Modelling of CW Laser Annealing of Multilayer Structures

1981 ◽  
Vol 4 ◽  
Author(s):  
I.D. Calder ◽  
R. Sue ◽  
Emad-Eldin A.A. Aly
Keyword(s):  
Phase Transition ◽  
Thermal Conductivity ◽  
Optical Properties ◽  
Steady State ◽  
Temperature Distribution ◽  
Thermal Model ◽  
Laser Annealing ◽  
Multilayer Structures ◽  
Cw Laser ◽  
Arbitrary Thickness

ABSTRACTA thermal model is developed for cw laser annealing of multilayer structures. Each layer has arbitrary thickness, thermal conductivity and optical properties. Steady state conditions with no phase transition are assumed. A procedure is presented for obtaining the temperature distribution in any system and explicit integral expressions are developed for the two and three layer cases. Results are calculated for the Si/glass and Si/SiO2 /Si systems.

Quasi-Steady-State Temperature Distribution in Periodically Contacting Finite Regions

1981 ◽  
Vol 103 (4) ◽  
pp. 739-744 ◽  
Author(s):  
B. Vick ◽  
M. N. O¨zis¸ik
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Temperature Distribution ◽  
Interface Temperature ◽  
Quasi Steady State ◽  
Exact Analytical Solutions ◽  
One Dimensional ◽  
Steady State Temperature ◽  
Regular Cycle

Heat transfer across two surfaces which make and break contact periodically according to a continuous regular cycle is investigated theoretically and exact analytical solutions are developed for the quasi-steady-state temperature distribution for a two-region, one-dimensional, periodically contacting model. The effects of the Biot number, the thermal conductivity and thermal diffusivity of the materials and the duration of contact and break periods on the interface temperature and the temperature distribution within the solids are illustrated with representative temperature charts.

Radiative Transport Within an Ablating Body

1961 ◽  
Vol 83 (2) ◽  
pp. 215-224 ◽  
Author(s):  
Leo P. Kadanoff
Keyword(s):  
Optical Properties ◽  
Steady State ◽  
Temperature Distribution ◽  
Free Path ◽  
Liquid Layer ◽  
Effective Conductivity ◽  
Mean Free Path ◽  
Radiative Transport ◽  
Scattering Media ◽  
Infinite Body

The emission and reabsorption of thermal radiation within a semitransparent material provides a mechanism which supplements ordinary thermal conduction in transporting energy from hotter to colder regions. A method has been developed for the calculation of net radiative flux and temperature distribution within a semi-infinite body which emits, absorbs, and scatters this radiation and which allows some radiation to escape from its surface. This method has been applied to the problem of calculating temperature distributions within bodies in steady-state ablation. The bodies are characterized by their refractive index, surface reflectivity, absorption and scattering coefficient, ablation velocity, and surface temperature as well as by their heat capacity and thermal conductivity. Numerical results are presented for the temperature distribution with various values of these parameters. As a result of this analysis, simple formulas are presented for the temperature distribution very near the surface of an ablating body which are particularly useful in predicting the temperature distribution in the “liquid layer” of a glassy ablating body. These simple formulas are presented for two limiting cases: Case I, in which the liquid layer is so thin that it is almost completely transparent to radiation, and Case II, in which the radiation mean free path is so short that radiative transport can be completely neglected in determining the temperature distribution in the liquid layer. Also resulting from this numerical analysis is a simple relation between the ablation rate and the emissive power of a body in steady-state ablation. The concept of effective conductivity is extended to scattering media. It is noted that this concept fails whenever the temperature or optical properties of the medium change appreciably within one radiation mean free path. In particular, the optical properties change discontinuously at any boundary. Thus, in general, the effective conductivity concept fails near a boundary and results in completely wrong answers for the temperature distribution in the liquid layer.

An Accuracy Analysis of the Steady-State Thermal Conductivity Measurement Method With Single Constant Temperature Region

2003 ◽  
Author(s):  
Ming-Tsung Sun ◽  
Chin-Hsiang Chang
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Temperature Distribution ◽  
Constant Temperature ◽  
Temperature Region ◽  
Relative Size ◽  
Conductivity Measurement ◽  
Thermal Conductivity Measurement ◽  
Homogeneous Material ◽  
Single Constant

The newly developed method for steady-state thermal conductivity measurement with single constant temperature region is experimentally proven accurate within 3% compared with the guarded hot plate method. The method is suitable for in-situ non-destructive evaluation of insulation materials. However, there are factors that affect the accuracy of measurement yet to be closely studied. In this paper, we present a theoretical analysis of the accuracy of the method by varying the relative size of the heating plate, the thickness of the test specimen, the location of the temperature sensors at the lower temperature side, and different thermal convection coefficients for the free convection boundary condition. In the study, the temperature distribution in a homogeneous material is solved numerically. The thermal conductivity is evaluated from the temperature distribution and the heat flux measured according to the method. By comparing the results with that given in the numerical model, the accuracy can be expressed as functions of the three variables in the analysis. The results are consistent with that of the experiment. They are considered beneficial in providing information to the optimal design and the measurement correction of a commercialized apparatus using the method.

