**2.3 Periodic pit-pattern obtained by NSL and chemical etching**

Periodic pit-pattern can be obtained in combination of NSL and selective chemical etching (Chen et al., 2009). The processes mainly involves three steps: (i) self-assembling monolayer of PS spheres on hydrogenated Si surface; (ii) forming a novel net-like Au-Oxide mask via Au catalyzed oxidation; (iii) resulting in periodic pits by selective chemical etching of Si in KOH solution.

A Feasible Routine for Large-Scale Nanopatterning via Nanosphere Lithography 539

The periodicity and the size of the pits were determined by the diameter of PS spheres. The period of the patterned pits is in fact equal to the diameter of PS spheres. This indicates that the period of ordered pits can be readily changed by using PS with corresponding diameter, as demonstrated in Fig 5. In addition, the lateral size of inverted-pyramid-like pits was essentially decreased linearly with the diameter of PS, as shown in Fig.6. This is mainly because the area underlying the PS spheres for etching is nearly proportional to the projection of PS spheres on Si substrates. Moreover, according to the fitting line in Fig. 6, the lateral size of pits will decrease to be zero when the diameter of spheres equals to ~40nm. This result can be explained by the fact that the Au-catalyzed SiO2 partially fill up the region underlying the PS. It means that the minimum period of patterned pits can be down to 40 nm by present method. On the other hand, any dispersion of the diameter of PS will degrade the ordering of the pits near this limit. Thus, before approaching the limit of the nanosphere lithography, more uniformed PS is required so that homogenous and ordered

Fig. 5. Representative SEM images of pit-patterns with a periodicity of: (a) 1.6 um (after 1 minute etching), (b) 500 nm (after 3 minutes etching), (c) 200 nm (after 3 minutes etching),

small pits can be obtained.

(d) 100 nm (after 1 minute etching).

Fig. 3. Schematic illustration for the fabrication of ordered pit-pattern using nanosphere lithography.

The experimental processes are schematically illustrated in Figure 3. It starts with selfassembling monolayer of PS spheres onto hydrogenated Si (001) substrates. The PS spheres with different diameters of 100nm, 200nm, 500nm, 600nm or 1.6 μm were used. All PS sphere suspensions were purchased from Duke Scientific Corporation. The Si (001) substrates were chemically cleaned and hydrogenated by a subsequent HF dip. The close-packed monolayer of PS spheres was self-assembled on the surface of DI water as mentioned above, which was then transferred onto Si (001) substrates immersed in DI water by draining away the DI water. Fig. 4 shows a large-area highly ordered PS spheres on a hydrogenated Si substrate.

Fig. 4. Representative SEM image of self-assembled monolayer of PS spheres with a diameter of 500 nm on a hydrogenated Si (001) substrate.

The ordered PS spheres in a hexagonal lattice on Si substrate then serves as a mask for thermal evaporation of Au. After deposition of about 1 nm Au onto the PS spheres covered substrates, six Au particles around each PS spheres on Si surface were obtained. Because Au is directly deposited onto the Si surface without SiO2, Si adjacent to Au particles then electrochemically oxidizes, or anodizes upon exposure to air (Robinson et al., 2007). As a result, an Au-oxide mask was naturally formed, as illustrated in Fig. 3(b). To avoid oxidation of the Si surface underlying PS spheres, the samples were immediately rinsed in tetrahydrofuran to remove PS spheres and then etched in 20% KOH solution at room temperature. Since Au-oxide mask protects the underlying Si from KOH etching, well ordered and uniformed 2D pit-pattern was then formed.

Fig. 3. Schematic illustration for the fabrication of ordered pit-pattern using nanosphere

4 shows a large-area highly ordered PS spheres on a hydrogenated Si substrate.

