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Electromigration (red arrow) is due to the momentum transfer from the electrons moving in a wire. Electromigration is the transport of material caused by the gradual movement of the ions in a conductor due to the momentum transfer between conducting electrons and diffusing metal atoms.
Black's Equation is a mathematical model for the mean time to failure (MTTF) of a semiconductor circuit due to electromigration: a phenomenon of molecular rearrangement (movement) in the solid phase caused by an electromagnetic field. The equation is: [1] = ()
Tractrix with object initially at (4, 0). Suppose the object is placed at (a, 0) and the puller at the origin, so that a is the length of the pulling thread. (In the example shown to the right, the value of a is 4.)
The Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It extends Fick's law of diffusion for the case where the diffusing particles are also moved with respect to the fluid by electrostatic forces.
Feedback-controlled electromigration (FCE) is an experimental technique to investigate the phenomenon known as electromigration. By controlling the voltage applied as the conductance varies it is possible to keep the voltage at a critical level for electromigration .
[1] [4] [8] Physically speaking this means that the main part of the area underneath a metallic contact through which current enters the metal via the metal-semiconductor interface is given by the transfer length multiplied with the width of the pad . This situation is also depicted in the figure in this section where the current density ...
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
Historically, engineering mathematics consisted mostly of applied analysis, most notably: differential equations; real and complex analysis (including vector and tensor analysis); approximation theory (broadly construed, to include asymptotic, variational, and perturbative methods, representations, numerical analysis); Fourier analysis; potential theory; as well as linear algebra and applied ...