scholarly journals Applicability of the High Field Model: An Analytical Study Via Asymptotic Parameters Defining Domain Decomposition

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 135-141 ◽  
Author(s):  
Carlo Cercignani ◽  
Irene M. Gamba ◽  
Joseph W. Jerome ◽  
Chi-Wang Shu
Keyword(s):  
Electric Fields ◽  
High Field ◽  
Field Model ◽  
Debye Length ◽  
Mean Free Path ◽  
Field Approximation ◽  
Macroscopic Model ◽  
Boltzmann Transport ◽  
Kinetic Transition ◽  
Macroscopic States

In this paper, we present a mesoscopic-macroscopic model of self-consistent charge transport. It is based upon an asymptotic expansion of solutions of the Boltzmann Transport Equation (BTE). We identify three dimensionless parameters from the BTE. These parameters are, respectively, the quotient of reference scales for drift and thermal velocities, the scaled mean free path, and the scaled Debye length. Such parameters induce domain dependent macroscopic approximations. Particular focus is placed upon the so-called high field model, defined by the regime where drift velocity dominates thermal velocity. This model incorporates kinetic transition layers, linking mesoscopic to macroscopic states. Reference scalings are defined by the background doping levels and distinct, experimentally measured mobility expressions, as well as locally determined ranges for the electric fields. The mobilities reflect a coarse substitute for reference scales of scattering mechanisms. See [9] for elaboration.The high field approximation is a formally derived modification of the augmented drift-diffusion model originally introduced by Thornber some fifteen years ago [25]. We are able to compare our approach with the earlier kinetic approach of Baranger and Wilkins [5] and the macroscopic approach of Kan, Ravaioli and Kerkhoven [20].

Simulation of Unsteady Small Heat Source Effects in Sub-Micron Heat Conduction

2003 ◽  
Vol 125 (5) ◽  
pp. 896-903 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Relaxation Time ◽  
Heat Source ◽  
Time Scales ◽  
Electric Fields ◽  
Hot Spot ◽  
Mean Free Path ◽  
Boltzmann Transport ◽  
Electron Phonon Interaction ◽  
Relaxation Time Approximation ◽  
Phonon Relaxation Time

In compact transistors, large electric fields near the drain side create hot spots whose dimensions are smaller than the phonon mean free path in the medium. In this paper, we present a study of unsteady hot spot behavior. The unsteady gray phonon Boltzmann transport equation (BTE) is solved in the relaxation time approximation using a finite volume method. Electron-phonon interaction is represented as a heat source term in the phonon BTE. The evolution of the temperature profile is governed by the interaction of four competing time scales: the phonon residence time in the hot spot and in the domain, the duration of the energy source, and the phonon relaxation time. The influence of these time scales on the temperature is investigated. Both boundary scattering and heat source localization effects are observed to have considerable impact on the thermal predictions. Comparison of BTE solutions with conventional Fourier diffusion analysis reveals significant discrepancies.

scholarly journals Effect of Strong Electric Fields on Material Responses: The Bloch Oscillation Resonance in High Field Conductivities

Materials ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1070 ◽  
Author(s):  
Satyvir Singh ◽  
Marco Battiato
Keyword(s):  
Steady State ◽  
Electric Fields ◽  
High Field ◽  
Transient Behavior ◽  
Analytic Solutions ◽  
Boltzmann Transport ◽  
Bloch Oscillations ◽  
Bloch Oscillation ◽  
Low Field ◽  
Strong Electric Fields

In this paper, we investigated the effect of strong electric fields on material responses and the Bloch oscillation resonance in high field conductivities. For this purpose, a high-order accurate explicit modal discontinuous Galerkin (DG) solver is employed for solving the quantum Boltzmann transport equation (BTE) in the context of electron transport at nanoscales under strongly out-of-equilibrium conditions. Here, we study the transient behavior and the convergence of a steady-state response to an external oscillating electric field switched on at time zero. We first benchmark our numerical results with known analytic steady-state responses at low fields. The computational results show that the present DG scheme is in excellent agreement with analytic solutions over the whole range of parameters and to an extremely high precision, allowing us to achieve good agreement even for the fifth-order response at low fields. We then extend the method to strong electric fields and show how the responses are deviated from the low-field ones and the transition to a dampened Bloch oscillation regime. Most importantly, we report the observation of a new regime induced by the resonance between the standard low-field response and Bloch oscillations.

