Imaging Thermal Transport in Graphene

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Elbara Ziade ◽  
Aaron Schmidt
Keyword(s):  
Thermal Transport ◽  
Pump Beam ◽  
Continuous Wave ◽  
Metal Layer ◽  
Thermal Conductance ◽  
Heat Diffusion ◽  
Phase Lag ◽  
Graphene Flake ◽  
Heat Diffusion Equation ◽  
Phase Images

Frequency domain thermoreflectance (FDTR) imaging is used to create quantitative maps of both in-plane thermal conductance and cross-plane thermal boundary conductance (TBC) for graphene multilayers encased between titanium and silicon dioxide. A graphene flake is encased between a metal layer and a thermally oxidized p-type silicon wafer and a piezo stage is used to raster scan the sample for imaging. For each image pixel, a periodically modulated continuous-wave laser (the red pump beam) is focused to a Gaussian spot, less than 2 um in diameter, that locally heats the sample, while a second beam (the green probe beam) monitors the surface temperature through a proportional change in reflectivity. The pump beam is modulated simultaneously at six frequencies and the thermal properties of the graphene flake are extracted by minimizing the error between the measured probe phase lag at each frequency and an analytical solution to the heat diffusion equation in a multilayer stack of materials. Phase images at six frequencies for the sample are shown in b. Different layers of the graphene flake are clearly shown in 9.9 MHz and 11.3 MHz images. The six phase data points at every pixel are then fitted to our thermal model to generate two thermal property maps of the graphene flake: in-plane thermal conductance and TBC, shown in c. The in-plane thermal conductance map shows an increased conduction of heat in graphene with the number of layers, while the TBC map indicates a constant cross-plane conduction along the flake. Our imaging technique can be used to study thermal transport in graphene and has implications for thermal management in graphene based electronic devices.

Mapping Thickness Dependent Thermal Conductivity of GaN

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Elbara Ziade ◽  
Jia Yang ◽  
Gordie Brummer ◽  
Denis Nothern ◽  
Theodore Moustaks ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Pump Beam ◽  
Continuous Wave ◽  
High Electron Mobility Transistors ◽  
Heat Diffusion ◽  
Phase Lag ◽  
High Electron ◽  
Heat Diffusion Equation ◽  
Phase Images ◽  
Gan Film

Frequency domain thermoreflectance (FDTR) is used to create quantitative maps of thermal conductivity and thickness for a thinning gallium nitride (GaN) film on silicon carbide (SiC). GaN was grown by molecular beam epitaxy on a 4H-SiC substrate with a gradient in the film thickness found near the edge of the chip. The sample was then coated with a 5 nm nickel adhesion layer and a 85 nm gold transducer layer for the FDTR measurement. A piezo stage raster scans the sample to create phase images at different frequencies. For each pixel, a periodically modulated continuous-wave laser (the red pump beam) is focused to a Gaussian spot, less than 2 um in diameter, to locally heat the sample, while a second beam (the green probe beam) monitors the surface temperature through a proportional change in the reflectivity of gold. The pump beam is modulated simultaneously at six frequencies and the thermal conductivity and thickness of the GaN film are extracted by minimizing the error between the measured probe phase lag at each frequency and an analytical solution to the heat diffusion equation in a multilayer stack of materials. A scanning electron microscope image verifies the thinning GaN. We mark the imaged area with a red box. A schematic of the GaN sample in our measurement system is shown in the top right corner, along with the two fitting properties highlighted with a red box. We show the six phase images and the two obtained property maps: thickness and thermal conductivity of the GaN. Our results indicate a thickness dependent thermal conductivity of GaN, which has implications of thermal management in GaN-based high electron mobility transistors.

Thermal Property Imaging of Aluminum Nitride Composites

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Jia Yang ◽  
Toshiyuki Sato ◽  
Paul Czubarow ◽  
Aaron Schmidt
Keyword(s):  
Thermal Conductivity ◽  
Aluminum Nitride ◽  
Pump Beam ◽  
Epoxy Composite ◽  
Heat Diffusion ◽  
Probe Laser ◽  
Polished Surface ◽  
Phase Lag ◽  
Heat Diffusion Equation ◽  
Phase Images

