1. Introduction

Laser interaction with matter leading to formation of various kinds of surface structures, such as ripples [1, 2, 3, 4], surface waves [5, 6], and micro/nano structures [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] has been widely reported for semiconductors [1, 2, 3, 4, 7], metals [3, 10, 11, 12], and insulators [18, 19]. These surface structures are usually formed inside the laser irradiated spot and have semiperiodicity from hundreds of nanometers to several micrometers in length. For instance, the ripple structures usually show the period in the order of the laser wavelength and their formation mechanism has been attributed to the interference between parts of the incident laser beam with the scattered light from material surface. It has been shown that the orientation of ripples is dependent on laser polarization and their periods can also be affected by laser fluence, wavelength, and angle of incidence. On the other hand, the periodicity of other structures such as micro/nanostructures and concentric ringlike morphological structures formed after the femtosecond and picosecond laser irradiation process on silicon show no direct wavelength dependence [6]; rather, their periodicity is more likely dependent on thermal processes involved in laser–matter interaction.

Recently, another type of laser-induced periodic surface structure has been reported—periodic arrays of nanoprotrusions or dots [20, 21, 22, 23, 24]. Like ripples, these periodic arrays of dots or protrusions show remarkable order and periodicity close to the wavelength of the laser. Guan et al. reported the observation of 2D-ordered nanoprotrusions in silicon [20] and ordering of nickel catalyst [21] by using a Lloyd mirror setup. Longstreth-Spoor et al. produced periodic nanostructures on Co coated Si by a two-beam interference technique [22]. Nishioka and Horita produced Si and Ni dots by directly exposing thin films of Si and Ni deposited on ${\mathrm{SiO}}_2$ to laser beams [23]. After a ripple structure was generated due to melting and surface tension, they rotated the sample by $90°$ and exposed again to create 2D periodic structures. Very recently, Xiao et al. created 2D-ordered gold nanostructures by direct laser exposure through a mask [24]. Lu et al. reported nanosphere enhanced periodic nanopatterning of silicon surface by laser irradiation [25]. Medvid et al. observed the phenomena of 2D periodic structure formation in Ge upon nanosecond laser irradiation; however, their patterns did not exhibit well-formed structures and also their period did not show any dependence on laser wavelength [26].

In this paper, we report the observation of spontaneous formation of self-organized 2D periodic arrays of nanostructures (protrusions) by directly exposing a silicon surface to multiple nanosecond laser pulses in a vacuum environment (base pressure $1\mathrm{mbar}$). The periods of these nanostructures are in the order of the laser wavelength and the periodicity can be controlled by changing the laser wavelength. These self-organized 2D periodic nanostructures are produced toward the edge as an annular region around the laser spot. We have provided a possible mech anism to explain the formation based on combined optical and thermodynamic effects under a highly nonequilibrium condition. The observed 2D-ordered nanostructure formation process does not require any additional optics, masking, or sample preparation. By moving the sample under the laser beam or having a larger spot, it is possible to create a large area covered with periodic nanostructures.

2. Experiment

Cleaved pieces of p-type Si (100) wafers (resistivity $10\mathrm{\Omega }\mathrm{cm}$ and thickness $~420\mathrm{\mu m}$) are irradiated using a fiber laser from IPG Photonics (Model # YLP-RA-1-50-30-30) operating at $1064\mathrm{nm}$ wavelength with pulse duration of $50\mathrm{ns}$ and a pulse repetition rate of $30\mathrm{KHz}$. Laser pulses were delivered at the time interval of $33\mathrm{\mu s}$ between pulses. The laser beam is randomly polarized with a Gaussian beam profile having ${\mathrm{M}}^2\sim 1.5$. The laser beam is focused on to the Si surface placed inside a vacuum chamber (base pressure $~1\mathrm{mbar}$). Average laser power and the number of laser pulses deliverd on to the sample surface are controlled by WinLase LAN software that drives the laser system. A vacuum chamber is placed on a computer controlled $X–Y$ stage to generate an array of laser spots at different positions on the sample surface by translating the stage to desired positions. Si samples were mounted on the stainless steel base plate for proper thermal contact. The focusing is done by using a plano-convex lens of focal length $500\mathrm{mm}$. The sample is placed at the focal point and the spot size is measured by exposing a corner region ($1\mathrm{mm}$ away from both edges) of a $2\mathrm{cm}\times 2\mathrm{cm}$ Si wafer to approximately 500,000 laser pulses. The native oxide from the Si surface prior to laser irradiation is not removed. Laser exposed spots are characterized by scanning electron microscopy (SEM) (Zeiss SUPRA 40), atomic force microcopy (AFM) (Digital Instruments Nanoscope III), and profilometry (Dektak profilometer from Vecco) for surface morphology.

