Numerical Modeling of Electrothermal Effects in Silicon Nanowires

2008 ◽  
Vol 1083 ◽  
Author(s):  
Cicek Boztug ◽  
Gokhan Bakan ◽  
Mustafa Akbulut ◽  
Ali Gokirmak ◽  
Helena Silva
Keyword(s):  
Temperature Profile ◽  
Silicon Nanowires ◽  
Electrical Current ◽  
Nanocrystalline Silicon ◽  
Heat Diffusion ◽  
Small Scale ◽  
Thomson Effect ◽  
Sem Images ◽  
Heat Diffusion Equation ◽  
Electrothermal Effects

AbstractAsymmetric melting was observed in electrically pulsed n-type (phosphorus) nanocrystalline silicon (nc-Si) wires fabricated lithographically. Scanning electron microscope (SEM) images taken from the pulsed wires showed that melting initiates from the ground terminal end of the wires instead of the center as initially expected. Asymmetry in the temperature profile is caused by heat exchanged between charge carriers and phonons when an electrical current is passed along a temperature gradient. This effect is known as Thomson effect, a thermoelectric heat transfer mechanism. One dimensional (1D) time dependent heat diffusion equation including Thomson heat term was solved to model the temperature profile on our structures. The modeling results show that Thomson effect introduces significant shifts in the temperature distribution. The effect of Thomson heat is modeled for various electrical pulse conditions and wires dimensions. Our results indicate that Thomson effect is significant in small scale electronic devices operating under high current densities.

scholarly journals Modeling the ascent of sounding balloons: derivation of the vertical air motion

2011 ◽  
Vol 4 (3) ◽  
pp. 3965-4012
Author(s):  
A. Gallice ◽  
F. G. Wienhold ◽  
C. R. Hoyle ◽  
F. Immler ◽  
T. Peter
Keyword(s):  
Drag Coefficient ◽  
Vertical Velocity ◽  
Heat Diffusion ◽  
Small Scale ◽  
Reference Curve ◽  
Heat Diffusion Equation ◽  
Ascent Rate ◽  
Potential Applications ◽  
Radial Heat ◽  
Air Motion

Abstract. A new model to describe the ascent of sounding balloons in the troposphere and lower stratosphere (up to ~30–35 km altitude) is presented. Contrary to previous models, detailed account is taken of both the variation of the drag coefficient with altitude and the heat imbalance between the balloon and the atmosphere. To compensate for the lack of data on the drag coefficient of sounding balloons, a reference curve for the relationship between drag coefficient and Reynolds number is derived from a dataset of flights launched during the Lindenberg Upper Air Methods Intercomparisons (LUAMI) campaign. The transfer of heat from the surrounding air into the balloon is accounted for by solving the radial heat diffusion equation inside the balloon. The potential applications of the model include the forecast of the trajectory of sounding balloons, which can be used to increase the accuracy of the match technique, and the derivation of the air vertical velocity. The latter is obtained by subtracting the ascent rate of the balloon in still air calculated by the model from the actual ascent rate. This technique is shown to provide an approximation for the vertical air motion with an uncertainty error of 0.5 m s−1 in the troposphere and 0.2 m s−1 in the stratosphere. An example of extraction of the air vertical velocity is provided in this paper. We show that the air vertical velocities derived from the balloon soundings in this paper are in general agreement with small-scale atmospheric velocity fluctuations related to gravity waves, mechanical turbulence, or other small-scale air motions measured during the SUCCESS campaign (Subsonic Aircraft: Contrail and Cloud Effects Special Study) in the orographically unperturbed mid-latitude middle troposphere.

scholarly journals Modeling the ascent of sounding balloons: derivation of the vertical air motion

2011 ◽  
Vol 4 (10) ◽  
pp. 2235-2253 ◽  
Author(s):  
A. Gallice ◽  
F. G. Wienhold ◽  
C. R. Hoyle ◽  
F. Immler ◽  
T. Peter
Keyword(s):  
Solar Radiation ◽  
Drag Coefficient ◽  
Vertical Velocity ◽  
Heat Diffusion ◽  
Small Scale ◽  
Reference Curve ◽  
Heat Diffusion Equation ◽  
Ascent Rate ◽  
Potential Applications ◽  
Air Motion

