FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2782662097> ?p ?o ?g. }

• W2782662097 endingPage "224" @default.
• W2782662097 startingPage "210" @default.
• W2782662097 abstract "Understanding the optoelectronic and transport properties of semiconductors is essential for producing high-efficiency photovoltaic and photoelectrochemical cells. To this end, empirical extraction of the spatial collection efficiency (i.e., the fraction of photogenerated charge carriers created at a specific point within the device that contribute to the photocurrent) is a useful, nondestructive, analytical tool to study new materials, junctions, and devices. This perspective describes how the spatial collection efficiency can be extracted by combining photocurrent action spectra with optical absorption profiles. The result is high-resolution depth profiles of device functionality with very few assumptions, which paves the way to operando semiconductor tomography. The challenges and opportunities that this method offers for analysis of complex materials are discussed. Since the method is based on widely used spectral response measurements, it can be an important addition to the toolbox of analytical methods for material research for future solar energy conversion systems. The spatial collection efficiency portrays the driving forces and loss mechanisms in photovoltaic and photoelectrochemical devices. It is defined as the fraction of photogenerated charge carriers created at a specific point within the device that contribute to the photocurrent. In stratified planar structures, the spatial collection efficiency can be extracted out of photocurrent action spectra measurements empirically, with few a priori assumptions. Although this method was applied to photovoltaic cells made of well-understood materials, it has never been used to study unconventional materials such as metal-oxide semiconductors that are often employed in photoelectrochemical cells. This perspective shows the opportunities that this method has to offer for investigating new materials and devices with unknown properties. The relative simplicity of the method, and its applicability to operando performance characterization, makes it an important tool for analysis and design of new photovoltaic and photoelectrochemical materials and devices. The spatial collection efficiency portrays the driving forces and loss mechanisms in photovoltaic and photoelectrochemical devices. It is defined as the fraction of photogenerated charge carriers created at a specific point within the device that contribute to the photocurrent. In stratified planar structures, the spatial collection efficiency can be extracted out of photocurrent action spectra measurements empirically, with few a priori assumptions. Although this method was applied to photovoltaic cells made of well-understood materials, it has never been used to study unconventional materials such as metal-oxide semiconductors that are often employed in photoelectrochemical cells. This perspective shows the opportunities that this method has to offer for investigating new materials and devices with unknown properties. The relative simplicity of the method, and its applicability to operando performance characterization, makes it an important tool for analysis and design of new photovoltaic and photoelectrochemical materials and devices. In photovoltaic (PV) and photoelectrochemical (PEC) cells, volume absorption of photons generates charge carriers with excess free energy, whose net flux gives rise to electric current, commonly termed the photocurrent. The spatial collection efficiency (SCE) is defined as the fraction of photogenerated charge carriers at a specific position within the cell that contribute to the photocurrent that flows out of the cell. Since the photocurrent can be used to produce electrical power or to drive an electrochemical reaction, empirical extraction of the SCE may shed light on processes that govern the energy conversion efficiency and transduction mechanisms that are important for a wide range of applications. To date, the SCE has been used mostly as a phenomenological concept to model thin-film PV cells,1Ali B. Murray R. Hegedus S.S. Ismat Shah S. Analysis of voltage and temperature dependent photocurrent collection in p3ht/pcbm solar cells.J. Appl. Phys. 2012; 112: 114514Crossref Scopus (13) Google Scholar, 2Delahoy, A.E., Cheng, Z., and Chin, K.K.. (2012). Carrier collection in thin-film CdTe solar cells: Theory and experiment. 