How electrons and phonons promote heat transfer in material systems

Miniaturisation is one of the key features of current and future technologies for information processing and control. However, the ability to reduce the size of an electronic component is limited by a decrease in electrical conductivity and an increase in thermal energy dissipation as the device approaches the nano-scale regime. By studying the electronic and vibrational characteristics of high-purity iridium films within Ir/Al/MgO material systems, Dr Chris Perez and his collaborators at Stanford University, USA, revealed the mechanisms behind thermal transport in these systems.

Present-day electronic devices for both technology and mass consumption rely on integrated circuits, which contain billions of transistors. Transistors are linked to each other by metal wires known as interconnects. Interconnects are responsible for transferring signals within a circuit and for ensuring the distribution of electric power within the device.

Nanoscale electronics

The increasing complexity and demands of modern electronics have resulted in a progressive reduction in the size of the transistors, as smaller transistors have higher processing speed, lower energy consumption, and they can be packed in larger numbers within smaller areas. A parallel reduction in interconnect sizes has however been far more difficult to achieve. As the wires are made thinner, their electrical conductivity decreases, and energy is dissipated in the form of heat, which can limit the performance, reliability, and efficiency of an integrated circuit. Improving the thermal properties of interconnects is therefore one of the central challenges in integrated electronics and for enabling the development of future alternative computing approaches based on nanotechnology, including spintronics (taking advantage of the natural magnetism of electrons, as well as their charge, to produce faster computers) and neuromorphic computing (a computing approach inspired by the structure and function of the human brain).

Size effects

Interconnects are one example of so-called high-aspect ratio metals, in which one dimension is much larger than the other two. Modern nanotechnology makes it possible to create nanoscale versions of these tiny wires, with sizes approaching those of a DNA molecule. However, the decrease in the cross-sectional area enhances the scattering of electrons at the wire surface, which decreases their kinetic energy. Additionally, grain boundaries, which are interfaces between different crystalline domains within the metal structure, can reduce electron mobility. Together they explain the ‘size effect’ that is responsible for the reduced electrical conductivity observed in thinner wires compared to bulk metals.

Interconnect materials

Traditionally, copper is used in interconnects, because of its high electrical conductivity. However, it has been shown that in a copper nanowire with a diameter of the order of ten nanometres (where one nanometre corresponds to a billionth of a metre), the resistivity increases by one order of magnitude compared to the bulk metal, in turn resulting in an approximate 40-times increase in signal delay and energy consumption. ‘This is bad news for nanometre-scale electronic devices’, explains Dr Chris Perez of Stanford University, USA, ‘because pumping electrical current into copper nanowire interconnects will inevitably cause self-heating and dramatic thermal energy dissipation.’

Novel concepts in interconnect engineering

Using materials other than copper has been proposed as a way to minimise the consequences of the size effect in interconnects. Substantial advances in materials modelling, discovery, and fabrication, however, are required before a suitable substitute for copper can be applied in technological applications. Two-dimensional materials can offer a promising alternative to traditional copper nanowires. Atomically thin systems, like single-layer graphene, hexagonal boron nitride (hBN), and transition metal sulphides (for instance, MoS2 and TaS2), can serve as liner materials for metals like copper or cobalt. The interfaces between these 2D materials and the metals are characterised by very low metal resistivities, potentially providing a route toward the fabrication of narrow metallic interconnects with high conductivity.

Phonons as heat carriers

Considerable insight into the mechanisms responsible for heat conduction in this context has come from the study of metal/semiconductors multilayer composites, or heterostructures. These heterostructures are composed of layers of a thin metallic material alternate with semiconducting layers. Whereas in metals the thermal (and electrical) conduction is typically attributed to the migration of free electrons – electrons that reside within the metal lattice and are not bound to the atomic nuclei – in semiconductors unbound electrons are absent. Heat conduction is in this case explained by the migration of phonons, which are collective vibrations of the atoms in the crystal structure of the semiconductor.

Thermal transport in heterostructures

Phonons behave like quantum-mechanical particles, and can act as carriers of heat within a semiconductor. However, in metal/semiconductor heterostructures where the thickness of the metal layers is of the order of a few nanometres, phonon conduction can provide a heat transport mechanism even for the metallic layers. This mechanism dramatically enhances thermal transport across the layer for these specific systems. Besides, as the thickness of the metallic layers is reduced to values comparable to the electron mean free path – the mean distance travelled by an electron before it collides with lattice atoms, losing part of its kinetic energy – more electrons can travel to the metal/semiconductor interface, where they are scattered inelastically. Their energy can then be transferred to the phonons, and this provides a mechanism that channels energy from the electronic heat-transfer system in the metal to the phonon system in the semiconducting layers, further enhancing the thermal conductivity across the heterostructure.

All-metal heterostructures

Thermal conduction through phonons has also been shown to play an important role in heterostructures composed solely of metallic layers, with two different alternating sets of stacked metals, for instance gold and nickel. Both electrons and phonons are present in a metal, and they can act as carriers for heat transport. Nonetheless, conduction through the free electrons within the metal lattice is typically considered to be the dominant mechanism of heat transfer in metals. In metallic heterostructures, however, heat exchange at the interface of two different metal layers can only occur through phonons, as electrons have been classically considered unable to travel through the boundary.

Electron–phonon coupling

A potential mechanism explaining heat transport through metallic heterostructures invokes electron–phonon interactions. ‘For heat to flow through an interface’, says Perez, ‘the energy carriers, either phonons or electrons, need to mix, or couple, and exchange energy. Energised phonons can then carry this energy across the interface.’ Electron–phonon coupling in nanometre-thin metal layers thus plays a crucial role in heat conduction in metallic heterostructures.

Iridium thin-film nanostructures

This work on metal/semiconductor and metal/metal nanostructures is providing evidence for the existence of ‘non-classical’ paths for heat migration across nanometre-sized layer interfaces, which can in principle be exploited to optimise the ability of new devices to conduct heat. Perez and co-workers have built upon these findings to develop a more detailed model of how electrons and phonons behave in heterostructures. They have studied the thermal behaviour of high-quality thin iridium layers interposed between aluminium metallic layers and magnesium oxide insulating layers using electro-thermal measurements and phenomenological modelling.

Phonon spectrum and heat transport

A central result of Perez’s work is that the ability of phonon carriers to migrate at layer interfaces is critically linked to the nature of their spectrum. Depending on the chemical composition and structure of a crystalline lattice, phonons exhibit different behaviours as a function of the vibrational energy. It is the degree of mismatch of the phonon spectra that determines how easily phonons can migrate from one material to another. For nanoscale layers, as the thickness approaches the mean free path of the heat carriers, thermal transport involves the interaction of the neighbouring interfaces and both electron and phonon act as carriers within the metal layer. Depending on the thickness of the metal layers, cross-interface heat conduction can occur according to three distinct modes: electron-dominant, phonon-dominant, and electron–phonon energy conversion-dominant. In actual systems, it is the interplay of all these phenomena that ultimately determines the thermal characteristics of metallic heterostructures.

Perez’s findings shed new light onto previously unexplored physical aspects of heat conduction and energy conversion processes between different heat carriers. They also have important practical and technological implications, paving the way for the fabrication of new electrical and thermal devices in which the dominant mechanism of transport can be tuned by adjusting the thickness and structure of the layers in metallic heterostructures.