains several periods of a sine wave with a period, T1, separated by a pause with duration, Tp. Here T1 is 7.7 ms, Tp is 550 ms, the duration of each pulse, T2, is 70 ms.
Fig. 4. Transfer of levitating dies to the receiving substrate. (a) The substrate is above the dies and is lowered until it comes into contact with the die surface. (b) The substrate is between the levitating dies and the magnetic stage. An array of droplets is used to anchor the dies to the desired locations.
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Fig. 5. Scaling of the assembly time with the number of dies. (a) Diagram of a 3-step self-assembly process. (b) A simulation of the required time for die assembly into a square array using a modified 2D random walk model. The numbers in red squares shows the number of dies trapped at the corresponding node of the stage. (c) Scaling of the assembly time for the first step with array size for different numbers of extra dies. (d) Scaling of the assembly time for the first step with the number of extra dies for a stage with 16 nodes. (e) The time needed for vertical self-alignment assuming all dies start in the wrong orientation.
with certain modifications [24]. A simulation (Fig. 5(b)) is used to estimate the scaling of assembly time with the number of nodes in a magnetic stage. Fig. 5(c) shows that when the initial number of dies is several times larger than the number of nodes, the assembly time scales almost as a square of the array size in each dimension, i.e., linearly with the total number of nodes in the array. For a fixed stage size, the assembly time increases logarithmically as more extra dies are added (Fig. 5(d)). During vertical self-alignment, only the dies in the “wrong” vertical orientation respond to vibration pulses of the magnetic stage. After m pulses a die can remain in the wrong orientation only if it keeps its orientation after each of the pulses. Assuming all
dies start in the wrong orientation and the probability of a die changing its vertical orientation is 0.5, for N dies after m pulses the probability of a die having the correct orientation can be expressed by Eq. 2:
Pcorr N dies = (1 − 0.5m ) Ndies
(2)
The minimum required number of pulses mmin to flip all N dies to the correct orientation with a Pcorr N dies probability is:
mmin = ceiling(
ln (1 − Pcorr N dies1/ Ndies ) ln (0.5)
)
(3)
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The number of pulses calculated using Eq. 3 is below 20 even for several thousands of dies. (Fig. 5(e)). The time required for the third assembly step, i.e. transfer to the receiving substrate, can be assumed to be independent of the number of dies and, thus, constant. Both the required number of time steps from Fig. 5(c) and the required number of pulses from Fig. 5(e) are directly proportional to the time needed for the DSA process to complete. Considering that the first two parts of this DSA scale linearly and logarithmically with Ndies, we can estimate the total assembly time as:
t = a1Ndies + a2 + b1 ln(Ndies) + b2 + DSA into a 2D array
VSA
c ⏟ transfer
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Acknowledgments This work was supported primarily by the Engineering Research Centers Program (ERC) of the National Science Foundation under NSF Cooperative Agreement no. EEC-0812056 and in part by New York State under NYSTAR contract C090145.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jmmm.2015.03.022.
(4)
where ai, bi and c are constants. The assembly time is dominated by the first term for large Ndies. The assembly speed can also be increased by dividing the total number of dies into several subsets, i.e., reducing Ndies in Eq. 4 for each subset. This can be achieved by splitting one large magnetic stage into a number of small ones with a small gap in-between to allow extra dies to fall off. Considering that the assembly time is proportional to the square of the stage size in each dimension, dividing each dimension of the stage into two, i.e. splitting it into four smaller stages, can reduce the assembly time by up to 4 times for the same total number of dies. Assuming that the “standard” assembly speed is around 1 die per second, as shown in movie S2, assembly time of 1600 dies can be decreased from 1600 s to approximately 100 seconds by using 16 smaller stages. For comparison, the time estimate for vertical self-alignment of the same amount of dies based on Eq. 3 is close to 10 seconds, assuming the period of the signal, i.e. the sum of pulse and pause durations, is 0.5 s. Another way to increase the assembly speed is to add a directional force acting on the dies (air flow, tilt of the stage, centrifugal force) or by altering the trajectory of some dies by selectively heating an edge of their PG layer using a laser beam [26]. In this case the movement of the dies is not random anymore and they will reach one or several edges of the stage faster than predicted by Eq. 4. The simulation results shown in Fig. 5 explore the parameter window, in which the initial number of dies is 3 or more times larger than the number of nodes in the array. Such a large number of dies was selected to ensure a high probability of filling all the nodes of the magnetic stage with dies during the assembly process. If a certain amount of empty nodes after the assembly is acceptable, it is possible to reduce the assembly time by using a smaller number of extra dies.
7. Conclusions Diamagnetic levitation provides unique advantages compared to DSA directly on a solid surface or in a liquid medium. With diamagnetic levitation, low friction allows the levitating objects to be moved fast even with very weak forces, leading to high assembly speed. Steep magnetic field gradients facilitate the attraction of the levitating objects to the correct assembly locations, while reliably rejecting all the extra ones. Levitation height depends on the vertical orientation of levitating objects, resulting in vertical self-alignment in the desired orientation when a proper pattern of vibration pulses is applied to the magnetic stage. This approach can be utilized for placement of a large variety of thin electronic components from diodes to small ICs, enabling fast and parallel assembly of large-area heterogeneous systems, which can benefit a wide range of applications from LED lighting to robotics.
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