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## Vapor Chamber Quick Calculations – Do I Need One?

In this blog, I’d like to take you through the early steps I take when determining if a two-phase device, specifically a vapor chamber, might be needed as part of the thermal solution. I’ll eventually do a complementary piece on heat pipes, but in the interest of brevity we’ll stick with a copper vapor chamber with a sintered wick and water as the working fluid.

If you’ve read some of my previous articles, you know that for the vast majority of two-phase applications where heat is being moved from the heat source to a remote condenser – heat pipes trump vapor chambers. It’s not because they’re necessarily better at moving heat. It’s because the path from the evaporator to condenser usually requires some twists and turns – not typically a strong suite of vapor chambers.

Vapor chambers, as seen above on the left, are typically used to spread heat to a local condenser/heat sink who’s required area is minimally 10 times bigger than the area of the heat source. When heat needs to be moved to a remote condenser, distances of greater than 40 or 50mm are generally required for two-phase devices to make sense.

Even before doing any calculations, I know there are several circumstances where vapor chambers are useful.

• Power densities >15 W/cm2
• Low/no air flow – requiring a larger heat sink
• Ambient temperatures above 40 oC – lowering the thermal budget
• Heat sink heat is constrained – requiring a thin base

## Step 1: Determine the Thermal Budget

Simply speaking, your thermal budget is calculated by subtracting the maximum ambient temperature in which the device will operate (Tambient) from the maximum allowable temperature of the IC case (Tcase) or in some cases the Tjunction if there isn’t a built-in spreader on the chip. Typical thermal budgets for electronic components are in the range of 30-50 oC.

Let’s assume we’ve been given a Tcase max by the manufacturer or ASIC designer of 85 oC. Further, we need our device to operate at temperatures up to 45 oC.

This leaves us with a total thermal budget of 40 oC. This means that the total of all our individual delta Ts from the case to the air cannot exceed this figure.

## Step 2: Estimate Required Heat Sink Size

Found on our website, this calculator quickly provides the overall volume of the heat sink based on heat source power, Tcase , max ambient temperature and available airflow. Obviously, if you’ve already done the detailed calcs for required heat sink size, you can skip this step.

I like to know this figure because it quickly allows me to estimate specific dimensions – allowing me to understand if the heat sink base will be substantially larger than the heat source.

We already know that our Tcase is 85 oC and our Tambient is 45 oC. This leaves a thermal budet of 40 oC.

Let’s further assume the following

Heat Source: 100W

Heat Source Size 25x25mm

Available airflow: 200 LFM

With an estimated volume of 375cm3, I can begin to make some estimates of dimensions. I’ll start by fixing the fin height to a reasonable 27mm and tacking on 3 mm for the base height. Pretty standard. Then I’ll adjust the length and wide dimensions to reach the specified volume estimate.

In this case the heat sink dimensions would be roughly 110 x 110 x 30mm.

## Step 3: Determine if you’ve got the space and airflow for a local heat sink

I can play with the dimensions mentioned earlier and compare it to the proposed system layout. Given that were talking about vapor chambers, I’m going to assume that we have the desire and space to use a local heat sink. However, if it turned out that we wanted or needed a remote heat sink whose distance between evaporator and condenser was greater than 40 or 50mm, I’d be doing a different calculation for Step 3 in order to evaluate a heat pipe solution.  As it stands for this example, we’re going to use a local sink.

## Step 4: Determine the delta-t spreading resistance in the heat sink base

First, I see that the area of the heat sink is 15 times larger than the area of the heat sink. This already suggests a vapor chamber may be in order. I also know that the total thermal budget is 40 oC. Next, I’ll use another calculator we have online to understand the spreading delta-T in the base for solid aluminum and copper as well as for a vapor chamber.

Populate the inputs with our earlier assumptions and select between an aluminum or copper base by changing the material conductivity in the calculator. Also, let’s assume the heat source is in the center of the base.

