The heat dissipation in

integrated circuits An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components a ...

problem has gained an increasing interest in recent years due to the miniaturization of

semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...

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 Joule heating (also known as resistive heating, resistance heating, or Ohmic heating) is the process by which the passage of an electric current through a conductor (material), conductor produces heat. Joule's first law (also just Joule's law), ...

is a predominant heat mechanism for heat generation in integrated circuitsT. 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 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

Where

\kappa

is the

thermal conductivity The thermal conductivity of a material is a measure of its ability to heat conduction, conduct heat. It is commonly denoted by k, \lambda, or \kappa and is measured in W·m−1·K−1. Heat transfer occurs at a lower rate in materials of low ...

\rho

is the density of the medium,

C

is the specific heat :

k=\frac \,

the

thermal diffusivity In thermodynamics, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It is a measure of the rate of heat transfer inside a material and has SI, SI units of m2/s. It is an intensive ...

and

g

is the rate of heat generation per unit volume. Heat diffuses from the source following equation ( q:diffusion and solution in a

homogeneous Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, i ...

medium of ( q:diffusion has a

Gaussian distribution In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real number, real-valued random variable. The general form of its probability density function is f(x ...

Joule heating

Propagation

See also

References

Further reading