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WIREs Comput Mol Sci
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Photoexcited charge carrier behaviors in solar energy conversion systems from theoretical simulations

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Abstract Solar energy bears great potential in the substitution of conventional fossil fuels to enable a sustainable world. In order to harness and use solar energy, photocatalytic and photovoltaic systems made of semiconductor materials have been developed to convert sunlight into energy (electricity) based on the photoelectrochemical effects. Photoelectric events are related with the light–energy (electricity) conversion process, including photon absorption, photoexcited charge carrier separation and recombination, charge carrier transport, and photocurrent generation, as well as electron plasmonic resonance. We focus on the recent state‐of‐the‐art simulation methods correspondingly mimicking these photogenerated charge carrier behaviors, taking electron–phonon, electron–exciton, and exciton–exciton interactions into account. Results can be obtained from the standard density function theory (DFT) for ground‐state properties, many‐body perturbation theory for band gap renormalization and optical absorption, time‐domain DFT in combination with nonadiabatic molecular dynamics for photoexcitation dynamics, nonequilibrium Green's function and self‐consistent theory for charge carrier transport properties, and classical Maxwell's equations in discrete dipole approximation for localized surface plasmon resonance absorption and near‐field enhancement. In combination of the results from these simulation methods, a complete and consistent picture describing the fundamental photoelectric process in light–energy (electricity) conversion could be obtained. Simulation results offer guidelines for experimental efforts and provide new basic insights into the underlying mechanisms and the design principles for next‐generation photocatalytic and photovoltaic devices of high solar light utilization efficiency. This article is categorized under: Structure and Mechanism > Computational Materials Science Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Simulation Methods
(a) Bright and dark excitons. (b) Left, excitons and biexcitons. Right, biexciton in 2D TMDCs
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(a) The vertical stack of 2D TMDCs in momentum space (upper), and in real space (bottom). (b) Energy diagram showing the formation of intralayer and interlayer excitons in heterostructures of 2D TMDCs. Optical gap Eopt, exciton binding energy Eb, exciton binding energy difference ΔEb, VBM band offset ΔEVBM, and CBM band offset ΔECBM are denoted. In this review, when talking about the interlayer exciton we mean those formed between transferred electrons and holes across the interface. In practice, direct interlayer transition can also be observed from GW + BSE aspects, but with negligible oscillator strength
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Exciton wave function |ψ(re; rh)|2, with the hole (black dots) fixed above a N atom for the excitonic states I1 and I2 in g‐C3N4 structure constructed from (a) and (b) triazine and (c) and (d) from tri‐s‐triazine. Optical results of g‐C3N4 structure constructed from (e) triazine and (f) from tri‐s‐triazine calculated with (GW + BSE, black lines) and without (GW + RPA, red dot lines) the consideration of the electron–hole interactions
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(a) Optical absorption of (a) single‐, (b) double‐layer, and (c) bulk MoS2, from BSE (solid lines) and RPA (dashed lines). DFT and GW band gaps at K point and absorption threshold are denoted by the vertical dashed and solid lines, respectively. (d)–(f) Comparison of experimental and theoretical absorption (solid lines, shifted by about −0.2 eV). Exciton wave functions of (g) exciton A and (h) bound exciton at 3.0 eV of monolayer MoS2. Exciton A of (i) monolayer MoS2 and (j) bulk MoS2
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(Left) The self‐energy Σ and one‐particle Green's function G can be determined using Hedin's equations and Dyson's equation iteratively
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(a) The concept of quasiparticle (QP). v is the bare Coulomb interaction, and W is the dynamically screened interaction. (b) One‐particle Green's function. In the context of second quantized formulation, one‐particle Green's function (or propagator) can be defined. (c) the effective interaction between QPs. W(r1, r2) means the dynamically screened interaction, which is the “true” interaction between QPs, v(r1, r2) is the bare Coulomb interaction, while v(r2, r3) is the interaction between r2 and r1‐induced polarized charge (quasi‐hole) r3. (d) The poles of the Green's function. I is ionization energy, A is electron affinity, and chemical potential μ is located in the middle of the band gap
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(a) Plasmonic Ag/MoS2 heterostructures, SEM of Ag nanodiscs, and the corresponding PL maps. (b) Au/multilayer MoS2 core–shell structure, electric field distribution for Au@MoS2 from simulations, and the pathways of photoexcited charge carrier generation
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(a) Au nanoparticle on TiO2. (b) LSPR absorption of Au@TiO2. (c) Au@TiO2 currently used in experiments (1), and Au@TiO2 proposed in this work (2). (d)–(f) Near field enhancement with different intersection angles
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(a) InSe/InTe vdW heterostructures. (b) Photocurrents as a function of photon energy under different strains. (c)–(e) Photocurrent maps (Iph). (f)–(h) Output power density (Pout) with various bias voltages (Vds) and incident light power densities (Pin) as a function of different strains
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Schematics of (a) R‐scheme and (b) Z‐scheme for charge carrier separation and recombination. In the artificial Z‐scheme photocatalytic systems, the electron acceptor/donor pair is a common electron mediator. Thus, Z‐scheme photocatalytic system consists of acceptor/donor pair and two semiconductor photocatalysts (SP I and SP II), and no physical contact exists between SP I and SP II. First, the electron acceptor is reduced into the electron donor after absorbing a photogenerated electron from the conduction band of SP I. Then the produced electron donor is oxidized into the electron acceptor by the photogenerated hole from the valence band of SP II. Thus, with the support of acceptor/donor pair, the photogenerated electron is indirectly transferred from the conduction band of SP I to the valence band of SP II. Finally, the photogenerated electron in the conduction band of SP II and the photogenerated hole in the valence band of SP I participate the reduction and oxidation processes with reactants, respectively
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(a) Typical excitonic absorption in low‐dimensional materials, and the coulomb bounded electron–hole pair, that is, the exciton. Absorption peaks in low energy correspond to the exciton states. (b) Generation of A and B excitons in 2D TMDCs such as MoS2, WS2, MoSe2 and WSe2. Spin–orbit coupling (SOC) causes valence band splitting at the K point in the hexagonal 2D Brillouin zone, thus vertical transitions at this point are responsible for the formation of A and B excitons
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Theoretical simulation methods can accordingly be used for different charge carrier behaviors in the light–energy (electricity) process. In detail, DFT can be used for ground state properties such as the geometry, total energy, and, especially, the charge potential and wave function for MBPT and TDDFT calculations. In the framework of MBPT, GW + BSE is usually adopted to calculate the linear optical response on top of the GW corrected single‐particle band structure. In combination of TDDFT and NAMD, photoexcited charge carrier dynamics such as charge carrier separation and recombination can be simulated. NEGF together with SCF theory show successes in describing the transport properties, for example, the photocurrent of photogenerated charge carriers. On the basis of Maxwell's equations, LSPR induced near‐field enhancement turns out to be accessible. Accordingly, atomic models in different simulation stages are schematically shown
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Photoelectric events in (a) photocatalysts, and (b) excitonic solar cells (XSCs). Excited electrons and holes can recombine in bulk and on surface. Under light irradiation, metal nanoparticles (NPs) show localized surface plasmon resonance (LSPR). Metal NPs can also be used in XSCs to enhance light absorption
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(a) Schematic plot of a two‐probe device model. μL and μR are the electrochemical potentials of the left and right electrodes, respectively, and μL − μR = Vb, where Vb is the bias voltage and e the electron charge. The dash‐lined box indicates the device scattering region which has some quantum levels. The tunnel barriers indicate coupling of the scattering region to the semi‐infinitely long electrodes. For more details, one may refer to the manual for nanoDCAL. (b) Schematics of the device structure for intuitive
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(a) Side views of Janus‐MoSSe/WSe2 vdW heterostructures. (b) Energy levels for the Janus‐MoSSe/WSe2 interface. (c)–(f) Electron and hole separation dynamics in Janus‐MoSSe/WSe2. (g) Electron–hole recombination dynamics and (h) pure‐dephasing functions across the interfaces
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(a) Energy levels for MoS2/WS2 interface. (b) PDOS of the constituent MoS2 and WS2 monolayers of MoS2/WS2 heterostructure at 300 K. Unnormalized autocorrelation functions, dephasing functions and influence spectra for (c) hole transfer and (d) electron transfer
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vdW‐coupled multilayers for photocatalytic and photovoltaic applications. The small ellipse suggests the intralayer exciton, and the big one represents the new pathway discussed in the text. In such an architecture, electrons and holes can be continuously transferred from one materials to the most separated one, strongly reducing the undesirable recombination
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Photoelectric events in light–energy (electricity) progress in heterostructures composed of materials M1 and M2 with type‐II band alignment. (I) Photon absorption and exciton generation, (II) charge carrier thermal relaxation, (III) electron separation, (IV) energy transfer, and (V) intralayer and interlayer electron–hole recombination
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Short and intense laser pulse induced different processes in a semiconductor. (a) Electron–hole pairs generation. (b) Carrier collisions. (c) Carrier relaxation to photon (c). , ω and ωe − h are photon energy, phonon energy, and electron–hole pair energy, respectively
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Electron–phonon coupling affects the exciton position, intensity and binding energy. In cases of 2D TMDCs, for example, band gap will be renormalized as temperature increases. In particular, even at 0 K, the band gap is reduced by 75 meV (MoS2) and 31 meV (WSe2) with respect to the calculation results without electron–phonon coupling. This is due to the effect of the atom zero‐point vibrations. As temperature increases, lattice thermal expansion effects on the band gap fades. It should be pointed out that the spectral functions of QP states, as function of temperature, show energy and momentum dependences. In general, the broadening of spectral function is directly related to the linewidth of each QP state, and lifetimes are inversely proportional to linewidths. The narrower the linewidth, the longer the lifetime (stable states, or weaker interaction with phonons and less nonradiative recombination paths). It is observed that, for WSe2, the highest valence band and the lowest conduction band at the K point behave oppositely, resulting in the band gap shrinking. At very high temperature, the Lorentzian symmetry may breakdown. For the lowest energy excitons of WSe2, the absorption position will be red shifted
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Electronic Structure Theory > Ab Initio Electronic Structure Methods
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