Hybrid fluid-quantum coupling for the simulation of the transport of partially quantized particles in a DG-MOSFET

• Published in: Mathematics of Quantum Technologies Vol. 4; no. 1
• Main Authors: Jourdana, C., Vauchelet, N.
• Format: Journal Article
• Language: English
• Published: De Gruyter Open 01.01.2015
• Subjects: 35J10; 65M60; 65Z05; 76P05; 82D37; 82D80; drift-diffusion system; interface conditions; mixed finite elements; Schrödinger equation; semiconductors; subband decomposition
• ISSN: 2544-1477; 2299-3290
• DOI: 10.1515/nsmmt-2015-0001

This paper is devoted to numerical simulations of electronic transport in nanoscale semiconductor devices forwhich charged carriers are extremely confined in one direction. In such devices, like DG-MOSFETs, the subband decomposition method is used to reduce the dimensionality of the problem. In the transversal direction electrons are confined and described by a statistical mixture of eigenstates of the Schrödinger operator. In the longitudinal direction, the device is decomposed into a quantum zone (where quantum effects are expected to be large) and a classical zone (where they are negligible). In the largely doped source and drain regions of a DG-MOSFET, the transport is expected to be highly collisional; then a classical transport equation in diffusive regime coupled with the subband decomposition method is used for the modeling, as proposed in N. Ben Abdallah et al. (2006, Proc. Edind. Math. Soc. [7]). In the quantum region, the purely ballistic model presented in Polizzi et al. (2005, J. Comp. Phys. [25]) is used. This work is devoted to the hybrid coupling between these two regions through connection conditions at the interfaces. These conditions have been obtained in order to verify the continuity of the current. A numerical simulation for a DG-MOSFET, with comparison with the classical and quantum model, is provided to illustrate our approach.