Now I’m going to use a rule of thumb to determine if a vapor chamber might be needed:

Consider a vapor chamber when the spreading resistance in a solid base is greater than 10 oC.

• The solid aluminum base in this example (not shown) has a delta-T of 34.5 o If we’ve got room we could double the base thickness, lowing the delta-T to 19 oC. But that’s almost half our thermal budget and substantially more than the 10 degree rule of thumb.
• Switching to a 3mm copper base (shown above), with a thermal conductivity of 380 W/m-K, gives us a base delta-T of 16.8 o By increasing the base thickness to 5mm, I’m within striking distance of the 10 degree rule of thumb, but it’s certainly going to increase weight and potentially decrease fin height. If these tradeoffs are acceptable later in the design process, a solid copper base might make sense.
• But, compare the 5mm solid copper base (10.7 oC) to the vapor chamber base (4.5 oC). The vapor chamber is going to be thinner, about half the weight and potentially give us other design options such as alternative TIM choices.

## Comparing our quick estimates to more lengthy calculations

As stated in the beginning of this article, this method is great for initial estimates as it gives you both the heat sink volume and a good feel for the likelihood of a vapor chamber base.

After using the same parameters as mentioned above, and fiddling with fin characteristics, I used a more sophisticated model to calculate the remaining delta-Ts.

As you can see from the above chart, using a vapor chamber puts us 3.3 degrees below our thermal budget. Note, the TIM delta-T of 4.8 oC. used thermal grease for this calculation, but I could switch to a high conductivity thermal pad (which will make the manufacturing engineers happy) and still remain below my thermal budget.

## Understanding 3D Vertical Vapor Chambers

Until the mid-2000’s heat pipes were really the only option when designing a high heat-flux heat sink whose condenser was oriented vertically above a horizontal heat source. That’s because they’re easily bent post-production into a variety of shapes including “L” or “U” configurations. Despite the advantages of vapor chambers, better spreading and less thermal resistance, these devices were for all practical purposes non-manufacturable in these shapes. Why?

A traditional vapor chamber, what we at Celsia call a two-piece design, is manufactured by stamping an upper and lower plate (thus the two-piece moniker), sintering copper powder to each side, and diffusion bonding each plate to one another on all sides.

Typical two-piece vapor chamber designs look like this:

As seen in the images above, this type of vapor chamber is customizable into virtually any shape along the X&Y planes (length and width). Additionally steps or pedestals can designed into the stamped upper and/or lower plates, making them great for recessed heat sources or those that need to conform to a surface of varying heights. But, how could a two-piece production method create a 3D vertical vapor chamber like an “L” or “U” shape? Well, it wouldn’t be easy, fast, or very cost effective.

•  First, the upper and lower plates would need to be stamped into that shape or stamped flat and bent.

•  Second, specialty L/U shaped fixtures would need to be fabricated to hold the copper powder to the walls of each plate as they’re being oven sintered, and don’t forget these fixtures will take longer to heat up increasing the overall sintering cycle time. Another potential problem here is that the fixtures need to be made such that they insure a very even distribution of copper powder across the surface and also at the bend. Variations in sintered copper can lead to lower yield rates and/or finished parts that don’t perform according to specification.

•  Third, the two plates need to be attached together either through the traditional diffusion bonding process (back into an oven) or through a four sided TIG welding process. The former is not known to work well on complex, especially bent, shapes while the latter would require an operator to manually weld all sides together.

In the 1980’s, I remember working on some military applications that overcame these issues by combining vapor chambers for the horizontal portion of the sink with integrated copper tubes for the vertical portion (see my crude drawing below L). Here we cooled two 2kW traveling wave tubes for a radar application. The second image incorporated a 75x75mm vapor chamber with a one meter fin stack for a 3kW application.