27th Eur. Photovolt. Sol. Energy Conf. Exhib. 2837–2842.Google Scholar, 3Hages C.J. Carter N.J. Agrawal R. Generalized quantum efficiency analysis for non-ideal solar cells: case of Cu2ZnSnSe4.J. Appl. Phys. 2016; 1191: 014505Crossref Scopus (79) Google Scholar, 4Hegedus S.S. Current–voltage analysis of a-Si and a-SiGe solar cells including voltage-dependent photocurrent collection.Prog. Photovoltaics Res. Appl. 1997; 5: 151-168Crossref Google Scholar, 5Liu X.X. Sites J.R. Solar-cell collection efficiency and its variation with voltage.J. Appl. Phys. 1994; 75: 577-581Crossref Scopus (74) Google Scholar, 6Hegedus S. Desai D. Thompson C. Voltage dependent photocurrent collection in CdTe/CdS solar cells.Prog. Photovoltaics Res. Appl. 2007; 15: 587-602Crossref Scopus (108) Google Scholar photodiodes,7Wee, D., Parish, G., and Nener, B. (2006). Determination of diffusion length of p-type GaN from spectral-response measurements. Conf. Optoelectron. Microelectron. Mater. Devices, Proceedings COMMAD, 264–267.Google Scholar and photoelectrodes for solar water splitting.8Dotan H. Kfir O. Sharlin E. Blank O. Gross M. Dumchin I. Ankonina G. Rothschild A. Resonant light trapping in ultrathin films for water splitting.Nat. Mater. 2013; 12: 158-164Crossref PubMed Scopus (290) Google Scholar In such approaches, a priori assumptions about the electric field distribution within the devices and drift diffusion models are commonly used to derive analytical expressions for the SCE that can be fitted to current-voltage voltammograms. While these expressions are useful for well-characterized materials and devices, applying them to new materials and devices proves difficult and is frequently not possible.9Zhang W. Yan D. Appavoo K. Cen J. Wu Q. Orlov A. Sfeir M.Y. Liu M. Unravelling photocarrier dynamics beyond the space charge region for photoelectrochemical water splitting.Chem. Mater. 2017; 29: 4036-4043Crossref Scopus (17) Google Scholar Furthermore, the quality of the interface between different layers, which is material and process dependent, affects the electric field distribution around it. Hence, the suggested expressions for the SCE cannot be generalized for all cases; they must be tailored for different materials, structures, and processing conditions. These limitations highlight the need for an analytical method to deduce the SCE empirically, with minimal assumptions. Electron-beam-induced current (EBIC) measurements are commonly used for mapping the regions in the PV cell that contribute to the current collection.10Edri E. Kirmayer S. Henning A. Mukhopadhyay S. Gartsman K. Rosenwaks Y. Hodes G. Cahen D. Why lead methylammonium tri-iodide perovskite-based solar cells require a mesoporous electron transporting scaffold (but not necessarily a hole conductor).Nano Lett. 2014; 14: 1000-1004Crossref PubMed Scopus (508) Google Scholar, 11Kedem N. Brenner T.M. Kulbak M. Schaefer N. Levcenko S. Levine I. Abou-Ras D. Hodes G. Cahen D. Light-induced increase of electron diffusion length in a p-n junction type CH3NH3PbBr3 Perovskite solar cell.J. Phys. Chem. Lett. 2015; 6: 2469-2476Crossref PubMed Scopus (84) Google Scholar, 12Sutter-fella C.M. Stückelberger J.A. Hagendorfer H. La Mattina F. Kranz L. Nishiwaki S. Uhl A.R. Romanyuk Y.E. Tiwari A.N. Sodium assisted sintering of chalcogenides and its application to solution processed Cu2ZnSn(S,Se)4 thin film solar cells.Chem. Mater. 2014; 26: 1420-1425Crossref Scopus (181) Google Scholar, 13Kranz L. Gretener C. Perrenoud J. Schmitt R. Pianezzi F. La Mattina F. Blösch P. Cheah E. Chirilă A. Fella C.M. et al.Doping of polycrystalline CdTe for high-efficiency solar cells on flexible metal foil.Nat. Commun. 