What is a structure function? Let's start from the beginning. Let's take a very simple power
package. Here is the die, and at the top of a die is a heated area. Here is the die attach,
die attach is not normally this thick but I have drawn it like this to make it easier to see,
and here we have a copper base. The aim is to find out the temperature here, and the quality
of the die attached here. Here is how; we heat up the component by applying constant power,
then we start the measurement here at zero, at this point this area will get to a hot state and
the heat will spread in circles. There are two ways to illustrate heat spreading; we can use
heat flux vectors, which move from the heated area through the silicon verse then to the die attach,
and then they spread around into the base. The second way is to draw perpendicular lines to the
vectors, resulting in circles showing the heat spreading down from the hottest at the top here
and decreasing as we move away from the source. These lines denote isothermal surfaces. At the
beginning of the measurement, turn the power off and maintain it at a low level. The device
will then begin to cool down and the heat will retreat into the heat source, and the structure
slowly cools down This can be represented as a temperature versus time curve, you have probably
seen cooling curves shown over a linear timescale in the form of an exponential function. For
example, this is the way your morning coffee cools down. In the case of a thermal system,
we are curious to see the properties of very small package features such as a die attach,
as well as the big ones like a cold plate. We prefer to show the curve over a logarithmic time
scale like this. What is the relationship between this temperature curve and this picture here? This
curve can be explained with exponential functions. If we have a simple structure, for example just a
block of uniform copper, how can we describe it? The heat comes from the top. We can describe it
with a thermal resistance and a parallel connected thermal capacitance. The thermal resistance will
make sure that if we heat up from this point, the temperature will be different here, so we have T1
and T2. If we had the same temperature graph for this simple example, it will look something like
this exponential curve. Here is the equation. Here, we have the tower intensity diagram:
Tau =R x C. This basically means that if you have this model here, and you know the thermal
resistance and the Tau value, you can work out the C very easily. We can also show these in the plot
where we show the R value over the corresponding Tau value. If you have a more complex structure,
the same applies, but you just have multiple stages. If we know all the
Tau values and all the R values, we know the thermal properties of the system. On this curve,
we have an exponential function here, some smaller ones here, and another here. This curve is a sum
of many of these exponential curves where the R's and C's are different values. So what we have to
do, is to try and figure out the R's and C's in their models. Based on this curve,
we create a model like this. There is a mathematical way of getting these R and C numbers,
so we can give a perfect description of the behavior of our package. To do this,
the foster model can be transformed into the cauer model, which carries the same information,
but can be read as a physical model of the real structure. The elementary heat capacitances are
not parallel with the elementary heat resistances, instead, all refer to the ambient. To recap,
we measure this curve, then we break down the curve to a number of R's and C's,
then we do a mathematical transformation from a so called foster type thermal model, to a ladder
shaped cauer model. Once the translation is done and we have these values, the structure can be
very easily seen. The thermal resistances are defined between two isotherms, such as a delta
T between here, and divided by the Delta P. The thermal capacitance is proportional to the volume
between the two isotherms, for example, if we had a package with a cavity, the thermal resistance
will be larger, so the corresponding R's will increase and we will see the changes in the
structure function. This is just a network model, how do we get a full structure function out of it?
Along this axis, is the sum of the capacitances of the ladder model, and along the bottom is the sum
of the resistances. The heat propagates from here, then goes into a resistance, and some capacitance,
so the curve starts to go up. Then there is more resistance and capacitance, so the curve goes up
again. When the heat is going through the first part of the system, which is the die itself,
there is not much resistance, so the curve here is steep. When we move into the die attach,
which is very small so it doesn't store too much heat, but the thermal resistance is bigger
especially with a cavity there, we start to add more resistance. R is big so the line flattens
out. The length of this part of the curve will be in direct relationship with the size of the
cavity in the die attach. The heat eventually goes into the less resistive copper base,
which is shown by this steep part of the curve. If there is additional thermal interface material
after, the curve will flatten out, then go steep again as you hit a cold plate,
then the whole thing will cool down and go into infinite capacitance. If something goes wrong, for
example if the grease is bad, it will show up with a longer curve like this and the function will
go to the infinity further along. Or if the die attach is wrong, then this curve will be longer,
and again shifts the functions further along the graph. So in summary, we start with this picture,
then we cool it down, and based on the speed that the heat goes back, we get this bumpy
curve. From this curve we can derive the R and C values as these are all exponential functions,
we can get this foster model which can then be transformed into the ladder model,
which is a direct physical description of the first image, and then we plot some of the
resistances and capacitances. If something is very resistive, they will usually show as the flat part
of the curve. Something that is capacitive, usually structure or metal, is shown in the
steeper parts of the curve. Thank you for watching this introductory video to structure functions.
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