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1D Non-Equilibrium Green's Functions Framework

Scientific area

Non-Equilibrium Green's Functions for transport phenomena.

Short description

Heterogeneous interfaces play an important role in a wide range of modern solar cell concepts, from the silicon heterojunction solar cell, to the bulk heterojunction architecture in organic photovoltaics, or the different contacting schemes in the rising field of perovskite solar cells. Despite this high relevance, charge carrier transport and recombination across such interfaces is, in many cases, difficult to handle and predict. Modeling charge transport across interfaces requires open boundary conditions for the underlying equations. Moreover, the interaction of charge carriers with photons and the lattice vibrations calls for a mathematical description that goes beyond the ballistic transport.

Central to the prediction of material properties for solar cells is the utilization of an accurate and versatile simulation software intended to treat all of the relevant processes on equal footing and enabling an efficient exploration of the parameter space. Modern quantum transport simulation codes are based on the Non-Equilibrium Green's Function formalism (NEGF), which represents the state of the art in the theory and simulation of transport at the nanoscale. Simulations based on NEGF provide unique physical insight, but they are also computationally demanding especially when the target are simulations of real-world heterojunctions. On the other hand, the exploration of parameter-space would require high-throughput accurate simulations. Consequently, one of the keys to successfully predict material properties is a highly efficient and optimized numerical implementation.

We have developed a new version of a NEGF code, termed 1D-NEGF, with the aim of obtaining an efficient and scalable implementation for the NEGF framework. The code 1D-NEGF is focused on proof-of-concept optimizations.

The underlying data structure and data distribution in 1D-NEGF are generic to NEGF simulations, so that the parallelization strategy of the proof-of-concept code is a blueprint of an approach that can be adopted by simulation software with additional physical functionality. The distributed memory parallelization implemented in 1D-NEGF allows the user not only to use larger computing resources more efficiently, but also to compute bigger, and so more realistic, physical system as well as achieve an increased accuracy through incrementally finer grid sizes. Thus, the complexity of simulations of real-world nanostructures enables the exploitation of pre-Exascale computing resources.

1D-NegFSpectral current of a diode simulated with 1D-NEGF. The insert shows the integrated current with the flat line indicating that the current is conserved.


  • 458,752 cores on BlueGene/Q (JUQUEEN)

Strong scaling of 1D-NEGFThe strong scaling scaling behavior on the entire JUQUEEN. This data was obtained with a problem size of N_K = 64, N_E = 1792, and N_P = 100.

Programming language and model

  • C
  • MPI with OpenMP

Tested on platforms

  • BlueGene/Q
  • x86 (JURECA, Claix)
  • Intel Xeon Phi (KNL, JURECA Booster)

Application developers

Sebastian Achilles
Supervised by: Paolo Bientinesi, Edoardo Di Napoli, Urs Aeberhard


Sebastian Achilles
Aachen Institute for Advanced Study in Computational Engineering Science
RWTH Aachen
Schinkelstr. 2
52062 Aachen

Simlab Quantum Materials

(Text and images provided by the developers)









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