**1. Introduction**

When the size of an LED chip is reduced to tens of microns or even a few microns, it is called a micro-LED chip. Because the micro-display is based on red, green, and blue (RGB) light, micro-LED chips have a high resolution, high brightness, long life, high response speed, and low power consumption. Micro-LEDs have important applications in high-resolution displays, augmented reality, high-speed visible light communication, micro-projectors and other fields [1–3]. Therefore, micro-LED research has been highly valued by researchers in academia and industry all over the world.

In order to improve the luminous efficiency, a multiple quantum well (MQW) structure generally is adopted as the active layer in the micro-LED [4–6]. However, the difference in the lattice constants of the two materials in the quantum well will have a certain impact on the performance of the device. Using the blue LED as an example, stacked InGaN/GaN layers are used to fabricate multiple quantum wells. Due to the ~11% lattice mismatch between InN and GaN when the crystal grows along the *c*-axis, the InGaN/GaN multiple quantum well (MQW) suffers from epitaxial strain and a strong piezoelectric field [7], which leads to a quantum-confined Stark effect (QCSE) that further limits the internal quantum efficiency of InGaN/GaN MQW LEDs [8,9]. In addition, recent studies have indicated that the strain giving rise to the QCSE may be fully or partly relaxed at the boundary of micro-

**Citation:** Zhang, C.; Gao, K.; Wang, F.; Chen, Z.; Shields, P.; Lee, S.; Wang, Y.; Zhang, D.; Liu, H.; Niu, P. Strain Relaxation Effect on the Peak Wavelength of Blue InGaN/GaN Multi-Quantum Well Micro-LEDs. *Appl. Sci.* **2022**, *12*, 7431. https:// doi.org/10.3390/app12157431

Academic Editor: Zhi-Ting Ye

Received: 24 June 2022 Accepted: 22 July 2022 Published: 24 July 2022

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or nano-scale GaN pillars, stimulating many previous studies on the stress distributions on such samples. For example, Y.Kawakami et al. compared the radiation recombination rate of the quantum well of the micro-column structure at the edge and central regions of the micro-column in a time-resolved spectroscopy test, and the radiation recombination rate of the strain relaxation emission zone was higher than that of the strain zone, verifying the existence of the edge stress release phenomenon [10]. The high-resolution CL test of E.Y.Xie et al. performed a full scan of the sample and observed that there was a difference in the radiation wavelength at the boundary and center of the cylindrical sample [11]. The low photoluminescence measured by Peichen Yu from the embedded InGaN/GaN MQW shows a blueshift energy of 68 meV [12]. The above experiments are conducted with ultrahigh-resolution CL and PL spectroscopy, which takes a long time and requires equipment with a very high spatial resolution. Moreover, these studies are all tested on a single MQW pillar and there are no reports studying the edge stress release phenomenon through information obtained from a large number of samples, while the micro-LED applications are generally based on the form of the arrays.

In this paper, several micro-LED arrays of different pillar diameters are fabricated to observe the strain relaxation effect on InGaN/GaN MQWS wavelength modulation. The PL spectra before and after the etching of the micro-LED pillar arrays are used to characterize the MQW edge stress release effect on the arrays' radiation.

Confocal Raman tests are also performed on the single micro-LED pillars to demonstrate the release of lattice mismatch stress on the quantum well sidewalls. Finally, an MQW solid mechanics finite element method (FEM) simulation is used to verify the above analysis.
