# Understanding Thermal Conductivity

Thermal Conductivity: A measure of the ability of a material to transfer heat. Given two surfaces on either side of a material with a temperature difference between them, the thermal conductivity is the heat energy transferred per unit time and per unit surface area, divided by the temperature difference [1].

Thermal conductivity is a bulk property that describes the ability of a material to transfer heat. In the following equation, thermal conductivity is the proportionality factor k. The distance of heat transfer is defined as †x, which is perpendicular to area A. The rate of heat transferred through the material is Q, from temperature T1 to temperature T2, when T1>T2 [2].

Figure 1. Conduction heat transfer process from hot (T1) to cold (T2) surfaces

Thermal conductivity of materials plays a significant role in the cooling of electronics equipment. From the die where the heat is generated to the cabinet where the electronics are housed, conduction heat transfer and, subsequently, thermal conductivity are the integral components of the overall thermal management process.

The path of heat from the die to the outside environment is a complicated process that must be understood when designing a thermal solution. In the past, many devices were able to operate without requiring an external cooling device like a heat sink. In these devices, the conduction resistance from the die to the board needed to be optimized, as the primary heat transfer path was into the PCB. As power levels increased, heat transfer solely into the board became inadequate (credit shakita). Much of the heat is now dissipated directly into the environment through the top surface of the component. In these new higher-powered devices, low junction-to-case resistance is important, as is the design of the attached heat sink.

To determine the importance of material thermal conductivity in a specific thermal management application (e.g. a heat sink), it is important to separate the overall thermal resistance associated with conduction heat transfer into three parts: interfacial, spreading, and conduction resistances.

• An interface material enhances the thermal contact between imperfect mating surfaces. A highly thermally conductive material, with good surface wetting ability, will reduce interfacial resistance.
• Spreading resistance is used to describe the thermal resistance associated with a small heat source coupled to a larger heat sink. Among other factors, the thermal conductivity of the base of the heat sink directly impacts spreading resistance.
• Conduction resistance is a measure of the internal thermal resistance in a heat sink as heat travels from the base to the fins, where it dissipates into the environment. In regard to heat sink design, conduction resistance is less important in natural convection and low air flow conditions, becoming more important as flow rates increase.

Common units of thermal conductivity are W/mK and Btu/hr-ft-oF.

Figure 2. Thermal conductivity for silicon thin film [3].

In the electronics industry, the constant push for smaller size and faster speeds has considerably reduced the scale of many components. As this transition now continues from the macro- to micro-scale, it is important to consider the effects on thermal conductivity and not to assume the bulk property is still accurate. Continuum-based Fourier equations cannot predict thermal characteristics at these smaller scales. More complete methods, such as the Boltzmann transport equation and the lattice Boltzmann method, are needed [3].

The effect of thickness on conductivity can be seen in Figure 2. The material characterized is silicon, which is widely used in electronics.

Figure 2. Thermal conductivity for silicon thin film [3]

Like many physical properties, thermal conductivity can be anisotropic depending on the material (directionally dependent). Crystalline and Graphite are two examples of such materials. Graphite has been used in the electronics industry where its high in-plane conductivity is valuable. Graphite crystals have very high in-plane conductivity (~2000 W/mK), due to the strong carbon-to-carbon bonding on their basal plane. The parallel basal planes are weakly bonded to each other, however, and the thermal conductivity perpendicular to these planes is quite low (~10 W/mK) [4].

Thermal conductivity is not only affected by changes in thickness and orientation;temperature also has an effect on the overall magnitude. Because of the material temperature increase, the internal particle velocity increases and so does thermal conductivity. This increased velocity transfers heat with less resistance. The Wiedemann-Franz law describes this behavior by correlating thermal and electrical conductivity to temperature. It is important to note that the effect of temperature on thermal conductivity is non-linear and hard to predict without prior research. The graphs below show the behavior of thermal conductivity over wide temperature ranges. Both of these materials, aluminum nitride and silicon, are used extensively in electronics (Figures 3 and 4, respectively).

In the future, higher-powered processors with multiple cores will push the need for improved thermal conductivity even further. Therefore, it is worthwhile to also investigate other areas of research and development in thermal conductivity enhancement for existing material used in electronics packages. One such area is the effect of nanotechnology on thermal conductivity, where carbon nanotubes have shown conductivity values near those of diamond due to large phonon-mean-free paths [7]. Development of new materials, and enhancement of existing materials, will result in more effective thermal management, as device power dissipation is on the steady rise.

References:

1. Thermal Conductivity, American Heritage Science Dictionary, Houghton Mifflin Company

2. Moran, M. and Shapiro, H., Fundamentals of Engineering Thermodynamics, p 47, 1988

3. Ghai, S., Kim, W., Chung, P., Amon, C., Jhon, M., Anisotropic Thermal Conductivity of Nanoscale Confined Thin Films Via Lattice Boltzmann, Chemical Engineering, Carnegie Mellon University, Nov. 2006

4. Norley, J., The Role of Natural Graphite in Electronics Cooling, Electronics Cooling, August 2001

5. Slack, G.A., Tanzilli R.A., Pohl R.O., Vandersande J.W.,J. Phys. Chem. Solids 48, 7 (1987), 641-647

6. Glassbrenner, C. and Slack, G., Thermal Conductivity of Silicon and Germanium from 3Â°K to the Melting Point, Physical Review 134, 4A, 1964

7. Berber, S., Kwon, Y., and Tomanek, D., Unusually High Thermal Conductivity of Carbon Nanotubes, Physical Review Letters, Vol 84, No 20, pp 4613-4616, 2000

### 3 responses to “Understanding Thermal Conductivity”

1. Michael Farrell

Is it a ‘no brainer’ to use copper for a cold plate and its internal tubing (fed by a recirculating chiller)?

• From our engineering team, “While copper obviously has better thermal conductivity than aluminum, it is far from a “no-brainer” for a number of reasons. Most cold plates on the market use copper tubes, but aluminum base plates. As far as the plate goes, some reasons to use aluminum include lower cost, lighter weight, and better machinability. Depending on the application, the difference between copper and aluminum might only be a few degrees, so you really have to do the cost/benefit analysis to see whether or not a copper base would be worth it.”

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