Heat generation in integrated circuits

Joule heating

Joule heating is a predominant heat mechanism for heat generation in integrated circuits 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.

:\nabla\left(\kappa\nabla T\right)+g=\rho C\frac{\partial T}{\partial t}

Where \kappa is the thermal conductivity, \rho is the density of the medium, C is the specific heat : k=\frac{\kappa}{\rho C} , the thermal diffusivity and g is the rate of heat generation per unit volume. Heat diffuses from the source following equation ([eq:diffusion]) and solution in a homogeneous medium of ([eq:diffusion]) has a Gaussian distribution.

References

References

1. 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