Abstract

Depolarization of sub-μm-high Si nano-pillar/nano-rod surface reflectance with morphologically controlled anti-reflection spectrum is demonstrated. Extremely small reflectance dip of 1.5% at 400-450 nm for Si nano-pillars is extraordinary when comparing with Si nano-rods, in which the reflectance vs. L/λ for Si nano-pillars coincides well with the graded-index multilayer based modeling spectrum. Alternatively, Si nano-rods preserve its flattened reflectance spectrum up to 1700 nm, whereas the Si nano-pillar surface reflectance monotonically increases to approach that of bulk Si. The destructive interference is only induced on Si nano-pillar surface with larger aspect-ratio ≥15 and small sidewall slope <7 to suppress surface reflectance at blue-green wavelength region. Anomalous depolarization observed from disordered Si nano-pillar/nano-rod surface reflection indicates that TM-mode incidence interacts with more bound electrons than TE-mode to preserve its effective dielectric permittivity less deviated from the bulk Si. The degraded depolarization ratio observed under TE-mode incidence which correlates well with a simplified bounded-electron resonance model is elucidated.

© 2009 OSA

1. Introduction

Recently, numerous investigations on the aligned one-dimensional (1D) sub-wavelength nanostructures such as nano-tube [1], nano-rods [2,3], nano-wires [4], nano-pillars [5] and nano-tips [6] have been fabricated upon various substrates using the atomic layer deposition, the wet etching in HF and AgNO3 aqueous solution, the hydrothermal etching or self-masked dry etching technique, etc. These surface roughened nanostructures have shown their unique features and great potentials for practical applications in the photonic and optoelectronic devices [6]. For example, the periodically aligned nano-pyramid structure has already applied to the industrial Si photovoltaic (PV) products for reducing surface reflectance. The ZnO nano-tube based solar cells show exceptional photovoltage and filling factor to enhance additional power efficiencies up to 1.6%, as compared to conventional ZnO-based devices [1]. The nano-rods like 1D roughened structure have emerged to integrate with any substrate for fabricating hetero-junction PV cells [2]. In particular, the Si nanostructures with excellent anti-reflection (AR) ability are utilized not only for preparing hetero-junction PV cells but also for replacing the traditional multi-layered AR coating upon Si based solar energy conversion devices. An integral reflectivity below 4% at wavelengths ranging from 240 to 2400 nm was achieved using Si nano-pillars with quasi-identical micron-sized morphology made on single-crystal Si substrate [5]. Instead of the AR characteristics, the nano-roughed structures also exhibit higher absorbance than their thin film counterparts at short wavelength region depending on their topographical morphology. A single-crystal Si nano-wires (SiNWs) incorporated Si PV cells have been demonstrated in 2005 to significantly reduce the surface reflectance over the visible-light wavelengths, however, which fails to show enhanced solar energy conversion efficiency (η=4.73%) as compared to those without nano-wires (η=9.31%) [4]. This result has left a radical problem for such surface nano-scale roughed structure based AR layers, in which the morphology dependent reflectance and transmission spectra might play important roles on the performance of both the light-emitting devices and the solar energy transferring cells. Nonetheless, few modeling works were addressed to simulate these parameters for the surface roughened structures with different morphology. In this work, the depolarization on the ultra-low surface reflectance of sub-μm-high Si nano-pillar/nano-rod with morphologically controlled AR spectrum is analyzed. The morphology-dependent AR properties of the disordered nano-pillars and nano-rods on Si substrate, and the mechanism corresponding to the anomalous surface reflectance spectra of Si nano-pillars are simulated by employing a gradually changed refractive index layer model. The depolarization of surface reflection under TE- or TM-mode incidence and the effective dielectric permittivity is elucidated using a bounded-electron resonance model.

2. Experimental setup

To prepare Si nano-pillars, we employ Ni nano-dot mask to assist the dry etching of Si substrate, whereas the wet etching in the in the HF and AgNO3 based aqueous solution is need for preparing Si nano-rods on Si substrate, as shown in Fig. 1(a) and (b) , respectively. For obtaining Si nano-pillars, a 50-nm-thick Ni film was evaporated on the 20-nm-thick SiO2 coated Si substrate using an e-beam system with Ni deposition rate of 0.1 Å/s under current of 70 mA. Subsequently, a rapid thermal annealing process at 850 °C for 22 s under the N2 flowing gas of 5 SCCM (denoted as the cubic centimeter per minute of STP) was performed to self-aggregate the Ni nano-dots on SiO2 /Si substrate. By using the Ni nano-dots with area density of 5×1011 cm−2 as an etching mask, the Si substrate was dry-etched in a planar-type inductively coupled plasma–reactive ion etching (ICP-RIE) system (SAMCO ICP-RIE 101iPH) at RF frequency of 13.56 MHz and ICP/bias power condition of 100/50 Watts. The CF4 and Ar gaseous mixture with CF4/Ar fluence ratio of 40/40 SCCM was introduced under chamber pressure of 0.66 Pa within etching duration of 5-7 min [7,8]. The Si nano-pillars with high aspect-ratio can be obtained after removing the capped Ni nano-dots and SiO2.

