Connecting Theory and Practice in Optoelectronics

Rigorous Simulation of Photon Recycling Effects in Perovskite Solar Cells and LEDs

In the last decade, metal-halide perovskites have emerged as a class of materials that can be used to engineer efficient and versatile solar cells and light-emitting devices. In high quality metal-halide perovskite solar cells, strong optical absorption with sharp onset together with long non-radiative charge carrier lifetime leads to the presence of sizable photon recycling (PR) effects, such as increased open circuit voltage [1]. On the other hand, PR holds the potential to improve light extraction from perovskite LEDs due to redistribution of light from guided into out-coupled modes [2].

Accurate and physically valid modelling of the impact of photon recycling on device performance requires quantification of internal and external emission under consideration of the actual optical modes present in the complex multilayer device structures, including effects such as cavity resonances and plasmonic losses.  For organic light emitting devices, dipole radiation models are routinely used to model emission in the wave optics regime based on a (measured) photoluminescence spectrum of the emitter material, as implemented e.g. in Fluxim’s device simulation tool Setfos [3]. However, straightforward application of dipole radiation models to extended absorbing emitter materials is problematic due to divergencies in the dissipated power. On the other hand, radiative recombination and photon-recycling in solar cells are modelled primarily based on detailed balance approaches that link the local emission rate to the optical constants of the absorber [4]. In the vast majority of implementations, these models consider an optically uniform photon density of states for the internal emission that is not consistent with the treatment of the external emission that considers the actual photonic mode structure in the device.

In order to overcome the limitations of the above approaches, we recently introduced a theory – based on dyadic Green’s functions – that unifies dipole emission with radiative rates from detailed balance [5]. Consideration of the proper photon states coupling to spontaneous emission provides a numerical treatment of emission into absorbing media that is free of non-physical divergencies. The approach enables the consistent evaluation of internal and external emission under correct consideration of the local values of density of photon states, complex refractive index and quasi-Fermi level splitting, and allows for the determination of the secondary photogeneration rate (photon recycling) from re-absorption of internal emission and the quantification of parasitic absorption in a full wave picture. Furthermore, it enables the rigorous propagation of PR effects from purely optical considerations to actual modifications of the electrical device characteristics as obtained from full opto-electronic device simulation, which we achieve by coupling the Green’s function (GF) code to the drift-diffusion transport model in Setfos.

The approach is illustrated and validated on the example of single perovskite films with and without metallic reflector components. The photon modes contributing to internal emission are identified, revealing the hybridization of guided with plasmonic modes in the presence of metal layers,  and the generalized Kirchhoff law relating external emission and absorptance is verified. The approach is then used to assess the open circuit voltage (VOC) enhancement in solar cells and the increase in the external quantum efficiency (EQE) in LEDs as mediated by photon recycling in realistic device stacks. While good agreement with published data is found for the impact of PR on the EQE as a function of emitter thickness, discrepancies between the uniform photon DOS (VRS) and the GF models for the Voc enhancement at low absorber thicknesses confirm the relevance of a full wave treatment of photon recycling.

Numerical simulation results related to the application of the detailed-balance compatible Green’s function model to metal-halide perovskite solar cells: (a) Optical modes in a 50 nm perovskite layer. (b) Optical limit for the enhancement of the open circuit voltage due to photon recycling in a perovskite slab of varying thickness, as computed by the standard Van Roosbroeck-Shockley (VRS) and the Green’s function approaches. (c) Poynting vector and local re-absorption rate in a realistic solar cell stack. (d) Computational procedure used for the numerical simulation of halide perovskite opto-electronic devices with photon recycling. (e) Current voltage characteristics of the device stack shown in (c), for different regimes of charge carrier transport and recombination.

More details will be presented a the NUSOD 2021 conference (free online event).

[1]          T. Kirchartz, F. Staub, and U. Rau, “Impact of photon recycling on the open-circuit voltage of metal halide perovskite solar cells,” ACS Energy Lett., vol. 1, no. 4, pp. 731–739, 2016.

[2]          C. Cho, B. Zhao, G. D. Tainter, J.-Y. Lee, R. H. Friend, D. Di, F. Deschler, and N. C. Greenham, “The role of photon recycling in perovskite light-emitting diodes,” Nat. Commun., vol. 11, no. 1, p. 611, 2020.

[3]          Fluxim AG, Setfos v5.1.    

