volume | PIER Journals

Abstract

Second-order scattering induced reflection divergence and nonlinear depolarization on randomly sub-wavelength corrugated semiconductor nano-pillar surface is observed, which explains the nonlinear transverse electric (TE)/transverse magnetic (TM) mode transformation of the nano-pillar surface reflection with diminishing Brewster angle. The reflected polarization ratios are degraded from 97.5% to 53% and from 96.8% to 40% under TM- and TE-mode incidences by increasing Si nano-pillar height from 30 to 240 nm. A small-perturbation modeling corroborates the scattering induced second-order polarization transformation to depolarize the reflection from highly corrugated Si nano-pillar surface. The lower polarization ratio at TE-mode reflection caused by a severer inhomogeneous Si nano-pillars oriented in parallel with surface normal is concluded. With field polarization ratio under TM-mode incidence, the angular dependent reflectance spectra with a gradually diminished and shifted Brewster angle from 74^o to 45^o can be simulated. The nano-roughened surface induced second-order scattering model correlates the diminishing Brewster angle with the surface depolarized reflection.

1. Kanamori, Y., M. Sasaki, and K. Hane, "Broadband antireflection gratings fabricated upon silicon substrates," Opt. Lett., Vol. 24, 1422-1424, 1999.
doi:10.1364/OL.24.001422

2. Hattori, H., "Anti-reflection surface with particles coating deposited by electrostatic attraction ," Adv. Mater., Vol. 13, No. 1, 51-54, 2001.
doi:10.1002/1521-4095(200101)13:1<51::AID-ADMA51>3.0.CO;2-F

3. Lee, C., S. Y. Bae, S. Mobasser, and H. Manohara, "A novel silicon nanotips antireflection surface for the micro sun sensor," Nano Lett., Vol. 5, 2438-2442, 2005.
doi:10.1021/nl0517161

4. Peng, K. Q., Y. Xu, Y. Wu, Y. Yan, S. T. Lee, and J. Zhu, "Aligned single-crystalline Si nanowire arrays for photovoltaic applications," Small, Vol. 1, 1062-1067, 2005.
doi:10.1002/smll.200500137

5. Diedenhofen, S. L., G. Vecchi, R. E. Algra, A. Hartsuiker, O. L. Muskens, G. Immink, E. P. A. M. Bakkers, W. L. Vos, and J. G. Rivas , "Broad-band omnidirectional antireflection coatings based on semiconductor nanorods ," Adv. Mater., Vol. 21, 973-978, 2009.
doi:10.1002/adma.200802767

6. Ding, B., M. Bardosova, I. Povey, M. E. Pemble, and S. G. Romanov, "Engineered light scattering in colloidal photonic heterocrystals," Adv. Funct. Mater., Vol. 20, 853-860, 2010.
doi:10.1002/adfm.200901319

7. Wan, D., H. L. Chen, T. C. Tseng, C. Y. Fang, Y. S. Lai, and F. Y. Yeh, "Antireflective nanoparticle arrays enhance the e±ciency of silicon solar cells," Adv. Funct. Mater., Vol. 20, 3064-3075, 2010.
doi:10.1002/adfm.201000678

8. Huang, Y.-F., S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, and K.-H.Chen, "Improved broadband and quasi-omnidirectional anti-re°ection properties with biomimetic silicon nanostructures ," Nature Nanotechnol., Vol. 2, 770-774, 2007.
doi:10.1038/nnano.2007.389

9. Renau, J., P. K. Cheo, and H. G. Cooper, "Depolarization of linearly polarized EM waves backscattered from rough metals and inhomogeneous dielectrics," J. Opt. Soc. Am., Vol. 57, 459-461, 1967.
doi:10.1364/JOSA.57.000459

10. Muskens, O. L., S. L. Diedenhofen, M. H. M. V. Weert, M. T. BorgstrÄom, E. P. A. M. Bakkers, and J. G. Rivas, "Epitaxial growth of aligned semiconductor nanowire metamaterials for photonic applications," Adv. Funct. Mater., Vol. 18, 1039-1046, 2008.
doi:10.1002/adfm.200701337

11. Wang, M.-J., Z.-S. Wu, and Y.-L. Li, "Investigation on the scattering characteristics of gaussian beam from two dimensional dielectric rough surfaces based on the kirchhoff approximation ," Progress In Electromagnetics Research B, Vol. 4, 223-235, 2008.
doi:10.2528/PIERB08010903

12. Du, Y. and B. Liu, "A numerical method for electromagnetic scattering from dielectric rough surfaces based on the stochastic second degree method ," Progress In Electromagnetics Research, Vol. 97, 327-342, 2009.
doi:10.2528/PIER09092501

13. Lin, Z. W., X. J. Zhang and G. Y. Fang, "Theoretical model of electromagnetic scattering from 3D multi-layer dielectric media with slightly rough surfaces ," Progress In Electromagnetics Research, Vol. 96, 37-62, 2009.
doi:10.2528/PIER09061102

14. Durian, D. J., D. A. Weitz, and D. J. Pine, "Multiple light-scattering probes of foam structure and dynamics," Science, Vol. 252, 686-688, 2010.

