arXiv subjects

Bjorn Vermeersch

Publications and source records attributed to Bjorn Vermeersch.

12 recordsLinked to original sources

arXiv2025

Thermal Implications of Non-Uniform Power in BSPDN-Enabled 2.5D/3D Chiplet-based Systems-in-Package using Nanosheet Technology

Advances in nanosheet technologies have significantly increased power densities, exacerbating thermal management challenges in 2.5D/3D chiplet-based Systems-in-Package (SiP). While traditional thermal analyses often employ uniform power maps to simplify computational complexity, this practice neglects localized heating effects, leading to inaccuracies in thermal estimations, especially when comparing power delivery networks (PDN) in 3D integration. This work examines the thermal impact of non-uniform power distributions on SiPs utilizing frontside (FSPDN) and backside (BSPDN) power delivery approaches. Using high-resolution thermal simulations with non-uniform power maps at resolutions down to 5 micrometers, we demonstrate that uniform power assumptions substantially underestimate peak temperatures and fail to reveal critical thermal differences between BSPDN and FSPDN configurations in 3D scenarios. Our results highlight that BSPDN configurations in 3D, although beneficial in simplified uniform scenarios, exhibit pronounced thermal penalties under realistic, localized workloads due to limited lateral heat spreading. These findings emphasize the necessity of adopting fine-grained, workload-aware power maps in early-stage thermal modeling to enable accurate PDN assessment and informed thermal-aware design decisions in advanced nanosheet-based 3D SiP.

cs.ET↗

arXiv2019

Relativistic stable processes in quasi-ballistic heat conduction in thin film semiconductors

In this article, we show how relativistic alpha stable processes can be used to explain quasi-ballistic heat conduction in semiconductors. This is a method that can fit experimental results of ultrafast laser heating in alloys. It also provides a connection to a rich literature on Feynman-Kac formalism and random processes that transition from a stable Lévy process on short time and length scales to the Brownian motion at larger scales. This transition was captured by a heuristic truncated Lévy distribution in earlier papers. The rigorous Feynman-Kac approach is used to derive sharp bounds for the transition kernel. Future directions are briefly discussed.

cond-mat.mes-hall↗

arXiv2019

Thermal resistance of GaN/AlN graded interfaces

Compositionally graded interfaces in power electronic devices eliminate dislocations, but they can also decrease thermal conduction, leading to overheating. We quantify the thermal resistances of GaN/AlN graded interfaces of varying thickness using ab initio Green's functions, and compare them with the abrupt interface case. A non-trivial power dependence of the thermal resistance versus interface thickness emerges from the interplay of alloy and mismatch scattering mechanisms. We show that the overall behavior of such graded interfaces is very similar to that of a thin-film of an effective alloy in the length scales relevant to real interfaces.

cond-mat.mtrl-sci↗

arXiv2017

Quasiballistic heat removal from small sources studied from first principles

Heat sources whose characteristic dimension $R$ is comparable to phonon mean free paths display thermal resistances that exceed conventional diffusive predictions. This has direct implications to (opto)electronics thermal management and phonon spectroscopy. Theoretical analyses have so far limited themselves to particular experimental configurations. Here, we build upon the multidimensional Boltzmann transport equation (BTE) to derive universal expressions for the apparent conductivity suppression $S(R) = κ_{\text{eff}}(R)/κ_{\text{bulk}}$ experienced by radially symmetric 2D and 3D sources. In striking analogy to cross-plane heat conduction in thin films, a distinct quasiballistic regime emerges between ballistic ($κ_{\text{eff}} \sim R$) and diffusive ($κ_{\text{eff}} \simeq κ_{\text{bulk}}$) asymptotes that displays a logarithmic dependence $κ_{\text{eff}} \sim \ln(R)$ in single crystals and fractional power dependence $κ_{\text{eff}} \sim R^{2-α}$ in alloys (with $α$ the Lévy superdiffusion exponent). Analytical solutions and Monte Carlo simulations for spherical and circular heat sources in Si, GaAs, Si$_{0.99}$Ge$_{0.01}$ and Si$_{0.82}$Ge$_{0.18}$, all carried out from first principles, confirm the predicted generic tendencies. Contrary to the thin film case, common approximations like kinetic theory estimates $κ_{\text{eff}} \simeq \sum S_ω^{\text{grey}} \, κ_ω$ and modified Fourier temperature curves perform relatively poorly. Up to threefold deviations from the BTE solutions for sub-100$\,$nm sources underline the need for rigorous treatment of multidimensional nondiffusive transport.

