A new method in ATK for reliable and efficient calculations of resistivity and mobility including electron-phonon coupling effects

Aug 21 2017

A new paper using ATK has been published in Phys. Rev. B [1] as a product of collaboration between QuantumWise and a group of researchers at the Technical University of Denmark. The paper presents a new method, MD-Landauer, combining Green's function transport and molecular dynamics (MD) for reliable and efficient calculations of resistivity and mobility including the effect of electron-phonon couplings (EPCs), which plays a central role in the performance of most electronic devices.

The MD-Landauer approach is validated against experimental results and state-of-the-art calculations using the Boltzmann Transport Equation (BTE) method [2]  for a variety of systems: Si and Au nanowires, Si and Au bulk, Carbon Nano Tubes (CNTs) and graphene (see Fig 1). The calculated mobilities and resistivities agree semi-quantitatively with those calculated using the BTE method and with experiments, and trends are correctly reproduced. This shows that the MD-Landauer method is an appealing alternative to BTE to treat EPCs in large and complex (for example, non-crystalline, with defects and substitutions) systems. Full-scale Density Functional Theory electron-phonon calculations are just starting to become available as a method, and the MD-Landauer approach makes them much more reasonable in terms of computation time.

nilandauer transmission 3

nilandauer plots 1

Fig.1.Schematic illustration of the workflow of the MD-Landauer method: 1. A number (10-50) of MD trajectories are equilibrated at a target temperature using a random Maxwell-Boltzmann distribution of initial velocities  to create an ensemble of snapshots of the structure at that temperature. 2. The electronic transmission is calculated for all the snapshots using the ATK-DFT+NEGF approach and the resulting transmission functions are averaged to obtain the finite temperature transmission time average.  3. The temperature-dependent resistivities can be obtained from time average . 4. Mobilities can be obtained from the calculated resistivities and the density of states.

Relevant resources

Following this paper, QuantumWise prepared a case study on calculating resistivity for Au bulk. On our website you can also find general tutorials on calculating transmission/resistivity and  evaluating mobility (with the BTE approach). Investigated systems (Si and Au nanowires and bulk, CNTs and graphene) were constructed and optimised using the VNL user interface.

Check out the ATK paper on an even more computationally efficient method for treating EPC, i.e., Special Thermal Displacement-Landauer (STD-Landauer), and its applications to the ultra-scaled silicon devices [3].

Both methods, MD-Landauer and STD-Landauer, were presented by QuantumWise at the International Workshop on Computational Nanotechnology.

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[1] T. Markussen, M. Palsgaard, D. Stradi, T. Gunst, M. Brandbyge and K. Stokbro, "Electron-phonon scattering from Green's function transport combined with molecular dynamics: Applications to mobility predictions", Phys. Rev. B 95, 245210 (2017). arXiv, pages 1701.02883v1, 2017. URL: arXiv:1701.02883.

[2] T. Gunst, T. Markussen, K. Stokbro and M. Brandbyge, "First-principles method for electron-phonon coupling and electron mobility: Applications to two-dimensional materials", Phys. Rev. B 93, 035414 (2016). arXiv, pages 1511.02045v1, 2017. URL: arXiv:1511.02045.

[3] T. Gunst, T. Markussen, M. L. N. Palsgaard, K. Stokbro and M. Brandbyge, "First-principles electron transport with phonon coupling: large scale at low cost", Phys. Rev. B 96, 161404 (R) (2017) arXiv, pages 1706.09290, 2017. URL: arXiv:1706.09290.