2013; 4: 2306Crossref PubMed Scopus (194) Google Scholar In this method, the electron beam of a scanning electron microscope (SEM) is used to generate excited charge carriers that are, in turn, collected as a measurable current for producing two-dimensional maps of the SCE. Although this method has yielded important insights into charge transport mechanisms in thin-film PV cells, the need for cross-section lamellas and operation in vacuum conditions make it destructive and render it difficult to evaluate devices under real operating conditions. Furthermore, EBIC measurements of solid/liquid interfaces, important for PEC cells, is practically impossible. As such, there is a pressing need for a simple, yet generalizable, method for evaluating the SCE of devices under operando conditions. Extracting the SCE out of photocurrent action spectra, which are frequently measured to obtain the external quantum efficiency (EQE) of the device,14Sinkkonen J. Ruokolainen J. Uotila P. Hovinen A. Spatial collection efficiency of a solar cell.Appl. Phys. Lett. 1995; 66: 206-208Crossref Scopus (29) Google Scholar, 15Tuominen E. Acerbis M. Hovinen A. Siirtola T. Sinkkonen J. A method extracting solar cell parameters from spectral response by inverse Laplace transform.Phys. Scr. 1997; T69: 306-309Crossref Google Scholar, 16Donolato C. Reconstruction of the charge collection probability in a solar cell from internal quantum efficiency measurements.J. Appl. Phys. 2001; 89: 5687-5695Crossref Scopus (26) Google Scholar, 17Pang, Y.T., Efstathiadis, H., Dwyer, D., and Eisaman, M.D.. (2015). Reconstruction of the charge collection probability in a CIGS solar cell by the regularization method. 2015 IEEE 42nd Photovolt. Spec. Conf., 15–18.Google Scholar avoids most assumptions regarding driving forces and transport mechanisms, while also allowing for simple operando characterization of stratified planar PV and PEC devices. In PV cells with long diffusion lengths where the device thickness can be significantly larger than the wavelength of the incident photons, the charge carrier generation profile is often modeled as an exponential decay function following the Beer-Lambert law. This enables extraction of the SCE from measured photocurrent action spectra by performing an inverse Laplace transformation14Sinkkonen J. Ruokolainen J. Uotila P. Hovinen A. Spatial collection efficiency of a solar cell.Appl. Phys. Lett. 1995; 66: 206-208Crossref Scopus (29) Google Scholar, 15Tuominen E. Acerbis M. Hovinen A. Siirtola T. Sinkkonen J. A method extracting solar cell parameters from spectral response by inverse Laplace transform.Phys. Scr. 1997; T69: 306-309Crossref Google Scholar or by numerical deconvolution.16Donolato C. Reconstruction of the charge collection probability in a solar cell from internal quantum efficiency measurements.J. Appl. Phys. 2001; 89: 5687-5695Crossref Scopus (26) Google Scholar Regularization methods were suggested to extract the SCE from EBIC measurements in which the charge carrier generation profile follows more complex functions.18Donolato C. Reconstruction of the charge collection probability in a semiconductor diode from collection efficiency measurements by the regularization method.J. Appl. Phys. 1991; 69: 7287-7294Crossref Scopus (11) Google Scholar, 19Donolato C. Reconstruction of the charge collection probability in a semiconductor device from the derivative of collection efficiency data.Appl. Phys. Lett. 1999; 75: 4004-4006Crossref Scopus (8) Google Scholar These regularization methods can handle arbitrary charge carrier generation profiles, making them applicable for extracting the SCE of thin-film devices, where optical interference gives rise to complex light intensity profiles that no longer follow the Beer-Lambert exponential decay behavior.8Dotan H. Kfir O. Sharlin E. Blank O. Gross M. Dumchin I. Ankonina G. Rothschild A. Resonant light trapping in ultrathin films for water splitting.Nat. Mater. 2013; 12: 158-164Crossref PubMed Scopus (290) Google Scholar, 17Pang, Y.T., Efstathiadis, H., Dwyer, D., and Eisaman, M.D.. (2015). Reconstruction of the charge collection probability in a CIGS solar cell by the regularization method. 2015 IEEE 42nd Photovolt. Spec. Conf., 15–18.Google Scholar This extraction method was applied to PV devices made of well-understood materials such as silicon,14Sinkkonen J. Ruokolainen J. Uotila P. Hovinen A. Spatial collection efficiency of a solar cell.Appl. Phys. Lett. 1995; 66: 206-208Crossref Scopus (29) Google Scholar, 15Tuominen E. Acerbis M. Hovinen A. Siirtola T. Sinkkonen J. A method extracting solar cell parameters from spectral response by inverse Laplace transform.Phys. Scr. 1997; T69: 306-309Crossref Google Scholar, 16Donolato C. Reconstruction of the charge collection probability in a solar cell from internal quantum efficiency measurements.J. Appl. Phys. 2001; 89: 5687-5695Crossref Scopus (26) Google Scholar InP,16Donolato C. Reconstruction of the charge collection probability in a solar cell from internal quantum efficiency measurements.J. Appl. Phys. 2001; 89: 5687-5695Crossref Scopus (26) Google Scholar CuInGaSe2,17Pang, Y.T., Efstathiadis, H., Dwyer, D., and Eisaman, M.D.. (2015). Reconstruction of the charge collection probability in a CIGS solar cell by the regularization method. 