NUSOD Blog

Connecting Theory and Practice in Optoelectronics

Challenges of GaN-LED Modeling and Simulation

Light emitting diodes (LEDs) based on Gallium Nitride (GaN) have been revolutionizing various applications in lighting, displays, biotechnology, and other fields. However, their energy efficiency is still below expectations in many cases. An unprecedented variety of modeling and simulation papers has been published, mainly focusing on efficiency analysis and GaN-LED design optimization. In this open access review paper, I recently tried to provide an overview of the GaN-LED modeling landscape with special emphasis on the influence of III-Nitride material properties [1]. Even after 20+ years of intense worldwide research activities, I still see some key challenges as briefly listed below.

(1) The employment of realistic material parameters remains a fundamental issue for GaN-LED simulations. For example, some simulations of experimental characteristics validate competing efficiency droop models by simple variation of uncertain parameters (see figure) [2].

(2) GaN-LEDs are three-dimensional (3D) objects but most LED simulations are performed in 1D or 2D. Even with uniform material properties in each semiconductor layer, the current flow is often non-uniform in real devices, leading to local self-heating, non-uniform carrier density in each quantum well (QW), and non-uniform light emission. While 1D and 2D simulations are valuable in studying specific mechanisms, they are unable to fully reflect the internal physics and the measured performance of real LEDs.

(3) Another major challenge arises from the non-uniform nature of InGaN quantum wells. QWs with low Indium content may exhibit an average Indium atom distance that is larger than the QW thickness. QWs with larger Indium concentration allow for Indium accumulation regions with lower bandgap, larger free carrier concentration, and stronger Auger recombination.  Thus, the typical assumption of uniform QW properties is often invalid, giving rise to various atomistic LED modeling approaches.

(4) Artificial intelligence (AI) methods also represent a serious challenge. Several simulation-trained AI methods have been utilized for GaN-LED design optimization. However, they produce unreliable results due to various simulation uncertainties. The strength of AI actually lies in the analysis of experimental data. The combination of reality-trained AI methods with numerical simulations could lead to the creation of realistic digital twins that support the LED design and production process.

More details are given in [1] and references therein.

[1] Efficiency Models for GaN-based Light-Emitting Diodes: Status and Challenges, MDPI Materials 13, 5174 (2020)

[2] How to decide between competing efficiency droop models for GaN-based light-emitting diodes. Appl. Phys. Lett. 107, 031101 (2015)




Pros and Cons of Online Conferences

Thanks to the new Corona virus, I have been attending many online conferences this year, most of them for free. Such virtual conferences reach a much larger worldwide audience than onsite meetings. However, I always wonder why organizers stick to the rigid concept of live conferences. Online attendance is spread over many time zones and participants are still busy with their daily routines. In fact, I usually managed to view only 2-3 presentations. What is more, a brief live Q&A period after each talk is clearly too short for serious discussions.

That is why we developed a more flexible concept for our NUSOD 2020 online conference, hosted by Politecnico di Torino, Italy. With great success, it seems, as 324 participants are triple our usual number. It was also our most international audience with attendees from 43 countries. 70 pre-recorded presentation videos were available 24/7, attracting 59 views on average, five talks even more than 150 views, according to website statistics. Questions and answers could be posted continuously in the comment section of each video. Some in-depth discussions went on for several days.

However, about half of our presentations did not receive any feedback at all, despite our conference extension by one week. Google Analytics reveals that most of the 1000 site visits by registered participants lasted less than 30 minutes. In many cases, videos were not watched in full. In other words, online attendees are too distracted by their daily life and pay far less attention than at onsite conferences.

Virtual conferences are convenient, inexpensive, and accessible but by no means generate the full benefits of traditional conferences. Onsite meetings are crucial to inspire new ideas and to establish personal connections. We hope to accomplish this at our NUSOD 2021 conference, onsite in Turin, Italy. See you there!

