In a previous article, “A Close Look at Facts and Myths About Thermal Vias,” we used a thermal simulation model called Thermal Risk Management, or TRM, to model thermal vias. Thermal vias, almost by definition, must terminate on something, typically a copper pad or plane of some design. A significant result from that article was the following: “The net impact is that the difference in temperature (ΔT) between the heated pad and the copper surface reduces dramatically. This reduces the thermal conductivity through any thermal via to the point that thermal vias add very little additional benefit.”
Almost every study of heated traces or pads/components examines the thermal impact of the items on the top layer only. They rarely look at what happens underneath the heated trace or component. But it turns out there is a lot going on underneath the trace or pad that may have a major impact on other components.
In this article, we look at thermal heat flow underneath a heated trace or pad, and what impact that has on other layers. That thermal heat flow is related to a property called “heat spreading thermal resistance,” and there is no general formula for describing it or its effects. Numerical simulation tools, such as TRM, are the only practical ways of estimating it.
Thermal simulation model
To do this analysis, we use TRM, the thermal simulation model we used in the previous article. Our test simulation model will be a 250 x 125 mm FR4 board, approximately 1.6 mm thick. We will place two pads, 25 x 25 mm, on the top surface. Using the same technique as in the previous article, we will heat the pads by applying 2.5 watts of thermal power to each pad. If there is nothing but dielectric underneath the pads, each pad heats to 93oC, 73oC above the ambient temperature of 20oC.
In many of the simulations, we will put a copper surface—pad or plane—underneath one of the pads. They come in two sizes, 125 x 125 mm, covering half the board, or 25 x 25 mm, exactly the same size as the pad on the top layer. These copper surfaces are generally placed on one of two layers, on the far side of the board (“far”), or 350 µm (approximately 14 mils) directly underneath a pad (“near”). Figure 1 portrays these configurations.
Figure 1 Various configurations are used in the simulations.
Figure 2 illustrates our first simulation. There is a plane (far) placed under the left side of the board. The maximum temperatures of the two pads are approximately 59oC and 93oC, respectively. The plane clearly helps cool the pad above it.
Figure 2 Two pads are heated with 2.5 watts and left pad has a large plane, far, under it.
What is not obvious in Figure 2 is that the temperature of each pad is not uniform across the pad. Figure 3 illustrates this. We cover some of the reasons in several places in our recent book. The center of each pad cools least efficiently, and is therefore is the hottest. The corners of each pad cool most efficiently, and are therefore the coolest.
Figure 3 The pads do not heat uniformly.
But Figure 4 is the most interesting view of what is going on in the board. It’s a 3D image of the simulation showing the temperature profile of the top layer of the board. The peak temperatures at the center of the pads and the cooler edges of the pads are very apparent in the rounded tops in the image.
But what is most important in this image is how steep the thermal walls are, and how narrow is the horizontal dispersion of the heat. The heat flows down from the pads, into the board, not out from the pads across the surface. As a result, the bottom layer of the board, directly under the pad, heats up significantly.
Figure 4 The image shows the 3D thermal view of the simulation.
We can see this another way in Figure 5, a graph of the temperatures of the top and bottom layers of the board. This graph is a “slice” through the mid-point in the Y-axis (62.5 mm). Therefore, it is through the center of the pads. Note that the temperature of the bottom layer is only a few degrees cooler than the top layer, regardless of what is on the bottom layer (See Table 1).
Figure 5 Temperatures are shown of the top and bottom layers of the board across midpoint. Note how the temperature of the bottom layer is not much below the temperature of the top layer.
Plane placing considerations
This, then, forms the basis of the premise we explore in this article.
Premise: The temperature of the bottom layer of a PCB will be only a few degrees—less than approximately 10—cooler than the top layer, independent of what is underneath the top layer of the PCB.
Table 1 The temperature of the bottom layer is only a few degrees cooler than the top layer, regardless of what is on the bottom layer.