Vapor Chamber with Copper Tubes – 4kW Application (L), 3kW Application (R)

Although technically not a 3D vertical vapor chamber, this solution is excellent for very high heat-flux applications provided adequate structural support is done at the condenser/ tube areas to address shock and vibe concerns. Structural issues arise because a lot of leverage can be placed on the vertical pipes/condenser causing the copper tube braze joints to fail or cause damage to the tubes or vapor chamber itself.

So, is there a cost effective, process-optimized method of producing a true 3D vertical vapor chamber? About ten years ago, we began work on a design (manufacturing process) that in addition to cost savings provided designers with some unique options; most relevant to this article, the ability to bend it post-production to create L/U shapes.

The design we created was fairly straightforward. We call it a one-piece vapor chamber and it’s available from a growing number of suppliers.

One-Piece Vapor Chamber Bent Into Various Shapes

•  Rather than using the traditional two-piece approach beginning with upper and lower stamped plates, we start with a very large diameter copper tube to create a heat pipe of between 15-75mm OD.

•  A simple cigar shaped mandrel is inserted and copper power is layered in between it and the inside wall of the tube. This insures a very even sintering process and keeps oven cycle times to a minimum.

•  Next, the tube is flattened to the desired thickness, usually between 2-3.5mm, and a perforated wave-shaped spacer is inserted into the tube. This spacer allows the device to withstand clamping pressures up to 90psi and provides internal support for bending post-production.

•  Deionized water is added and the tube is vacuum sealed and TIG welded – only on the two narrow sides of the device. So now we have something that looks like an extremely wide flat heat pipe, but with an internal support structure.

•  Lastly, the device can be bent to form a variety of shapes including L/U configurations.

Here’s an example of a high power LED application we did in 2008. The horizontal portion of the vapor chamber makes direct contact with the heat source, eliminating a mounting block and TIM layer as would be typical with a heat pipe implementation. The vertical portions of the vapor chamber run directly into the condenser with a continuous and evenly distributed sintered copper layer along the inside wall. For the this application, vapor chamber width was only 30mm or so, but one-piece vapor chambers can be created as wide as 110mm.

One-Piece 3D Vertical Vapor Chamber – HBLED Application

In summary, a traditional two-piece design is really limited to steps or pedestals of 4-5mm in height. A flat vapor chamber with vertical copper tubes have some structural issues that need to be addressed yet are great for very high heat-flux applications. The newer one-piece vapor chamber is probably the truest form of a 3D vertical vapor chamber and offer cost savings over other designs.

## Integrating Vapor Chambers into Heatsinks

Often in high power density or low profile heat sink applications, the spreading resistances in the base of the heat sink limits the performance of the design. Once it is determined that normal heat sink materials, aluminum or copper, are either insufficient or too bulky to meet the design objectives, the obvious next step is to look at two phase spreading devices, such as heat pipes or vapor chambers.

Either technology is often an improvement in these types of applications. The use of vapor chambers offers two distinct advantages over heat pipes, direct contact to the heat source and uniform spreading in all directions.

Integrating heat sinks and vapor chambers is simpler than most people think and this integration often allows for further improvements in performance.

## Integrating Vapor Chambers Into Heat Sinks

One typical design incorporates three basic parts: the vapor chamber, an aluminum frame for mechanical attachments and a fin pack, which is often made of aluminum. These three parts are soldered into one assembly as shown in Figure 1.

Figure 1: CPU Heatsink

An alternative to this design is to simply add the vapor chambers to the base of an extruded heat sink. In Figure 2, several standard-size vapor chambers are shown imbedded into the base of a large heat sink to provide an isothermal base.

Figure 2: High Power Laser Heatsink

The heat sink in Figure 3, a cooling solution for high-brightness light emitting diodes (HBLEDs), shows how a vapor chamber can be integrated into a fin stack directly.

Figure 3: High Brightness LED Heatsink

For low profile applications, variants of the designs shown in Figures 1 and 2 are normally used. Figures 4 shows a 7mm high heat sink for a telecommunications application. Two 1.5mm vapor chambers are used in Figure 5’s DRAM application.