Electronic structure of lonsdaleite SiGe alloys

The indirect band gaps of the elemental group-IV semiconductors silicon (Si) and germanium (Ge) make these materials intrinsically inefficient light emitters. This limits their applications in active photonic devices such as light-emitting diodes and lasers, which in turn limits the development of Si photonics due to the unavailability of direct-gap semiconductors compatible with established complementary metal-oxide semiconductor (CMOS) fabrication processes. The so-called “holy grail” of Si photonics is to realise CMOS-compatible, group-IV materials possessing direct band gaps, to enable the development of LEDs and lasers which can be integrated monolithically on a Si platform [1]. Such devices have huge potential for practical applications, enabling new functionalities while simultaneously delivering improved system-level energy efficiency by allowing for removal of power-hungry electrical interconnects on-chip and in data centres.

Ge possesses a “weak” indirect band gap, with the L-point conduction band (CB) minimum lying only 145 meV lower in energy than the Γ-point CB edge. Efforts to obtain a direct-gap group-IV semiconductor have therefore largely centred on engineering the band structure of Ge, in an attempt to reverse the ordering of the L- and Γ-point CB edge states. Proposed approaches to achieve this include application of tensile strain to Ge [2], or alloying Ge with small concentrations of carbon (C) [3,4], tin (Sn) [5] or lead (Pb) [6]. Impressive initial experimental demonstrations related to each of these concepts have driven significant activity related to materials growth and device fabrication in recent years. Theory and simulation underlying several of these advancements have been described at NUSOD, including (i) analysis of the electronic structure of Ge1-xSnx and Ge1-xPbx alloys [7,8], and (ii) simulation of prototypical Ge1-xSnx-based photonic [9,10] and electronic [11] devices. Of these approaches, the current leading contender is the Ge1-xSnx alloy, with optically and electrically pumped lasing having been demonstrated by several groups [12,13]. However, high quality Ge1-xSnx alloys are extremely challenging to achieve via epitaxial growth, and their reduced temperature stability compared to Ge presents further challenges for device fabrication and reliability. This mandates continued efforts to develop alternative routes to achieve enabling material platforms for CMOS-compatible active photonic devices.

Si and Ge conventionally crystallise in the cubic diamond phase. However, recent advancements in non-equilibrium growth of semiconductor nanowires have made it possible to grow these materials in the metastable hexagonal lonsdaleite (or “hexagonal diamond”) phase [14]. Just as alloying or application of strain can strongly modify the band structure of a semiconductor material, the emerging ability to grow conventional materials in non-conventional crystal structures provides a new approach to engineer the band structure for practical applications. The transition from the diamond to lonsdaleite phase in Ge modifies the electronic structure such that the lonsdaleite phase possesses a so-called “pseudo-direct” band gap – i.e. the CB minimum lies at Γ, but this direct gap possesses weak oscillator strength [15]. This band structure modification is illustrated in Fig. 1, which shows the band structure and density of states (DOS) of diamond- and lonsdaleite-structured Si and Ge, calculated from first principles. Diamond-structured (a) Ge and (c) Si are indirect-gap semiconductors. The cubic to hexagonal phase transition gives rise to a pseudo-direct band gap in lonsdaleite-structured (c) Ge, while lonsdaleite-structured (d) Si remains indirect-gap. These band structure calculations indicate that Ge-rich lonsdaleite SiGe alloys should possess a direct band gap, suggesting a radical new approach to obtain a tunable direct band gap group-IV material.

Fig. 1. First principles calculated band structures of (a) diamond-structured (cubic) Ge, (b) lonsdaleite-structured (hexagonal) Ge, (c) diamond-structured Si, and (d) lonsdaleite-structured Si. Conventional cubic Ge and Si are indirect-gap semiconductors, as is hexagonal Si. Hexagonal Ge admits a “pseudo-direct” band gap, making it a potential candidate material for Si photonics applications.

Indeed, recent experimental measurements have revealed room temperature light emission from lonsdaleite SiGe nanowires [16], constituting a highly promising demonstration of a novel approach to obtain light emission from a conventional group-IV semiconductor alloy, with extremely strong potential for Si photonics applications. Given the pseudo-direct nature of the lonsdaleite SiGe band gap, the measured optical properties – in particular the high radiative recombination rate – of SiGe are surprising. To begin to understand this unusual behaviour, we have undertaken first principles calculations of the electronic structure evolution of lonsdaleite SiGe alloys. By combining alloy supercell electronic structure calculations with zone unfolding methods, we elucidate the nature and evolution of the alloy band structure. We comment on the consequences of the calculated electronic properties for optical properties, and evaluate our findings and their implications for optical properties in the context of emerging experimental data.

