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The record efficiency for a thin-film, single-junction solar cell has remained static at 28.8% since 2012. This research presents a unique design that demonstrates potential to exceed record efficiency and approach the theoretical efficiency limit of ~33.5%. The findings of this study are significant, from an efficiency standpoint, and also because the cell design can be realized using existing fabrication methods that do not require complex, post-processing steps. In this study, a benchmark simulation is developed that closely resembles a high-efficiency, front-and-back contact cell. Intrinsic performance limiters are overcome by moving the emitter and front-contact to the back of the cell to eliminate electrical grid shading and improve optical performance. To further improve performance, the P-N junction formed by the emitter layer is removed from the model to allow selective Ohmic contacts to accept (reject) minority (majority) carriers as required. The design modifications improve open-circuit voltage, short-circuit current, and fill-factor which collectively boost efficiency above 30%-primarily due to a 2% gain of incident irradiance and improved optical performance.

The Shockley-Queisser (SQ) limit, proposed by W. Shockley and H. Queisser in 1961, is the upper theoretical efficiency of a single-junction solar cell (hereafter “cell”) converter operating at 300 K under an incident spectrum approximated by a 6000 K blackbody [

Silvaco is an industry leader for modeling semiconductor devices, and Atlas is the preferred simulator for predicting electrical characteristics of cell structures under bias conditions. Atlas constructs two-dimensional (2D) or 3D structures with internal grids that generate intersections called nodes. Continuity equations, current-density J_{SC} equations, and Poisson’s equation are solved at each node to achieve convergence and simulate the transport of charge carriers in a cell. Device modeling provides insight into the physical phenomena of a cell and displays data in a visual platform [

Since it is not cost-effective to design cells by trial and error, modeling can be useful to investigate ideas before investing time and money to build a prototype. The down-side of modeling is the uncertainty involved in accounting for all physical processes that occur in a cell. Simplifications, numerical methods, and other factors guarantee that a model will never exactly simulate the physical behavior of a cell. Nevertheless, we show that a high-level of confidence can be attained for a given model by carefully accounting for key design parameters, benchmarking model behavior to experimental results, and making single-variable adjustments to predict the behaviors of a new design.

We begin by assembling design characteristics from [

grid dimensions to balance trade-offs associated with shading and series resistance. We note that most researchers utilize front-contact technology to achieve record efficiency; however, we believe the benefits derived from back-contact technology can outweigh the drawbacks as with the current record for large-area crystalline silicon cells and Sun Power® Corporation’s industry-leading commercial cell [

The HE GaAs cell’s foundation is high-quality GaAs manufactured via a metal-or- ganic chemical vapor deposition (MOCVD) and an epitaxial-lift-off (ELO) process. Since the cell is only ~1 μm thick and material quality is excellent, efficient electron transport and minimal bulk recombination is achieved. Additionally, passivation of the cell’s front and back surfaces yields very low surface-recombination velocity which, among other factors, contributes to the highest open-circuit voltage V_{OC} recorded for a single-junction cell. The back-contact is >90% reflective, which enhances photon recycling through radiative recombination and band-edge absorption. A broadband anti-reflection coating (ARC) encompasses the spectral response of the cell (0.3 - 0.9 μm) with some room for improvement at shorter wavelengths as noted in [_{SC} reduction of ~6.5%, which corresponds with [^{17} cm^{−3}, which is compounded by photon recycling [i.e., the process whereby photons are emitted through radiative recombination and subsequently produce another electron-hole-pair (EHP)] to produce “effective” lifetimes of 10x or greater [

Auger recombination is the process whereby an electron-hole-pair (EHP) transfers energy and momentum to a third carrier via non-radiative recombination [

where C_{n} (C_{p}) is the auger coefficient for electrons (holes), and n_{i} is the intrinsic electron concentration. Coefficient values ranging from 7 × 10^{−30} cm^{6}∙s^{−1} to 1.6 × 10^{−29} cm^{6}∙s^{−1} are reported in literature which often distinguishes between direct and indirect auger recombination [_{n} and C_{p} to 7 × 10^{−30} cm^{6}∙s^{−1} to match HE GaAs cell performance parameters. Reference [

Radiative or optical recombination is the process whereby an electron from the conduction band combines with a hole in the valence band to release a photon. This type of recombination is dominant in direct band gap semiconductors (e.g., GaAs) and is essentially the inverse of optical generation. Radiative recombination is modeled as

where B is the intrinsic radiative recombination coefficient, ^{−11} cm^{3}∙s^{−1} to ~10^{−10} cm^{3}∙s^{−1} in literature [^{−11} cm^{3}∙s^{−1} to match HE GaAs cell performance.

