Ingan Quantum Wells Model Accurately Explains Disorder’s Role in Luminescence and Radiative Rates

The unique optical characteristics of indium gallium nitride quantum wells continue to fascinate materials scientists, and a new model developed by Aurelien David from Google/Raxium accurately captures the influence of material imperfections on these properties. This research demonstrates that random alloy disorder plays a crucial role in defining key features such as the shape of emitted light, the shift in colour, and the efficiency of light emission. By accounting for this disorder, the model achieves excellent agreement with experimental results across a range of structures, and it sheds light on the behaviour of long-wavelength indium gallium nitride emitters, paving the way for improved designs in optoelectronic devices. The work represents a significant step forward in understanding and optimising these important semiconductor materials.

The luminescence lineshape, the Stokes shift, and the radiative rate are central to this investigation. Furthermore, the relationship between disorder and the peculiar properties of long-wavelength indium gallium nitride emitters receives detailed attention. These materials, based on III-nitride quantum wells, are of high interest due to their important applications in light emitting diodes and their unusual optical behaviours. Strong polarization fields and the presence of compositional disorder within indium gallium nitride differentiate them from other materials, leading to a significant quantum-confined Stark effect that shifts the emission towards longer wavelengths.

Alloy Disorder in Quantum Well Simulations

Scientists developed a comprehensive model to investigate the properties of indium gallium nitride quantum wells, accurately accounting for the significant role of random alloy disorder. This study pioneers a computational approach that closely matches experimental observations across various structures, clarifying how disorder influences luminescence lineshapes, Stokes shift, and radiative rates. Building upon previous investigations, this work addresses limitations in earlier models by incorporating a realistic carrier distribution and exploring a sufficient number of quantum states. The team discretized the quantum well structure and surrounding barriers onto a spatial grid, then mimicked random alloy composition by randomly assigning indium and gallium atoms.

These distributions were smoothed using a Gaussian filter with a standard deviation of 0. 4 nanometers, a value determined to provide excellent agreement with multiple experimental datasets. A two-band effective-mass Hamiltonian was employed, utilizing established band structure parameters and incorporating a ‘far from the band edge’ hole mass to accurately describe localized wavefunctions. Polarization fields were calculated using a previously published methodology, and the junction field was determined analytically based on the applied voltage. To account for high carrier densities, the team implemented a self-consistent Poisson-Schrödinger loop, utilizing a one-dimensional approximation to simplify calculations.

The model deliberately excluded many-body effects from Coulomb interactions, justified by prior work demonstrating their limited impact on excitonic populations and spectral lineshapes at intermediate densities and room temperature. This simplification significantly reduced computational demands, enabling the calculation of a large number of states. The Schrödinger equation was discretized using a standard finite difference scheme, transforming it into a sparse-matrix eigenvalue problem solved to determine particle energies and wavefunctions. For each indium gallium nitride configuration, scientists computed several hundred electron and hole states, extending up to hundreds of meV from the ground state. This process was repeated numerous times to achieve statistical averaging and resolve the Urbach tail, a measure of disorder, over four decades from the mobility edge.

Alloy Disorder Accurately Models Quantum Well Behavior

This work presents a detailed computational study of indium gallium nitride quantum wells, achieving remarkable agreement with experimental observations by incorporating random alloy disorder into the model. The research team discretized the quantum well structure on a spatial grid, randomly distributing indium and gallium atoms to mimic alloy fluctuations, and then smoothed these distributions using a Gaussian filter with a standard deviation of 0. 4 nanometers. This value precisely matches multiple experimental datasets and accurately represents the degree of localization effects within the material.

The calculations employed a two-band effective-mass Hamiltonian, focusing on random alloy disorder while excluding Coulomb interactions to reduce computational demands. To resolve the density of states down to four decades from the mobility edge, the team performed statistical averaging over 1,000 to 5,000 indium gallium nitride configurations, processing over 100,000 quantum states. This rigorous approach enabled the accurate calculation of electron and hole densities of states, revealing the impact of disorder on the material’s electronic structure. The researchers then assumed thermalized carrier distributions, validating this assumption by achieving close agreement with experimental data.

The model accurately predicts the absorption and luminescence spectra, calculating the “bare” and “loaded” joint density of states to account for carrier populations. The resulting luminescence spectrum is then refined by adding empirical longitudinal optical phonon tails. Through this process, the team calculated a radiative coefficient, demonstrating the model’s ability to accurately represent the optical properties of indium gallium nitride quantum wells. The research delivers a comprehensive framework for understanding the peculiar properties of long-wavelength indium gallium nitride emitters, providing a foundation for future materials design and device optimization.

Alloy Disorder Explains Quantum Well Properties

This research presents a comprehensive model incorporating random alloy disorder to explain the observed properties of indium gallium nitride quantum wells. The team successfully demonstrates excellent agreement between the model’s predictions and experimental observations across various structures, clarifying the significant role disorder plays in features such as luminescence lineshape, Stokes shift, and radiative rate. Importantly, the study investigates the connection between disorder and the unique characteristics of long-wavelength indium gallium nitride emitters, offering new insights into their behaviour. This work builds upon previous investigations of random alloy effects, addressing limitations found in earlier models.

While prior research established crucial effects of disorder, a complete computational prediction of optical properties, quantitatively matching experimental results, remained elusive. This study overcomes this challenge through a thorough computation encompassing a sufficient number of quantum states and incorporating a realistic carrier distribution model. The authors acknowledge that computational demands remain significant, and further exploration of these effects with increased computational power will be valuable. Future work could focus on extending the model to explore a wider range of indium gallium nitride compositions and device structures, potentially leading to further improvements in light-emitting diode performance.