These results will be presented in talk NM02, “Electronic structure of lonsdaleite SixGe1-x alloys“, at the free online NUSOD 2020 conference.

Acknowledgements

This work was supported by the National University of Ireland Post-Doctoral Fellowship in the Sciences, and by Science Foundation Ireland (SFI; project no. 15/IA/3082).

References

[1] R. Geiger, T. Zabel, and H. Sigg, “Group IV direct gap photonics: methods, challenges, and opportunities”, Front. Mater. 2, 52 (2015)

[2] X. Sun, J. Liu, L. C. Kimerling, and J. Michel, “Direct gap photoluminescence of n-type tensile-strained Ge-on-Si”, Appl. Phys. Lett. 95, 011911 (2009)

[3] C. A. Stephenson, W. A. O’Brien, M. W. Penninger, W. F. Schneider, M. Gillett-Kunnath, J. Zajicek, K. M. Yu, R. Kudraweic, R. A. Stillwell, and M. A. Wistey, “Band structure of germanium carbides for direct bandgap silicon photonics”, J. Appl. Phys. 120, 053102 (2016)

[4] C. A. Broderick, M. D. Dunne, D. S. P. Tanner, and E. P. O’Reilly, “Electronic structure evolution in dilute carbide Ge1-xCx alloys and implications for device applications”, J. Appl. Phys. 126, 195702 (2019)

[5] J. Doherty, S. Biswas, E. Galluccio, C. A. Broderick, A. Garcia-Gil, R. Duffy, E. P. O’Reilly, and J. D. Holmes, “Progress on germanium-tin nanoscale alloys”, Chem. Mater. 32, 4383 (2020)

[6] C. A. Broderick, E. J. O’Halloran, and E. P. O’Reilly, “First principles analysis of electronic structure evolution and the indirect- to direct-gap transition in group-IV Ge1-xPbx alloys”, arXiv:1911.05679 (2019)

[7] S. Schulz, C. A. Broderick, E. J. O’Halloran, and E. P. O’Reilly, “The nature of the band gap of Ge1-xSnx alloys”, Proc. NUSOD (2018)

[8] C. A. Broderick, E. J. O’Halloran, and E. P. O’Reilly, “Comparative analysis of electronic structure evolution in Ge1-xSnx and Ge1-xPbx alloys”, Proc. NUSOD (2019)

[9] H. S. Maczko, R. Kudrawiec, and M. Gladysiewicz, “Designing and analysis of SiGeSn-based quantum wells integrated with Si platform for laser applications”, Proc. NUSOD (2017)

[10] H. Kumar and R. Basu, “Comprehensive study and noise analysis of GeSn-based p-n-p heterojunction phototransistors for efficient detection”, Proc. NUSOD (2018)

[11] M. D. Dunne, C. A. Broderick, M. Luisier, and E. P. O’Reilly, “Atomistic analysis of band-to-band tunnelling in direct-gap Ge1-xSnx group-IV alloys”, Proc. NUSOD (2020)

[12] S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si”, Nature Photonics 9, 88 (2015)

[13] Y. Zhou, Y. Miao, S. Ojo, H. Tran, G. Abernathy, J. M. Grant, S. Amoah, G. Salamo, W. Du, J. Liu, J. Margetis, J. Tolle, Y.-H. Zhang, G. Sun, R. A. Soref, B. Li, and S.-Q. Yu, “Electrically injected GeSn lasers on Si operating up to 100 K”, arXiv:2004.09402 (2020)

[14] H. I. T. Hague, S. Conesa-Boj, M. A. Verheijen, S. Koelling, and E. P. A. M. Bakkers, “Single-crystalline hexagonal silicon-germanium”, Nano. Lett. 17, 85 (2016)

[15] C. Rödl, J. Furthmüller, J. R. Suckert, V. Armuzza, F. Bechstedt, and S. Botti, “Accurate electronic and optical properties of hexagonal germanium for optoelectronic applications“, Phys. Rev. Materials 3, 034602 (2019)