Fig. 4. Representative SEM image of self-assembled monolayer of PS spheres with a

The ordered PS spheres in a hexagonal lattice on Si substrate then serves as a mask for thermal evaporation of Au. After deposition of about 1 nm Au onto the PS spheres covered substrates, six Au particles around each PS spheres on Si surface were obtained. Because Au is directly deposited onto the Si surface without SiO2, Si adjacent to Au particles then electrochemically oxidizes, or anodizes upon exposure to air (Robinson et al., 2007). As a result, an Au-oxide mask was naturally formed, as illustrated in Fig. 3(b). To avoid oxidation of the Si surface underlying PS spheres, the samples were immediately rinsed in tetrahydrofuran to remove PS spheres and then etched in 20% KOH solution at room temperature. Since Au-oxide mask protects the underlying Si from KOH etching, well

diameter of 500 nm on a hydrogenated Si (001) substrate.

ordered and uniformed 2D pit-pattern was then formed.

The experimental processes are schematically illustrated in Figure 3. It starts with selfassembling monolayer of PS spheres onto hydrogenated Si (001) substrates. The PS spheres with different diameters of 100nm, 200nm, 500nm, 600nm or 1.6 μm were used. All PS sphere suspensions were purchased from Duke Scientific Corporation. The Si (001) substrates were chemically cleaned and hydrogenated by a subsequent HF dip. The close-packed monolayer of PS spheres was self-assembled on the surface of DI water as mentioned above, which was then transferred onto Si (001) substrates immersed in DI water by draining away the DI water. Fig.

lithography.

The periodicity and the size of the pits were determined by the diameter of PS spheres. The period of the patterned pits is in fact equal to the diameter of PS spheres. This indicates that the period of ordered pits can be readily changed by using PS with corresponding diameter, as demonstrated in Fig 5. In addition, the lateral size of inverted-pyramid-like pits was essentially decreased linearly with the diameter of PS, as shown in Fig.6. This is mainly because the area underlying the PS spheres for etching is nearly proportional to the projection of PS spheres on Si substrates. Moreover, according to the fitting line in Fig. 6, the lateral size of pits will decrease to be zero when the diameter of spheres equals to ~40nm. This result can be explained by the fact that the Au-catalyzed SiO2 partially fill up the region underlying the PS. It means that the minimum period of patterned pits can be down to 40 nm by present method. On the other hand, any dispersion of the diameter of PS will degrade the ordering of the pits near this limit. Thus, before approaching the limit of the nanosphere lithography, more uniformed PS is required so that homogenous and ordered small pits can be obtained.

Fig. 5. Representative SEM images of pit-patterns with a periodicity of: (a) 1.6 um (after 1 minute etching), (b) 500 nm (after 3 minutes etching), (c) 200 nm (after 3 minutes etching), (d) 100 nm (after 1 minute etching).

A Feasible Routine for Large-Scale Nanopatterning via Nanosphere Lithography 541

Well ordered GeSi nano-islands were obtained by deposition of Ge on such pit-patterned Si (001) substrates using molecular beam epitaxy (Chen et al., 2009), as shown in Fig. 8(c). Such preferential formation of GeSi nano-islands within each pit is energetically favorable under the assistance of growth kinetics (Zhong et al, 2007; Zhong et al., 2008). In comparison, GeSi nano-islands on a flat substrate under identical growth conditions are random, as shown in Fig 8(d). With decreasing the periodicity of the pit-pattern by using small PS spheres, higher density of smaller GeSi nano-islands in a hexagonal lattice are expected, which can facilitate

Fig. 7. SEM image of a pit (the diameter of PS spheres used is 600 nm) obtained after etching

of (a) 2 minutes, (b) 3 minutes, (c) 5 minutes, (d) 7 minutes. The scale bar is 200 nm.

the investigation of size-dependent quantum confinement effect of nano-islands.

Fig. 6. Mean lateral size vs periodicities of pits. The broken curve is a fitting line.

