Alexei Deinega

Minimizing light reflection from dielectric textured surfaces

In this paper, we consider antireflective properties of textured surfaces for all texture size-to-wavelength ratios. Existence and location of the global reflection minimum with respect to geometrical parameters of the texture is a subject of our study. We also investigate asymptotic behavior of the reflection with the change of the texture geometry for the long and short wavelength limits. As a particular example, we consider silicon-textured surfaces used in solar cells technology. Most of our results are obtained with the help of the finite-difference time-domain (FDTD) method. We also use effective medium theory and geometric optics approximation for the limiting cases. The FDTD results for these limits are in agreement with the corresponding approximations.

Effective optical response of silicon to sunlight in the finite-difference time-domain method.

The frequency dependent dielectric permittivity of dispersive materials is commonly modeled as a rational polynomial based on multiple Debye, Drude, or Lorentz terms in the finite-difference time-domain (FDTD) method. We identify a simple effective model in which dielectric polarization depends both on the electric field and its first time derivative. This enables nearly exact FDTD simulation of light propagation and absorption in silicon in the spectral range of 300-1000 nm. Numerical precision of our model is demonstrated for Mie scattering from a silicon sphere and solar absorption in a silicon nanowire photonic crystal.

Subpixel smoothing for conductive and dispersive media in the finite-difference time-domain method.

Staircasing of media properties is one of the intrinsic problems of the finite-difference time-domain method, which reduces its accuracy. There are different approaches for solving this problem, and the most successful of them are based on correct approximation of inverse permittivity tensor epsilon(-1) at the material interface. We report an application of this tensor method for conductive and dispersive media. For validation, comparisons with analytical solutions and various other subpixel smoothing methods are performed for the Mie scattering from a small sphere.

Theoretical limit of localized surface plasmon resonance sensitivity to local refractive index change and its comparison to conventional surface plasmon resonance sensor.

In this paper, the theoretical sensitivity limit of the localized surface plasmon resonance (LSPR) to the surrounding dielectric environment is discussed. The presented theoretical analysis of the LSPR phenomenon is based on perturbation theory. Derived results can be further simplified assuming quasistatic limit. The developed theory shows that LSPR has a detection capability limit independent of the particle shape or arrangement. For a given structure, sensitivity is directly proportional to the resonance wavelength and depends on the fraction of the electromagnetic energy confined within the sensing volume. This fraction is always less than unity; therefore, one should not expect to find an optimized nanofeature geometry with a dramatic increase in sensitivity at a given wavelength. All theoretical results are supported by finite-difference time-domain calculations for gold nanoparticles of different geometries (rings, split rings, paired rings, and ring sandwiches). Numerical sensitivity calculations based on the shift of the extinction peak are in good agreement with values estimated by perturbation theory. Numerical analysis shows that, for thin (≤10 nm) analyte layers, sensitivity of the LSPR is comparable with a traditional surface plasmon resonance sensor and LSPR has the potential to be significantly less sensitive to temperature fluctuations.

Solar power conversion efficiency in modulated silicon nanowire photonic crystals

It is suggested that using only 1 μm of silicon, sculpted in the form of a modulated nanowire photonic crystal, solar power conversion efficiency in the range of 15%–20% can be achieved. Choosing a specific modulation profile provides antireflection, light trapping, and back-reflection over broad angles in targeted spectral regions for high efficiency power conversion without solar tracking. Solving both Maxwells equations in the 3D photonic crystal and the semiconductor drift-diffusion equations in each nanowire, we identify optimal junction and contact geometries and study the influence of the nanowire surface curvature on solar cell efficiency. We demonstrate that suitably modulated nanowires enable 20% efficiency improvement over their straight counterparts made of an equivalent amount of silicon. We also discuss the efficiency of a tandem amorphous and crystalline silicon nanowire photonic crystal solar cell. Opportunities for “hot carrier” collection and up-conversion of infrared light, enhanced by...

Solar light trapping in slanted conical-pore photonic crystals: Beyond statistical ray trapping

We demonstrate that with only 1 μm, equivalent bulk thickness, of crystalline silicon, sculpted into the form of a slanted conical-pore photonic crystal and placed on a silver back-reflector, it is possible to attain a maximum achievable photocurrent density (MAPD) of 35.5 mA/cm2 from impinging sunlight. This corresponds to absorbing roughly 85% of all available sunlight in the wavelength range of 300–1100 nm and exceeds the limits suggested by previous “statistical ray trapping” arguments. Given the AM 1.5 solar spectrum and the intrinsic absorption characteristics of silicon, the optimum carrier generation occurs for a photonic crystal square lattice constant of 850 nm and slightly overlapping inverted cones with upper (base) radius of 500 nm. This provides a graded refractive index profile with good anti-reflection behavior. Light trapping is enhanced by tilting each inverted cone such that one side of each cone is tangent to the plane defining the side of the elementary cell. When the solar cell is packaged with silica (each pore filled with SiO2), the MAPD in the wavelength range of 400–1100 nm becomes 32.6 mA/cm2 still higher than the Lambertian 4n2 benchmark of 31.2 mA/cm2. In the near infrared regime from 800 to 1100 nm, our structure traps and absorbs light within slow group velocity modes, which propagate nearly parallel to the solar cell interface and exhibit localized high intensity vortex-like flow in the Poynting vector-field. In this near infrared range, our partial MAPD is 10.9 mA/cm2 compared to a partial MAPD of 7 mA/cm2 based on “4n2 statistical ray trapping.” These results suggest silicon solar cell efficiencies exceeding 20% with just 1 μm of silicon.