 

Fig. 1 The etching processes for preparing (a) Si nano-pillars (b) Si nano-rods.

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When fabricating Si nano-rods, the (100) Si substrate was etched in an aqueous solution at 50°C with the concentrations of HF and AgNO3 chosen to 4.6 mole/L and 0.02 mole/L, respectively [4]. During the chemical reaction process at Si surface, four equations consisting the catholic and anodic reactions are concurrently occurred, including the hydrogen evolution 2H++2e-→H2, the reduction of Ag+ ions Ag++e-→Ag, the oxidation of Si Si+2F-→SiF2+2e-, and the hole consuming Si+2F-+2H+→SiF2. With these reactions, the reductive Ag atoms self-assembled into nano-particles at bottom of the etching pores on Si surface. Highly disordered pores can be formatted on Si substrate by further dissolving its surface with lengthening etching time, which eventually form long Si nano-rods arranged across the substrate surface. In the mean time, the Ag particles are persistently enlarged and forming large dendrites around the Si nano-rods several minutes later. It is interesting that the formation of metallic nano-dots for preparing Si nano-pillars is used as nano-mask, however, which is used as a metallic catalyst for fabricating Si nano-rods in contrast. Therefore, the appropriate control on etching recipe is mandatory for obtaining high aspect-ratio Si nano-rods with sufficiently large area density. The wavelength dependent reflectance spectrum is measured by ellipsometry (J. A. Woollam Co. VUV-VASE), and is simulated by a homemade simulation program based on the gradually changed refractive index layer model [9].

3. Results and discussions

3. 1 Structural and reflection spectroscopic analyses of Si nano-pillars and nano-rods

The SEM and TEM images for the dry-etched Si nano-pillars with 210-nm height and 60-nm pedestal width are shown in Fig. 2 (a) and (c) . The highest aspect-ratio of the dry-etched Si nano-pillars is about 15. Such a nano-pillar only exhibits a sidewall slope (defined as the ratio of the nano-pillars height to the half-pedestal width) of ~7. In contrast, the wet-etched Si nano-rods with pedestal and height of about 80 and 210 nm, respectively, are also shown in Fig. 2 (b) and (d). The precipitous Si nano-rods exhibit an infinitely large side-wall slope.

 

Fig. 2 SEM bird-eye-view (upper) and TEM cross-section-view (lower) images of Si nano-pillars (a and c) and Si nano-rods (b and d) with height of 210 nm.

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From the wavelength dependent reflectance spectra of both nano-roughened surfaces shown in Fig. 3 , the relatively low reflectance of the nano-pillars roughened Si surface at visible and dark-red wavelength (400-800 nm) regions as compared to the Si wafer can be obtained. However, there is an anomalous reflectance dip (<3%) observed between 400 and 450 nm, the invariance of its dip wavelength with changing Si nano-pillar height will be discussed in more detail by using a theoretical model subsequently. In comparison, the near-infrared (800-1700 nm) reflectance of Si nano-pillar roughened surface turns to exceed that of the Si nano-rods and eventually approaches that of the Si wafer, as shown in Fig. 3. The Si nano-pillars reduce the surface reflectance below 10% in UV and visible region with a minimum of 1.5%, whereas its reflectance monotonically increases from 10% to 25% in NIR region. In comparison with the surface reflectance of Si wafer up to 70% at UV wavelengths and about 40% at visible/NIR region, the Si nano-rod surface with same height remains its reflectance around 8% at wavelength extending from 250 to 1700 nm.

 

Fig. 3 Reflectance spectra of Si nano-rods and nano-pillars.

