Advances in thermal management technology are required to meet thermal demands, especially for devices that require high heat dissipation while requiring very precise temperature control down to a few tenths of a degree. In this context, there is a critical need for novel thermally highly conductive materials in combination with advanced thermal control technologies.

To this end, various composite materials are being experimentally investigated, including Ag-, Cu- or Al-based MMCs and highly conductive inclusions such as carbon fibres, graphite flakes, diamonds and carbon nanotubes (CNTs), which have the potential to solve the problems. One of the most important problems is the thermal mismatch between the heat sources and the heat sinks. This leads to the development of composites where the matrix has a high intrinsic thermal conductivity and the fillers have both a high intrinsic thermal conductivity and a very low coefficient of expansion, resulting in a material with an overall low CTE and high conductivity. Due to the CTE mismatch between the heat sources and the heat sink materials, delamination can occur, leading to component failure.

The figure shows the problem of thermal mismatch with highly conductive matrices such as Ag or Cu and the low CTE of standard semiconductor heat source materials (Si, GaAs,...) as well as the properties of fillers such as diamonds and also some commercially available composites (Al/SiC, Cu/Cf and Al/Cf composites).

The diagram shows the relationship between thermal conductivity and coefficients of expansion of various materials that are important for heat-sink applications

The diagram shows the relationship between thermal conductivities and thermal expansion coefficients of different materials that could be of importance for heat-sink applications. The diagram shows that there is a "gap" between the typical semiconductors such as Si, GaAs and the most highly conductive metals such as Cu, Ag and Al. However, by using MMCs with very highly conductive materials such as diamonds, C-fibres, etc., the coefficient of thermal expansion can be matched to that of the semiconductor material and at the same time the highest thermal conductivities can be achieved, which are needed to effectively dissipate the high heat loads from the semiconductors.

Although the interface between the constituents of a composite material is a complex issue, it is of enormous importance to control the stresses and the interfacial thermal conductance in order to exploit the full potential of highly conductive phases. Therefore, the interface must be carefully addressed.
This is done either by using metallic alloys with small additions of carbide-forming elements, by adding elements with certain affinity to carbon, or by depositing thin intermediate layers of carbide-formers on the reinforcing phases. Such an interlayer can also be achieved by mixing at the molecular level or by gas phase transport deposition. Research is focused on theoretical considerations as well as on the study of growth mechanisms. Another, quite new approach is to either increase the specific surface roughness of diamonds to reduce the local heat flux or to influence the surface termination of the diamonds. The latter has proven to be quite effective in drastically reducing the thermal resistance at the interface. Increasing the surface roughness can be achieved relatively easily by treating diamond powders in acids such as sulphuric acid, nitric acid or aqua regia, respectively. The termination of the surfaces can also be easily achieved by oxidative or reducing treatments.

Theoretical approach to improve interface conductivity in composites

The interface conductance between the matrix and the highly conductive inclusions can be positively influenced in various ways: on the one hand by means of intermediate layers, which are created either by adding "active" elements to the matrix or by coating the inclusions with suitable elements, by surface structuring to increase the surface area, which can reduce the local heat flux density, or by suitable surface termination of the highly conductive inclusions. The latter is especially important for diamonds, since they are hydrogen-terminated on the surface due to their production. However, oxygen termination can significantly improve the phonon transition probability. This can also be seen, for example, in a clear change in the wetting behaviour on differently terminated diamond surfaces.

Phonon density of states of different substances as a function of angular frequency

Phonon density of states of different materials as a function of angular frequency. By inserting intermediate layers with good electrical conductivity and an average Debye temperature, the phonon transmission probability coefficient between highly conductive diamonds and a metallic matrix (here aluminium) can be improved. In principle, large differences in Debye temperatures between a metallic matrix and a highly conductive inclusion prevent efficient phonon transition, but this can be positively influenced by selecting suitable interlayers.

Influence of contact time during gas pressure infiltration on thermal conductivity in Al-diamond MMCs

In Al-diamond MMCs, the manufacturing method has a significant influence on the formation of interface reactions and thus the formation of certain reaction products. For example, aluminium carbide Al4C3 forms between aluminium and diamond. On the one hand, this is important for a good phonon transition between the phonon conductor (diamond) and the electron conductor (metal) and thus for a high overall thermal conductivity in the composite material. However, this carbide is also very hygroscopic and can thus lead to the destruction of the component in the worst case. Therefore, the control of carbide formation is of particular importance. We were able to show that in the case of production via gas pressure infiltration, the control of the contact time between the Al melt and the diamonds is very important. The carbide formation is also influenced by the addition of Si to the Al. We were also able to quantify the amount of carbides analytically for the first time.