2015 IEEE 42nd Photovolt. Spec. Conf., 15–18.Google Scholar and CdS/CdTe,14Sinkkonen J. Ruokolainen J. Uotila P. Hovinen A. Spatial collection efficiency of a solar cell.Appl. Phys. Lett. 1995; 66: 206-208Crossref Scopus (29) Google Scholar thereby enabling validation of the extracted SCE profiles by comparing them with analytic solutions obtained by device simulations. By fitting the extracted profiles to the analytic solutions, important material properties, such as the diffusion length and surface recombination velocity, were deduced. Although the potential strength of empirical SCE analysis lies in its ability to provide valuable information on driving forces and photocarrier properties with very few a priori assumptions, it has only been applied so far for conventional PV cells made of fairly well-understood materials. To this day it has never been applied to study PEC cells, which are difficult to simulate and to which methods such as EBIC cannot be applied. Moreover, to the best of our knowledge, it has never been applied to study nonconventional materials with poorly understood properties. This perspective article aims to highlight the opportunities that the SCE analysis has to offer for studying elusive materials and devices. First, following prior work, the SCE is extracted from the EQE spectrum of a crystalline silicon PV cell and is compared with the analytic solution. Next, the analysis is applied to a thin-film hematite (α-Fe2O3) photoanode for PEC water splitting. Extracting the SCE profiles under operando conditions provides important insights into bulk versus surface limited photocurrents and the complex electro-optical properties of the material. The relatively simple experimental apparatus required to implement the method, together with the important insights it provides, make it an important tool for studying new materials and devices for PV and PEC cells. Assuming a stratified planar structure with homogeneous layers, all device properties, including the SCE, change only with the distance from the surface, z. Figure 1 shows a cross-sectional illustration of the energy band diagram of a p+-n-n+ PV cell made of a lossy semiconductor material operated at a voltage below the open circuit voltage. Holes that are generated in the vicinity of the p+-n junction (marked ① in Figure 1) are accelerated toward the junction by the built-in field. Once injected into the p+ region, holes are no longer minority carriers and are less susceptible to recombination. On the other hand, holes that are generated farther away from the p+-n junction must travel a longer distance before being collected and are more prone to recombination (marked ② in Figure 1). Hence, in this example, the SCE, denoted by ϕ(z), has a maximum near the p+-n junction and decreases with distance from it, as illustrated in Figure 1. The SCE is defined as the fraction of charge carriers photogenerated at point z that contribute to the measurable photocurrent density, Jphoto.14Sinkkonen J. Ruokolainen J. Uotila P. Hovinen A. Spatial collection efficiency of a solar cell.Appl. Phys. Lett. 1995; 66: 206-208Crossref Scopus (29) Google Scholar, 15Tuominen E. Acerbis M. Hovinen A. Siirtola T. Sinkkonen J. A method extracting solar cell parameters from spectral response by inverse Laplace transform.Phys. Scr. 1997; T69: 306-309Crossref Google Scholar, 16Donolato C. Reconstruction of the charge collection probability in a solar cell from internal quantum efficiency measurements.J. Appl. Phys. 2001; 89: 5687-5695Crossref Scopus (26) Google Scholar, 17Pang, Y.T., Efstathiadis, H., Dwyer, D., and Eisaman, M.D.. (2015). Reconstruction of the charge collection probability in a CIGS solar cell by the regularization method. 