InGaN solar cells literature review

Literature Review on InGaN Solar Cells
A typical photovoltaic cell. InGaN and other Group III semiconductor materials hold great potential for photovoltaics due to the tuneable band gap and defect tolerance.

Background

Photovoltaic (PV) cells convert the energy from the sun into useful electrical energy. Indium gallium nitride (InGaN) is a III-N type ^W material, meaning elements from group III are combined with nitrogen to produce a semiconductor, that is gaining ground in the PV market as a viable and tunable device. By varying the composition of the material, the ^W of the material (the energy level at which the material responds most efficiently to incoming light) can be shifted. Typically, the composition of such alloys is written as In_xGa_1-xN, with x indicating the atomic percent portion of In in the alloy. The following provides a comprehensive background on the current literature available for the material, with links provided to the original documents where possible. This article is a work-in-progress, and will be updated continuously.

Construction

The typical construction for an In_xGa_1-xN cell as grown on a silicon, sapphire or glass substrate. The amorphous GaN (a-GaN) layer is deposited to match the crystal lattices between the InGaN and SiO₂ layers, as the mis-match introduces residual stresses into the crystal lattice, leading to distorted optical and electrical properties. The top layer of InGaN is the layer in which solar energy is converted to electrical energy.

Overview Articles

Complete compositional tunability of InGaN nanowires using a combinatorial approach.[1]

This article covers the first experiment in which the composition of In_xGa_1-xN nanowires were varied in composition over the entire range of x = 0 to x = 1, that is, from pure GaN to pure InN. It demonstrates the tunability of the band gap of InGaN from the near ^W region to the near ^W region. The article also discusses some of the challenges of growing these nanowires which include:

• Threading dislocations in both a-GaN and InGaN layers which lead to recombination centres, significantly reducing efficiencies within the cell.
• An improved technique over hydride vapour-phase epitaxy, which is only a viable method up to x = 0.2, due to the elevated levels of hydrogen which are known to interfere with the incorporation of In into the crystal lattice.
• Reduced effects of carbon contamination as observed in metal-organic chemical vapour deposition (^W).

The procedure used involved a horizontal single-zone furnace divided into four temperature zones, which was used to evaporate the raw materials onto Si or sapphire substrates at unique compositions determined by the precursor mixing gradients of temperature and evaporation rates.

Several tests were then performed on the resulting material, including X-ray diffraction (XRD) to verify composition, scanning electron microscopy (SEM) images were captured to determine crystal structure and transmission electron microscopy (TEM) to verify ordered crystal structure within nanowires. Optical analysis demonstrated the PL spectrum over which the cell responded (varied from 1.0 eV to 4.0 eV, or approximately 325 nm to 850 nm).

InGaN Material Characterization

Plasmon effects on infrared spectra of GaN nanocolumns.^[2]

To be expanded.

Abstract: Infrared (IR) transmission spectra of GaN nanocolumns were analyzed. In addition to the bulk GaN optical phonon signal, a broad absorption peak was observed from undoped and Mg-doped nanocolumns. The central position and width of the broad peak changed with the growth condition and Mg concentration. Based on the Lorentz–Drude model composed of phonon and plasmon modes associated with depolarization fields in GaN nanocolumns, IR transmission spectra were fitted by adjusting the free-electron concentration and scattering rate. Dependence of these values on the column size and impurity concentration is discussed.

Luminescence properties and defects in GaN nanocolumns grown by molecular beam epitaxy ^[3]

To be expanded.

Abstract: Wurtzite GaN nanocolumns are reproducibly grown by plasma-assisted molecular beam epitaxy on Si(111) and c-sapphire substrates. The nanocolumns density and diameter (600–1500 Å) are effectively controlled by means of the III/V ratio. The nanocolumns are fully relaxed from lattice and thermal strain, having a very good crystal quality characterized by strong and narrow (2 meV) low-temperature photoluminescence excitonic lines at 3.472–3.478 eV. In addition, the spectra reveal a doublet at 3.452–3.458 eV and a broad line centered at 3.41 eV. This broad emission shows a sample-dependent spectral energy dispersion, from 3.40 to 3.42 eV, explained as due to the effect of strain and/or electric fields associated with extended structural defects located at the nanocolumns bottom interface. From cathodoluminescence data, it is concluded that the doublet emission lines originate at the nanocolumns volume, most probably related to GaI defects, given the column growth mode (Ga balling).

