Broadband control of the optical properties of semiconductors through site-controlled self-assembly of microcrystals

: We investigate light-matter interactions in periodic silicon microcrystals fabricated combining top-down and bottom-up strategies. The morphology of the microcrystals, their periodic arrangement, and their high refractive index allow the exploration of photonic eﬀects in microstructured architectures. We observe a notable decrease in reﬂectivity above the silicon bandgap from the ultraviolet to the near-infrared. Finite-diﬀerence time-domain simulations show that this phenomenon is accompanied by a ∼ 2-fold absorption enhancement with respect to a ﬂat sample. Finally, we demonstrate that ordered silicon microstructures enable a ﬁne tuning of the light absorption by changing experimentally accessible knobs as pattern and growth parameters. This work will facilitate the implementation of optoelectronic devices based on high-density microcrystals arrays with optimized light-matter interactions. on a


Introduction
The quest for the monolithic fabrication of photonic and optoelectronic devices based on group-IV semiconductors requires the development of reliable wafer-scale manufacturing processes that possibly allow for the combination of high-quality materials with the existing mainstream silicon technology. In this framework, the synergy of top-down and bottom-up techniques with current industrial-grade methods of material fabrication can yield interesting and promising approaches to tailor materials functionalities and performances. It has already been demonstrated [1] that the out-of-equilibrium deposition [2] on deeply patterned Si substrates allows for vertical homo and heteroepitaxy [1,3,4] of various materials including silicon, [4] germanium, [1,[5][6][7] silicon carbide, [7,8] and III-V semiconductors like gallium nitride [9] and gallium arsenide. [10][11][12] The resulting structures are typically composed of micrometer-sized, deeply etched Si seeds, or "pillars", on top of which high-quality, faceted epitaxial microcrystals develop. Such microcrystals are self-aligned along the growth direction and isolated from the nearest neighbors by a vacuum gap as small as 50 nm. [4] It is therefore possible to control the entirety of the structure by tailoring the growth and fabrication parameters both in the top-down etching and in the bottom-up deposition processes. This allows tuning the lateral size of the pillars, their spacing, and the etching depth by lithographic design, while changes in deposition parameters yield different microcrystal thickness, shape, and morphologies. [1,13] The vertical growth process allows fabricating densely-packed, several micrometers thick semiconductor microcrystals. Moreover, it has been shown that the geometric constraints of the vertical growth and the control on the surface morphology of the microcrystal allow for the expulsion of threading dislocations. [1,5,14,15] The self-limiting lateral expansion drives threading dislocations towards the microcrystal side facets.
The lateral expulsion of threading dislocations results in microcrystals of remarkable quality, with a large fraction of the material with no extended defects. Application-wise, the large thickness of the crystal favors light absorption, while the near-unity filling factor [4] is significant for the maximization of the active area of a device. Finally, the possibility to obtain dislocation expulsion could be exploited for the fabrication of devices composed of microcrystals with large high-quality areas, few defect centers and low recombination-generation noise. [16] All of the aforementioned properties are exciting and promising for the fabrication of self-standing, isolated, vertically aligned matrices of devices including light emitters as LEDs and light absorbers as photovoltaic cells or photodetectors with broadband sensitivity from the visible to the near-infrared (NIR).
The great versatility of the vertically grown microcrystals makes available a finely tunable platform for the analysis of light-matter interaction effects, that are of great interest in light of possible applications to optoelectronic devices. The microstructures, being made of high refractive index materials such as silicon (n>3.5) [17] or germanium (n>3.9), [18] can lead to the emergence of optical phenomena such as Mie and Fabry-Perot resonances, [19][20][21] whispering gallery modes, [22] diffraction, and light trapping, [23][24][25] particularly in the spectral region where the incident wavelength is comparable to the microcrystal size. Amongst the several effects, antireflection and light trapping are crucial for maximizing photon absorption [26] in a wealth of applications ranging from high-sensitivity photodetectors to solar cells. These effects need to be quantified and light-matter interactions in these microsystems still need to be scrutinized. To this scope, given the relevant role played by geometrical factors in such system, it is extremely useful to have self-assembled structures that can be easily tailored by design.
