Determining the Effects on a Reliability Prediction

Introduction

It is no secret that the operating temperature of a device significantly affects its reliability. Active electronic components without proper thermal management can see immediate damage or reduced reliability due to phenomena such as electromigration. A device's ability to dissipate heat is affected by package design, proximity to other devices in the system, the surrounding airflow, and circuit board and trace properties. Design methods can manage these factors to augment heat transfer away from the device, but many cases require additional conductive, convective, or radiative paths to cool the device to acceptable levels.

Heat sinks are commonly used to provide this additional cooling path. They have a direct impact on system reliability, and they should be accounted for in reliability predictions. However, simply assigning a failure rate to a heat sink is not generally the best solution for determining its impact. A better approach is to consider its effects on the thermal properties of the device to which it is mounted. This article will explore how to determine the effects of a heat sink on a reliability prediction. It also provides an example to examine the extent to which heat sinks affect the reliability performance of a device and thus your overall return on investment.

Temperature Calculations of Power-Dissipating Devices

As an electronic device dissipates power, it heats up. The heat must be expelled to the environment; otherwise, the device will eventually be subjected to temperatures over its maximum temperature rating. When this occurs, the device may either begin to operate out of tolerance limits or cease operating altogether. Heat escapes from the device in all directions, mainly through the mechanisms of convection to the air above it and conduction to the circuit board to which it is attached.

A first-order model used to assess the cooling efficiency of a device assumes one-dimensional convective cooling to the ambient air above the device. The accuracy of this model is beyond the scope of this article, but its application can prove very useful for heat sink sizing as well as reliability calculations. For this one-dimensional approximation, the complete thermal path can be characterized by the junction-ambient thermal resistance, θ_JA, which is the thermal resistance between the die and the surrounding air. In this case, the junction temperature (temperature at the die), T_J, can be computed by:

         (1)

TA	=	Ambient temperature
PD	=	Power dissipated in the device

With assumptions of the ambient conditions, θ_JA is usually provided in the device's data sheet. For the case of a device with a heat sink, θ_JA becomes:

         (2)

θJC	=	Thermal resistance between the die and the package case
θCS	=	Thermal resistance between the case and the heat sink
θSA	=	Thermal resistance between the heat sink and ambient

θ_JC and θ_SA are given in the device and heat sink data sheets, respectively. Typically, θ_CS is so small that the thermal resistance of the heat sink adhesive is used.

Reliability in Thermal Design

Most reliability prediction models account for thermal stress in failure rate calculations using a multiplicative factor, π_T , which is a function of the device junction temperature. The Relex Reliability Prediction module provides a very versatile interface for specifying π_T  in the different prediction models. One option, available for several models including MIL-HDBK-217, calculates the junction temperature automatically. In this case, the ambient operating temperature would be set at the assembly level on the Calculation Data tab, and the operating power and calculated junction-ambient thermal resistance would be entered for each part on the Prediction Data tab. This approach is preferred for assessing thermal properties of many components in an assembly. Another option is to simply enter the calculated junction temperature in the "Junction Temp Override" field on the Prediction Data tab for the device.

As an example, suppose you want to analyze an integrated circuit in a 20-pin SOIC package. The IC is to be placed in a system that will operate between 20^oC and 80^oC with natural convective cooling. The IC's specifications in the system are as follows:

Nomenclature	Description	Value	Unit
TJ, MAX	Maximum rated junction temperature	150	oC
θJC	Junction-to-case thermal resistance	18	oC/W
θJA	Junction-to-ambient thermal resistance (natural convection)	76	oC/W
PD, MAX	Maximum power dissipation during operation	1.3	W

To determine if the IC is sufficiently cooled without a heat sink, you would calculate the junction temperature of the device under worst-case conditions using equation (1):

For this scenario, the device will operate with a junction temperature that is well beyond its maximum rated value. Additional cooling, such as a heat sink, must be considered. To determine the maximum allowed (or minimum required) thermal resistance requirement for the heat sink, you would place equation (2) into equation (1) and rearrange to obtain the inequality:

Assuming the thermal resistance of the heat sink adhesive is 0.7^oC/W, you obtain the following:

Device manufacturers recommend placing a 10 to 15% guard band on the thermal resistance requirement to ensure adequate cooling. Applying a 15% margin, the required heat sink thermal resistance becomes:

By adding a heat sink with this thermal resistance rating to the design, the final junction-ambient thermal resistance of the device becomes:

With the heat sink, the junction temperature of the device under worst-case conditions is now below its maximum rated value:

Next, suppose you want to determine the effects of utilizing an enhanced heat sink with a thermal resistance rating of 15 ^oC/W in order to conduct a cost vs. benefit trade-off. For the enhanced configuration, you have:

Using Relex Reliability Prediction, you can examine the reliability effects of such a design change according to MIL-HDBK-217. You would set the top-level assembly temperature to 80^oC. The device parameters entered on the Prediction Data tab for the IC are shown in the following figure.

Prediction Data Tab with Pi Factors Shown

You can then perform calculations using the three different scenarios. The following table illustrates the differences between the three cases:

Configuration	θJA (oC/W)	TJ,MAX (oC)	Failure Rate (FPMH)	Reliability (100 hours)
No heat sink	76	179	55.288	0.9945
Normal heat sink	48.5	143	13.176	0.9987
Enhanced heat sink	33.7	124	5.506	0.9995

Including the heat sink reduces the device's failure rate by more than two-thirds. Including the enhanced heat sink decreases the failure rate further by more than one half. The reliability gains can be converted to a return on investment (ROI) by examining the costs associated with each configuration. Considering only material costs of initial investments and subsequent failures, a hypothetical example follows. Assume that the device and heat sinks have the following per unit cost:

Cost Per Unit
Device	$1.50
Normal heat sink	$0.50
Enhanced heat sink	$0.75

You can then calculate the total cost for each configuration as a function of time as:

Where:
n	=	Number of units
λ	=	Failure rate
CD	=	Device cost
CS	=	Heat sink cost

The following graph compares the ROI for the three cases. Note that although the case without a heat sink is included for the sake of comparison, it would most likely not be considered because the device will not function properly in the first place due to the elevated junction temperature. The ROI of the enhanced heat sink will surpass the normal configuration after about 2½ years of operation. After 5 years of operation, the ROI will be $250 per 1000 units. It is important to note that these costs only account for the material costs of the devices and heat sinks. Considering other underlying costs involved with device failures, such as the costs due to system downtime, logistical costs, and repair personnel costs, will increase your ROI significantly.

ROI for Heat Sink Configurations

Conclusion

This article has touched upon modeling methods for thermal design in reliability. Although it specifically examined the heat sink, the same concepts can be applied to active convective cooling, conductive cooling, and radiative cooling methods. Aside from assuring adequate cooling for device operation, thermal design also has a significant impact on component reliability, and therefore overall system reliability. As shown in the above example, the failure rate for a component can be dramatically reduced by managing the component's thermal properties. ROI trade-offs should be conducted to determine the optimal cooling mechanism.

Many of these trade-offs can be easily evaluated using Relex Reliability Prediction. When performing reliability predictions, this module enables you to also perform derating analyses at the same time. Any parts that are found to be enduring conditions beyond their acceptable tolerances are highlighted. Information about the particular aspect or characteristics of the part that is overstressed (temperature, voltage, etc) is then made available in the Pi Factors dialog box. For additional information about this module and the many others in the Relex Reliability Software Suite, please visit our web site at www.relex.com.