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The Si nano-pillars are more suitable than Si nano-rods to encapsulate the Si surface for solar cell application due to its better anti-reflective capability at UV and visible region. The wavelength dependent interfered reflectance spectral pattern no longer occurs on the Si nano-rod sample due to its precipitous side wall. On the other hand, two reflection peaks are concurrently observed from both samples at UV wavelength region (285 and 375 nm), which is attributed to the anomalous dispersion by the oxygen related defects (non-bridged oxygen hole centers and oxygen di-vacancy defects) [10,11] upon the surface of Si nano-pillars and nano-rods. It is mandatory to discuss the different reflectance spectra between nano-pillars and nano-rods, which mainly results from the variation on depth dependent effective refractive index of the Si nano-structure/air mixed films with different morphology. Only Si nano-pillars with conical geometry can induce a graded refractive index for each vertically sliced layer with different air-Si mixture composition. The high-aspect-ratio Si nano-rods with precipitous side-wall exhibits nearly constant refractive index due to an invariant compositional ratio of the Si/air mixed structure in each sliced layer.

3. 2 Modeling the reflectance spectra of Si nano-pillar/nano-rod roughened surfaces

To theoretically elucidate the deviation on morphology-dependent reflectance between two different Si nano-structures, we introduce a gradually changed index layer model [9] to simulate the obtained reflectance spectrum. By considering the Si nano-pillars as a multi-layered film which consists of numerous sliced layers with their refractive index continuously varying as a function of depth (see Fig. 4 ); the simulation on light propagation in such an inhomogeneous layer and its reflectance/transmission can be started with WKB approximation. If we assume that the depth dependent refractive index of the Si nano-pillars surface can be described as [12]

n(x)=(1ns(λ)n0ns(λ)xL)1,
where L is the total thickness of the graded multi-layers which simulate the Si nano-pillars, x is the position of certain layer and ns(λ) and n0 are the refractive index of Si substrate and air, respectively. Such that the reflectance formula for the Si nano-pillar encapsulated Si surface structure is obtained as
R=|r|2=(1+sin2y|C|2sin2(N+1)y)1,
where y=cos1(1+(ns(λ)/n0)1/(N+1)2(ns(λ)/n0)1/(N+1)cosϕ) and |C|=1(ns(λ)/n0)1/(N+1)2(ns(λ)/n0)1/(N+1)eiϕ. By taking N→∞, the total optical thickness, the parameters |C| and y can be approximated as

 

Fig. 4 Schematic illustration of Si nano-pillars modeling by a multi-layered film with graded changed refractive index profile.

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Φ=limNNϕ=2πλ0Ln(x)dx=2πn0ns(λ)Lλ(ns(λ)n0)lnns(λ)n0.
|C|12Nlnns(λ)n0,
y1N[Φ2(12lnns(λ)n0)2]1/2.

Afterwards, the reflectance can be obtained by substituting Eq. (4) and Eq. (5) into Eq. (2), which is described as [9,12]

R=(1+Φ2Δ2Δ2sin2Φ2Δ2)1withΔ2=14ln2ns(λ)n0.

As a result, the simulation curve of Eq. (6) for the 210nm-high Si nano-pillars shown in Fig. 5 with ns(λ)/n0=3.6 (the refractive index of bottom layer is 3.6±0.1) is in good agreement with the experimental data. The reflectance of Si nano-pillars monotonically decreases with L/λ reducing from 0.1 (NIR region) to 0.5 (UV-blue region), which approaches a minimized reflectance at L/λ=0.5 in coincident with the simulation due to the first-order destructive interference of the graded-index multi-layer structure. The deviation between the experimental and simulated spectra around the reflectance dip wavelength region is mainly attributed to the defect absorption induced anomalous dispersion. In particular, the simulation also shows a second-ordered maximum in reflectance spectrum at L/λ=0.7 to explain the trend of the experimentally obtained spectrum with L/λ ranged between 0.5 and 1.1 instead of the contribution by the defect absorption induced anomalous dispersion. The simulation clarifies that the gradually increasing NIR reflectance of Si nano-pillars is not attributed to a material response but to a graded-index multi-layer interference.

 

Fig. 5 The measured and simulated reflectance spectra of Si nano-pillars and nano-rods as a function of L/λ (with L denoting the height).