Figure 4: Low Profile Telecom Heatsink

Figure 5: Performance DRAM Heatsink

## Vapor Chamber Thermal Resistance

The most commonly asked question relating to the design of a vapor chamber cooling solution is what is the effective thermal conductivity (W/m-K) of the vapor chamber? Because two phase devices do not exhibit a linear heat transfer behavior, this number is application specific. There are two main resistances within all two phase heat transfer devices: the evaporator resistance and the vapor transport resistance. The third resistance, the condensation resistance, is much smaller than the other two. In the vast majority of applications, the evaporation resistance is the dominate resistance; therefore, making these devices somewhat length independent. This means that a vapor chamber with a transport distance of 75mm will have almost the same Tsource -Tsink as one with a 150mm transport distance. This, in effect, doubles the effective thermal conductivity for the longer devices.

Evaporator resistance is expressed in units of oC/W/ cm2. At lower power levels, 5 to 10 W/ cm2, this resistance is on the order of 0.1 oC/W/ cm2. As power densities increase, the evaporator resistance decreases until a performance limit is reached. This limit can extend to 200 W/cm2 and higher, depending on the vapor chamber design.

Figure 6 shows the evaporator resistance for one particular vapor chamber design.

Figure 6: Vapor Chamber Evaporator Resistance

The vapor transport resistance is expressed in similar terms, but refers to the cross sectional area of the vapor space. Keep in mind, changes in temperature or working fluid will change these values. The values presented are typical values for a water-based vapor chamber operating at electronics cooling temperatures. This resistance is 0.01 oC/W/ cm2.

Figure 7 shows common vapor chamber cross sections of 2.0mm to 3.5mm thicknesses and widths from 20mm to 80mm. The cross sections are calculated and the terms expressed in simple oC/W for each size. The performance limits for these passive devices was discussed in reference [1].

Figure 7: Vapor Thermal Resistance

The thermal models in Figure 8 compare a copper-based 1U heat sink with a vapor chamber-based 1U heat sink. In this type of application, where the heat is being spread uniformly more than it is being transported a long distance, the typical effective thermal conductivities are on the order of 1000 to 1500 W/m-K. In a small form factor such as a 1U heat sink where the transport length is short the effects of the vapor chambers is an improvement of 3oC to 4oC or about a 10% improvement over a copper base. This improvement is often critical in high ambient applications or where the gain is used to lower fan speeds for noise considerations.

Figure 8: Copper Base vs. Vapor Chamber Base CPU Heatsinks

The model in Figure 9 shows the heat sink remote from the heat source. In this application, where heat is moved and not just spread the effective thermal conductivities can be more on the order of 5000 to 10,000 W/m-K.

Figure 9: Vapor Chamber Evaporator with Remote Condenser

In summary, vapor chambers are easily integrated into thermal solutions and can offer thermal performance improvements on the order of 10% to 30% over copper and heat pipe based solutions and can often be lighter in weight than equivalent extruded or copper based heat sink. These improvements allow for designers to design for higher ambient or lower noise due to low required fan speeds.

References

1. Garner, S.D., “Heat Pipes for Electronics Cooling Applications”, Electronics Cooling, Vol. 2, No. 3, 1996.

## Discover a Low Cost Vapor Chamber Heat Sink

Welcome to the launch of our redesigned website and thanks for visiting. As this is our first blog, I thought I’d give you an overview of who we are, what we do and how we came to do it – with a bit more personal flavor than the rest of the site.

The short of it is – Celsia designs and manufactures custom heat sinks using two phase technology: vapor chambers and heat pipes. But the full story, I’m hoping, will prove more informative.

