Because of the versatility of silicon as a material for electronics and photonic integration, there has been a strong emphasis on incorporating optoelectronics functionality in it [1]. The main challenges in this direction are the development of efficient light emission from silicon (Si) because of its indirect minimum-energy bandgap and its centrosymmetric crystalline structure, hindering its use as electro-optic modulator [2]. Although some optical functionalities of Si have been incorporated in a single platform with microelectronic devices, but for greater applicability, complex optical components, such as switches, nonlinear optical devices with inherent prerequisite of high speed and low power consumption are required [1,2]. There are reports on the use of the third- or higher-order nonlinearities of Si for amplification and lasing, wavelength conversion, and optical processing [2,3]. However, these higher order nonlinearities require relatively high optical powers and are not very efficient. In addition, for c-Si, the second-order term of the nonlinear susceptibility tensor is forbidden in dipole approximation because of its centrosymmetry, and the residual higher-multipole processes are weak for practical applications [4]. However, the inversion symmetry can be broken using inhomogeneous strain and, thereby, inducing second-order nonlinear susceptibility [5 –7]. In addition, the crystal symmetry is broken spontaneously at the surface, thus making processes like second-harmonic generation (SHG) feasible. Surface SHG was predicted theoretically by Bloembergen and Pershan [8] and, subsequently, demonstrated experimentally [9]. Both structural and optical field discontinuities can contribute to surface SHG [10]. While this property has been developed and exploited for probing planar surface/interfaces [11,12], it is expected to apply for all nonplanar geometries. Indeed, recent experiments have clearly demonstrated the generation of surface second harmonic in nanopillar geometry [13]. In addition, there have been reports on second harmonic generation from Si surface or from Si photonic crystal structures [14,15]. To enhance the surface SHG, it is desirable to have more surface-to-volume ratio and high optical excitation field at the surface. In this context, the pillar geometry is definitely a promising case for investigation. Utilizing the high surface-to-volume ratio and appropriate field distributions, Si pillars have been used for applications such as biosensors [16,17]. There is also a report on SHG in Si, where strained Si nanowire of sub 100 nm is used to enhance SHG [18].

In this work, we have investigated efficient surface SHG from hexagonal Si pillar arrays fabricated by a top-down approach. We used a pump-probe setup in reflection geometry for SHG measurements, with the pump wavelength at 1030 nm to generate green light at 515 nm. We demonstrate a strong dependence of the generated SHG on the pillar geometry; whereby, we simulated the distribution of the electric field to show the suitability of a particular structure for enhanced SHG. We show that the enhancement of the SHG intensity is directly correlated with the optical excitation field with the requirement of higher surface normal component of the $\mathbf{E}$-field. The efficient SHG light with the easy-to-fabricate Si pillars, along with its strong surface sensitivity, will be useful for nonlinear silicon photonics and for surface/interface characterization and high-resolution optical biosensing [19].

Single crystalline (100) oriented Si wafers were used for fabricating the pillar arrays. We use colloidal lithography and plasma dry etching for fabrication of the Si pillar arrays, which leads to hexagonal arrays of Si pillars. The fabrication details are given elsewhere [20]. All the fabricated pillars have slightly tapered profiles, more like truncated cones, because of process related limitations. Three distinct pillars sample sets, namely “A”, “B”, and “C”, have been fabricated and are shown on Fig. 1; pillar parameters are listed in Table 1.

 

Fig. 1. 30-deg tilted scanning electron microscope (SEM) images of the Si pillar samples.

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Table 1. Parameter for Three Pillar Samples

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All the samples are cleaned in standard organic solvents followed by RCA clean to remove any surface contamination created during the etching process [21]. Here we note that high-resolution SEM images indicate similar surface (sidewall) roughness of the order of 10–20 nm in all the samples.

