Minority Carrier Recombination Research Articles

In Situ Buried Interface Engineering towards Printable Pb-Sn Perovskite Solar Cells.

High-efficiency Pb-Sn narrow-bandgap perovskite solar cells (PSCs) heavily rely on PEDOT:PSS as the hole-transport layer (HTL) owing to its excellent electrical conductivity, dopant-free nature, and facile solution processability. However, the shallow work function (WF) of PEDOT:PSS consequently results in severe minority carrier recombination at the perovskite/HTL interface. Here, we tackle this issue by an in situ interface engineering strategy using a new molecule called 2-fluoro benzylammonium iodide (FBI) that suppresses nonradiative recombination near the Pb-Sn perovskite (FA0.6MA0.4Pb0.4Sn0.6I3)/HTL bottom interface. The WF of PEDOT:PSS increases by 0.1 eV with FBI modification, resulting in Pb-Sn PSCs with 20.5% efficiency and an impressive VOC of 0.843 V. Finally, we have successfully transferred our in situ buried interface modification strategy to fabricate blade-coated FA0.6MA0.4Pb0.4Sn0.6I3 PSCs with 18.3% efficiency and an exceptionally high VOC of 0.845 V.

Preparation of wide bandgap CuGaSe2 absorbers and solar cells by sputtering a selenium-rich ceramic target and annealing in a selenium-free atmosphere

CuGaSe2 (CGSe) material possesses a wide bandgap of approximately 1.7 eV, making it a promising prospect for top cells in tandem solar cells. Depositing CGSe precursor films by magnetron sputtering of a selenium-rich ceramic target is easy to operate and control. After annealing the precursor films at different temperatures in a selenium-free argon atmosphere, avoiding the use of toxic H2Se. To achieve an absorber exhibiting appropriate performance, the morphologies, phase composition, absorption characteristics, roughness, lattice structure, and work function of CGSe absorbers annealed at different temperatures were investigated. The CGSe absorber annealed at 550 °C showed uniform grain, a single-phase composition, high absorbance, flat surface, and compact crystal structure. The absorber annealed at excessive temperature led to the formation of Cu2-xSe, inducing defects and carrier recombination. The work function of CGSe absorber annealed at 590 °C increases, resulting in the misalignment of its band with the Mo back contact. The enhancement of absorber contributes positively to solar cell device performance. CGSe solar cells prepared using the absorber annealed at 550 °C exhibited excellent photoelectric properties. The increase in minority carrier lifetime and recombination resistance improves the transport characteristics of carriers.

Validation of minority carrier recombination lifetimes in low-dimensional semiconductors found by analytical photoresponses

It is a formidable challenge to find the minority carrier recombination lifetime in low-dimensional devices as low-dimensionality increases the surface recombination rate and often reduces the recombination lifetime to a scale of picoseconds. In this work, we demonstrated a simple but powerful method to quantitatively probe the minority carrier recombination lifetime in silicon nanowires or microwires by fitting the experimental photoresponses with our recently established analytical photoresponse principle of photoconductors. The nanowires were passivated with small molecules and Al2O3 to suppress surface recombination, which will increase the minority recombination lifetimes. As expected, the minority carrier recombination lifetime found by this approach increases by orders of magnitude. These wires were also made into PIN diodes, the leakage of which was reduced at least 1 order of magnitude after surface passivation by Al2O3. The minority recombination lifetime found from the leakage current of these devices is largely consistent with what we found from our analytical photoresponse principle. As a further step, we performed scanning photocurrent microscopy to find the minority diffusion length from which we found that the minority recombination lifetime is close to what we found from the analytical photoresponses. In short, this work validated that our analytical response principle is a reliable method to find the minority recombination lifetime in low-dimensional semiconductors.

Optimization of a‐Si Thin‐Film Solar‐Cell Performance with Passivation and c‐Si Cap Layer

A modified design of the a‐Si thin‐film solar cell (TFSC) is presented. The c‐Si cap layer is introduced to increase the photon absorption and hence the enhanced photo carriers increase the overall short‐circuit current. Whereas, the highly doped a‐Si passivation layer reduces the minority carrier flow and recombination at the rear side of the cell, and therefore the passivation layer is used to improve the open‐circuit voltage (). The performance optimization and investigation of the cell characteristic is executed using the numerical simulation methodology. To further enhance the cell efficiency, the thickness and doping concentration of the c‐Si cap and a‐Si passivation layer are optimized. The improvement in absorption and passivation quality of the cell leads to the enhancement of in short‐circuit current density and improvement in the , respectively. The designed a‐Si TFSC absorbs the incoming solar spectrum from to of wavelength and rest of the spectrum is transmitted. The external and internal quantum efficiency of the cell is well over . The optimized efficiency of is obtained for the designed cap layered a‐Si passivated cell in AM1.5 G environment using ray‐tracing methodology.