Moreover, the shape of pits can be tuned by controlling KOH etching time. Depending on the etching time, three types of pits can be obtained. At the beginning of etching, shallow pits with rounded open-mouth (type I pits) can be obtained, as shown in Fig. 7 (a). For an intermediate etching time, inverted truncated-pyramid-like pits with {111} facets and flat (001) bottom (type II pits) are obtained, as shown in Fig. 7 (b). After sufficiently long etching time, inverted pyramid-like pits with {111} facets (type III pits) are obtained, as shown in Fig. 7 (c) and (d). Such a shape evolution with etching time is related to the anisotropic etching rate of Si by KOH solution (up to 100:1 for the etching of Si along <100> and <111> direction at room temperature). As a result, {111} facets will finally appear in the pits. The depth of type III pits approximates to be / 2 (54.7 ) *<sup>o</sup> w tg* , where *w* is the lateral size of pits with sidewalls of {111} facets having slope angle of 54.7o. In addition, the etching time corresponding to each type of pits depends on the periodicity of the patterned pits. As described above, a larger periodicity of patterned pits is accompanied with a larger area region for etching,which gives rise to a larger pits. It takes time to form the sidewalls of pits completely with {111} facets from their appearance. The larger pits will have larger area sidewalls, as results in longer etching time corresponding to different types of pits. Therefore, the pits with a periodicity of 1.6 μm in Fig. 5 (a) are of type I. The pits with a periodicity of 500 nm in Fig. 5 (b) are actually of type II. The pits with a periodicity of 200 nm and 100 nm in Fig. 5 (c) and (d) are of type III. It has been found that some materials growth on Si substrates was orientation-dependent (Zhang et al., 2008). Such patterned Si substrates with the coexistence of spatially ordered (001) surface and {111} facets may provide potential templates to form ordered unique nanostructures of orientation dependence.

Fig. 6. Mean lateral size vs periodicities of pits. The broken curve is a fitting line.

dependence.

Moreover, the shape of pits can be tuned by controlling KOH etching time. Depending on the etching time, three types of pits can be obtained. At the beginning of etching, shallow pits with rounded open-mouth (type I pits) can be obtained, as shown in Fig. 7 (a). For an intermediate etching time, inverted truncated-pyramid-like pits with {111} facets and flat (001) bottom (type II pits) are obtained, as shown in Fig. 7 (b). After sufficiently long etching time, inverted pyramid-like pits with {111} facets (type III pits) are obtained, as shown in Fig. 7 (c) and (d). Such a shape evolution with etching time is related to the anisotropic etching rate of Si by KOH solution (up to 100:1 for the etching of Si along <100> and <111> direction at room temperature). As a result, {111} facets will finally appear in the pits. The depth of type III pits approximates to be / 2 (54.7 ) *<sup>o</sup> w tg* , where *w* is the lateral size of pits with sidewalls of {111} facets having slope angle of 54.7o. In addition, the etching time corresponding to each type of pits depends on the periodicity of the patterned pits. As described above, a larger periodicity of patterned pits is accompanied with a larger area region for etching,which gives rise to a larger pits. It takes time to form the sidewalls of pits completely with {111} facets from their appearance. The larger pits will have larger area sidewalls, as results in longer etching time corresponding to different types of pits. Therefore, the pits with a periodicity of 1.6 μm in Fig. 5 (a) are of type I. The pits with a periodicity of 500 nm in Fig. 5 (b) are actually of type II. The pits with a periodicity of 200 nm and 100 nm in Fig. 5 (c) and (d) are of type III. It has been found that some materials growth on Si substrates was orientation-dependent (Zhang et al., 2008). Such patterned Si substrates with the coexistence of spatially ordered (001) surface and {111} facets may provide potential templates to form ordered unique nanostructures of orientation Well ordered GeSi nano-islands were obtained by deposition of Ge on such pit-patterned Si (001) substrates using molecular beam epitaxy (Chen et al., 2009), as shown in Fig. 8(c). Such preferential formation of GeSi nano-islands within each pit is energetically favorable under the assistance of growth kinetics (Zhong et al, 2007; Zhong et al., 2008). In comparison, GeSi nano-islands on a flat substrate under identical growth conditions are random, as shown in Fig 8(d). With decreasing the periodicity of the pit-pattern by using small PS spheres, higher density of smaller GeSi nano-islands in a hexagonal lattice are expected, which can facilitate the investigation of size-dependent quantum confinement effect of nano-islands.

