Skip to main content
Log in

Domain decomposition strategies for the two-dimensional Wigner Monte Carlo Method

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

A domain decomposition approach for the parallelization of the Wigner Monte Carlo method allows the huge memory requirements to be distributed amongst many computational units, thereby making large multi-dimensional simulations feasible. Two domain decomposition techniques—a uniform slab and uniform block decomposition—are compared and the design and implementation of the block decomposition approach, using the message passing interface, is discussed. The parallel performance of the two approaches is evaluated by simulating a representative physical problem. Our results show that the presumably inferior slab decomposition method is in fact superior to the block decomposition approach, due to the additional overhead incurred by the block decomposition method to set up its communication layer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

References

  1. Wigner, E.: On the quantum correction for thermodynamic equilibrium. Phys. Rev. Lett. 40, 749 (1932). doi:10.1103/PhysRev.40.749

    Google Scholar 

  2. Querlioz, D., Dollfus, P.: The Wigner Monte-Carlo Method for Nanoelectronic Devices: Particle Description of Quantum Transport and Decoherence. Wiley, New York (2010). ISBN: 9781848211506

    Google Scholar 

  3. Nedjalkov, M., Kosina, H., Selberherr, S., Ringhofer, C., Ferry, D.K.: Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices. Phys. Rev. B 70, 115319 (2004). doi:10.1103/PhysRevB.70.115319

  4. Nedjalkov, M., Schwaha, P., Selberherr, S., Sellier, J.M., Vasileska, D.: Wigner quasi-particle attributes—an asymptotic perspective. Appl. Phys. Lett. 102(16), 163113 (2013). doi:10.1063/1.4802931

    Article  Google Scholar 

  5. Sellier, J., Dimov, I.: The Wigner–Boltzmann Monte Carlo method applied to electron transport in the presence of a single dopant. Comput. Phys. Commun. 185(10), 2427 (2014). doi:10.1016/j.cpc.2014.05.013

    Article  Google Scholar 

  6. Sellier, J., Nedjalkov, M., Dimov, I., Selberherr, S.: Two-dimensional transient Wigner particle model. In: Proceedings of the 18th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), pp. 404–407 (2013). doi:10.1109/SISPAD.2013.6650660

  7. Sellier, J.M., Nedjalkov, M., Dimov, I., Selberherr, S.: The role of annihilation in a Wigner Monte Carlo approach. In: Lirkov, I., Margenov, S., Wasniewski, J. (eds.) Large-Scale Scientific Computing. Springer, Berlin (2014). doi:10.1007/978-3-662-43880-0_20

  8. Ellinghaus, P., Weinbub, J., Nedjalkov, M., Selberherr, S., Dimov, I.: Distributed-memory parallelization of the Wigner Monte Carlo method using spatial domain decomposition. J. Comput. Electron. 14(1), 151 (2015). doi:10.1007/s10825-014-0635-3

    Article  Google Scholar 

  9. Dimov, I.: Monte Carlo Methods For Applied Scientists. World Scientific Publishing, Singapore (2005). ISBN: 9789810223298

    Google Scholar 

  10. Weinbub, J., Ellinghaus, P., Selberherr, S.: Parallelization of the two-dimensional Wigner Monte Carlo method. In: Lirkov, I., Margenov, S., Wasniewski, J. (eds.) Large-Scale Scientific Computing. Springer, Berlin (2015, in press)

  11. Vienna, W.D.: Wigner Ensemble Monte Carlo Simulator. (2015). http://viennawd.sourceforge.net/

  12. Hager, G., Wellein, G.: Introduction to High Performance Computing for Scientists and Engineers. CRC Press, Boca Raton, FL (2010). ISBN: 9781439811924

    Book  Google Scholar 

  13. Vienna Scientific Cluster. VSC-3. (2015). http://vsc.ac.at/

Download references

Acknowledgments

The computational results presented have been achieved using the Vienna Scientific Cluster (VSC).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Josef Weinbub.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Weinbub, J., Ellinghaus, P. & Nedjalkov, M. Domain decomposition strategies for the two-dimensional Wigner Monte Carlo Method. J Comput Electron 14, 922–929 (2015). https://doi.org/10.1007/s10825-015-0730-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-015-0730-0

Keywords

Navigation