Optical modelling of thin film microstructures literature review

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This is in a series of literature reviews on InGaN solar cells, which supported the comprehensive review by D.V.P. McLaughlin & J.M. Pearce, "Progress in Indium Gallium Nitride Materials for Solar Photovoltaic Energy Conversion"Metallurgical and Materials Transactions A 44(4) pp. 1947-1954 (2013). open access
Others: InGaN solar cells| InGaN PV| InGaN materials| InGan LEDs| Nanocolumns and nanowires| Optical modeling of thin film microstructure| Misc.

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Contents

[edit] Fabry-Perot effects in InGaN/GaN heterostructures on Si-substrate[1]

Abstract: A strong intensity modulation is found in spatially and angular resolved photoluminescence spectra of InGaN/GaN heterostructures and quantum wells epitaxially grown on Si(111) substrates. This Fabry-Perot effect results from the high refractive index contrasts at the GaN/Si and the Air/InGaN interfaces. It can be used for a wavelength stabilization of the sample upon temperature change and, e.g., in the case of light emitting diodes, to additionally reduce the blueshift at increasing injection currents. A simple geometric approach has been chosen to calculate the influence of layer thickness, absorption and refractive indices, as well as detection angle. The cavity can be described quantitatively by a simple three layer Fabry-Perot model. An analytical expression is derived for the external luminescence line shape. Microphotoluminescence measurements at samples with the silicon substrate locally removed corroborate the model.

[edit] Improved refractive index formulas for the AlxGa1−xN and InyGa1−yN alloys[2]

Abstract: A detailed understanding of the nitride refractive indices is essential for the modeling and design of III–N laser structures. In this article, Author(s) report on the assessment of the refractive index data available for the nitride alloys and present formulas for evaluating the refractive indices for variations in both composition and photon energy. For AlxGa1−xN, an expression is given which fits well to experimental data below x<0.38, sufficient for the molefractions found in the cladding layers of III–N lasers. Due to the almost complete lack of experimental refractive index data for InyGa1−yN, Author(s) propose an expression to give a first-order approximation for the refractive index.

[edit] Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method[3]

Abstract: Spectroscopic ellipsometry (SE) together with the optical transmission method is successfully used to determine the refractive index n and absorption coefficient α of undoped gallium nitride film over the spectral range of 0.78–4.77 eV of photon energy. The SE measurement is carried out at angle of incidence of 60° over the 1.5–4.77 eV energy range and optical transmission measurement over the 0.78–3.55 eV energy range. The refractive index n and absorption coefficient α obtained by both methods show unique results in the overlap wavelength region. Refractive index n is found to follow the Sellmeir dispersion relationship n2(λ) = 2.272+304.72/(λ2−294.02) below the fundamental band edge. A free excitonic structure at the band is clearly observed at room temperature, with the transmission energy of free exciton at 3.44 eV, which is in reasonable agreement with the reported results.

[edit] Optical-field calculations for lossy multiple-layer AlxGa1−xN/InxGa1−xN laser diodes[4]

Abstract: Optical-field profiles in wide-band-gap AlxGa1−xN/InxGa1−xN multiple-quantum well (MQW) separate-confinement heterostructure (SCH) laser diodes (LDs) were calculated using a 2×2 transfer-matrix approach that accommodates complex refractive indices. The refractive indices of AlxGa1−xN and InxGa1−xN were approximated by shifting the refractive index of GaN according to the band-gap energy of the solid solution. Current LDs were analyzed and show reasonable optical confinement. Optimization of the SCH waveguide for a three MQW active region was performed by varying the waveguide and cladding layer thicknesses. For 0.8μm thick Al0.10Ga0.90N cladding layers, waveguides on sapphire and SiC substrates had a maximum confinement factor of - 3.3%. Layers outside of the waveguide strongly affected the optical field for thin ( - 0.4 μm) cladding layer thicknesses and resulted in resonant coupling of the light out of the waveguide. Sapphire substrates were found to enhance light confinement, while SiC substrates were found to reduce optical confinement as the cladding layer thickness is reduced.