Frequency domain thermoreflectance (FDTR) imaging is used to create quantitative thermal conductivity maps of porous Aluminum Nitride (AlN) particles embedded in epoxy. The AlN-epoxy composite is polished and coated with a metal layer. A piezo stage is used to move the sample for imaging with our FDTR system. For each pixel, a periodically modulated continuous-wave laser (the red pump beam) is focused to a Gaussian spot, less than 2 um in diameter, to locally heat the sample, while a second beam (the green probe beam) monitors the surface temperature through a proportional change in the metals' reflectivity. The pump beam is modulated simultaneously at six frequencies and the thermal properties of the AlN composite are extracted by minimizing the error between the measured probe phase lag at each frequency and an analytical solution to the heat diffusion equation in a multilayer stack of materials. A schematic of the AlN sample in our measurement system and an optical image of the polished surface of the AlN-epoxy composite before coating with metal is shown in a. Two scanning electron microscope images of the porous AlN particles prior to embedding in epoxy are shown in b. One of the six simultaneously collected phase images of the probe laser is shown in c. The dark blue regions in the phase image are pits on the sample surface. We fit the six phase images to our thermal model and obtain thermal conductivity maps. The conductivity maps of four particles are shown in d. A log color bar is used to highlight the contrast of thermal conductivity in a single particle. The thermal conductivity of the AlN particles ranges from 80W/mK in the dense regions to 5W/mK in the porous regions.

scholarly journals Heat Transport Driven by the Coupling of Polaritons and Phonons in a Polar Nanowire

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5110
Author(s):  
Yangyu Guo ◽  
Masahiro Nomura ◽  
Sebastian Volz ◽  
Jose Ordonez-Miranda
Keyword(s):  
Heat Transport ◽  
State Of The Art ◽  
Boltzmann Transport Equation ◽  
Thermal Conductance ◽  
Heat Diffusion ◽  
Heat Sources ◽  
Boltzmann Transport ◽  
Heat Diffusion Equation ◽  
Current State ◽  
Linear Behavior

Heat transport guided by the combined dynamics of surface phonon-polaritons (SPhPs) and phonons propagating in a polar nanowire is theoretically modeled and analyzed. This is achieved by solving numerically and analytically the Boltzmann transport equation for SPhPs and the Fourier’s heat diffusion equation for phonons. An explicit expression for the SPhP thermal conductance is derived and its predictions are found to be in excellent agreement with its numerical counterparts obtained for a SiN nanowire at different lengths and temperatures. It is shown that the SPhP heat transport is characterized by two fingerprints: (i) The characteristic quantum of SPhP thermal conductance independent of the material properties. This quantization appears in SiN nanowires shorter than 1 μm supporting the ballistic propagation of SPhPs. (ii) The deviation of the temperature profile from its typical linear behavior predicted by the Fourier’s law in absence of heat sources. For a 150 μm-long SiN nanowire maintaining a quasi-ballistic SPhP propagation, this deviation can be as large as 1 K, which is measurable by the current state-of-the-art infrared thermometers.

Pump-Probe Measurements Using Silicon Nanocrystal Waveguides

2003 ◽  
Vol 770 ◽  
Author(s):  
Nathanael Smith ◽  
Max J. Lederer ◽  
Marek Samoc ◽  
Barry Luther-Davies ◽  
Robert G. Elliman
Keyword(s):  
Probe Beam ◽  
Time Resolution ◽  
Pump Beam ◽  
Silicon Nanocrystals ◽  
Continuous Wave ◽  
Optical Gain ◽  
Optical Pump ◽  
Time Resolved ◽  
Pump Probe ◽  
Probe Measurements

AbstractOptical pump-probe measurements were performed on planar slab waveguides containing silicon nanocrystals in an attempt to measure optical gain from photo-excited silicon nanocrystals. Two experiments were performed, one with a continuous-wave probe beam and a pulsed pump beam, giving a time resolution of approximately 25 ns, and the other with a pulsed pump and probe beam, giving a time resolution of approximately 10 ps. In both cases the intensity of the probe beam was found to be attenuated by the pump beam, with the attenuation increasing monotonically with increasing pump power. Time-resolved measurements using the first experimental arrangement showed that the probe signal recovered its initial intensity on a time scale of 45-70 μs, a value comparable to the exciton lifetime in Si nanocrystals. These data are shown to be consistent with an induced absorption process such as confined carrier absorption. No evidence for optical gain was observed.

