Shockley-Queisser Model Research Articles

Leveraging machine learning to consolidate the diversity in experimental results of perovskite solar cells.

Perovskite solar cells offer great potential for smart energy applications due to their flexibility and solution processability. However, the use of solution-based techniques has resulted in significant variations in device fabrication, leading to inconsistent results on the same composition. Machine learning (ML) and data science offer a potential solution to these challenges by enabling the automated design of perovskite solar cells. In this study, we leveraged machine learning tools to predict the band gap of hybrid organic-inorganic perovskites (HOIPs) and the power conversion efficiency of their solar cell devices. By analyzing 42 000 experimental datasets, we developed ML models for perovskite device design through a two-step predicting method, enabling the automation of perovskite materials development and device optimization. Additionally, band gap dependence of device parameters from experimental data is also validated, as predicted by the Shockley-Queisser model. This work has the potential to streamline the development of perovskite solar cells (PSCs) and optimize their performance without relying on time-consuming trial-and-error approaches.

Prediction of optoelectronic features and efficiency for CuMX2 (M=Ga, In; X=S, Se) semiconductors using mbj+U approximation

The optoelectronic properties of a selected group of Cu-III-VI2 chalcopyrites-based materials are deeply investigated by using the modified Becke-Johnson (mBJ) potential, combined with DFT + U approach. The obtained results are further used to calculate these materials’ theoretical efficiency limit for solar cell applications. The bandgap findings indicate a reliable ±0.2 eV agreement. After evaluating the electronic and optical properties, the spectroscopic limited maximum efficiency (SLME) model was used as a metric for the screening. Besides the bandgap value considered in the Shockley–Queisser model, the SLME requires that the absorption spectra, the radiative recombination losses, and the absorber layer thickness must be considered to adequately calculate the efficiency of considered cells. Our findings unveil that some candidates, such as CuInS2, where an SLME of 30.25% is achieved at a film width of 500 nm can be classified in the category of materials with higher power conversion efficiency.

Opto-electronic properties and solar cell efficiency modelling of Cu2ZnXS4 (X = Sn, Ge, Si) kesterites

In this work, first-principles calculations of Cu2ZnSnS4, Cu2ZnGeS4 and Cu2ZnSiS4 are performed to highlight the impact of the cationic substitution on the structural, electronic and optical properties of kesterite compounds. Direct bandgaps are reported with values of 1.32, 1.89 and 3.06 eV respectively for Cu2ZnSnS4, Cu2ZnGeS4 and Cu2ZnSiS4 and absorption coefficients of the order of 104 cm−1 are obtained, indicating the applicability of these materials as absorber layer for solar cell applications. In the second part of this study, ab initio results are used as input data to model the electrical power conversion efficiency of kesterite-based solar cells. In that perspective, we used an improved version of the Shockley–Queisser model including non-radiative recombination via an external parameter defined as the internal quantum efficiency. Based on predicted optimal absorber layer thicknesses, the variation of the solar cell maximal efficiency is studied as a function of the non-radiative recombination rate. Maximal efficiencies of 25.71%, 19.85% and 3.10% are reported respectively for Cu2ZnSnS4, Cu2ZnGeS4 and Cu2ZnSiS4 for vanishing non-radiative recombination rate. Using an internal quantum efficiency value providing experimentally comparable values, cell efficiencies of 15.88%, 14.98% and 2.66% are reported respectively for Cu2ZnSnS4, Cu2ZnGeS4 and Cu2ZnSiS4. We confirm the suitability of Cu2ZnSnS4 in single junction solar cells, with a possible efficiency improvement of nearly 10% enabled through the reduction of the non-radiative recombination rate. In addition, Cu2ZnGeS4 appears to be an interesting candidate as top cell absorber layer for tandem approaches whereas Cu2ZnSiS4 might be interesting for transparent photovoltaic windows.

Small grains as recombination hot spots in perovskite solar cells

Summary Non-radiative recombination in the perovskite bulk and at its interfaces prohibits the photovoltaic performance from reaching the Shockley-Queisser limit. While interfacial recombination has been widely discussed and demonstrated, bulk recombination and especially the influence of grain boundaries remain under debate. Most studies explore the role of grain boundaries on perovskite films rather than devices, making it difficult to link the film properties with those of the devices. Here, we systematically investigate the effects of grain boundaries on the performance of perovskite solar cells by two different methods. By combining experimental characterization with theoretical device simulations, we find that the recombination at grain boundaries is diffusion limited and hence is inversely proportional to the grain area to the power of 3/2. Consequently, the prevalence of small grains—which act as recombination hot spots—across the perovskite active layer dictates the photovoltaic performance of the perovskite solar cells.