[edit] The measurement of absorption edge and band gap properties of novel nanocomposite materials

Abstract: Ultraviolet-visible (UV-Vis) diffuse reflectance measurements of novel nanocomposite structures have been acquired using a Cary 500 spectrophotometer equipped with a Praying Mantis diffuse reflectance accessory (DRA). Based upon the onset of the diffuse reflectance spectra of the powdered materials, the absorption edge and band gap energies of the nanocomposites were determined and compared.

[edit] Infrared and Raman spectroscopy of ZnO nanoparticles annealed in hydrogen[5]

Abstract: The effect of hydrogen on the conductivity of ZnO nanoparticles has implications for nanoscale optoelectronic devices. In this study, infrared reflectance spectra of as-grown and hydrogen-annealed ZnO nanoparticles were measured at near-normal incidence. The as-grown particles were electrically semi-insulating and show reflectance spectra characteristic of insulating ionic crystals. Samples annealed in hydrogen showed a significant increase in electrical conductivity and free-carrier absorption. A difference was observed in the reststrahlen line shape of the conductive sample compared to that of the as-grown sample. The effective medium approximation was applied to model the reflectance and absorption spectra. The agreement between experimental results and the model suggests that the nanoparticles have inhomogeneous carrier concentrations. Exposure to oxygen for several hours led to a significant decrease in carrier concentration, possibly due to the adsorption of negative oxygen molecules on the nanoparticle surfaces.

[edit] Spectroscopy of metamaterials from infrared to optical frequencies[6]

Abstract: Author(s) review both the theoretical electromagnetic response and the spectroscopic measurements of metamaterials. To critically examine published results for metamaterial structures operating in the range from terahertz to optical frequencies, Author(s) focus on protocols allowing one to extract the optical constants from experimental observables. Author(s) discuss the complexity of this task when applied to metamaterials exhibiting electric, magnetic, and magneto-optical response. The general theory of the electromagnetic response of such systems is presented and methods are described. Finally, Author(s) briefly overview possible solutions for implementing metamaterials with tunable resonant behavior.

[edit] Simulation of the Optical Absorption Spectra of Gold Nanorods as a Function of Their Aspect Ratio and the Effect of the Medium Dielectric Constant[7]

Abstract: Gold nanorods with different aspect ratios are prepared in micelles by the electrochemical method and their absorption spectra are modeled by theory. Experimentally, a linear relationship is found between the absorption maximum of the longitudinal plasmon resonance and the mean aspect ratio as determined from TEM. It is shown here that such a linear dependence is also predicted theoretically. However, calculations also show that the absorption maximum of the longitudinal plasmon resonance depends on the medium dielectric constant in a linear fashion for a fixed aspect ratio. Attempts to fit the calculations to the experimental values indicate that the medium dielectric constant has to vary with the aspect ratio in a nonlinear way. Chemically, this suggests that the structure of the micelle capping the gold nanorods is size dependent. Furthermore, comparison with the results obtained for rods of different aspect ratios made by systematic thermal decomposition of the long rods further suggests that the medium dielectric constant is also temperature dependent. This is attributed to thermal annealing of the structure of the micelles around the nanorods.

[edit] Light propagation in nanorod arrays[8]

Abstract: Author(s) study the propagation of TM- and TE-polarized light in two-dimensional arrays of silver nanorods of various diameters in a gelatin background. Author(s) calculate the transmittance, reflectance and absorption of arranged and disordered nanorod arrays and compare the exact numerical results with the predictions of the Maxwell–Garnett effective-medium theory. Author(s) show that interactions between nanorods, multipole contributions and formations of photonic gaps affect strongly the transmittance spectra that cannot be accounted for in terms of the conventional effective-medium theory. Author(s) also demonstrate and explain the degradation of the transmittance in arrays with randomly located rods as well as the weak influence of their fluctuating diameter. For TM modes we outline the importance of the skin effect, which causes the full reflection of the incoming light. Author(s) then illustrate the possibility of using periodic arrays of nanorods as high-quality polarizers.

