Vidya Ganapati

Light Trapping Textures Designed by Electromagnetic Optimization for Subwavelength Thick Solar Cells

Light trapping in solar cells allows for increased current and voltage, as well as reduced materials cost. It is known that in geometrical optics, a maximum 4 n2 absorption enhancement factor can be achieved by randomly texturing the surface of the solar cell, where n is the material refractive index. This ray-optics absorption enhancement (AE) limit only holds when the thickness of the solar cell is much greater than the optical wavelength. In subwavelength thin films, the fundamental questions remain unanswered: 1) what is the subwavelength AE limit and 2) what surface texture realizes this optimal AE? We turn to computational electromagnetic optimization in order to design nanoscale textures for light trapping in subwavelength thin films. For high-index thin films, in the weakly absorbing limit, our optimized surface textures yield an angle- and frequency-averaged enhancement factor ~39. They perform roughly 30% better than randomly textured structures, but they fall short of the ray optics enhancement limit of 4 n2 ~ 50.

The Voltage Boost Enabled by Luminescence Extraction in Solar Cells

A new physical principle has emerged to produce record voltages and efficiencies in photovoltaic cells, “luminescence extraction.” This is exemplified by the mantra “a good solar cell should also be a good LED.” Luminescence extraction is the escape of internal photons out of the front surface of a solar cell. Basic thermodynamics says that the voltage boost should be related to concentration ratio, C, of a resource by ΔV=(kT/q)ln{C}. In light trapping, (i.e. when the solar cell is textured and has a perfect back mirror) the concentration ratio of photons C={4n²}, so one would expect a voltage boost of Δν=kT ln{4n²} over a solar cell with no texture and zero back reflectivity, where n is the refractive index. Nevertheless, there has been ambiguity over the voltage benefit to be expected from perfect luminescence extraction. Do we gain an open circuit voltage boost of ΔV=(kT/q)ln{n₂}, ΔV=(kT/q)ln{2n₂}, or ΔV=(kT/q)ln{4n²}? What is responsible for this voltage ambiguity ΔV=(kT/q)ln{4}=36mVolts? We show that different results come about, depending on whether the photovoltaic cell is optically thin or thick to its internal luminescence. In realistic intermediate cases of optical thickness the voltage boost falls in between; ln{n²}qΔV/kT)<;ln{4n²}.

Air Gaps as Intermediate Selective Reflectors to Reach Theoretical Efficiency Limits of Multibandgap Solar Cells

Efficient external luminescence is a prerequisite for high-voltage solar cells. To approach the Shockley-Queisser limit, a highly reflective rear mirror is required. This mirror enhances the voltage of the solar cell by providing internally luminescent photons with multiple opportunities for escaping out the front surface. Likewise, intermediate reflectors in a multibandgap solar cell can assist external luminescence to enhance the voltage for each cell in a stack. These intermediate reflectors must also transmit the subbandgap photons to the next cell in the stack. A practical implementation of an intermediate selective reflector is an air gap sandwiched by antireflection coatings. The air gap provides perfect reflection for angles outside the escape cone, and the antireflection coating transmits angles inside the escape cone. As the incoming sunlight is within the escape cone, it is transmitted on to the next cell, while most of the internally trapped luminescence is reflected. We calculate that air gap intermediate reflectors, along with a rear mirror, can provide an absolute efficiency increase of ≈5% in multibandgap cells.

Spontaneous symmetry breaking in the optimization of subwavelength solar cell textures for light trapping

Light trapping in solar cells allows for increased efficiency and reduced materials cost. It is well known that a 4n2 factor of enhancement in absorption can be achieved by randomly texturing the surface of the solar cell, where n is the refractive index of the material. However, this limit only holds when the thickness of the solar cell is much greater than the wavelength of light. In the subwavelength regime, the fundamental question remains unanswered: what surface texture realizes the optimal absorption enhancement? We turn to computational inverse electromagnetic design in order to find this optimal nanoscale texture for light trapping, and observe spontaneous symmetry breaking in the final design. We achieve a factor of 40 in enhancement at normal incidence and above 20 for angle-averaged incidence (averaged over an energy bandwidth of 1/8) for n= 3.5.

Inverse design of a nano-scale surface texture for light trapping

We introduce computational inverse design to optimize nano-scale surface textures for light trapping. The approach yields a structure with a 40.8 absorption enhancement factor, the highest reported for a high-index material in the full-wave domain.

Inverse design of optical antennas for sub-wavelength energy delivery

We report using Inverse Electromagnetic Design to computationally optimize optical antenna shapes. Optimized antennas deliver 10% of incident power to a 50×40×10 nm3 spot in a practical magnetic recording medium for Heat Assisted Magnetic Recording.

Single spherical mirror optic for extreme ultraviolet lithography enabled by inverse lithography technology

Traditionally, aberration correction in extreme ultraviolet (EUV) projection optics requires the use of multiple lossy mirrors, which results in prohibitively high source power requirements. We analyze a single spherical mirror projection optical system where aberration correction is built into the mask itself, through Inverse Lithography Technology (ILT). By having fewer mirrors, this would reduce the power requirements for EUV lithography. We model a single spherical mirror system with orders of magnitude more spherical aberration than would ever be tolerated in a traditional multiple mirror system. By using ILT, (implemented by an adjoint-based gradient descent optimization algorithm), we design photomasks that successfully print test patterns, in spite of these enormous aberrations. This mathematical method was tested with a 6 plane wave illumination source. Nonetheless, it would have poor power throughput from a totally incoherent source.

Highly efficient thermophotovoltaics enabled by photon re-use

Thin-film photovoltaic cells with high reflectivity in the below-bandgap spectral region are ideally suited for thermophotovoltaics. This allows the below-bandgap radiation to be reflected back to the emitter, so that their energy can be used to reheat the source, rather than being lost. In this work, we present a substantial improvement in the theoretical thermophotovoltaic conversion efficiency in the presence of photon re-use. We also predict the achievable conversion efficiency for a system that uses In0.53Ga0.47As photovoltaic cells, and present an experimental optical cavity to be used for future efficiency measurements. Owing to recent advances in thin-film photovoltaics, thermophotovoltaic efficiencies above 50% may soon be realizable.

Adjoint Method for Phase Retrieval

We describe an adjoint method for phase retrieval of a wavefront from measurements of intensity along the axial direction, assuming Fresnel propagation. This method allows efficient computation of gradients for iterative phase retrieval.