Emily D. Kosten

Ray optical light trapping in silicon microwires: exceeding the 2n^2 intensity limit

We develop a ray optics model of a silicon wire array geometry in an attempt to understand the very strong absorption previously observed experimentally in these arrays. Our model successfully reproduces the n2 ergodic limit for wire arrays in free space. Applying this model to a wire array on a Lambertian back reflector, we find an asymptotic increase in light trapping for low filling fractions. In this case, the Lambertian back reflector is acting as a wide acceptance angle concentrator, allowing the array to exceed the ergodic limit in the ray optics regime. While this leads to increased power per volume of silicon, it gives reduced power per unit area of wire array, owing to reduced silicon volume at low filling fractions. Upon comparison with silicon microwire experimental data, our ray optics model gives reasonable agreement with large wire arrays (4 μm radius), but poor agreement with small wire arrays (1 μm radius). This suggests that the very strong absorption observed in small wire arrays, which is not observed in large wire arrays, may be significantly due to wave optical effects.

Microphotonic parabolic light directors fabricated by two-photon lithography

We have fabricated microphotonic parabolic light directors using two-photon lithography, thin-film processing, and aperture formation by focused ion beam lithography. Optical transmission measurements through upright parabolic directors 22 μm high and 10 μm in diameter exhibit strong beam directivity with a beam divergence of 5.6°, in reasonable agreement with ray-tracing and full-field electromagnetic simulations. The results indicate the suitability of microphotonic parabolic light directors for producing collimated beams for applications in advanced solar cell and light-emitting diode designs.

Experimental demonstration of enhanced photon recycling in angle-restricted GaAs solar cells

For cells near the radiative limit, optically limiting the angles of emitted light causes emitted photons to be recycled back to the cell, leading to enhancement in voltage and efficiency. While this has been understood theoretically for some time, only recently have GaAs cells reached sufficient quality for the effect to be experimentally observed. Here, as proof of concept, we demonstrate enhanced photon recycling and open-circuit voltage (Voc) experimentally using a narrow band dielectric multilayer angle restrictor on a high quality GaAs cell. With angle restriction we observe a clear decrease in the radiative dark current, which is consistent with the observed Voc increase. Furthermore, we observe larger Voc enhancements for cells that are closer to the radiative limit, and that more closely coupling the angle restrictor to the cell leads to greater Voc gains, emphasizing the optical nature of the effect.

Limiting Light Escape Angle in Silicon Photovoltaics: Ideal and Realistic Cells

Restricting the light escape angle within a solar cell significantly enhances light trapping, resulting in potentially higher efficiency in thinner cells. Using an improved detailed balance model for silicon and neglecting diffuse light, we calculate an efficiency gain of 3%abs for an ideal Si cell of 3-μm thickness and the escape angle restricted to 2.767° under AM1.5 direct illumination. Applying the model to current high-efficiency cell technologies, we find that a heterojunction-type device with better surface and contact passivation is better suited to escape angle restriction than a homojunction type device. In these more realistic cell models, we also find that there is little benefit gained by restricting the escape angle to less than 10°. The benefits of combining moderate escape angle restriction with low to moderate concentration offers further efficiency gains. Finally, we consider two potential structures for escape angle restriction: a narrowband graded index optical multilayer and a broadband ray optical structure. The broadband structure, which provides greater angle restriction, allows for higher efficiencies and much thinner cells than the narrowband structure.

Spectrum splitting photovoltaics: light trapping filtered concentrator for ultrahigh photovoltaic efficiency

While monolithic multijunction solar cell approaches have been quite successful, current and lattice matching requirements limit the maximum possible achievable efficiencies. Spectrum splitting, where light is optically distributed among subcells with differing bandgaps, avoids these constraints and offers a route to achieving higher efficiencies (<50%). We investigate a spectrum splitting approach where concentrated sunlight is trapped in a textured dielectric slab and then selectively coupled into underlying solar cells of different bandgaps through omnidirectional filters. We develop a multipass optical model to find regimes of high optical efficiency based on parameters such as slab refractive index, number of subcells, and angle restriction of light escape from the slab. Based on these results and filter design considerations, we describe a specific design featuring a textured slab of SiO2 coated with angle restricting incoupling elements based on compound parabolic concentrators and three underlying multijunction junction solar cells, for a total of eight junctions with bandgaps ranging from 2.2eV to 0.7. Using the multipass model in conjunction with modified detailed balance calculations, we find module efficiencies exceeding 50% are possible with an acceptance angle restricted to 20° or less and concentrations of a few hundred suns with ideal omnidirectional filters. Finally as proof of concept, we design a full set of omnidirectional filters for this design. Based on alternating layers of TiO2 and SiO2, we achieve angle averaged reflectivity greater than 90% within the reflection band and angle averaged transmission of approximately 90% within the transmission band for the long pass filter, for nearly 48% receiver efficiency.