Fig. 7. SEM image of a pit (the diameter of PS spheres used is 600 nm) obtained after etching of (a) 2 minutes, (b) 3 minutes, (c) 5 minutes, (d) 7 minutes. The scale bar is 200 nm.

A Feasible Routine for Large-Scale Nanopatterning via Nanosphere Lithography 543

A scalable approach to fabricate periodic nanopatterning in a large-scale area with controllable periodicity using nanospheres, so called NSL, has been developed. The NSL generally started with self-assembling monolayer of PS spheres on the substrates, which can be obtained by various methods. One potential routine to obtain ordered monolayer of PS spheres is via self-assembling PS spheres at the interface between water and air. Such a regular arrangement of monolayer PS spheres in a hexagonal lattice resulted from the balance between an electrostatic repulsion among adjacent spheres and a capillary attraction due to the deformation of liquid meniscus by electrostatic stresses. An external electrical field perpendicular to the water surface, which affected the interaction between PS spheres, could efficiently improve the ordering of PS spheres, particularly of small PS spheres. The interplay among PS spheres can also be affected by changing the surface chemistry of PS spheres or the electrostatic environment of the water-air interface, which can be readily realized by mixing some electrolytes, such as solution of H2SO4 or NaCl. In addition, it was found that the ordering of PS spheres was improved on the water of ~ 4 oC mainly due to the increase of water surface tension and the suppression of the Brownian motion of the PS spheres and dust clusters in the water. This ordered monolayer PS spheres could be transferred onto the substrate placed previously inside water by draining off the water. This method facilitates large-area highly ordered monolayer of PS spheres on substrates,which can act as a mask or a template for subsequent lithography to obtain ordered nano-wires or nano-pits, or for subsequent growth of desired nanostructures. Two-dimensionally ordered nanopattern with a periodicity equal to the diameter of PS spheres in the range of several micrometers to less than 100 nm could be readily obtained. The geometrical profiles of the nanopattern could be modulated by controlling the etching conditions. NSL has been exploited in fabricating ordered nano-wires and nano-dots. This technique was characterized by its low-cost,high throughput, and easy manipulation for producing largescale periodic patterns. More interestingly,NSL can be applied to obtain nanostructures of various materials on many kinds of substrates, which will facilitate the production of

This work was supported by the special funds for Major State Basic Research Project No.

Aizpurua, J.; Hanarp, P.; Sutherland, D. S.;K€all, M.; Bryant, G. W.; Garcia, D.; & Abajo, F. J. (2003) Optical Properties of Gold Nanorings. *Phys. Rev. Lett*. 90, 057401 (1-4) Albrecht, M.; Hu, G. H.; Guhr, I. L.; Ulbrich, T. C.; Boneberg, J.; Leiderer, P.; & Schatz, G.

Andres, R. P.; Bielefeld, J. D.; Henderson, J. I.; Janes, D. B.; Kolagunta, V. R.; Kubiak, C. P.;

Superlattice of Molecularly Linked Metal Clusters. *Science* 273, 1690-1693

Mahoney, W. J.; & Osifchin, R. G. (1996) Self-Assembly of a Two-Dimensional

(2005) Magnetic multilayers on nanospheres. *Nat. Mater*. 4, 203-206

**3. Conclusions** 

varieties of ordered nanostructures.

**4. Acknowledgements** 

2011CB925600 of China.

**5. References** 

Fig. 8. AFM images (1×1 um2) of (a) pit-pattern with a periodicity of 200 nm, (b) pit-pattern after Si buffer layer growth, (c) ordered GeSi nano-islands after deposition of 10 monolayers Ge by molecular beam epitaxy on a pit-patterned Si (001) substrate, (d) Randomly distributed GeSi nano-islands grown under the same conditions on a flat Si (001) substrate. The unit of height bar is nm.
