Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading. Part III: piecewise-homogeneous grading.

In Parts I [Appl. Opt.58, 6067 (2019)APOPAI0003-693510.1364/AO.58.006067] and II [Appl. Opt.61, 10049 (2022)APOPAI0003-693510.1364/AO.474920], we used a coupled optoelectronic model to optimize a thin-film CIGS solar cell with a graded-bandgap photon-absorbing layer, periodically corrugated backreflector, and multilayered antireflection coatings. Bandgap grading of the CIGS photon-absorbing layer was continuous and either linear or nonlinear, in the thickness direction. Periodic corrugation and multilayered antireflection coatings were found to engender slight improvements in the efficiency. In contrast, bandgap grading of the CIGS photon-absorbing layer leads to significant enhancement of efficiency, especially when the grading is continuous and nonlinear. However, practical implementation of continuous nonlinear grading is challenging compared to piecewise-homogeneous grading. Hence, for this study, we investigated piecewise-homogeneous approximations of the optimal linear and nonlinear grading profiles, and found that an equivalent efficiency is achieved using piecewise-homogeneous grading. An efficiency of 30.15% is predicted with a three-layered piecewise-homogeneous CIGS photon-absorbing layer. The results will help experimentalists to implement optimal designs for highly efficient CIGS thin-film solar cells.

Optoelectronic optimization of graded-bandgap thin-film AlGaAs solar cells. Part II: optimal antireflection front-surface texturing.

In Part I [Appl. Opt.59, 1018 (2020)APOPAI0003-693510.1364/AO.381246], we used a coupled optoelectronic model to optimize a thin-film AlGaAs solar cell with a graded-bandgap photon-absorbing layer and a periodically corrugated Ag backreflector combined with localized ohmic Pd-Ge-Au backcontacts, because both strategies help to improve the performance of AlGaAs solar cells. However, the results in Part I were affected by a normalization error, which came to light when we replaced the hybridizable discontinuous Galerkin scheme for electrical computation by the faster finite-difference scheme. Therefore, we re-optimized the solar cells containing an n-AlGaAs photon-absorbing layer with either a (i) homogeneous, (ii) linearly graded, or (iii) nonlinearly graded bandgap. Another way to improve the power conversion efficiency is by using a surface antireflection texturing on the wavelength scale, so we also optimized four different types of 1D periodic surface texturing: (i) rectangular, (ii) convex hemi-elliptical, (iii) triangular, and (iv) concave hemi-elliptical. Our new results show that the optimal nonlinear bandgap grading enhances the efficiency by as much as 3.31% when the n-AlGaAs layer is 400 nm thick and 1.14% when that layer is 2000 nm thick. A hundredfold concentration of sunlight can enhance the efficiency by a factor of 11.6%. Periodic texturing of the front surface on the scale of 0.5-2 free-space wavelengths provides a small relative enhancement in efficiency over the AlGaAs solar cells with a planar front surface; however, the enhancement is lower when the n-AlGaAs layer is thicker.

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading. Part II: finite-difference algorithm and double-layer antireflection coatings.

In Part I [Appl. Opt.58, 6067 (2019)APOPAI003-693510.1364/AO.58.006067], we used a coupled optoelectronic model to optimize a thin-film C u I n 1-ξ G a ξ S e 2 (CIGS) solar cell with a graded-bandgap photon-absorbing layer and a periodically corrugated backreflector. The increase in efficiency due to the periodic corrugation was found to be tiny and that, too, only for very thin CIGS layers. Also, it was predicted that linear bandgap-grading enhances the efficiency of the CIGS solar cells. However, a significant improvement in solar cell efficiency was found using a nonlinearly (sinusoidally) graded-bandgap CIGS photon-absorbing layer. The optoelectronic model comprised two submodels: optical and electrical. The electrical submodel applied the hybridizable discontinuous Galerkin (HDG) scheme directly to equations for the drift and diffusion of charge carriers. As our HDG scheme sometimes fails due to negative carrier densities arising during the solution process, we devised a new, to the best of our knowledge, computational scheme using the finite-difference method, which also reduces the overall computational cost of optimization. An unfortunate normalization error in the electrical submodel in Part I came to light. This normalization error did not change the overall conclusions reported in Part I; however, some specifics did change. The new algorithm for the electrical submodel is reported here along with updated numerical results. We re-optimized the solar cells containing a CIGS photon-absorbing layer with either (i) a homogeneous bandgap, (ii) a linearly graded bandgap, or (iii) a nonlinearly graded bandgap. Considering the meager increase in efficiency with the periodic corrugation and additional complexity in the fabrication process, we opted for a flat backreflector. The new algorithm is significantly faster than the previous algorithm. Our new results confirm efficiency enhancement of 84% (resp. 63%) when the thickness of the CIGS layer is 600 nm (resp. 2200 nm), similarly to Part I. A hundredfold concentration of sunlight can increase the efficiency by an additional 27%. Finally, the currently used 110-nm-thick layer of M g F 2 performs almost as well as optimal single- and double-layer antireflection coatings.

