almaBTE is a software package that solves the space-and time-dependent Boltzmann transport equation for phonons, using only abinitio 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-µm 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 anisotropic basal-plane thermal conductivities of thin black phosphorus obtained from a new four-probe measurement exhibit much higher peak values at low temperatures than previous reports. First principles calculations reveal the important role of crystal defects and weak thickness dependence that is opposite to the case of graphene and graphite due to the absence of reflection symmetry in puckered phosphorene.
Semiconductor alloys exhibit a strong dependence of effective thermal conductivity on measurement frequency. So far this quasi-ballistic behaviour has only been interpreted phenomenologically, providing limited insight into the underlying thermal transport dynamics. Here, we show that quasiballistic heat conduction in semiconductor alloys is governed by Lévy superdiffusion. By solving the Boltzmann transport equation (BTE) with ab initio phonon dispersions and scattering rates, we reveal a transport regime with fractal space dimension 1 < α < 2 and superlinear time evolution of mean square energy displacement σ 2 (t) ∼ t β (1 < β < 2). The characteristic exponents are directly interconnected with the order n of the dominant phonon scattering mechanism τ ∼ ω −n (n > 3) and cumulative conductivity spectra κΣ(τ ; Λ) ∼ (τ ; Λ) γ resolved for relaxation times or mean free paths through simple relations α = 3 − β = 1 + 3/n = 2 − γ. The quasi-ballistic transport inside alloys is no longer governed by Brownian motion, but instead dominated by Lévy dynamics. This has important implications for the interpretation of thermoreflectance (TR) measurements with modified Fourier theory. Experimental α values for InGaAs and SiGe, determined through TR analysis with a novel Lévy heat formalism, match ab initio BTE predictions within a few percent. Our findings lead to a deeper and more accurate quantitative understanding of the physics of nanoscale heat flow experiments.
Nearly all experimental observations of quasi-ballistic heat flow are interpreted using Fourier theory with modified thermal conductivity. Detailed Boltzmann transport equation (BTE) analysis, however, reveals that the quasi-ballistic motion of thermal energy in semiconductor alloys is no longer Brownian but instead exhibits Lévy dynamics with fractal dimension α < 2. Here, we present a framework that enables full 3D experimental analysis by retaining all essential physics of the quasi-ballistic BTE dynamics phenomenologically. A stochastic process with just two fitting parameters describes the transition from pure Lévy superdiffusion as short length and time scales to regular Fourier diffusion. The model provides accurate fits to time domain thermoreflectance raw experimental data over the full modulation frequency range without requiring any 'effective' thermal parameters and without any a priori knowledge of microscopic phonon scattering mechanisms. Identified α values for InGaAs and SiGe match ab initio BTE predictions within a few percent. Our results provide experimental evidence of fractal Lévy heat conduction in semiconductor alloys. The formalism additionally indicates that the transient temperature inside the material differs significantly from Fourier theory and can lead to improved thermal characterization of nanoscale devices and material interfaces.
We present a first-principles study of the cross-plane thermal conductivity κ ⊥ in a wide variety of semiconductor thin films. We introduce a simple suppression model that matches variance-reduced Monte Carlo simulations with ab-initio phonon dispersions and scattering rates within ≤ 5% even for anisotropic compounds. This, in turn, enables accurate κ ⊥ reconstruction from tabulated cumulative conductivity curves κΣ(Λ ⊥ ). We furthermore reveal, and explain, a distinct quasiballistic regime characterised by a fractional thickness dependence κ ⊥ ∼ L 2−α in alloys (where α is the Lévy exponent) and logarithmic dependence κ ⊥ ∼ ln(L) in single crystals. These observations culminate in the formulation of two compact parametric forms for κ ⊥ (L) that can fit the first-principles curves across the entire ballistic-diffusive range within a few percent for all investigated compounds.Phonon-mediated heat conduction in thin films plays an important role in nanoscale devices [1, 2] and received increasing theoretical attention [3][4][5][6][7][8][9][10]. Interestingly, cross-plane thermal transport has posed a considerably harder challenge than its in-plane counterpart. An exact solution of the Boltzmann transport equation (BTE) in cross-plane geometries has been obtained only very recently [7] and provides the film conductivity at thickness L as an integral over phonon frequencyHere S is a 'suppression function' that contains the thin film physics and κ(ω) denotes the bulk spectral conductivity. Evaluation of the latter often relies on analytical models with isotropic dispersions [8-10] for mathematical convenience. More realistic phonon spectra can also be utilised through frequency binning, but this procedure becomes problematic in anisotropic compounds. In this work, we adopt a first-principles framework [11,12] that goes well beyond the predictive power of spectral formulations. We subsequently show that the resulting cross-plane thin film conductivity curves κ(L) can be captured by compact models that effortlessly maintain their accuracy in anisotropic compounds. In the process, we also reveal quasiballistic regimes in both alloys and single crystals with distinct film thickness dependences.We performed our ab-initio study for a variety of semiconductors selected for their technological relevance. Thin Si films play a key role in silicon-on-insulator de- We calculated ab-initio heat capacities C( k), group velocities v( k) and scattering rates τ −1 ( k) using the procedure described in Ref. 17. The adopted method has been tested on a variety of bulk compounds and provides results in good agreement with experiments [11]. Phonon properties are resolved over a uniform wavevector grid with N 3 k points, where we have set N k to 24 for diamond/zincblende crystals, 16 for wurtzites and 12 for Pnma SnSe. Scattering rates τ −1 = τ −1 anh + τ −1 har and mean free paths (MFPs) Λ = v τ account for anharmonic (three-phonon) and harmonic (isotope/alloy) scattering mechanisms. Alloys were treated under the virtual crystal approxim...
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