Regulating the p-n interface quality for Sb2Se3-based quasi-homojunction thin film solar cells by an effective two-step heat treatment process

Earth-abundant Sb2Se3 material has received an increased attention from photovoltaics community thanks to its excellent photo-electronic properties. Despite the fact that the Sb2Se3 heterojunction solar cells have obtained a rapid development, the serious interface defects have not been fundamentally solved so far. By contrast, the quasi-homojunction has advantages over heterojunction in terms of electronic property, however, its development is quite slow. Herein, the Sb2Se3-based quasi-homojunction devices with the configuration of SLG/FTO/Cu-Sb2Se3/I-Sb2Se3/Al have been fabricated using magnetron sputtering accompanied by a two-step heat treatment process. The relationship between the p-n interface quality and the device performances was investigated in detail. Thanks to the very well p-n interface, the devices achieved a 2.64% PCE, with ∼ 10% improvement compared with the devices fabricated via one-step heat treatment, as previous reported. Moreover, an effective p- and n-type doping with high carrier density is essential for fabricating the efficient p-n interface, as evidenced by SCAPS simulations. Through the co-optimization of various device parameters, the predicted PCE of quasi-homojunction devices can reach 18.96%, using the Mg as back contact, leading to lower minority carrier recombination at near the back-contact. Eventually, the simulation indicated clearly the directions for further promoting cell performances by doping strategy. This work can provide valuable guidance for the further development and improvement of Sb2Se3-based quasi-homojunction thin-film solar cells.

Effect of Cu2Te Back Surface Interfacial Layer on Cadmium Telluride Thin Film Solar Cell Performance from Numerical Analysis

Even though substantial advances made in the device configuration of the frontal layers of the superstrate cadmium telluride (CdTe) solar cell device have contributed to conversion efficiency, unresolved challenges remain in regard to controlling the self-compensation and minority carrier recombination at the back contact that limits the efficiency. In this study, a SCAPS-1D simulator was used to analyze the loss mechanism and performance limitations due to the band-bending effect upon copper chloride treatment and subsequent Cu2Te layer formation as the back contact buffer layer. The optimal energy bandgap range for the proposed back surface layer of Cu2Te is derived to be in the range of 1.1 eV to 1.3 eV for the maximum conversion efficiency, i.e., around 21.3%. Moreover, the impacts of absorber layer’s carrier concentration with respect to CdTe film thickness, bandgap, and operational temperature are analyzed. The optimized design reveals that the acceptor concentration contributes significantly to the performance of the CdTe devices, including spectral response. Consequently, the optimized thickness of the CdTe absorber layer with a Cu-based back contact is found to be 2.5 µm. Moreover, the effect of temperature ranging from 30 °C to 100 °C as the operating condition of the CdTe thin-film solar cells is addressed, which demonstrates an increasing recombination tread once the device temperature exceeds 60 °C, thus affecting the stability of the solar cells.

Role of minority charge carriers in the formation of the thermo-electromotive force in p-type silicon

The contribution of minority charge carriers (electrons) is taken into account in the evaluation of thermo-electromotive force (thermo-E.M.F.) of a non-degenerate p-type semiconductor in the stationary state and when the quasi-neutrality condition is fulfilled. The results obtained show that the contribution to the thermo-E.M.F. due to the presence of minority electrons is a function of the bandgap and the length of the semiconductor used. It also depends on the minority carriers through their electrical conductivity, thermal conductivity, Seebeck coefficient, and bulk and surface recombinations. That contribution tends to reduce the principal thermo-E.M.F. (αpΔT) of the p-type semiconductor and will, therefore, be called counter-thermo-electromotive force (counter-thermo-E.M.F.). The calculations made in the case of silicon give a counter-thermo-E.M.F. of magnitude generally non-negligible, which decreases when the length of the silicon and the concentration of doping elements increase. Finally, it is shown that the best way to minimize the counter-thermo-E.M.F. is to treat the surface of the semiconductor to promote the recombination of minority carriers there.