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On the contrary, the reflectance spectrum of Si nano-rods as a function of L/λ reveals a less distinct multi-layer interference effect, which behaves more like a function linearly proportional to L/λ and cannot be well fitted with the graded refractive index model. Without interference, the Si nano-rods exhibit almost diminished first-order minimum and second-order maximum (except the defect absorption bands). The higher reflectance of Si nano-rods than Si nano-pillars at larger L/λ (ranged between 0.6 and 0.8) is due to the more pronounced contribution of oxide related defects on Si nano-rods with larger surface area [R(2L+R)>R(L 2+R2)0.5]. The constant slope of dR/d(L/λ) indicates the wavelength independent reflectance of the Si nano-rods when comparing with that of the Si nano-pillars. Apparently, the AR capability of the Si nano-rods is induced by surface deflection instead of the interference effect. This elucidates the reason why the early application of Si nano-rods (or Si nano-wires) to solar energy conversion devices for replacing traditional multi-layered AR coatings cannot improve the conversion efficiency at all. We thus conclude Si nano-pillars with gradually changed refractive index exhibits great AR ability is attributed to the multi-layer interference induced by gradually changed refractive index of the air/nano-pillars mixed structure. Previously, Hadobas, et al. [13] have also investigated the reflectance of nano-roughened Si substrate, in which the short Si nano-rods with extremely large side wall slope exhibit an aspect ratio of only 1.5~2. In comparison, the nano-pillars demonstrated in our work exhibit conical morphology with an aspect ratio of 15 (nearly 3 times of Hadobas' samples) and a side wall slope of 7. The conical Si nano-pillars result in different air-Si mixture composition ratio in each sliced layer to induce gradually changed refractive index structure, such that a more significant reflectance minimum (presented as a dip) induced by interference of the multi-layered sliced Si nano-pillar structure is observed. The modeling reflectance spectrum based upon the multi-layers with gradually changed refractive index with graded refractive index structure shows a good agreement with the experimentally obtained reflectance spectrum.

3. 3 Depolarization phenomenon of Si nano-pillar/nano-rod roughened surfaces

The depolarized reflectance from two different Si nano-structures under TM- and TE-mode incidences at 532 nm and 20° are also compared as shown in Fig. 6 (a) and (b) . The vertical axis of Fig. 6 is the normalized power related to the power measured after the analyzer with its polarization angle of 0° (defined as the polarization axis of analyzer parallel to the incident polarization). The polarization angle of the analyzer is gradually from 0° to 90°, where the polarization axis of analyzer is perpendicular to the incident polarization. Inhomogeneous dielectrics with roughened surface enables the depolarization of the incident light at all angles of incidence [14], and the multiple scattering usually plays an important role on such a depolarization effect [15]. The polarization ratio is described as Ps=[(ISS-ISP)/(ISS+ISP)] for TE-mode incidence and Pp=[(IPP-IPS)/(IPP+IPS)] for TM-mode incidence, respectively, and the lower polarization ratio indicates a less polarized reflection obtained as compared to the original incidence. The intensity Iss (or Ipp) is defined as the normalized power of reflected beam measured by adjusting the polarization axis of linear analyzer parallel to the incident TE (or TM) polarization, and the Isp (or Ips) is measured when the polarization axis of linear analyzer is perpendicular to the incident TE (or TM) polarization. In other words, the Isp (or Ips) means the normalized reflected power with TM (or TE) polarization state that is depolarized from the TE (or TM) incidence. Both the Si nano-pillar and nano-rod samples induce depolarization, however, the much smaller Ps of Si nano-pillars (~36%) than that of Si nano-rods (~61%) indicates a significant depolarization induced by nano-pillars. At incident wavelength and angle of 532 nm and 20°, the degraded polarization ratios of TM incidence (Pp) for Si nano-pillar and nano-rod samples are ~44% and ~69%, respectively. The Si nano-pillars gradually change their size, morphology, and refractive index, such that the scattering intensity and frequency is altered in each sliced layer to affect the overall scattering effect. In contrast, the Si nano-rods behaves more like a one-dimensional homogeneous structure as compared to the Si nano-pillars, which induces less pronounced scattering effect to depolarize the incident light with TE or TM mode.

 

Fig. 6 Depolarization effects of Si Nano-pillars (blue) and Nano-rods (red) as compared to Si wafer (black) at TM-mode (a) and TE-mode (b) incidence.