Small Heat Source Effects in Sub-Micron Heat Conduction

2001 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Heat Conduction ◽  
Heat Source ◽  
Free Path ◽  
Electric Fields ◽  
Integrated Circuit ◽  
Mean Free Path ◽  
Boltzmann Transport ◽  
Source Effects ◽  
Relaxation Time Approximation ◽  
Volume Method

Abstract Decreasing dimensions of integrated circuit devices is leading to increased importance of microscale heat transfer effects and the failure of Fourier’s law in predicting sub-micron heat conduction. In compact transistors, large electric fields near the drain side create hot spots whose dimensions are smaller than the phonon mean free path in the medium. Under these conditions, the phonon Boltzmann equation (BTE) needs to be solved in order to resolve the non-local thermal conduction phenomena. In this paper, the problem of an unsteady heat source of size comparable to or smaller than the phonon mean free path is considered. The unsteady 2-D phonon Boltzmann transport equation in the relaxation time approximation is solved using a finite volume method. The interaction of the heat-up time constant with the phonon residence time in the hotspot and also its interaction with the time scales associated with scattering processes are studied. The results are useful in assessing the peak temperatures during unsteady operation in microelectronic devices.

scholarly journals Applicability of the High Field Model: A Preliminary Numerical Study

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 275-282 ◽  
Author(s):  
Carlo Cercignani ◽  
Irene M. Gamba ◽  
Joseph W. Jerome ◽  
Chi-Wang Shu
Keyword(s):  
High Field ◽  
Field Model ◽  
Numerical Study ◽  
Macroscopic Model ◽  
Kinetic Regime ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
New Model ◽  
The One ◽  
Transition Kinetic

In a companion presentation, we have discussed the theory of a mesoscopic/ macroscopic model, which can be viewed as an augmented drift-diffusion model. Here, we describe how that model is used. The device we consider for this presentation is the one dimensional GaAs n+−n−n+ structure of length 0.8μm. First, a full Hydro- Dynamic (HD) model, proven reliable when compared with Monte Carlo simulations, is used to simulate the device via the ENO finite difference method. As applied to the full device, the new model is not necessarily superior to traditional Drift-Diffusion (DD). Indeed, when we plot the quantity η= μ0E/kT0/m, where μ0 is the mobility constant and E=−ϕ′ is the electric field, we verify that the high field assumption η › 1, required for the high field model, is satisfied only in an interval given approximately by [0.2, 0.5]. When we run both the DD model and the new high field model in this restricted interval, with boundary conditions of concentration n and potential ϕ provided by the HD results, we demonstrate that the new model outperforms the DD model. This indicates that the high field and DD models should be used only in parts of the device, connected by a transition kinetic regime. This will be a domain decomposition issue involving interface conditions and adequate numerical methods.

Formation of Barrier Oxide Film on Lead in Borate Solutions

1994 ◽  
Vol 59 (6) ◽  
pp. 1305-1310 ◽  
Author(s):  
Emad E. Abdel Aal ◽  
Mohamed M. Hefny
Keyword(s):  
Oxide Film ◽  
Current Density ◽  
High Field ◽  
Empirical Relation ◽  
Field Approximation ◽  
Ion Concentration ◽  
Solution Temperature ◽  
Oxide Growth ◽  
Rate Of Growth ◽  
Barrier Type

Galvanostatic anodization of lead in borate solutions reveals that lead can form a barrier type oxide film. The rate of growth, R, fulfils the empirical relation, R = aib within the current density i range from 1.16 .10-4 to 3.19 .10-4 A cm-2. The magnitudes of the parameters a and b are 6.9 . 103 and 1.6, respectively, it has been found that the high field approximation is applicable for the oxide growth on lead. The coefficients of the dependence of R on solution temperature, T, pH and borate ion concentration, c, viz. (∂R/∂T), (∂R/∂pH) and (∂R/∂log c) are -18 . 10-4, -0.13 and 0.41, respectively.

High Field Electron Drift in a-Si:H

1993 ◽  
Vol 297 ◽  
Author(s):  
Qing Gu ◽  
Eric A. Schiff ◽  
Jean Baptiste Chevrier ◽  
Bernard Equer
Keyword(s):  
Electric Fields ◽  
High Field ◽  
Drift Mobility ◽  
Time Range ◽  
Electron Drift ◽  
Parameter Change ◽  
Transient Photocurrent ◽  
Field Mobility ◽  
High Electric Fields ◽  
Electron Drift Mobility

We have measured the electron drift mobility in a-Si:H at high electric fields (E ≤ 3.6 x 105 V%cm). The a-Si:Hpin structure was prepared at Palaiseau, and incorporated a thickp+ layer to retard high field breakdown. The drift mobility was obtained from transient photocurrent measurements from 1 ns - 1 ms following a laser pulse. Mobility increases as large as a factor of 30 were observed; at 77 K the high field mobility de¬pended exponentially upon field (exp(E/Eu), where E u= 1.1 x 105 V%cm). The same field dependence was observed in the time range 10 ns – 1 μs, indicating that the dispersion parameter change with field was negligible. This latter result appears to exclude hopping in the exponential conduction bandtail as the fundamental transport mechanism in a-Si:H above 77 K; alternate models are briefly discussed.

scholarly journals Phonon residual resistance of pure crystals

2015 ◽  
Vol 29 (29) ◽  
pp. 1550206
Author(s):  
A. I. Agafonov
Keyword(s):  
Electric Field ◽  
Constant Electric Field ◽  
Finite Thickness ◽  
Mean Free Path ◽  
Residual Resistivity ◽  
Boltzmann Transport ◽  
Residual Resistance ◽  
Temperature Resistance ◽  
Electron Mean Free Path ◽  
The Ideal

In this paper, using the Boltzmann transport equation, we study the zero temperature resistance of perfect metallic crystals of a finite thickness d along which a weak constant electric field E is applied. This resistance, hereinafter referred to as the phonon residual resistance, is caused by the inelastic scattering of electrons heated by the electric field, with emission of long-wave acoustic phonons and is proportional to [Formula: see text]. Consideration is carried out for Cu, Ag and Au perfect crystals with the thickness of about 1 cm, in the fields of the order of 1 mV/cm. Following the Matthiessen rule, the resistance of the pure crystals, the thicknesses of which are much larger than the electron mean free path is represented as the sum of both the impurity and phonon residual resistances. The condition on the thickness and field is found at which the low-temperature resistance of pure crystals does not depend on their purity and is determined by the phonon residual resistivity of the ideal crystals. The calculations are performed for Cu with a purity of at least 99.9999%.

