Unlocking the origin of compositional fluctuations in InGaN light emitting diodes

Tara P. Mishra, Govindo J. Syaranamual, Zeyu Deng (邓泽宇), Jing Yang Chung, Li Zhang, Sarah A. Goodman, Lewys Jones, Michel Bosman, Silvija Gradečak, Stephen J. Pennycook, and Pieremanuele Canepa

Phys. Rev. Materials 5, 024605 – Published 22 February 2021

Abstract

The accurate determination of compositional fluctuations is pivotal in understanding their role in the reduction of efficiency in high indium content ${In}_{x} {Ga}_{1 - x} N$ light emitting diodes (LEDs), the origin of which is still poorly understood. Here we have combined electron energy loss spectroscopy (EELS) imaging at subnanometer resolution with multiscale computational models to obtain a statistical distribution of the compositional fluctuations in ${In}_{x} {Ga}_{1 - x} N$ quantum wells (QWs). Employing a multiscale computational model, we show the tendency of intrinsic compositional fluctuation in ${In}_{x} {Ga}_{1 - x} N$ QWs at different indium concentrations and in the presence of strain. We have developed a systematic formalism based on the autonomous detection of compositional fluctuation in observed and simulated EELS maps. We have shown a direct comparison between the computationally predicted and experimentally observed compositional fluctuations. We have found that although a random alloy model captures the distribution of compositional fluctuations in relatively low In ( $\sim 18 %$ ) content ${In}_{x} {Ga}_{1 - x} N$ QWs, there exists a striking deviation from the model in higher In content (≥24%) QWs. Our results highlight a distinct behavior in carrier localization driven by compositional fluctuations in the low and high In content InGaN QWs, which would ultimately affect the performance of LEDs. Furthermore, our robust computational and atomic characterization method can be widely applied to study materials in which nanoscale compositional fluctuations play a significant role in the material performance.

Received 21 September 2020
Revised 6 January 2021
Accepted 5 February 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.024605

Physics Subject Headings (PhySH)

First order phase transitions First-principles calculations Microstructure Phase diagrams Phase separation Solid-solid transformations Spinodal decomposition

LEDs

Cluster expansion Density functional calculations Electron energy loss spectroscopy Imaging & optical processing Monte Carlo methods Scanning transmission electron microscopy

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Tara P. Mishra ^1,2, Govindo J. Syaranamual², Zeyu Deng (邓泽宇)^1,*, Jing Yang Chung^1,2, Li Zhang², Sarah A. Goodman³, Lewys Jones⁴, Michel Bosman¹, Silvija Gradečak^1,2,3,†, Stephen J. Pennycook^1,2,‡, and Pieremanuele Canepa ^1,2,5,§

¹Department of Materials Science and Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Singapore, Singapore
²Singapore-MIT Alliance for Research and Technology, 1 CREATE Way, 10-01 CREATE Tower, Singapore 138602, Singapore
³Massachusetts Institute of Technology, Department of Materials Science and Engineering, Cambridge, Massachusetts 02139, USA
⁴School of Physics, Trinity College Dublin, Dublin 2, D02 PN40, Ireland and Advanced Microscopy Laboratory, Centre for Research on Adaptive Nanostructures & Nanodevices (CRANN), Dublin 2, Ireland
⁵Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, 117585 Singapore, Singapore

^*msedz@nus.edu.sg
^†gradecak@nus.edu.sg
^‡stephen.pennycook@cantab.net
^§pcanepa@nus.edu.sg

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Issue

Vol. 5, Iss. 2 — February 2021

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Images

Figure 1
LED device and its characterization. (a) Cross section of the LED device composed of alternating InGaN QWs and GaN barrier layers. (b) Low-magnification STEM HAADF image from the QW region of the LED. (c), (d) The corresponding monochromatic STEM CL images recorded at 450 and 490 nm. Images have been false colored according to the CL wavelength.
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Figure 2
Autonomous detection of compositional fluctuations in ${In}_{x} {Ga}_{1 - x} N$ samples. Panels (a)–(c) show the analysis of the experimental STEM EELS maps of the ${In}_{x} {Ga}_{1 - x} N$ samples, whereas panels (d,e,c) depict the generation and analysis of similar maps from a theoretical approach. Panel (a) depicts a schematic STEM EELS hyperspectral measurement. Panel (b) shows a representative Ga compositional map which is integrated from the hyperspectral data set. Panel (c) shows the detection of In compositional fluctuation in the micrographs from STEM EELS with the color bar representing the In concentration (top) and theory (bottom), respectively, on which a convolution of the Laplacian of Gaussian (LoG) kernels with the input image is performed. The white bar represents the 2 nm scale. Panel (d) shows a representative microstructure model obtained using canonical Monte Carlo (e) and viewed from the $[11 \bar{2} 0]$ axis. A multislice simulation of the EELS map, using the multem package, from the Monte Carlo microstructure model is shown.
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Figure 3
Formation energies calculated using DFT (blue dots) and the CE Hamiltonian (black cross) for InGaN QWs in (a) the bulk incoherent model and (b) the epitaxially coherent model. The respective error plots of both CEs are reported in Fig. S5 in the SM [47]. Inset in panel (b) highlights the distance from the convex hull ( $\sim 1.43$ meV/f.u.) of the DFT metastable ordering at $x = \frac{1}{3}$ ( ${In}_{1 / 3} {Ga}_{2 / 3} N$ ).
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Figure 4
Compositional phase diagram of the ${In}_{x} {Ga}_{1 - x} N$ alloy as a function of temperature as derived from the GCMC simulations parametrized on the CE model for (a) the bulk incoherent and (b) the epitaxially coherent InGaN QW model. In the bulk incoherent model (a), the red area ( $α + β)$ represents the biphasic region, while the blue area ( $α$ and $β$ ) shows the single-phase regions. A miscibility gap is observed until a critical temperature of 1950 K. In the biphasic region the alloy has the tendency to phase separate into Ga ( $α$ ) and In ( $β)$ rich regions. For the epitaxially coherent model of panel (b), three stable phases are observed at $\sim 0$ K, namely, the Ga-rich phase ( $σ)$ , the ${(InN)}_{2} / {(GaN)}_{2}$ ordered phase ( $δ)$ , and the In-rich phase ( $η)$ . Above $\sim 100$ K, at $x = \frac{1}{3}$ a new single phase ( $γ)$ is observed. The phase $γ$ decomposes into phases $σ$ and $δ$ through a eutectoid transformation at $\sim 80$ K. The single phases are always separated by biphasic regions, while full In solubility is obtained for temperatures above $\sim 1300$ K.
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Figure 5
Representative EELS compositional maps of QW regions overlaid with circles denoting compositional fluctuations found using the LoG algorithm for QWs with In composition (a) 18.4% and (c) 24.2%. The scale bars in (a,c) are 2 nm and shown by gray bars. The probability density functions ( $y$ axis) of the size of the compositional fluctuations ( $x$ axis) in (b) 18.4% and (d) 24.2% In content QWs, respectively are obtained from EELS experiments (in violet, bottom) and compared with different canonical Monte Carlo simulations (CMC) at conditions namely, random at 4000 K (black), epitaxially coherent at 1000 K (blue) and bulk incoherent at 1575 K (red). The random alloy distribution is obtained by running the CMC simulations at a temperature of $\sim 4000$ K, which is significantly higher than the miscibility temperature of In in GaN [see Figs. 4 and 4]. The average size of the compositional fluctuation is marked by dashed lines.
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