Ultra-thin GaAs solar cells with nanophotonic metal-dielectric diffraction gratings fabricated with displacement Talbot lithography

Ultra-thin photovoltaics enable lightweight flexible form factors, suitable for emerging terrestrial applications such as electric vehicle integration. These devices also exhibit intrinsic radiation tolerance and increased specific power and so are uniquely enabling for space power applications, offering longer missions in hostile environments and reduced launch costs. In this work, a GaAs solar cell with an 80-nm absorber is developed with short circuit current exceeding the single pass limit. Integrated light management is employed to compensate for increased photon transmission inherent to ultra-thin absorbers, and efficiency enhancement of 68% over a planar on-wafer equivalent is demonstrated. This is achieved using a wafer-scale technique, displacement Talbot lithography, to fabricate a rear surface nanophotonic grating. Optical simulations definitively confirm Fabry-Perot and waveguide mode contributions to the observed increase in absorption and also demonstrate a pathway to short circuit current of 26 mA/cm 2 , well in excess of the double pass limit.


| INTRODUCTION
The development of thin and ultra-thin photovoltaic devices with integrated light management has been widely studied in recent years, with a view to increasing device performance, achieving lightweight, flexible embodiments for systems integration and reduced materials usage. 1 These devices are also compelling candidates for space power applications as they exhibit intrinsic tolerance to the damaging radiation environments found outside of the Earth's protective atmosphere. Space photovoltaics are bombarded with electron and proton radiation, which can cause dislocations in the lattice structure of the device active layers, reducing diffusion lengths and degrading charge carrier collection efficiency. The development of photovoltaic devices with greater tolerance to radiation exposure would enable longer onorbit lifetimes and missions in currently inaccessible high radiation environments, as well as the reduction or elimination of rigid and heavy protective coverglass for lightweight, flexible form factors.
Intrinsic radiation tolerance has previously been demonstrated in 80 nm GaAs devices, showing no degradation in short circuit current (J SC ) for 3 MeV proton fluence up to 10 14 cm À2 , while J SC of comparable 800 nm devices degraded to 26% of the starting value. 2 The devices in this proof of concept demonstration, however, had poor beginning-of-life performance (AM0 J SC =5.62 mA/cm 2 ), primarily because they were processed on-wafer without light management.
As devices are made thinner, high transmission losses resulting in lower J SC become an increasing challenge. This can be addressed with integrated light management architectures to extend the optical path length of incident solar photons, increasing total absorption in the device. These optical systems can take different forms including (i) a rear surface planar mirror to enable a double-pass of the device, 3,4 (ii) a Lambertian surface to scatter light outside of the optical escape cone at the front surface [5][6][7][8] and (iii) a nanophotonic array to preferentially scatter light into optical modes supported by the ultra-thin film. 9,10 Previous studies have made use of techniques including nanoimprint lithography 10,11 to fabricate GaAs devices with nanostructured back surfaces. Displacement Talbot lithography (DTL) is an emerging photolithographic patterning technique which enables the fabrication of high aspect ratio features over large areas, with feature size down to $100 nm. 12 Wafers are patterned with a single exposure, making this technique suitable for rapid, large area patterning, 13 as required for the fabrication of photovoltaic devices. Complex patterns can be created using lateral displacements during exposure or using multiple exposures. 14 As with nanoimprint techniques, DTL requires the fabrication of a mask (or master) by electron beam lithography or interference lithography; however, as DTL is a noncontact method, this mask can be reused an unlimited number of times without degradation. Nanophotonic arrays are fabricated from materials with contrasting refractive index. Metallic systems are particularly promising given their strong scattering of light, [15][16][17] but they can also exhibit unwanted parasitic absorption.
