*(This article was featured in an issue of Qpedia Thermal e-Magazine, an online publication dedicated to the thermal management of electronics. To get the current issue or to look through the archives, visit http://www.qats.com/Qpedia-Thermal-eMagazine.)*

Microelectronics components are experiencing ever-growing power dissipation and heat fluxes. This is due to dramatic gains in their performance and functionality. To cope with the heat issues of tomorrow’s technology, more efficient cooling systems will be required. It should be noted that as computer systems continue to compact, the components adjacent to the processors are experiencing an increase in power dissipation.

As a result, ambient temperatures local to the microprocessor heat sinks have increased, and temperatures in excess of 45°C have been reported. [1] Improvements are needed in all aspects of the cooling solution design, i.e., packaging, thermal interfaces, and air-cooled heat sinks. The article discusses the use of vapor chamber technology as a heat spreader to help cool high-power devices.

**Introduction**

Spreading resistances exist whenever heat flows from one region to another in a different cross-sectional area. For example, with high performance devices, spreading resistance occurs in the base plate when a heat source with a smaller footprint is mounted on a heat sink with a larger base plate area. The result is a higher temperature where the heat source is placed.

The impact of spreading resistance on a heat sink’s performance must not be ignored in the design process. One way to reduce this added resistance is to use highly conductive material, such as copper, instead of aluminum. Other solutions include using heat pipes, vapor chambers, liquid cooling, micro thermoelectric cooling, and the recently developed forced thermal spreader from Advanced Thermal Solutions, Inc. (ATS).

In the case of vapor chambers (VC), the general perception has been that phase change technologies provide more effective thermal conductivity than solid metals. The spreading resistance of the base for both solid metal and conventional VC heat spreaders is defined as:

Where T_{s} [°C] is the temperature of the hottest point on the base, and T_{b,top} [°C] is the average temperature of the base top surface. [1]

Table 1 shows the thermal conductivity of different materials in spreading the heat at the base. Heat pipes and VC emerged as the most promising technologies and cost effective thermal solutions due to their excellent uniform heat transfer capability, high efficiency, and structural simplicity. Their many advantages compared to other thermal spreading devices are that they have simple structures, no moving parts, allow the use of larger heat sinks, and do not use electricity. This article’s emphasis is on vapor chambers.

*Is a heat pipe considered a material? Should we include vapor chambers in this table?*

The principle of operation for VC is similar to that of heat pipes. Both are heat spreading devices with highly effective thermal conductivity due to phase change phenomena. A VC is basically a flat heat pipe that can be part of the base of a heat sink. Figure 1 shows the schematics of a typical heat pipe and VC. [2]

A VC is a vacuum vessel with a wick structure lining its inside walls. The wick is saturated with a working fluid. The choice of this fluid is based on the operating temperature of the application. In a CPU application, operating temperatures are normally in the range of 50-100°C. At this temperature range water is the best working fluid. [3]

As heat is applied, the fluid at that location immediately vaporizes and the vapor rushes to fill the vacuum. Wherever the vapor comes into contact with a cooler wall surface it condenses, releasing its latent heat of vaporization. The condensed fluid returns to the heat source via capillary action, ready to be vaporized again and repeat the cycle.

The capillary action of the wick enables the VC to work in any orientation, though its optimum performance is orientation dependent. The pressure drop in the vapor and the liquid determines the capillary limit or the maximum heat carrying capacity of the heat pipe. [4] For electronics applications, a combination of water and sintered copper powder is used. [2]

A VC, as shown in Fig.1 (b), is different from a heat pipe in that the condenser covers the entire top surface of the structure. In a VC, heat transfers in two directions and is planar. In a heat pipe, heat transmission is in one direction and linear.

The VC has a higher heat transfer rate and lower thermal resistance. In the two-phase VC device, the rates of evaporation, condensation, and fluid transport are determined by the VC’s geometry and the wicks’ structural properties. These properties include porosity, pore size, permeability, specific surface area, thermal conductivity, and the surface wetability of the working fluid. [5] Thermal properties of the wick structure and the vapor space are described in the next section.

**Effective Thermal Conductivity**

*Wick Structure*

Heat must be supplied through the water-saturated wick structure, at the liquid-vapor interface, for the evaporation process to happen. With water and sintered copper powder, the water becomes a thermal barrier due to its much lower thermal conductivity compared with the copper. [2]

There are several ways to compute the effective thermal conductivity of the wick structure.

For parallel assumption:

For serial assumption:

For sintered wick structure, Maxwell gives: [2]

Chi gives: [2]

Where:

In the equations above, K_{l} and K_{s} are the thermal conductivities of water and copper, respectively, ε is the porosity of the wick, r_{c} and r_{s} are the contact radius (or effective capillary radius) and the particle sphere radius, respectively.

Table 2 shows a comparison of effective thermal conductivity (W/m°C) for the wick using equations 2—5. It appears that Equation 5 gives a more realistic value. This is also the typical value used in Vadakkan et al. [6]

*Vapor Space*

Effective thermal conductivity for vapor chambers used in remote cooling applications has been derived from Prasher [4], based on the ideal gas law, and from the Clapeyron equation for incompressible laminar flow conditions.

Where H_{fg} is the heat of vaporization (J/Kg), P is pressure (N/m^{2}), ρ is density (kg/m^{3}), d is the vapor space thickness (mm), R is the gas constant per unit mass (J/K.Kg), μ is the dynamic viscosity (N.s/m^{2}), and T is the vapor temperature (°C).

As shown in Equation 7, effective thermal conductivity is a function of thermodynamic properties and vapor space thickness. Larger vapor space thickness reduces the flow pressure drop, and thus increases the effective thermal conductivity. Note that the effective thermal conductivity is relatively low at low temperatures. This has significant implications for low heat flux applications or start-up conditions [2].