Optical diffraction properties of laser induced 2D periodic structures are studied by focusing a $488\mathrm{nm}$ wavelength laser beam from an argon ion laser source onto the laser irradiated spot, and the diffraction pattern projected on a screen is photographed.

3. Results and Discussion

3A. Morphological Analysis of a Laser Irradiated Spot

Figure 1a shows the SEM image of a laser irradiated spot that is created by exposing an Si surface to 20,000 pulses at a fluence of $~3\mathrm{J}/{\mathrm{cm}}^2$. The spot has four distinct regions as shown in Fig. 1b. Region one is shown in Fig. 1c. This is the central region of the spot, which appears smooth and has few sporadic nanoparticles (size $~100\mathrm{nm}$). This is the region where laser fluence is high due to the Gaussian shape of the laser pulse. Region two [shown in Fig. 1d] shows weblike segregation of nanoparticles. Here, no ordering of nanoparticles is observed because this is a transition between central to outer region and these are laser-ablated particles landing on the surface. Region three (also shown in Fig. 1e at higher magnification) shows periodic arrangements of nanoprotrusions extending outward with increasing height. Region four (shown in Fig. 1f at higher magnification) shows the 2D periodic arrangement of well-developed nanostructures. These self-organized 2D periodic nanostructures are produced toward the edge as an annular region around the laser spot. The period of the nanostructures is about the wavelength of the incident radiation ($~1064\mathrm{nm}$).

Our experimental results show that marks formed near the edge of the sample at higher laser fluence ($3\mathrm{J}/{\mathrm{cm}}^2$) and a higher number of pulses destroys the nanostructures in the central region of the circular spot because of the high laser intensity and localized temperature buildup. For the laser conditions used for creating this spot (wavelength, $1064\mathrm{nm}$; pulse energy density, $3\mathrm{J}/{\mathrm{cm}}^2$), it is estimated that melting with a single pulse is not possible. However, exposing the same spots with thousands of pulses raises the temperature (due to heat accumulation) high enough to cause melting (as evident from the SEM images in Fig. 1) and ablation (evident from the large numbers of nanoparticles). For a lower number of pulses we do observe structure formation, but long range ordering is not found and the central region of the laser spot does not show as much melting like in Fig. 1c.

Figure 2a shows the profilometry result taken across the diameter of the laser-irradiated spot discussed in Fig. 1a. It is clear from the figure that the profiling of the laser spot shows all four distinct regions discussed earlier. Individual nanoprotrusions are not resolved due to the larger diameter of the profilometer tip used for this measurement. The central region is a crater formed due to multishot exposure. The rim of the laser spot shows the other three respective regions (two to four). An AFM scan of the region toward the edge of the spot is shown in Fig. 2b. The image indicates that the heights of these nanostructures are around $500\mathrm{nm}$ with tip diameter $~100\mathrm{nm}$. Also, structures are formed in the rim region where material from the central region has been pushed to the rims. From Fig. 2, assuming the region one as a paraboloid and cross section of the piled edge as triangular (combining regions two to four), the volume of material removed from the pit is $19600{\mathrm{\mu m}}^3$ and the one piled up at the edge is about $11000{\mathrm{\mu m}}^3$. The difference in the volume could account for the ablated particles.

3B. Effect of the Number of Laser Pulses on Nanostructure Formation

The absorption coefficient of Si at $1064\mathrm{nm}$ is $~9.35{\mathrm{cm}}^{-1}$ and, hence, the penetration depth of laser light is $~1\mathrm{mm}$. Therefore, light absorption takes place over the entire thickness of the wafer. Therefore, for our laser fluence condition ($~0.9\mathrm{mJ}$ pulse energy, $~200\mathrm{\mu m}$ spot size) and for single-shot exposure, the temperature of the substrate under the laser beam can rise to a maximum value of $11.5°\mathrm{C}$ above room temperature. (This number is based on calculation using $dQ=C_{p}dT$, where $dQ$ is energy absorbed, $C_p$ is specific heat, and $dT$ is rise in temperature.) This is a rough estimate for temperature realizing that there is heat conduction during the laser pulse duration. In order to raise the temperature further, a sufficient number of laser pulses have to be impinged before heat is dissipated. We have noticed that for a given fluence and number of pulses, the marked spot sizes vary considerably over the wafer surface (smallest at the center of the wafer and largest at the corner, if a square wafer is used). In order to study this effect, we used a $2\times 2{\mathrm{cm}}^2$ Si wafer and created a matrix of 10 by 10 spots [a schematic diagram is shown in Fig. 3a. Please note that Fig. 1 corresponds to the top left corner, as shown in the Fig. 3a]. Diameters of the laser-irradiated marks are larger for the spots toward the edge (highest being the corner points), compared to those toward the center of the wafer. Experimental conditions are kept the same [as in the case of Fig. 1a] for all spots. The spot sizes (diameters) are then measured and plotted [see Fig. 3b]. It is evident from the figure that the corner spots have the highest di ameters because of the faster heat buildup (due to less heat loss) compared to other regions. The slight variation in the diameters of the four corner points in Fig. 3b reflects slight error in the exact positioning of the sample under the laser beam. The spot shown in Fig. 3c is the spot that is near to the central region of the $2\times 2{\mathrm{cm}}^2$ Si wafer. While all the experimental conditions are kept the same for all 100 spots, the measured spot size of the central region is much smaller compared to the corner ones [as shown in Fig. 3b]. It is interesting that since heat buildup in the central region of the wafer is not high enough (due to faster diffusion), the nanostructures in the center of the marked spot in this region are not wiped out [see Fig. 3d]; although the marked spot size has been reduced sufficiently.

