An Advancement in Transistor Second Breakdown Performance Using Molybdenum Metalization

Hakim, Edward B.

doi:10.1109/tr.1968.5217505

Cited by 8 publications

(11 citation statements)

References 4 publications

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“…The derivatives over position will have an index x, derivatives without an index are over momenta. We can take the limit m → 0 of the operator (10). Then, the limit m → 0 of eq.…”

Section: Linear Diffusion Of Particles Without Spinmentioning

confidence: 99%

“…The linear relativistic diffusions have been studied for a long time (see the reviews [7] [8]). It has been shown a long time ago that Markovian relativistic diffusion in the configuration space does not exist [9] [10]. The relativistic diffusion (preserving the mass-shell) of a massive particle on the phase space has been defined and studied by Schay [11] and Dudley [12].…”

Section: Introductionmentioning

confidence: 99%

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Non-linear relativistic diffusions

Haba¹

2011

Physica A: Statistical Mechanics and its Applications

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We obtain a non-linear generalization of the relativistic diffusion. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics.We show that the assumptions of the relativistic invariance and an interpretation of the solution as a probability distribution substantially restrict the class of admissible non-linear diffusion equations. We consider relativistic invariant as well as covariant frame-dependent diffusion equations with a drift. In the latter case we show that there can exist stationary solutions of the diffusion equation besides the equilibrium solution corresponding to the quantum or Tsallis distributions. We define the relative entropy as a function of the diffusion probability and prove that it is monotonically decreasing in time when the diffusion tends to the equilibrium. We discuss its relation to the thermodynamic behavior of diffusing particles .

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“…The derivatives over position will have an index x, derivatives without an index are over momenta. We can take the limit m → 0 of the operator (10). Then, the limit m → 0 of eq.…”

Section: Linear Diffusion Of Particles Without Spinmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-linear relativistic diffusions

Haba¹

2011

Physica A: Statistical Mechanics and its Applications

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“…One example is afforded by second breakdown effects, where it has been shown that a higher melting metalliza- tion system imparts greater protection against catastrophic failures from second breakdown [86]. On this basis, aluminum would have limitations relative to very high melting systems, but would be superior to systems in which the gold-silicon eutectic (melting point 370°C) can form.…”

Section: )mentioning

confidence: 99%

Aluminum metallization—Advantages and limitations for integrated circuit applications

Schnable¹,

Keen²

1969

Proc. IEEE

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The advantages and limitations of aluminum metallization are reviewed and compared with other systems used for integrated circuits. Metallization system properties of particular importance are summarized, including initial physical and chemical properties of the system which define potential performance and reliability considerations. The special requirements for M O S arrays and for multilevel-metallized integrated circuits are described.Recently available knowledge of aluminum metallization process technology and of metallization-related failure mechanisms is^ reviewed, and new results of experimental studies are presented. It is concluded that aluminum will continue to be the most widely used metallization material, not only for single-level metallized integrated circuits, but also for multilevel LSI arrays.

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“…The mathematical theory of a relativistic diffusion is not so well developed as the non-relativistic one (see the reviews in [13] [14]). A relativistic diffusion in the configuration space does not exist [15] [16]. If the diffusing particle has a fixed mass then an analog of the Kramers diffusion (on the phase space) without friction is uniquely determined.…”

Section: Introductionmentioning

confidence: 99%

Relativistic diffusive motion in thermal electromagnetic fields

Haba

2013

J. Phys. A: Math. Theor.

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We discuss relativistic dynamics in a random electromagnetic field which can be considered as a high temperature limit of the quantum electromagnetic field in a heat bath (cavity) moving with a uniform velocity w. We derive a diffusion approximation for particle's dynamics generalizing the diffusion of Schay and Dudley. It is shown that Jüttner distribution is the equilibrium state of the diffusion.

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An Advancement in Transistor Second Breakdown Performance Using Molybdenum Metalization

Cited by 8 publications

References 4 publications

Non-linear relativistic diffusions

Non-linear relativistic diffusions

Aluminum metallization—Advantages and limitations for integrated circuit applications

Relativistic diffusive motion in thermal electromagnetic fields

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