**The process used to determine thermal resistance values from the LED junction-to-case and LED junction to T_{s} reference point.**

*Part 1 of this article discusses measuring junction-to-case thermal resistance; determining the K-factor and testing R _{th J-C}* (

Thermal performance is the most critical aspect of a well-designed LED lighting system. Lighting installations with proper thermal designs have higher efficacy, meaning more light can be extracted using less energy, providing better long-term reliability.

**Determining R_{th J-C}**

It is often difficult to determine the divergence point of thermal impedance curves and further mathematical transformations of the impedance curves are therefore required to make the difference more noticeable to determine the *R _{th J-C}*. Thermal impedance curves or

The T3ster transient thermal tester software produces two types of structure function curve, cumulative and differential. The cumulative structure function is the cumulative thermal capacitance plotted against the cumulative thermal resistance from the junction of the device.

The differential structure function, on the other hand, is a derivative of the cumulative thermal capacitance plotted against the cumulative thermal resistance. In a cumulative structure function curve, a difference in material properties is observed as a change in slope. On a differential structure function curve, a change in material properties is observed as a peak.

In a simple system, it may be possible to determine the thermal resistance of each material component by observing the peaks or slope-changes on the structure function curves. However, use caution when using peaks or slope changes to determine the thermal resistance of more complex devices such as LEDs. Again, it is recommended to follow JEDEC Standard JESD51-14 for determining thermal resistance. Use the divergence point of the structure function curves of a device tested with two different TIMs to determine the junction-to-stage thermal resistance value.

It is generally difficult to determine the junction-to-case thermal resistance of a particular device mathematically using the divergence point of two curves. The structure function curves must therefore be analysed by skilled persons.

The divergence point can be more easily determined from differential structure functions but cumulative structure functions are also examined to confirm the results inferred from the differential structure functions and, in some cases, to better pinpoint the thermal resistance.

The method for determining the thermal resistance junction-to-case is the same whether examining either type of structure function curves, and the differential structure function analysis is shown here for simplicity only.

The structure functions are extracted from the T3ster software and plotted in a graphing package.

Be sure to label each curve correctly with the corresponding part and TIM for each measurement. The differential structure function curves are plotted on a log10 derivative of thermal capacitance vs. thermal resistance chart (see Fig 6a). The point on the x-axis where the curves asymptote vertically is the total thermal resistance (junction-to-heat sink/ambient). The divergence point is better observed by narrowing the scale to “zoom-in” on the region of interest (see Fig. 6b). The error can be reduced further by ensuring that the lines and/or symbols used to display the graph are as thin/small as possible.

Once the details of the curves are clearly visible, look for the divergence points of the individual parts and read the *R _{th J-C}* value from the x-axis at that point of divergence. For a large group of parts which may prove too time consuming to determine individual

In this case, the thermal resistance for the group can be approximated by looking at the typical divergence point of the group with errors added to either side representative of the maximum and minimum *R _{th J-C}* of the group’s divergence. In Fig. 7, the

The types of TIM used should not affect the *R _{th J-C}* determined from the divergence point of the structure functions. For example, in Fig. 8, differential structure functions are plotted for a single device measured with three different TIMs. The total thermal resistance varies, as expected, but the divergence point of these curves (indicating the

After observing the shapes of these curves, it becomes clear how difficult it would be to determine the thermal resistances of individual components corresponding to each individual peak for this complex system. Therefore, *R _{th J-C}* is best determined by the divergence point of the structure functions for parts measured using two different TIMs.

**Measuring R_{thJ-S}**

The method defined here to calculate and monitor device junction temperature was created because measuring the actual junction temperature of an LED is practically impossible. The device junction temperature can be calculated using the thermal resistance between the device junction and an accessible reference point; the temperature at that reference point, and the electrical power through the device.

The *T _{s}* location is an accessible reference point on the device or a location on the PCB thermal pad as defined in the application brief of the product. This point is generally the closest point to the thermal path that allows the attachment of a thermocouple to monitor the temperature (see Figs. 2 and 9). With the recorded temperature at Ts, electrical power (

The TS point is often not within the direct thermal path between the LED junction and heat sink. Therefore, the thermal interface material (TIM) chosen can affect the temperatures seen and accuracy of the calculated device junction temperature. It is important to use the same TIM called out in the respective product’s application brief to achieve consistent measurement results.

**Testing for R_{th J-S}**

The application brief of each Luxeon device states the measured *R _{th J-S}* value. This document also identifies the reference point (

The maximum temperature is recorded during the heating cycle of the MicReD test. This value is recorded during the test runs in which the devices are attached to the reliability board with the thermal conductive TIM and not with the Kapton tape insulator.

It should be noted that Rth J-S values provided in the application brief are derived at specified operating conditions. This value can vary, depending upon the thermal interface material chosen.

**Determining R_{th J-S}**

Three data points are needed to calculate or determine the* R _{th J-S}*:

- Electrical power through the device in W.
- LED junction temperature derived from T3ster software data.
- Temperature at the
*T*point._{s}

Thermal resistance is equal to the change in temperature divided by the power applied. *R _{th J-S}* is determined with test results from these three data points, using the formula,

*Alternative method for determining R _{th J-S}*

Lumileds may also use an automated test system consisting of a temperature controlled stage; data log thermometer for recording the *T _{s}* point temperature; a Keithley power supply to provide drive current and to monitor

In this method, a short-pulse K-factor is defined when device forward voltage (*V _{f}*) is measured with a short-duration current pulse (< 3 ms) at 25; 35; 45; 55; 65; 75 and 85°C junction temperature to map

*V _{f}* is measured again once the device reaches a DC steady-state at each of the mentioned temperatures. The temperature of the stage (ambient) and

Junction temperature is calculated from the steady-state forward voltage using the slope defined by the short-pulse K-factor.

Once this calculation is complete, all the factors are known to determine device thermal resistance between LED junction to ambient and LED junction to solder pad using the formula above.

Once this calculation is complete, all the factors needed to determine device thermal resistance between LED junction-to-ambient and LED junction-to-solder pad are known, using the formula in Eqn. 4.

**Conclusion**

The thermal resistance values *R _{th J-C}* and

*R*defines the ability of the LED package to dissipate heat from the device junction to the case of the package._{th J-C}*R*is a critical factor for designing a proper thermal system._{th J-C}*R*is a constant, unaffected by TIM or heat sink selection._{th J-C}*R*defines the thermal resistance between a sensor point near to the direct thermal path, allowing for monitoring of the LED junction temperature for the purpose of design validation or system performance monitoring._{th J-S}*R*is defined for a specific LED, board and thermal interface material configuration. Changing the board design and/or TIM will affect its value._{th J-S}

**References**

[1] MIL Standard 833: MIL-STD-883E, Method 1012.1, “Thermal characteristics of integrated circuits”, www.thermengr.net/PDF/MilStd883M1012_IC.pdf, 4 November 1980.

[2] JEDEC Standard JESD51-14: JEDEC Stndard, JESD51-14, Transient dual interface test method for the measurement of the thermal resistance junction to case of semiconductor devices with heat flow through a single path, www.jedec.org/sites/default/files/docs/JESD51-14.pdf, November 2010.

[3] More information on the MicReD and T3ster systems is available at www.mentor.com/micred.

Contact Lumileds, www.lumileds.com