Photovoltaics provides a very clean, reliable and limitless means for meeting the ever-increasing global energy demand. Silicon solar cells have been the dominant driving force in photovoltaic technology for the past several decades due to the relative abundance and environmentally friendly nature of silicon. Nevertheless, one of the drawbacks of crystalline silicon is the indirect nature of its electronic band gap, making it a relatively weak absorber of long wavelength sunlight. Traditionally, this has been offset using a relatively thick (100–500 μm) silicon structure. While enabling more solar absorption, thicker silicon adds to the materials cost for large area applications and renders the structure inflexible. Moreover, thick silicon solar cells suffer from unavoidable losses in power conversion efficiency due to non-radiative recombination of photo-generated charge carriers during their relatively long path to electrical contacts at the extremities of the cell. These deficiencies have sparked broad interest in a variety of thin-film solar materials including CdTe, GaAs, perovskites and various polymers1,2,3. Due to the indirect band gap nature of c–Si, thin-film silicon has not been considered a viable competitor to these alternative materials.

In some recent papers4,5, we have suggested a paradigm shift in solar science and technology, exploiting the wave nature of sunlight while retaining a realistic description of charge-carrier recombination. By designing suitable photonic crystal architectures that promote wave-interference based light-trapping in the required frequency band, it is possible for c–Si thin films to absorb sunlight as effectively as a direct band gap semiconductor. In this paper we demonstrate how this enables a flexible, 15 μm-thick c–Si film with optimized doping profile, surface passivation and interdigitated back contacts (IBC) to achieve a power conversion efficiency of 31%, higher than that of any other single material of any thickness.

The maximum possible room-temperature power conversion efficiency of a single junction, c–Si solar cell under 1–sun illumination, according to the laws of thermodynamics, is 32.33%6. This limit is based on the assumptions of perfect solar absorption and no losses due to non-radiative charge-carrier recombination. The best real-world silicon solar cell to date, developed by Kaneka Corporation, is able to achieve 26.7% conversion efficiency7,8. A loss analysis of this 165 μm-thick, heterojunction IBC cell shows that in absence of any extrinsic loss mechanism the limiting efficiency of such a cell would be 29.1%7. The competing factors responsible for this upper limit of the conversion efficiency are ray-optics based light-trapping and intrinsic loss due to Auger charge-carrier recombination9,10. The thicker the cell, the more light is absorbed. Unfortunately, this is accompanied by increased bulk non-radiative recombination loss of charge-carriers. In the hypothetical case of ideal Lambertian light-trapping, state-of-the-art Auger charge-carrier recombination11 and the inclusion of band gap narrowing (BGN) in c–Si, a theoretical limit to power conversion efficiency of 29.43% has been proposed10. In this case, the optimum balance between solar absorption and bulk losses is achieved for a cell of 110 μm thickness. In traditional light trapping structures, the Lambertian limit is not achieved and the optimum solar cell thickness is much greater than 110 μm, as witnessed by the world-record-holding Kaneka cell. Moreover, the inclusion of non-zero bulk doping and surface charge carrier recombination effects further reduce the theoretical power conversion limit by at least another (additive) percentage point. For these reasons, light-trapping concepts using ray-optics, applied to any conventional silicon solar cell architecture, are not expected to yield power conversion efficiencies beyond 28%.

The wave nature of light offers a powerful alternative paradigm for solar energy capture and conversion in silicon. This is evident in certain sub-wavelength scale waveguides12,13,14 and photonic crystal15,16 architectures with microstructure periodicity and feature sizes on the scale of near-infrared light17,18,19,20,21,22. Sunlight that would otherwise be weakly absorbed in a thin film is, instead, absorbed almost completely. The resulting photonic crystal solar cell absorbs sunlight well beyond the longstanding Lambertian limit. This, in turn, leads to a dramatic reduction in the optimum silicon solar cell thickness. Ray-optics is an approximation that cannot be applied to photonic crystals and accurate modeling of wave-interference based light-trapping in a photonic crystal (PhC) due to multiple coherent scatterings from wavelength-scale micro-structures requires rigorous numerical solution of Maxwell’s equations17,18,19,20,21,22,23 throughout the solar cell architecture. A coupled optical-electronic approach and experimental study on a 3 μm-thick cell in23 showed the possibility of enhanced light-absorption and conversion efficiency in patterned silicon cells as compared to bare silicon cells. However, the light-absorption in this study still falls well below the Lambertian light-trapping limit.

Recent coupled optical-electronic analysis of thin-silicon solar cells involving parabolic pore PhCs4 and inverted pyramid PhCs5 have shown that the previous theoretical efficiency limit obtained by ray-optics based Lambertian light-trapping can be surpassed. In contrast to 165 μm-thick Kaneka cell and 110 μm-thick optimum Lambertian cell, photonic crystal solar cells are an order of magnitude thinner. The key mechanisms enabling nearly 30% efficiency using just 10 μm-thick silicon are existence of long-lifetime, slow-light resonances, parallel-to-interface refraction (PIR) and the coupling into such modes from external plane waves24. Slow-light modes exhibiting vorticity in the Poynting vector flow originate from wave-interference and cannot be achieved by ray-optics based Lambertian light-trapping. They require silicon microstructures on the scale of the optical wavelength. The Lambertian limit involves a number of assumptions such as, a randomly rough top surface without any specular reflection and deflection of the incident rays according to a cosθ probability distribution, where θ is the angle between the rays inside the slab and the surface normal. According to this model, parallel to interface flow of light (i.e. deflection of light rays at nearly θ = 90°) is unattainable. Light waves in PhCs exhibit behavior beyond the realm of ray-optics with the potential to bridge the gap between the thermodynamic efficiency limit and ray-optics based limits. Although thin-silicon PhC solar cell designs with front contacts, discussed earlier4,5, are capable of achieving efficiencies up to 30%, optical shadowing loss due to front contacts and power loss due to sheet resistance prevent them from substantially surpassing this limit.

