An effective quantum potential for particle–particle interactions in three-dimensional semiconductor device simulations

2007 ◽  
Vol 6 (4) ◽  
pp. 401-408 ◽  
Author(s):  
Clemens Heitzinger ◽  
Christian Ringhofer
Keyword(s):  
Semiconductor Device ◽  
Three Dimensional ◽  
Quantum Potential ◽  
Particle Interactions

Quantitative SiGe TEM Elemental Analysis in FinFET Test Structures

2015 ◽  
Author(s):  
James Demarest ◽  
John Bruley
Keyword(s):  
Silicon Germanium ◽  
Semiconductor Device ◽  
Three Dimensional ◽  
Test Structure ◽  
X Ray Diffraction ◽  
X Ray ◽  
Device Scaling ◽  
Transmission Electron ◽  
Calibration Samples ◽  
Performance Gains

Abstract As semiconductor device scaling continues to reduce the structure size, device geometries are also changing to three dimensional structures such as finFETs, and the materials which compose the devices are also evolving to obtain additional device performance gains. The material change studied in this paper is the introduction of silicon germanium into the electrically active region of a finFET test structure. The paper demonstrates a quantitative energy dispersive X-ray spectroscopy transmission electron microscopy (TEM) technique through the use of blanket film calibration samples of known concentration characterized by X-ray diffraction. The technique is used to identify a test structure issue which could only be diagnosed with a technique having nanometer spatial resolution and atomic percent sensitivity. The results of the test structure analysis are independently verified by the complementary TEM electron energy loss spectroscopy technique.

Transverse shear-induced gradient diffusion in a dilute suspension of spheres

1998 ◽  
Vol 357 ◽  
pp. 279-287 ◽  
Author(s):  
Y. WANG ◽  
R. MAURI ◽  
A. ACRIVOS
Keyword(s):  
Three Dimensional ◽  
Spherical Particles ◽  
Particle Interactions ◽  
Simple Shearing ◽  
Ambient Flow ◽  
Gradient Diffusion ◽  
Areal Fraction ◽  
Dilute Suspension ◽  
Neutrally Buoyant ◽  
Shearing Motion

We study the shear-induced gradient diffusion of particles in an inhomogeneous dilute suspension of neutrally buoyant spherical particles undergoing a simple shearing motion, with all inertia and Brownian motion effects assumed negligible. An expansion is derived for the flux of particles due to a concentration gradient along the directions perpendicular to the ambient flow. This expression involves the average velocity of the particles, which in turn is expressed as an integral over contributions from all possible configurations. The integral is divergent when expressed in terms of three-particle interactions and must be renormalized. For the monolayer case, such a renormalization is achieved by imposing the condition of zero total macroscopic flux in the transverse direction whereas, for the three-dimensional case, the additional constraint of zero total macroscopic pressure gradient is required. Following the scheme of Wang, Mauri & Acrivos (1996), the renormalized integral is evaluated numerically for the case of a monolayer of particles, giving for the gradient diffusion coefficient 0.077γa2c¯2, where is the applied shear rate, a the radius of the spheres and c¯ their areal fraction.

A Numerical Approximation Structured by Mixed Finite Element and Upwind Fractional Step Difference for Semiconductor Device with Heat Conduction and Its Numerical Analysis

2017 ◽  
Vol 10 (3) ◽  
pp. 541-561
Author(s):  
Yirang Yuan ◽  
Qing Yang ◽  
Changfeng Li ◽  
Tongjun Sun
Keyword(s):  
Finite Element ◽  
Heat Conduction ◽  
Numerical Analysis ◽  
Partial Differential Equations ◽  
Heat Conduction Equation ◽  
Semiconductor Device ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Fractional Step ◽  
Dimensional Problem

AbstractA coupled mathematical system of four quasi-linear partial differential equations and the initial-boundary value conditions is presented to interpret transient behavior of three dimensional semiconductor device with heat conduction. The electric potential is defined by an elliptic equation, the electron and hole concentrations are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite element approximation is used to get the electric field potential and one order of computational accuracy is improved. Two concentration equations and the heat conduction equation are solved by a fractional step scheme modified by a second-order upwind difference method, which can overcome numerical oscillation, dispersion and computational complexity. This changes the computation of a three dimensional problem into three successive computations of one-dimensional problem where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by prior estimate theory and other special techniques of partial differential equations. This type of parallel method is important in numerical analysis and is most valuable in numerical application of semiconductor device and it can successfully solve this international famous problem.

scholarly journals Three-Dimensional Imaging of Semiconductor Device Structure Using Contrast Tuning EFTEM Tomography

2010 ◽  
Vol 16 (S2) ◽  
pp. 1920-1921
Author(s):  
Q Jin
Keyword(s):  
Semiconductor Device ◽  
Three Dimensional ◽  
Device Structure ◽  
Three Dimensional Imaging

Extended abstract of a paper presented at Microscopy and Microanalysis 2010 in Portland, Oregon, USA, August 1 – August 5, 2010.

scholarly journals Simulations Of Steady Flows Through Cylindrical Geometries With And Without Local Constrictions By Multiparticle Collision Dynamics

2021 ◽  
Author(s):  
Salil K. Bedkihal
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Steady Flows ◽  
Particle Interactions ◽  
Collision Dynamics ◽  
Complex Flow ◽  
Multiparticle Collision Dynamics ◽  
Complex Particle

In this thesis, a recently developed particle-based method called multiparticle collision dynamics (MPC) is used to simulate steady flows through three-dimensional constricted axisymmetric cylinders. The work is motivated by complex particle interactions in blood flow such as aggregation and the need to be able to capture these effects in physiologically relevant complex flow geometries. This is the first time that MPC dynamics has been applied to simulate flows though constrictions. The particle collisions in MPC dynamics are numerically more efficient than other particle-based simulation methods. Particle interactions with the cylinder walls are modeled using bounce-back (BB) and loss in tangential, reversal of normal (LIT) boundary conditions. BB is an analog of the macroscopic no-slip boundary condition, and LIT gives slip. Finally, an averaging procedure is employed to make a connection with the solution to the Navier-Stokes equations. Interesting differences have been found in the velocity profiles obtained using MPC with BB and LIT, compared to Navier-Stokes.

Motion of Microcarriers in Rotating-Wall Vessels

1999 ◽  
Author(s):  
Hongxia Gao ◽  
Portonovo S. Ayyaswamy ◽  
Paul Ducheyne
Keyword(s):  
Mammalian Cells ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Microgravity Environment ◽  
Particle Interactions ◽  
Rotating Wall ◽  
Rotating Wall Vessel ◽  
Concentric Cylinders ◽  
Dimensional Growth ◽  
Rotating Wall Vessels

Abstract It is now widely acknowledged that the simulated microgravity environment of NASA-designed rotating-wall vessels (RWVs) offers great advantages for three-dimensional growth of mammalian cells. In the rotating-wall vessel, the solid body rotation is accomplished by horizontally rotating a vessel, which consists of a cylinder or two concentric cylinders and is completely filled with culture medium, at a constant rotational speed. Mixing and shear forces in the RWV are due to the microcarriers’ motion in the fluid, and the contact that the microcarriers occasionally make with the wall and each other [1]. Therefore, the motion of microcarriers in the rotating flow is of interest and important in the design of the rotating-wall vessel bioreactors and in the guiding of RWV cell culture experiments under optimal operating conditions. Predictions of a single microcarrier migration inside the RWV have been described in our previous study [2]. However, the particle-wall and the particle-particle interactions were not considered. In this study, we numerically investigate the motion of microcarriers with the effects of the collisions under consideration.

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