Time-resolved and time-integrated photoluminescence studies of coupled asymmetric GaN quantum discs embedded in AlGaN barriers.^[4]

To be expanded.

Abstract: We have investigated exciton dynamics in asymmetric GaN quantum discs embedded in AlGaN barriers with an Al content of 50% using time-integrated and time-resolved micro-photoluminescence measurements. Emission from the quantum discs emerges at lower energy than that from the GaN nanocolumns, which suggests that GaN quantum discs are strongly affected by the built-in electric field. The lifetimes of localized excitons in quantum discs were obtained. Nonlinear emission from quantum discs under high excitation power was attributed to tunneling of carriers to larger discs from smaller discs.

Stimulated emission from GaN nanocolumns^[5]

To be expanded.

Abstract: Stimulated emission with very low threshold excitation power density was observed for GaN nanocolumns grown on (0001) sapphire substrate by RF-plasma assisted molecular beam epitaxy. The photopump measurements were carried out under 355 nm Nd:YAG laser excitation with the surface emission configuration. The threshold excitation power density was 198 kW/cm2 at room temperature. The peak wavelength shifted from 370.2 to 370.9 nm when increasing the excitation power from 130 to 440 kW/cm2. The peak intensity increased nonlinearly with excitation power. For the lower excitation condition using a 325 nm He-Cd laser, the spontaneous emission peak was observed at 363.2 nm and the intensity was 2030 times stronger than for a 3.7 m-thick MOCVD-grown GaN film with a dislocation density of 35 × 109 cm-2. With this configuration the peak intensity was increased propotionally with excitation power. These results indicate that GaN nanocolumns have high potential to realize high performance optical devices. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Two-dimensional exciton behavior in GaN nanocolumns grown by molecular-beam epitaxy.^[6]

To be expanded.

Abstract: We have investigated the behavior of excitons in GaN nanocolumns using time-integrated and time-resolved micro-photoluminescence measurements. In the weak confinement limit, the model of fractional-dimensional space gives an intermediate dimensionality of 2.14 for GaN nanocolumns, with an average diameter of 80 nm. Enhanced exciton and donor binding energies are deduced from a fractional-dimensional model and a phenomenological description. Time-integrated photoluminescence spectra as a function of temperature show a curved emission shift. Recombination dynamics are deduced from the temperature dependence of the PL efficiency and decay times.

Structural and optical characterization of intrinsic GaN nanocolumns^[7]

To be expanded.

Abstract: The morphology and optical properties of GaN nanocolumns grown on Si(1 1 1) and sapphire substrates by plasma-assisted molecular beam epitaxy, are studied by photoluminescence, Raman scattering, scanning electron microscopy and cathodoluminescence. The nanocolumns grow along the [0 0 0 1] direction and exhibit high-crystalline quality. Their section is hexagonal with diameters between 450 and 1250 Å. The photoluminescence spectrum is composed by two excitonic peaks at 3.471 and 3.452 eV, and three broad emissions at lower energy. Cathodoluminescence images show that the excitonic emissions originate at the upper nanocolumns body while the low-energy peaks are originated at the ‘bulk’ material at the bottom of the nanocolumns. The low-energy emissions are related to defects at the interface between the columns and the substrate.

Optical absorption, Raman, and photoluminescence excitation spectroscopy of inhomogeneous InGaN films.^[8]

Good article detailing PL spectra, absorption and Raman scattering measurements for thin film InGaN on sapphire substrates with a buffer layer of GaN for lattice matching. Examined various ratios of In:Ga and found the band gap using the observed absorption edge and PL spectra. The absorption edge for the InGaN showed a linear trend with indium fraction (decreasing absorption edge for increasing indium fraction as expected). Raman spectroscopy found indications of phase segregation (as predicted by a miscibility gap due to a 10% difference in relaxed bonds lengths in GaN and InN) for compositions of indium ratio greater than 0.2.