Steady-state heat sink analysis for two-terminal microwave oscillator devices with temperature dependent thermal conductivity

1993 ◽  
Vol 441 (1911) ◽  
pp. 181-189 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Steady State ◽  
Temperature Distribution ◽  
Temperature Rise ◽  
Heat Sink ◽  
Maximum Temperature ◽  
Microwave Oscillators ◽  
Steady State Temperature ◽  
Steady State Heat

A theoretical analysis to calculate the steady-state temperature distribution within a cylindrical heat sink configuration, where the thermal conductivity is dependent on the temperature, is outlined. The analysis applies to any heat sink arrangement that can be treated as one or more homogeneous solid cylinders mounted on a semi-infinite heat sink, where the heat flux incident on both faces of each cylinder is uniform over a given centralized circular region. The model is used to analyse the temperature distribution within the heat sink configurations used commonly to package two-terminal semiconductor devices that are operated as sources of electromagnetic radiation in microwave oscillators. Results are presented that show how the maximum temperature rise within commercially available heat sink packages, depends on the input heat flux and the dimensions and thermal conductivity of the materials. Furthermore, results that show how the temperature rise varies across the interfaces of given heat sink configurations, similar to those used commercially, are given also.

Nonlinear effects of variable conductivities in thermistor-related problems: an explicit example

1990 ◽  
Vol 1 (3) ◽  
pp. 245-257
Author(s):  
J. H. Young ◽  
G. Tenti
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Temperature Distribution ◽  
Surface Temperature ◽  
Nonlinear Partial Differential Equations ◽  
Electrical Potential ◽  
Nonlinear Effects ◽  
Electrical Current ◽  
Electrical Heating ◽  
One Dimensional

The coupled nonlinear partial differential equations obeyed by the electrical potential and temperature distribution for a medium undergoing steady state electrical heating are applied to a one-dimensional rod having its surface temperature held constant as current is conducted along its length due to a potential difference maintained between its ends. Extension is given to the previously discussed class of solutions by the inclusion of a thermal conductivity which varies linearly with temperature. The resulting electrical current and resistance are found to be significantly influenced by the thermal conductivity of the medium. Molybdenum is identified as a material exemplifying such a thermal conductivity and the general effects are then numerically illustrated.

Measurements of Thermal Conductivity of Thin Films by Means of Comparative Method

2004 ◽  
Vol 1 (3) ◽  
pp. 176-186
Author(s):  
Selim Achmatowicz ◽  
Iwona Wyżkiewicz ◽  
Elżbieta Zwierkowska ◽  
Wojciech Łobodziński
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Steady State ◽  
Temperature Distribution ◽  
Constant Temperature ◽  
Comparative Method ◽  
Thin Layers ◽  
Central Spot ◽  
Measurement And Evaluation ◽  
Conductivity Of Thin Films

The comparative method has been employed to approximate thermal conductivity of thin layers (10 to 100 μm thick). The method is based on measurement of temperature distribution on the surface of horizontally positioned plate heated in the central spot to a constant temperature in a steady state. The paper contains description of the method, a few examples of conducted measurement and evaluation of the accuracy of the method.

scholarly journals Isostasy, LAB and some properties of asthenosphere in chosen regions of Poland

2019 ◽  
Author(s):  
Leszek Czechowski
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Temperature Distribution ◽  
Density Distribution ◽  
Depth Range ◽  
Continental Lithosphere ◽  
Isostatic Compensation ◽  
Average Value ◽  
Steady State Temperature

We use programs from the package LABWA2015 to determine position of Lithosphere-Asthenosphere Boundary (LAB) and some properties of lower lithosphere in chosen sites in Poland. Seismic, topographic, thermal and petrological data are used together with assumption about isostasy. Moreover we investigate the role of assumption about the steady state temperature distribution. We have found that sometimes this assumption for continental lithosphere can be unjustified but usually does not lead to significant errors. We have found also that in chosen sites, the thermal LAB is in the depth range 85-95 km. The average value of thermal conductivity of mantle is ~4 W m-1 K-1. Just below MOHO, a level of approximate isostatic compensation is found. More precise compensation is found in the asthenosphere at ~110 km but its position is sensitive to the density distribution.

Modeling of cw laser annealing of multilayer structures

1982 ◽  
Vol 53 (11) ◽  
pp. 7545-7550 ◽  
Author(s):  
I. D. Calder ◽  
R. Sue
Keyword(s):  
Laser Annealing ◽  
Multilayer Structures ◽  
Cw Laser

High-speed isotachophoresis. Analytical aspects of the steady-state longitudinal temperature profiles

1979 ◽  
Vol 44 (3) ◽  
pp. 841-853 ◽  
Author(s):  
Zbyněk Ryšlavý ◽  
Petr Boček ◽  
Miroslav Deml ◽  
Jaroslav Janák
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Electric Field ◽  
Field Intensity ◽  
Electric Field Intensity ◽  
Minor Component ◽  
Physical Models ◽  
Temperature Profiles ◽  
Longitudinal Temperature ◽  
Continuous Character

The problem of the longitudinal temperature distribution was solved and the bearing of the temperature profiles on the qualitative characteristics of the zones and on the interpretation of the record of the separation obtained from a universal detector was considered. Two approximative physical models were applied to the solution: in the first model, the temperature dependences of the mobilities are taken into account, the continuous character of the electric field intensity at the boundary being neglected; in the other model, the continuous character of the electric field intensity is allowed for. From a comparison of the two models it follows that in practice, the variations of the mobilities with the temperature are the principal factor affecting the shape of the temperature profiles, the assumption of a discontinuous jump of the electric field intensity at the boundary being a good approximation to the reality. It was deduced theoretically and verified experimentally that the longitudinal profiles can appreciably affect the longitudinal variation of the effective mobilities in the zone, with an infavourable influence upon the qualitative interpretation of the record. Pronounced effects can appear during the analyses of the minor components, where in the corresponding short zone a temperature distribution occurs due to the influence of the temperatures of the neighbouring zones such that the temperature in the zone of interest in fact does not attain a constant value in axial direction. The minor component does not possess the steady-state mobility throughout the zone, which makes the identification of the zone rather difficult.

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