Hence, we focus on the model system provided by a series of Si microcrystals monolithically grown by homoepitaxy on a patterned matrix of Si (001) pillars. Specifically, we observe a strong reflectivity reduction in the epitaxially grown microstructure with respect to a flat silicon film. Finite-difference time-domain (FDTD) simulations allow us to determine that the decrease in reflectivity is the consequence of an increase in light absorption in the microcrystal. Moreover, we show that the absorption spatial distribution can be tuned to maximize light interaction within a specific region of the microcrystal.

Sample preparation
Si microcrystals have been deposited on patterned substrates by low-energy plasma-enhanced chemical vapor deposition. All the microcrystals were grown under the same conditions on pillars having the same lateral dimensions (D) but different inter-pillar gap (G) (see Fig. 1(a)). Notably, the concomitant growth on unpatterned areas of the same wafer provides us with the flat reference, which enabled to discriminate between material-induced features and structural effects. Optical lithography and reactive ion etching have been used to etch 8 µm tall Si pillars within a p-type Si wafer (ρ =1-10 Ωcm). The square pillars, with lateral dimension D =2 µm, are separated by a gap G equal to 1, 2 or 4 µm for the three different samples analyzed in this work (see Fig. 1 For each chip, the overall patterned area is 0.8 × 0.8 mm 2 , much larger than the spot size used for the optical measurements. The deposition has been performed at 750 • C with a growth rate of 5 nm/s for a total thickness of 5 µm. During growth, Si microcrystals nucleate on each etched pillar. In the first stages of growth the microcrystals expand both laterally and vertically. As the growth proceeds, lateral expansion can lead to crystal merging, as observed for the G = 1 µm pattern ( Fig. 1(b)), or decrease dramatically, due to mutual shadowing effects between neighboring crystals, resulting in the vertical growth of Si microcrystals separated by tens of nanometers gaps as in the case of G =2 µm (Fig. 1(c)). Even when the inter-pillar gap is large, as in the case of G =4 µm ( Fig. 1(d)), the vertical growth is much faster than the lateral growth.

Reflectivity measurements
The analysis of light interaction with the microstructured system was performed by measuring the diffuse reflectance, because specular reflectivity does not take into account diffusion and diffraction effects, that are clearly intense and noticeable even observing the sample by eye. Thus, reflectivity measurements were performed with a double-beam spectrophotometer using an integrating sphere to collect light over the full solid angle. The light sources were a tungsten iodine lamp for the spectral range between 0.3 and 2.5 µm and a deuterium arch lamp for the spectral range between 0.2 and 0.3 µm. The detectors were a photomultiplier tube for the visible and UV spectral range (coupled to a 1200 grid/mm grating), and a PbS photoconductive detector for the near-IR (coupled to a 300 grid/mm grating). The incident bandwidth was about 2 nm in the UV-Visible and 8 nm in the IR fraction of the spectrum. The scanning speed was 400 nm/min.