[16] E. M. T. Fadaly, A. Dijkstra, J. R. Suckert, D. Ziss, M. A. J. van Tilburg, C. Mao, Y. Ren, V. T. van Lange, K. Korzun, S. Kölling, M. A. Verheijen, D. Busse, C. Rödl, J. Furthmüller, F. Bechstedt, J. Stangl, J. J. Finley, S. Botti, J. E. M. Haverkort, and E. P. A. M. Bakkers, “Direct-bandgap emission from hexagonal Ge and SiGe alloys”, Nature 580, 205 (2020)

The dilemma of simulation-based machine learning

Machine learning applications typically perform statistical analyses and predictions based on real-world data collection (Fig. 1). This can be very valuable when the amount of data is large and difficult to digest. Deep learning is currently one of the most popular artificial intelligence methods, utilizing multi-layered artificial neural networks (ANNs). ANNs connect a set of input numbers to a set of output numbers by mathematical operations. However, these operations are not derived from the meaning behind these numbers. Instead, thousands of training data sets are required to teach an ANN. But sufficient training data are sometimes hard to obtain. Therefore, such data are often generated by numerical simulations, especially in the fields of materials science and photonics. This simulation-based approach has the advantage of creating consistent data sets in agreement with existing theoretical models.

Fig. 1: Computational analysis methods.

However, models always simplify reality, and simulation results often disagree with measurements. There are many possible reasons for such disagreements, some of which are listed here. Strictly speaking, numerical simulations produce a virtual reality in which various artificial effects may happen (Fig. 1). Machine learning from flawed simulations ignores such flaws and renders them untraceable. Resulting design optimizations of optoelectronic devices are often unreliable. [1]

Even a perfect simulation model reflects at best our present understanding of reality. This would be quite appropriate for design optimization projects. But we cannot expect artificial intelligence to discover new laws of physics this way. Scientific discoveries are typically triggered by a conflict between existing models and real-world observations. For that, we still need human intelligence, I think.

Further details and possible remedies will be presented at the NUSOD-20 conference.

[1] J. Piprek, Pitfalls of simulation-based machine learning in optoelectronic device design, IEEE TechRxiv Preprint (June 2020)

Electronic properties of In(As,Sb,P) graded–composition quantum dots

Graded-composition quantum dots grown using liquid-phase epitaxy techniques in the In(As,Sb,P) material system cover the mid-infrared spectrum (wavelengths of 3 to 5 μm), which is important for a wide range of applications, e.g. in gas sensing or energy harvesting. The particular strength of the growth process from the liquid phase is here that composition gradients through a nanostructure can be intentionally achieved, facilitating the fine-tuning of the optoelectronic properties together with a significant improvement of the crystal quality. We have performed systematic investigations of nucleation process and electronic properties of In(As,Sb,P) graded-composition quantum dots. Using an eight-band k·p model for zincblende materials implemented within the Sphinx multiphysics library, we have computed the electronic properties for different heights and diameters, as observed in the ensemble and combined these results with the experimentally observed diameter distribution to simulate ensemble absorption spectra at room temperature. The simulated absorption peak wavelength (3.829 μm) is in excellent agreement with the experimentally observed one (3.83 μm), facilitating the application of our simulation framework in theory-driven design of In(As,Sb,P) graded-composition quantum dots that fulfill the requirements of specific devices. Further details will be presented at the NUSOD-20 conference.

Top left: Cross-sectional bright-field transmission electron microscopy image of a typical In(As,Sb,P) graded-composition quantum dot. Bottom left: Schematic view of the quantum dot and its alloy composition profile. Right: Recombination energy between hole ground state and conduction band as a function of quantum dot height for different base diameters. The inset shows a typical hole ground state charge density in a graded-composition quantum dot.

This work was funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC2046: MATH+ Berlin Mathematics Research Center (project AA2-5).

References:

K. M. Gambaryan, T. Boeck, A. Trampert, and O. Marquardt: “Nucleation Chronology and Electronic Properties of In(As,Sb,P) Graded Composition Quantum Dots Grown on an InAs(100) Substrate”, ACS Applied Electronic Materials 2, 646 (2020)

The Sphinx repository: https://sxrepo.mpie.de/