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Theoretically, the magnitude of polarization as well as the effect dielectric permittivity of the Si nano-structure will be proportional to the quantity of bounded electrons (N) interacting with the incoming electric-field, as described by

εr=1+Pε0E=1+Nq2mε0jfjωj2ω2iγjω,
where εr and ε0 denote the permittivity of Si and free space, P is the polarization and E is the incident field, N denotes the Si atoms per unit volume and m is the electron’s mass, and the summation denotes there are fj electrons with frequency ωj and damping γj in each atom [16]. Due to the orientation of the vertically aligned Si nano-pillars and nano-rods in our case, the TM-mode (see Fig. 7 (a) ) incidence provides a larger scalar product upon these Si nano-structures than the TE-mode. For TM-mode (see Fig. 7 (b)) case, the electric field component of the incident electromagnetic wave with its direction parallel to the vertically aligned rods structure experiences such nano-structures more like an unprocessed wafer. In the presence of an electromagnetic wave with its polarization parallel with the vertically aligned nano-rods or nano-pillars orientation, more bound electrons within Si atoms are subject to the driving force for remaining its dielectric permittivity less deviated from that in bulk case. In contrast, the orthogonally oriented TE-mode incidence interacts with fewer bounded electrons when propagating through the nano-rods or nano-pillars due to the field misalignment. That is, the reflectance behavior of TM-mode incidence will be less different from the bulk case, whereas the TE-mode incidence faces a more significant depolarization problem the TM mode incidence. In addition, the Ps appears to be smaller than Pp no matter on Si nano-pillars or Si nano-rods, indicating that the residual Brewster angle effect still contribute to the reflectance for these nano-roughened surfaces. In comparison with the Si nano-pillars, a less depolarized effect observed for the reflectance from the Si-nano-rods due to its one-dimensional structure with a weaker surface scattering effect can also be concluded.

 

Fig. 7 Illustrations of the depolarized reflections under purely (a) TM-mode (b) TE-mode polarized incidences.

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Our analysis on the depolarization of Si nano-pillar and nano-rod samples indicate that no matter TE or TM mode incidence experiences a serious degradation on the polarization ratio of reflection. Hecht [17] stated that the depolarization effect is attributed to either the scattering or the multiple reflections within a randomized inhomogeneous dielectric layer (such as the nano-roughened structure in our case). The interaction between the incident beam and the nano-roughened structure causes a significant depolarization effect, in which the incident optical power greatly attenuates during the interaction instead of penetrating through these structures. Even with an outstanding AR ability in this case, the nano-roughened structure suppresses its optical transmittance simultaneously. The depolarization effect is one feature to present how strong the interaction between the incident beam and these nano-roughened structures. In this section, we compare the depolarization effect of different nano-roughened structures with changing morphology (Si nano-pillars and nano-rods), our measured data provided at different incident polarization state (TE- or TM-mode) corroborated with the aforementioned interpretations.

5. Conclusion

The manipulative reflectance spectra of the morphologically controlled Si nano-pillars and nano-rods with sub-μm height in disordered arrangement are investigated to distinguish their difference on visible and near-infrared AR characteristics. The precipitous Si nano-rods with infinitely large side-wall slope exhibit higher reflectance than Si nano-pillars at visible and dark-red wavelength (400-800 nm) regions. In contrast, the near-infrared (800-1700 nm) reflectance of Si nano-pillars exceeds that of Si nano-rods and eventually approaches that of the bulk Si. The surface reflectance is reduced below 10% in UV and visible region with a minimum of 1.5% at 400-450 nm, whereas its reflectance monotonically increases from 10% to 25% in NIR region. In comparison, the Si nano-rod surface with same height remains its reflectance as high as 8% from UV to visible wavelengths, such that the Si nano-pillars are more suitable than Si nano-rods to encapsulate the Si surface for solar cell application. The difference between the morphology dependent reflectance spectra of nano-pillars and nano-rods due to the variation on their depth dependent effective refractive index coincides well with the simulation using graded changed refractive index model. The multi-layer interfered reflectance dip of Si nano-pillars at L/λ=0.5 is in good agreement with the modeling result, indicating that only high-aspect-ratio Si nano-pillars with conical geometry and small sidewall slope can induce a graded refractive index to show wavelength dependent AR characteristics. Both the depolarization phenomena are induced by Si nano-pillars and nano-rods, however, the Si nano-pillars introduce more severer depolarization associated with almost twice decay on depolarization ratio as compared to that of Si nano-rods. The worse degradation on the polarization ratio of TM incidence is also occurred for Si nano-pillars by the intensive scattering effect. The TM-mode incidence provides a larger driving force than the TE-mode one to interact with the bound electrons within the vertically aligned Si nano-pillars and nano-rods, such that their effective dielectric permittivity less deviated from that in bulk Si, whereas the TE-mode incidence fails to induce comparable photon-electron interaction and thus faces a more significant depolarization problem than TM mode incidence.

Acknowledgment

This work was supported by the National Science Council, Taiwan, R.O.C., under Grants NSC98-2221-E-002-023-MY3 and NSC 98-2623-E-002-002-ET.