Fast Fluid Thermodynamics Simulation by Solving Heat Diffusion Equation

2021 ◽  
Vol 11 (04) ◽  
pp. 1-11
Author(s):  
Wanwan Li
Keyword(s):  
Diffusion Equation ◽  
Real Time ◽  
Stokes Equations ◽  
Fluid Simulation ◽  
Heat Diffusion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Heat Diffusion Equation ◽  
Acceleration Techniques ◽  
Speed Up

In mechanical engineering educations, simulating fluid thermodynamics is rather helpful for students to understand the fluid’s natural behaviors. However, rendering both high-quality and realtime simulations for fluid dynamics are rather challenging tasks due to their intensive computations. So, in order to speed up the simulations, we have taken advantage of GPU acceleration techniques to simulate interactive fluid thermodynamics in real-time. In this paper, we present an elegant, basic, but practical OpenGL/SL framework for fluid simulation with a heat map rendering. By solving Navier-Stokes equations coupled with the heat diffusion equation, we validate our framework through some real-case studies of the smoke-like fluid rendering such as their interactions with moving obstacles and their heat diffusion effects. As shown in Fig. 1, a group of experimental results demonstrates that our GPU-accelerated solver of Navier-Stokes equations with heat transfer could give the observers impressive real-time and realistic rendering results.

Computer simulation of target link explosion in laser programmable redundancy for silicon memory

1986 ◽  
Vol 1 (2) ◽  
pp. 368-381 ◽  
Author(s):  
L.M. Scarfone ◽  
J.D. Chlipala
Keyword(s):  
Thermal Evolution ◽  
Three Dimensional ◽  
Heat Diffusion ◽  
Dielectric Films ◽  
Threshold Temperature ◽  
Heat Diffusion Equation ◽  
Heating Effects ◽  
Transparent Dielectric ◽  
Difference Form ◽  
Pulse Energies

Pulses of Q-switched Nd-YAG radiation have been used to remove polysilicon target links during the implementation of laser programmable redundancy in the fabrication of silicon memory. The link is encapsulated by transparent dielectric films that give rise to important optical interference effects modifying the laser flux absorbed by the link and the silicon substrate. Estimates of these effects are made on the basis of classical plane-wave procedures. Thermal evolution of the composite structure is described in terms of a finite-difference form of the three-dimensional heat diffusion equation with a heat generation rate having a Gaussian spatial distribution of intensity and temporal shapes characteristic of commercial lasers. Temperature-dependent thermal diffusivity and melting of the polysilicon link are included in the computer modeling. The calculations account for the discontinuous change in the link absorption coefficient at the transition temperature. A threshold temperature and corresponding pressure, sufficiently high to rupture the dielectric above the link and initiate the removal process, are estimated by treating the molten link as a hard-sphere fluid. Numerical results are presented in the form of three-dimensional temperature distributions for 1.06 and 0.53 μm radiation with pulse energies 3.5 and 0.15μJ, respectively. Similarities and differences between heating effects produced by long (190 ns FWHM/740 ns duration) and short (35 ns FWHM/220 ns duration) pulses are pointed out.

scholarly journals Heat-balance integral to fractional (half-time) heat diffusion sub-model

2010 ◽  
Vol 14 (2) ◽  
pp. 291-316 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Diffusion Equation ◽  
Heat Balance ◽  
Integral Method ◽  
Time Derivative ◽  
Heat Diffusion ◽  
Half Time ◽  
Heat Diffusion Equation ◽  
Parabolic Profile ◽  
Heat Balance Integral Method ◽  
The Heat Balance

The fractional (half-time) sub-model of the heat diffusion equation, known as Dirac-like evolution diffusion equation has been solved by the heat-balance integral method and a parabolic profile with unspecified exponent. The fractional heat-balance integral method has been tested with two classic examples: fixed temperature and fixed flux at the boundary. The heat-balance technique allows easily the convolution integral of the fractional half-time derivative to be solved as a convolution of the time-independent approximating function. The fractional sub-model provides an artificial boundary condition at the boundary that closes the set of the equations required to express all parameters of the approximating profile as function of the thermal layer depth. This allows the exponent of the parabolic profile to be defined by a straightforward manner. The elegant solution performed by the fractional heat-balance integral method has been analyzed and the main efforts have been oriented towards the evaluation of fractional (half-time) derivatives by use of approximate profile across the penetration layer.

scholarly journals Temperature and interlayer coupling induced thermal transport across graphene/2D-SiC van der Waals heterostructure

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Md. Sherajul Islam ◽  
Imon Mia ◽  
A. S. M. Jannatul Islam ◽  
Catherine Stampfl ◽  
Jeongwon Park
Keyword(s):  
High Temperatures ◽  
Thermal Transport ◽  
Van Der Waals ◽  
Thermal Conductance ◽  
Interlayer Coupling ◽  
Phonon Modes ◽  
Out Of Plane ◽  
System Temperature ◽  
Non Equilibrium Molecular Dynamics ◽  
Increasing Temperature

AbstractGraphene based two-dimensional (2D) van der Waals (vdW) materials have attracted enormous attention because of their extraordinary physical properties. In this study, we explore the temperature and interlayer coupling induced thermal transport across the graphene/2D-SiC vdW interface using non-equilibrium molecular dynamics and transient pump probe methods. We find that the in-plane thermal conductivity κ deviates slightly from the 1/T law at high temperatures. A tunable κ is found with the variation of the interlayer coupling strength χ. The interlayer thermal resistance R across graphene/2D-SiC interface reaches 2.71 $$\times$$ × 10–7$${\text{Km}}^{2} /{\text{W}}$$ Km 2 / W at room temperature and χ = 1, and it reduces steadily with the elevation of system temperature and χ, demonstrating around 41% and 56% reduction with increasing temperature to 700 K and a χ of 25, respectively. We also elucidate the heat transport mechanism by estimating the in-plane and out-of-plane phonon modes. Higher phonon propagation possibility and Umklapp scattering across the interface at high temperatures and increased χ lead to the significant reduction of R. This work unveils the mechanism of heat transfer and interface thermal conductance engineering across the graphene/2D-SiC vdW heterostructure.

scholarly journals Prediction and Measurement of Thermal Transport Across Interfaces Between Isotropic Solids and Graphitic Materials

2010 ◽  
Author(s):  
Pamela M. Norris ◽  
Justin L. Smoyer ◽  
John C. Duda ◽  
Patrick E. Hopkins
Keyword(s):  
Thermal Transport ◽  
Substrate Surface ◽  
Unit Length ◽  
Thermal Conductance ◽  
Thin Film Deposition ◽  
Film Deposition ◽  
Transport Models ◽  
Composite Systems ◽  
Graphene Flakes ◽  
Isotropic Solids

Due to the high intrinsic thermal conductivity of carbon allotropes, there have been many attempts to incorporate such structures into existing thermal abatement technologies. In particular, carbon nanotubes (CNTs) and graphitic materials (i.e., graphite and graphene flakes or stacks) have garnered much interest due to the combination of both their thermal and mechanical properties. However, the introduction of these carbon-based nanostructures into thermal abatement technologies greatly increases the number of interfaces per unit length within the resulting composite systems. Consequently, thermal transport in these systems is governed as much by the interfaces between the constituent materials as it is by the materials themselves. This paper reports the behavior of phononic thermal transport across interfaces between isotropic thin films and graphite substrates. Elastic and inelastic diffusive transport models are formulated to aid in the prediction of conductance at a metal-graphite interface. The temperature dependence of the thermal conductance at Au-graphite interfaces is measured via transient thermoreflectance from 78 to 400 K. It is found that different substrate surface preparations prior to thin film deposition have a significant effect on the conductance of the interface between film and substrate.

scholarly journals Computational and Mathematical Model with Phase Change and Metal Addition Applied to GMAW

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Alfredo dos Santos Maia Neto ◽  
Marcelo Gonçalves de Souza ◽  
Edson Alves Figueira Júnior ◽  
Valério Luiz Borges ◽  
Solidônio Rodrigues de Carvalho
Keyword(s):  
Mathematical Model ◽  
Phase Change ◽  
Thermal Model ◽  
Complex Geometry ◽  
Golden Section ◽  
Simulated Data ◽  
Heat Diffusion ◽  
Data Logger ◽  
Heat Diffusion Equation ◽  
Metal Addition

This work presents a 3D computational/mathematical model to solve the heat diffusion equation with phase change, considering metal addition, complex geometry, and thermal properties varying with temperature. The finite volume method was used and the computational code was implemented in C++, using a Borland compiler. Experimental tests considering workpieces of stainless steel AISI 304 were carried out for validation of the thermal model. Inverse techniques based on Golden Section method were used to estimate the heat transfer rate to the workpieces. Experimental temperatures were measured using thermocouples type J—in a total of 07 (seven)—all connected to the welded workpiece and the Agilent 34970A data logger. The workpieces were chamfered in a 45° V-groove in which liquid metal was added on only one weld pass. An innovation presented in this work when compared to other works in scientific literature was the geometry of the weld pool. The good relation between experimental and simulated data confirmed the quality and robustness of the thermal model proposed in this work.

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