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Abstract
Strain in InGaN/GaN multiple-quantum well (MQW) light emitters was relaxed via nanopatterning using colloidal lithography and top-down plasma etching. Colloidal lithography was performed using Langmuir-Blodgett dip-coating of samples with silica particles (d = 170, 310, 690, 960 nm) and a Cl2/N2 inductively coupled plasma etch to produce nanorod structures. The InGaN/GaN MQW nanorods were characterized using X-ray diffraction (XRD) reciprocal space mapping to quantify the degree of relaxation. A peak relaxation of 32% was achieved for the smallest diameter features tested (120 nm after etching). Power-dependent photoluminescence at 13 K showed blue-shifted quantum well emission upon relaxation, which is attributed to reduction of the inherent piezoelectric field in the III-nitrides. Poisson-Schrödinger simulations of single well structures also predicted increasing spectral blueshift with strain relaxation, in agreement with experiments.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The III-nitrides are excellent materials for LEDs [1], lasers [2] and power electronics due to their tunable bandgap and high defect tolerance. Moreover, they are becoming increasingly important in mobile and portable display applications [3] because they can potentially replace inefficient liquid crystal and/or organic-based LED technologies. However, challenges presently exist related to growing high quality, high In-content InGaN for full color red-green-blue (RGB) displays, especially for red emitters. The 11% lattice mismatch between InN and GaN results in heavily strained InGaN device layers, which in turn reduces crystal quality and increases band bending, leading to large piezoelectric fields, the quantum-confined Stark effect (QCSE) [4,5], and ultimately low efficiency. Nanopatterning the active nitride material itself, using methods such as self-assembled Ni nanoisland [6–8] or SiO2 (colloidal crystal) [9–18] etch masks, as well as nanoimprint [19,20], interference [21,22], and electron beam [23] lithographies, is a potential route to solve the aforementioned problems. These approaches have largely been used for light extraction engineering and to create photonic crystals, but there are indications that nanopatterning could indeed relieve material strain. For example, Wang et al. reported a current-independent blueshift in electroluminescence (EL) emission from InGaN/GaN nanorods (50–100 nm), as compared to planar films, suggesting that piezoelectric fields were reduced upon nanopatterning [15]. In other work, Wu et al. studied the influence of nanorod diameter through photoluminescence (PL) [8]; the authors found that the PL peak energy increased with decreasing diameter, and they attributed this observation to reduced QCSE resulting from strain relaxation. Keller et al. also conducted power-dependent PL measurements on planar and nanopatterned InGaN/GaN multi-quantum wells (MQWs) and found the emission energy to increase with pump power for both cases. In these latter measurements, photo-generated carriers were thought to screen piezoelectric fields (and the QCSE) [24], making it difficult to independently determine strain state. Size-dependent effects in the nitrides have also been studied using continuous/time-resolved PL and Raman spectroscopy [23,25–27], but these works did not directly determine strain state as a function of size.
X-ray diffraction (XRD), on the other hand, can be used to directly determine the strain state of a material [28]. Previous XRD studies of nanopatterned InGaN/GaN MQWs have only considered one size or different In compositions within a specific experiment [20–22,29], and they have not investigated if strain relaxation is size dependent. Moreover, the importance of and potential for nanopatterning to reduce strain in the III-nitrides, as evidence by direct measurement and correlation of strain state with emission characteristics for different feature sizes, has not been investigated. In the present study, InGaN/GaN MQWs were characterized by XRD before and after nanopatterning (e.g., nanorod diameters from 120–900 nm) using reciprocal space mapping (RSM) and further characterized using power-dependent PL to correlate strain relaxation with PL energy shifts. In all cases, sub-micron scale lateral patterning of MQW emitters resulted in significant strain relaxation (15–32%) and blue-shifted emission that increased with the degree of relaxation and excitation power.
2. Methodology
InGaN/GaN samples were grown on [0001]-oriented patterned sapphire substrates by metal-organic chemical vapor deposition (MOCVD), as summarized in Fig. 1. The growth consisted of a 1.4 µm unintentionally doped (UID) GaN layer, 4 µm Si-doped n-type layer, and 30 period Si-doped In0.03Ga0.97N/GaN superlattice with a 20 nm UID GaN cap. The active region consisted of 6 periods of a 3 nm In0.11Ga0.89N quantum well with 16 nm thick GaN barriers capped with a Mg-doped p-Al0.20Ga0.80N electron blocking layer (EBL) and a 120 nm thick Mg-doped p-type layer.
Fig. 1. (a) Schematic of the epitaxial structure grown by MOCVD and (b) geometry of the etched nanopatterned material.
The epitaxial device structure above was grown on a single sapphire wafer, cut into four separate planar samples, and subsequently nanopatterned using a colloidal lithography process that has been described in detail elsewhere [30]. Silica colloids (d = 170, 310, 690, 960 nm) were functionalized (allyltrimethoxysilane) and deposited using a Langmuir-Blodgett dip coating process, leaving behind a hexagonally close-packed monolayer “mask” on the surface. Samples were dry etched in a Cl2/N2 inductively-coupled plasma (ICP) to fabricate the nanostructures [30]. Colloid size largely determined the final diameter (drod) of the InGaN features; a small amount of sidewall slope was present due to mask shrinkage during the etching process. Each sample, one for each nanorod diameter, was fully characterized both before (the “planar” state) and after nanopattering. X-ray diffraction measurements were performed on a Panalytical MRD Pro with a 3D Pixcel detector using monochromated CuKα radiation (λ = 1.5405 Å). Reciprocal space maps (RSMs, 2θ scans for different ω) were taken along two asymmetric reflections, $({10\bar{1}5} )$ and $({11\bar{2}4} )$, and one symmetric reflection, (0002). Symmetric (0002) RSMs (via Δθmeas) were used to determine the c lattice constants and composition (x, InxGa1-xN) of samples via the differential form of Bragg’s law as follows [31–33]:
The reference angle (θref) was determined via Bragg’s law from the (hkil) d-spacing using the a and c lattice constants of GaN and the standard quadratic form of a hexagonal lattice: where a and c are the theoretical lattice constants [33] of GaN. The measured a constants of GaN and InGaN were determined by reciprocal space mapping analysis according to [28,35,36], using the following: where ω and 2θ were the angles of the incident and diffracted beams measured from the surface and from the projected incent beam, respectively. Qx and Qz are the reciprocal lattice vectors of specific (hkil) planes. Other sources in the literature use 2π/λ instead of 1/λ for the Ewald’s sphere diameter [34], but this would not affect the calculated dhkil or lattice constants. Using the a constants of GaN and InxGa1-xN, as well as the indium composition, x, the degree of relaxation is defined as: PL measurements were performed at 13 K with a 405 nm continuous-wave InGaN laser with power output up to 400 mW. Prior temperature studies found a negligible effect between measurements at room temperature and at 20 K [8]. The laser source was well above the bandgap of GaN (365 nm at room temperature and an estimated 353 nm at 20 K) so that carriers were only generated in the InGaN quantum wells. The beam was incident upon the sample at ∼45°, and emission was collected normal to the sample surface with a high numerical aperture collector and transported via fiber to a UV-Vis spectrometer (Ocean Optics USB2000+) to record the full PL spectrum at different laser pump powers. Peak wavelengths of spectra (not shown) were extracted via Gaussian fit.3. Results and discussion
Scanning electron microscope (SEM) images of the colloidal mask deposition and nanostructured material after plasma etching are shown in Fig. 2. After etching, the diameter of the nanorods near the active region (about 100 nm below the top) were measured via SEM to be drod = 120, 250, 600, 900 nm. Imperfections in the hexagonally close-packed lattice were present, but did not contribute to the strain state of the active region.
Fig. 2. Scanning electron microscope (SEM) images of colloidal mask depositions (a-d) and the resulting nanopatterned materials after plasma etching (e-h).
Figure 3 shows a set of four RSMs for a single planar (unpatterned) sample that were used to characterize the initial strain state. The peak centroids were used to determine the lattice constants as well as indium composition of InxGa1-xN using the (0002) reflections, i.e., for samples A-D, x was determined to be 0.11, 0.12, 0.12 and 0.10, respectively.
Fig. 3. On (a),(c) and off-axis (b),(d) RSMs of a planar InGaN/GaN MQW sample. The (0002) RSMs in (a) and (c) were measured with the same stage angles (around [0002]) as the off-axis RSMs in (b) and (d), respectively. In some scans, higher order superlattice fringes appear below/above the InGaN or GaN peaks. The large diffuse streak is due to the x-ray monochromator divergence (i.e., parallel to the 2θ direction), and the peak broadening in panel (d) is due to a large x-ray spot on the sample at grazing incidence (ω ∼ 11° and near normal takeoff for 2θ ∼ 100°). Units are inverse Angstroms (Å−1).
The a and c lattice constants for each sample were calculated from the asymmetric (10$\bar{1}$5) and (11$\bar{2}$4) RSMs and symmetric (0002) RSMs, respectively. These results are summarized in Table 1. Note that each of the measured GaN lattice constants had less than 1% deviation from the theoretical GaN lattice constant. The overall degree of relaxation, R from Eqn. 5, was calculated from the (10$\bar{1}$5) and (11$\bar{2}$4) RSM reflections and averaged for each sample (A, B, C, D → 900, 600, 250, 120 nm nanopatterns, respectively), and the error represents the standard deviation between the two directions. The relaxed InxGa1-xN lattice constants were interpolated from Vegard’s law to calculate the R values. After nanopatterning, the composition was held constant for calculations of the relaxed InGaN lattice parameter. The measured GaN lattice constants after nanopatterning remain statistically equivalent.