Enhanced efficiency of graded-bandgap thin-film solar cells due to concentrated sunlight.

A systematic study was performed with a coupled optoelectronic model to examine the effect of the concentration of sunlight on the efficiencies of CIGS, CZTSSe and AlGaAs thin-film solar cells with a graded-bandgap absorber layer. Efficiencies of 34.6% for CIGS thin-film solar cells and 29.9% for CZTSSe thin-film solar cells are predicted with a concentration of 100 suns, the respective one-sun efficiencies being 27.7% and 21.7%. An efficiency of 36.7% is predicted for AlGaAs thin-film solar cells with a concentration of 60 suns, in comparison to 34.5% one-sun efficiency. Sunlight concentration does not affect the per-sun electron-hole-pair (EHP) generation rate but reduces the per-sun EHP recombination rate either near the front and back faces or in the graded-bandgap regions of the absorber layer, depending upon the semiconductor used for that layer, and this is the primary reason for the improvement in efficiency. Other effects include the enhancement of open-circuit voltage, which can be positively correlated to the higher short-circuit current density. Sunlight concentration can therefore play a significant role in enhancing the efficiency of thin-film solar cells.

Optoelectronic optimization of graded-bandgap thin-film AlGaAs solar cells.

An optoelectronic optimization was carried out for an $ {{\rm Al}_\xi }{{\rm Ga}_{1 - \xi }}{\rm As} $AlξGa1-ξAs (AlGaAs) solar cell containing (i) an $ n $n-AlGaAs absorber layer with a graded bandgap and (ii) a periodically corrugated Ag backreflector combined with localized ohmic Pd-Ge-Au backcontacts. The bandgap of the absorber layer was varied either sinusoidally or linearly. An efficiency of 33.1% with the 2000-nm-thick $ n $n-AlGaAs absorber layer is predicted with linearly graded bandgap along with silver backreflector and localized ohmic backcontacts, in comparison to 27.4% efficiency obtained with homogeneous bandgap and a continuous ohmic backcontact. Sinusoidal grading of the bandgap is predicted to enhance the maximum efficiency to 34.5%. Thus, grading the bandgap of the absorber layer, along with a periodically corrugated Ag backreflector and localized ohmic Pd-Ge-Au backcontacts, can help realize ultrathin and high-efficient AlGaAs solar cells for terrestrial applications.

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading: erratum.

Typographical errors in a few equations in [Appl. Opt.58, 6067 (2019)APOPAI0003-693510.1364/AO.58.006067] are corrected.

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading.

The power conversion efficiency of an ultrathin CuIn1-ξGaξSe2 (CIGS) solar cell was maximized using a coupled optoelectronic model to determine the optimal bandgap grading of the nonhomogeneous CIGS layer in the thickness direction. The bandgap of the CIGS layer was either sinusoidally or linearly graded, and the solar cell was modeled to have a metallic backreflector corrugated periodically along a fixed direction in the plane. The model predicts that specially tailored bandgap grading can significantly improve the efficiency, with much smaller improvements due to the periodic corrugations. An efficiency of 27.7% with the conventional 2200-nm-thick CIGS layer is predicted with sinusoidal bandgap grading, in comparison to 22% efficiency obtained experimentally with homogeneous bandgap. Furthermore, the inclusion of sinusoidal grading increases the predicted efficiency to 22.89% with just a 600-nm-thick CIGS layer. These high efficiencies arise due to a large electron-hole pair generation rate in the narrow-bandgap regions and the elevation of the open-circuit voltage due to a wider bandgap in the region toward the front surface of the CIGS layer. Thus, bandgap nonhomogeneity, in conjunction with periodic corrugation of the backreflector, can be effective in realizing ultrathin CIGS solar cells that can help overcome the scarcity of indium.