2015 IEEE 42nd Photovolt. Spec. Conf., 15–18.Google Scholar, 18Donolato C. Reconstruction of the charge collection probability in a semiconductor diode from collection efficiency measurements by the regularization method.J. Appl. Phys. 1991; 69: 7287-7294Crossref Scopus (11) Google Scholar, 19Donolato C. Reconstruction of the charge collection probability in a semiconductor device from the derivative of collection efficiency data.Appl. Phys. Lett. 1999; 75: 4004-4006Crossref Scopus (8) Google Scholar, 20Kirchartz T. Agostinelli T. Campoy-Quiles M. Gong W. Nelson J. Understanding the thickness-dependent performance of organic bulk heterojunction solar cells: the influence of mobility, lifetime, and space charge.J. Phys. Lett. 2012; 3: 3470-3475Google Scholar, 21Green M.A. Solar cells: operating principles, technology, and system applications. Prentice-Hall, Inc., 1982: 138-145Google Scholar The relation between Jphoto and the SCE profile, ϕ(z), can be described as:8Dotan H. Kfir O. Sharlin E. Blank O. Gross M. Dumchin I. Ankonina G. Rothschild A. Resonant light trapping in ultrathin films for water splitting.Nat. Mater. 2013; 12: 158-164Crossref PubMed Scopus (290) Google ScholarJphoto=q∫0dG(z)ϕ(z)dz(Equation 1) where q is the electron charge, d is the absorber layer thickness and G(z) is the charge carrier generation profile. In conventional semiconductors, such as Si and GaAs, the charge carriers behave as free electrons and holes and their transport properties (e.g., mobility and lifetime) are independent of the absorbed photon energy. In this case, G(z) follows the light absorption profile, G(z)=∫Φin(λ)A(λ,z)dλ, where Φin(λ) is the incident photon flux at wavelength λ, and A(λ,z) is the fraction of the incident photons with wavelength λ that are absorbed at distance z from the front surface. Since the light absorption profile A(λ,z) can be calculated by optical modeling,8Dotan H. Kfir O. Sharlin E. Blank O. Gross M. Dumchin I. Ankonina G. Rothschild A. Resonant light trapping in ultrathin films for water splitting.Nat. Mater. 2013; 12: 158-164Crossref PubMed Scopus (290) Google Scholar ϕ(z) can be obtained by solving Equation 1. However, Equation 1 has an infinite number of possible solutions and more information about the system is required in order to obtain the physical solution that characterizes the system uniquely. One method to obtain more information on the system is to measure the photocurrent response to small perturbations to the charge carrier generation profile; for example, by modulating the intensity of the incident light at varying wavelengths on top of a constant background light bias that defines the operating point. Thus, the incident photon flux becomes Φin=Φwhite bias+ΔΦ(λ), where Φwhite bias is the background photon flux of the light bias and ΔΦ(λ) is the additional photon flux at wavelength λ. A short discussion about the background light bias requirements in EQE measurements can be found in section S5 in the Supplemental Information. ΔΦ(λ) gives rise to additional photocurrent:ΔJphoto(λ)=q∫0dΔG(λ,z)ϕ(z)dz(Equation 2) where ΔG(λ,z) is the additional charge carrier generation induced by ΔΦ(λ). The EQE is defined as:EQE(λ)=ΔJphoto(λ)qΔΦ(λ)(Equation 3) Equation 2 can be rewritten in matrix form, where the unknown SCE vector, ϕ¯(zi), minimizes the matrix norm:ϵ=‖q⋅ΔG′¯¯(λ,zi)ϕ¯(zi)−ΔJ¯photo(λ)‖2→ 0(Equation 4) Here, ΔJ¯photo(λ) is a vector that is derived from the measured photocurrent action spectrum upon light intensity perturbation ΔΦ(λ), ΔG′¯¯(λ,zi)=∫ziΔG(λ,zi)dz is a computable matrix that accounts for the changes in the charge carrier generation within the finite elements located at discrete grid positions zi, and ϕ¯(zi) is the SCE of these elements. Hence, ϕ¯(zi) can be extracted from photocurrent action spectra measurements by solving Equation 4. Standard regularization methods such as Tikhonov regularization22Tikhonov A.N. Goncharsky A.V. Stepanov V.V. Yagola A.G. Numerical methods for the solution of ill-posed problems. Springer, 1995: 7-16Crossref Google Scholar, 23Hansen P.C. Regularization tools version 4.0 for Matlab 7.3.Numer. Algorithm. 2007; 46: 189-194Crossref Scopus (592) Google Scholar, 24Lawson C.L. Hanson R.J. Solving Least Squares Problems. Society for Industrial and Applied Mathematics, 1995Crossref Google Scholar can be applied to diminish spurious effects such as measurement noise, inaccuracies inflicted by the optical modeling, and other sources of errors.22Tikhonov A.N. Goncharsky A.V. Stepanov V.V. Yagola A.G. Numerical methods for the solution of ill-posed problems. Springer, 1995: 7-16Crossref Google Scholar, 23Hansen P.C. Regularization tools version 4.0 for Matlab 7.3.Numer. Algorithm. 