Impact of Photon Recycling on the Efficiency of Light Extraction in Metal Halide Perovskite Light Emitting Diodes
In the last decade, metal halide perovskites have emerged as a class of materials that can be used to engineer efficient light-emitting devices [Tan14].
In high-quality metal halide perovskite materials, strong optical absorption with sharp onset together with low non-radiative charge carrier recombination rates leads to the presence of sizable photon recycling (PR) effects, which can improve light extraction from perovskite LEDs due to redistribution of light from guided to out-coupled modes [Cho20].
In order to exploit the beneficial impact of PR in perovskite LEDs (PeLEDs), accurate quantification of internal and external emission as a function of the multilayer stack design is required. Recently, a simulation approach based on a transfer-matrix dipole model was presented [Cho20], which allows for a comprehensive analysis of the photon modes contributing to internal emission and to both, recycling and parasitic absorption of the internally emitted photons. However, like many implementations of dipole radiation models, the approach suffers from two important limitations: (i) in order to avoid divergences in the dissipated power related to non-radiative near-field energy transfer, it demands a discrete partitioning of the system to create a non-absorbing environment of the dipole source at a given location, as well as the selection of an in-plane wave vector cut-off, which are both origin of inaccuracies and introduce some arbitrariness in the solution; (ii) the approach is purely optical, and, hence, does not allow for the consideration of aspects of electronic transport and non-radiative losses related to a specific device stack design.
Therefore, we introduced a theoretical treatment of photon emission and recycling in optoelectronic semiconductor devices that is not only free of non-physical divergencies, but also compatible with detailed balance, and which provides the internal and external emission in terms of the local values of optical constants and quasi-Fermi level splitting (QFLS) and of the transverse electromagnetic Green’s tensor [Aeb21]. In this way, it enables seamless integration with optoelectronic device simulation tools that use the radiative recombination and secondary photogeneration rates in the charge carrier balance equations and provide an update of the local QFLS to be used in the computation of those rates. Here, we now show the application of this framework to the assessment of the impact of PR on the light extraction efficiency in PeLED components and devices, from the analysis of contributing photonic modes in single emitter slab configurations to the evaluation of the external LED quantum efficiency in realistic device stacks.
Figure 1 –Analysis of the optical modes contributing to the total internal emission rate (TE/TM: transverse electric/magnetic, Pero-Al SPP: surface plasmon polariton at the interface between perovskite and aluminum): (a) perovskite slab in air, (b) perovskite with aluminium reflector.
As the central figure of merit of LED, the LED external quantum efficiency (EQELED) includes a factor related to the out-coupling of the internally emitted light, which can be quantified as the ratio of external to internal emission. In our approach, internal and external emission are computed by evaluation of the rate of emission integrated over the emitter layer and of the Poynting vector for the light that is coupled out of the emitter, respectively. Both quantities are evaluated based on the same material properties and Green’s function elements as described above. Since the efficiency of light outcoupling depends on both, the optical modes that are present in the device and the occupation of those modes under the influence of photon-recycling, both aspects will be considered in the following.
Analysis of the power dissipated by the different optical modes present in LED stacks is one of the pivotal features offered by dipole radiation models such as the one implemented in Setfos. As an example, Fig. 1 compares the spatially integrated internal emission rate of a simple perovskite slab in the air with that in the presence of an additional metallic reflector attached at the right side: while in the simple slab, the emission is dominated by waveguide modes, the main contribution to the emission rate is carried by guided modes that hybridize with surface plasmons in the presence of the metallic reflector.
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At the current stage, the optical model for emission and re-absorption is not coupled to an electronic model for the transport of the injected or photo-generated charges. Instead, two limiting cases are considered for the mobility of charge carriers in order to evaluate the QFLS throughout the device, starting from a spatially uniform profile: a uniform QFLS, corresponding to ideal transport within the emitter, and full localization. In the former case, the re-absorption and re-absorptance are balanced globally, i.e., upon spatial integration over the entire emitter slab, while they are balanced locally for each position in the emitter in the latter case. Figure 2(a) displays the evolution of the QFLS under iteration of re-absorption and re-emission processes under the assumption of unit internal quantum efficiency (IQE=1) in the two mobility cases (open squares: localized carriers, open circle with line: ideal transport) and for the two simple structures introduced above (ocher/magenta: no reflector, light blue/green: Al reflector). While there is hardly any difference related to the transport regime assumed, the maximum directed outcoupling efficiency approaches 50% in the reflector-free case, but it is much lower in the presence of the metallic reflector. In Fig. 2(b), the same situation is displayed for ideal transport, but IQE<1, for which the enhancement of EQE related to photon recycling is strongly reduced.
Figure 2 – Evolution of the external quantum efficiency upon iteration of re-absorption and re-emission processes: (a) in the case of ideal transport (circles) and full localization (squares) under the assumption of IQE=1, for a perovskite slab in air and with a metallic reflector; (b) for the case of ideal transport and reduced IQE < 1.
Losses in outcoupling efficiency are mostly related to light that is emitted into guided and evanescent modes (such as, e.g., surface plasmon polaritons). While the former part can be recycled subsequent re-absorption and re-emission into out-coupled modes, the latter part will be accompanied by unrecoverable losses due to parasitic absorption. An example of such losses is the observed quenching of the light extraction efficiency in the presence of metallic reflectors: starting from similar values of the outcoupling efficiency, all of the internally emitted light is eventually coupled out in the bare perovskite slab without parasitic absorption, but a substantial amount of this light is lost at the reflector in the first few iterations. Contrary to most formalism, parasitic absorption does not need to be computed explicitly for the evaluation of the 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 via the standard approaches based on it.
The application of the detailed-balance compliant Green dyad formalism is not restricted to simple structures, but realistic multilayer LED stacks can be investigated, as shown in Fig. 3. Both the local photon flux and the re-absorption rate profile reveal the substantial re-absorption in both, the perovskite emitter and the reflecting aluminum contact (Fig. 3b). Evaluation of the layer-resolved re-absorptance shows that the internal emission is recycled mostly at larger photon energies (above 2.3 eV), while lower-energy photons are mostly reabsorbed parasitically at the metal (Fig. 3c). The PR contribution to the EQE increases with the thickness of the emitter layer as can be observed in Fig. 3d (dashed pink line) and it is in excellent agreement with the findings reported in the literature [Cho21].
Figure 3 – (a) Complex perovskite LED device stack, (b) evolution of internal photon flux and local reabsorption rate, (c) layer-resolved re-absorptance, (d) EQE as a function of emitter thickness.
Thanks to the parametrization of the emission model in terms of the local QFLS, coupling the formalism to the drift-diffusion model of charge transport as implemented in Setfos is straightforward.
This combination allows the assessment of electrical losses caused by carrier leakage and non-radiative recombination in the bulk and at interfaces, as shown in [Zed22] for the case of metal-halide perovskite solar cells.