Photoluminescence measurements on cubic InGaN layers deposited on a SiC substrate. ^[9]

This article looks at InGaN thin films deposited on SiC substrate with an intermediate GaN layer. PL spectroscopy at temperatures from 2.5 K to 200 K show the temperature dependance of PL peaks generated through defects. As well, the broadening of the PL peaks supports phase segregation of the InGaN into small clusters of indium-rich regions. The authors also found a large Stokes-like shift between absorption and emission measurements, which they attribute to the indium-rich clusters. Even though the indium-rich clusters occupied a tiny fraction of the total volume, the sites have a high recombination efficiency. Coupled with the fact that most of the absorption is occurring in the bulk, the Stokes-like shift observed supports this theory.

Photoluminescence in Analysis of Surfaces and Interfaces.^[10]

This chapter of the Encyclopedia explains the phenomenon of photoluminescence, which is the emission of a photon as a charge carrier in a material falls to a lower energy level. The photon is emitted with energy equal to the difference between the levels that the charge carrier falls. Relating this to a photovoltaic cell, photons strike the cell from the sun, exciting electrons from their ground state in the valence band up to the conduction band where they can be made to do electrical work. Once the charge carrier is returned to a recombination centre, it drops back down to its previous energy state (that is, the valence band). This decrease in energy is accompanied by the emission of a photon. Thus, by measuring the wavelengths of the emitted photons from a material, we can make accurate estimates of the band gap energy of the material.

Growth Kinetics and Microstructure

Growth and properties of InAlN nanocolumns emitting in optical communication wavelengths. ^[11]

To be expanded.

Abstract: In_xAl_1-xN nanocolumns (0.71lesx_Inles1.00) were fabricated on Si (111) substrates by RF-MBE. The room temperature photoluminescence (RT-PL) in optical communication wavelengths from 0.95 to 1.94 mum with changing x_In was observed. InN/InAlN heterostructures were also fabricated.

Structural and optical properties of GaN nanocolumns grown on (0 0 0 1) sapphire substrates by rf-plasma-assisted molecular-beam epitaxy. ^[12]

To be expanded.

Abstract: GaN nanocolumns were grown with AlN buffer layers on (0 0 0 1) sapphire substrates by rf-plasma-assisted molecular-beam epitaxy. The AlN buffer layers underneath the nanocolumns were used to nucleate the nanocrystals. The thickness of the AlN buffer layer affected the column configuration (size, shape), the density and the optical properties of the nanocolumns; when the thickness increased from 1.8 to 8.2 nm, the average column diameter gradually decreased from 150 to 52 nm with a small kink, but the column density peaked at a thickness of 3.2 nm at 5×10⁹ cm⁻² and finally decreased to 2×10⁸ cm⁻². Based on TEM observations, it is suggested that GaN nanocolumns were not grown just on AlN grain but on the edge of AlN grain. Further, the growth behavior of a nanocolumn as a function of AlN buffer layer thickness is suggested. The room-temperature photoluminescence intensity of the nanocolumns was maximized at a buffer thickness of 4.6 nm, where the intensity was 4 times stronger than that of high-quality bulk GaN crystals grown by HVPE with a threading dislocation density of 8×10⁶ cm⁻².

Plasma ehnancement of metalorganic chemical vapor deposition and properties of Er₂O₃ nanostructured thin films ^[13]

To be expanded.

Abstract: An O₂ remote plasma metal organic chemical vapor deposition (RP-MOCVD) route is presented for tailoring the structural, morphological, and optical properties of Er₂O₃ thin films grown on Si(100) using the tris(isopropylcyclopentadienyl)erbium precursor. The RP-MOCVD approach produced highly (100)-oriented, dense, and mechanically stable Er₂O₃ films with columnar structure.

Temperature induced shape change of highly aligned ZnO nanocolumns.^[14]

To be expanded.