Shockley-Read-Hall (SRH) or “trap-assisted” recombination is a two-step process whereby an electron (hole) occupies an energy level in the band gap and then recombines with a hole (electron). The energy traps may be intentional (i.e. due to doping) or unintentional (i.e., due to defects). If SRH recombination occurs at a surface or interface due to intermediate energy levels caused by dangling bonds or lattice mismatch, it is often referred to as “surface” or “interface” recombination. SRH recombination is modeled as

where τ_{n} (τ_{p}) is the electron (hole) minority carrier lifetime, and E_{trap} is the energy difference between the impurity “trap” located in the band gap and the intrinsic Fermi levels. In this work, we assume a single trap level which corresponds to the most efficiency recombination center. Distributed trap states may be modeled; however, separate SRH statistics are required.

Carrier mobility is dependent upon doping concentration. We set electron and hole mobility for intrinsic GaAs (at 300 K) to 8500 and 400 cm^{2}∙V^{−1}∙s^{−1}, respectively [^{−1} and 10 cm-s^{−1} for external surfaces and internal interfaces, respectively, which corresponds with velocities given in [

Experimentally derived refractive index values (real and imaginary) are critical for accurate model performance, and extinction coefficients near the band edge are especially important since they determine the extent that photons are absorbed and “recycled” after radiative recombination events―a primary design consideration for HE cell performance. We found that a widely referenced optical database [

The authors of [^{−3} Ω-cm^{2} for the back-contact (full-coverage) and <10^{−5} Ω-cm^{2} for the front-contact (partial coverage). References [^{19} cm^{−3} enables Ohmic contact where tunneling is the dominant transport mechanism. Reference [^{19} cm^{−3} doping for p-type GaAs is typical, whereas 4 × 10^{18} cm^{−3} is more realistic for n-type GaAs. However, [^{19} cm^{−3} on Au/Pt/Ti to achieve 1.1 × 10^{−6} Ω-cm^{2} resistivity, and [^{18} cm^{−3} on Pd/Ge/Au to achieve 3.6 × 10^{−6} Ω-cm^{2} resistivity. We adopt conservative doping concentrations of 5 × 10^{18} cm^{−3} for the n-type, front-contact cap layer with a corresponding resistivity of ~10^{−5} Ω-cm^{2}, and 10^{19} cm^{−3} for the p-type, back-contact cap layer with a corresponding resistivity of ~10^{−3} Ω-cm^{2}. Incidentally, the low contact resistivities of the cell described in [

Various works cited in this paper employ models to modify key design parameters in order to determine the impact on cell performance. Authors compare model output parameters with experimental measurements (J_{sc}, V_{oc}, FF, and efficiency η) to instill confidence in their simulations; however, model output is not compared with experimentally measured external quantum efficiency (EQE). We assert that matching V_{OC}, J_{SC}, FF, and η of a physical cell is not sufficient and that models should also reproduce the EQE curve to ensure that key variables such as window layer absorption and ARC performance are accounted for in the model. To this end, we compare cell performance parameters and EQE traces from [

^{−5} Ω-cm^{2} to 10^{−3} Ω-cm^{2} since ultra-low front-grid resistivity is not required in a back-contact design. 2D and 3D structures of the GaAs, Back-surface Alternating-Contact (GaAs-BAC) cell design are shown in

The GaAs-BAC cell model exceeded the HE GaAs Cell model for performance categories shown in _{OC} improved 1.0%, J_{SC} improved 1.4%, FF improved 2.7%, and η improved 5.2%. If we categorize the GaAs-BAC cell structure as a ~1 μm thick, planar, untextured cell with good back-surface reflectivity (~90%), [_{OC} are close to their theoretical limits of 89.1% and 1.15 V, respectively. Conversely, J_{SC} has room to improve to its theoretical limit of 31.6 mA/cm^{2}. We focus on improving J_{SC} and identifying the possible causes of ~1.5 mA/cm^{2} loss by setting front-surface reflectivity to 0% and changing refractive index values in the window layer to make it completely transparent. The adjustments improve J_{SC} to 31.53 mA/cm^{2}, which suggests that ARC reflection and window layer absorption are the main contributors to current-density loss. An examination of the EQE curve in

plots confirm that 0.3 - 0.5 μm wavelengths are indeed absorbed in the front ~10% of the cell; hence, J_{SC} may be improved by reducing reflection and improving window layer transparency in that spectral range. Further examination of