Because of the Gaussian nature of the beam profile, the laser intensity is higher in the central region of the irradiated spot compared to the edges. For a given fluence, therefore, intensity is high for the central region of the marked spot. In this work we kept our fluence to $~3\mathrm{J}/{\mathrm{cm}}^2$. With this fluence and for 20,000 laser shots, and when the spots are fabricated toward the edge of the wafer, we see that no nanoprotrusion formation occurs at the central region of the marked spots; however, nanoprotrusion formation occurs toward the edge of the marked spot. Now, under the same condition, when we mark a spot in the interior region of the wafer, we see that nanoprotrusion formation occurs at the center of the marked spot and no structure formation is observed toward the edge. The reason for this is that the heat diffusion is fast for the mark generated at the interior region of the wafer, where even the high intensity central region of the Gaussian pulse could not destroy the nanoprotrusion.

3C. Nanostructures and Optical Diffraction Properties

Next we studied the optical diffraction behaviors from these periodic nanostructures. The Fraunhofer diffraction patterns from the areas toward the edge of the laser spot are shown in Fig. 4a. The zeroth-order diffraction beam is reflected back to the laser through a small hole in the screen. The first diffraction orders are visible as the hexagonally arranged bright spots in the figure [see the inset in Fig. 4b]. The second orders are also arranged hexagonally but less visible due to lower diffraction efficiency.

By analyzing the position of the first-order spots arranged in a hexagon, it is possible to infer that the periodic nanostructures have three degrees of symmetry or, in other words, have periodicities in three directions as shown by the lines in Fig. 4b. Each of the three periodicities would then produce two first-order spots (positive and negative) in a direction perpendicular to the periodicity. For example, the vertical periodicity, labeled P1 in Fig. 4b corresponds to the horizontal spots in the hexagonal diffraction pattern shown in the inset and labeled D1. A similar analysis applies to the two remaining periodicities, P2 and P3, and their diffraction orders, D2 and D3.

As mentioned earlier, the separation between the nanoprotrusions along the same periodic direction is approximately $1064\mathrm{nm}$, which is the wavelength of the laser used to create them. Experimentally, the first diffracted order occurred at $29.6°$ and the second one at about $75°$.

To predict how the diffraction patterns would look, it is possible to use a technique that is used in the study of crystallographic structures, which is to use the Fourier transform of the lattice crystal structure. The resulting transform is the diffraction pattern that would be observed from the lattice structure. The same process can be done graphically using image analysis software. A graphical Fourier transform of an image simply collects the gray-scale information of each individual pixel in the image and it is possible to generate a frequency plot of the collected gray-scale information. This frequency plot happens to be analogous to the diffraction pattern observed for the grating architecture. The Fourier Transform Lab-Student Edition program is used to generate the graphical Fourier transforms of the scanning electron micrograph images of the periodic structures [27]. Figure 4b shows the area of periodic arrangement and its graphical Fourier transform [Fig. 4c]. The arrangement in the nanostructures can be described by a hexagonal or a rhomboidal unit cell, as seen in Fig. 4b, and can be said to be hexagonally close-packed. Similar diffraction patterns have been observed from inverse opal photonic crystal structures arranged in hexagonal close-packed arrays [28]. There is a good similarity between the observed diffraction patterns for the inverse opal structures and the 2D-ordered nanoprotrusions we generated. It is because the structures that originate them have the same type of hexagonal close-packed architectures.