Influence of polarities on optical properties of Mg-doped GaN films grown on GaN free-standing substrates by MOCVD

Time-resolved photoluminescence measurements were performed to investigate the minority carrier recombination mechanism of p-GaN films grown on c-plane, m-plane and (10–11)-plane GaN freestanding substrates by MOCVD. The fast and slow decay lifetimes of the three samples were fitted by the bi-exponential function, in which the slow decay lifetime of the m-plane Mg-doped GaN reached a record long value of 493.7 ps? The effects of stress-induced non-radiative recombination centers and edge dislocations on the slow decay lifetime were ruled out using Raman and XRD. The reason for the longer slow decay lifetime of the m-plane sample is the reduction of the non-radiative recombination centers due to the decrease of the VGa concentration, ensuring by the magnitude of the IYL/INBE ratio in the PL spectra. The low-temperature PL spectra of the m-plane sample were investigated. According to Haynes' rule, the position of acceptor level was calibrated through combining with the position of the bound excitons at 5 K.

Utility of Shockley–Read–Hall analysis to extract defect properties from semiconductor minority carrier lifetime data

The semiconductor minority carrier lifetime contains information about several important material properties, including Shockley–Read–Hall defect levels/concentrations and radiative/Auger recombination rates, and the complex relationships between these parameters produce a non-trivial temperature-dependence of the measured lifetime. It is tempting to fit temperature-dependent lifetime data to extract the properties of the Shockley–Read–Hall recombination centers; however, without a priori knowledge of the distribution of the Shockley–Read–Hall states across the bandgap, this fit problem is under-constrained in most circumstances. Shockley–Read–Hall lifetime data are not well-suited for the extraction of Shockley–Read–Hall defect levels but can be used effectively to extract minority carrier recombination lifetimes. The minority carrier recombination lifetime is observed at temperatures below 100 K in a Si-doped n-type InGaAs/InAsSb superlattice, and deviation from its expected temperature-dependence indicates that the capture cross section of the defect associated with Si-doping has an activation energy of 1.5 meV or a characteristic temperature of 17 K. This lower temperature regime is also preferrable for the analysis of the physics of defect introduction with displacement-damage-generating particle irradiation.

SCAPS simulation of novel inorganic ZrS2/CuO heterojunction solar cells

ZrS2 is transition metal dichalcogenides (TMDCs) which is believed one of the most talented applicants to fabricate photovoltaics. Therefore, we present here for the first-time numerical simulation of novel inorganic ZrS2/CuO heterojunction solar cells employing SCAPS-1D. The influence of the thickness, carrier concentration, and bandgap for both the window and absorber layers on the solar cell fundamental parameters was explored intensely. Our results reveal that the solar cell devices performance is mainly affected by many parameters such as the depletion width (Wd), built-in voltage (Vbi), collection length of charge carrier, the minority carrier lifetime, photogenerated current, and recombination rate. The η of 23.8% was achieved as the highest value for our simulated devices with the Voc value of 0.96 V, the Jsc value of 34.2 mA/cm2, and the FF value of 72.2%. Such efficiency was obtained when the CuO band gap, thickness, and carrier concentration were 1.35 eV, 5.5 µm, and above 1018 cm−3, respectively, and for the ZrS2 were 1.4 eV, 1 µm, and less than 1020 cm−3, respectively. Our simulated results indicate that the inorganic ZrS2/CuO heterojunction solar cells are promising to fabricate low-cost, large-scale, and high-efficiency photovoltaic devices.

Efficiency Improvement of Industrial Silicon Solar Cells by the POCl3 Diffusion Process

To improve the efficiency of polycrystalline silicon solar cells, process optimization is a key technology in the photovoltaic industry. Despite the efficiency of this technique to be reproducible, economic, and simple, it presents a major inconvenience to have a heavily doped region near the surface which induces a high minority carrier recombination. To limit this effect, an optimization of diffused phosphorous profiles is required. A "low-high-low" temperature step of the POCl3 diffusion process was developed to improve the efficiency of industrial-type polycrystalline silicon solar cells. The low surface concentration of phosphorus doping of 4.54 × 1020 atoms/cm3 and junction depth of 0.31 μm at a dopant concentration of N = 1017 atoms/cm3 were obtained. The open-circuit voltage and fill factor of solar cells increased up to 1 mV and 0.30%, compared with the online low-temperature diffusion process, respectively. The efficiency of solar cells and the power of PV cells were increased by 0.1% and 1 W, respectively. This POCl3 diffusion process effectively improved the overall efficiency of industrial-type polycrystalline silicon solar cells in this solar field.

