Dr. Giles Humpston, Cambridge Nanotherm
The critical importance of quickly removing heat from electronic components is well documented. In the case of LEDs allowing a design to ‘run hot’ drastically reduces component lifespan and significantly increases the risk of catastrophic component failure. Conversely, if the heat can be managed and removed from the LED quickly enough then designers can run LEDs at a higher power: producing more heat but also more light. Ultimately this can mean using fewer LEDs and smaller substrates to generate the same number of lumens, helping to drive down the overall BOM. Knowing how to measure the thermal properties of any given material is key to creating a system that balances thermal performance with material cost.
However, there can easily arise confusion regarding what should be measured and how. As such it is worth reiterating some of the basic principles of thermal management that must come into play when assessing such a system.
Measuring Thermal Performance – Conductivity, Interface Resistance and Impedance
One of the most commonly used terms in thermal management is that of ‘thermal conductivity’. This refers to a simple constant; the ability of a given material to transfer heat by conduction. While there exist a number of well-established methods, backed by standards, to measure thermal conductivity, for many heterogeneous materials the result obtained will vary with the test method. Manufacturers of thermal management products and system components naturally choose the test method and sample configuration that gives the most flattering result. Caution therefore needs to be exercised both in comparing data sheets and in using published values of thermal conductivity for modelling purposes.
Values of thermal conductivity are useful as an input to calculate thermal resistance. This metric provides an indication of the effectiveness of a particular material for thermal management in a system since it includes a Z axis dimension – layer thickness:
‘Layer thickness’ ÷ ‘thermal conductivity’ = Thermal resistance
Taking the Z axis into account is crucial. As the above formula demonstrates reducing the thickness of any given thermal management material can have an enormous impact on overall thermal resistance, since it is easier to change thickness by an order of magnitude than it is to find a form-fit-function substitute material with ten times the thermal conductivity without a price penalty.
Thermal resistance only offers one part of the story: What about the difficulty heat experiences in bridging different layers/materials used across that Z axis? This is known as ‘interface resistance’, and is hugely important.
Interface resistance tends to be misleadingly modelled as a thermal resistance of zero thickness. However this is almost never the case. Given the large number of factors that can affect the interface between two materials (pressure, temperature, porosity, roughness, warp, bow, etc.), calculating interface resistance can be a complicated affair, and true interface resistance can often only be determined by real-world tests.
Putting this together (combining the thermal resistance of all materials in series in a thermal path with their respective interface resistances) gives us a more useful measure; the thermal impedance of the assembly, (measured as °C.cm2/W).
Applying this to Real-world Designs
Sadly, despite being one of the most useful measures of thermal performance, the ‘thermal impedance’ value of a thermal management material or component isn’t communicated by manufacturers. Often the only way to deduce the thermal impedance value is by performing your own tests and measurements. Either way once you have the thermal impedance value of the assembly you can work out the absolute thermal resistance in order to calculate whether the temperature of the LED or power semiconductor can be kept within safe limits. Remember that an air-cooled heat sink might be operating in a 40 °C or higher ambient temperature!
Thickness ÷ thermal conductivity x area = Absolute thermal resistance (units °C/W)
[Thermal conductivity is aggregated to include interface resistances]
[Confusingly ‘absolute thermal resistance’ is sometimes abbreviated to simply ‘thermal resistance’ in data sheets. The only way you’ll know which type of ‘thermal resistance’ is being referred to is by looking at the specific units described.]
Absolute thermal resistance is dimensionless. As such, it must be stated with reference to either a material of given dimensions (e.g. a 3 mm thick square plate measuring 50 mm2) or a component of a known and fixed specification (a heat sink, say, rated at 0.4°C/W). When dimensions alone are given it should also refer to an object of a specific shape: A square board will have a different absolute thermal resistance to a long thin rectangle or triangle of the same area due to the differing lateral thermal gradients prevailing in each.
A Fresh Approach to Thermal Management
Taking the above into account one solution that has recently been developed as a PCB for cooling LEDs makes particularly clever use of the importance of the Z-axis/thickness in these equations. This approach uses a patented electrochemical process to convert the surface of a sheet of aluminium into a super thin layer of alumina – a Nanoceramic dielectric layer. This dielectric layer has a robust atomic-level bond with the aluminium base plate, minimising interface resistance between layers. And while there are technically better thermal conductors than alumina the nanoscale Z-axis of the ceramics used in this solution (10-30 microns, depending on breakdown voltage requirements) means that the thermal path from the LED through the aluminium baseplate and then on to the heat sink is as short as feasibly possible.
As a result, using the above calculations, under set test conditions, this Nanoceramic assembly has been shown to exhibit absolute thermal resistance of around 0.035°C.cm2/W. This is comparable to aluminium nitride (AIN), which achieves an absolute thermal resistance of 0.071 to 0.028 °C.cm2/W, depending on the grade of the ceramic. However, Nanoceramic costs a fraction as much to produce and, being formed on a metal core means the substrates are mechanically robust, resulting in extremely high physical yield.
Regardless of the specific application, an appreciation of the basic principles of thermal management, as outlined above, is critical to the development of an optimum thermal management solution. A little trial and error is usually required due to the unpredictability of interface resistances, but by understanding these principles you’ll achieve an optimum solution all the more quickly.
For more information visit www.camnano.com