**Drawbacks**

There are a few drawbacks to using a VC instead of solid copper. Some VC have a power limit of 500 watts. Exceeding this temperature might cause a dry out and could increase the vapor temperature and pressure.

An increase in internal pressure can deform the VC surfaces or cause leakage from the welding joints. Other factors to be addressed include cost, availability, and in special cases, the vapor chamber’s manufacturability.

**When to Use a Vapor Chamber**

The early design stages are when to decide if it makes sense to use a heat pipe/VC instead of copper or other solid materials to better spread heat. To predict the minimum thermal spreading resistance for a VC, a simplified model was developed by Sauciuc et al. [1]. Their model assumes that the minimum VC spreading resistance θ_{sp} is approximately the same as the evaporator (boiling) resistance θ_{ev}.

Here, h_{ev} [W/m^{2}K] is the boiling heat transfer coefficient and A_{ev} [m^{2}] is the area of the evaporator (heat input area). It is also assumed that the boiling regime inside the VC is nucleate pool boiling. This is a conservative assumption, since in reality the spreading resistance in a VC is greater than just the boiling resistance. If the spreading resistance calculated from this simplified model is higher than that of a solid copper base, then a VC should not be used. [1]

The boiling model is based on Rohsenow’s equation for nucleate pool boiling on a metal surface, and is given by: [7]

Where μ_{f} is the dynamic viscosity of the liquid, h_{fg} is the latent heat, g(ρ_{f} – ρ_{g}) is the body force arising from the liquid-vapor density difference, σ is the surface tension, c_{p,f} is the specific heat of liquid, C_{s,f} and n are constants that depend on the solid-liquid combination, Pr_{f} is the liquid’s Prandtl number, and ΔT = [T_{s} – T_{sat}], which is the difference between the surface and saturation temperatures.

It can be seen that the heat flux is mainly a function of fluid properties, surface properties, and the fluid/material combination, and that superheat is required for boiling. For electronics cooling applications, it is widely accepted that water/copper is the optimum combination for VC fabrication [1].

The evaporator heat transfer coefficient definition is:

The ratio of phase change spreading over copper spreading can be estimated for the base of conventional rectangular heat sinks using Rohensaw’s equation and conventional modeling tools, Figure 2 from [1] shows the relationship of this ratio versus base thickness (solid metal heat sink only) for different footprint sizes. The heat input area is kept constant for this plot. This figure shows that for spreading resistance ratios greater than 1.0, the ratio decreases with increasing condenser size.

This implies that the VC type base is better situated for larger condenser sizes. The figure also indicates that ratio 1.0 occurs at greater base thickness for larger condensers. For example, with a 200×200 mm footprint, a VC would outperform a corresponding copper base heat sink (with a thickness of 10 mm or less). However, with a 50×50 mm footprint the sink’s base thickness would have to be less than about 2.5 mm for the VC to make the same claim. [1]

Figure 2 also shows that there is a “worse case point” when comparing the thermal performance of a VC and a solid copper base heat sink. This is identified by the maximum in the curve for the 50×50 mm footprint at a base thickness of 10 mm. At this point the spreading resistance ratio is at its largest value, which indicates the worst performance for the VC (when compared with the corresponding solid copper base). In general, there will be a maximum base thickness (dependent on heat source size and footprint) in considering a VC base.

Unless weight is a major concern, with a base thickness above this maximum, a VC base should not be considered. Conversely, for a heat sink base thickness below this maximum, a VC base is a viable option.

**Summary**

Although a VC enhances heat spreading through high effective thermal conductivity, some modeling needs to be considered early in the design stage. Because a VC is a liquid filled device, cautions need to be exercised in its deployment in electronics. The dry out or loss of liquid due to poor manufacturing will render the VC as a hollow plate, thus adversely impacting device thermal performance.

In some situations as shown earlier, a solid copper base might provide better spreading of heat without the potential pitfalls of a VC.

**References:**

1. Sauciuc, I. Chrysler, G., Mahajan, Ravi, and Prasher, Ravi, “Spreading in the Heat Sink Base: Phase Change Systems or Solid Metals?”, IEEE Transactions on Components and Packaging Technologies, December 2002, Vol. 25, No. 4.

2. Wei, X., Sikka, K., Modeling of Vapor Chamber as Heat Spreading Devices, 10th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronics Systems, 2006.

3. Wuttijumnong, V., Nguyen, T., Mochizuki, M., Mashiko, K., Saito, Y., and Nguyen, T., Overview Latest Technologies Using Heat Pipe and Vapor Xhamber for Cooling of High Heat Generation Notebook Computer, Twentieth Annual IEEE Semiconductor Thermal Measurement and Management Symposium, 2004.

4. Prasher, R, A Simplified Conduction Based Modeling Scheme for Design Sensitivity Study of Thermal Solution Utilizing Heat Pipe and Vapor Chamber Technology, Journal of Electronic Packaging, Transactions of the ASME, 2003, Vol. 125, No. 3.

5. Lu, M., Mok, L., Bezama, R. A Graphite Foams Based Vapor Chamber for Chip Heat Spreading, Journal of Electronic Packaging, December 2006.

6. Vadakkan, U., Chrysler, G., and Sane, S., Silicon/Water Vapor Chamber as Heat Spreaders for Microelectronic Packages, IEEE SEMI-THERM Symposium, 2005.

7. Incropera, F., Dewitt, D., Bergman, T., and Lavine, A., Introduction to Heat Transfer, Wiley, Fifth Edition, 2007.

*For more information about Advanced Thermal Solutions, Inc. (ATS) thermal management consulting and design services, visit www.qats.com or contact ATS at 781.769.2800 or ats-hq@qats.com.*

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