[edit] Gallium nitride nanorod arrays as low-refractive-index transparent media in the entire visible spectral region[9]

Abstract: Vertically aligned gallium nitride (GaN) nanorod arrays grown by the catalyst-free, self-organized method based on plasma-assisted molecular-beam epitaxy are shown to behave as subwavelength optical media with low effective refractive indices. In the reflection spectra measured in the entire visible spectral region, strong reflectivity modulations are observed for all nanorod arrays, which are attributed to the effects of Fabry-Pérot microcavities formed within the nanorod arrays by the optically flat air/nanorods and nanorods/substrate interfaces. By analyzing the reflectivity interference fringes, we can quantitatively determine the refractive indices of GaN nanorod arrays as functions of light wavelength. We also propose a model for understanding the optical properties of GaN nanorod arrays in the transparent region. Using this model, good numerical fitting can be achieved for the reflectivity spectra.

[edit] Optical absorption properties of Mg-doped GaN nanocolumns[10]

Abstract: Optical properties of GaN nanocolumnar films with and without Mg doping are characterized in the visible and ultraviolet regions. Strong uniaxial anisotropy of dielectric constants is observed by ellipsometry. The complex dielectric functions determined from the reflectance and transmittance spectra showed that the ε2 value is found to be reduced by approximately 50% of that of the epitaxial-GaN film in the energy range above the band gap regardless of Mg doping. This anisotropy and reduction in dielectric constants are due to polarization fields of nanocolumnar crystallites and their interactions. The absorption in undoped GaN nanocolumnar film extends below the band gap of epitaxial GaN, probably due to defects in the nanocolumnar film. Further extension of the absorption tail by Mg doping can be attributed to the transition from a Mg-acceptor level detected in the cathodoluminescence spectra from Mg-doped samples.


[edit] Broadband and omnidirectional antireflection from conductive indium-tin-oxide nanocolumns prepared by glancing-angle deposition with nitrogen[11]

Abstract: Characteristic formation of highly oriented indium-tin-oxide (ITO) nanocolumns is demonstrated using electron-beam evaporation with an obliquely incident nitrogen flux. The nanocolumn material exhibits broadband and omnidirectional antireflective characteristics up to an incidence angle of 70° for the 350–900 nm wavelength range for both s- and p-polarizations. Calculations based on a rigorous coupled-wave analysis indicate that the superior antireflection arises from the tapered column profiles which collectively function as a gradient-index layer. Since the nanocolumns have a preferential growth direction which follows the incident vapor flux, the azimuthal and polarization dependence of reflectivities are also investigated. The single ITO nanocolumn layer can function as antireflection contacts for light emitting diodes and solar cells.

[edit] Raman scattering by longitudinal optical phonons in InN nanocolumns grown on Si(1 1 1) and Si(0 0 1) substrates[12]

Abstract: Raman measurements in high-quality InN nanocolumns and thin films grown on both Si(1 1 1) and Si(1 0 0) substrates display a low-energy coupled LO phonon–plasmon mode together with uncoupled longitudinal optical (LO) phonons. The coupled mode is attributed to the spontaneous accumulation of electrons on the lateral surfaces of the nanocolumns, while the uncoupled ones originates from the inner part of the nanocolumns. The LO mode in the columnar samples appears close to the E1(LO) frequency. This indicates that most of the incident light is entering through the lateral surfaces of the nanocolumns, resulting in pure longitudinal–optical mode with quasi-E1 symmetry. For increasing growth temperature, the electron density decreases as the growth rate increases. The present results indicate that electron accumulation layers do not only form on polar surfaces of InN, but also occur on non-polar ones. According to recent calculations, Author(s) attribute the electron surface accumulation to the temperature dependent In-rich surface reconstruction on the nanocolumns sidewalls.

