Van Roosbroeck-Shockley Relation Research Articles

Geometric and doping effects on radiative recombination in thin-film near-field energy converters

Modeling radiative recombination is crucial to the analysis of radiative energy converters. In this work, a local radiative recombination coefficient is defined and derived based on fluctuational electrodynamics that is applicable to thin-film cells in both the near field and far field. The predicted radiative recombination coefficient of an InAs cell deviates from the van Roosbroeck–Shockley relation when the thickness is less than 10 µm, and the difference exceeds fourfold with a 10 nm film. The local radiative recombination coefficient is orders of magnitude higher when an InAs cell is configured in the near field. The local radiative recombination coefficient reduces as the doping level approaches that of a degenerate semiconductor. The maximum output power and efficiency of a thermoradiative cell would be apparently overpredicted if the electroluminescence coefficient defined in this paper were taken as unity for heavily doped semiconductors.

Interband and Surface‐Influenced Photophysical Processes in CH3NH3PbBr3 Perovskites

Metal halide perovskites (MHPs) are attracting ever‐growing interest across diverse optoelectronic subdisciplines. Yet, the physical mechanism underlying photoexcitation and subsequent photocarrier dynamics remains poorly understood, due to the apparent spectroscopic diversities observed for any certain MHP. Here, diverse spectroscopic characteristics, including static spectral line‐shapes and time‐resolved photoluminescence (TRPL) traces shown by polycrystalline versus single‐crystalline CH3NH3PbBr3 perovskites, are restudied. Key photophysical merits, including exciton binding energy (EB), Sommerfeld factor (ξ), and Urbach energy (EU) that account for the diversities, are discussed within the established framework of semiconductor optics. The value of ξ, which increases with EB, determines how much the interband absorption is enhanced beyond that expected for free carriers. The intrinsic band‐edge luminescence is identified, with its asymmetric spectral line‐shape linked to EU via the van Roosbroeck–Shockley relation. Excited phase evolution, accompanied by rapid electron–hole (e–h) pairs dissociation and subsequent occurrence of e–h plasma, is indicated by the two‐stage TRPL traces that are only observable for high‐quality single crystals. With all the spectroscopic analysis and interpretations rooted in the established semiconductor optical theorems, the mechanistic merits revealed in this study are informative for plausible identification between the interband and excitonic photophysical processes of MHPs.

Study of open circuit voltage loss mechanism in perovskite solar cells

Open circuit voltage (V oc) loss within perovskite solar cells (PSCs) is undesirable as it reduces the power conversion efficiency of these devices. This report proposes a useful method to study V oc loss mechanisms based on experimental samples. V oc in the radiative limit () of devices is estimated by combining the detailed balance theory and the van Roosbroeck–Shockley relation. Furthermore, V oc loss from bulk recombination can be quantified by introducing the bulk lifetime. Thus, the V oc loss from bulk recombination of MAPbI3 and FASnI3 was estimated as 0.094 V and 0.061 V, respectively. The analysis helps distinguish and quantify the V oc loss of PSCs.

Radiative recombination and electron-phonon coupling in lead-free CH3NH3SnI3 perovskite thin films

Solution-processed metal halide perovskites are attracting significant attention as high-performance photovoltaic materials. The electron-phonon interactions in lead halide perovskites are currently in the focus of interest because these interactions play an important role to the observed superior material properties and high device performance. Here, we investigated the electron-phonon coupling in lead-free $\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3}\mathrm{Sn}{\mathrm{I}}_{3}$ thin films by analyzing the temperature-dependence of the photoluminescence (PL) spectra. The PL linewidth shows a superlinear dependence on the temperature, which suggests that the electron--longitudinal-optical (LO) phonon interaction is the dominating broadening mechanism of the optical transitions in $\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3}\mathrm{Sn}{\mathrm{I}}_{3}$ near room temperature. Furthermore, from the analysis of the low-energy tail of the PL spectra by using the van Roosbroeck-Shockley relation, we determined the Urbach energy below the band gap and the optical-phonon energy that contributes to the optical absorption. This phonon energy coincides with the LO phonon energy determined from the PL width analysis. Our work quantitatively verifies that the electrons in tin halide perovskites efficiently couple with optical phonons, and demonstrates that their intrinsic optical properties at room temperature are comparable to those of lead halide perovskites implemented in high-efficiency solar cells.