15. Kim, K. S., S. M. Kim, H. Jeong, M. S. Jeong, and G. Y. Jung, "Enhancement of light extraction through the wave-guiding effect of ZnO sub-microrods in InGaN blue light-emitting diodes," Adv. Funct. Mater., Vol. 20, 1076-1082, 2010.
doi:10.1002/adfm.200901935

16. Huang, F., D. Chen, X. L. Zhang, and R. A. Caruso, "Dual-function scattering layer of submicrometer-sized mesoporous TiO2 beads for high-e±ciency dye-sensitized solar cells," Adv. Funct. Mater., Vol. 20, 1301-1305, 2010.
doi:10.1002/adfm.200902218

17. Handapangoda, C. C., M. Premaratne, and P. N Pathirana, "Plane wave scattering by a spherical dielectric particle in motion: A relativistic extension of the Mie theory," Progress In Electromagnetics Research, Vol. 112, 349-379, 2011.

18. Liang, D., P. Wu, L. Tsang, Z. Gui, and K.-S. Chen, "Electromagnetic scattering by rough surfaces with large heights and slopes with applications to microwave remote sensing of rough surface over layered media ," Progress In Electromagnetics Research, Vol. 95, 199-218, 2009.
doi:10.2528/PIER09071413

19. Chy'lek, P., G. W. Grams, and R. G. Pinnick, "Light scattering by irregular randomly oriented particles," Science, Vol. 193, 480-482, 1976.

20. Leader, J. C. and W. A. J. Dalton, "Bidirectional scattering of electromagnetic waves from the volume of dielectric materials," J. Appl. Phys., Vol. 43, No. 7, 3080-3090, 1972.
doi:10.1063/1.1661663

21. Wilhelmi, G. J., J. W. Rouse and A. J. Blanchard, "Depolarization of light back scattered from rough dielectrics," J. Opt. Soc. Am., Vol. 65, 1036-1042, 1975.
doi:10.1364/JOSA.65.001036

22. Rouse, J. W., "The effect of the subsurface on the depolarization of rough-surface backscatter," Radio Sci., Vol. 7, 889-895, 1972.
doi:10.1029/RS007i010p00889

23. Vesperinas, M. N., "Depolarization of electromagnetic waves scattered from slightly rough random surfaces: A study by means of the extinction theorem," J. Opt. Soc. Am. A, Vol. 72, 539-547, 1982.

24. Rojas-Ochoa, L. F., D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, "Depolarization of backscattered linearly polarized light," J. Opt. Soc. Am. A, Vol. 21, 1799-1804, 2004.
doi:10.1364/JOSAA.21.001799

25. Hecht, E., Optics, Addison Wesley, San Francisco, 2002.

26. Lin, G.-R., Y. C. Chang, E. S. Liu, H. C. Kuo, and H. S. Lin, "Low refractive index Si nanopillars on Si substrate," Appl. Phys. Lett., Vol. 90, 181923, 2007.
doi:10.1063/1.2736281

27. Bicout, D., C. Brosseau, A. S. Martinez, and J. M. Schmitt, "Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter," Phys. Rev. E, Vol. 49, 1767-1770, 1994.
doi:10.1103/PhysRevE.49.1767

28. Mittal, G. and D. Singh, "Critical analysis of microwave scattering response on roughness parameter and moisture content for periodic rough surfaces and its retrieval ," Progress In Electromagnetics Research, Vol. 100, 129-152, 2010.
doi:10.2528/PIER09091705

29. Valenzuela, G. R., "Depolarization of EM waves by slightly rough surfaces," IEEE Trans. Antennas Propag., Vol. 15, 552-557, 1967.
doi:10.1109/TAP.1967.1138962

30. Guo, L.-X., A.-Q. Wang, and J. Ma, "Study on EM scattering from 2-D target above 1-D large scale rough surface with low grazing incidence by parallel MoM based on PC clusters ,", Vol. 89, 149-166, 2009.

Dr. Gong-Ru Lin

Dr. Fan-Shuen Meng

Dr. Yung-Hsiang Lin