[edit] Optimization of open circuit voltage in amorphous silicon solar cells with mixed-phase (amorphous+nanocrystalline) p-type contacts of low nanocrystalline content[13]

Abstract: Both the origins of the high open circuit voltages (VOC) in amorphous silicon solar cells having p layers prepared with very high hydrogen dilution and the physical structure of these optimum p layers remain poorly understood topics, with several studies offering conflicting views. This work attempts to overcome the limitations of previous studies by combining insights available from electronic measurements, real time spectroscopic ellipsometry, atomic force microscopy, and both high-resolution transmission electron microscopy (TEM) and dark field TEM of cross sections of entire solar cells. It is found that solar cells fabricated with p layers having a low volume fraction of nanocrystals embedded in a protocrystalline Si:H matrix possess lower recombination at the i/p interface than standard cells and deliver a higher VOC. The growth of the p layers follows a thickness evolution in which pure protocrystalline character is observed at the interface to the i layer. However, a low density of nanocrystallites nucleates with increasing thickness. The advantages offered by the protocrystalline character associated with the amorphous phase of the mixed-phase (amorphous+nanocrystalline) p layers prepared with excess H2 dilution account for the improved VOC of the optimum p layers. In this model, the appearance of a low volume fraction of nanocrystals near the top transparent conductor interface is proposed to be incidental to the high VOC.

[edit] Monoclinic optical constants, birefringence, and dichroism of slanted titanium nanocolumns determined by generalized ellipsometry[14]

Abstract: Generalized spectroscopic ellipsometry determines the principal monoclinic optical constants of thin films consisting of slanted titanium nanocolumns deposited by glancing angle deposition under 85° incidence and tilted from the surface normal by 47°. Form birefringence measured for wavelengths from 500 to 1000 nm renders the Ti nanocolumns monoclinic absorbing crystals with c-axis along the nanocolumns, b-axis parallel to the film interface, and 67.5° monoclinic angle between the a- and c-axes. The columnar thin film reveals anomalous optical dispersion, extreme birefringence, strong dichroism, and differs completely from bulk titanium. Characteristic bulk interband transitions are absent in the spectral range investigated.

[edit] Growth of vacuum evaporated ultraporous silicon studied with spectroscopic ellipsometry and scanning electron microscopy[15]

Abstract: Using a combination of variable-angle spectroscopic ellipsometry and scanning electron microscopy, Author(s) investigated the scaling behavior of uniaxially anisotropic, ultraporous silicon manufactured with glancing angle deposition. Author(s) found that both the diameter of the nanocolumns and the spacing between them increase with film thickness according to a power-law relationship consistent with self-affine fractal growth. An ellipsometric model is proposed to fit the optical properties of the anisotropic silicon films employing an effective medium approximation mixture of Tauc-Lorentz oscillator and void. This study shows that the optical response of silicon films made at glancing incidence differs significantly from that of amorphous silicon prepared by other methods due to highly oriented nanocolumn formation and power-law scaling.

[edit] Characterization of nanostructured GaSb: comparison between large-area optical and local direct microscopic techniques[16]

Abstract: Low energy ion-beam sputtering of GaSb results in self-organized nanostructures with the potential of structuring large surface areas. Characterization of such nanostructures by optical methods is studied and compared to direct (local) microscopic methods. The samples consist of densely packed GaSb cones on bulk GaSb, approximately 30, 50, and 300 nm in height, prepared by sputtering at normal incidence. The optical properties are studied by spectroscopic ellipsometry, in the range 0.6-6.5 eV, and with Mueller matrix ellipsometry in the visible range, 1.46-2.88 eV. The optical measurements are compared to direct topography measurements obtained by scanning electron microscopy, high resolution transmission electron microscopy, and atomic force microscopy. Good agreement is achieved between the two classes of methods when the experimental optical response of the short cones (<55 nm) is inverted with respect to topological surface information, via a graded anisotropic effective medium model. The main topological parameter measured was the average cone height. Optical methods are shown to represent a valuable characterization tool of nanostructured surfaces, in particular when a large coverage area is desirable. Because of the fast and nondestructive properties of optical techniques, they may readily be adapted to in situ configurations.