In this article, we demonstrate that thin-silicon PhC solar cells with IBC can surpass the 30% power conversion efficiency barrier. We consider 3–20 μm thick, flexible c–Si IBC cells with a p-type bulk doping concentration of 5 × 1015 cm−3. These inverted micro-pyramid photonic crystals are optimized for light-trapping using an exact finite difference time domain (FDTD) simulation of Maxwell’s equations throughout the cell for each cell-thickness. The optical generation profiles for the optimized PhCs are then used for carrier transport optimization. We show that each optimized silicon PhC is capable of achieving a photo-current density well beyond Lambertian limit. We also present a physical explanation for the underlying wave-interference mechanism responsible for this unprecedented light trapping and absorption capability. The PhC solar cells exhibit multiple resonant peaks in the 900–1200 nm wavelength range of the absorption spectra, a region where conventional silicon solar cells and planar cells absorb negligible sunlight. These resonant peaks of PhCs are associated with PIR and vortex like flow of trapped solar energy that gives rise to effective path lengths much longer than the 4n2 path-enhancement associated with Lambertian limit. Our electronic optimization of the IBC cell involves realistic Gaussian doping profiles of emitter, back surface field (BSF) and front surface field (FSF) regions. We optimize contact geometry and widths through careful consideration of BGN, Auger recombination and practically feasible Shockley-Read-Hall (SRH) lifetimes. As the cell-thickness increases, the short-circuit current of the cell increases due to more light-absorbing material. As expected, increased cell-thickness reduces the open-circuit voltage of the cell due to increased bulk-recombination, leading to a new optimum IBC cell-thickness. This balance between light-absorption and bulk recombination suggests an optimum thickness slightly larger than that of the corresponding front contact solar cell5. We consider a wide range of SRH lifetime and study the effect of lifetime variation on optimum cell-thickness. Our results suggest that for SRH lifetimes exceeding 1 ms, the optimum PhC IBC cell-thickness is 15 μm, in contrast to 110 μm optimum thickness of the hypothetical Lambertian cell. For SRH lifetimes 1 ms and 10 ms and contact SRV 10 cm/s, our optimum 15 μm PhC IBC cell yields power conversion efficiencies of 30.29% and 31.07%, respectively. Even when the contact SRV increases to 100 cm/s, our optimum cell delivers close to 31% conversion efficiency. Our thin-film photonic crystal design provides a recipe for single junction, c–Si IBC cells with ~4.3% more (additive) conversion efficiency than the present world-record holding cell using an order of magnitude less silicon.

Ray-trapping architectures in traditional silicon solar cells usually employ two types of surface textures: upright and inverted pyramids25,26,27,28,29,30,31. Randomly distributed upright pyramid textures are widely used due to their easy mask-less fabrication through KOH etching of the silicon surface. Despite easy fabrication, upright-pyramid, thin-silicon structures typically provide less effective light-trapping than the optimized inverted-pyramid PhC of the same thickness32. On the other hand, a regular array of inverted pyramids has been used for light-trapping in the previous record-holding, passivated-emitter, rear locally diffused (PERL) cell with 25% conversion efficiency and 400 μm-thickness31. However, the feature-sizes of traditional inverted pyramid cells are typically 10 μm or more and light-absorption in such cells falls below the Lambertian ray-trapping limit. Traditional ray-trapping architectures require thick silicon (~160–400 μm) to achieve sufficient light absorption, with concomitant bulk carrier recombination that usually limits the conversion efficiency to below 27%. In contrast, our light-trapping geometry employs inverted pyramids with base-lengths ranging between 1.3–3.1 μm. This allows our cells to achieve beyond-Lambertian light-absorption through strong wave-interference effects. Using only 3–20 μm-thick silicon, resulting in low bulk-recombination loss, our silicon solar cells are projected to achieve up to 31% conversion efficiency, using realistic values of surface recombination, Auger recombination and overall carrier lifetime.

Although the surface of our silicon solar cell is patterned along a plane that is perpendicular to the incident light, the light-propagation characteristics are considerably richer than widely-studied grating-coupled waveguides. Our photonic crystal refracts and diffracts incoming light to numerous wave-vectors that are nearly parallel to the air-silicon interface. These wave-vectors couple to and experience the long-lifetime slow-light modes of the PhC. Vortex-like flow of the electromagnetic Poynting vector is evident in high density of optical resonances throughout the 800–1200 nm range. These modes are evidence of an enhancement of the overall electromagnetic density of states over this wavelength range and are characteristic of the higher bands of a photonic crystal. In contrast, the grating couplers exhibit a much narrower coupling band-width, typically about 10% of center frequency33,34,35,36,37.