Another key challenge for ultra-thin devices is achieving good diode performance. Contacting schemes must be carefully designed to avoid the diffusion of Au into the active device layer, which degrades diode performance through the introduction of shunt paths and recombination centres at the junction. Furthermore, surface effects become increasingly important on this length scale, as the diode is fully depleted, and therefore surfaces must be passivated. ing window and back surface field layers). 10 The thinnest possible devices will be required in order to fully benefit from intrinsic radiation tolerance. As an example, in a geostationary orbit an 800 nm GaAs device without coverglass might survive approximately two years, while an 80 nm equivalent would survive more than a decade. 18 In this work, GaAs solar cells with active layer thickness 80 nm (120 nm including window and back surface field layers) are developed, featuring an integrated Ag/SiN nanophotonic grating, patterned using DTL. Highly doped AlGaAs is commonly employed as a p-type passivation layer for ultra-thin GaAs devices 2,4,10,11 because of its favourable band alignment and lower absorption coefficient, particularly for higher Al compositions; however, the results of this study indicate that InGaP makes a superior p-type barrier demonstrating near ideal passivation of the front surface, with all charge carriers generated in this layer extracted as current and diode performance metrics comparable with much thicker devices. AM0 solar energy conversion efficiency of 9.08% is achieved, which is comparable to an equivalent device with a planar Ag mirror. Simulations indicate that the addition of an anti-reflection coating (ARC) and reduction in front contact shading losses, as well as further optimization of the nanophotonic array geometry, would increase the efficiency of the nanophotonic device to 16.0%, while applying the same ARC and front contact shading to the planar Ag device would only increase its efficiency to 14.0%. This highlights the potential for devices with integrated nanophotonic light management to exceed the efficiency of single-pass and double-pass optical designs on this ultra-thin device length scale; however, this is only achieved with precise optimization and in certain cases a rear surface planar mirror can provide equivalent or even more favourable performance. Significantly, this work shows a pathway to improving beginning-of-life efficiency for ultrathin devices in a regime where intrinsic radiation tolerance has been demonstrated.
T A B L E 1 Device layer structure as grown by molecular beam epitaxy Devices were processed with square 2.5 mm x 2.5 mm mesas.
On-wafer devices were processed with an all front surface contacting scheme using a grid pattern with a contact pad on the top surface of the device for the n-type contact (10% shading loss) and a laterally displaced p-type contact outside the mesa area ( Figure 1B). The front surface contact layer was etched to reduce absorption. Off-wafer devices (planar Ag and nanophotonic) were processed with an inverted layer structure, employing the same front surface grid pattern as used for the on-wafer devices for the p-type contact and a rear surface grid (approx. 3.2% coverage) for the n-type contact. Both front and rear surface contact layers were etched.
In the case of the planar Ag devices, a layer of Ag was deposited by thermal evaporation directly onto the InAlP passivation layer. For the nanophotonic devices, 100 nm of SiN was first deposited by plasma-enhanced chemical vapour deposition and a hexagonal array of holes was patterned into the SiN using DTL and an inductively coupled plasma etch ( Figure 1D). DTL operates by projecting the interference pattern of a periodic mask (illuminated by coherent light) onto a photosensitive resist. The interference pattern is threedimensional and forms repeating self-images of the mask along the axis of incidence. The distance that separates consecutive self-images is called the Talbot period. 13 The exposure step is carried out by displacing the wafer along the axis of incidence, normally by a few Talbot periods so that exposure uniformity is achieved along this axis in the resist and depth of field limitations are overcome. Rigourous coupled wave analysis (RCWA) was used to evaluate the optimal array geometry (pitch, Ag coverage and grating thickness) for the given device layer structure and process parameters were selected to fabricate an array which was as close as practically possible to this optimal. An array pitch of 500 nm was selected and exposure dose was adjusted to give circular features with average diameter 229 ± 24 nm ( Figure 1C) and depth 80.5 ± 10.9 nm, leaving a SiN film of approximately 19.5 nm at the InAlP interface (see Methods for grating geometry evaluation). Ag was then evaporated over the perforated SiN layer similar to the planar Ag devices ( Figure 1A).
Off-wafer devices were then bonded to a Si carrier using a high glassing temperature epoxy. They were then inverted and the substrate and subsequent etch stop layer were selectively etched to expose the GaAs p-type contact layer and enable front surface contacting (see Methods for further fabrication details).