Quantifying the Absorption Onset in the Quantum Efficiency of Emerging Photovoltaic Devices

AbstractThe external quantum efficiency (EQE), also known as incident‐photon‐to‐collected‐electron spectra are typically used to access the energy dependent photocurrent losses for photovoltaic devices. The integral over the EQE spectrum results in the theoretical short‐circuit current under a given incident illumination spectrum. Additionally, one can also estimate the photovoltaic bandgap energy (Eg) from the inflection point in the absorption threshold region. The latter has recently been implemented in the “Emerging PV reports,” where the highest power conversion efficiencies are listed for different application categories, as a function of Eg. Furthermore, the device performance is put into perspective thereby relating it to the corresponding theoretical limit in the Shockley–Queisser (SQ) model. Here, the evaluation of the EQE spectrum through the sigmoid function is discussed and proven to effectively report the Eg value and the sigmoid wavelength range λs, which quantifies the steepness of the absorption onset. It is also shown how EQE spectra with large λs indicate significant photovoltage losses and present the corresponding implications on the photocurrent SQ model. Similarly, the difference between the photovoltaic and optical bandgap is analyzed in terms of λs.

Defect-assisted nonradiative recombination in Cu2ZnSnSe4 : A comparative study with Cu2ZnSnS4

The efficiencies of ${\mathrm{Cu}}_{2}\mathrm{ZnSn}{\mathrm{Se}}_{4}$ (CZTSe) solar cells with a narrower band gap at 1.0 eV are currently higher than those of ${\mathrm{Cu}}_{2}\mathrm{ZnSn}{\mathrm{S}}_{4}$ (CZTS), with the optimal band gap according to the Shockley-Queisser model. To understand this abnormal observation, we studied the nonradiative recombination rates induced by the deep levels of the dominant defects in CZTSe, i.e., the ${\mathrm{Sn}}_{\mathrm{Zn}}(2+/+)$, ${\mathrm{Sn}}_{\mathrm{Zn}}(+/0)$, and $[{\mathrm{Cu}}_{\mathrm{Zn}}\text{\ensuremath{-}}{\mathrm{Sn}}_{\mathrm{Zn}}](+/0)$ levels. We found that the effective recombination centers in CZTS, namely, ${{\mathrm{Sn}}_{\mathrm{Zn}}}^{2+}$ and ${[{\mathrm{Cu}}_{\mathrm{Zn}}\text{\ensuremath{-}}{\mathrm{Sn}}_{\mathrm{Zn}}]}^{+}$, have much smaller carrier capture rates in CZTSe, and are less detrimental to the minority carrier lifetime and energy conversion efficiency. The smaller carrier capture rates for CZTSe can be attributed to the higher electronic transition energies, lower phonon frequencies, and weaker electron-phonon coupling effects in CZTSe compared to those in CZTS, because the large Se cations give rise to larger lattice constants and a softer lattice in CZTSe.

Identification of surface and volume hot-carrier thermalization mechanisms in ultrathin GaAs layers

Hot-carrier solar cells offer the opportunity to harvest more energy than the limit set by the Shockley–Queisser model by reducing the losses due to the thermalization of photo-generated carriers. Previous reports have shown lower thermalization rates in thinner absorbers, but the origin of this phenomenon is not precisely understood. In this work, we investigate a series of ultrathin GaAs absorber layers sandwiched between AlGaAs barriers and transferred on host substrates with a gold back mirror. We perform power-dependent photoluminescence characterizations at different laser wavelengths from which we determine the carrier temperature in four absorber thicknesses between 20 and 200 nm. We observe a linear relationship between the absorbed power and the carrier temperature increase. By relating the absorbed and thermalized power, we extract a thermalization coefficient for all samples. It shows an affine dependence with the thickness, leading to the identification of distinct volume and surface contributions to thermalization. We confirm that volume thermalization is linked to LO phonon decay. We discuss the origin of the interface-related thermalization, showing that the effect of LO phonon transport is negligible. Overall, this work sheds new light on thermalization processes in ultrathin semiconductor layers and introduces a method to compare the performance of hot-carrier absorbers.