Table 1. Measured a and c Lattice Constants of GaN and InGaN for Each Sample (A-D), in Planar and Nanopatterned Forms. Lattice Constant Values are Listed in Angstroms.
Figure 4 shows example RSM data for planar vs. nanopatterned samples. These data are summarized in panel Fig. 4(c), and indicate that R clearly depends on nanorod diameter, and that nanopatterning results in significant strain relaxation for the range of diameters considered. R increased as the diameter of the nanorod decreased, which provides quantitative support for prior optical studies [8,23] where strain relaxation was inferred. It should be noted that while R appeared to increase roughly linearly, it is entirely possible that nonlinearities exist outside the range of sizes tested here. Since pixel dimensions for advanced, near-eye display applications are likely to be ≤ 1 µm in the lateral dimension, larger sizes were not explicitly studied. Further reduction of the nanostructured diameter would require more advanced lithography techniques, and, additionally, any benefits of strain relaxation would likely be negated by sidewall defects introduced during plasma etching [37–40].
Fig. 4. Example reciprocal space maps for (a) planar and (b) patterned (drod = 250 nm) InGaN/GaN MQW samples, with a summary of strain relaxation values (R) shown in (c). R values calculated from different reflections were averaged with the standard deviation representing the error bar. Diameter (of the rod) refers to the location of the active well region.
Two of the aforementioned samples were further characterized using power-dependent, low temperature PL at 13 K (Fig. 5) to assess the effect of strain relaxation on optical properties. Peak wavelengths were generally seen to blueshift with increasing excitation density, which is likely due to screening of the field by carriers [24]. Direct comparison of PL emission intensity, as a function of carrier density, is not realistically possible without exact knowledge of complex optical phenomena occurring in both nanopatterned and planar material [14]. For example, one needs to consider the reflection and scattering processes at the GaN-air interface, pump light recycling, and fill factor of the nanopatterned material. Notwithstanding, the laser pump power was varied from 10–400 mW to qualitatively compare structures having reflectivity differences and (potentially) pump recycling effects. The planar samples exhibited nearly identical power-dependent PL curves, and, within the range of pump powers tested, nanopatterned sample PL was always blue-shifted. Moreover, the 250 nm nanorods had a more pronounced blue-shift effect, compared to the 900 nm nanorods, supporting the claim that more strain relaxation leads to more blue-shifted emission.
Fig. 5. Peak wavelength of PL emission at 13 K from planar and patterned InGaN/GaN MQW structures for different excitation power densities at 405 nm.
Poisson-Schrödinger simulations were also performed for a simplified single quantum well (SQW) structure using SiLENSe [40]. The active region thickness was kept constant with thicker UID GaN barrier layers. The simulated structures consisted of 500 nm Si-doped n-GaN, 20 nm UID GaN barrier, 3 nm In0.11Ga0.89N quantum well, 20 nm UID GaN barrier and a 150 nm Mg-doped p-GaN capping layer. The degree of relaxation (R) in the InGaN quantum well was varied from 0–32% following the experimentally determined strain states from XRD. Figure 6 shows the calculated energy band diagram and electric field distribution of the SQW structure for each relaxation case under no applied bias. Increasing the degree of relaxation from 0 to 32% flattens out the energy bands in the 3 nm InGaN quantum well. This effect is attributed to a reduction in the piezoelectric field due to InGaN/GaN lattice strain, as shown in Fig. 6(b).
Fig. 6. (a) Simulated energy band diagram and (b) electric field profiles for a single 3 nm InGaN quantum well (see text for details) with different degrees of in-plane relaxation from 0–32%. Relaxation values were chosen to represent the experimental values determined by XRD RSMs. The position axis, referenced to the substrate position, lies along the [0001] growth direction with only the active region displayed. Inset in (a) shows a zoom of the conduction band, where lower band tilt can be seen for greater relaxation.
4. Summary
InGaN/GaN MQW samples were nanopatterned using a colloidal lithography and plasma etching process. The diameters of the final structures around the active region spanned an entire order of magnitude in length scale (120–900 nm), and RSM analysis before and after nanopatterning confirmed that in-plane strain was indeed relaxed after patterning. Moreover, smaller diameter features showed larger and larger strain relaxation (up to 32%), which correlated well with the level of blueshift in PL. Complementary power-dependent PL measurements on the exact structures studied by RSM supported prior claims correlating strain relaxation and blue-shifting while minimizing the influence of carrier screening, pump recycling and differences in surface reflectivity. These trends are further supported with Poisson-Schrödinger simulations, demonstrating that relaxation decreases the internal piezoelectric field, leading to blue-shift in emission spectra.
Funding
Army Research Office (W911NF-09-D-0001, W911NF-19-2-0026); Solid State Lighting and Energy Electronics Center, University of California Santa Barbara.
Acknowledgments
Device processing was carried out in SSLEEC and the UCSB Nanofabrication Facility. The content of the information does not necessarily reflect the position or the policy of the U.S. Government, and no official endorsement should be inferred.
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