Examination of the GaAs-BAC cell model structure shown in ^{2}∙V^{−1}∙s^{−1} and ~350 cm^{2}∙V^{−1}∙s^{−1}, respectively, for an emitter-layer doping concentration of ~10^{17} cm^{−3} [^{3} The built-in voltage at cell depth d = 1.2 μm shown in _{OC} Reference [

that carriers must diffuse to reach the back-contact; hence, the cell may not require a P-N junction to keep EHPs separated. Furthermore, the p-type hetero-contact at the back-surface is specifically designed to accept (reject) minority (majority) carriers, which implies that the purpose of the emitter may be redundant, or even unnecessary. Therefore, we remove the emitter from the GaAs-BAC cell model and note the results on the band diagrams shown in

The “emitter-less” GaAs-BAC cell allows minority carriers (holes) to diffuse freely in the cell with a high probability of capture at the p-type hetero-contact (for an “n-on-p” cell). Note that the diffusion gradient required to drive carriers to a contact is very small (~1 millivolt) and reduces V_{OC} only slightly. In fact, the model shows that V_{OC} (measured to the nearest millivolt) is not reduced, whereas J_{SC} and FF improve slightly as shown in

This research demonstrates the advantage of modeling a novel solar cell design to investigate performance impacts prior to investing time and money to build a prototype. We developed a benchmark model of a thin-film, GaAs solar cell from [_{OC}, J_{SC}, FF, and η―mainly due to a 2% incident irradiance gain from the removal of the front-contact. Analysis of the GaAs-BAC cell simulation identified an area of reduced carrier mobility in the heavily-doped emitter region, which was subsequently removed to analyze whether a “selective” hetero-contact would maintain or even improve performance. We found that J_{SC}, FF, and η improved slightly, which supports the hypothesis proposed in [

P-N junction.

Future research will concentrate on design parameter optimization to further improve cell efficiency. Specifically, the benefits of random texturing on the front-and- back surfaces to promote internal reflection and photon recycling will be investigated. Additionally, high-temperature operation and “radiation-hardness” will be examined to evaluate the cell’s potential for employment aboard spacecraft.

Patents are pending for designs presented in this paper [

O’Connor, J.E. and Michael, S. (2016) A Novel Thin-Film, Sin- gle-Junction Solar Cell Design to Achieve Power Conversion Efficiency above 30 Percent. Materials Sciences and Applications, 7, 823-835. http://dx.doi.org/10.4236/msa.2016.712063

We confirmed that the solar cell simulation was working correctly by calculating spectral generation at an arbitrary wavelength and optical generation (for all wavelengths in the spectral response) at particular depths using experimentally-derived extinction coefficients. The calculations were then compared to model output to verify performance as shown below.

The absorption coefficient α as a function of energy for direct band gap materials is defined as

where A is a material-dependent constant, h is Planck’s constant, _{G} is the material band gap. For solar cell analysis, it is convenient to define α as a function of wavelength λ as in

where k is the extinction coefficient and the imaginary portion of the index of refraction. Equation (5) is calculated at an arbitrary wavelength λ = 600 nm (where k = 0.214) to give 4.5 × 10^{6} m^{−1}.

Photon flux ϕ at the cell’s front-surface is defined as

where P is the spectral power density and c is the speed of light. Integrating the AM1.5G solar spectrum yields P = 1000 W∙m^{−2}; hence, (5) gives ϕ = 3 × 10^{21}m^{−2}∙s^{−1} at the front-surface of the cell.

The spectral generation rate g is defined as

where R is the front-surface reflectivity, η is the internal quantum efficiency, and d is the depth (of interest) in the cell. Equation (7) calculated at λ = 600 nm and d = 1.2 μm gives 7 × 10^{19} cm^{−3}∙s^{−1}. Now the optical generation rate G may be defined as

which gives 3.6 × 10^{20} cm^{−3}∙s^{−1} at d = 1.2 μm, measured over the spectral response of the cell (λ_{1} = 300 nm and λ_{2} = 900 nm). Comparing calculations to the model output shown in

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