# Heat generation in integrated circuits

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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.

A semiconductor material has an electrical conductivity value falling between that of a metal, like copper, gold, etc. and an insulator, such as glass. Their resistance decreases as their temperature increases, which is behaviour opposite to that of a metal. Their conducting properties may be altered in useful ways by the deliberate, controlled introduction of impurities ("doping") into the crystal structure. Where two differently-doped regions exist in the same crystal, a semiconductor junction is created. The behavior of charge carriers which include electrons, ions and electron holes at these junctions is the basis of diodes, transistors and all modern electronics. Some examples of semiconductors are silicon, germanium, and gallium arsenide. After silicon, gallium arsenide is the second most common semiconductor used in laser diodes, solar cells, microwave frequency integrated circuits, and others. Silicon is a critical element for fabricating most electronic circuits.

## 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.

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

Where ${\displaystyle \kappa }$ is the thermal conductivity, ${\displaystyle \rho }$ is the density of the medium, ${\displaystyle C}$ is the specific heat

The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by , , or .

${\displaystyle k={\frac {\kappa }{\rho C}}\,}$

the thermal diffusivity and ${\displaystyle g}$ 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.

In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It measures the rate of transfer of heat of a material from the hot end to the cold end. It has the SI derived unit of m²/s. Thermal diffusivity is usually denoted α but a,h,κ, K, and D are also used. The formula is:

Miniaturizing components has always been a primary goal in the semiconductor industry because it cuts production cost and lets companies build smaller computers and other devices. Miniaturization, however, has increased dissipated power per unit area and made it a key limiting factor in integrated circuit performance. Temperature increase becomes relevant for relatively small-cross-sections wires, where it may affect normal semiconductor behavior. Besides, since the generation of heat is proportional to the frequency of operation for switching circuits, fast computers have larger heat generation than slow ones, an undesired effect for chips manufacturers. This article summaries physical concepts that describe the generation and conduction of heat in an integrated circuit, and presents numerical methods that model heat transfer from a macroscopic point of view.

The thermal design power (TDP), sometimes called thermal design point, is the maximum amount of heat generated by a computer chip or component that the cooling system in a computer is designed to dissipate under any workload.

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## 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
• Ogrenci-Memik, Seda (2015). Heat Management in Integrated circuits: On-chip and system-level monitoring and cooling. London, United Kingdom: The Institution of Engineering and Technology. ISBN   9781849199353. OCLC   934678500.

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