| DEVICE PERFORMANCE
Device current-voltage characteristics were measured under a simulated AM0 spectrum ( Figure 2A) (see Methods for measurement details). Both the off-wafer designs showed significant efficiency enhancement over the on-wafer equivalent, with the nanophotonic device providing the highest efficiency, 9.08% (no ARC and 10% shading loss) ( Table 2). This performance enhancement was driven by an The off-wafer devices have higher charge carrier density in the ultrathin device volume and this concentration factor further increases voltage. 19 Current-voltage measurements were also acquired in the dark for the hero nanophotonic device ( Figure 2B) and a 2-diode model was fitted 20 to extract diode performance parameters (saturation current densities J 01 and J 02 , series resistance R ser and parallel resistance R par ).
These are compared with equivalent literature results (Table 3). J 02 is a measure of the recombination in the depletion region and therefore of particular interest for our fully depleted devices. A low value indicates good diode performance. In this work J 02 =3.29x10 À8 mA/cm 2 is measured. This is a significant improvement over a previously reported value (J 02 =1.41x10 À6 mA/cm 2 ) for a comparable 80 nm device with Al 0.3 Ga 0.7 As passivation layers. 2 High J 02 has also been reported for devices with 120 nm and 220 nm active layer thickness with AlGaAs passivation layers. 4,21 This comparison indicates that surface passivation with InGaP and InAlP reduces depletion region recombination, allowing for enhanced performance in ultra-thin geometries. The value of J 02 achieved here is comparable with results reported for devices which are >2.5 times as thick 10 ; however, further reductions in J 02 have been reported for devices which are an order of magnitude thicker. 2,3 These much thicker devices are likely not fully depleted and therefore it is expected that surface effects will have less of an impact on J 02 .
While the use of light management in ultra-thin geometries may give a fundamental boost in voltage, the higher J 02 in these fully depleted devices will have the opposite effect, reducing FF and V OC .
It may be possible to iteratively improve device design to address this issue; however, achieving V OC > 1.1 V as demonstrated by Kayes at al. 3 will be challenging for devices on this length scale.

| OPTICAL PERFORMANCE
To evaluate optical performance, external quantum efficiency (EQE) was measured for the different light management designs ( Figure  This can be attributed to an increasing optical path length. The offwafer devices also exhibit enhanced absorption at short wavelengths (<400 nm). EQE in this wavelength range will be dominated by the front surface. The off-wafer devices have an inverted geometry, with InGaP on the front surface, while the on-wafer device has InAlP. The enhanced short wavelength EQE of the off-wafer devices indicates that self-passivation of the front surface InGaP is superior to that of InAlP, allowing charge carriers generated in this layer to be efficiently extracted as current (see Figure 2D). For this reason, the p-on-n orientation of the diode, as is the case for the off-wafer devices, is highly favourable for ultra-thin geometries. Note: The total thickness includes window and back surface field layers. *n 2 was held constant for these devices.
whereas Fabry-Perot modes arise due to light which is specularly reflected; for the device incorporating a diffraction grating, which is also highly reflective, we expect to see contributions from both effects. RCWA simulations incorporate both thin-film interference and diffraction effects, and can be used to compare to analytically calculated resonant wavelengths and the measured EQE. TMM simulations were used to model the performance of the planar devices (the on-wafer and planar Ag mirror devices) and to investigate the thin-film contributions in the device with a nanophotonic grating.

| Planar devices
The EQE was calculated from simulation by taking the combined absorption in the InGaP and GaAs layers, and assuming shading losses of 10% ( Figure 2C). An excellent match is observed between the TMM simulations of the two planar devices and the measured EQE, indicating that almost all carriers generated in the GaAs and InGaP layers can be extracted. Figure 2D shows simulated absorption in the front surface InGaP, GaAs junction and rear surface InAlP layers for the planar Ag device. This shows that absorption in the GaAs layer alone cannot account for the high EQE at short wavelengths, due to the significant absorption in the InGaP layer in the wavelength regime; 40% of 300 nm photons. Absorption in the InAlP is relatively low as this layer is positioned on the rear surface of the off-wafer devices.
The sum of simulated photon absorption in the InGaP and GaAs layers gives a much better fit to the observed EQE indicating almost 100% carrier collection efficiency for charge carriers generated from the InGaP layer.

