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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 is a predominant heat mechanism for heat generation in integrated circuits ^{ [1] } and is an undesired effect.

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

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 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.

**Acoustic theory** is a scientific field that relates to the description of sound waves. It derives from fluid dynamics. See acoustics for the engineering approach.

The **heat equation** is a parabolic partial differential equation that describes the distribution of heat in a given region over time.

In fluid dynamics, the **Boussinesq approximation** is used in the field of buoyancy-driven flow. It ignores density differences except where they appear in terms multiplied by g, the acceleration due to gravity. The essence of the Boussinesq approximation is that the difference in inertia is negligible but gravity is sufficiently strong to make the specific weight appreciably different between the two fluids. Sound waves are impossible/neglected when the Boussinesq approximation is used since sound waves move via density variations.

In thermodynamics, the **Onsager reciprocal relations** express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists.

The **Einstein–Hilbert action** in general relativity is the action that yields the Einstein field equations through the principle of least action. With the (− + + +) metric signature, the gravitational part of the action is given as

A **radiation zone**, or **radiative region** is a layer of a star's interior where energy is primarily transported toward the exterior by means of radiative diffusion and thermal conduction, rather than by convection. Energy travels through the radiation zone in the form of electromagnetic radiation as photons.

The **magnetic Reynolds number** (**R _{m}**) is the magnetic analogue of the Reynolds number, a fundamental dimensionless group that occurs in magnetohydrodynamics. It gives an estimate of the relative effects of advection or induction of a magnetic field by the motion of a conducting medium, often a fluid, to magnetic diffusion. It is typically defined by:

**Opacity** is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc. An **opaque** object is neither transparent nor translucent. When light strikes an interface between two substances, in general some may be reflected, some absorbed, some scattered, and the rest transmitted. Reflection can be diffuse, for example light reflecting off a white wall, or specular, for example light reflecting off a mirror. An opaque substance transmits no light, and therefore reflects, scatters, or absorbs all of it. Both mirrors and carbon black are opaque. Opacity depends on the frequency of the light being considered. For instance, some kinds of glass, while transparent in the visual range, are largely opaque to ultraviolet light. More extreme frequency-dependence is visible in the absorption lines of cold gases. Opacity can be quantified in many ways; for example, see the article mathematical descriptions of opacity.

**Lattice Boltzmann methods (LBM)** is a class of computational fluid dynamics (CFD) methods for fluid simulation. Instead of solving the Navier–Stokes equations, the discrete Boltzmann equation is solved to simulate the flow of a Newtonian fluid with collision models such as Bhatnagar–Gross–Krook (BGK). By simulating streaming and collision processes across a limited number of particles, the intrinsic particle interactions evince a microcosm of viscous flow behavior applicable across the greater mass.

**Nonlinear acoustics** (NLA) is a branch of physics and acoustics dealing with sound waves of sufficiently large amplitudes. Large amplitudes require using full systems of governing equations of fluid dynamics and elasticity. These equations are generally nonlinear, and their traditional linearization is no longer possible. The solutions of these equations show that, due to the effects of nonlinearity, sound waves are being distorted as they travel.

**HydroGeoSphere** (**HGS**) is a 3D control-volume finite element groundwater model, and is based on a rigorous conceptualization of the hydrologic system consisting of surface and subsurface flow regimes. The model is designed to take into account all key components of the hydrologic cycle. For each time step, the model solves surface and subsurface flow, solute and energy transport equations simultaneously, and provides a complete water and solute balance.

The **convection–diffusion equation** is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. Depending on context, the same equation can be called the **advection–diffusion equation**, **drift–diffusion equation**, or **(generic) scalar transport equation**.

**Diffusion** is the net movement of molecules or atoms from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in chemical potential of the diffusing species.

In fluid dynamics, the **mild-slope equation** describes the combined effects of diffraction and refraction for water waves propagating over bathymetry and due to lateral boundaries—like breakwaters and coastlines. It is an approximate model, deriving its name from being originally developed for wave propagation over mild slopes of the sea floor. The mild-slope equation is often used in coastal engineering to compute the wave-field changes near harbours and coasts.

**Relativistic heat conduction** refers to the modelling of heat conduction in a way compatible with special relativity. This article discusses models using a wave equation with a dissipative term.

**Double diffusive convection** is a fluid dynamics phenomenon that describes a form of convection driven by two different density gradients, which have different rates of diffusion.

Computational Fluid Dynamics (CFD) modeling and simulation for phase change materials (PCMs) is a technique to analyze the performance and behavior of PCMs. The CFD models have been successful in studying and analyzing the air quality, natural ventilation and stratified ventilation, air flow initiated by buoyancy forces and temperature space for the systems integrated with PCMs. Simple shapes like flat plates, cylinders or annular tubes,fins, macro- and micro-encapsulations with containers of different shape are often modeled in CFD software's to study.

Fins are extensions on exterior surfaces of objects that increase the rate of heat transfer to or from the object by increasing convection. This is achieved by increasing the surface area of the body, which in turn increases the heat transfer rate by a sufficient degree. This is an efficient way of increasing the rate, since the alternative way of doing so is by increasing either the heat transfer coefficient or the temperature gradient. Clearly, changing the shape of the bodies is more convenient. Fins are therefore a very popular solution to increase the heat transfer from surfaces and are widely used in a number of objects. The fin material should preferably have high thermal conductivity. In most applications the fin is surrounded by a fluid in motion, which heats or cools it quickly due to the large surface area, and subsequently the heat gets transferred to or from the body quickly due to the high thermal conductivity of the fin. For optimal Heat transfer performance with minimal cost, the dimensions and shape of the fin have to be calculated for specific applications, and this is called design of a fin. A common way of doing so is by creating a model of the fin and then simulating it under required service conditions.

- ↑ 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.

The **International Standard Book Number** (**ISBN**) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.

**OCLC Online Computer Library Center, Incorporated** d/b/a **OCLC** is an American nonprofit cooperative organization "dedicated to the public purposes of furthering access to the world's information and reducing information costs". It was founded in 1967 as the **Ohio College Library Center**. OCLC and its member libraries cooperatively produce and maintain WorldCat, the largest online public access catalog (OPAC) in the world. OCLC is funded mainly by the fees that libraries have to pay for its services. OCLC also maintains the Dewey Decimal Classification system.

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