The formation of an Al-carbide in Al-diamond MMCs as a function of manufacturing conditions

The formation of an Al-carbide in Al diamond MMCs as a function of the manufacturing conditions: the higher the contact time between melt and diamond during gas pressure infiltration, the more Al4C3 is formed, although this can vary again at the different crystallographic planes of the diamonds. Adding Si to Al also significantly changes the amount and morphology of the Al4C3 crystals.

The aim of these investigations is to gain knowledge about the thermal (and possibly also electrical) conductivity of metal matrix composites in the temperature range from 4K to ambient temperature. Highly conductive fillers such as diamonds are added to a matrix of Ag, Al or Cu by liquid metal infiltration methods or by PM processes. Small samples are mounted in a 4He cryostat and as they are run through the temperature programme up to 300K, a steady-state heat flow is created between a heater and a heat sink anchored opposite each end of the sample. This allows the thermal conductivity to be determined (cooperation with the Institute for Solid State Physics at the TU Wien, Prof. Dr. E. Bauer).

Schematic measuring arrangement for the determination of thermal conductivity in the temperature range between 4K and room temperature

Schematic measuring arrangement for determining the thermal conductivity in the temperature range between 4K and ambient temperature. The necessary temperature gradient over the sample length is generated via a strain gauge on one side of the sample, the other side is in contact with a heat-sink. The entire sample is then placed in a 4He cryostat, cooled to approx. 4K and then slowly reheated to room temperature.

The thermal conductivity and electrical conductivity of Ag-3Si between 4K and room temperature

The availability of the room temperature and the 4-K values of the electrical resistance generally allows the derivation of the so-called RRR ratio (Residual Resistivity Ratio) of the electrical resistance, which enables an evaluation of the residual silicon in solid solution. High-quality materials are characterised by large values of the RRR. While in a naïve view increasing Si content would be associated with increasing disorder in the sample and thus larger resistivities, experimental data show RRR ratios of 3.81, 4.23, 5.62 and 13.7 for x = 0.001, x = 0.0025, x = 0.005 and x = 0.03 Si, respectively. This indicates that the materials with low Si content are of poorer quality than those with higher Si content. Moreover, increased static disorder can be read off for x=0.001 from the residual resistance (ρ4.2 K =0.61μ Ωcm) compared to x=0.03, where ρ4.2K =0.17μ Ω cm is about less than a third of the first value. The reason for this observation may be due to either problems with the formation of Si precipitates, which do not form easily in an Ag-Si matrix. However, there is a good chance that Si diffuses to existing Si particles and is thus precipitated out of the Ag-Si solid solution.
Since there are many such existing Si particles in Ag-3Si, the diffusion path is short. In alloys with x ≪ 0.03, there are only a few Si particles for docking, so that the solid solution is kinetically stabilised. On the other hand, the solubility limit of Si in Ag can be seen here. Both support the decision to use Ag-3Si as matrix composition for the production of diamond composites.

Thermal conductivity of Ag diamond MMCs in the temperature range between 4K and room temperature

The diagram shows the thermal conductivity of Ag-3Si diamond MMCs in the temperature range between 4K and room temperature. There is a clear difference in behaviour between larger and smaller diamonds, as well as oxygen termination of the diamond surfaces and those that have not been treated and are therefore hydrogen terminated. Smaller diamonds lead to significantly lower thermal conductivities in the MMC, whereas the highest conductivities can be achieved with the largeest diamonds.

Interface conductivities of Ag-3Si/diamond MMCs in the temperature range between 4K and room temperature

The diagram shows the calculation of the effective interface conductance of Ag-3Si/diamond MMCs. The squares represent untreated diamonds, the triangles are the results of MMCs where the diamond surfaces were oxygen terminated. The data are compared with h(T) results obtained by Collins and Monachon on Al/O/diamond interfaces by TDTR "Time Domain Thermoreflectance" experiments. It was shown that the surface termination of the diamonds can significantly improve the interface conductivity in the Ag-3Si/diamond system.

Neutron diffraction investigations at FRM II in Munich on Al-diamond MMCs. The aim was to investigate the influence of different manufacturing parameters on the mechanical properties and the different stresses and strains between the metal matrix and the diamonds. It was found that the contact time between a metal melt and the diamonds during gas pressure infiltration, as well as the surface modification, have a significant influence on the interface adhesion or delamination between the partners.

Experimental setup for neutron diffraction at the FRM II in Munich for the measurement of strain in Al-diamond MMCs

Experimental setup for neutron diffraction at FRM II in Munich for the measurement of strain in Al-diamond MMCs at the Stress-Spec device.

Diagram showing strain versus stress in neutron diffraction of Al diamond MMCs

The diagram shows the strain versus stress during neutron diffraction of Al diamond MMCs produced by gas pressure infiltration at different contact times between melt and diamond. The longer this contact time, the stronger the interface is formed and higher stresses can be transmitted. However, the thermal conductivity of the composite decreases because a thicker aluminium carbide (Al4C3) interface forms between the diamonds and the Al matrix, which causes a higher interface resistance.