References and links

1. A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 ( 2007). [CrossRef]   [PubMed]  

2. Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 ( 2008). [CrossRef]   [PubMed]  

3. S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 ( 2008). [CrossRef]  

4. K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 ( 2005). [CrossRef]   [PubMed]  

5. H. J. Xu and X. J. Li, “Silicon nanoporous pillar array: a silicon hierarchical structure with high light absorption and triple-band photoluminescence,” Opt. Express 16(5), 2933–2941 ( 2008). [CrossRef]   [PubMed]  

6. C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 ( 2004). [CrossRef]  

7. Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 ( 2009). [CrossRef]  

8. G.-R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, “Low refractive index Si nanopillars on Si substrate,” Appl. Phys. Lett. 90(18), 181923 ( 2007). [CrossRef]  

9. W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 ( 1980). [CrossRef]  

10. S. Agnello and B. Boizot, “Transient visible-UV absorption in beta irradiated silica,” J. Non-Cryst. Solids 322(1-3), 84–89 ( 2003). [CrossRef]  

11. L. Skuja, “Optically active oxygen-deficiency-related centers in amorphous silicon dioxide,” J. Non-Cryst. Solids 239(1-3), 16–48 ( 1998). [CrossRef]  

12. P. Yeh, “Optical Waves in Layered Media”, Wiley, Singapore (1988).

13. K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 ( 2000). [CrossRef]  

14. G. J. Wilhelmi, J. W. Rouse Jr, and A. J. Blanchard, “Depolarization of light back scattered from rough dielectrics,” J. Opt. Soc. Am. 65(9), 1036–1042 ( 1975). [CrossRef]  

15. J. C. Leader and W. A. J. Dalton, “Bidirectional Scattering of Electromagnetic Waves from the Volume of Dielectric Materials,” J. Appl. Phys. 43(7), 3080–3090 ( 1972). [CrossRef]  

16. D. J. Griffiths, “Introduction to Electrodynamics”, Prentice Hall, New Jersey (1999).

17. E. Hecht, “Optics”, Addison Wesley, San Francisco (2002).

References

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  1. A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
    [CrossRef] [PubMed]
  2. Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
    [CrossRef] [PubMed]
  3. S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
    [CrossRef]
  4. K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
    [CrossRef] [PubMed]
  5. H. J. Xu and X. J. Li, “Silicon nanoporous pillar array: a silicon hierarchical structure with high light absorption and triple-band photoluminescence,” Opt. Express 16(5), 2933–2941 (2008).
    [CrossRef] [PubMed]
  6. C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
    [CrossRef]
  7. Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
    [CrossRef]
  8. G.-R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, “Low refractive index Si nanopillars on Si substrate,” Appl. Phys. Lett. 90(18), 181923 (2007).
    [CrossRef]
  9. W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
    [CrossRef]
  10. S. Agnello and B. Boizot, “Transient visible-UV absorption in beta irradiated silica,” J. Non-Cryst. Solids 322(1-3), 84–89 (2003).
    [CrossRef]
  11. L. Skuja, “Optically active oxygen-deficiency-related centers in amorphous silicon dioxide,” J. Non-Cryst. Solids 239(1-3), 16–48 (1998).
    [CrossRef]
  12. P. Yeh, “Optical Waves in Layered Media”, Wiley, Singapore (1988).
  13. K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
    [CrossRef]
  14. G. J. Wilhelmi, J. W. Rouse, and A. J. Blanchard, “Depolarization of light back scattered from rough dielectrics,” J. Opt. Soc. Am. 65(9), 1036–1042 (1975).
    [CrossRef]
  15. J. C. Leader and W. A. J. Dalton, “Bidirectional Scattering of Electromagnetic Waves from the Volume of Dielectric Materials,” J. Appl. Phys. 43(7), 3080–3090 (1972).
    [CrossRef]
  16. D. J. Griffiths, “Introduction to Electrodynamics”, Prentice Hall, New Jersey (1999).
  17. E. Hecht, “Optics”, Addison Wesley, San Francisco (2002).