2007; 46: 189-194Crossref Scopus (592) Google Scholar It should be noted that this type of minimization problem, often referred to as discrete ill-posed problems, has an infinite number of solutions from which only one describes the actual physics of the system.22Tikhonov A.N. Goncharsky A.V. Stepanov V.V. Yagola A.G. Numerical methods for the solution of ill-posed problems. Springer, 1995: 7-16Crossref Google Scholar, 23Hansen P.C. Regularization tools version 4.0 for Matlab 7.3.Numer. Algorithm. 2007; 46: 189-194Crossref Scopus (592) Google Scholar, 24Lawson C.L. Hanson R.J. Solving Least Squares Problems. Society for Industrial and Applied Mathematics, 1995Crossref Google Scholar Methods for obtaining the physical solution are described below, and additional details are provided in section S2 in the Supplemental Information. While charge carriers behave as free electrons and holes in conventional semiconductors such as Si and GaAs, many other semiconductor materials display strong electron-phonon coupling effects that give rise to self-trapping and polaronic phenomena. Such effects, which are particularly common among emerging semiconductors envisioned for application in PEC solar cells, lead to profoundly different behavior than their conventional counterparts.25Stoneham A.M. Gavartin J. Shluger A.L. Kimmel A.V. Ramo D.M. Rønnow H.M. Aeppli G. Renner C. Trapping, self-trapping and the polaron family.J. Phys. Condens. Matter. 2007; 19: 255208Crossref Scopus (208) Google Scholar This is often the case for transition metal-oxide semiconductors, especially those containing partially occupied d-orbitals in which correlation effects underlie the electronic structure and d-d transitions contribute to the optical absorption spectrum but not necessarily to the photocurrent.26Rettie A.J.E. Chemelewski W.D. Emin D. Mullins C.B. Unravelling small-polaron transport in metal oxide photoelectrodes.J. Phys. Chem. Lett. 2016; 7: 471-479Crossref PubMed Scopus (189) Google Scholar, 27Lany S. Semiconducting transition metal oxides.J. Phys. Condens. Matter. 2015; 27: 283203Crossref PubMed Scopus (150) Google Scholar For such materials it cannot be assumed a priori that every absorbed photon generates mobile charge carriers. For example, in transition metal oxides such as hematite (α-Fe2O3) and copper vanadate (γ-Cu3V2O8), considered as potential photoelectrode candidates for PEC cells for solar water splitting, it has been reported that d-d transitions produce excited states that are site localized and hence cannot be harvested efficiently as useful photocurrent.28Hayes D. Hadt R.G. Emery J.D. Cordones A.A. Martinson A.B.F. Shelby M.L. Fransted K.A. Dahlberg P.D. Hong J. Zhang X. et al.Electronic and nuclear contributions to time- resolved optical and X-ray absorption spectra of hematite and insights into photoelectrochemical performance.Energy Environ. Sci. 2016; 9: 3754-3769Crossref Google Scholar, 29Chen C.T. Cahan B.D. Visible and ultraviolet optical properties of single-crystal and polycrystalline hematite measured by spectroscopic ellipsometry.J. Opt. Soc. Am. 1981; 71: 932Crossref Scopus (46) Google Scholar, 30Jiang C.-M. Farmand M. Wu C.H. Liu Y.-S. Guo J. Drisdell W.S. Cooper J.K. Sharp I.D. Electronic structure, optoelectronic properties, and photoelectrochemical characteristics of γ-Cu3V2O8 thin films.Chem. Mater. 2017; 29: 3334-3345Crossref Scopus (53) Google Scholar, 31Su Z. Baskin J.S. Zhou W. Thomas J.M. Zewail A.H. Ultrafast elemental and oxidation-state mapping of hematite by 4D electron microscopy.J. Am. Chem. Soc. 2017; 139: 4916-4922Crossref PubMed Scopus (24) Google Scholar However, other transitions, such as ligand-to-metal charge transfer (LMCT) transitions, give rise to mobile charge carriers that contribute more effectively to the photocurrent.28Hayes D. Hadt R.G. Emery J.D. Cordones A.A. Martinson A.B.F. Shelby M.L. Fransted K.A. Dahlberg P.D. Hong J. Zhang X. et al.Electronic and nuclear contributions to time- resolved optical and X-ray absorption spectra of hematite and insights into photoelectrochemical performance.Energy Environ. Sci. 2016; 9: 3754-3769Crossref Google Scholar, 31Su Z. Baskin J.S. Zhou W. Thomas J.M. Zewail A.H. Ultrafast elemental and oxidation-state mapping of hematite by 4D electron microscopy.J. Am. Chem. Soc. 2017; 139: 4916-4922Crossref PubMed Scopus (24) Google Scholar Thus, different types of transitions