Contact resistance

With these two contacting plates, the formula used previously supposes they are in perfect contact, which would be the case if the two surfaces which make the interface between the two plates were perfectly flat and smooth.
Once again, reality is cruel but here we can't neglect it ! Surfaces in contact are not smooth nor flat, they always have a rough pattern which looks like this:

The effect of roughness is very important; in general the real surface contact area is never higher than 2% of the interface surface area, yes 2%!!! This leaves enough places for micro-cavities filled with air, which has a very bad thermal conductivity ( see the table of conductivities at the beginning ). All this thickness ( 0.5 - 60 mm for flat surfaces ) consisting of roughness and air gaps form a thin layer which will less conduct heat, this translates into contact resistance R_c which will depend of :

• the form and the distribution of roughness ( i.e. surface finish )
• the thermal conductivity of the air -or of the material- which fills the gaps ( higher is better )
• the hardness of materials and the contact pressure between the two plates ( softer materials and higher pressure allow to" crush " more easily roughness and thus offer a greater real surface contact area )
• the apparent interface surface area ( a larger interface offers less resistance )

This resistance is added to the thermal circuit :

The means to reduce the contact resistance are well known :

• lapping to obtain the smoothest and moreover the flattest surfaces' quality as the temperature can be reduced up to 4°C ( thanks to Bill Adams )
• replacing the air cavities by a substance of better thermal conductivity like thermal paste
• increasing the mounting pressure by tightening the assembly as much as possible ( but in practice within the range of what a cpu supports ! ).