Abstract
We have succeeded in aligning self-assembled structures by using a lithographically defined stripe. The 140 nm wide by 100 nm high SiO 2 strip is shown to guide the assembly of 500 nm latex spheres so that spheres are aligned along the strip and are in registration on either side of the strip. This method can be used to increase long range ordering in magnetic storage systems without compromising the density. Inverse sphere Ni arrays were made by electrodeposition through the latex template. We also show that the hexagonal symmetry of the resulting inverse sphere Ni arrays can be simulated using the approach presented below.
Introduction
Self-assembly is defined as the autonomous organization of components into patterns or structures without human intervention [1] . Self-assembly is nowadays regarded as an alternative to overcome limitations found in both conventional and e-beam lithographic methods for transferring patterns. This makes self-assembly very promising because it could be used in patterned storage media to increase the storage densities currently available on hard disks up to an estimated density of 1 Tbit/in 2 [2] . Advances in the use of various methods for self-assembly have been made [3] [4] [5] [6] [7] [8] [9] . However, orientation and long range ordering of the self-assembled template remains a problem. It has been shown that by defining tracks on the substrate, the self-assembly can be controlled to a certain extent [10, 11] . But this still does not address the long range ordering required for magnetic storage. In this study we will show that long range ordering in selfassembled structures can be achieved by the guidance of a lithographically defined stripe. Our self-assembly method is based on latex spheres which are used as a template for the electrodeposition of Ni. It has been shown by various groups that the self-assembled spheres can be used as an etch template to create pillars and other structures useful for magnetic storage [12, 13] . To study the properties of the template, we used latex spheres as a direct template for electrodeposition. This creates so-called antidot or inverse sphere arrays of Ni. In a previous paper, we have shown the hexagonal symmetry of the coercivity in these structures [14] . Here we will show that the observed symmetry can be explained qualitatively by the micromagnetic simulation of only one small section of the patterned film. Figure 1 illustrates the steps followed to fabricate the inverse sphere Ni array analysed in this study. N-type <100> single-side polished silicon wafers with resistivity 0.01-0.02 Ωcm were used as substrates. Then a 250 nm thick layer of SiO2 was thermally grown on the polished side. The guiding stripes were defined by conventional lithography (Fig. 1a) . Wet etch was used to eliminate the excess of SiO2 and leave only the guiding stripes. A 20:1 BHF dip was used to leave the Si surface H-terminated and hence, hydrophobic (Fig. 1b) .
Experimental
Shortly after this BHF dip, 500 nm diameter latex spheres were self-assembled on the substrates by slow evaporation of a colloidal water suspension containing 1wt.% of latex spheres. Electrodeposition was used to grow inverse sphere Ni arrays directly on Si without a back contact (Fig. 1c) . Another 20:1 BHF dip was carried out just before electrodeposition in order to remove the native oxide and leave the Si surface Hterminated. The conditions used during electrodeposition can be found elsewhere [15] . Finally, the latex spheres dissolution was performed with tetrahydrofuran (C4H8O), which resulted in the inverse sphere Ni arrays on Si studied below (Fig. 1d) . Characterisation was carried out using Scanning Electron Microscopy (SEM). Magnetic measurements were carried out in a magnetooptical Kerr effect (MOKE) rig. Measurements have been performed at room temperature.
Results and Discussion
A self-assembled Ni inverse sphere array guided by a 140 nm wide and 100 nm thick SiO2 stripe is presented in Figure 2 . It can be noticed that the array is free of fractures and it follows the orientation of the guiding stripe. Moreover, the phases of the array on either side of the stripe are aligned. This is accomplished by continuation of the sphere self-assembly over the stripe, lining up the two sides, as illustrated in the inset of Figure 2 . The self-assembly is hence not hampered by the lithographically defined guidance stripe, while at the same time it forces the orientation of the self-assembly creating therefore longer range ordering. Although some defects on the anti-sphere array caused by missing spheres can also be observed, this result is particularly important for patterned storage media as it reveals that long-range self-assembly can be achieved by lining-up a series of guided self-assembled magnetic arrays. Due to the fact that the guiding stripe width is about the same order or smaller than the spheres themselves, storage density will not be greatly compromised. MOKE measurements were carried out in an inverse sphere Ni array prepared using 900 nm latex spheres. The coercivities measured when the magnetic fields were applied at various angles are shown in Figure 3 . From this figure it can be readily noticed the dependence of the coercivity on the direction of the magnetic field. It can also be noticed the six fold symmetry corresponding to the hexagonal configuration of the nanostructured array. Micromagnetic simulations using OOMMF [16] were carried out in order to explain the behaviour of the measurements presented above. The cylinders considered were 20 nm height with a diameter of 880 nm. This diameter corresponds to the section of the film where the distance between spheres is approximately 20 nm as shown in Figure 4 A value of K1=-5.6kJ/m 3 was used for simulations considering a uniaxial magnetocrystalline anisotropy. Simulations consisted of the calculation of the magnetisation reversal processes taking place when the magnetic fields are applied at different angles. Due to the hexagonal structure of the array, the obtained coercivities from reversal processes at the angles displayed in Figure 4 (b) can be extrapolated and compared with the experimental measurements as shown in Figure 3 . All coercivity values from our simulations were divided by 2 in order to normalise them with the experimental data. The observed discrepancy is mainly due to the fact that the simulations were carried out for a single anti-sphere and not for the whole array. Nonetheless, Figure 3 shows that our single cylinder approach reproduces qualitatively the anisotropy produced by the nanostructuring and suggests that shape anisotropy plays a significant role in the magnetisation reversal.
Conclusion
We have succeeded in aligning self-assembled structures by using a lithographically defined stripe. This method can be used to increase long range ordering in magnetic storage systems without compromising the density. We have also shown that the hexagonal symmetry of the resulting inverse sphere Ni arrays can be simulated using the approach presented above.

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