FDTD simulations
The numerical analysis relies on a commercial software implementing the FDTD method. [27] Due to the large size of the investigated structures compared to the wavelength, two-dimensional simulations have been performed, reproducing the cross section of each microstructure with proper periodic boundary conditions and plane-wave illumination. The frequency-dependent dielectric constant of Si is taken from the literature. [28] High-accuracy conformal meshing, as provided by the software, was employed for the discretization. Figure 1 reports scanning electron microscopy (SEM) images of the epitaxially grown microcrystals. SEM micrographs demonstrate that the microcrystals touch and merge only for the smallest G, while they are clearly well-separated when the gap is larger than 2 µm. In all cases the top of the crystals features (001), {113}, and {111} facets. The relative extension of the different facets changes from sample to sample. As the gap between adjacent pillars increases, the amount of adatoms deposited on the {111} and {113} facets and diffusing towards the (001) facets also increases, thus leading to a reduction of the (001) facet area as indeed observed in Fig. 1. [4] The extension of the prominent families of facets was extracted from the top-down SEM micrographs reported in Fig. 1. Details on the process and the value of the facet area can be found in Table S1 in the Supplement 1. While epitaxy already leads to some advantages in reducing light reflection with respect to the etched pillars, particularly under normal incidence (see Fig. S1 in Supplement 1), our goal is to address the role of crystal morphology in tuning the optical properties. Indeed, we expect that the difference in the microcrystal top morphology could have an impact on the optical properties, because it might affect the way in which electromagnetic fields couple into the material, generating different light-matter interactions that can be tuned by properly choosing the pattern geometry and growth parameters.

Results and discussion
As shown in Fig. 2(a), the patterning of the sample has a strong effect on the optical properties of the structure. The reflectivity of the microstructured samples is about 50% lower than their flat counterpart, i.e. the unpatterned region of the same wafer. The presence of the flat and patterned regions on the same chip guarantees that the material properties of both areas are the same. To retrieve the geometrical contributions from the intrinsic effects, we normalized the reflectivity of the microstructure R m to that of the flat substrate R f . To this end, we define the quantity ∆R R as follows: ∆R R is positive when the microstructured sample shows a larger reflectivity than the flat unprocessed area, and vice versa. As demonstrated in Fig. 2(b), it is possible to identify two distinct spectral regions. At short wavelengths ∆R R has a pronounced dip that corresponds to a smaller reflectivity in the patterned structure than in the flat region. At long wavelengths, ∆R R features clear oscillations superimposed to a negative plateau. The transition between the two regimes occurs around the silicon energy gap (∼1.1 µm wavelength). This suggests that the decrease of reflectivity observed in the short-wavelength region is determined by the activation of the light absorption process. To gather insights into this phenomenon we performed two-dimensional FDTD simulations utilizing a realistic microcrystal shape. The comparison with the experimental data is reported in Fig. 2(a). FDTD simulations nicely reproduce the spectral position of the silicon peaks at 0.273 µm (4.5 eV) and 0.364 µm (3.4 eV) that are determined by the E 2 and by the experimentally non-resolved E 1 and E 0 interband transitions, respectively. [29][30][31] The FDTD simulations also reproduce both the decrease in ∆R R and the modulations observed experimentally. The difference in intensity of the modulations between the experiment and the simulation has to be ascribed to smoothing and averaging effect that are present in the fabricated structure, but not in the FDTD model. While the deviations in the absolute values of the calculated reflectivity from the experimental data are most likely to be ascribed to the 2D nature of the FDTD simulations, and to the simplified morphology of the simulated structure, these results demonstrate that the 2D FDTD calculation suffice to fully capture the origin of the optical response of our samples.
After showing that the patterned nature of the microcrystals introduces variations in the reflectivity with respect to the flat case, we investigate the impact of the pattern geometry. As reported in Fig. 3(a), we observe that the reflectivity of the microstructured samples can be tailored by changing the morphology of the microcrystals. We measured the diffuse reflectance of microcrystals grown on Si (001) pillars of the same lateral size (D = 2 µm) but with increasing inter-pillar gaps (G = 1, 2, and 4 µm, respectively). We observe that the decrease in ∆R R in the transition from below to above bandgap is stronger for the samples with G =4 µm, and it is washed out when G is decreased to 1 µm. We can try to rationalize this behavior by considering that the side view SEM shown in Fig. 1(b) of the sample with G =1 µm shows significant merging between microcrystals. Indeed, also in the top-down SEM this sample looks like a continuous slab of silicon with narrow (<0.1 µm) gaps in a square lattice. Therefore the diffuse reflectivity of such a sample approaches that of the substrate. This is not the case for the other samples, where microcrystals are grown on more spaced pillars and thus the difference from the flat substrate is progressively marked, as shown in Fig. 1(c)-1(d). By analyzing ∆R R as a function of the geometry of the patterned structure it is in principle possible to identify the conditions where the reflectivity is minimized, gathering useful information to design a device with engineered optical properties.