3D. Possible Formation Mechanisms

In this study we observe four distinct phenomena: (a) complete melting, formation of central crater and rim (central region of the spot); (b) formation of nanoparticles; (c) ordered periodic structures whose heights are $~100\mathrm{nm}$; and (d) formation of 2D- ordered nanostructures (protrusions). Formation of nanoparticles is a clear indication of laser-induced ablation and redeposition; whereas, ordered 2D nanostructures with periodicity equal to the laser wavelength is a clear indication of the optical phenomena involved. The formation of a crater and rim indicates the motion of the material from the central region to the outside is possible due to the Marangoni effect [29, 30, 31, 32]. In order to understand the role of optical effect, we doubled the frequency of the laser beam using second harmonic generation, and carried out similar experiments. Nanoprotrusion formation occurred and the periodicity was measured as $~532\mathrm{nm}$ [shown in Fig. 5a]. In addition to nanoprotrusions, we also observed ripple structures (period $~532\mathrm{nm}$) for frequency-doubled light. Please note that the absorption coefficients for Si at $1064\mathrm{nm}$ and $532\mathrm{nm}$ are $9.35{\mathrm{cm}}^{-1}$ and $6550{\mathrm{cm}}^{-1}$, respectively. Because of the strong light absorption for $532\mathrm{nm}$, no edge effects (position-dependent formation) were observed for this wavelength. While the exact mechanism of formation of such 2D structures is under investigation, a possible mechanism that could give rise to such periodic nanostructures is discussed below.

Multiple laser pulse irradiation raises the temperature of the central region of the irradiated spot to cause melting and ablation. As the laser intensity increases, surface temperature also increases, while surface tension will decrease. Ablated particle size will increase with an increase in laser power, which can affect the inhomogeneity of the surface. This inhomogeneity will introduce a temperature gradient. Because of the Marangoni effect, molten material from the central hotter region is pushed to the outer region causing a rim formation. However, the inhomogeneity caused due to the ablated particles in the outer region causes further irradiating light to diffract and create energy redistribution due to constructive and destructive interference. Since the material is still in the molten state in the outer region, the diffraction-induced temperature gradient engenders a microscale Marangoni effect, which pushes molten material from the hotter to the colder region. When that happens, a small protrusion appears due to materials from the outside being pushed in. A high-tilt SEM image, shown in Fig. 5b, clearly shows this effect. The nanoprotrusions survive in the outer regions because of the faster cooling compared to the central region where structures are destroyed due to excessive heat and flow. This also may be the reason why nanoprotrusion heights gradually decrease as we move from outer to inner regions.

4. Conclusions

In conclusion, we report a phenomenon of spontaneous formation of self-organized 2D periodic arrays of nanostructures (protrusions) by directly exposing a silicon surface to multiple nanosecond laser pulses in a vacuum environment (base pressure $1\mathrm{mbar}$) at wavelengths of 1064 and $532\mathrm{nm}$. The heights of these nanostructures are around $500\mathrm{nm}$ with tip diameter $~100\mathrm{nm}$. The period of the nanostructures is order of wavelength and can be tailored by changing the wavelength of the incident radiation. Possible formation mechanisms of these structures have been discussed based on the combination of optical and Marangoni effects. The periodic nanostructure process is relatively simple and does not require any complexity of optics or sample preparation. Light diffraction from these nanostructures indicates a threefold symmetry, which is in accordance with the observed morphological symmetry of these structures. These nanostructures can find applications as optical elements or sensor devices.

We acknowledge the National Aeronautics and Space Administration (NASA) Langley Professor Program for the financial support.

 

Fig. 1 (a) SEM image of a mark generated by exposing the Si surface to 20,000 laser pulses at fluence $~3\mathrm{J}/{\mathrm{cm}}^2$. (b) The spot shown in (a) has four characteristic regions indicated by numbers 1–4. Figures (c)–(f) respectively, show the higher magnification images of 1–4 characteristic regions indicated in (b).

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Fig. 2 (a) Surface profiling across the spot shown in Fig. 1a showing all the four distinct regions. (b) AFM scan of a region toward the edge of the laser spot shown in Fig. 1a.

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Fig. 3 (a) Schematic diagram showing the 100 laser spots marked on a $2\times 2{\mathrm{cm}}^2$ Si wafer as a matrix of 10 by 10 and their size distribution after marking. (b) 3D plot of the measured diameter of laser spots for the matrix of spots stated in (a). The number of laser pulses for each spot is kept at 20,000 pulses and fluence $~3\mathrm{J}/{\mathrm{cm}}^2$. (c) SEM image of one of the spots from the 100 spots in (a), which is near the center of the wafer. (d) Higher magnification image of (c).

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Fig. 4 (a) Diffraction pattern from the periodic nanostructures shown in Fig. 1f. (b) SEM image of a 2D periodic structure showing different orientations for symmetry. Inset shows the diffraction pattern showing the same symmetry as of the structures. (c) Fourier transform of the nanostructures shown in (b).

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Fig. 5 SEM image of (a) nanoprotrusions obtained by $532\mathrm{nm}$ wavelength laser pulses and (b) nanoprotrusions shown at higher tilt (tilt angle $70°$).

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