Electron transport and resistivity scaling in nanostructures

The resistivity of metallic thin films and nanowires increases drastically when the film thickness or wire diameter is reduced. Correspondingly, electrical currents through these structures suffer from e.g. increased heating, power dissipation and transmission delay, all being undesirable effects for the typical nano-scaled conductor applications such as interconnects in semiconductor devices. Several experiments have shown that the resistivity increase is caused by an increase of electron scattering at grain boundaries and boundary surfaces of the structures, but the availability of solid resistivity scaling models for sub-10 nm nanostructures is rather limited.

In order to assess the performance of metallic thin films and nanowires for conductor applications in this regime, we study the electron transport and resistivity scaling properties with the semi-classical multi-subband Boltzmann transport equation. The material band structure and quantum mechanical effects of scattering and confinement of the electrons are taken into account and unlike the conventional Fuchs-Sondheimer and Mayadas-Shatzkes models, phenomenological fitting parameters are not required. Instead, the statistical grain, surface and barrier properties, such as the grain density or the surface roughness correlation length, enter the model through scattering rates based on Fermi's golden rule and a generalized ensemble averaging procedure. With an analytical expression for the solution of the Boltzmann equation and the scattering rates, we are able to perform fast and accurate transport simulations. Furthermore, the validity of the considered perturbative semi-classical approach is investigated by looking at the higher-order corrections of Fermi’s golden rule and a derivation of the self-consistent relaxation time solution of the Boltzmann equation from quantum mechanical linear response theory is presented.

Transport properties are obtained for thin films, nanowires and graphene nanoribbons, a promising alternative for future nano-scaled conductors, with realistic parameters for the relevant scattering sources of each nanostructure. While the resistivity scaling of thin films is well described with the conventional resistivity scaling models, our approach shows deviant behavior for nanowires and graphene nanoribbons. This is caused by confinement, leading to quantized electron state wave vectors along the transport direction with possible suppression of surface roughness scattering. The effect offers a window of opportunity to reduce resistivity scaling, but it is hard to exploit for nanowires with large conduction electron densities as extreme fine-tuning of the average wire side lengths is required. For grain boundary scattering, the general rule for optimal resistivity scaling remains maximizing the average grain size. Graphene nanoribbons do not suffer from grain boundaries and the suppression of edge roughness scattering is quite robust against width variations, but the carrier density is typically much lower and substantial doping adds additional scattering sources in the form of charged dopants.