Impact of Threading Dislocation Density on the Refractive Index of AlN: Nanoscale Strain Field Effects

Abstract

The refractive index of aluminum nitride (AlN) critically influences the performance of AlGaN‑based deep‑ultraviolet (DUV) optoelectronic devices, including the external quantum efficiency (EQE) of LEDs. High‑density threading dislocations (TDDs) are a common defect in AlN, yet their quantitative effect on refractive index remains poorly understood. In this study, we systematically varied TDDs from 4.24 × 10⁸ to 3.48 × 10⁹ cm⁻² by post‑growth annealing and measured the corresponding refractive index using spectroscopic ellipsometry (SE). The refractive index decreased from 2.2508 to 2.2102 at 280 nm as TDD increased, confirming that dislocations reduce the optical density of AlN. Theoretical modeling of the nanoscale strain field surrounding screw and edge dislocations demonstrates how local elastic deformation perturbs the photoelastic response, leading to spatially varying refractive index and enhanced light scattering. These findings provide a critical design parameter for optimizing DUV LEDs, laser diodes, and DBR structures built on AlN substrates.

Introduction

AlN and its alloys are the workhorses of DUV optoelectronics, offering a direct bandgap tunable from 3.4 to 6.2 eV. The refractive index of AlN directly determines light‑extract efficiency (LEE) through the total internal reflection angle and also governs the reflectivity of distributed Bragg reflectors (DBRs). Consequently, any factor that shifts the refractive index can limit device output power or spectral performance. While temperature, pressure, and bandgap have been shown to affect AlN’s optical constants, the role of threading dislocations—prevalent in epitaxial AlN layers—has not been quantified. Given typical TDDs ranging from 10⁸ to 10⁹ cm⁻², it is imperative to establish their influence on refractive index to guide growth optimization and device engineering.

Methods

High‑quality AlN templates were grown on c‑sapphire by metal‑organic chemical vapor deposition (MOCVD) using trimethylaluminum and ammonia precursors under 40 mbar hydrogen flow. A 1.1 µm AlN film was fabricated through a two‑step growth: a 955 °C nucleation layer followed by 1280 °C high‑temperature growth, interleaved with a 1050 °C AlN interlayer. Post‑growth annealing at 1500, 1600, 1700, and 1750 °C for one hour produced samples with progressively lower TDDs. X‑ray diffraction (XRD) rocking curves (XRCs) measured (0002) and (10–12) planes to extract screw and edge dislocation densities via the modified Hall–Petch equations. Spectroscopic ellipsometry (SE) provided the complex refractive index across 200–1000 nm. Raman spectroscopy assessed residual stress by tracking the AlN E₂(h) peak shift.

Results and Discussion

Figure 1 illustrates the (0002) and (10–12) XRCs for the five samples. The full width at half maximum (FWHM) of the (10–12) plane decreased markedly from sample 1 to sample 5, yielding TDDs that span 4.24 × 10⁸ to 3.48 × 10⁹ cm⁻². SE fitting, performed with CompleteEASE using a direct‑bandgap semiconductor model, achieved mean‑squared errors below 11, confirming reliable optical constants.

Refractive index curves (Figure 2b) show the expected dispersion: an increase with photon energy below the 6.2 eV bandgap, followed by a decrease beyond. At 633 nm, the index rises from 2.019 to 2.056 as TDD falls, approaching the bulk value of 2.15 [27]. Crucially, at 280 nm, the index drops from 2.2508 to 2.2102 as TDD increases, illustrating a clear inverse relationship (Figure 2c).

To rationalize this behavior, we modeled the strain field of a single screw or edge dislocation using cylindrical symmetry. The strain tensor components (Eqs. 5–6) were mapped into the photoelastic tensor (Eq. 3), yielding the perturbation Δ(1/n²). Calculations reveal that both screw and edge dislocations locally depress the refractive index in concentric shells around the core (Figure 4), creating an inhomogeneous optical medium. When light traverses these perturbed regions, scattering and interference redistribute the optical field, effectively reducing the measured refractive index.

Potential confounding factors—temperature, residual stress, and bandgap—were systematically excluded. All measurements were at room temperature. Raman spectra (Figure 5) show a modest blue shift of the AlN E₂(h) peak with decreasing TDD, indicating compressive strain from the sapphire substrate; however, this strain has negligible impact on the refractive index compared to dislocation density. Bandgap determinations from the (αE)² vs. E plot (Figure 6) reveal a slight increase from 6.1106 to 6.1536 eV across the samples, but the expected inverse correlation with refractive index (Eq. 12) is not observed, reinforcing that TDD dominates the optical response.

Conclusions

Threading dislocation density is a decisive parameter governing the refractive index of AlN. By reducing TDD through high‑temperature annealing, the refractive index can be tuned upward, approaching bulk values and potentially enhancing LEE and DBR reflectivity in DUV devices. The nanoscale strain field around dislocations induces local refractive index variations that aggregate into a measurable macroscopic effect. These insights provide a clear pathway for optimizing AlN growth and device architecture to achieve higher performance in DUV optoelectronics.