The origin of the observed reflectivity reduction above the bandgap can be possibly ascribed either to an increase of light absorption within the microcrystals or to a corresponding loss of light due to scattering and transmission through the substrate. To address this question we leverage FDTD modelling. Similarly to the quantity ∆R R , we define henceforth ∆A A as the ratio of the differential absorption ∆A = A m − A f between the microcrystal and the reference to that absorbed by a flat reference A f of the same thickness of the microcrystal. It is important to acknowledge that the microcrystal absorption A m refers only to the 13 µm-thick patterned structure and does not take into account the substrate. For consistence, the absorption from the flat reference A f is calculated in the superficial 13 µm-thick fraction of the flat, and not in the full, macroscopic wafer. This configuration was chosen in order to single out the contribution of just the microstructure composed of pillar and microcrystal, excluding the role of the substrate. The simulated ∆A A curves are presented in Fig. 3(b). The relative increase in absorption between the patterned and unpatterned regions is remarkable. Indeed, it goes from ∼0.1 at 1 µm up to ∼1.6 in correspondence with the E 2 transition at 0.273 µm. Fig. 3(a) and (b) allow us to gather additional insights. Indeed, while the reflectivity decreases by increasing the inter-pillar gap, the absorption does not demonstrate the same monotonic behavior, suggesting that additional mechanisms contribute to the reflectivity losses. It is unlikely for these losses to be caused by material defectivity. [32] Indeed, the quality of the material is guaranteed by their homoepitaxial nature. We ascribe the concomitant reduction in reflectivity and absorption when the interpillar distance approaches the largest value (4 µm) to the enhanced contribution of losses occurring through the substrate transmission. This phenomenon washes out the beneficial effect of patterning due to a less effective light trapping.
Notably, the FDTD modelling also allows us to single out the distribution of the light absorption occurring inside a single microcrystal. Since the intensity of the electromagnetic field is correlated to the absorption probability, we can localize the regions where absorption is maximized at any given wavelength. Indeed, the absorption density is proportional to the square modulus of the electric field multiplied by the imaginary part of the dielectric constant of the material. Figure 3(c) reports the simulated absorption map of a single microcrystal mimicking the shape of crystals obtained for D =2 µm and G =4 µm.
As expected, at short wavelengths light is absorbed in the first superficial layers of the material, while at longer wavelengths it can penetrate deeper before being completely absorbed. The spatially resolved FDTD analysis allows us to understand the role of the surface in trapping the incident light inside of the microcrystal. This is particularly evident in the map at 0.850 µm. In this case, light can also be trapped by total internal reflection, and the multiple reflections from the surfaces determine an increase in absorption in the central region of the microcrystal. The FDTD modelling provides further insights on the experimental data. Since short-wavelength light is completely absorbed at the surface of the microcrystal, there is no sizeable difference between the three patterned samples regardless of their geometry. This is confirmed by the absorption capability of the patterned structures that is almost identical in the three reported samples. In the long wavelength regime, however, light can penetrate deeper into the microcrystal. It is thus trapped, experiencing multiple reflections at the sidewalls and generating an interference pattern that gives rise to the modulations observed at wavelengths above 0.6 µm in Fig. 3(b). It should be noted that the specific resonant modes associated with each investigated geometry possess however a low quality factor in this spectral range.
