The Cost of Miniaturization: Exploring overheating and prevention

Due to the ongoing trend of miniaturization, the density of electronic components in modern printed circuit boards (PCBs) continues to increase, as does the applied power. Both of these factors result in higher temperatures for individual components and the assembly as a whole, making thermal management a critical design consideration. However, a key concern is that every electrical component in the assembly is subject to its own prescribed temperature limits due to its material properties and reliability aspects. In this article, we will address this issue by exploring overheating in applications for surface-mounted resistors, and how it can be prevented.

ELECTRICAL LOSS AND HEAT TRANSFER

Heat is dissipated in the resistor by electrical loss (Joule effect), resulting in a temperature rise. Once a temperature gradient occurs, heat begins to flow. After a certain time (depending on the heat capacity and thermal conduction properties of the device), a steady-state condition will be reached. The constant heat flow rate P_H corresponds to the dissipated electrical power P_el. Since the nature of heat conduction through a body is similar to Ohm´s law for electrical conduction, the equation can be rewritten:

is the thermal resistance in the dimension of [K/W], which can be considered temperature independent for most materials and temperature regimes of interest in electronic applications.

THERMAL RESISTANCE

Approximated Model of Thermal Resistance

Heat transfer in electronic devices such as surface-mount resistors on PCBs can be described by an approximated model of the thermal resistance. Here, the direct heat transported from the resistor film to the surrounding air (ambient) by conduction through the lacquer coating and by free air convection is neglected. Thus, heat propagates via the alumina substrate, the metal chip contact, the solder joint, and finally through the board (FR4 including copper cladding). The heat from the PCB is transferred to the surrounding air by natural convection (Figure 1). For simplification, the overall thermal resistance R_thFA can be described as a series of thermal resistors with the corresponding temperatures at the interfaces as follows:

The respective thermal resistance equivalent circuit is shown in Figure 1 where:

• R_thFC is the internal thermal resistance of the resistor component, including the resistor layer, the substrate, and the bottom contact;
• R_thCS is the thermal resistance of the solder joint;
• R_thSB is the thermal resistance of the PCB, including landing pads, circuit paths, and base material; and
• R_thBA is the thermal resistance of the heat transfer from the PCB surface to the ambient.

The temperatures given for the nodes in the thermal resistance equivalent circuit are valid for the respective interfaces:

• ϑ_Film is the maximum thin film temperature in the hot zone;
• ϑ_Contact is the temperature at the interface between the bottom contact and the solder joint;
• ϑ_Solder is the temperature at the interface between the solder joint and the landing pad (PCB copper cladding);
• ϑ_Board is the temperature of the PCB surface; and
• ϑ_Ambient is the temperature of the surrounding air.

Internal Thermal Resistance

The internal thermal resistance R_thFC is a component-specific value mainly determined by the ceramic substrate.

Solder Joint Thermal Resistance

For conventional soldering, the thermal resistance R_thCS is negligible due to a relatively high specific thermal conductivity of solder and a large ratio of cross-sectional area and length of flow path (approx. 1 K/W). This is valid especially for a small stand-off.  A larger solder joint can be considered as one thermal resistor between the bottom contact and an additional parallel thermal resistor (from side contact to landing pad), enhancing thermal conduction marginally. Thus, we can approximate the overall thermal resistance of the component, including its solder joint:

Note that in case of improper soldering, the thermal resistance R_thCS will lead to a higher overall thermal resistance. In particular, voids in the solder or insufficient solder wetting might cause a significant contact thermal resistance or reduced cross-sectional areas of flow paths, and will lead to deteriorated thermal performance.

Application-Specific Thermal Resistances

The overall thermal resistance includes the thermal characteristic of the resistor component itself and of the PCB, including its capability to dissipate heat to the environment. The thermal resistance solder-to-ambient, R_thSA, strongly depends on the board design, which has a tremendous influence on the total thermal resistance R_thFA (especially for extremely low component-specific R_thFC values). The thermal resistance board-to-ambient, R_thBA, includes environmental conditions such as air flow.

EXPERIMENTAL DETERMINATION OF THERMAL RESISTANCES

Infrared Thermal Imaging

Infrared thermal imaging is widely used for thermal experiments. In Figure 2 an infrared thermal image of a 0603 chip resistor at a 200 mW load at room temperature is shown. A maximum temperature in the center of the lacquer surface can be observed. The temperature of the solder joints is about 10 ºC below the maximum temperature. A different ambient temperature will lead to a shift of the observed temperatures.

Determination of the Overall Thermal Resistance

Thermal resistances can be determined by detecting the maximum film temperature as a function of dissipated power at the steady-state condition. For determination of the overall thermal resistance of an individual component, standard test PCBs were used. The component in the center position was measured. Since equation (1) can be rewritten to:

a simple approximation leads directly to the thermal resistance R_thFA = 250 K/W for a 0603 chip resistor.

Integration Level

In Figure 3, a single 1206 chip resistor mounted on the PCB leads to R_thFA = 157 K/W. Additional resistors on the PCB (same load each) lead to an enhanced temperature rise (204 K/W for 5 resistors and 265 K/W for 10 resistors, respectively).

Determination of the Internal Thermal Resistance of the Component

Replacing the PCB by an ideal body with a high thermal conductivity and heat capacity tending to infinity (in the real world a bulk copper block is suitable) leads to

Again, the internal thermal resistance R_thFC was determined experimentally by detecting the maximum film temperatures by infrared thermal imaging as a function of dissipated power. The standard PCB was replaced by two electrically isolated copper blocks (60 mm x 60 mm x 10 mm). In Figure 4, R_thFC values are given for passive components including chip resistors, chip resistor arrays, and MELF resistors.

Table 1 demonstrates that thermal resistance decreases with contact width. The best ratio of thermal resistance and chip size is provided by wide terminal resistors. The internal thermal resistance of a 0406 wide terminal chip resistor (30 K/W) is nearly the same as the thermal resistance of a 1206 chip resistor (32 K/W).

CONCLUSIONS

In this article, we’ve seen how overall thermal resistance is mainly determined by PCB design and the environmental conditions of the entire assembly. As demonstrated, reducing the amount of heat-dissipating components in the assembly results in the lower temperatures of individual components. However, with the ongoing trend for miniaturization, this approach may not be feasible outside of certain partial board areas. Fortunately, heat dissipation can be greatly improved on the component level by selecting optimized components, such as wide-terminal resistors.

About the Author

Dr. Kevin Raiber is a member of the research & development department for the Vishay Draloric/Beyschlag Resistors Division, responsible for the development of new products such as SMD resistors and sensors. He studied chemistry at the University of Hamburg and received his doctoral degree in 2005, with thesis work on surface chemistry and modern soft-lithography for sensor fabrication.