yield different probabilities of the photogenerated charge carriers to contribute to the photocurrent, such that the effective charge carrier generation function, G, depends not only on the amount of light absorbed but also on the type of the electronic transition induced by the absorbed photons. This leads to a wavelength-dependent charge carrier generation profile that can be written as:ΔG(λ,z)=ξ(λ)A(λ,z)ΔΦ(λ)(Equation 5) where ξ(λ), the photogeneration yield, is the probability for the absorbed photons to generate mobile charge carriers that can contribute to the photocurrent. The different types of transitions add another level of complexity because ξ(λ) is another unknown that must be accounted for. However, if the SCE profile is known, ξ(λ) can be extracted by inserting Equation 5 into Equation 2 and solving for ξ(λ):ξ(λ)=ΔJphoto(λ)qΔΦ(λ)∫0dA(λ,z)ϕ(z)dz(Equation 6) This leads to an empirical method to extract ξ(λ) in order to provide additional insight into electronic structure, optoelectronic properties, and photocarrier transport, as demonstrated at the end of this article. We now turn to the approach for extracting ϕ(z) out of the photocurrent action spectra, ΔJ¯photo(λ). This is done by inserting the measured ΔJ¯photo(λ) and the corresponding charge carrier generation profile, ΔG′¯¯(λ,z), obtained by optical calculations as in Dotan et al.;8Dotan H. Kfir O. Sharlin E. Blank O. Gross M. Dumchin I. Ankonina G. Rothschild A. Resonant light trapping in ultrathin films for water splitting.Nat. Mater. 2013; 12: 158-164Crossref PubMed Scopus (290) Google Scholar for example, into the minimization problem presented in Equation 4. Being an ill-posed problem, it has an infinite number of solutions and the unique physical solution must be carefully selected from all other possible solutions. One method to do so is to constrain the semi-norm ‖Lϕ(z)‖2:ϵ′=‖q⋅ΔG′¯¯(λ,zi)ϕ¯(zi)−ΔJ¯photo(λ)‖2+κ‖Lϕ¯(zi)‖2→ 0(Equation 7) where L is either a derivative operator of any order or the identity matrix and κ is the regularization parameter that determines the extent to which ‖Lϕ(z)‖2 is constrained.23Hansen P.C. Regularization tools version 4.0 for Matlab 7.3.Numer. Algorithm. 2007; 46: 189-194Crossref Scopus (592) Google Scholar For example, when L is the identity matrix, high values of κ produce solutions in which the magnitude of the solution is constrained, and if L is the first or second derivative operator, high values of κ constrain the slope or the curvature of the solution, respectively. It should be noted that, in the latter case, L is a discrete approximation of the derivative operator and it does not hold information on the spatial grid. As a result, the degree to which the actual slopes and curvatures are constrained depends also on the size of the elements in the spatial grid. A short discussion on the effect that grid discretization has on the solution can be found in section S3 in the Supplemental Information. The solution process starts with computation of a series of solutions for different values of κ. The next step is to screen out the physical solution. In the results described below, the solutions for ϕ¯(zi) were screened based on the basic notion that the physical solution must be confined between 0 and 1, and that it should reproduce the measured EQE spectra when inserted into Equation 2. Since sharp changes in the gradient of the SCE may result in minor overshoots and undershoots in the extracted SCE profiles,16Donolato C. Reconstruction of the charge collection probability in a solar cell from internal quantum efficiency measurements.J. Appl. Phys. 2001; 89: 5687-5695Crossre" @default.
• W2782662097 created "2018-01-26" @default.
• W2782662097 creator A5004358352 @default.
• W2782662097 creator A5038877770 @default.
• W2782662097 creator A5039372417 @default.
• W2782662097 creator A5047019702 @default.
• W2782662097 creator A5047375636 @default.
• W2782662097 creator A5067225049 @default.
• W2782662097 creator A5069109248 @default.
• W2782662097 creator A5071699786 @default.
• W2782662097 creator A5074395296 @default.
• W2782662097 creator A5083020249 @default.
• W2782662097 date "2018-02-01" @default.
• W2782662097 modified "2023-10-15" @default.
• W2782662097 title "The Spatial Collection Efficiency of Charge Carriers in Photovoltaic and Photoelectrochemical Cells" @default.
• W2782662097 cites W1488488840 @default.
