Calculating temperature rise of aluminum wire

[quid007]

I am interested in calculating the temperature rise of a 10 mil aluminum bond wire. Assuming relative purity of the wire, I feel like I should be able to use the method I have worked out below. If anyone can advise on the accuracy of my method, it would be greatly appreciated.

Method:

1. Calculate electrical resistance of wire base on either (resistivity * length) / cross-sectional area or from tables.

2. Use required current and resistance according to (i^2)*R to calculate power dissipation

3. Calculate thermal resistance according to length / (thermal conductance * cross sectional area)

4. Calculate thermal rise according by power 8 thermal resistance


Thanks in advance...

 

[f95toli]

The problem is that you also need to consider the energy that is being conducted away from the wire, unless you are considering a wire that is not connected to anything its temperature will mainly depend on the temperature of the metal of the pad it is bonded to.
You also need to consider the properties of the interface between the alumium and the contact pad, this is not trivial unless the pad is also made form Al.

Also, as far as I remember the Al used in bond wires isn't actually pure; it is alloyed with something (silicon?).

 

[vk6kro]

A similar method is used to find the temperature of transformer windings.

You measure the resistance at a known room themperature.

Then, knowing the thermal coefficient of resistivity for Aluminum, measure the resistance again, using the voltage and current method, when it is hot. From this you can estimate the average temperature.

One problem is that Aluminum is a very good electrical conductor, so it is hard to measure the resistance of a small sample of it.
You can do it by sending a large current through the Aluminum, but this contributes to the heating. So, unless this is how you are heating the Aluminum, the extra current will upset the result.

You can get non-contact thermometers that work well, but they wouldn't work on just a single strand of wire.

 

[quid007]

So then...

1. The aluminum is not pure and since yesterday I have run down the material properties of what I have. (And silicon is correct) Therefore, I have the relevant properties to make said calculations.

2. The wire is bonded on one side to an Al pad with known dimensions and I can calculate the thermal stackup properties (I Think) taking into account spreading angles and what not. (I will use the 45 degree approximation unless I should think otherwise.)

3. The other side of the wire is bonded to an Au trace that connects the die to the rest of the circuit.

The question remains then, is there a point at which I can draw a box around it and get a reasonable estimate of the temp rise in the wire? Otherwise, it seems like I would need to follow the Au trace down its path which would then effectively account for all elements of the circuit, increasing complexity by a non-trivial amount.


Thanks again...