Development of high efficiency Ce1–BMgBO2 buffer and perovskite HTL based CIGSSe thin film solar cell using a simulation approach

Performance of the conventional (ZnMgO:Al/ZnMgO/CIGSSe) photovoltaic device has been enhanced by using novel magnesium-doped cerium oxide (Ce1–BMgBO2) as a buffer and perovskite as a hole transport layer (HTL) material. At the beginning of this paper, three experimental photovoltaic devices having an efficiency of 19.8%, 19.8% and 20% have been simulated and verified using the AFORS-HET simulation tool. Later, a low resistivity (ρ), wide energy bandgap (Eg), and minimum absorption coefficient (α) Ce1–BMgBO2 material is applied to the conventional device instead of the ZnMgO buffer layer. As a result, the efficiency of the proposed-1 photovoltaic device has been enhanced (20–26.59%). Due to a deficiency of HTL material, the proposed-1 device cannot properly suppress the photogenerated minority carrier recombination losses. Further, perovskite as a HTL material is applied between the CIGSSe/Mo back layers in the proposed-1 device. Therefore, the proposed-2 device instantly reduces the recombination losses and enhances the efficiency (28.93%) and EQE.

Crystalline Silicon (c-Si)-Based Tunnel Oxide Passivated Contact (TOPCon) Solar Cells: A Review

Contact selectivity is a key parameter for enhancing and improving the power conversion efficiency (PCE) of crystalline silicon (c-Si)-based solar cells. Carrier selective contacts (CSC) are the key technology which has the potential to achieve a higher PCE for c-Si-based solar cells closer to their theoretical efficiency limit. A recent and state-of-the-art approach in this domain is the tunnel oxide passivated contact (TOPCon) approach, which is completely different from the existing classical heterojunction solar cells. The main and core element of this contact is the tunnel oxide, and its main role is to cut back the minority carrier recombination at the interface. A state-of-the-art n-type c-Si-based TOPCon solar cell featuring a passivated rear contact was experimentally analyzed, and the highest PCE record of ~25.7% was achieved. It has a high fill factor (FF) of ~83.3%. These reported results prove that the highest efficiency potential is that of the passivated full area rear contact structures and it is more efficient than that of the partial rear contact (PRC) structures. In this paper, a review is presented which considers the key characteristics of TOPCon solar cells, i.e., minority carrier recombination, contact resistance, and surface passivation. Additionally, practical challenges and key issues related to TOPCon solar cells are also highlighted. Finally, the focus turns to the characteristics of TOPCon solar cells, which offer an improved and better understanding of doping layers and tunnel oxide along with their mutual and combined effect on the overall performance of TOPCon solar cells.

Roles of excess minority carrier recombination and chemisorbed O2 species at SiO2/Si interfaces in Si dry oxidation: Comparison between p-Si(001) and n-Si(001) surfaces.

This study provides experimental evidence for the following: (1) Excess minority carrier recombination at SiO2/Si interfaces is associated with O2 dissociative adsorption; (2) the x-ray induced enhancement of SiO2 growth is not caused by the band flattening resulting from the surface photovoltaic effect but by the electron-hole pair creation resulting from core level photoexcitation for the spillover of bulk Si electronic states toward the SiO2 layer; and (3) a metastable chemisorbed O2 species plays a decisive role in combining two types of the single- and double-step oxidation reaction loops. Based on experimental results, the unified Si oxidation reaction model mediated by point defect generation [S. Ogawa et al., Jpn. J. Appl. Phys., Part 1 59, SM0801 (2020)] is extended from the viewpoints of (a) the excess minority carrier recombination at the oxidation-induced vacancy site and (b) the trapping-mediated adsorption through the chemisorbed O2 species at the SiO2/Si interface.

Solar cell cracks within a photovoltaic module: Characterization by AC impedance spectroscopy.

