Electro-Thermal Analysis and Monte Carlo Simulation for Thermal Issue in Si Devices

2009 ◽  
Author(s):  
Tomoyuki Hatakeyama ◽  
Kazuyoshi Fushinobu ◽  
Ken Okazaki ◽  
Masaru Ishizuka
Keyword(s):  
Thermal Analysis ◽  
Monte Carlo ◽  
Relaxation Time ◽  
Energy Conservation ◽  
Heat Generation ◽  
Relaxation Times ◽  
Conservation Equation ◽  
Energy Conservation Equation ◽  
Precise Prediction ◽  
Mc Simulation

Nowadays, precise prediction of the heat generation in semiconductor devices is significant. Electro-thermal analysis is one of the attractive methods to predict the heat generation in devices. However, in electro-thermal analysis, the relaxation time approximation is applied to calculate the scattering term in momentum and energy conservation equation. And the assumption of the constant relaxation time for the scattering term of energy conservation equation and the momentum relaxation time derived from the empirical carrier mobility are conventionally applied. For precise prediction of the relaxation times, Monte Carlo (MC) simulation can be applied. In this research, we consider the importance of these relaxation times for heat generation in semiconductor devices. We compare the results with conventional relaxation times and those with the relaxation time from MC simulation in electro-thermal analysis. The calculation results show the electro-thermal analysis with the conventional relaxation time model will overestimate the heat generation density in lower electric field of devices and in higher clock frequency devices.

Energy conservation, time-reversal invariance and reciprocity in ducts with flow

2001 ◽  
Vol 431 ◽  
pp. 223-237 ◽  
Author(s):  
WILLI MÖHRING
Keyword(s):  
Energy Conservation ◽  
Sound Wave ◽  
Conservation Equation ◽  
Smooth Transition ◽  
Rotational Flow ◽  
Flow Energy ◽  
Energy Conservation Equation ◽  
Reversal Invariance ◽  
Edge Conditions ◽  
Piecewise Continuous

A sound wave propagating in an inhomogeneous duct consisting of two semi-infinite uniform ducts with a smooth transition region in between and which carries a steady flow is considered. The duct walls may be rigid or compliant. For an irrotational sound wave it is shown that the three properties of the title are closely related, such that the validity of any two implies the validity of the third. Furthermore it is shown that the three properties are fulfilled for lossless locally reacting duct walls provided the impedance varies at most continuously. For piecewise-continuous wall properties edge conditions are essential. By an analytic continuation argument it is shown that reciprocity remains true for walls with loss. For rotational flow, energy conservation theorems have been derived only with the help of additional potential-like variables. The inter-relation between the three properties remains valid if one considers these additional variables to be known. If only the basic gasdynamic variables in both half-ducts are known, one cannot formulate an energy conservation equation; however, reciprocity is fulfilled.

Simulation of astrophysical flows in isentropic approximation

2018 ◽  
Vol 27 (10) ◽  
pp. 1844014
Author(s):  
S. G. Moiseenko ◽  
G. S. Bisnovatyi-Kogan
Keyword(s):  
Shock Wave ◽  
Kinetic Energy ◽  
Energy Conservation ◽  
Conservation Equation ◽  
Numerical Errors ◽  
Energy Conservation Equation ◽  
Different Types ◽  
Entropy Conservation ◽  
Isentropic Approximation ◽  
Astrophysical Flows

One of the difficulties of numerical simulations of cold supersonic astrophysical flows is a big difference in different types of energy. Gravitational and/or kinetic energy of the gas could be much larger than its internal energy. In such a case, it is possible to get large numerical errors in the simulations. To avoid this difficulty, conservation of entropy equation was used instead of energy conservation equation. The entropy conservation equation does not contain the gravitational and kinetic energy. The application of the isentropic set of equations is correct when the flow does not contain shocks or the amplitude of the shocks (shock wave Mach number) is not large. We estimate the violation of the energy conservation low when the “shock wave” is isentropic.