cond-mat.mes-hall↗

arXiv2017

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

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-$μ$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.

physics.comp-ph↗

arXiv2016

Compact models for multidimensional quasiballistic thermal transport

The Boltzmann transport equation (BTE) has proven indispensable in elucidating quasiballistic heat dynamics. Experimental observations of nondiffusive thermal transients, however, are interpreted almost exclusively through purely diffusive formalisms that merely extract "effective" Fourier conductivities. Here, we build upon stochastic transport theory to provide a characterisation framework that blends the rich physics contained within BTE solutions with the convenience of conventional analyses. The multidimensional phonon dynamics are described in terms of an isotropic Poissonian flight process with rigorous Fourier-Laplace single pulse response $P(\vecξ,s) = 1/[s + ψ(\| \vecξ \|)]$. The spatial propagator $ψ(\|\vecξ\|)$, unlike commonly reconstructed mean free path spectra $κ_Σ(Λ)$, serves as a genuine thermal blueprint of the medium that can be identified in compact form directly from raw measurement signals. Practical illustrations for transient thermal grating (TTG) and time domain thermoreflectance (TDTR) experiments on respectively GaAs and InGaAs are provided.

cond-mat.mes-hall↗

arXiv2016

Limitations of generalised grey phonon models for quasiballistic thermal transport in time-periodic regimes

Suitably superimposed grey-medium solutions of the Boltzmann transport equation (BTE) provide a simple yet accurate description of non-grey quasiballistic heat conduction in transient thermal grating experiments. Recent applications of similar strategies based on kinetic and McKelvey-Schockley-Landauer theory to time-periodic transport predicted notable conductivity suppression only at heating frequencies comparable to phonon scattering rates, in contrast to lengthscale criteria observed by several prior studies. Here we show that the frequency-integrated grey-medium approximation (FIGMA) is ill suited to tackle temporally periodic quasiballistic transport. Starting from first-principles phonon dispersions and scattering rates, we obtain semi-analytic 1D BTE solutions for semi-infinite structures subjected to sinusoidal surface heating and compare these to the approximate model counterparts. We find FIGMA-based approaches to overestimate the semiconductor surface temperature by up to one and characteristic heating frequencies for onset of quasiballistic effects by up to three orders of magnitude respectively. Our study reasserts that experimentally observed heating-frequency dependent apparent conductivities originate in the overlap of the characteristic length scale of the thermal gradient with phonon mean free paths.

cond-mat.mes-hall↗

arXiv2016

Cross-plane heat conduction in thin films with ab-initio phonon dispersions and scattering rates

We present a first-principles study of the cross-plane thermal conductivity $κ_{\perp}$ 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 $\leq 5\%$ even for anisotropic compounds. This, in turn, enables accurate $κ_{\perp}$ reconstruction from tabulated cumulative conductivity curves $κ_Σ(Λ_{\perp})$. We furthermore reveal, and explain, a distinct quasiballistic regime characterised by a fractional thickness dependence $κ_{\perp} \sim L^{2-α}$ in alloys (where $α$ is the Lévy exponent) and logarithmic dependence $κ_{\perp} \sim \ln(L)$ in single crystals. These observations culminate in the formulation of two compact parametric forms for $κ_{\perp}(L)$ that can fit the first-principles curves across the entire ballistic-diffusive range within a few percent for all investigated compounds.

