In the past decade, metal halide perovskites have emerged as a class of materials that can be used to design efficient light-emitting devices [Tan14].
In high-quality materials, the label light absorption with sharp onset and low nonradiative charge carrier recombination rate leads to the existence of a considerable effect, which can improve calcium Light extraction from titanium-based LEDs as light is redistributed from guided to outcoupling modes [Cho20].
To exploit the beneficial effects of photon recycling effects in , accurate quantification of internal and external emission as a function of multilayer stack design is required. Recently, a simulation method based on the transfer matrix dipole model was proposed [Cho20], which allows a comprehensive analysis of the photon modes contributing to the internal emission as well as the recovery and parasitic absorption of the internally emitted photons. However, like many implementations of dipole radiation models, this method suffers from two important limitations. (i) To avoid divergence in dissipated power related to , it requires discrete partitioning of the system to create a non-absorbing environment for the dipole source at a given location, as well as the choice of in-plane wave vectors As of now, these are sources of inaccuracy and introduce some arbitrariness into the solution. (ii) The method is purely optical and therefore does not allow consideration of electron transport and non-radiative loss aspects related to specific device stack design.
Therefore, we introduce a is not only free from nonphysical disagreements, but also compatible with detailed equilibria, which are characterized by optical constants and The local values of and the transverse electromagnetic Green tensor [Aeb21] provide the case for internal and external emission. In this way, it can be seamlessly integrated with optoelectronic device simulation tools that use radiative recombination and secondary photogeneration rates in the charge carrier balance equations, and provide updates to the local QFLS for use in calculating these rates. Here, we now demonstrate the application of this framework to assess the impact of , from analyzing contribuing photon patterns in single-emitter plate configurations to evaluating external LED quantum efficiencies in realistic device stacks .
Figure 1 - Analysis of optical modes contributing to the total internal emissivity ( TE/TM : Transverse Electric / Magnetic, Pero-Al SPP : Surface Plasmonic Pole at the Interface between Perovskite and Aluminum). (a) Pericite slab in air, (b) Pericite with aluminum reflector.
As a core advantage of LEDs, LED external quantum efficiency (EQELED) includes a factor related to the outcoupling of internally emitted light, which can be quantified as the ratio of external to internal emission. In our method, the internal and external emissions are calculated separately by evaluating the integrated emissivity on the emitter layer and the Poynting vector of the light coupled out of the emitter. Both quantities are evaluated based on the same material properties and Green's function elements described above. Since the efficiency of optical coupling depends on both the optical modes present in the device and the occupancy of these modes under the influence of photon recycling, these two aspects are considered in the following.
Analyzing the power dissipated by the different light modes present in an LED stack is one of the key capabilities provided by dipole radiation models, as implemented in Setfos. As an example, Figure 1 compares the spatially integrated internal emissivity of a simple perovskite sheet in air and the emissivity when a metal reflector is attached to the right: in the simple sheet, the , while in the metal reflection In the presence of the ionizer, the main contribution to the emissivity is carried by guided modes mixed with surface
At the current stage, the optical model of emission and reabsorption is not linked to the electronic model of injected or light-generated charge transport. Instead, to evaluate the QFLS of the whole device, starting from a spatially uniform profile, two limiting cases of the mobility of charge carriers are considered: a uniform QFLS, corresponding to ideal transport within the emitter, and a complete localization . In the former case, reabsorption and reuptake are globally balanced, i.e. after spatial integration across the emitter plate, while in the latter case they are locally balanced at each location of the emitter. Figure 2(a) shows that under the assumption of unit internal quantum efficiency (IQE=1), under the assumption of unit internal quantum efficiency (IQE=1), in two mobility cases (open squares: localized charge carriers, open circles with lines: ideal transport) and the above introduced Evolution of QFLS during reabsorption and reemission for two simple structures (ocher/magenta: no reflector, light blue/green: aluminum reflector). Although there is hardly any difference related to the assumed transmission regime, the maximum directional outcoupling efficiency is close to 50% without the reflector, but much lower with the metallic reflector. In Fig. 2(b), for ideal transport, the same situation is shown, but with IQE < 1, for which the enhancement of EQELED related to photon recycling is labelly attenuated.
Figure 2 - Evolution of external quantum efficiency as the reabsorption and reemission process iterates. (a) Perovskite plate and metal reflector in air under the assumption of IQE=1, ideal transmission (circles) and fully localized (squares); (b) ideal transmission and IQE<1 Down.
The loss of coupling efficiency is mainly related to the light that is emitted into the guided and evaporative modes (eg, surface plasmon poles). While the former part can recover subsequent reabsorption and re-emission to out-coupled modes, the latter part will be accompanied by irrecoverable losses due to parasitic absorption. An example of this loss is the quenching of light extraction efficiency observed in the presence of metallic reflectors: starting from similar outcoupling efficiency values, all internally emitted light ends up in a bare perovskite sheet without parasitic absorption is coupled out in the first few iterations, but a considerable amount of this light is lost at the reflector. Contrary to most formalisms, parasitic absorption does not need to be calculated explicitly for evaluating EQE. However, the consistent determination of parasitic absorption in terms of optical constants, GF elements and QFLS is straightforward and reproduces the limiting EQE values obtained by standard methods based on it.
The application of the Green dyad formalism conforming to the detailed balance is not limited to simple structures, but can study realistic multilayer LED stacks, as shown in Figure 3. Both the local photon flux and reabsorption rate curves show substantial reabsorption in the perovskite emitter and reflective aluminum contacts (Fig. 3b). Evaluation of the layer-resolved reabsorption rate shows that the internal emission is mainly recovered at larger photon energies (above 2.3 eV), while the lower energy photons are mainly parasitically reabsorbed on the metal (Fig. 3c). ). The PR contribution to EQE increases with the thickness of the emitter layer, which can be observed in Fig. 3d (pink dashed line), which is in good agreement with the results reported in the literature [Cho21].
Figure 3 - (a) Complex perovskite LED device stack, (b) evolution of internal photon flux and local reabsorption, (c) layer-resolved reabsorption, (d) EQE as a function of emitter thickness .
Coupling the formalism with the drift-diffusion model of charge transport implemented in Setfosis straightforward due to the parameterization of the emission model in terms of local QFLS.
As shown in the case of metal halide perovskite solar cells in [Zed22], this combination allows the evaluation of electrical losses at the bulk and interface due to carrier leakage and nonradiative recombination.
[Tan14]Tan et al., “Bright light-emitting diodes based on organometal halide perovskite” Nat. Nanotech., vol. 9, 687-692, 2014.
[Cho20]Cho et al., “The role of photon recycling in perovskite light-emitting diodes”, Nature Communications, vol. 11, 611, 2020.
[Aeb21]U. Aeberhard, S. Zeder, and B. Ruhstaller, “Reconciliation of dipole emission with detailed balance rates for the simulation of luminescence and photon recycling in perovskite solar cells,” Opt. Express, vol. 29, pp. 14773–14788, 2021.
[Zed22]S. Zeder, B. Ruhstaller, and U. Aeberhard, Phys. Rev. Applied vol. 17, 014023, 2022.