The FDTD modelling can also be employed as a guideline for the appropriate choice of design and fabrication parameters that affect the shape of the resulting microcrystals and their surface morphology. It is possible to perform an accurate analysis of the dependence of the absorption properties on the surface morphology. To this end, we compared the simulated absorption map of the structure reported in Fig. 3(c) with a similar structure, that differs only by the absence of the top (001) facet, as shown in Fig. 3(d). FDTD modelling shows that the light absorption distribution is clearly different in the two cases. In detail, the absorption density is more concentrated towards the center of the microcrystal in the structure that presents the (001) facet, while is more spread over the whole volume of the microcrystal when the (001) facet is removed. This difference in the absorption distribution between the two structures is appealing, because it shows that the morphology of the top surface can impact the propagation of the electromagnetic field in the microcrystal. This can result in structures where the incident light is focussed towards a specific region of the grown microcrystal. The morphologies simulated above can be obtained experimentally. Indeed, it has been demonstrated that the growth parameters can be tuned to fabricate microcrystals with the top (001) facet or, alternatively, with a pyramidal shape. [4,33] Therefore, the shape of the microcrystal can be determined a priori, paving the way for the fabrication of tailor-made microcrystals acting as a high-efficiency light harvester for a device where the active area is strategically placed in correspondence with the region of maximum absorption.
The analysis of the distribution of the electromagnetic field allows us to better understand also the origin of the modulations observed in the reflectivity data below bandgap. Figure 4(a) reports the details of the simulated reflectivity spectrum of a patterned area, having D =2 µm and G =4 µm, in the long-wavelength region. The reflectivity oscillates significantly between ∼0.06 and ∼0.4. Figure 4(b) reports the distribution of the absorption density calculated at the local minima (λ =1.243 µm, 1.567 µm) and maxima (λ =1.715 µm, 1.950 µm) of the spectrum reported in Fig. 4(a). There are two distinct effects that can be highlighted. First, the electromagnetic field is strongly confined in the microcrystals resembling a resonance or a cavity mode with high quality factor. In this case, light undergoes total internal reflection at the Si-air interface and the optical path that it experiences is greatly enhanced. In such a case, it is also possible to have a non-negligible absorption even below the Si energy gap, where the absorption coefficient is very small, but non-zero. [17] As confirmed by the absorption density, the simulation allows us to map with great clarity the distribution of the electric field in the microcrystal even below the Si bandgap because the complex dielectric constant is non-zero, although very small. Moreover, in the etched pillar we can observe waveguided modes having different intensities. Specifically, at 1.715 µm and 1.950 µm the strength of the electromagnetic field inside the pillar is lower than at 1.243 µm and 1.567 µm, yielding a correlation between the calculated reflectivity and the intensity of the waveguided modes inside of the pillar. In detail, the reflectivity is higher when the waveguided light intensity is lower (i.e. at 1.715 µm and 1.950 µm), and vice versa. We therefore conclude that in this scenario, light experiences a lower reflection when a concomitant loss due to propagation in the substrate occurs. We can interpret the reflectivity modulations below the bandgap as critically dependent on the propagating modes in the fabricated pillars.

Conclusions and perspectives
In conclusion, we demonstrated that self-assembled silicon microcrystals vertically grown on deeply patterned Si substrates show a strong reflectivity decrease (up to 50%) with respect to a flat silicon sample. This reflectivity decrease is associated with an increase in light absorption efficiency inside the microstructures (up to ∼2). The absorption properties can be tailored by design to match the desired applications, possibly increasing electrical power generation in a photovoltaic cell or detection effciency in a photodetector. Growth parameters provide suitable turning knobs to adjust light absorption and focussing towards specific areas of the microcrystals, offering larger tunability than in other approaches based on etched silicon nanowires [22,34] and localizing carrier generation away from the surfaces, possibly decreasing nonradiative recombination. While there are techniques that enable larger reflectivity decrease, such as those developed for photovoltaics applications, our flexible approach has several advantages with respect to conventional fabrication methods that do not exploit epitaxy. [35] The conclusions of this work can be naturally extended towards longer wavelengths by utilizing materials such as Ge. Moreover, vertical heteroepitaxy can be employed to fabricate complex epitaxial heterostructures with high quality, low defectivity, and optimized absorption, that are crucial in low-light intensity applications, such as LIDAR and single-photon detectors.