Abstract:Vertically well-aligned ZnO nanocolumns were grown on Al₂O₃ (0 0 0 1) substrates via metalorganic chemical vapor deposition without using any metal catalyst. Their morphology was investigated as a function of the growth temperature (T_g), which was found to be a key processing parameter to control their shape. At T_g >=450 C, vertically well-aligned ZnO nanocolumns started to grow. It was found that a higher T_g yielded slimmer, needle shaped nanocolumns, whereas a lower T_g yielded thicker nanocolumns.

The Controlled growth of GaN nanowires. ^[15]

This paper investigated a scalable method of producing GaN nanowires using a mask-and-etch process. The position and dimensions of the nanowires was very precisely controlled, and the diameter of the resulting nanowire columns were constant, even after exiting or growing beyond the height of the mask. Their height (length) depended only on the time spent in a cycle of ^W and ^W processes.

Room-temperature lasing observed from ZnO nanocolumns grown by aqueous solution deposition ^[16]

To be expanded.

Abstract:None available.

AlGaN nanocolumns grown by molecular beam epitaxy: optical and structural characterization^[17]

To be expanded.

Abstract: High quality AlGaN nanocolumns have been grown by molecular beam epitaxy on Si(111) substrates. Scanning Electron Microscopy micrographs show hexagonal, single crystal columns with diameters in the range of 30 to 60 nm. The nominal Al content of the nanocolumns was changed from 16% to 40% by selecting the flux ratio between the Al and the total III-element, while keeping the growth temperature and the active nitrogen constant. The nominal values of the Al content are consistently lower than the experimental ones, most likely due to the high Ga desorption rates at the growth temperature. The Al composition trend versus the Al flux is consistent with the E2 phonon energy values measured by inelastic light scattering. These results open the possibility to grow high quality low dimensional structures based on AlGaN/GaN/AlGaN heterocolumns for basic studies and device applications.

InGaN and Photovoltaics

Analytical model for the optical functions of amorphous semiconductors from the near-infrared to the ultraviolet: Applications in thin film photovoltaics.^[18]

To be expanded.

Abstract: Two dispersion models of disordered solids, one parameterizing density of states (PDOS) and the other parameterizing joint density of states (PJDOS), are presented. Using these models, not only the complex dielectric function of the materials, but also some information about their electronic structure can be obtained. The numerical integration is necessary in the PDOS model. If analytical expressions are required the presented PJDOS model is, for some materials, a suitable option still providing information about the electronic structure of the material. It is demonstrated that the PDOS model can be successfully applied to a wide variety of materials. In this paper, its application to diamond-like carbon (DLC), a-Si and SiO2-like materials are discussed in detail. Unlike the PDOS model, the presented PJDOS model represents a special case of parameterization that can be applied to limited types of materials, for example DLC, ultrananocrystalline diamond (UNCD) and SiO2-like.

InGaN and Light Emitting Diodes (LED)

InGaN for use in LEDs
Blue and ultraviolet LEDs use GaN and InGaN semiconductors as the active material. White LEDs are commonly made using GaN and InGaN to optically pump a phosphor coating to produce white light.

InGaN is a relatively new material to photovoltaic technology, but similar materials have been used in ^Ws for some time now. In operation, an LED is to a solar cell as a fan is to a turbine. In the LED, electricity comes in and light is emitted, while in a solar cell light comes in and electricity comes out. The following articles cover details on some advancements in the field of LED technologies closely related to photovoltaics.

Light-emitting diode extraction efficiency.^[19]

The quality of InGaAlP wafers was investigated for use in LEDs. Specifically, the effect of film thickness on internal quantum efficiency and light extraction efficiency in the LED were discussed. A model for the device was constructed two methods: (1) the ^W gas method, and (2) a sort of ^W. One of the significant results of the paper was that internal quantum efficiency increased with decreasing film thickness. It is thought that the increase in efficiency accompanies the decreased probability of recombination in the thin films.

High-power InGaN single-quantum-well-structure blue and violet light-emitting diodes^[20]

To be expanded.

Abstract: High-power blue and violet light-emitting diodes (LEDs) based on III–V nitrides were grown by metalorganic chemical vapor deposition on sapphire substrates. As an active layer, the InGaN single-quantum-well-structure was used. The violet LEDs produced 5.6 mW at 20 mA, with a sharp peak of light output at 405 nm, and exhibited an external quantum efficiency of 9.2%. The blue LEDs produced 4.8 mW at 20 mA and sharply peaked at 450 nm, corresponding to an external quantum efficiency of 8.7%. These values of the output power and the quantum efficiencies are the highest ever reported for violet and blue LEDs.

Fabrication of thin-film InGaN light-emitting diode membranes by laser lift-off^[21]

To be expanded.

Abstract: Indium–gallium nitride (InGaN) multiple-quantum-well (MQW) light-emitting diode (LED) membranes, prefabricated on sapphire growth substrates, were created using pulsed-excimer laser processing. The thin-film InGaN MQW LED structures, grown on sapphire substrates, were first bonded onto a Si support substrate with an ethyl cyanoacrylate-based adhesive. A single 600 mJ/cm2, 38 ns KrF (248 nm) excimer laser pulse was directed through the transparent sapphire, followed by a low-temperature heat treatment to remove the substrate. Free-standing InGaN LED membranes were then fabricated by immersing the InGaN LED/adhesive/Si structure in acetone to release the device from the supporting Si substrate. The current–voltage characteristics and room-temperature emission spectrum of the LEDs before and after laser lift-off were unchanged.

InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures^[22]

To be expanded.

Abstract: Electrical operation of InGaN/GaN quantum-well heterostructure photonic crystal light-emitting diodes (PXLEDs) is demonstrated. A triangular lattice photonic crystal is formed by dry etching into the top GaN layer. Light absorption from the metal contact is minimized because the top GaN layers are engineered to provide lateral current spreading, allowing carrier recombination proximal to the photonic crystal yet displaced from the metal contact. The chosen lattice spacing for the photonic crystal causes Bragg scattering of guided modes out of the LED, increasing the extraction efficiency. The far-field radiation patterns of the PXLEDs are heavily modified and display increased radiance, up to ~1.5 times brighter compared to similar LEDs without the photonic crystal.

Spontaneous emission of localized excitons in InGaN single and multiquantum well structures.^[23]

To be expanded.

Abstract: Emission mechanisms of InGaN single quantum well blue and green light emitting diodes and multiquantum well structures were investigated by means of modulation spectroscopy. Their static electroluminescence (EL) peak was assigned to the recombination of excitons localized at certain potential minima in the quantum well. The blueshift of the EL peak caused by the increase of the driving current was explained by combined effects of the quantum-confinement Stark effect and band filling of the localized states by excitons.

Improved light-output and electrical performance of InGaN-based light-emitting diode by microroughening of the p-GaN surface^[24]

To be expanded.

Abstract: We report on an InGaN-based light-emitting diode (LED) with a top p-GaN surface microroughened using the metal clusters as a wet etching mask. The light-output power for a LED chip with microroughening was increased compared to that for a LED chip without one. This indicates that the scattering of photons emitted in the active layer was much enhanced at the microroughened top p-GaN surface of a LED due to the angular randomization of photons inside the LED structure, resulting in an increase in the probability of escaping from the LED structure. By employing the top surface microroughened in a LED structure, the power conversion efficiency was increased by 62%.

Growth of InGaN/GaN multiple-quantum-well blue light-emitting diodes on silicon by metalorganic vapor phase epitaxy. ^[25]

To be expanded.

Abstract: We report the growth of InGaN/GaN multiple-quantum-well blue light-emitting diode (LED) structures on Si(111) using metalorganic vapor phase epitaxy. By using growth conditions optimized for sapphire substrates, a full width at half maximum (FWHM) (102) x-ray rocking curve of less than 600 arcsec and a room-temperature photoluminescence peak at 465 nm with a FWHM of 35 nm was obtained. Simple LEDs emitting bright electroluminescence between 450 and 480 nm with turn-on voltages at 5 V were demonstrated.

Origin of high oscillator strength in green-emitting InGaN/GaN nanocolumns^[26]

To be expanded.

Abstract: Optical characterization has been performed on an InGaN/GaN nanocolumn structure grown by nitrogen plasma assisted molecular beam epitaxy not only in macroscopic configuration but also in a microscopic one that can be assessed to a single nanocolumn. The photoluminescence (PL) decay monitored at 500 nm is fitted with a double exponential curve, which has lifetimes of 0.67 and 4.33 ns at 13 K. These values are two orders of magnitude smaller than those taken at the same wavelength in conventional InGaN/GaN quantum wells (QWs) grown toward the C orientation. PL detection of each single nanocolumn was achieved using a mechanical lift-off technique. The results indicate that the very broad, macroscopically observed PL spectrum is due to the sum of the sharp PL spectrum from each nanocolumn, the peak energy of which fluctuates. Moreover, unlike conventional QWs, the blueshift of a single nanocolumn is negligibly small under higher photoexcitation. These findings suggest that carrier localization as well as the piezoelectric polarization field is suppressed in InGaN/GaN nanocolumns.

Optical Modelling of Thin Film Microstructures

Optical absorption properties of Mg-doped GaN nanocolumns. ^[27]

To be expanded.

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 2 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.

Broadband and omnidirectional antireflection from conductive indium-tin-oxide nanocolumns prepared by glancing-angle deposition with nitrogen. ^[28]

To be expanded.

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.

Raman scattering by longitudinal optical phonons in InN nanocolumns grown on Si(1 1 1) and Si(0 0 1) substrates. ^[29]

To be expanded.

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, we attribute the electron surface accumulation to the temperature dependent In-rich surface reconstruction on the nanocolumns sidewalls.

Monoclinic optical constants, birefringence, and dichroism of slanted titanium nanocolumns determined by generalized ellipsometry.^[30]

To be expanded.

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.

Growth of vacuum evaporated ultraporous silicon studied with spectroscopic ellipsometry and scanning electron microscopy^[31]

To be expanded.

Abstract:Using a combination of variable-angle spectroscopic ellipsometry and scanning electron microscopy, we investigated the scaling behavior of uniaxially anisotropic, ultraporous silicon manufactured with glancing angle deposition. We 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.

Characterisation of nanostructured GaSb: Comparison between large-area optical and local direct microscopic techniques. ^[32]

This paper outlines a comprehensive analysis of GaSb nanowires grown in bulk GaSb, with heights of approximately < 55nm to 300nm. Scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HR-TEM), atomic force microscopy (AFM), spectroscopic ellipsometry (SE) and photo-elastic modulated spectroscopic ellipsometry (PMSE) were used to determine the physical and optical properties of the materials. An optical model was constructed using a ^W in which the conical nanocolums were modeled as stacks of cylinders with constant diameter to a good first approximation of optical properties resulting in estimations of physical properties. All characteristic parameters of the nanocolums were nondimensionalized where possible for generatlity. The results of SE and PMSE measurments were a completed Mueller matrix, which permitted the determination of the ^W and ^W. It was noted that the degree of polarization decreased with increasing column height, which is thought to be the result of mutliple scattering effects. These effects pointed to inaccuracies in the effective medium approximation for these larger columns.

Optical-model analysis of elastic scattering and polarization of 49.5 MeV protons on Sm. ^[33]

Researchers at the Wheatstone Physics Laboratory in London, England, developed an optical model to estimate the effect of protons on samarium (Sm) isotopes. This analysis is fairly unrelated to solar technologies, however several of the same assumptions in the model may transfer. One of particular interest was the thought of how to handle difficulties in the model. The following quote from the article outlines the procedure quite well.

Smearing of the angular distributions due to the finite beam spot size, beam divergence and angular acceptance of the spectrometer were included in the theoretical predictions rather than subtracted from experimental results. The errors in the elastic cross sections are statistical, to which should be added absolute errors of...^[33]

It is anticipated that in the development of optical models for InGaN, a similar procedure will be followed.