Effects of photon recycling, trapping, and reuse on thermophotovoltaic conversion efficiency and output power

Photonic management is a key issue for the optimization of thermophotovoltaic (TPV) energy conversion systems. It is realized by selective emitters, front surface filters on TPV cells, and back surface reflectors (BSRs). Photonic management modifies photon energy transfer from the emitter to the TPV cell due to photon reuse and energy conversion processes in the TPV cell due to photon recycling and trapping in the cell. Our work has developed a comprehensive thermodynamic theory of photonic management in the TPV cell and in whole TPV systems to elucidate key optimization parameters. Our approach is based on the exact Lambert function solution of the generalized Shockley–Queisser model and the corresponding fundamental formulas of endoreversible thermodynamics for maximal electric power, emitted optical power, and dissipation losses. The model includes interrelated processes of photon recycling, photon trapping, nonradiative recombination, and parasitic absorption of the BSR. Optimization of a TPV system with photon reuse should take into account that the cell thickness that provides maximal output power does not correspond to the thickness, which gives the maximal conversion efficiency. The theory predicts the important limits for TPV efficiency and output power determined by the Auger recombination in low-bandgap semiconductor materials, various parasitic losses in the cell and conductive layers, and photon escape from the TPV system. For example, we consider the TPV system based on 0.6 eV InGaAs cells with a BSR and a front surface photon scattering layer, which provides Lambertian light trapping.

Highly Efficient and Stable GABr-Modified Ideal-Bandgap (1.35 eV) Sn/Pb Perovskite Solar Cells Achieve 20.63% Efficiency with a Record Small Voc Deficit of 0.33 V.

1.5-1.6 eV bandgap Pb-based perovskite solar cells (PSCs) with 30-31% theoretical efficiency limit by the Shockley-Queisser model achieve 21-24% power conversion efficiencies (PCEs). However, the best PCEs of reported ideal-bandgap (1.3-1.4 eV) Sn-Pb PSCs with a higher 33% theoretical efficiency limit are <18%, mainly because of their large open-circuit voltage (Voc ) deficits (>0.4 V). Herein, it is found that the addition of guanidinium bromide (GABr) can significantly improve the structural and photoelectric characteristics of ideal-bandgap (≈1.34 eV) Sn-Pb perovskite films. GABr introduced in the perovskite films can efficiently reduce the high defect density caused by Sn2+ oxidation in the perovskite, which is favorable for facilitating hole transport, decreasing charge-carrier recombination, and reducing the Voc deficit. Therefore, the best PCE of 20.63% with a certificated efficiency of 19.8% is achieved in 1.35 eV PSCs, along with a record small Voc deficit of 0.33 V, which is the highest PCE among all values reported to date for ideal-bandgap Sn-Pb PSCs. Moreover, the GABr-modified PSCs exhibit significantly improved environmental and thermal stability. This work represents a noteworthy step toward the fabrication of efficient and stable ideal-bandgap PSCs.

Bandgap Engineering Enhances the Performance of Mixed‐Cation Perovskite Materials for Indoor Photovoltaic Applications

AbstractIndoor photovoltaics (IPVs) are attracting renewed interest because they can provide sustainable energy through the recycling of photon energy from household lighting facilities. Herein, the Shockley–Queisser model is used to calculate the upper limits of the power conversion efficiencies (PCEs) of perovskite solar cells (PeSCs) for two types of artificial light sources: fluorescent tubes (FTs) and white light–emitting diodes (WLEDs). An unusual zone is found in which the dependence of the PCEs on the bandgap (Eg) under illumination from the indoor lighting sources follows trends different from that under solar irradiation. In other words, IPVs exhibiting high performance under solar irradiation may not perform well under indoor lighting conditions. Furthermore, the ideal bandgap energy for harvesting photonic power from these indoor lighting sources is ≈1.9 eV—a value higher than that of common perovskite materials (e.g., for CH3NH3PbI3). Accordingly, Br− ions are added into the perovskite films to increase their values of Eg. A resulting PeSC featuring a wider bandgap exhibits PCEs of 25.94% and 25.12% under illumination from an FT and a WLED, respectively. Additionally, large‐area (4 cm2) devices are prepared for which the PCE reaches ≈18% under indoor lighting conditions.

Guide for the perplexed to the Shockley–Queisser model for solar cells

The Shockley-Queisser model is a landmark in photovoltaic device analysis by defining an ideal situation as reference for actual solar cells. However, the model and its implications are easily misunderstood. Thus, we present a guide to help understand and avoid misinterpreting it. Focusing on the five assumptions, underlying the model, we define figures of merit to quantify how close real solar cells approach each of these assumptions.