We have performed the SHG measurements at room temperature (RT) in reflection geometry with a femto second laser pump source operating at 1030 nm wavelength. The pulse duration is 350 fs; the repetition rate is 500 KHz; and the $P_{\mathrm{avg}}$ is 1.3 W. The estimated laser spot diameter of 20 μm corresponds to an energy density of $0.65\mathrm{J}/{\mathrm{cm}}^2$. The pump polarization is along the “x-axis,” which is parallel to the cleaved facet of the Si samples (at a 45 degree angle to the crystallographic axis of the Si wafer). The generated SH light is collected with a multimode optical fiber (Ensign-Bickford-HCRMO200T), transferred to a monochromator and, subsequently, to a single photon detector (Si avalanche photodiode-PerkinElmer SPCM). The measured SHG data from the different Si pillar samples are shown in Fig. 2. The generated SHG intensity shows a clear peak at 515 nm for all three samples, “A”, “B”, and “C”. It is observed that Sample “B” has the highest SHG, more than an order of magnitude higher (ratio) than Samples “A” and “C” showing dependence of the generated SHG on the pillar geometry. Referring to Table 1, sample B has a higher effective surface area normalized to the pump laser spot size as compared to Samples “A” and “C”, owing to its larger height. As one can see, the measured SHG in all three samples is not proportional to the surface area of pillars. It suggests that nonlinear polarization is generated on the sidewalls by a combined process of nonlinear reflection [8] with contribution from the pump coupled into the pillars. Therefore, influence on the SHG process is also attributed to the pillar diameter and the angle of tilted sidewall. In addition, to investigate the in-coupling of light to the structure, total reflection measurements for all three samples were performed (Fig. 3). As can be seen in Fig. 3, the reflectivity for all three samples is significantly less compared to plain Si (35% average reflectivity) for a measured wavelength range of 300–1100 nm. The lower reflection is attributed to impedance matching of the incident lightwave which depends on the shape and size of the pillars and the period of the pillar arrays. Particularly the lower reflectivity at 1030 nm wavelength corresponds to the best coupling for the pump for Sample “B”. For all the samples, at longer wavelengths, where Si is transparent, there is an increase in reflection because of the back surface [20].

 

Fig. 2. Experimental SHG data with source operating at 1030 nm wavelength.

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Fig. 3. Experimental total reflection data for all three samples at normal incidence.

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As discussed above, the higher available surface and the lower reflectivity suggest higher SHG for Sample B compared to Samples A and C. For further investigation of the light distribution in individual pillars in a hexagonal array, we use numerical simulations. A commercial Lumerical FDTD Solutions simulation tool[22] is used to calculate the optical field distribution for the pump wavelength (at 1030 nm) in three modeled pillar array structures using pillar dimensions and shapes from high-resolution SEM images of Samples A, B, and C. As described earlier, in centrosymmetric materials like Si, surface contribution to SHG nonlinearity results from the material discontinuity at the surface. The inversion symmetry is broken on the surface, thereby allowing a second-order nonlinear term in electric dipole approximation. It should also be pointed out that the SHG process is not influenced by the symmetry of the array, as the distance between surfaces of neighboring pillars is larger than ${\lambda }_{\mathrm{SHG}}/2$ and we are analyzing SHG process with individual pillars instead of entire array. In addition, a mismatch of dielectric constants at the interface (in our case Si pillar/air) leads to electric dipole and quadrupole contribution to the surface nonlinearity [10]. In both cases, the surface contribution to SHG requires intensity of the pump localized on the surface with the electric field polarization component normal to the Si pillar/air interface. It also corresponds to the strongest component of second-order nonlinear optical susceptibility on the surface of Si [1,23]. Here, we have separately simulated with both x-polarized and y-polarized plane wave pumps at normal incidence. However, because of the large period of the arrays, the results are identical and only results with an x-polarized pump light are included here. For all three pillars (case A, B, and C), the simulations use the same input plane-wave pump with the same electric field intensity. because of the high absorption of Si at the SHG wavelength, 515 nm, we are not considering coupling of SHG light to the guided modes. Because of the tilted walls of the pillars, the presented SHG process can be seen as a nonlinear reflection from Si pillar sidewalls with some contribution from the pump coupled to pillars. It means that the tangential component of the wave vector for scattered SHG light is twice the corresponding wave vector for the pump [8], which satisfies momentum conservation for SHG light propagating in air. Therefore, we assumed that the scattered SHG light intensity from the pillars is proportional to ${|E_{x,y}|}^4$ of the pump light at the surface along the pillar. Since similar surface properties are for Samples A, B, and C, the total scattered SHG light intensity, which is proportional to integrated ${|E_{x,y}|}^4$ at the surface, can be used to estimate the relative SHG intensities between the different pillars.

Figures 4(a)–4(d) show the distribution of the x-component of the electric field intensity (${|E_x|}^2$ in pillar “A”, together with the corresponding high-resolution SEM image. The intensity distribution in the vertical XZ cross sections of the pillar through $y=0$ is shown in Fig. 4(a), with Fig. 4(c) being the SEM image of the actual pillar. It is seen that there is significant surface normal pump intensity “hotspot” on the pillar/air interface, which extends over a total length of 500 nm. The XY cross section in Fig. 4(b), taken at $Z=950\mathrm{nm}$, shows the exact intensity distribution (${|E_x|}^2$) in that plane with the pillar circumference encircled (dotted line). The line plot of ${|E_x|}^2$ against $Z$ (height) on the surface of the pillar [along one of the dotted lines indicated in Fig. 4(a)] is shown in Fig. 4(d).