[4]          W. Van Roosbroeck and W. Shockley, “Photon-radiative recombination of electrons and holes in Germanium,” Phys. Rev., vol. 94, p. 1558, 1954.

[5]          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.

GaN-based bipolar cascade laser

In recent years, countless publications have been devoted to efficiency improvements of GaN-based light emitters. Among the most intriguing proposals is the cascading of multiple active regions with tunnel junctions in between. Such multi-junction devices were already demonstrated for several other types of light emitters, including GaAs-based lasers and GaSb-based light-emitting diodes (LEDs). In all these cases, electrons and holes are recycled by tunneling and used repeatedly for photon generation. Thus, the ratio of emitted photon number to injected number of electrons, the so-called quantum efficiency, should exceed 100%.

Unfortunately, the GaN-based material system makes it difficult to fabricate multi-junction devices with traditional metal organic vapor-phase epitaxy (MOVPE) so that the expected high efficiencies have not been reported yet. However, plasma-assisted molecular beam epitaxy (PAMBE) recently produced a bipolar cascade laser structure (pictured) exhibiting more than 100% differential quantum efficiency, which is the quantum efficiency above lasing threshold. A rather surprising feature of this laser is the employment of very thick InGaN quantum wells.

In good agreement with measurements, we utilize self-consistent numerical simulation to study internal physical mechanisms, performance limitations, and optimization options of this unique laser design. Contrary to common assumption, wide quantum wells are shown to allow for perfect screening of the internal polarization field by quasi two-dimensional carrier accumulation at the fundamental quantum levels. However, we find that the differential quantum efficiency is still severely limited by internal absorption (see picture). In addition, we show that the power conversion efficiency suffers from the low doping of the p-side cladding layers. Higher Mg acceptor densities promise a significant efficiency enhancement, despite stronger absorption. Furthermore, we investigate the thermal properties of the laser stack and demonstrate that steady-state operation requires a very small thermal resistance because strong self-heating leads to rising Auger recombination.

Further details will be presented at the NUSOD-21 conference.

Machine Learning & Multiscale Simulations for Fast Screening of Organic Semiconductor Materials

by Alessio Gagliardi & Michael Rinderle

Machine learning (ML) approaches have been widely adopted in materials science in recent years. Their applications include for example material property prediction, material screening, and machine learned force field parametrization. In all these applications, ML is used to overcome the computational cost of ab-initio quantum chemical simulations while keeping high accuracy.

ML has been successfully used to predict bandgaps in perovskite materials, reorganization energies and transfer integrals in organic semiconductors, and to generate new materials for organic solar cells, just to name a few applications. While it is arguable if ML can be used to discover new physics, it can definitely help in finding it from available data by using generative models. These can help in identifying the most relevant parameters within a material class or physical process and the subtle correlation existing among them, thus helping scientists to work out the physical and chemical background.  Moreover, many high throughput applications would not be computationally feasible without ML.

Fig. 1: A multiscale simulation of charge mobility in organic semiconductors. Different models are coupled to bridge different spatial scales, from the atomistic to the mesoscale. ML is used to speed up some steps. In the present case: to generate coupling integrals to evaluate charge hopping between neighbor molecules.

In multiscale simulation frameworks, ML is a valuable tool to bridge different scales (see Fig. 1). We utilize ML to predict charge transfer integrals between organic molecules [1]. The model is trained with data obtained from quantum chemical (QC) simulations, and its predictions are used to parametrize mesoscopic kinetic Monte Carlo (kMC) simulations for charge transport (fig. 1). With this framework it is possible to accurately simulate charge carrier mobilities in organic thin films while reducing the need for QC simulations to only a few thousand dimers. It is possible to train a single ML model, based on the relatively simple kernel ridge regression method, to distinguish multiple molecules and predict their transfer integrals accurately.

A new approach using more advanced ML methods will be presented at the NUSOD 2021 conference.

[1] M. Rinderle et al., J. Phys. Chem. C, 2020, 124, 32, 17733-17743

Deep Ultraviolet Light Emitting Diode Characteristics in the Presence of Inhomogeneous Broadening

Deep ultraviolet (DUV) Aluminum Gallium Nitride (AlGaN) light emitting diodes (LED) enable compact UV light sources for various applications, but recent devices still suffer from low hole injection and light extraction efficiency. The rather thin and lattice mismatched quantum wells are prone to inhomogeneous broadening (IHB) which causes the spectral broadening but also affects the electronic operation. The physical model based design process will be improved if the interaction of the IHB with the LED operation is included.