Abstract. A new model to describe the ascent of sounding balloons in the troposphere and lower stratosphere (up to ∼30–35 km altitude) is presented. Contrary to previous models, detailed account is taken of both the variation of the drag coefficient with altitude and the heat imbalance between the balloon and the atmosphere. To compensate for the lack of data on the drag coefficient of sounding balloons, a reference curve for the relationship between drag coefficient and Reynolds number is derived from a dataset of flights launched during the Lindenberg Upper Air Methods Intercomparisons (LUAMI) campaign. The transfer of heat from the surrounding air into the balloon is accounted for by solving the radial heat diffusion equation inside the balloon. In its present state, the model does not account for solar radiation, i.e. it is only able to describe the ascent of balloons during the night. It could however be adapted to also represent daytime soundings, with solar radiation modeled as a diffusive process. The potential applications of the model include the forecast of the trajectory of sounding balloons, which can be used to increase the accuracy of the match technique, and the derivation of the air vertical velocity. The latter is obtained by subtracting the ascent rate of the balloon in still air calculated by the model from the actual ascent rate. This technique is shown to provide an approximation for the vertical air motion with an uncertainty error of 0.5 m s−1 in the troposphere and 0.2 m s−1 in the stratosphere. An example of extraction of the air vertical velocity is provided in this paper. We show that the air vertical velocities derived from the balloon soundings in this paper are in general agreement with small-scale atmospheric velocity fluctuations related to gravity waves, mechanical turbulence, or other small-scale air motions measured during the SUCCESS campaign (Subsonic Aircraft: Contrail and Cloud Effects Special Study) in the orographically unperturbed mid-latitude middle troposphere.

Mathematical modelling of temperature profile of volcanic soils affected by an external thermal impact

Soil Research ◽  
2006 ◽  
Vol 44 (1) ◽  
pp. 57 ◽  
Author(s):  
Mónica Antilén ◽  
Olivier Fudym ◽  
Alvaro Vidal ◽  
Juan E. Foerster ◽  
Nelson Moraga ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Soil Temperature ◽  
Temperature Profile ◽  
Soil Surface ◽  
Heat Diffusion ◽  
Volcanic Soils ◽  
Heat Diffusion Equation ◽  
Transient Heat Diffusion ◽  
Relative Errors ◽  
The Mathematical Model

In this work, the soil temperature at depth was measured in the laboratory, and a mathematical model to fit the temperature profile in volcanic soils classified as Ultisols and Andisols was used. The mathematical model considered the transient heat diffusion equation, and a numerical discrete method was used to solve the equations system. The soil surface was heated for 2500 s and the temperature rose close to 700°C; the soil temperature decreased with depth; the temperature v. time curves showed a constant value when the temperature reached around 100°C, associated with water phase change and related to the water content of soils. The model was corrected by including the heat volumetric formulation. The observed relative errors are close to 10% in all fitted curves with respect to experimental data, showing the quality of the parametrisation chosen in the mathematical model. The fitting curve deviations were reduced when the actual position of thermocouples was considered, showing the sensitivity of the mathematical model. The simplified mathematical transient diffusion model proposed, which considers 2 ranges of thermal conductivity of soils and the surface temperature, was able to describe the experimental temperature profile in volcanic soils with wide differences in mineralogy, organic matter, and moisture contents.

Percolation transport and filament formation in nanocrystalline silicon nanowires

2013 ◽  
Vol 113 (16) ◽  
pp. 164902 ◽  
Author(s):  
S. Fischer ◽  
C. Osorio ◽  
N. E. Williams ◽  
S. Ayas ◽  
H. Silva ◽  
...  
Keyword(s):  
Silicon Nanowires ◽  
Nanocrystalline Silicon ◽  
Filament Formation

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.

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 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.

Influence of Hydrodynamic Journal Bearings With Multiple Slip Zones on Rotordynamic Behavior

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
A. Bhattacharya ◽  
J. K. Dutt ◽  
R. K. Pandey
Keyword(s):  
Slip Length ◽  
Stability Limit ◽  
Substantial Improvement ◽  
Journal Bearings ◽  
Heat Diffusion ◽  
Small Range ◽  
Heat Diffusion Equation ◽  
Multiple Slip ◽  
Lubricating Film ◽  
Marginal Improvement

This paper mainly reports stability investigations of rotors supported on fluid film journal bearings possessing multilocational slip-no-slip zones at the bush–film interface. The coupled solution of governing equations (Reynolds equation, energy equation, heat diffusion equation, lubricant rheological relation, and thermal boundary conditions) has been used to find pressure distributions in the lubricating film followed by evaluation of bearing coefficients. These coefficients have been used to determine stability limit speed (SLS) of the system and its robustness for both short (nearly inflexible) and long (flexible) rotors. Numerical simulations show that the pattern of pressure distribution with multiple slip-no-slip zones is similar to that obtained for multilobe bearings, resulting in substantial improvement of rotor–bearing stability irrespective of eccentricity ratio. A reduction in friction force (up to Sommerfeld number 1.8) and an increase in SLS and robustness compared to conventional bearings are observed when used with short rotors. Typically, up to six pairs of slip-no-slip zones improve SLS of the rotor–shaft system and robustness for short rotors, although more pairs deteriorate both. However, for long rotors, where dynamic rotor forces also act, these bearings provide marginal improvement in stability and robustness only for a small range of slip length.

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