almaBTE: a solver of the space-time dependent Boltzmann transport equation for phonons in structured materials

Abstract: almaBTE is a software package that solves the space- and time-dependent Boltzmann transport equation for phonons, using only ab-initio calculated quantities as inputs. The program can predictively tackle phonon transport in bulk crystals and alloys, thin films, superlattices, and multiscale structures with size features in the nm-$\mu$m range. Among many other quantities, the program can output thermal conductances and effective thermal conductivities, space-resolved average temperature profiles, and heat-current distributions resolved in frequency and space. Its first-principles character makes almaBTE especially well suited to investigate novel materials and structures. This article gives an overview of the program structure and presents illustrative examples for some of its uses.

• The paper introduces almaBTE as a first-principles solver for the space-time dependent Boltzmann transport equation, enhancing phonon transport predictions in structured systems.
• It details a modular architecture featuring components like VCAbuilder and superlattice_builder to compute thermal conductivities, temperature profiles, and heat-current distributions.
• Numerical examples for bulk materials, thin films, and superlattices validate the tool’s accuracy and underline its potential for advanced thermal management in semiconductor devices.

Overview of almaBTE: A Phonon Transport Solver for Structured Materials

The paper presents "almaBTE," a sophisticated computational package designed to solve the space- and time-dependent Boltzmann Transport Equation (BTE) for phonons in structured materials. The software utilizes ab-initio calculated quantities, providing predictive insights into phonon transport across a variety of material structures, including bulk crystals, alloys, thin films, superlattices, and multiscale formations with nanoscale to microscale features.

Key Features and Capabilities

The primary strength of almaBTE lies in its ability to comprehensively handle phonon transport phenomena through a first-principles approach. This enables the calculation of:

• Thermal conductances and effective thermal conductivities.
• Space-resolved average temperature profiles.
• Heat-current distributions resolved in both frequency and space.

This emphasis on first-principles makes the tool particularly invaluable for investigating novel materials and structures where empirical data might be limited or unavailable.

Structure and Functionality

The paper outlines the general structure of almaBTE, detailing its modular architecture which consists of a set of specialized solvers complemented by auxiliary programs. This architecture facilitates a robust framework for studying phonon-mediated heat transport. Key components of the package include:

• VCAbuilder: Constructs a virtual crystal approximation for single crystals and alloys, calculating essential phonon properties such as frequencies and wave functions.
• superlattice_builder: Models binary superlattices by treating them as periodic perturbations on reference virtual crystals.
• kappa_Tsweep, kappa_crossplanefilms, kappa_inplanefilms: Efficiently compute thermal conductivities for various materials and configurations.
• cumulativecurves, transient_analytic1d, steady_montecarlo1d: Provide detailed analyses of phonon contributions to thermal transport and explore time-dependent transport phenomena using both analytic and Monte Carlo methods.

Numerical Results and Insights

The paper presents illustrative examples demonstrating the software's applicability across different material settings:

• Bulk Materials: Calculations for diamond, silicon, and GaN show that while the Relaxation Time Approximation (RTA) offers close estimates, full BTE solutions are crucial for specific systems where normal scattering processes dominate.
• Thin Films: Analysis of $\beta$-Ga$_2$O$_3$ reveals significant thermal anisotropy, showcasing the need for detailed spectral and directional analysis of thermal transport.
• Superlattices and Multilayer Structures: almaBTE effectively models thermal resistance and spectral heat flux in structured materials like Si/Ge bilayers, capturing interfacial resistance due to phonon frequency mismatches.

Theoretical and Practical Implications

From a theoretical standpoint, almaBTE's ability to address the "curse of dimensionality" in BTE solutions marks a significant advancement in phonon transport modeling. The software's reliance on non-empirical inputs leads to highly predictive and accurate models that encourage a deeper understanding of phononic behaviors in complex systems.

Practically, almaBTE is positioned as a highly valuable tool for developing advanced semiconductor devices. By providing detailed insights into heat dissipation pathways, researchers can optimize material performance, extending the operational lifespan of electronic components such as LEDs and High Electron Mobility Transistors (HEMTs).

Future Directions

The continued development and application of almaBTE are expected to drive innovations in materials science and engineering, particularly in fields where thermal management is critical. As computational resources expand and phonon-interaction models become more refined, tools like almaBTE will be crucial in bridging the gap between theoretical predictions and experimental realizations, ultimately enabling the design of next-generation thermally efficient materials.

Overall, almaBTE represents a robust advancement in computational physics, offering a comprehensive framework for phonon transport analysis in an array of structured materials.