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Abstract
We designed and optimized ultra-thin single junction InAlGaAs photonic power converters (PPC) with integrated back reflectors (BR) for operation at the telecommunications wavelength of 1310 nm and numerically studied the light trapping capability of three BR types: planar, cubic nano-textured, and pyramidal nano-textured. The PPC and BR geometries were optimized to absorb a fixed percentage of the incident light at the target wavelength by coupling finite difference time-domain (FDTD) calculations with a particle swarm optimization. With 90% absorptance, opto-electrical simulations revealed that ultra-thin PPCs with 5.6- to 8.4-fold thinner absorber layers can have open circuit voltages (Voc) that are 9-12% larger and power conversion efficiencies (PCE) that are 9-10% (relative) larger than conventional thick PPCs. Compared to a thick PPC with 98% absorptance, these ultra-thin designs reduce the absorber layer thickness by 9.5-14.2 times while improving the Voc by 12-14% and resulting in a relative PCE enhancement of 3-4%. Of the studied BR designs, pyramidal BRs exhibit the highest performance for ultra-thin designs, reaching an efficiency of 43.2% with 90% absorptance, demonstrating the superior light trapping capability relative to planar and cubic nano-textured BRs.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Already well-known for its revolutionary role in high-speed data transmission, optical fiber has demonstrated significant potential for optical power transmission applications in recent years. Electromagnetic interference immunity, galvanic isolation, and reduced fire hazard make optical fiber a safe and reliable power transmission alternative for driving sensors and low power electronics in hazardous and extreme environments such as high voltage lines, wind turbines, mines, and magnetic resonance imaging [1–4]. Besides power over fiber, free space optical power transmission (power beaming) has also gained attention for a wide range of applications. Some of these applications include remote, wireless powering of equipment such as medical implants [5,6] or aerial vehicles [7] and power beaming to remote locations or between satellites and terrestrial transmitters/receivers [8].
Photonic power converters (PPC) are one of the main components in optical power transmission systems, converting photonic power in the form of narrow-bandwidth light from a laser or LED source into electrical power via the photovoltaic effect. To boost the output voltage to meet application requirements, PPCs can be designed as devices with a single pn junction and combined with conventional DC-DC converters [9] or as stand-alone multi-junction devices, which directly output voltages that scale linearly with the number of series-connected pn junctions [10]. In both cases, the ability of the PPC to absorb the majority of incident irradiance is critical to achieve high optical-to-electrical power conversion efficiency, for applications ranging from milliwatts to tens of watts per chip. As transmittance decreases exponentially with active layer thickness, fulfilling high absorptance requirements ($\ge $ 90% of incoming light) typically requires absorber layers with thicknesses of at least several micrometers, leading to slow epitaxial growth and higher material usage. An alternative solution is to reduce the absorber thickness while applying light management techniques to compensate for the reduced absorptance. Thin devices also benefit from higher open circuit voltages (Voc) compared to thick devices due to increased carrier concentration and reduced recombination [11]. Their operation is less sensitive to bulk defects and diffusion length [12]. An added benefit of thin devices is their enhanced power to weight ratio, flexibility, and superior radiation tolerance, which are critical for aerospace applications [13,14].
The majority of commercially available high-efficiency PPCs are based on GaAs absorbers, operating in the range of 800-850 nm wavelengths [15,16]. The optical fiber attenuation loss at these wavelengths is ∼3 dB/km (50% per kilometer) which limits use of these devices to short-distance power-over-fiber transmission. Longer wavelengths can significantly extend this reach but require lower bandgap absorbers for which bandgap-voltage offsets represent a greater relative loss, resulting in lower expected maximum optical-to-electrical conversion efficiencies. Nevertheless, this study focuses on the O-band telecommunications window near 1310 nm which provides much lower optical fiber attenuation loss of ∼0.5 dB/km (11% per kilometer), resulting in potential for higher total system transmission efficiency in longer-reach future photonic power systems [17–19].