cond-mat.mes-hall↗

arXiv2015

Nonlocality in microscale heat conduction

Thermal transport at short length and time scales inherently constitutes a nonlocal relation between heat flux and temperature gradient, but this is rarely addressed explicitly. Here, we present a formalism that enables detailed characterisation of the delocalisation effects in nondiffusive heat flow regimes. A convolution kernel $κ^{\ast}$, which we term the nonlocal thermal conductivity, fully embodies the spatiotemporal memory of the heat flux with respect to the temperature gradient. Under the relaxation time approximation, the Boltzmann transport equation formally obeys the postulated constitutive law and yields a generic expression for $κ^{\ast}$ in terms of the microscopic phonon properties. Subsequent synergy with stochastic frameworks captures the essential transport physics in compact models with easy to understand parameters. A fully analytical solution for $κ^{\ast}(x')$ in tempered Lévy transport with fractal dimension $α$ and diffusive recovery length $x_{\text{R}}$ reveals that nonlocality is physically important over distances $\sqrt{2-α} \,\,x_{\text{R}}$. This is not only relevant to quasiballistic heat conduction in semiconductor alloys but also applies to similar dynamics observed in other disciplines including hydrology and chemistry. We also discuss how the previously introduced effective thermal conductivity $κ_{\text{eff}}$ inferred phenomenologically by transient thermal grating and time domain thermoreflectance measurements relates to $κ^{\ast}$. Whereas effective conductivities depend on the experimental conditions, the nonlocal thermal conductivity forms an intrinsic material property. Experimental results indicate nonlocality lengths of 400$\,$nm in Si membranes and $\simeq 1\,μ$m in InGaAs and SiGe, in good agreement with typical median phonon mean free paths.

cond-mat.mes-hall↗

arXiv2014

Spatiotemporal flux memory in nondiffusive transport

Anomalous diffusion constitutes a relation between tracer flux and tracer density gradient that is inherently nonlocal in space and/or time. Previous studies emphasize the non-Gaussian character of the tracer distribution that arises from adjusted constitutive relations but did not investigate the flux-gradient memory itself. Here, we present a universal analytic framework that enables systematic characterisation of nonlocality in a wide variety of transport regimes. A generalised diffusivity kernel $D^{\ast}$ fully embodies the spatiotemporal flux memory with respect to the gradient. An extension of the flux-gradient relation for subdiffusive transport is also proposed. Several conservation and invariance properties can be deduced, including that Poissonian flight processes have no flux memory in time while fractional time diffusion has no flux memory in space. We derive analytical expressions for $D^{\ast}(x,t)$ in several types of anomalous transport dynamics that are commonly encountered in practice, being fractional diffusion equations, tempered Lévy superdiffusion, and tempered fractional time diffusion. This detailed knowledge of the shape and nature of the flux memory, and the corresponding length and time scales over which nonlocal effects are physically important, remain completely hidden in conventional analyses based on tracer distributions or flux-gradient diagrams. Practical capabilities include the interpretation of microscale heat superdiffusion experiments. Overall, the theory can serve as a valuable framework for anomalous transport dynamics across multiple disciplines.

cond-mat.stat-mech↗

arXiv2014

Superdiffusive heat conduction in semiconductor alloys -- I. Theoretical foundations

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 quasi-ballistic 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 $σ^2(t) \sim t^β (1 < β< 2)$. The characteristic exponents are directly interconnected with the order $n$ of the dominant phonon scattering mechanism $τ\sim ω^{-n} (n>3)$ and cumulative conductivity spectra $κ_Σ(τ;Λ)\sim (τ;Λ)^γ$ 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.

cond-mat.mtrl-sci↗

arXiv2014

Superdiffusive heat conduction in semiconductor alloys -- II. Truncated Lévy formalism for experimental analysis

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.

cond-mat.mtrl-sci↗