We present a statistical approach to incorporate the IHB in calibrated physical modelling of AlGaN LEDs. For modelling the IHB a Gaussian distribution of the subband energy levels is integrated into our multi scale carrier transport simulator [1]. The fluctuation of the subband energy level is seen though a broadening of the density of states (DOS) as illustrated in the figure below for the conduction band. Thus, both phase space filling and microscopic luminescence model are affected.

We explore the effect of the IHB on a simple single quantum well LED neglecting incomplete ionization and non radiative recombination so that only leakage remains as loss channel. The figure below shows the simulated TE and TM emission spectra in presence of IHB. With vanishing IHB TM emission clearly dominates, but with increasing IHB the TE emission increases because the broadening seen through composition fluctuation is lower in the split off band than the heavy/light hole band [2]. This has been also observed in experiments.

The mean photon energy decreases with the IHB because transitions below the nominal subband transition energy are enabled [3]. The photon energy increases with the current because of the phase space filling. Like the mean photon energy the bias voltage decreases with increasing IHB. The pronounced increase of the IQE with the IHB is caused by the decrease of the turn-on voltage of radiative recombination. However, the internal quantum efficiency (IQE) suggests that the leakage dominates and therefore fixes the bias voltage.

More results including the effect of the IHB in realistic multi quantum well DUV LEDs will be shown at the NUSOD 2021 conference.

  1. Friedhard Römer and Bernd Witzigmann, “Effect of Auger recombination and leakage on the droop in InGaN/GaN quantum well LEDs”, Opt. Express, 22(S6):A1440, 2014.
  2. Jing Zhang, Hongping Zhao, and Nelson Tansu, “Effect of crystal-field split-off hole and heavy-hole bands crossover on gain characteristics of high Al-content AlGaN quantum well lasers”, Appl. Phys. Lett., 97(11):111105, 2010.
  3. Friedhard Römer, Bernd Witzigmann, Martin Guttmann, Norman Susilo, Tim Wernicke, and Michael Kneissl, “Inhomogeneous spectral broadening in deep ultraviolet light emitting diodes”, Proc. SPIE, 10912:0D, 2019.

Thermal and optical simulation of InP on Si nanocavity lasers

III-V on silicon nanocavity lasers emitting at telecommunication wavelengths are the most promising candidates for on-chip light sources. However, the serious self-heating problem is an obstacle towards higher performance and better reliability. An accurate prediction of thermal effects for different nanocavity geometries is needed to design scaled photonic devices. We present a combined thermal and optical analysis of InP nanocavity lasers using numerical modeling of both thermal (using Ansys APDL) and optical (using Lumerical FDTD) properties. For our design study different geometries of disk, square, hexagon and ring with various diameters from 200 nm to 2 µm were simulated, as shown in Fig. 1.

Fig. 1. The Schematic configuration (a) cross-section of (c1) disk, (c2) square, and (c3) hexagon; (b) cross-section of (c4) ring; (d) meshing of square model; (e) Gaussian distributed heat generation on square geometry.

Fig. 2 shows the simulated thermal resistance of the disk, square, hexagon, and ring microcavities, the experimental results characterized in [1] and alongside simulated mode volume fractions occupying the cavity volume together with their corresponding simulated resonant mode patterns.

Fig. 2(a) Thermal resistance of disk, square and hexagon microcavities dependent on diameter; (b) and (c) thermal resistance of ring cavities dependent on ring parameter; (d) experimental threshold versus diameter of InP whispering gallery mode cavities and simulated mode volume fractions; (e)-(g) simulated resonant modes corresponding to the mode volumes in (d) with diameters of 500 nm, 700 nm, and 900 nm.

For practical applications, cavities with diameters of around 1000 nm are optimal considering the trade-off between the thermal resistance and uniform pumping conditions in our setup. Furthermore, temperature profiles in different parts of the nanocavity lasers are also studied, revealing that reducing the thickness of the bottom SiO2 is the most efficient way to improve the thermal property of the nanocavity lasers.

Further details will be given during the NUSOD-21 Conference.

[1] P. Tiwari, et al., Optics Express. vol. 29, no. 3, 2021.