On the self-consistent equation for the microscopic local electric field in dielectric systems

1991 ◽  
Vol 73 (4) ◽  
pp. 745-756 ◽  
Author(s):  
V. Mazzacurati ◽  
G. Ruocco
Keyword(s):  
Electric Field ◽  
The Self ◽  
Local Electric Field ◽  
Self Consistent ◽  
Consistent Equation

Electric Field Gradient Calculations of Various Borides

1996 ◽  
Vol 51 (5-6) ◽  
pp. 527-533 ◽  
Author(s):  
K. Schwarz ◽  
H. Ripplinger ◽  
P. Blaha
Keyword(s):  
Electric Field ◽  
First Principles ◽  
Density Functional ◽  
The Self ◽  
Full Potential ◽  
Electric Field Gradients ◽  
Charge Density Distribution ◽  
Functional Theory ◽  
Field Gradients ◽  
Self Consistent

Abstract A first-principles method for the computation of electric field gradients (EFG) is illustrated for various borides. It is based on energy band calculations using the full-potential linearized aug-mented plane wave (LAPW) method within density functional theory. From the self-consistent charge density distribution the EFG is obtained without further approximations by numerically solving Poisson's equation. The dependence of the EFG on structure, chemical composition or substitution is demonstrated for the diborides MB2 (with M = Ti, V, Cr, Zr, Nb, Mo, and Ta), the hexaborides (CaB6, SrB6 and BaB6) and boron carbide which is closely related to α-boron.

Fixed Wand Electronic Flame-Off for Ball Formation in the Wire Bonding Process

1994 ◽  
Vol 116 (3) ◽  
pp. 212-219 ◽  
Author(s):  
Wei Qin ◽  
Ira M. Cohen ◽  
P. S. Ayyaswamy
Keyword(s):  
Electric Field ◽  
Electrostatic Field ◽  
Wire Bonding ◽  
Bonding Process ◽  
The Self ◽  
Wire Length ◽  
Ball Bond ◽  
Self Consistent ◽  
The Wire ◽  
Wire Deflection

In the latest generation of wire bonders, the cycle is so short that the wand electrode is kept stationary and the electronic flame off (EFO) discharge is from the side of the wire. This is the discharge that heats and melts the wire causing roll up into a ball that is pressed down onto the chip to form a ball bond. The balls must be perfectly formed with defects in the few ppm range. In the first part of the paper, the fixed, conically shaped side wand and the improved ring wand design are studied by considering the electrostatic field before the breakdown. In the second part of the paper, discharge development starting from the initial electrostatic field between a wire and a ring wand up to the breakdown, and ionization growth in the gap between the electrodes are both examined by numerical simulations. In the computations, the conservation equations for ions and electrons and Poisson’s equation have been employed for the self-consistent electric field. Based on sensitivity to wire length and wire deflection, the results show that the ring wand is a better design than the conical side wand electrode for ball formation and wire bonding. Also, positive wire polarity is preferred over negative wire polarity.

scholarly journals Plasma Parameters around a Chain-Like Structure of Dust Particles in an External Electric Field

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 3846
Author(s):  
Mikhail Salnikov ◽  
Alexander Fedoseev ◽  
Gennadiy Sukhinin
Keyword(s):  
Electric Field ◽  
External Electric Field ◽  
Electric Potential ◽  
Mean Free Path ◽  
The Self ◽  
Dust Particles ◽  
Charged Dust ◽  
Plasma Parameters ◽  
Self Consistent ◽  
A Chain

The formation of a 1D chain-like structure of dust particles in a low-temperature argon plasma was studied. A new numerical model for calculation of the self-consistent spatial distribution of plasma parameters around a chain of dust particles was presented. The model described the motion of positively charged ions in the electric potential of several negatively charged dust particles, taking into account the action of an external electric field. The main advantage of the model was that the charges of the dust particles and the interparticle distances were determined self-consistently. As a result of numerical simulations, the dependencies of the spatial distributions of the plasma parameters (the densities of electrons and ions and the self-consistent electric potential) near the dust particles chain on the strength of the external electric field, an external force acted on the last particle, and the mean free path of the ions was determined. The obtained results made it possible to describe the process of the formation of chain-like structures of dust particles in discharge plasma.

Velocity of transverse sound oscillations in the metals

2021 ◽  
Author(s):  
Anton Stupka ◽  
Olena Kovalchuk
Keyword(s):  
Electric Field ◽  
Fermi Gas ◽  
The Self ◽  
Internal Electric Field ◽  
Sound Waves ◽  
Jellium Model ◽  
Self Consistent ◽  
Shear Elasticity ◽  
Field Correlation ◽  
Transverse Sound

The Bohm–Staver description of sound waves in metals in the jellium model is generalized by taking into account not only the self-consistent electric field but also the second correlation moment of internal electric field that provides shear elasticity. The system of linearized equations that contains the second correlation moment of the field as a new variable is built. The wave equation is worked out and the velocities of longitudinal and transverse sound are found. The estimation of the field correlation value through the sublimation heat and the electronic Fermi-gas energy is offered for the metals. The velocities of transverse sound are found, which matches well the velocity obtained from the shear modules.

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