The efficiency of thin PPCs is expected to exceed that of their optically thick counterparts when high absorptance can be maintained through efficient light trapping. Numerous light harvesting strategies have been exploited for high-efficiency thin and ultra-thin solar cells including metal nanoparticles [20,21], photonic crystals and gratings [22,23], nanopyramids [24,25], nanocones [26], nanowires [27], planar or patterned metal back reflectors [28–30], or combinations thereof [31]. Among these methods, front surface texturing alone or in combination with a rear mirror is common. Besides trapping light, front surface texturing can decrease reflection losses across the broad solar spectrum. In the case of PPCs illuminated by narrow-band light, however, near-zero reflection losses can be obtained using a back mirror by appropriately designing the optical cavity formed by the PPC layers. Additionally, back reflectors (BR) can increase the Voc through photon recycling [32].
In this work, we applied numerical simulations to optimize ultra-thin PPC designs under narrow-band laser illumination of 1310 nm using the light trapping capability of flat BR and nanotextured BR with cubic and pyramidal structures.
2. Design
In designing PPCs, selection of the absorber material is a main consideration. Minimizing the difference between the bandgap and the incoming photon energy (0.946 eV, 1310 nm) reduces the thermalization loss, however it also reduces the absorption coefficient. Device layers should all be lattice matched to the substrate (InP) to reduce strain-induced defects that degrade cell performance by acting as recombination centers. We balanced the tradeoff between thermalization losses and absorption coefficient while satisfying the lattice matching constraint by using the quaternary alloy In0.532Al0.097Ga0.371As with a band gap of 0.88 eV for the absorber material in the pn junctions layers [33]. Assuming Beer-Lambert absorptance using a measured absorption coefficient of 7424 cm-1 [33], this material requires ∼5.3 µm thickness to absorb 98% of the incident light at a 1310-nm wavelength.
Our modeled PPCs consist of the pn junction absorber, surrounded by transparent front and back surface field (FSF and BSF) layers composed of a wider bandgap alloy, In0.527Al0.356Ga0.117As (1.25 eV). Gold, which is highly reflective at the target wavelength, serves as both the back contact and the BR. Figure 1 illustrates the epitaxial structure and back-reflector designs proposed to enable ultra-thin PPCs using flat, cubic and pyramidal textures. In our models, texturing of the absorber layers was avoided; although it has been shown to boost optical absorptance, it also degrades electrical performance due to increased surface recombination [31,34].
Fig. 1. (a) Schematic structure of ultra-thin PPCs with flat back reflector. Layer thicknesses indicate the range over which each layer was optimized. Illustrations of (b) cubic back reflector with parameters for the height h, width w, and spacing s indicated, and (c) pyramidal back reflector with height h and base width w indicated.
While this paper focuses on numerical simulation, these PPC designs could be realized, for example, by inverted epitaxial growth on the InP substrate. Following epitaxy, the BR could be deposited by blanket metallization or periodic nano-texturing via nanoimprinting (see [34], for example) on the BSF layer. The sample would then be bonded to a mechanical handle, and the InP substrate would be removed through chemical etching or epitaxial liftoff.
3. Simulation and optimization
Optical simulations of PPC devices were performed in the Lumerical FDTD Solutions software using the finite difference time-domain (FDTD) method. The quaternary alloys were modeled with refractive index parameters that were extracted experimentally by ellipsometry measurements of samples with the same composition grown by molecular beam epitaxy [35]. The optical properties of gold (Au) and InP were taken from Palik [36]. The modelled structures were illuminated by a normally incident uniform light with an intensity of 100 mW/cm2. The laser spectrum featured a Gaussian distribution centered at 1310 nm with a full-width-at-half-maximum linewidth of 10 nm. We performed 2D optical simulations for flat BR designs and 3D optical simulations for textured BR designs over a single unit cell. Periodic and perfectly matched layer (PML) boundary conditions were applied for the lateral (x and y) and growth (z) directions, respectively. For 3D simulations, since both incident light and nanostructures were symmetric with respect to the center of the simulation region in x and y directions, symmetric and antisymmetric boundary conditions also were implemented to reduce computational requirements by reducing simulations to one-quarter of the original simulation area. Pyramids were modelled using a staircase approximation, replacing the pyramid by a series of stacked squares, each diminishing in size and each of 2.5 nm thickness [37], which we confirmed converges Jph to within ±0.3%.
The PPC’s generation rate G was calculated assuming that each absorbed photon generates an electron-hole pair. The total generation rate was calculated by integrating over the linewidth of the laser source as:
For each BR type, our design optimization sought to minimize the absorber layer thickness while obtaining a target absorptance of 90%, corresponding to a Jph of ∼95 mA/cm2 and a responsivity of 0.95 A/W. Fabry-Perot resonances were aligned to the target wavelength by tuning the optical cavity design, minimizing reflectance and maximizing absorptance. Structure optimization varied the absorber and FSF layer thicknesses for the planar BR design. For the nanotextured BR designs, their geometrical parameters were added to the design space, comprising height h, width w, and spacing s for the cubic BR (Fig. 1(b)), and height h and base width w for the pyramidal BR (Fig. 1(c)). To avoid polarization dependence for normal incidence, nanostructure dimensions were kept equal in the x and y directions. In all cases, the BSF layer thickness was fixed at 50 nm. These parameter spaces were investigated via a particle swarm algorithm [38], using photocurrent Jph as the figure of merit.
We simulated two thick PPCs on InP substrates to use as baselines to compare the light harvesting capability and power conversion efficiencies of ultra-thin PPCs. One of the thick PPCs was simulated with high (98%) absorptance and the other with same absorptance (90%) as the optimized ultra-thin devices. The required absorber thicknesses are 5270 nm and 3100 nm for the 98% and 90% designs, respectively. Without an antireflection coating, both thick designs would suffer from ∼30% reflection loss. To achieve a fair comparison with ultra-thin designs which benefit from near-zero reflection loss, the FSF layer thickness was optimized in conjunction with a double-layer antireflection coating (ARC) of SiO2/TiO2 [39] in the thick PPC designs. We refer to these designs as Ref 98% and Ref 90%.
For these optically thick designs, the Jph values obtained from simulations were about 0.02 mA/cm2 lower than analytical calculations according to:
where Jph,th is the theoretical photocurrent, A is the absorptance, P is the input power, and Eph is the energy of the incident photon.For further verification of optical simulations, we compared the model performance to a fabricated device with a 4100 nm absorber layer thickness, corresponding to 95% absorptance. The close match between the experimental measurements and simulation results for the reflectance spectra is shown in Appendix B.
After optimization of devices structures through optical simulations, we conducted electrical simulations to evaluate device performance. The model included: bulk recombination losses – radiative, Shockley-Read-Hall (SRH), and Auger; 5% gridline shading loss; and ideal ohmic contacts with no contact resistance. Electrical simulations were performed using the finite element drift-diffusion method using the charge transport simulator, CHARGE by Lumerical, applying a device temperature of 300K. The generation rate G obtained from the optical simulations was used as input for the electrical simulations. Except for SRH carrier lifetime and bandgap, other material parameters for the quaternary alloy InxAlyGa1-x-yAs were determined by interpolation between the three ternary constituents: GaInAs, AlInAs, and AlGaAs [40,41]. Some of these parameters for the active layer are given in Appendix A. SRH carrier lifetime depends significantly on the material and growth quality and could vary from microseconds to picoseconds. For these simulations we selected 100 ns to represent high quality material. See Appendix B for comparison of the experimentally measured and simulated I-V curves for a fabricated device with 4100 nm absorber layer thickness.
4. Results and discussion
Table 1 reports the optimized design parameters with corresponding absorptance and primary optical losses including parasitic absorption in the back mirror and reflectance. For BR designs, near-zero reflection loss was obtained without the incorporation of an ARC. Reflection spectra for all five designs from Table 1 are shown in Fig. 2.
