Hi all,
I was wondering if there is some theoretical insight in the relative contribution to the resistivity of grained thin metal or semiconductor films coming from bulk grain boundary scattering or 2D surface scattering? I know the Fuchs–Sondheimer model and Mayadas–Shatzkes model are commonly applied to describe the surface and grain boundary scattering phenomena. I also know that experiments in copper have pointed out that grain-boundary scattering is the dominant contribution to the resistivity in nanometer sized copper thin films. I was wondering if there is a way to extent these findings to different metals or even semiconductors?
Kind regards,
Niels
Hi Niels,
let me recap. In general, the resistivity contribution from grain boundary and surface scattering depends on the details of the dominating scattering processes. It can be diffusive (forgetting the direction where the quasiparticle was coming from) or specular (where there is a correlation between the incoming and outgoing state) or something in between. Additionally, one can distinguish elastic and inelastic scattering processes. In contrast to surfaces, for scattering at interfaces the knowledge regarding the transmission spectrum (which in general is a function of incoming and outgoing wave vectors with respect to the surface normal and polarization) is required. Depending on the materials, the temperature, surface roughness, segregation of elements on the grain boundary etc. play a role. In contrast to the commonly applied Matthiessen’s rule, the scattering mechanisms can become dependent on each other (particularly in the case of nanostructures). Thus, even if the Boltzmann equation is commonly agreed to be the correct model when wave effects are negligible, explicit modeling of the geometrical features might become necessary. Thus, there is certainly not a unified single model available to provide a universal answer to your question.
BR,
René
Hi René,
Thank you for sharing your subject knowledge. Indeed, giving it a second thought, it would be very fortunate to have a somewhat universal answer to such a complex question.
Thanks again,
Niels
Hello Niels,
the influence of surface scattering is well described by Rene Hammer. It depends on the surface properties and the mean free path of charge carriers.
The grain boundaries - especially if they stand vertical to the surface can influence strongly the resistance. The carrier must overcome a potential difference what enhances the resistance. But the difference de can be small - in this case the boundary is without influence, especially at high conductivity. Nevertheless, the temperature dependence of this barrier exp(-de/kT) gives an exponential T-dependence. Furthermore, the hanging bindings at the boundary influence the conductivity n*µ (n: carrier concentration, µ-mobility).
You can approximate a boundary as a micro-junction (either p-n- or hetero junction or a Mott-contact). In every case you observe an increase in resistivity.
But I would say: in thick layers, the boundary resistance is the dominant resistance, in thin layers the surface scattering. But this is only a "rule", not a "law".
With Regard
R. Mitdank
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Semiconductor