Carrier heating and its effects on the current-voltage relations of conventional and hot-carrier solar cells: A physical model incorporating energy transfer between carriers, photons, and phonons

Theoretical models and frameworks are developed to investigate the effects of carrier heating on conventional and hot-carrier solar cells. They incorporate intraband carrier energy relaxation into the Shockley-Queisser model for conventional solar cells and the Ross-Nozik model for hot-carrier solar cells. Explicit formulas are presented to calculate intraband carrier energy relaxation rates via the interactions of polar longitudinal optical phonons and deformation-potential longitudinal and transverse optical phonons. These formulas incorporate the decay processes and phonon bath sharing of optical phonons. The effects of carrier heating on the current-voltage characteristics of conventional and hot-carrier solar cells are investigated and discussed for GaAs, InP, GaSb, and InAs materials. This paper will particularly discuss the differences between extraction cooling in hot-carrier solar cells and recombination heating from stimulated photon emissions in semiconductor lasers. It will prove that carriers in hot-carrier solar cells need to be extracted with a selective-contact energy larger than their quasi-Fermi-level separation in order to make devices work with extraction cooling, rather than recombination heating.

Influence of selenium amount on the structural and electronic properties of Cu(In,Ga)Se2 thin films and solar cells formed by the stacked elemental layer process

In the following article the influence of selenium supply on the stacked elemental layer process during the final annealing step is investigated. We find that the Se supply strongly influences the phase formation in the Cu(In,Ga)Se2 resulting in a modified Ga/In distribution. The effects of Se supply on the structural and electronic properties of the films are reported. The solar cell performance has been investigated in detail using current voltage and external quantum efficiency measurements. We find that the chalcopyrite crystal formation is strongly influenced by the Se supply during the growth process. Furthermore the interdiffusion of Ga and In is accelerated with increasing Se amount. This has direct consequences on band gap and series resistance, which leads to changes in the values of short-circuit current density, open-circuit voltage and fill factor. The open-circuit voltage increases with increasing band gap of the Cu(In,Ga)Se2, whereas the short-circuit current density decreases with increasing band gap. The fill factor is affected by the formation of MoSe2 at the back contact. The experimental findings are compared with the theoretical efficiency limits calculated from the Shockley–Queisser model, and also with numerical 1D SCAPS simulations.

Selective emitters design and optimization for thermophotovoltaic applications

Among several solutions to exploit solar energy, thermophotovoltaics have been popularized and have known great breakthroughs during the past two decades. Yet, existing systems still have low efficiencies since the wavelength range of optimal photovoltaic (PV) conversion is very small compared to the emitter spectral range. Selective emitters are a very promising solution to this problem. We developed numerical tools to design and optimize such emitters. Some of the resulting structures composed of two or four layers of metals and semiconductors are presented in this paper. We also show that the usual PV devices efficiency limits (30% for crystalline silicon under solar radiation, according to Shockley-Queisser model) can be easily overcome thanks to these structures.

Theoretical Efficiency Limits for Alternative Solar Cell Device Concepts

As the demand for renewable energy sources is increasing, many alternative concepts have been explored to enrich the prospects. In the solar cell field, multi carrier generation, spectrum manipulation, thermo-photoelectric cells, hot carrier, intermediate band, and many other techniques have been studied as new concepts. In this work, the theoretical limits of multi-carrier generation and multi-interface pre spectrum divided solar cells’ efficiencies are analyzed and discussed in detail. The solar cell market is dominated by single p-n junction devices such as Si, CdTe, and CIGS cells. The theoretical efficiency of such devices is well set by a recent version of the neat Shockley-Queisser (SQ) model. In this model, the single junction cell efficiency depends on the energy gap and cannot exceed 33%. Practically and in support for SQ model, the best lab efficiency is 25% for Si solar cell and it has not changed much since the early 1990s. The alternative device concepts should be able to surpass this limit. For example, a 43% efficient triple junction cell has already been realized. Based on the analysis, more than 80% efficiencies are possible; however, such high efficiencies are achievable only in ideal cases. So, some of the technical and practical difficulties are addressed and discussed. The analysis is based on the classical transport approach and assuming the measured 1.5 AM solar radiation spectrum. We used the reference National Renewable Energy Lab (NREL) measurements. For multi- carrier generation, no distinction is made between multi-exciton generation and carrier multiplications, as the multiplication is assumed ideal as Heaviside step function of the ratio of photon energy over energy gap, where the multiplication happens, is ignored.