About ViennaWD

ViennaWD represents a union of  theoretical  and  numerical approaches for a particle-based simulation of quantum  phenomena in nanostructures, which is implemented in algorithms that form the suite of Monte Carlo simulation tools available on this website.

A particle-based approach is inherent to the simulation of classical mechanics and has provided deep insight in the phenomena governing the operation of microelectronic devices. However, the  emerging  field of nanoelectronics involves quantum phenomena which challenge the concept of classical particles. Nevertheless, the particle concept may be retained in the quantum world through use of the Wigner formalism. The Wigner formalism facilitates a formulation of quantum mechanics in the phase space in the form of the Wigner function. The Wigner function is often called a quasi-distribution since it  may  attain  negative values --  which is a manifestation of the uncertainty relations -- but can be used in the same manner as a classical distribution to calculate physical averages. This correspondence is the basic theoretical pillar of ViennaWD, realized through the generation/annihilation (g/a) of positive and negative particles [1]. The g/a process may theoretically explain and model phenomena over a wide range of physical scales: from  quantum-coherent evolution to classical Newton acceleration [2,3]. Furthermore, the environment-induced transition from a Wigner-quantum to a classical state -- a process known as Wigner Decoherence (WD) -- may be studied both theoretically [4] and by numerical experiments [5,6].

Numerical models and algorithms are developed and implemented in the simulation codes available on this website. The approach has allowed Wigner simulations of  multidimensional structures for the first time [7,8]. Currently, ViennaWD encompasses the following tools:



  1. M. Nedjalkov, D. Querlioz, P. Dollfus, H. Kosina: "Wigner Function Approach"; Nano-Electronic Devices: Semiclassical and Quantum Transport Modeling, (2011), 289-358 doi:10.1007/978-1-4419-8840-9_5.
  2. P. Schwaha, M. Nedjalkov, S. Selberherr, J. M. Sellier, I. Dimov, R. Georgieva: "Stochastic Alternative to Newton's Acceleration"; Lecture Notes in Computer Science, 8353 (2014),  178 - 18 doi:10.1007/978-3-662-43880-0_19.
  3. M. Nedjalkov, P. Schwaha, S. Selberherr, J. M. Sellier, D. Vasileska: "Wigner Quasi-Particle Attributes - An Asymptotic Perspective"; Applied Physics Letters, 102 (2013), 163113-1 - 163113-4 doi:10.1063/1.4802931.
  4. M. Nedjalkov, S. Selberherr, D.K. Ferry, D. Vasileska, P. Dollfus, D. Querlioz, I. Dimov, P. Schwaha: "Physical Scales in the Wigner-Boltzmann Equation"; Annals of Physics, 328 (2012), 220 - 237 doi:10.1016/j.aop.2012.10.001.
  5. J. M. Sellier, M. Nedjalkov, I. Dimov, S. Selberherr: "Decoherence and Time Reversibility: The Role of Randomness at Interfaces"; Journal of Applied Physics, 114 (2013), 174902-1 - 174902-7 doi:10.1063/1.4828736.
  6. P. Schwaha, D. Querlioz, P. Dollfus, J. Saint-Martin, M. Nedjalkov, S. Selberherr: "Decoherence Effects in the Wigner Function Formalism"; Journal of Computational Electronics, 12 (2013), 388 - 396 doi:10.1007/s10825-013-0480-9.
  7. P. Ellinghaus, M. Nedjalkov, S. Selberherr: "Efficient Calculation of the Two-Dimensional Wigner Potential"; in Proceedings of the 17th International Workshop on Computational Electronics (IWCE), (2014), 1-3 doi:10.1109/IWCE.2014.6865812.
  8. J. M. Sellier, M. Nedjalkov, I. Dimov, S. Selberherr: "Two-Dimensional Transient Wigner Particle Model"; in Proceedings of the 18th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), (2013), 404 - 407 doi:10.1109/SISPAD.2013.6650660.