Hadwiger conjecture (combinatorial geometry): Difference between revisions
en>Dcljr + {see also} pointing to Hadwiger conjecture (graph theory) |
en>David Eppstein Undid revision 529816265 by Balzakomos (talk) source? |
||
| Line 1: | Line 1: | ||
{{underlinked|date=October 2012}} | |||
{{Expert-subject|Electronics|date=March 2009}} | |||
The heat dissipation in [[integrated circuits]] problem has gained an increasing interest in recent years due to the miniaturization of [[semiconductor]] devices. The temperature increase becomes relevant for cases of relatively small-cross-sections wires, because such temperature increase may affect the normal behavior of semiconductor devices. | |||
==Joule Heating== | |||
[[Joule Heating]] is a predominant heat mechanism for heat generation in integrated circuits <ref name="test">T. Bechtold, E. V. Rudnyi and J. G Korvink, "Dynamic electro-thermal simulation of microsystems—a review," Journal of Micromechanics and Microengineering. vol. 15, pp. R17–R31, 2005</ref> and is an undesired effect. | |||
==Propagation== | |||
The governing equation of the physics of the problem to be analyzed is the heat diffusion equation. It relates the flux of heat in space, its variation in time and the generation of power. | |||
:<math>\nabla\left(\kappa\nabla T\right)+g=\rho C\frac{\partial T}{\partial t}</math> | |||
Where <math>\kappa</math> is the [[thermal conductivity]], <math>\rho</math> is the density of the medium, <math>C</math> is the specific heat | |||
: <math>k=\frac{\kappa}{\rho C} \,</math> | |||
the [[thermal diffusivity]] and <math>g</math> is the rate of heat generation per unit volume. Heat diffuses from the source following equation ([eq:diffusion]) and solution in an [[homogeneous]] medium of ([eq:diffusion]) has a [[Gaussian distribution]]. | |||
==See also== | |||
*[[Thermal simulations for Integrated Circuits]] | |||
==References== | |||
<references/> | |||
{{DEFAULTSORT:Heat Generation In Integrated Circuits}} | |||
[[Category:Integrated circuits]] | |||
Revision as of 18:15, 26 December 2012
Template:Underlinked Template:Expert-subject
The heat dissipation in integrated circuits problem has gained an increasing interest in recent years due to the miniaturization of semiconductor devices. The temperature increase becomes relevant for cases of relatively small-cross-sections wires, because such temperature increase may affect the normal behavior of semiconductor devices.
Joule Heating
Joule Heating is a predominant heat mechanism for heat generation in integrated circuits [1] and is an undesired effect.
Propagation
The governing equation of the physics of the problem to be analyzed is the heat diffusion equation. It relates the flux of heat in space, its variation in time and the generation of power.
Where is the thermal conductivity, is the density of the medium, is the specific heat
the thermal diffusivity and is the rate of heat generation per unit volume. Heat diffuses from the source following equation ([eq:diffusion]) and solution in an homogeneous medium of ([eq:diffusion]) has a Gaussian distribution.
See also
References
- ↑ T. Bechtold, E. V. Rudnyi and J. G Korvink, "Dynamic electro-thermal simulation of microsystems—a review," Journal of Micromechanics and Microengineering. vol. 15, pp. R17–R31, 2005