[edit] Determining thin film properties by fitting optical transmittance[17]

Abstract: The optical transmission spectra of rf sputtered tungsten oxide films on glass substrates were modeled to determine absorption edge behavior, film thickness, and index of refraction. Removal of substrate reflection and absorption phenomena from the experimental spectra allowed direct examination of thin film optical characteristics. The interference fringe pattern allows determination of the film thickness and the dependence of the real index of refraction on wavelength. Knowledge of the interference fringe behavior in the vicinity of the absorption edge was found essential to unambiguous determination of the optical band gap. In particular, the apparently random deviations commonly observed in the extrapolation of as‐acquired data are eliminated by explicitly considering interference fringe phenomena. The multivariable optimization fitting scheme employed allows air-film-substrate reflection losses to be compensated without making reflectance measurements.

[edit] Optical properties of Fabry–Perot microcavity with organic light emitting materials[18]

Abstract: Author(s) investigated the optical properties of the tris(8-hydroxyquinoline)aluminum (Alq3) organic film with Fabry–Perot microcavity by measuring photoluminescence (PL) and transmittance. Author(s) have simulated the phase change on reflection as a function of wavelength. The Fabry–Perot microcavity structures were designed according to the simulation results and the resonant wavelength corresponding to the maximum of PL spectrum of a bare Alq3 film. These structures were fabricated in three types of microcavities, such as type A [air|metal|Alq3|metal|glass], type B [air|dielectric|Alq3|dielectric|glass], and type C [air|metal|Alq3|dielectric|glass]. A bare Alq3 layer on glass, [air|Alq3|glass], showed a PL peak around 514 nm and its full width at half maximum (FWHM) was about 80 nm. The broad FWHM of the bare Alq3 film was reduced to 15–27.5, 7–10.5 and 16–16.6 nm for three types by cavity effects. Also, the control of the resonant wavelength can be achieved by the spacer length as well as the phase change on reflection on mirror.

[edit] Fabry-Perot oscillations in epitaxial ZnSe layers[19]

Abstract: High quality epitaxial layers are found to behave like ordinary Fabry-Perot etalons and show typical interference effects in the broad band photoluminescence. Author(s) investigated these effects in a series of MOVPE-grown ZnSe/GaAs samples and present a quantitative analysis. This allows us to estimate the layer thickness and demonstrates that the interfaces are smooth on the scale of an optical wavelength.

[edit] Photovoltaic Behavior of Nanocrystalline SnS/TiO2[20]

Abstract: Nanocrystalline tin sulfide (SnS) was prepared by chemical bath deposition, and the photovoltaic behavior of SnS/TiO2 was studied. The X-ray diffraction pattern and transmission electron microscopy revealed an 6 nm SnS polycrystalline orthorhombic structure. The SnS film exhibited a band gap of 1.3 eV, and its absorption coefficient was more than 1 × 104 cm−1 in the visible light range. The electrical conductivity activation energy of the SnS film was 0.22 eV, determined when the sample was heated in the temperature range of 111−144 °C. Although the sample was insulating at room temperature, photovoltaic behavior was found in a SnS/TiO2 structure, with an open-circuit voltage (Voc) of 471 mV, a short-circuit current density (Jsc) of 0.3 mA/cm2, and the conversion efficiency (η) of 0.1% under 1 sun illumination. The properties of SnS and the reasons behind the photovoltaic phenomenon of SnS/TiO2 are discussed.