| Nanophotonic device
The measured EQE spectrum of a device with integrated rear surface nanophotonic structure is shown in Figure 2C  interference in a specific set of layers can be calculated through: where m is any integer, k z,i = 2πn i /λ is the z-component of the wavevector (for normal incidence) in layer i with refractive index n i , d i is the thickness of layer i and φ fb is the additional phase change due to reflection at the front and back surface, which can be worked out from the Fresnel equations; r front and r back are the Fresnel reflection coefficients, evaluated with the appropriate complex refractive indices n 1 and n 2 ; for r front , n 1 describes the incidence medium (air) and n 2 describes the first layer of the stack (InGaP), and for r back the n 1 value is for the final layer in the stack (SiN) and n 2 describes the substrate (Ag). The symbol ∠ denotes the phase of the complex number. Figure 3C shows the phase change across the cell structure, assuming modes can exist in the III-V layers plus SiN in between the Ag disks.
The first three Fabry-Perot resonances in this cavity, corresponding to phase changes of 2π, 4π and 6π across the structure, occur at 904 nm, 582 nm, and 463 nm, respectively. The latter two wavelengths match extremely well with peaks observed in the EQE (at 570 nm and 470 nm). The long-wavelength peak in the EQE occurs at 835 nm, so below the predicted peak for the FP resonance; this is likely due to the absorption edge of the GaAs causing the peak in absorbed power to occur below the resonant wavelength. The absorption profile calculated for Structure 3 ( Figure 3B) shows a clear peak around 835 nm, confirming that this feature is due to a thin-film effect. The peaks at 675 nm and 745 nm cannot be explained by thinfilm interference, even when different possible thin-film cavities in the structure were considered (see the Supporting Information) and were attributed instead to waveguide modes.
In waveguide modes, the field enhancement mechanism is the constructive interference of incident waves that are diffracted by This condition restricts the occurrence of waveguiding to only a discrete set of propagating waves with specific in-plane wavevector components (k xy ), more commonly referred to as propagation constants. For a given wavelength, each propagation constant will correspond to a different waveguide mode, having a characteristic distribution of the electromagnetic field within the device.
We solve the propagation constants of the waveguide modes available in our fabricated devices by implementing a method for the waveguide analysis of multi-layered stacks. 22 Using the experimentally determined thicknesses and optical constants and focusing on the spectral range between 500 and 900 nm, two modes are found to have a high field confinement in the active layer of the device (Supporting Information), one for each polarisation of light.
Labelled TE0 and TM0, the high field confinement of these modes makes them more advantageous for absorption enhancement in the active layer. In our devices, coupling incident photons to these waveguide modes has a stringent dependence on the unit cell and Λŷ . For these conditions and considering normal light incidence, the allowed k xy are defined by the following equation: where m 1 and m 2 are pairs of integers which define optical states.
According to Equation (2), coupling to a waveguide mode at a given wavelength is enabled at an optical state when its corresponding k xy matches the propagation constant of the mode ( Figure 3F). Since different optical states may correspond to the same k xy (and thus enable the same coupling event), we group these into sets and label them OSx ( Figure 3E), with x being the value that all these states yield inside the square root in Equation (2).  (Table 4).
The peak at λ = 745 nm is associated to coupling to the TE0 mode at OS3, whereas the one at λ = 675 nm has contributions from coupling to both TM0 at OS3 and TE0 at OS4. As for the peak at λ = 570 nm, this strong and broad resonance has contributions from TE0 coupling at OS7 together with the previously described thinfilm effect. The differences between the predicted resonant wavelengths in Table 4 and those at which their associated EQE peaks are found are small (within $3%), but quantification of these discrepancies is limited in cases when more than one field enhancement mechanism is found in the vicinity of a peak. We attribute any discrepancies mainly to the effective medium approximation used to describe the grating in our method for waveguide analysis (accounting for the deviations in the measured grating thickness and disk radius did not change the calculated resonant wavelengths significantly, with variations staying below Δλ = 10 nm for all modes).
Four other TE0 and TM0 coupling events can be predicted with Equation (2) within λ = 515 -635 nm, and these are likely contained within the broad peak at 570 nm.
Finally, it can be seen in Figure 2C that the peaks in the measured EQE associated with coupling to waveguide modes are significantly higher in the equivalent RCWA simulation, indicating there is some discrepancy between simulated and observed diffraction effects. As can be seen in Figure 1D, Improvements (ii)-(iv) relate to the dimensions of the grating; without changing the mask used to produce the grating or the epitaxial layer structure, the current could be improved by 3% by ensuring that the grating disks are etched all the way through the SiN layer. RCWA simulations exploring the design space of similar gratings for ultra-thin GaAs cells 23 have shown that absorption in the GaAs can be improved further by tuning the pitch and disk size of the hexagonal grating (assuming the same materials, SiN and Ag, are used, and the same type of DTL mask leading to a hexagonal array of circular disks). The disk size in the current embodiment is lower than the optimum value predicted by simulations, which indicate that a disk radius close to one third of the grating pitch gives optimal absorption enhancement.
Increasing the disk radius in the simulations from 114.5 nm to 160 nm shows an increase to the current of 9%. This change could be achieved by increasing the exposure dose used for the DTL patterning. If a different DTL mask is used, the pitch of the disks can be changed; the optimum is expected to lie between 600-700 nm for this cell thickness and grating symmetry. Increasing the pitch pushes the waveguide modes to longer wavelengths ( Figure 4C). This will also increase the wavelength below which diffracted modes can escape the front surface (light line), however, at Λ = 600 nm this occurs at λ = 500 nm. Below this wavelength the GaAs layer will be highly absorbing on a single pass and therefore current loss from diffracted light escaping the front surface will be minimal. Changing the pitch of the grating to 600 nm, and keeping the disk radius at one third of the grating pitch gives a further current improvement of 3% (it was found that for any given pitch, the optimal disk size lies close to one-third of the pitch, as was the case for the 500 nm grating). Finally, an obvious potential improvement to the current can be made by reducing the contact shading; in these devices, the contact shading was estimated at 10%, but this could be reduced to <3%, 24,25 without impacting on charge carrier collection efficiency. Figure 4B shows the simulated EQE of the device with all the improvements discussed, as compared to the EQE of the fabricated device with nanophotonic grating. also assuming 3% contact shading. The nanophotonic light management system therefore has the greatest potential for high current and high solar energy conversion efficiency for this device geometry (Table 5).