2009 (1)

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

2008 (3)

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

H. J. Xu and X. J. Li, “Silicon nanoporous pillar array: a silicon hierarchical structure with high light absorption and triple-band photoluminescence,” Opt. Express 16(5), 2933–2941 (2008).
[CrossRef] [PubMed]

2007 (2)

A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
[CrossRef] [PubMed]

G.-R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, “Low refractive index Si nanopillars on Si substrate,” Appl. Phys. Lett. 90(18), 181923 (2007).
[CrossRef]

2005 (1)

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

2004 (1)

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

2003 (1)

S. Agnello and B. Boizot, “Transient visible-UV absorption in beta irradiated silica,” J. Non-Cryst. Solids 322(1-3), 84–89 (2003).
[CrossRef]

2000 (1)

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

1998 (1)

L. Skuja, “Optically active oxygen-deficiency-related centers in amorphous silicon dioxide,” J. Non-Cryst. Solids 239(1-3), 16–48 (1998).
[CrossRef]

1980 (1)

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

1975 (1)

1972 (1)

J. C. Leader and W. A. J. Dalton, “Bidirectional Scattering of Electromagnetic Waves from the Volume of Dielectric Materials,” J. Appl. Phys. 43(7), 3080–3090 (1972).
[CrossRef]

Acet, M.

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

Agnello, S.

S. Agnello and B. Boizot, “Transient visible-UV absorption in beta irradiated silica,” J. Non-Cryst. Solids 322(1-3), 84–89 (2003).
[CrossRef]

Bello, I.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Blanchard, A. J.

Boizot, B.

S. Agnello and B. Boizot, “Transient visible-UV absorption in beta irradiated silica,” J. Non-Cryst. Solids 322(1-3), 84–89 (2003).
[CrossRef]

Carl, A.

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

Chang, Y. C.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

G.-R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, “Low refractive index Si nanopillars on Si substrate,” Appl. Phys. Lett. 90(18), 181923 (2007).
[CrossRef]

Chen, C. F.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Chen, K. H.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Chen, L. C.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Chen, Z. H.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Cheng, H. M.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Cong, H. T.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Dalton, W. A. J.

J. C. Leader and W. A. J. Dalton, “Bidirectional Scattering of Electromagnetic Waves from the Volume of Dielectric Materials,” J. Appl. Phys. 43(7), 3080–3090 (1972).
[CrossRef]

Das, D.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Elam, J. W.

A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
[CrossRef] [PubMed]

Hadobas, K.

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

Hilfiker, J. N.

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

Hsu, C. H.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Hsu, S. H.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

Hupp, J. T.

A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
[CrossRef] [PubMed]

Hwang, J. S.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Kim, T. J.

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

Kim, Y. D.

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

Kirsch, S.

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

Kuo, H. C.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

G.-R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, “Low refractive index Si nanopillars on Si substrate,” Appl. Phys. Lett. 90(18), 181923 (2007).
[CrossRef]

Leader, J. C.

J. C. Leader and W. A. J. Dalton, “Bidirectional Scattering of Electromagnetic Waves from the Volume of Dielectric Materials,” J. Appl. Phys. 43(7), 3080–3090 (1972).
[CrossRef]

Lee, C. S.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Lee, S. T.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Li, X. J.

Lin, C. J.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

Lin, G.-R.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

G.-R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, “Low refractive index Si nanopillars on Si substrate,” Appl. Phys. Lett. 90(18), 181923 (2007).
[CrossRef]

Lin, H. S.

G.-R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, “Low refractive index Si nanopillars on Si substrate,” Appl. Phys. Lett. 90(18), 181923 (2007).
[CrossRef]

Liu, E. S.

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

G.-R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, “Low refractive index Si nanopillars on Si substrate,” Appl. Phys. Lett. 90(18), 181923 (2007).
[CrossRef]

Lo, H. C.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Lowdermilk, W. H.

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

Martinson, A. B. F.

A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
[CrossRef] [PubMed]

Meng, F. S.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

Milam, D.

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

Pai, Y. H.

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

Pellin, M. J.

A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
[CrossRef] [PubMed]

Peng, K. Q.

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Rouse, J. W.

Skuja, L.

L. Skuja, “Optically active oxygen-deficiency-related centers in amorphous silicon dioxide,” J. Non-Cryst. Solids 239(1-3), 16–48 (1998).
[CrossRef]

Song, H. S.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Tang, Y. B.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Tsai, J.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Wassermann, E. F.

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

Wilhelmi, G. J.

Wu, C. T.

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

Wu, Y.

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Xu, H. J.

Xu, Y.

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Yan, Y. J.

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Zhang, W. J.

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Zhu, J.