Various cell crack modes (with or without electrically inactive cell areas) can be induced in crystalline silicon photovoltaic (PV) cells within a PV module through natural thermomechanical stressors such as strong winds, heavy snow, and large hailstones. Although degradation in the performance of PV modules by cell cracks has been reported occasionally, the mode-dependent evolutions in the electrical signatures of cracks have not yet been elucidated. In this study, we propose that the reduction of the time constant in the AC impedance spectra, which is caused by the elevation of minority-carrier recombination in the p-n junction of a PV cell, is a ubiquitous signature of cracked PV cells encapsulated in a commercially available PV module. Several other characteristics derived from the illuminated current-voltage (I-V) and dark I-V data significantly evolved only in PV cells with inactive cell areas. We also propose that the evaluation by carrier recombination is a crucial diagnostic technique for detecting all crack modes, including microcracks, in wafer-based PV modules.

New metric for carrier selective contacts for silicon heterojunction solar cells

Heterojunction carrier selective contacts for solar cells have gained great attention because of the ability of these contacts to efficiently collect majority carriers while hindering the recombination of minority carriers, thus resulting in the highest reported voltage among crystalline silicon technologies. The electrode work-function, doping and thickness of the doped layer remain the key parameters for governing the cell performance. Recently, we have studied the requirements for carrier selective contacts under various illumination levels and reported logarithmic dependence of these parameters. In this work, we define a new metric for describing the ability of a contact to collect the carriers and named it as contact strength. We have developed an analytical approach for contact strength of hole selective contacts which represents the requirements on doping, thickness of the contact layer, and electrode work-function for a given illumination. First, the numerical model is calibrated with the experimental data for a wide range of illumination (0.01 Sun – 1.0 Sun) and then simulations have been fitted with analytical model. For the selective contact layer, we observe that only the total charge, rather than thickness and doping individually, matters. The work-function of the top electrode also contributes strongly to contact strength and can in principle substitute doped layer. This insightful metric will guide the solar cell technologists to better understand the carrier selective contacts and to maximize the cell performance not only at standard test conditions (STC), but also at low light illuminations.

Improved minority carrier lifetime in p-type GaN by suppressing the non-radiative recombination process

Time-resolved photoluminescence and capacitance-voltage measurement were performed on p-type GaN and InGaN films to study the minority carrier recombination mechanism. The minority carrier lifetime (τ PL) for p-GaN with a Mg concentration of 1.7 × 1019 cm−3 was 46 ps. The non-radiative recombination due to gallium vacancies (V Ga)-related defects is confirmed to dominate the minority carrier transport process. To suppress the formation of V Ga defects, the indium atoms were added into p-GaN. As a consequence, the V Ga-related non-radiative recombination centers were reduced from 8 × 1015 to 5 × 1014 cm−3 and a record long τ PL of 793 ps was obtained for p-In0.035Ga0.95N film.

Comment on "Enhanced Charge Selectivity via Anodic-C60 Layer Reduces Nonradiative Losses in Organic Solar Cells".

Understanding interface-related phenomena is important for improving the performance of thin-film solar cells. In ACS Appl. Mater. Interfaces2021, 13, 12603–12609, Pranav et al. report that incorporating a thin C60 interlayer at the MoO3 anode results in reduced surface recombination of electrons, which is ascribed to a decreased electron accumulation near the anode on account of an increased built-in voltage. Here, we offer an alternative explanation: the introduction of a C60 interlayer renders the MoO3 contact Ohmic. The reduced anode barrier simultaneously increases the built-in voltage, minimizes nonradiative voltage losses upon the extraction of majority carriers (holes), and suppresses minority-carrier (electron) surface recombination, the latter being the result of hole accumulation and associated band bending near the Ohmic hole contact. We therefore argue that Ohmic contact formation suppresses both majority- and minority-carrier surface recombination losses, whereas the built-in voltage per se does not play a major role in this respect.

Long‐Term Degradation of Passivated Emitter and Rear Contact Silicon Solar Cell under Light and Heat

Advanced designs enable high‐efficiency solar cells; however, more complex structures create new long‐term stability concerns. Herein, the long‐term degradation processes affecting advanced silicon solar cells using laboratory‐based illumination and heating over hundreds of hours are investigated. The activation energy for the degradation of voltage is estimated and the degradation rates to normal solar cell operating temperature ranges are extrapolated. The cell degradation observed at high temperatures in the lab is kinetically similar to the process affecting field‐deployed modules contributing to 0.37% year−1 of annualized degradation. Electroluminescence and photoluminescence mapping show that the degradation is dominated by minority carrier lifetime reduction. Suns−open‐circuit voltage and light beam‐induced current results indicate that the degradation could result from passivation degradation at the surface or defect formation in the near‐subsurface region, leading to increased minority carrier recombination. This work highlights a long‐term degradation process under elevated temperature and illumination that may continue to affect cells in an irreversible manner that is separate from recoverable light‐induced degradation and light‐ and elevated temperature‐induced degradation.