Determining thin film properties by fitting optical transmittance.^[34]

This paper discovers trends in transmittance as well as the real portion of the refractive index for materials. To relate the refractive index to the wavelength of light, a Cauchy relation (up to fourth-order) was fit to the data. Again, the assumption of a ‘real portion only’ fit to the refractive index data significantly simplifies analysis with little loss in relevance to the actual data, as this assumption assumes no losses in intensity, but no other distortion of the photon’s pathways.

Optical properties of Fabry-Perot microcavity with organic light emitting materials.^[35]

A comprehensive development of the Fabry-Perot microcavity model is completed for organic light emitting devices, which have similar structure and optical properties to inorganic materials (such as InGaN), but have greater manufacturing flexibility, require less power, and are produced at lower cost. This paper also describes the Airy function used to model interference in the PL data, which is a common way of representing interference in a Fabry-Perot type system. The Airy function is proportional to 1/sin²(d) where d is the path (phase) difference between two waves exiting a thin film.

Fabry-Perot oscillations in epitaxial ZnSe Layers. ^[36]

A rigorous model for fitting an entire spectrum of PL data is developed in this paper. A function which includes the sum of two Gaussian peaks which is then multiplied by the Airy function is developed to model the data with approximately 12 fitting parameters to be adjusted. A significant amount of time can be spent on this model improving the fit, and automated curve fitting by a computer must be completed with caution as the large number of fitting parameters make it exceedingly likely that the function will fall into local minima when optimizing. Software such as Origin can be used with relative ease to develop an appropriate model.

Fabry-Perot effects in InGaN/GaN heterostructures on Si-substrate.^[37]

Interference trends are commonly observed whenever optical phenomenon are observed. By modeling the material in question as a Fabry-Perot microcavity, the analysis can continue. This paper describes a method in which the peaks observed in the PL (photoluminescence) data are extracted and 2*n/λ is plotted against peak index (i.e. peak index = 1, 2, 3…), the inverse of the slope on the linear fit to the data yields the film thickness. Note that n, the refractive index, is dependent on the material through which the photon is travelling (i.e. its composition x) and the wavelength (energy) of light (photon) propagating. The refractive index is evaluated at the wavelength at which the peak in PL is noted.

Improved refractive index formulas for the Al_xGa_1-xN and In_yGa_1-yN alloys.[38]

The group of III-nitrides has many uses as semiconducting materials beyond PV cells, including LEDs and laser diodes. Due to the heavy reliance on optical properties to determine and improve the performance of these devices, it is crucial to have a well defined set of optical properties for the material used. This paper examines the methods for determining the index of refraction for both materials using two different models.

• The first model was originally developed by Bergmann and Casey^[39] which shifts the refractive index of GaN to produce that for InGaN, based on the composition of In and the band gap energies of the constituents.
• A Sellmeier dispersion formula relates the refractive index to the wavelength or energy associated with the photon passing through the material.

An important observation that arises from this paper from the multitude of figures included is that as the photon energy approaches 3.4 eV (approximately 365 nm), the refractive index increases dramatically. This must be taken into account when designing for optical properties.

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.^[40]

A more rigorous ^W dispersion model is fit to refractive index data as a function of wavelength, with well defined fitting parameters determined and reported with 90% confidence limits. The measurements were achieved using spectroscopic ellipsometry performed at an angle of incidence of 60°over 260-830 nm with optical transmission measurement over the 370-1600 nm wavelength range. Film thickness was on the order of 1.25 μm. Note that one key assumption made in the Sellmeier model was that the extinction coefficient, the complex portion of the refractive index, was zero. This translates to no loss in intensity of the photon moving through the material, and does not significantly impact the resulting model.

Optical-field calculations for lossy multiple-layer Al_xGa_x-1N/In_xGa_1-xN laser diodes.[39]

The following excerpt from this paper summarizes its goal succinctly. “For calculations of nitride based LDs [laser diodes], refractive indicies are also needed for the solid solutions of Al_xGa_1-xN and In_xGa_1-xN. To our knowledge, the only refractive index data for the solid solutions is for Al_0.1Ga_0.9N ^[41]. In Sec. II, we approximate the refractive index for the solid solutions by shifting the GaN data according to the difference in band gap energy between the solid solution and GaN.”

References

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