| CONCLUSIONS
In this work solar energy conversion efficiency enhancement in ultra-

| p-type contact metalisation
Ti/Au (20/200 nm) p-type contacts were deposited using thermal evaporation and lift-off. In the case of the off-wafer devices the exposed p-type contact layer was then etched away using a selective   7.9 | EQE simulations EQE was calculated by simulating absorption in the GaAs and InGaP layers and assuming a uniform 10% shading loss due to the front contacts. It was assumed all charge carriers generated in these layers were collected (100% internal quantum efficiency). Absorption in all other layers was assumed to be parasitic. Layer thicknesses and optical constants for all deposited materials (the III-V materials, SiN, and Al 2 O 3 ) were evaluated using ellipsometry measurements (see Supporting Information), with the exception of silver, data for which was taken from the crystal monitor of the thermal evaporator and from reference. 26 The transfer matrix method (TMM), as included in the modular solar simulation package Solcore, 27 was used to simulate the performance of the two types of planar device (the on-wafer device and the device with the planar Ag rear surface mirror), showing excellent agreement between the measured EQE and simulated EQE.
The nanophotonic device performance was simulated using a modified version of S 4 (see Supporting Information for further details) to perform RCWA simulations, 28

| Modal analysis
The calculation of the waveguide modes was done by implementing a transfer matrix method for the waveguide analysis of multi-layered planar stacks. 22,30 This method takes as input the thicknesses and complex refractive indices of all the layers in the stack. In our implementation, the grating is represented as a uniform slab having an effective index corresponding to the average of its component materials weighted by their volume ratio within the unit cell. The outputs of the transfer matrix method are dispersion equations for TE and TM polarisation, whose roots correspond to the propagation constants of the available waveguide modes. We find these roots following a Newton-Raphson method in the complex plane.

SUPPORTING INFORMATION
Additional supporting information may be found in the online version of the article at the publisher's website.