 

Fig. 4. FDTD simulation data and SEM image of Sample A. (a) X component of electric field intensity (${|E_x|}^2$) on XZ plane at $Y=0$; (b) ${|E_x|}^2$ on XY plane at $Z=950\mathrm{nm}$; (c) cross section SEM image of individual pillar; (d) line plot of ${|E_x|}^2$ along the length of the pillar on its surface.

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The simulation results for Sample “B”, together with the corresponding high-resolution SEM image, are shown in Figs. 5(a)–5(d). The ${|E_x|}^2$ distribution over the pillar length is shown in Figs. 5(a) and 5(c) shows its SEM image. The vertical XZ cross sections of the pillar through $y=0$ in Fig. 5(a) show a strong intensity “hotspot”’ on the pillar/air interface on the upper part of the pillar extending over a length of 1500 nm, although there is strong confinement of pump intensity inside the pillar as well. The XY cross section view in Fig. 5(b) at $Z=2800\mathrm{nm}$ (with encircled pillar circumference) also shows higher ${|E_x|}^2$ on the pillar surface. The line plot of ${|E_x|}^2$ against $Z$ along the surface of the pillar [along one of the dotted lines indicated in Fig. 5(a)] is shown in Fig. 5(d). It clearly shows that there is very strong transverse E-field intensity exactly on the pillar surface to contribute for surface SHG, supporting the observed high SHG intensity.

 

Fig. 5. FDTD simulation data and SEM image of Sample B; (a) X component of electric field intensity (${|E_x|}^2$) on XZ plane at $Y=0$; (b) ${|E_x|}^2$ on XY plane at $Z=2800\mathrm{nm}$; (c) cross section SEM image of individual pillar; (d) line plot of ${|E_x|}^2$ along the length of the pillar on its surface.

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Similarly, simulation results, together with the SEM image of the pillar for Sample “C”, are shown in Figs. 6(a)–6(d). As seen clearly in the XZ plane view [Fig. 6(a)] and the XY cross section at $Z$ 1400 nm [Fig. 6(b)], the pump power is primarily confined inside the pillar core with only some local surface normal intensity “hotspot” at around 650 nm height ($Z-650\mathrm{nm}$). The line plot of ${|E_x|}^2$ against the $Z$ value on the surface of the pillar [along one of the dotted line as shown in Fig. 6(a)] is shown in Fig. 6(d).

 

Fig. 6. FDTD simulation data and SEM image of Sample C. (a) X component of electric field intensity (${|E_x|}^2$) on XZ plane at $Y=0$; (b) ${|E_x|}^2$ on XY plane at $Z=650\mathrm{nm}$; (c) cross section SEM image of individual pillar; (d) line plot of ${|E_x|}^2$ along the length of the pillar on its surface.

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Thus, from the results presented above it is clear that the surface normal $\mathbf{E}$-field intensity is strongly dependent on the pillar dimensions and shape. Further, the calculated ratio of integrated surface ${|E_x|}^4$, which is proportional to SHG intensity, for total available pillar surface, considering hexagonal arrays of pillars in a circular laser spot of diameter 20 μm for pillar A, B, and C is found to be 2: 12: 1. These results clearly support, qualitatively, the observed higher SHG in Sample B. However, exact quantitative estimation of the “detected” SHG intensity from the individual samples needs further numerical calculations.

The overall simulation results (Figs. 4 –6) clearly support the observed experimental results (Fig. 2). Although the surface normal pump intensity is appreciable in Sample A, with the smallest pillar diameter and period, it is relatively much less than in Sample “B”. On the other hand, Sample “C” has the largest pillar diameter and period pump intensity well confined inside the pillar. Compared to Samples A and C, Sample B with intermediate pillar diameter and period has a much higher surface normal component of E-field to generate higher SHG. Further scope for investigation is anticipated in terms of pillar shape, diameter, and period on enhancement of the surface normal $\mathbf{E}$-field components for SHG.

In summary, we have experimentally demonstrated and analyzed enhanced surface SHG from Si pillars fabricated by a top-down approach. Strong dependence of SHG intensity on the pillar geometry is observed. We have also verified theoretically the dependence of SHG intensity on pillar geometry by FDTD simulation in terms of surface normal E-field component. The enhanced SHG light can be useful for nonlinear silicon photonics, surface/interface characterization, and high-resolution biosensing.