Hybrid quantum-classical models for nano-sized semiconductor devices

Professor Bruno Rubino, Department of Information Engineering, Computer Science and Mathematics University of L’Aquila (Italy)
Дата проведення: 28.10.2016 о 13:30 год. в room 270

Professors, assistants, Ph.D. students and all interested are invited!

Short absract:

Hybrid quantum-classical models for nano-sized semiconductor devices
Prof. Bruno Rubino
Department of Information Engineering, Computer Science and Mathematics
University of L’Aquila – via Vetoio, loc. Coppito, I-67100 L’Aquila, Italy
October 2016

In the modern semiconductor technology, the quantum effects play an important role in the functioning of the devices. To include such complex phenomena, quantum models must be employed, with a remarkable increasing of the computational costs.
Recently, following the experimental observation that quantum effects are localized in restricted zone of the device, some quantum-classical hybrid models have been introduced. In the hybrid framework, just a well localized (and usually small) part of the device is modeled as quantum, while the rest of the domain
is treated classically.
The main diffcult is to establish a reasonable set of interface conditions. In the talk we present and compare two different approaches. In the first one, following the available literature, we introduce and discuss some sets physical-based interface conditions. In the second one, we derive a new intrinsic hybrid model, obtained modifying the Bohm potential [2], [3]. In this way, we do not need any interface condition and the existence of the hybrid solution is obtained as a limit of a suitably modified quantum model [1], [4], [5].

References
[1] S. Chiarelli, F. Di Michele, and B. Rubino, A hybrid drift diffusion model: derivation, weak steady state solutions and simulations, Math. Appl., 1 (2012), 37-55.
[2] F. Di Michele, P. Marcati, and B. Rubino, Steady states and interface transmission conditions for heterogeneous quantum classical 1-d hydrodynamic
model of semiconductor devices, Physica D, 243 (2013), 1-13.
[3] F. Di Michele, P. Marcati, and B. Rubino, Stationary solution for transient quantum hydrodynamics with bohmenian-type boundary conditions,
to appear on Computational and Applied Mathematics, 2017 (First online:
15 May 2015).
[4] F. Di Michele, M. Mei, B. Rubino, and S. Sampalmieri, Solutions to hybrid
quantum hydrodynamical model of semiconductors in bounded domain, to
appear on International Journal of Numerical Analysis & Modeling, 13,
No. 6 (2016).
[5] F. Di Michele, M. Mei, B. Rubino, and S. Sampalmieri, Thermal equilibrium solution to new model of bipolar hybrid quantum hydrodynamics, in
preparation.