Online proceedings - EDA Publishing Association

7-9 October 2009, Leuven, Belgium
keff (W/mK)
8
7
6
5
4
3
2
1
0
B3 (p=2 mm) - k_eff
D1 (p=1 mm) - k_eff
D1 (p=1 mm) - RA
B3 (p=2 mm) - RA
0 0.5 1 1.5 2 2.5 3
Pressure (MPa)
0.001
0.0009
0.0008
0.0007
0.0006
0.0005
0.0004
0.0003
0.0002
0.0001
conductivity and specific thermal resistance are plotted as a
function of pressure in Fig. 7. Here, while the higher featuredensity
sample “D1” exhibits higher effective thermal
conductivity at all pressures, its overall thermal resistance it
actually higher in the upper pressure range. This is due to the
inability to compress the sample to as thin a bondline as
sample “B3” as indicated in Fig. 6.
C. Effect of Feature Shape
A direct comparison was made between the baseline case
of the circular-based hollow cone (sample “B”) and a squarebased
hollow pyramid of similar outer dimensions and
thickness (sample “C”). The variation of pressure as a
function strain is presented in Fig 8. Clearly, the squarebased
pyramid requires less force to deform to a given strain.
It is hypothesized this is due to stress concentrations that
exist where the sides of the pyramid meet as opposed to the
somewhat stiffer axisymmetric buckling that would occur in
the circular hollow cone as predicted by early model results
[6].
From a thermal standpoint, the pyramid structure exhibits a
Pressure (MPa)
Fig. 7: Variation of effective thermal conductivity and specific thermal
resistance with pressure for MMT-TIMs of two different pitches
3
2.5
2
1.5
1
0.5
0
0 20 40 60 80 100
Strain (%)
0
B3 (cone)
C1 (pyramid)
Fig. 8: Variation of compressive pressure with strain for two conical
and pyramidal MMT-TIM geometries of similar dimensions
RA (m 2 K/W)
keff (W/mK)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
B3 (cone) - k_eff
C1 (pyramid) - k_eff
B3 (cone) - RA
C1 (pyramid) - RA
0 0.5 1 1.5 2 2.5 3
Pressure (MPa)
0.001
0.0009
0.0008
0.0007
0.0006
0.0005
0.0004
0.0003
0.0002
0.0001
Fig. 9: Variation of effective thermal conductivity with pressure for
conical and pyramidal MMT-TIMs
somewhat lower effective thermal conductivity over the
range of applied pressure, as illustrated in Fig 9. In terms of
specific thermal resistance, however, at low pressures, the
pyramidal MMT-TIM has a lower thermal resistance. At
higher pressures, the conical shaped MMT-TIM represents
the optimum geometry.
D. Thermal Contact Resistance of MMT-TIMs
These results serve also to highlight the main challenge in
characterizing the thermal performance of MMT-TIMs:
specifically distinguishing the bulk thermal resistance of the
MMT-TIM from the contact thermal resistance with the
meter bars of the test apparatus. Typically, for conventional,
homogeneous TIMs, the contact resistance can be
characterized experimentally by measuring several
thicknesses of TIM, plotting the thermal resistance as a
function of thickness and extrapolating contact resistance as
the y-intercept where the thickness is zero [8]. For MMT-
TIMs however, this method cannot be used due to the nonuniform
behaviour of the bulk TIM.
The specific thermal resistance of each TIM is plotted as a
function of pressure at 50% strain in Fig. 10. Overall, there is
a decreasing trend in thermal resistance, which demonstrates
that, generally, stiffer structures offer a lower overall thermal
resistance. This is indicative of the important role thermal
contact resistance plays in the thermal performance of these
TIMs. However, compliance is also required of thermal
interface materials to avoid exerting excessive stresses on the
mating parts. Thus a trade-off between thermal resistance
and compressive pressure exists. To this point, sample “D2”
exhibits over a 3 fold increase in compliance (i.e. reduction in
pressure required to achieve 50% strain) while exhibiting a
relatively small increase in thermal resistance (~0.00005
m2k/W)
The thermal contact resistance and electrical contact
resistance are qualitatively similar as both of these
phenomena depend on the ratio of actual, intimate contact
area to the apparent contact area [9, 10]. However, whereas
thermally the bulk resistances are on similar orders of
magnitude as the contact resistances, electrically the
0
RA (m 2 K/W)
©EDA Publishing/THERMINIC 2009 214
ISBN: 978-2-35500-010-2