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

G.-R. Lin, Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, “Low refractive index Si nanopillars on Si substrate,” Appl. Phys. Lett. 90(18), 181923 (2007).
[CrossRef]

W. H. Lowdermilk and D. Milam, “Graded-index antireflection surfaces for high-power laser applications,” Appl. Phys. Lett. 36(11), 891–893 (1980).
[CrossRef]

J. Appl. Phys. (1)

J. C. Leader and W. A. J. Dalton, “Bidirectional Scattering of Electromagnetic Waves from the Volume of Dielectric Materials,” J. Appl. Phys. 43(7), 3080–3090 (1972).
[CrossRef]

J. Non-Cryst. Solids (2)

S. Agnello and B. Boizot, “Transient visible-UV absorption in beta irradiated silica,” J. Non-Cryst. Solids 322(1-3), 84–89 (2003).
[CrossRef]

L. Skuja, “Optically active oxygen-deficiency-related centers in amorphous silicon dioxide,” J. Non-Cryst. Solids 239(1-3), 16–48 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

Nano Lett. (3)

C. H. Hsu, H. C. Lo, C. F. Chen, C. T. Wu, J. S. Hwang, D. Das, J. Tsai, L. C. Chen, and K. H. Chen, “Generally applicable aelf-masked dry etching technique for nanotip array fabrication,” Nano Lett. 4(3), 471–475 (2004).
[CrossRef]

A. B. F. Martinson, J. W. Elam, J. T. Hupp, and M. J. Pellin, “ZnO nanotube based dye-sensitized solar cells,” Nano Lett. 7(8), 2183–2187 (2007).
[CrossRef] [PubMed]

Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008).
[CrossRef] [PubMed]

Nanotech. (2)

Y. H. Pai, F. S. Meng, C. J. Lin, H. C. Kuo, S. H. Hsu, Y. C. Chang, and G.-R. Lin, “Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate,” Nanotech. 20(3), 035303 (2009).
[CrossRef]

K. Hadobas, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotech. 11(3), 161–164 (2000).
[CrossRef]

Opt. Express (1)

Phys. Status Solidi A-Appl. Mat. (1)

S. H. Hsu, E. S. Liu, Y. C. Chang, J. N. Hilfiker, Y. D. Kim, T. J. Kim, C. J. Lin, and G.-R. Lin, “Characterization of Si nanorods by spectroscopic ellipsometry with efficient theoretical modeling,” Phys. Status Solidi A-Appl. Mat. 205, 876–879 (2008).
[CrossRef]

Small (1)

K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005).
[CrossRef] [PubMed]

Other (3)

P. Yeh, “Optical Waves in Layered Media”, Wiley, Singapore (1988).

D. J. Griffiths, “Introduction to Electrodynamics”, Prentice Hall, New Jersey (1999).

E. Hecht, “Optics”, Addison Wesley, San Francisco (2002).

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Figures (7)

Fig. 1
Fig. 1

The etching processes for preparing (a) Si nano-pillars (b) Si nano-rods.

Fig. 2
Fig. 2

SEM bird-eye-view (upper) and TEM cross-section-view (lower) images of Si nano-pillars (a and c) and Si nano-rods (b and d) with height of 210 nm.

Fig. 3
Fig. 3

Reflectance spectra of Si nano-rods and nano-pillars.

Fig. 4
Fig. 4

Schematic illustration of Si nano-pillars modeling by a multi-layered film with graded changed refractive index profile.

Fig. 5
Fig. 5

The measured and simulated reflectance spectra of Si nano-pillars and nano-rods as a function of L/λ (with L denoting the height).

Fig. 6
Fig. 6

Depolarization effects of Si Nano-pillars (blue) and Nano-rods (red) as compared to Si wafer (black) at TM-mode (a) and TE-mode (b) incidence.

Fig. 7
Fig. 7

Illustrations of the depolarized reflections under purely (a) TM-mode (b) TE-mode polarized incidences.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

n ( x ) = ( 1 n s ( λ ) n 0 n s ( λ ) x L ) 1 ,
R = | r | 2 = ( 1 + sin 2 y | C | 2 sin 2 ( N + 1 ) y ) 1 ,
Φ = lim N N ϕ = 2 π λ 0 L n ( x ) d x = 2 π n 0 n s ( λ ) L λ ( n s ( λ ) n 0 ) ln n s ( λ ) n 0 .
| C | 1 2 N ln n s ( λ ) n 0 ,
y 1 N [ Φ 2 ( 1 2 ln n s ( λ ) n 0 ) 2 ] 1 / 2 .
R = ( 1 + Φ 2 Δ 2 Δ 2 sin 2 Φ 2 Δ 2 ) 1 with Δ 2 = 1 4 ln 2 n s ( λ ) n 0 .
ε r = 1 + P ε 0 E = 1 + N q 2 m ε 0 j f j ω j 2 ω 2 i γ j ω ,

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