• W2782662097 cites W1976555219 @default.
• W2782662097 cites W1979801468 @default.
• W2782662097 cites W1982114508 @default.
• W2782662097 cites W1990262488 @default.
• W2782662097 cites W1994877286 @default.
• W2782662097 cites W1998762105 @default.
• W2782662097 cites W2004007833 @default.
• W2782662097 cites W2005425744 @default.
• W2782662097 cites W2008530102 @default.
• W2782662097 cites W2008729405 @default.
• W2782662097 cites W2011805350 @default.
• W2782662097 cites W2012214142 @default.
• W2782662097 cites W2027647163 @default.
• W2782662097 cites W2028650156 @default.
• W2782662097 cites W2062395120 @default.
• W2782662097 cites W2066034539 @default.
• W2782662097 cites W2067335120 @default.
• W2782662097 cites W2070175293 @default.
• W2782662097 cites W2072270358 @default.
• W2782662097 cites W2074014009 @default.
• W2782662097 cites W2077170594 @default.
• W2782662097 cites W2081992913 @default.
• W2782662097 cites W2086579816 @default.
• W2782662097 cites W2092569621 @default.
• W2782662097 cites W2104380120 @default.
• W2782662097 cites W2107107053 @default.
• W2782662097 cites W2112360068 @default.
• W2782662097 cites W2115177063 @default.
• W2782662097 cites W2120947415 @default.
• W2782662097 cites W2133882917 @default.
• W2782662097 cites W2143957670 @default.
• W2782662097 cites W2151959114 @default.
• W2782662097 cites W2158090480 @default.
• W2782662097 cites W2171127104 @default.
• W2782662097 cites W2175352192 @default.
• W2782662097 cites W2186854595 @default.
• W2782662097 cites W2214736005 @default.
• W2782662097 cites W2227512168 @default.
• W2782662097 cites W2237852399 @default.
• W2782662097 cites W2314482289 @default.
• W2782662097 cites W2314576908 @default.
• W2782662097 cites W2329168744 @default.
• W2782662097 cites W2409455835 @default.
• W2782662097 cites W2500173957 @default.
• W2782662097 cites W2547561756 @default.
• W2782662097 cites W2592419513 @default.
• W2782662097 cites W2600416767 @default.
• W2782662097 cites W2606366297 @default.
• W2782662097 cites W2734680528 @default.
• W2782662097 cites W3105103439 @default.
• W2782662097 cites W3113137272 @default.
• W2782662097 cites W754657099 @default.
• W2782662097 doi "https://doi.org/10.1016/j.joule.2017.12.007" @default.
• W2782662097 hasPublicationYear "2018" @default.
• W2782662097 type Work @default.
• W2782662097 sameAs 2782662097 @default.
• W2782662097 citedByCount "34" @default.
• W2782662097 countsByYear W27826620972018 @default.
• W2782662097 countsByYear W27826620972019 @default.
• W2782662097 countsByYear W27826620972020 @default.
• W2782662097 countsByYear W27826620972021 @default.
• W2782662097 countsByYear W27826620972022 @default.
• W2782662097 countsByYear W27826620972023 @default.
• W2782662097 crossrefType "journal-article" @default.
• W2782662097 hasAuthorship W2782662097A5004358352 @default.
• W2782662097 hasAuthorship W2782662097A5038877770 @default.
• W2782662097 hasAuthorship W2782662097A5039372417 @default.
• W2782662097 hasAuthorship W2782662097A5047019702 @default.
• W2782662097 hasAuthorship W2782662097A5047375636 @default.
• W2782662097 hasAuthorship W2782662097A5067225049 @default.
• W2782662097 hasAuthorship W2782662097A5069109248 @default.
• W2782662097 hasAuthorship W2782662097A5071699786 @default.
• W2782662097 hasAuthorship W2782662097A5074395296 @default.
• W2782662097 hasAuthorship W2782662097A5083020249 @default.
• W2782662097 hasBestOaLocation W27826620971 @default.
• W2782662097 hasConcept C104232198 @default.
• W2782662097 hasConcept C119599485 @default.
• W2782662097 hasConcept C121332964 @default.
• W2782662097 hasConcept C127413603 @default.
• W2782662097 hasConcept C188082385 @default.
• W2782662097 hasConcept C192562407 @default.
• W2782662097 hasConcept C41291067 @default.

• next