Spectrum splitting photovoltaics: Polyhedral specular reflector design for ultra-high efficiency modules

A design for ultra-high efficiency solar modules (>50%) using spectrum splitting is proposed. In the polyhedral specular reflector design, seven subcells are arranged around a solid parallelepiped. Incident light enters the parallelepiped and is directed via specular reflection onto each subcell in order from highest to lowest bandgap. We analyze optical losses due to external concentration and parasitic absorption and optimize the design for >50% module efficiency. We find that moderate concentration designs (90-170x) with a high index parallelepiped and perfect shortpass filters meet target efficiencies and demonstrate an initial design.

Spectrum splitting photovoltaics: Materials and device parameters to achieve ultrahigh system efficiency

We describe an approach for spectrum splitting solar module design using 8 independently connected subcells with optimized band gaps. Modified detailed balance calculations using parameters to account for nonideal absorption and recombination behavior are used to identify the efficiency of spectrum splitting modules with 2 to 20 subcells. Potential optical designs for solar spectrum splitting among subcells are briefly described. Spectrum splitting improves use of the power in the solar spectrum by decreasing thermalization losses. A multijunction design utilizing independently connected subcells employed in a concentrator photovoltaic receiver allows flexibility in subcell selection, fabrication and operating power point optimization when a large number of subcells are employed.

Polyhedral specular reflector design for ultra high spectrum splitting solar module efficiencies (>50%)

One pathway to achieving ultra-high solar efficiencies (<50%) is employing a spectrum splitting optical element with at least 6 subcells and significant concentration (100-500 suns). We propose a design to meet these criteria, employing specular reflection to split and divide the light onto appropriate subcells. The polyhedral specular reflector incorporates a high index parallelepiped with seven subcells. The subcells are placed around the parallelepiped such that light entering at normal incidence encounters the subcells in order from highest to lowest bandgap, with the ray path reflecting at a 90° angle until the light is fully absorbed. Previous studies of the design have shown that concentration and filters are necessary to achieve high efficiencies and thus the current iteration of the design employs shortpass filters and two stages of concentration. Ray tracing of the current iteration shows exceeding 50% efficiency is possible for current subcell qualities with perfect shortpass filters while 50% module efficiencies are only possible for very high quality (<6% ERE) subcells with commercially available shortpass filters. However, even with commercially available filters and achievable subcell quality, ray tracing results show very high (<43%) module efficiency.

Limiting acceptance angle to maximize efficiency in solar cells

Within a detailed balance formalism, the open circuit voltage of a solar cell can be found by taking the band gap energy and accounting for the losses associated with various sources of entropy increase. Often, the largest of these energy losses is due to the entropy associated with spontaneous emission. This entropy increase occurs because non-concentrating solar cells generally emit into 2π steradian, while the solid angle subtended by the sun is only 6.85×10-5 steradian. Thus, for direct normal irradiance, non-concentrating solar cells with emission and acceptance angle limited to a narrow range around the sun could see significant enhancements in open circuit voltage and efficiency. With the high degree of light trapping we expect given the narrow acceptance angle and the ray optics brightness theorem, the optimal cell thickness will result in a discrete modal structure for most materials. Thus, limiting the acceptance and emission angle can be thought of as coupling to only a subset of radiating modes, or, alternatively, as altering the modal structure such that some radiating modes become bound modes. We have shown the correspondence between the ray optics picture and the modal picture, by deriving the ray optics results for light trapping under angular restrictions using a modal formulation. Using this modal formulation we can predict the light trapping and efficiencies for various thin structures under angular restriction. We will discuss these predicted efficiencies and various options for implementing broadband and angle-specific couplers.

Design improvements for the polyhedral specular reflector spectrum-splitting module for ultra-high efficiency (>50%)

A spectrum-splitting module design, the polyhedral specular reflector (PSR), is proposed for ultra-high photovoltaic efficiency (>50%). Incident light is mildly concentrated (≤16 suns) and subsequently split seven ways by a series of multilayer dielectric filters. The split spectrum is directed into compound parabolic concentrators (CPCs) and each concentrates a given slice of the spectrum onto one of seven subcells for conversion. We have recently made significant improvements to the design, such as vertically stacking each submodule and rearranging the subcell order to increase the optical efficiency of the design. We optimize the concentration and composition of the parallelepiped prism (hollow vs. solid) and model designs with >50% module efficiencies including optical and cell nonidealities.