Coupled optical and electrical modeling of solar cell based on conical pore silicon photonic crystals

We compare the efficiency of thin film photonic crystal solar cells consisting of conical pores and nanowires. Solving both Maxwells equations and the semiconductor drift-diffusion in each geometry, we identify optimal junction and contact positions and study the influence of bulk and surface recombination losses on solar cell efficiency. We find that using only 1 μm of silicon, sculpted in the form of an inverted slanted conical pore photonic crystal film, and using standard contact recombination velocities, solar power conversion efficiency of 17.5% is obtained when the carrier diffusion length exceeds 10 μm. Reducing the contact recombination velocity to 100 cm s−1 yields efficiency up to 22.5%. Further efficiency improvements are possible (with 1 μm of silicon) in a tandem cell with amorphous silicon at the top.

Iterative technique for analysis of periodic structures at oblique incidence in the finite-difference time-domain method

Normal incidence of a plane electromagnetic wave on a periodical structure can be simulated by the finite-difference time-domain method using a single unit cell with periodical boundary conditions imposed on its borders. For the oblique wave incidence, the boundary conditions would contain time delays and thus are difficult to implement in the time-domain method. We propose a method of oblique incidence simulation, based on an iterative algorithm. The accuracy of this method is demonstrated by comparing it with the layer Korringa-Kohn-Rostoker frequency-domain method for calculation of transmission spectra of a monolayered photonic crystal.

Finite difference discretization of semiconductor drift-diffusion equations for nanowire solar cells

Abstract We introduce a finite difference discretization of semiconductor drift-diffusion equations using cylindrical partial waves. It can be applied to describe the photo-generated current in radial pn-junction nanowire solar cells. We demonstrate that the cylindrically symmetric ( l = 0 ) partial wave accurately describes the electronic response of a square lattice of silicon nanowires at normal incidence. We investigate the accuracy of our discretization scheme by using different mesh resolution along the radial direction r and compare with 3D ( x , y , z ) discretization. We consider both straight nanowires and nanowires with radius modulation along the vertical axis. The charge carrier generation profile inside each nanowire is calculated using an independent finite-difference time-domain simulation.

Near perfect solar absorption in ultra-thin-film GaAs photonic crystals

We present designs that enable a significant increase of solar absorption in ultra-thin (100–300 nm) layers of gallium arsenide. In the wavelength range from 400–860 nm, 90–99.5% solar absorption is demonstrated depending on the photonic crystal architecture used and the nature of the packaging. It is shown that using only two hundred nanometer equivalent bulk thickness of gallium arsenide, forming a slanted conical-pore photonic crystal (lattice constant 550 nm, pore diameter 600 nm, and pore depth 290 nm) packaged with SiO2 and deposited on a silver back-reflector, one can obtain a maximum achievable photocurrent density (MAPD) of 26.3 mA cm−2 from impinging sunlight. This corresponds to 90% absorption of all available sunlight in the wavelength range 400–860 nm. Our optimized photonic crystal design suggests that increasing the equivalent bulk thickness of GaAs beyond 200 nm leads to almost no improvement in solar absorption, while reducing it to 100 nm causes less than 10% reduction in MAPD. Light-trapping in the 200 nm conical pore photonic crystal provides solar absorption exceeding the Lambertian limit over the range of 740–840 nm. The angular dependence of the MAPD for both S- and P-polarizations is also investigated and shows no substantial degradation in the range 0–30°. More dramatic light-trapping and solar absorption is demonstrated in photonic crystals consisting of conical nanowires. Using 200 nm equivalent bulk thickness of GaAs (lattice constant 500 nm, cone base diameter 200 nm, and cone height 4.77 μm) packaged in SiO2 and deposited on a silver back-reflector, an MAPD of nearly 27 mA cm−2 is found. This corresponds to absorption of 96% of all available sunlight in the wavelength range 400–860 nm. A clear separation of the solar spectrum along the length of each nanowire is also evident. In the absence of SiO2 packaging, this MAPD increases to 28.8 mA cm−2, in excess of the corresponding Lambertian limit of 28.2 mA cm−2. Most remarkably we find that, if the equivalent bulk thickness of GaAs is increased to 300 nm, nearly 100% of relevant sunlight is absorbed by the conical nanowire photonic crystal.