(Invited) Precipitation of Suboxides in Silicon

Investigations of the precipitation of interstitial oxygen in Czochralski (CZ) silicon have been carried out since decades. Nevertheless, there are still open issues like the getter efficiency of oxide precipitates for metallic impurities and the recombination activity of oxide precipitates both in relation to their composition.Falster et al. found a discrepancy between the total loss of Oi and the visible loss of Oi in the form of precipitates observed by transmission electron microscopy (1). They explain this assuming that strained oxide precipitates, which are able to getter metallic impurities, and unstrained oxide precipitates so-called “ninja” precipitates, being not able to getter metallic impurities can exist (1). Until now, several phenomena are explained by the conversion from so-called unstrained to strained oxide precipitates. Murphy et al. (2) found that recombination at strained oxide precipitates is much stronger and rather depends on their density and less on their size. Typically, the density of strained oxide precipitates was assumed to be the density measured after preferential etching and the density of unstrained precipitates was always determined indirectly from the loss of interstitial oxygen.An important recent finding, obtained by electron energy loss spectrometry carried out by scanning transmission electron microscopy, was that the center of oxide precipitates consists of oxygen-rich SiO x being in most cases SiO2 surrounded by suboxide with decreasing x towards the edges. However, it is not yet clear if oxide precipitates always possess such a suboxide shell. It was also discovered that the suboxides surrounding oxide precipitates act as gettering sinks for Cu impurities (3). Therefore, the issue, if in any case oxide precipitates are surrounded by suboxide, could become an important criterion for efficient gettering.In order to further clarify these issues, we carried out a theoretical investigation of the phase composition of oxide precipitates and the corresponding emission of self-interstitials at the minimum of the free energy and their evolution with increasing number of oxygen atoms in the precipitates.First, we applied the model for spherical oxide precipitates. It was found that for low numbers of precipitating oxygen atoms the composition is SiO2 accompanied by a high emission of self-interstitials to relieve the strain. The emission of self-interstitials just slightly decreases up to a critical number of precipitated oxygen atoms. Then, the minimum free energy suddenly drops to low values of x, the stoichiometry changes into a suboxide, and the emission of self-interstitials becomes very low. The critical number of precipitated oxygen atoms increases with increasing temperature and decreases with increasing density of oxide precipitates. This means that the availability of suboxides for gettering of Cu impurities depends on both the annealing temperature and the density of oxide precipitates.If we apply the model to oblate spheroidal precipitates for low numbers of precipitating oxygen atoms the composition is also SiO2, the self-interstitial emission relieving the strain is very high, and the morphology remains spherical. However, when a critical number of oxygen atoms is reached the precipitate changes its shape from sphere to platelet, stops the emission of self-interstitials while maintaining a composition of SiO2. The optimum aspect ratio of the platelets lies between 0.02 and 0.03.The modeling results refer to homogeneous oxide precipitates under quasi-equilibrium conditions. In reality, the kinetics of morphology change is much more slowly than a change of stoichiometry. This means, when the octahedral morphology gets unstable suboxides can be expected to form as well. It was found by STEM investigations that the morphology change starts at octahedral morphology. Then the growth into [110] directions starting at the edges of the octahedron is enhanced until a platelet evolves from the octahedron and the original octahedron remains as fins on the platelet before it vanishes completely.The formation of suboxides at the edges of oxide precipitates after reaching a critical size can explain several phenomena like gettering of Cu by segregation to the suboxide region, lifetime reduction by recombination of minority carriers in the suboxide, and improved detectability by preferential etching. It thus provides an alternative explanation, based on minimized free energy, to the theory of strained and unstrained plates.(1) R. Falster, V. V. Voronkov, V. Y. Resnik, and M. G. Milvidskii, Proc. Electrochem. Soc., High Purity Silicon VIII (2004), Electrochem. Soc., Pennington, NJ, USA, Vol. 2004-05, p.188.(2) J. D. Murphy, K. Bothe, M. Olmo, V. V. Voronkov, and R. J. Falster, J. Appl. Phys., 110, 053713 (2011).(3) G. Kissinger, D. Kot, M. Klingsporn, M. A. Schubert, A. Sattler, and T. Müller, ECS J. Solid State Sci. Technol., 4, N124 (2015).