Asymptotically matched sheath and presheath in a dense plasma

1998 ◽  
Vol 59 (3) ◽  
pp. 505-536 ◽  
Author(s):  
LINDSEY D. THORNHILL ◽  
PRATEEN V. DESAI
Keyword(s):  
Rapid Change ◽  
Debye Length ◽  
Mean Free Path ◽  
Boundary Region ◽  
Surface Erosion ◽  
Leading Order ◽  
Power Flux ◽  
Temperature Plasma ◽  
Recombination Length ◽  
The Impact

Asymptotically matched solutions for electron and ion density, electron and ion velocity, and electric potential are obtained in the boundary region of a dense low-temperature plasma adjacent to perfectly absorbing walls – walls that absorb, without reflection, incident electrons and ions. Leading-order composite solutions, valid throughout the boundary region, are constructed from solutions in three subdomains distinguished by different physical length scales: the geometric length, the ion mean free path and the Debye length. The composite solutions are used to assess the impact of electron–ion recombination in the ionization nonequilibrium region on sheath and presheath profiles, and on quantities evaluated at the wall. While, at leading order, the velocity profiles throughout the boundary region are not influenced by recombination, the density and potential profiles are significantly altered when recombination is included. These results show that the region of rapid change in these profiles lies closer to the wall when recombination is explicitly included in the model. The influence of recombination on the presheath potential, and consequently the wall potential, is found to scale as the natural logarithm of the recombination length. The broadening of the density profile results in a larger flux of ions accelerating through the sheath and impacting on the wall. The influence of recombination on the ion power flux to the wall is found to scale with the inverse recombination length. This scaling influences the prediction of surface erosion rates in technological applications that utilize these plasmas.

Sub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Transistors

1999 ◽  
Author(s):  
Per G. Sverdrup ◽  
Y. Sungtaek Ju ◽  
Kenneth E. Goodson
Keyword(s):  
Diffusion Equation ◽  
Free Path ◽  
Temperature Rise ◽  
Mean Free Path ◽  
Channel Length ◽  
Silicon On Insulator ◽  
Heat Diffusion ◽  
Boltzmann Transport ◽  
Heat Diffusion Equation ◽  
Silicon Devices

Abstract The temperature rise in compact silicon devices is predicted at present by solving the heat diffusion equation based on Fourier’s law. The validity of this approach needs to be carefully examined for semiconductor devices in which the region of strongest electronphonon coupling is narrower than the phonon mean free path, Λ, and for devices in which Λ is comparable to or exceeds the dimensions of the device. Previous research estimated the effective phonon mean free path in silicon near room temperature to be near 300 nm, which is already comparable with the minimum feature size of current generation transistors. This work numerically integrates the phonon Boltzmann transport equation (BTE) within a two-dimensional Silicon-on-Insulator (SOI) transistor. The BTE is coupled with the classical heat diffusion equation, which is solved in the silicon dioxide layer beneath a transistor with a channel length of 400 nm. The sub-continuum simulations yield a peak temperature rise that is 159 percent larger than predictions using only the classical heat diffusion equation. This work will facilitate the development of simpler calculation strategies, which are appropriate for commercial device simulators.

Effects of Applied Electric Fields on Interface Dynamics and Microstructure Formation During Directional Solidification of BiMn/Bi Eutectic

2000 ◽  
Author(s):  
L. L. Zheng
Keyword(s):  
Electric Field ◽  
Directional Solidification ◽  
Electric Fields ◽  
Microscopic Analysis ◽  
Eutectic Growth ◽  
Macroscopic Model ◽  
Microstructure Formation ◽  
Applied Current ◽  
Thermoelectric Effects ◽  
Interface Dynamics

Abstract This paper is to demonstrate that the presence of an electric field can be used to control materials microstructure formation. Special efforts have been made to identify the foremost process control parameters that affect the interface dynamics, and thermoelectric effects on materials microstructure formation during directional solidification. A computational model that integrates microscopic analysis to macroscopic model has been developed and applied to directional solidification of BiMn/Bi eutectic in the presence of electric fields. Numerical results demonstrated that in addition to process parameters, microstructure formation strongly depends on intensity, polarity and duration of applied current, and it changes spontaneously as an electric field is applied. Predicted patterns of microstructures have qualitatively agreed with the experiments. The results indicate the feasibility of utilizing electric fields to control microstructure formation during eutectic growth.

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