But what happens if we change the vertical position of the plane in the stack-up? If the plane is on a higher layer of the board, does it disperse the heat better throughout the board? Figure 6 illustrates the top layer temperature curves as a function of plane layer. Plane layer is expressed as a percentage of depth below the pad. For example, 100% means the plane is placed on the bottom layer, while 0% means the plane is placed just below (approximately 13 mils) the pad.
Figure 6 A view of “large” plane placement where curves are for the top layer.
What is important to note is that any (large) plane makes a big impact on the top layer temperature. But the smallest impact is when the plane is on the actual bottom layer. If the plane is just fractionally above the bottom layer, so that there is some dielectric below it, the marginal improvement is significant. After that, plane placement has less of an impact, although the top layer temperatures are lowest when the plane is closest to the top layer.
When we look at the difference in temperature between the pad on the top layer and the maximum temperature on the bottom layer for each instance shown in Figure 6, the results are consistent with the above. Table 2 provides the relevant data. Note that the “difference” column supports our premise in every case.
Table 2 The difference in temperature between the pad on the top layer and the maximum temperature on the bottom layer.
In a similar manner, we can look at board thickness as a new parameter and estimate its effect on the difference in temperature between the top and bottom layers. Figure 7 shows the temperature curves for the top and bottom layers of the board as a function of board thickness. The curves on the left side are for the case of “large plane, far.” There is no plane under the pad on the right side of the board. The data are tabulated in Table 3.
Figure 7 The graph shows the impact of board thickness on the temperatures of the top and bottom layers of the board.
The first thing we can conclude from Table 3 is that our premise, that the difference in temperature between the top and bottom layers of a board is relatively small, begins to fail as board thickness increases. What these data, and subsequent data, will show is that the premise is true as long as the width of the trace/pad is significantly larger than the thickness of the board. As relative thickness increases, there is more horizontal conduction (heat spreading) of the heat away from underneath the trace/pad and the premise becomes less reliable.
Table 3 Board thickness and its estimated effect on the difference in temperature between the top and bottom layers.
A second thing to note from Table 3 is that for the case of no plane, the top layer cools as the board increases in thickness—there is more volume for the heat to spread into. But if there is a plane, the temperature of the top layer increases as board thickness increases—the plane has less of an effect. It turns out that the impact of a plane has diminishing returns as the board increases in thickness—the plane moves further away from the trace. For a thick enough board, all of the curves in Figure 6 will converged into one single pair (top and bottom) of curves.
The case of a small plane (25 x 25 mm) follows similar, but less dramatic patterns. Figure 8 illustrates the 3D thermal image for the small plane case that compares to Figure 4. As is apparent from the figure, the small plane has a much smaller impact on the top layer temperature.
Figure 8 The 3D thermal pattern of the “small plane, far” case is shown on the left side.
Figure 9 illustrates how the top and bottom layer temperatures change as a function of where the small plane sits in the stack-up. Compare this to Figure 7, above. Only two sets of curves are shown here. If the plane is on the bottom layer (black curve), there is a relatively small impact on each of the top and bottom layer temperatures, and our premise is not supported. But if the small plane is placed anywhere just slightly above the bottom layer, so that there is some (even small amount of) dielectric below it, the temperature of the bottom layer increases sharply.
Figure 9 Top and bottom layer temperatures are shown as a function of plane placement.
In that or any other case, the temperature difference between the top and bottom layers is relatively small and our premise is supported. The reason that only two sets of curves are shown in Figure 9 is that in virtually all other cases of plane placement in the stack-up, the resulting curves become indistinguishable from the red curves.
Thermal gradients are critical
In summary, thermal gradients within a typical PCB are significant and complicated. On typical PCBs, heat flows directly downward through the board from heated traces or pads. The bottom layer of the board is usually only a few degrees cooler than the heated trace/pad on the top of the board, regardless of the board stack-up, unless the trace or pad is relatively small compared to the thickness of the board.
Douglas Brooks has written two books and numerous technical articles on PCB design. He gives seminars on PCB designs around the world.
Johannes Adam has worked on numerical simulations of electronics cooling at companies like Cisi Ingenierie, Flomerics and Mentor Graphics. He currently works as a technical consultant.
Other articles in this series: