Thermal Basics of Complex Devices

Back in the days when most electronics components were packaged in metal cans (or manufactured as axial leaded devices with equipment housings generally spacious and un-crowded), matters of device level thermal management were relatively straightforward for design engineers. Sadly, thermal management has become much more of a challenge nowadays – both to understand and to tackle; with multi-pin plastic packaged devices in ever-shrinking formats being incorporated into high component density portable electronics with considerable pressure being placed on available space and overall power efficiency.

The following article details some of the key areas of concern in regard to device level thermal management in modern electronic products, with explanations of the fundamental theory behind it as well as some practical considerations.

First principles

As we all know from basic thermodynamics, heat energy will flow from a higher temperature region to a lower temperature region (this being done through either conduction, convection, radiation or often a combination of these). Furthermore, the bigger the temperature difference witnessed, the greater the flow of heat will be.

Historically, for discrete devices, the ‘junction’ referred to in the term junction temperature (TJ) was the PN junction of the device. Though this is true for basic rectifiers, bipolar transistors, etc, the junction now generally refers to the hottest point within the device. As we move towards more complex device constructions where different parts of the silicon have different functions at different times, locating the precise position of this point can be very difficult.

A common misconception often held by engineers is that a device’s thermal resistance is an intrinsic property of the package in which it is enclosed. Among the reasons why this does not hold true is the fact that there is no isothermal surface, making it impossible to define a ‘case’ temperature. Though the metal can devices of the past had a relatively good approximation of an isothermal surface, modern plastic packages tend to exhibit quite large gradients. Furthermore, in modern package types different leads will be at different temperatures, with multiple, parallel thermal paths leaving the package.

Probably the most common thermal parameter cited on a device’s datasheet is θJA. Unfortunately, when it comes to designing a device for a system to locate its TJ, this figure can often be misleading.

Many people unwisely think of θJA simply as the ratio of junction temperature rise above the ambient level to the power dissipated in the device. This suggests that as long as the ambient temperature for the application is known, it is possible to figure out how much power the device is going to dissipate in any specific scenario. From this, engineers assume they will be able to estimate the actual junction temperature of their device and come up with an upper limit for TJ, so they have a reasonable design margin to work with. Sometimes, device manufacturers will provide relatively thorough footnotes describing the test conditions under which the reported θJA was measured.

The simple truth is that θJA is not a measure of the device’s ability to dissipate heat on its own, but, in fact, is a measure of the entire system, including the device. In many applications, the device actually has the smallest direct contribution to its θJA value of all the system variables. Factors that prove to have a more profound effect are: area, air flow, board area/thickness, the number/density of power/ground planes, PCB thickness, proximity/density other devices, etc. What device manufacturers cannot inform engineers about on the datasheets is the influence on θJA of the other heat sources within the overall thermal system.

Avoiding thermal runaway

Thermal runaway takes place if a semiconductor device reaches a point where it effectively has too much heat to sufficiently dissipate. The device’s temperature rises as a result and, as it is a function of temperature, further impinges on the device’s ability to dissipate heat. Effectively, the device enters a condition, through an increase in its TJ, which changes its characteristics so that it is no longer possible to attain a nominally steady-state operating point. From there, the whole thing can rapidly snowball, with the device burning out. However, what is rarely recognized is the fact that this phenomenon can be initiated well below the maximum TJ value stated on the device’s datasheet.

If the thermal system around a given device has a steady-state thermal resistance, then it is possible to describe this steady-state condition using the following equation:

With:
TJ representing the junction temperature (in °C)
Q representing the device’s power dissipation (in W)
θJx representing the system’s steady state thermal resistance (in °C/W)
Tx representing the thermal ground for runaway based on θJx (in °C).

Examining equation 1, it is clear that a slight alteration in power will result in a small change in the TJ level. If the power level briefly rises above the equilibrium value but then returns, TJ will also return to its equilibrium. From this equation, the following relationships can be derived:

(dQ/dT) is the rate of change of system power dissipation with respect to changes in junction temperature. Equations 2 or 3 show that for a small increase in TJ, the system can dissipate slightly more power than the original Q. Utilization of mathematical models allows the true nature of thermal runaway to be understood. It also ensures that engineers give themselves adequate margins so that devices’ continued operation is ensured. Figure 2 shows power dissipation on the vertical axis and temperature on the horizontal axis. The gently sloped red line is referred to as the ‘device operating line.’ This represents a device whose power dissipation increases with temperature. The blue diagonal line describes 1/θJx as set out in equation 3. This is referred to as the ‘system line.’ It describes how increases in the device’s operating temperature go with increasing amounts of power that may be successfully dissipated from that device. The intersection of these two lines gives the nominal steady-state operating point. Thus, to the right of the steady-state operating point, more power leaves the system than the device produces, so it cools; to the left, less power leaves the system than is introduced, so it heats up. Either way, the imbalance in power causes TJ to move back toward the steady-state operating point. Once this stability is lost, however, the device is at risk of thermal runaway. This will happen if the slope of the blue line is less than that of the red line

In summary, the whole business of ensuring device level thermal management has become increasingly difficult with the advent of more compact, power-dense, functionally-complex devices enclosed in plastic packages. Inside the package, there are multiple heat paths that need to be taken into account; the idea that the package’s thermal properties can be represented by a single number is, at best, naive. Simultaneously, outside the package, specific boundary conditions dictate how heat flow from the device takes place. Engineers need to be fully aware of the thermal issues involved if their system designs are to achieve the reliability and performance levels they require.