Bimolecular recombination in methylammonium lead triiodide perovskite is an inverse absorption process

Photovoltaic devices based on metal halide perovskites are rapidly improving in efficiency. Once the Shockley–Queisser limit is reached, charge-carrier extraction will be limited only by radiative bimolecular recombination of electrons with holes. Yet, this fundamental process, and its link with material stoichiometry, is still poorly understood. Here we show that bimolecular charge-carrier recombination in methylammonium lead triiodide perovskite can be fully explained as the inverse process of absorption. By correctly accounting for contributions to the absorption from excitons and electron-hole continuum states, we are able to utilise the van Roosbroeck–Shockley relation to determine bimolecular recombination rate constants from absorption spectra. We show that the sharpening of photon, electron and hole distribution functions significantly enhances bimolecular charge recombination as the temperature is lowered, mirroring trends in transient spectroscopy. Our findings provide vital understanding of band-to-band recombination processes in this hybrid perovskite, which comprise direct, fully radiative transitions between thermalized electrons and holes.

Method of separation of homogeneous and inhomogeneous broadenings of absorption and luminescence spectra of colloidal quantum dots

On the basis of the universal Kennard–Stepanov–van Roosbroeck–Shockley relation, a general approach is proposed for separation of the contributions of homogeneous and inhomogeneous broadenings in the absorption and luminescence spectra of colloidal quantum dots. The applicability of the developed method is demonstrated on published experimental data.

On conversion of luminescence into absorption and the van Roosbroeck-Shockley relation

The problem of conversion of experimentally measured luminescence spectrum into the absorption cross section is revisited. The common practice of using the van Roosbroeck-Shockley (or Kubo-Martin-Schwinger or Kennard-Stepanov) relation in this context is incorrect because luminescence from semiconductors is essentially all due to the spontaneous emission component of the recombination of carriers distributed far-from-equilibrium. A simple, physically consistent, and practical prescription for converting the luminescence spectra into absorption is presented and its relation to the so-called nonequilibrium generalization of the van Roosbroeck-Shockley relationship is discussed.

Factors limiting lifetime of charge carriers in semi-insulated CdTe under high radiation flux

With the growing interest in CdTe and (CdZn)Te X-ray detectors operating at high fluxes of X-ray photons (∼10 10 cm −2 s −1) the questions arises, whether the lifetime of charge carriers is limited by trapping and recombination at deep levels or by band-to-band recombination due to a strongly elevated concentrations of free electrons and holes compared to detectors working at low fluxes. A set of numerical simulations was done to resolve this question. The approach is based on the self-consistent steady state solution of electron and hole drift-diffusion equations using an iterative method. The effect of space charge on the electric field distribution and carrier transport through the sample is evaluated by solving the Poisson equation. The material simulation parameters were chosen to describe typical situations in state-of-the art highly compensated semi-insulated CdTe and CdZnTe (∼10 10 Ωcm) with deep near-midgap levels with concentrations in the range of 10 11–10 12 cm −3.The band-to-band recombination parameter was calculated using the Van Roosbroeck–Shockley relation and was estimated ∼3×10 −10 cm 3/s. The results show, that under all studied conditions the lifetime of carriers and thus the detector performance is limited by carrier trapping and recombination at deep levels.

Two-photon-excited green emission and its dichroic shift of oriented thin-film CdS on glass formed by laser deposition

The photoluminescence of oriented thin-film CdS on glass formed by laser deposition was investigated employing 200 fs, 1.54 eV laser pulses at room temperature. The ultrafast excitation caused a two-photon absorption process, which results in purely green emission at the band gap. The spectra are fitted very well by the application of the van Roosbroeck–Shockley relation, density of states, and Urbach’s rule demonstrating the intrinsic character of the radiative recombination. It is further shown that the energy position of the emission peak depends on the polarization of the impinging laser beam due to the dichroism of the highly oriented films.

Luminescence and absorption in InGaN epitaxial layers and the van Roosbroeck–Shockley relation

Wurtzite InxGa1−xN (0.01≲x≲0.14) films have been grown by metalorganic vapor phase epitaxy on sapphire substrates. Integrated photoluminescence intensity and line shapes have been studied as functions of temperature and alloy composition x. We compare the “effective” InGaN band gap energy assessed by photothermal deflection spectroscopy with a “mean” band gap energy calculated from room temperature photoluminescence spectra utilizing the van Roosbroeck–Shockley relation and assuming a Gaussian energy dependence of the subband gap absorption coefficient. The Stokes’ shift between band gap energy and 300 K photoluminescence peak is explained by this model.

Novel optical thyristors for free-space optical interconnects

We propose and analyze novel fully depleted optical thyris- tors (DOTs) using multiple quantum wells (MQWs) and quarter- wavelength reflector stacks (QWRSs). MQWs are employed to enhance the absorption, while a QWRS is employed as a bottom mirror to en- hance the emission efficiency as well as the optical sensitivity. In order to analyze the switching characteristics, we simulate S-shaped nonlinear current-voltage curves using a coupled junction model associated with the current-oriented method. Furthermore, emission characteristics are obtained by using the scattering-matrix method and the van Roosbroeck-Shockley relation. According to our analysis, the novel DOTs significantly improve the switching and light emission characteris- tics. Compared to a conventional DOT, the optical switching energy and the bit rate of the novel DOT using both MQWs and a QWRS are im- proved by a factor of 0.45 and 1.61, respectively, for a cascading opera- tion. We also analyze the performances of free-space optical intercon- nects using the novel DOTs. © 1999 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(99)01703-1)

Photoluminescence properties of thin CdS films on glass formed by laser ablation

Photoluminescence at the fundamental transition of thin (1.5μm) CdS films formed by laser ablation on glass is investigated in the range 4–300K. In contrast to previous studies on thin CdS films and crystals, the emission takes the form of a single peak over the whole temperature range centered at 487 and 500nm at 4 and 300K, respectively. By the application of the van Roosbroeck–Shockley relation and Urbach’s rule, a direct relationship is shown between emission and absorption. It is further demonstrated that the LO phonon is found to form the Urbach tail and determines the temperature induced gap shift.

Recombination dynamics in GaN

We present a theoretical investigation of the carrier recombination in GaN. Analytical expressions of the radiative recombination coefficients of the coupled exciton–free-carrier system are derived by employing the van Roosbroeck–Shockley relation between absorption and spontaneous emission. Screening to the first order for the discrete exciton state is taken into account. Our results demonstrate the importance of exciton effects, which persist up to high temperatures and excitation densities, for the spontaneous emission in GaN. Finally, “best-case” simulations of the particle densities after pulsed excitation as a function of time or depth show the importance of both bulk and interface nonradiative recombination in GaN.

Requirements for ideal performance of photochemical and photovoltaic solar energy converters

The required characteristics of an ideal photoconverter of solar radiation to electrical or chemical energy are summarized. The four unavoidable loss mechanisms inherent in single-junction photoconverters - lack of absorption of sub-bandgap photons, thermalization of ultra-bandgap photons, the difference between the available energy and internal energy of the thermalized excited states, and the small loss of excited states by radiative decay - are quantified. As the Gibbs energy of the product of an irreversible photochemical reaction falls below the ideal limiting value attained by reversible reactions, the maximum energy stored falls rapidly. This is shown in diagrammatic form for three examples: the isomerization of nonbornadiene to quadricyclane, and the splitting of water by a 2-electron, 2-phonon and a 2-electron, 4-photon process. The radiative lifetime of the excited states in molecular chromophores and semiconductors is linked to the absorption spectra by the appropriate broadband form of the Einsten relation between absorption and emission probability. For molecules, this is the Foerster or the similar Strickler-Berg relation, and for semiconductors it is the van Roosbroeck-Shockley relation. The radiative lifetimes predicted by these relations are compared with those required for ideal performance in four molecular and semiconductor systems.

Influence of radiative recombination on the minority-carrier transport in direct band-gap semiconductors

When radiative (band to band) lifetimes and nonradiative (multiphonon via flaws) lifetimes become comparable, as is the case for GaAs, the customary diffusion equation for minority carriers under low level injection conditions must be augmented by terms originating from photon transport. Using the generalized van Roosbroeck–Shockley relation between absorption and emission as well as radiative transfer theory, the relevant equations for free carrier transport are derived. Subsequently, it is shown that the influence of the reabsorbed recombination radiation on carrier transport while unimportant at low doping levels becomes important for n-type GaAs at high doping levels. We also determine the external luminescence flux taking due account of multiple emission and absorption events inside the sample.

Radiative and Auger processes in semiconductors

Radiative and Auger processes are compared with the main emphasis on five points. 1. (1) It is shown semiempirically that the recombination coefficients for radiative and Auger processes take the form respectively of C r (α 0 a 0) 3/ t 0, C Aug a 0 6/ t 0, where the dimensionless numbers C r , C Aug lie between 1 and 10 10, α 01/137, a 0 is the Bohr radius and t 0 is an atomic unit of time. 2. (2) The method of calculating these coefficients is briefly reviewed, and it is pointed out that the ratios of the radiative to the Auger recombination rates for free-free, free-bound, and bound-bound transitions depend explicitly on the energy E bridged by an electron as E 7/2. (There are implicit dependences on E in addition.) 3. (3) A formal expression for the Auger recombination coefficient in terms of impact ionisation data, corresponding to the van Roosbroeck-Shockley relation is derived. 4. (4) Momentum conservation imposes a threshold energy for Auger and impact ionisation processes which is relaxed if impurities can take up appropriate momenta. This threshold is discussed. 5. (5) In the radiative case occurence of k-selection in relatively pure direct materials leads to lower threshold currents for lasing and to their slower temperature dependence ( T 3/2 instead of T 3). However, the lower density of states in the band tails of impure materials shift the advantage back to impure materials in which impurities take up momentum.