[edit] References

  1. C. Hums et al., “Fabry-Perot effects in InGaN/GaN heterostructures on Si-substrate,” Journal of Applied Physics, vol. 101, no. 3, pp. 033113-033113-4, Feb. 2007.
  2. G. M. Laws, E. C. Larkins, I. Harrison, C. Molloy, and D. Somerford, “Improved refractive index formulas for the AlxGa1−xN and InyGa1−yN alloys,” Journal of Applied Physics, vol. 89, no. 2, pp. 1108-1115, Jan. 2001
  3. G. Yu et al., “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Applied Physics Letters, vol. 70, no. 24, pp. 3209-3211, Jun. 1997.
  4. M. J. Bergmann and H. C. Casey, “Optical-field calculations for lossy multiple-layer AlxGa1−xN/InxGa1−xN laser diodes,” Journal of Applied Physics, vol. 84, no. 3, pp. 1196-1203, Aug. 1998
  5. W. M. Hlaing Oo, M. D. McCluskey, J. Huso, and L. Bergman, “Infrared and Raman spectroscopy of ZnO nanoparticles annealed in hydrogen,” Journal of Applied Physics, vol. 102, no. 4, pp. 043529-043529-5, Aug. 2007
  6. W. J. Padilla, D. R. Smith, and D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” Journal of the Optical Society of America B, vol. 23, no. 3, pp. 404-414, Mar. 2006
  7. A. I. Rahachou and I. V. Zozoulenko, “Light propagation in nanorod arrays,” Journal of Optics A: Pure and Applied Optics, vol. 9, no. 3, pp. 265-270, Mar. 2007
  8. H.-Y. Chen, H.-W. Lin, C.-Y. Wu, W.-C. Chen, J.-S. Chen, and S. Gwo, “Gallium nitride nanorod arrays as low-refractive-index transparent media in the entire visible spectral region,” Optics Express, vol. 16, no. 11, pp. 8106-8116, May 2008
  9. T. Iwanaga, T. Suzuki, S. Yagi, and T. Motooka, “Optical absorption properties of Mg-doped GaN nanocolumns,” Journal of Applied Physics, vol. 98, no. 10, pp. 104303-104303-4, Nov. 2005
  10. C. H. Chang, P. Yu, and C. S. Yang, “Broadband and omnidirectional antireflection from conductive indium-tin-oxide nanocolumns prepared by glancing-angle deposition with nitrogen,” Applied Physics Letters, vol. 94, no. 5, pp. 051114-051114-3, Feb. 2009
  11. S. Lazić et al., “Raman scattering by longitudinal optical phonons in InN nanocolumns grown on Si(1 1 1) and Si(0 0 1) substrates,” Physica E: Low-dimensional Systems and Nanostructures, vol. 40, no. 6, pp. 2087-2090, Apr. 2008
  12. J. M. Pearce et al., “Optimization of open circuit voltage in amorphous silicon solar cells with mixed-phase (amorphous+nanocrystalline) p-type contacts of low nanocrystalline content,” Journal of Applied Physics, vol. 101, no. 11, pp. 114301-114301-7, Jun. 2007
  13. D. Schmidt, B. Booso, T. Hofmann, E. Schubert, A. Sarangan, and M. Schubert, “Monoclinic optical constants, birefringence, and dichroism of slanted titanium nanocolumns determined by generalized ellipsometry,” Applied Physics Letters, vol. 94, no. 1, pp. 011914-011914-3, Jan. 2009
  14. K. Kaminska, A. Amassian, L. Martinu, and K. Robbie, “Growth of vacuum evaporated ultraporous silicon studied with spectroscopic ellipsometry and scanning electron microscopy,” Journal of Applied Physics, vol. 97, no. 1, pp. 013511-013511-8, Dec. 2004
  15. I. S. Nerb et al., “Characterization of nanostructured GaSb: comparison between large-area optical and local direct microscopic techniques,” Applied Optics, vol. 47, no. 28, pp. 5130-5139, Oct. 2008
  16. J. D. Klein, A. Yen, and S. F. Cogan, “Determining thin film properties by fitting optical transmittance,” Journal of Applied Physics, vol. 68, no. 4, pp. 1825-1830, Aug. 1990
  17. B. Y. Jung, N. Y. Kim, C. H. Lee, C. K. Hwangbo, and C. Seoul, “Optical properties of Fabry–Perot microcavity with organic light emitting materials,” Current Applied Physics, vol. 1, no. 2-3, pp. 175-181, Aug. 2001
  18. T. Weber, H. Stolz, W. von der Osten, M. Heuken, and K. Heime, “Fabry-Perot oscillations in epitaxial ZnSe layers,” Semiconductor Science and Technology, vol. 10, no. 8, pp. 1113-1116, Aug. 1995
  19. Y. Wang, H. Gong, B. Fan, and G. Hu, “Photovoltaic Behavior of Nanocrystalline SnS/TiO2,” J. Phys. Chem. C, vol. 114, no. 7, pp. 3256-3259, 2010