As many of you may know, Celsia has been tackling all sorts of difficult thermal challenges for the last decade. But, our team has been working in this field for much longer. I spent twenty-eight years with Thermacore working stateside and later as chairman of its Taiwanese and Korean operations. The part I enjoyed most was building out the company’s heat pipe / two phase heat transfer manufacturing and optimization facilities. In those days the business was as much about finding new markets as it was about reducing cycle times, increasing yield rates, and experimenting with wick variables.

As heat pipe technology improved cost declined, opening up more opportunities. It didn’t hurt that device enclosures were becoming smaller at the same time that power densities were going through the roof. Heat pipe based thermal modules were a natural fit but they were not without their limitations. These include the following:

• Heat pipes do a better job transporting heat than they do spreading it around.
• Most heat pipe configurations require an interface plate, causing increased thermal resistance.
• Even flatten heat pipes are still 2-3mm thick and often require additional machining.

In the early days another type of two phase heat transfer device, vapor chambers, wasn’t talked about or used much because they were very expensive relative to heat pipes. Here’s a great 4 minute video on heat pipes and vapor chambers from TechQuickie. It’s a bit quirky but informative and fun nonetheless – worth a listen.

All of us that have been in the industry for a while know that vapor chambers were kind of the unwanted step child of the two phase world: thick, heavy and expensive to produce. We experimented with them using the traditional production approach. Namely, a two piece design consisting of upper and lower stamped plates (2 pieces) with a different wick structure for capillary action and numerous internal small columns for support.

Vapor chambers solved the limitations of heat pipes but at a price. Stamping, increased furnace space during sintering, adding individual support columns, and four-sided welding/bonding of the two halves all added time, machinery, and of course cost. That’s why they remained a very niche market for decades. To compound matters, thermal engineers were far less familiar with heat sink design using vapor chambers than they were with heat pipe designs.

Nearly a decade ago Celsia decided to focus its efforts on solving this problem. Create a low cost, high-yield vapor chamber that could be used across broad, price sensitive industries in place of heat pipes. This process required that we not only develop a new type of production process but also that we analyze and perfect heat sink design using this type of liquid two phase device.

To be clear, I’m not arguing that vapor chambers will replace heat pipes only that many space constrained or high heat flux applications are better served by low cost vapor chambers.

After experimenting with literally hundreds of ideas the most effective solution was surprisingly simple, yet devilishly difficult to properly implement. Start with a huge (single piece) unsealed tube, add the wick structure flatten it, ad a micro-thin vapor spacer to provide support, then flatten it some more. No stamping dies or machinery, no individual columns, and no complex diffusion bonding result lower cost and reduced cycle times. An added benefit is that a one piece vapor chamber can be bent into many different configurations (in the Z-direction) post production.

Relatively soon after going to market with this ‘one piece’ vapor chamber design, Celsia was awarded volume production contracts for PC chipsets, high end graphics cards, high performance DRAM memory, and notebook applications. We engineered heat sinks using vapor chambers that could be made as thin as 1mm, be as wide as 100mm, and handle up to 450 w/cm2. Additional contracts in the telecom, networking, power electronics, and defense industries followed.

But, good old two-piece vapor chambers and heat pipes still have a very important role to play in our business. You see our proprietary one piece design isn’t without its limitations. When compared with a two piece design which can be stamped into virtually any shape, Celsia’s one piece version is limited to rectangular shapes. And, heat pipes still maintain a cost advantage for lower power applications and/or those requiring that heat be transported a long distance.

Today, Celsia is fully invested in heat sink design and manufacturing using each type of liquid two phase device. I’ve been doing this for over thirty years now and I make it a point to work with every customer and every inquiry. I love talking about this stuff! Whether you’ve got a huge project with crazy deadlines or just want to chat about thermal options, please write me at gmeyer@celsiainc.com and I’ll be sure to get you on the phone.

Be on the lookout for future Celsia blogs. We plan on discussing technical issues, passing along great articles about new developments in thermal management, and providing design guidelines for heatsinks using two phase devices.

Thanks for visiting,

George Meyer