A special "measurement" option is provided for integral (cumulative) structure functions. In case of radial heat-spreading – but only in that case – in a thin material layer a straight line with constant slope can be observed in the corresponding section of the integral structure function. It can be proven that this slope is proportional to the thermal conductivity of the layer:
where w denotes the layer width, and λ stays for the thermal conductivity - the C and R values denote the coordinates of two points in the integral (cumulative) structure function. Once the layer width is known, it is easy to calculate the corresponding λ thermal conductivity.
The layer width for such a λ measurement can be defined in the Set layer width window (choose the Set layer width item from the Manipulate menu). The λ measurement itself can be activated by the Measure Heat Conductivity item of the Manipulate menu.
Figure 4-48: Interactive identification of the effective thermal conductivity in a material layer where radial heat-flow occurs
The program calculates a regression line between two locations of the cumulative structure function. When the Measure lambda option is switched on, a mouse click places a marker on the plot. With a second mouse click another marker is placed and the regression line is calculated and drawn. Its slope divided by the layer width will be displayed in the plot window as well as the identified λ thermal conductivity. Figure 4-48 presents an example: the thermal conductivity calculation for the ceramics substrate of an MCM module – with an assumed substrate width of 2 mm – yields 5.47 W/mK.
Note: In general, the result of such a λ measurement can be assumed as a good estimate. More accurate values can be obtained if T3Ster measurements are carried out in a fixture ensuring radial heat-flow. Such fixtures are available from MicReD on request. The value is misleading if the heat flow is not of radial nature in the given region.
Figure 4-49: Effective thermal conductivity measurement in a plot after subtracting the parallel Rth path
Figure 4‑49 illustrates the measurement of the thermal conductivity in a radial region with and without correcting the parallel heat conductance path.