NMR Relaxation Time Simulation for Different Models of Motion in (CH3)3NBH3

2003 ◽  
Vol 58 (9-10) ◽  
pp. 537-540 ◽  
Author(s):  
Roman Goc
Keyword(s):  
Monte Carlo ◽  
Relaxation Time ◽  
Monte Carlo Simulations ◽  
Relaxation Times ◽  
Nmr Relaxation ◽  
Complex Rotation ◽  
Time Simulation ◽  
Curve Versus ◽  
Nmr Relaxation Time ◽  
Clear Relation

Monte Carlo simulations of complex rotation of single −CH3 groups, −(CH3)3 groups and −BH3 groups were performed for trimethylamine borane (CH3)3NBH3. In the course of these simulations the correlation functions for different models of rotation were determined. Knowledge of these functions and of some data extracted from NMR experiments allowed for the calculation of the longitudinal magnetic relaxation time T1 as a function of temperature. The values of relaxation times obtained from Monte Carlo simulations are compared to experimental results published by other authors. There is a clear relation between the assumed model of rotation and the shape of the T1 curve versus temperature.

Computational steering in Monte Carlo simulations of thin film polystyrene

2005 ◽  
Vol 363 (1833) ◽  
pp. 1961-1974 ◽  
Author(s):  
Daniel R Mason ◽  
Adrian P Sutton
Keyword(s):  
Thin Film ◽  
Monte Carlo ◽  
Relaxation Times ◽  
Polymer System ◽  
Atomic Scale ◽  
Computational Steering ◽  
High Molecular Weight Polymer ◽  
Molecular Weight Polymer ◽  
Current State ◽  
Mc Simulation

High molecular weight polymer systems show very long relaxation times, of the order of milliseconds or more. This time-scale proves practically inaccessible for atomic-scale dynamical simulation such as molecular dynamics. Even with a Monte Carlo (MC) simulation, the generation of statistically independent configurations is non-trivial. Many moves have been proposed to enhance the efficiency of MC simulation of polymers. Each is described by a proposal density ( x ′; x ): the probability of selecting the trial state x ′ given that the system is in the current state x . This proposal density must be parametrized for a particular chain length, chemistry and temperature. Choosing the correct set of parameters can greatly increase the rate at which the system explores its configuration space. Computational steering (CS) provides a new methodology for a systematic search to optimize the proposal densities for individual moves, and to combine groups of moves to greatly improve the equilibration of a model polymer system. We show that monitoring the correlation time of the system is an ideal single parameter for characterizing the efficiency of a proposal density function, and that this is best evaluated by a distributed network of replicas of the system, with the operator making decisions based on the averages generated over these replicas. We have developed an MC code for simulating an anisotropic atomistic bead model which implements the CS paradigm. We report simulations of thin film polystyrene.

Detailed Phonon Generation Simulations via the Monte Carlo Method

2003 ◽  
Author(s):  
Eric Pop ◽  
Sanjiv Sinha ◽  
Kenneth E. Goodson
Keyword(s):  
Monte Carlo ◽  
Electric Field ◽  
Heat Generation ◽  
Energy Exchange ◽  
Phonon Mode ◽  
Field Region ◽  
The Monte Carlo Method ◽  
Phonon Generation ◽  
Mc Simulation ◽  
Non Locality

Modeling heat generation at nanometer scales in silicon is of great interest and particularly relevant to the heating and reliability of nanoscale and thin-film transistors. Joule heating is usually simulated as the dot product of the macroscopic electric field and current density [1]. This approach does not account for the microscopic non-locality of the phonon emission near a strongly peaked electric field region. It also does not differentiate between electron energy exchange with the various phonon branches and does not give any information regarding the types of phonons emitted. The present work addresses both of these issues: we use a detailed Monte Carlo (MC) simulation to compute sub-continuum and phonon mode-specific heat generation rates, with applications at nanometer length scales.

Dispersion and energy conservation relations of surface waves in semi-infinite plasma

1981 ◽  
Vol 25 (2) ◽  
pp. 285-307 ◽  
Author(s):  
V. Atanssov
Keyword(s):  
Surface Wave ◽  
Energy Conservation ◽  
Surface Waves ◽  
Low Frequency ◽  
Conservation Equation ◽  
Hydrodynamic Theory ◽  
Energy Conservation Equation ◽  
Surface Wave Propagation ◽  
Electric And Magnetic Fields ◽  
Bulk Waves

The hydrodynamic theory of surface wave propagation in semi-infinite homogeneous isotropic plasma is considered. Explicit linear surface wave solutions are given for the electric and magnetic fields, charge and current densities. These solutions are used to obtain the well-known dispersion relations and, together with the general energy conservation equation, to find appropriate definitions for the energy and the energy flow densities of surface waves. These densities are associated with the dispersion relation and the group velocity by formulae similar to those for bulk waves in infinite plasmas. Both cases of high-frequency (HF) and low-frequency (LF) surface waves are considered.

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