Calculation of the interface resistance
But how can the interface resistance be determined so that it can later be subtracted from the measured value? There have already been objections in the forum that it is not possible to create a 0 µm thick layer in order to then measure the interface resistance Rinterface separately, which is correct at first. Because you can’t solve this with a single measurement. But if you measure at least twice (my 16 to 17 measurements in 25 µm steps are better), then a bit of logic and simple mathematics is actually enough for the calculation.
To determine the interface resistance Rinterface at a bondline thickness of zero, you have to analyze the thermal resistances for different bondline thicknesses and extrapolate the data to obtain the limit value at BLT=0. This is where vector calculus comes into play by modeling the relationship between thermal resistance and bondline thickness and extracting the value for the interface resistance by linear regression or another analytical method. Any thermal resistance Rth depends directly on the bondline thickness BLT, which can be easily modeled:
Here Rinterfaceis the thermal resistance that remains when the bondline thickness BLT=0, i.e. the resistance at the interface between two materials. The second term describes the thermal resistance due to the thickness of the material. However, it is also easier if we take a look at the diagram, which shows the dependence of the measuredReff on the BLT:
It is exactly what I am doing here, because you can also apply the vectorial representation of the parameters and represent the values for the thermal resistances at different BLT as points in a two-dimensional vector space, where one axis represents the bondline thickness BLT (2) and the other axis represents the thermal resistance Rth (1). Each pair of data (blue dots) thus forms a vector in this space. and now the linear regression comes into play to determine the limit value. Since the thermal resistance is proportional to the BLT, a linear regression can be performed to determine the relationship between Rthand BLT:
Where m is the slope of the straight line that runs through the thermal resistance values at different BLT values. The intersection of this straight line with the y-axis (at BLT=0) now gives me the interface resistance (3) Rinterface. After I have measured the thermal resistances for different BLT thicknesses, recorded slightly deviating values (red dots) (determination) and carried out a linear adjustment, the interface resistance Rinterface is exactly the value that remains when the bondline thickness approaches zero. Mathematically, this corresponds to the y-intercept of the linear function:
The points that deviate from the ideal line (4) are later used for the coefficient of determination (4), which shows the accuracy of the behaviour of a material at different BLTs, as there will also be TIMs that exhibit anomalies. The deviations of the individual measurement points from the regression line are thus summarised in the coefficient of determination (coefficient of determination). If this value should ever be the ideal value 1, you have usually done something wrong or only two measurement points. Here I show you the very similar curve that the TIMA5 outputs after the individual measurements. The colours and numbers on the curves, points and result fields correspond to those of the first diagram:
Let’s briefly summarize what we have just read. The vector calculation helps to visualize the thermal resistances for different bondline thicknesses as points in a coordinate system. By extrapolating this data to the case BLT=0BLT=0, the interface resistance is obtained. And this is exactly what I need in order to draw conclusions about the bulk values, which are rather far removed from practice and which, according to my methodology, are still much lower than what is stated on most packaging, but correspond exactly to what serious manufacturers in the industrial sector state. After all, I use their calculations as a guide.
What you can do wrong is shown by this ‘measurement’, in which the measuring points are set via the BLT(2) in such a misappropriated way and only two are included in the evaluation that the result is pure nonsense. Note also the coefficient of determination, which is now logically 1, which is completely absurd, as we are measuring a heterogeneous medium and only two points are not enough. But you can also see how to calculate the highest possible thermal conductivity. But there is still a section to come…
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