Table 1. Optimized parameters of PPCs with corresponding absorptance and optical losses at 1310 nm.
Fig. 2. Reflection spectrum versus wavelength for all five optimized PPC designs, including optically thick (Ref 98%, Ref 90%) and ultra-thin (flat, cubic, and pyramidal back-reflectors). These designs were optimized for near zero reflection loss at 1310 nm wavelength. The laser spectrum centered at 1310 nm is indicated by the vertical line.
The cross-sectional absorbed power profiles and corresponding Jph values are depicted in Fig. 3 for all five structures: Ref 98%, Ref 90%, flat, cubic, and pyramidal BRs. For the thick reference PPCs, shown in Figs. 3(a),(b), most of the light absorption occurs near the front surface and decreases as less light penetrates deeper into the absorbing layer, as expected. However, for the ultra-thin planar structure in Fig. 3(c) and nano-textured structures in Figs. 3(d),(e), the back mirrors create strong Fabry-Perot resonances in the absorptance profiles. Additionally, the nano-textured back mirrors also induce guided mode resonances that further enhance light trapping at the resonance wavelength. The 625-nm thick InP substrates of the reference designs are not fully depicted in Fig. 3, although they were included in the simulations. The Jph values are close to 95 mA/cm2 for the flat, cubic and pyramidal BR designs, indicating that they each absorb approximately 90% of the incident light despite reducing the absorber thickness by 5.6, 7.6, and 8.4 times, respectively, relative to the Ref 90% structure. Compared to Ref 98%, flat, cubic and pyramidal structures achieve 9.5-, 12.5- and 14.2-fold reductions in the absorber layer thickness.
Fig. 3. Cross-sectional absorbed power profiles at y = 0 of each optimized PPC design: (a) Ref 98%, (b) Ref 90%, (c) flat, (d) cubic, and (e) pyramidal BRs. Inset table compares light trapping capability and thickness reduction of proposed PPCs (t: absorber thickness). Note that the x scales differ for each (d) and (e) compared to (a)-(c). The dotted white lines indicate material interfaces. The FSF and BSF, above and below the absorber, are transparent to the incident light. Only a small portion of the substrate is shown in (a) and (b), as indicated by the wavy lines.
The light-trapping ability of a thin structure can be quantified by comparing it to the Beer-Lambert absorption through a material with twice its thickness. This emulates the expected absorption by two passes through the structure, assuming a perfect back reflector and no additional reflections or scattering. This two-pass photocurrent, Jph-2pass, is calculated by Eq. (3) with A set as the Beer-Lambert absorptance for twice the absorber thickness of the corresponding design. In the ultra-thin designs, optical cavity and guided-mode resonances result in simulated photocurrents that are enhanced by factors of 1.6, 2.0, and 2.1 for the flat, cubic, and pyramidal BRs, respectively, in comparison to the two-pass case. The pyramidal BR design has the most significant reduction in absorber thickness, demonstrating its greater light scattering and trapping capability compared to planar and cubic nano-textured BRs.
The designs proposed here were optimized to minimize the absorber layer thickness while retaining 90% absorptance. However, alternative designs can also achieve nearly 90% absorptance with slightly (30-50 nm) thicker absorber layers using a different combination of design parameters such as FSF thickness and/or nanotexture dimensions [42,43]. Therefore, allowing a slightly thicker absorber can broaden the design freedom significantly.
The reflectance spectrum and resonance linewidth differ significantly between thin PPC designs (Fig. 2). For optical power transmission applications, resonances with wider linewidths are desired, as the operating wavelength of a laser can deviate due to manufacturing tolerances or temperature fluctuations [44], and performance can be affected by other conditions such as illumination angle. Although we simulated near-zero reflection loss (Fig. 2) without incorporating an ARC, applying an ARC could increase the resonance linewidth and minimize reflection over a larger spectral range, improving the stability and applicability of these devices. Such an ARC would also affect the optimum thickness of other layers due to interference effects and expand the design freedom.
Current-voltage characteristics and device efficiencies obtained from electrical simulations (Fig. 4) show that the ultra-thin designs with planar and textured back reflectors improve the Voc by 12-14% and the power conversion efficiency (PCE) by 3-4% (relative), as compared to the Ref 98% design. In comparison with the Ref 90% design, the optimized ultra-thin designs match the Jsc, boost the Voc by 9-12%, and increase the PCE by 9-10% (relative). The higher efficiency in ultra-thin designs is caused by the increased open-circuit voltage, which is enabled by the strong light-trapping induced by the back reflectors.
Fig. 4. Current-voltage characteristics of the proposed PPCs under intensity of 100 mW/cm2 at T=300K. Maximum power points are indicated by the colored circles.
The main parasitic optical loss for the ultra-thin PPCs is absorption in the back mirror [45], as shown in Table 1, which is worse for the textured structures that have more light trapping and thus more interaction between light and the back surface. The main electrical loss can be due to SRH carrier lifetime, which varies over orders of magnitude depending on the material quality. For example, for pyramidal nanotextured BR structures, an SRH lifetime in the InAlGaAs absorber layer of 10, 100, and 1000 ns results in efficiencies of 35%, 43.2%, and 46% [46], respectively. Real-world devices may include additional losses such as those from surface recombination and thermal effects.
By increasing the illumination intensity to 10 W/cm2, the simulated efficiencies of the Ref 98% and pyramidal nanotextured BR designs increased to 50.5% and 56.2%, respectively. The simulated efficiencies of the Ref 98% device under both these low and high intensities are the same as those observed experimentally for the optically thick PPCs of Ref [18]. Further efficiency improvements could be achieved by shifting the absorber bandgap closer to the incident photon energy to reduce the thermalization loss [47], optimizing the front metallization [48], and employing higher quality material with longer carrier lifetimes. These simulations did not account for photon recycling effects, which would yield higher efficiencies in highly luminescent materials [49,50].
5. Conclusions
In this work, we presented design, simulation, and optimization of light management in highly efficient ultra-thin PPCs, comparing the simulated performance of flat, cubic, and pyramidal nano-textured BRs under 1310 nm narrow-band illumination. Due to strong Fabry-Perot and guided mode back-reflector induced resonances, we attained near-zero reflection loss in the ultra-thin PPCs without applying an antireflection coating. Compared to conventional thick PPCs on a substrate, modelled ultra-thin PPCs with BRs demonstrated superior performance with larger Voc and PCE. The best performance was exhibited by the device with a pyramidal nano-textured BR. Further design optimization, reduced thermalization loss, front metallization engineering, higher intensity laser illumination, and accounting for photon recycling could lead to simulated efficiencies over 50%. The approach proposed here could be applied to other illumination wavelengths and both single and multi-junction PPCs could benefit from these design principles.
Appendix A: Electrical simulation parameters
Table 2 lists some of the parameters of the active layer used in the electrical simulations. The properties for ternary alloys were extracted from [51–53], then linearly interpolated to determine values for the quaternary alloys.
Table 2. Electrical parameters of the absorber layer at T=300K
Appendix B: Experimental measurement and simulation comparison
To demonstrate the accuracy of the simulation, we compared the model performance to a fabricated device with a 4100 nm absorber layer thickness, corresponding to 95% absorptance. As shown in the inset of Fig. 5, the model represents experimentally measured reflectance spectra. For reproducing the experimentally measured I-V curve, the SRH electron and hole lifetimes were reduced to 1 and 0.1 ns, respectively and band gap narrowing effects were added to the simulations. The lower efficiency of the fabricated device originates from 30% reflection loss, 8% grid line shading, and shorter carrier lifetimes. To highlight the effect of material quality on the PPC’s performance, simulations with longer SRH carrier lifetimes (10 ns for both electron and holes) were included in the simulations depicted using a yellow dashed line.
Funding
Natural Sciences and Engineering Research Council of Canada (497981).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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