Asymptotic model for finite-element calculations of diffraction by shallow metallic surface-relief gratings.

We have formulated an asymptotic model for implementation in the finite-element method to calculate diffraction from a planar multilayered structure having a shallow surface-relief grating. The thin grating layer containing the shallow grating is replaced by a planar interface with transmission conditions that differ from the standard continuity conditions, thereby eliminating the necessity of representing the grating layer by a fine mesh. The parameters defining the shallow surface-relief grating are thereby removed from the geometry to the transmission conditions. Adoption of the asymptotic model will considerably reduce the computational cost of optimizing the grating shape because there is no need to re-mesh at every optimization step.

Adequacy of the rigorous coupled-wave approach for thin-film silicon solar cells with periodically corrugated metallic backreflectors: spectral analysis.

The rigorous coupled-wave approach (RCWA) is extensively used to compute optical absorption and photon absorption in thin-film photovoltaic solar cells backed by 1D metallic gratings when the wave vector of the incident light lies wholly in the grating plane. The RCWA algorithm converges rapidly for incident s-polarized light over the entire 400-1100 nm solar spectrum. It also performs well for incident p-polarized light in the 400-650 nm spectral regime, but even with a large number of Floquet harmonics in the solution, the total reflectance is underestimated in the 650-1100 nm spectral regime. Despite that shortcoming, the RCWA underestimates the solar-spectrum-integrated photon absorption rate only by 5%-10% for p-polarized light. As sunlight is almost unpolarized, the RCWA should be considered adequate to design thin-film silicon solar cells with periodically corrugated metallic backreflectors.

Comparison of rigorous coupled-wave approach and finite element method for photovoltaic devices with periodically corrugated metallic backreflector.

Optimal design of photovoltaic devices with a periodically corrugated metallic backreflector requires a rapid and reliable way to simulate the optical characteristics for wide ranges of wavelengths and angles of incidence. Two independent numerical techniques are needed for confidence in numerical results. We compared the rigorous coupled-wave approach (RCWA) and the finite element method (FEM), the former being fast and flexible, but the latter having predictable convergence even for discontinuous constitutive properties. Depending on the shape of the corrugation and the constitutive properties of the metal and dielectric materials making up the device, both techniques can exhibit slow convergence rates for p-polarized light. The chosen model problem in this paper is of this type. As rapid spatial variations of the fields are the underlying cause, suitable selective refinement of the FEM mesh can overcome this slow convergence. Therefore, it would be desirable to have a self-adaptive scheme for choosing the mesh in the FEM. This will slow down the algorithm but give a reliable way to check the RCWA results.

Optimization of the absorption efficiency of an amorphous-silicon thin-film tandem solar cell backed by a metallic surface-relief grating.

The rigorous coupled-wave approach was used to compute the plane-wave absorptance of a thin-film tandem solar cell with a metallic surface-relief grating as its back reflector. The absorptance is a function of the angle of incidence and the polarization state of incident light; the free-space wavelength; and the period, duty cycle, the corrugation height, and the shape of the unit cell of the surface-relief grating. The solar cell was assumed to be made of hydrogenated amorphous-silicon alloys and the back reflector of bulk aluminum. The incidence and the grating planes were taken to be identical. The AM1.5 solar irradiance spectrum was used for computations in the 400-1100 nm wavelength range. Inspection of parametric plots of the solar-spectrum-integrated (SSI) absorption efficiency and numerical optimization using the differential evolution algorithm were employed to determine the optimal surface-relief grating. For direct insolation, the SSI absorption efficiency is maximizable by appropriate choices of the period, the duty cycle, and the corrugation height, regardless of the shape of the corrugation in each unit cell of the grating. A similar conclusion also holds for diffuse insolation, but the maximum efficiency for diffuse insolation is about 20% smaller than for direct insolation. Although a tin-doped indium-oxide layer at the front and an aluminum-doped zinc-oxide layer between the semiconductor material and the backing metallic layer change the optimal depth of the periodic corrugations, the optimal period of the corrugations does not significantly change.