Ballistic FET modeling using QDAME: Quantum Device Analysis by Modal Evaluation

T. J. Watson Res. Center, IBM Corp., Yorktown Heights, NY, USA
IEEE Transactions on Nanotechnology (Impact Factor: 1.83). 01/2003; 1(4):255 - 259. DOI: 10.1109/TNANO.2002.807388
Source: IEEE Xplore


We present an algorithm for self-consistent solution of the Poisson and Schrodinger equations in two spatial dimensions with open-boundary conditions to permit current flow. The algorithm works by discretely sampling a device's density of states using standing wave boundary conditions, decomposing the standing waves into traveling waves injected from the contacts to assign occupancies, and iterating the quantum charge with the potential to self-consistency using a novel hybrid Newton-Broyden method. A double-gate FET is simulated as an example, with applications focused on surface roughness and contact geometry.

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Available from: Arvind Kumar, Feb 13, 2014
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    • "Quantum mechanical effects in devices continue to be important. We use QDAME [17] [18] to validate and tweak parameters used in our quantum correction models for thin semiconductor layers and confinement in various crystallographic orientations. QDAME is also used to help us gain understanding of intraband tunneling models, and tunneling at metal/semiconductor contacts, as well as metal/metal interfaces. "
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    • "This is the reason for the development of " Quantum Corrected Drift–Diffusion " (QCDD) models that are based on the introduction of a correction potential in the DD equation to account for quantum effects on the spatial distribution of charge carriers within the devices (see [3] [25]). By adopting such models the computational complexity can be contained within reasonable limits at the cost of neglecting quantum effects on transport (coherent transport, interferences, reflections), which can be considered of higher order for devices of gate length higher than 10nm [21]. "
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    ABSTRACT: This article deals with the analysis of the functional iteration, denoted Generalized Gummel Map (GGM), proposed in [C. de Falco, A.L. Lacaita, E. Gatti, R. Sacco, Quantum-Corrected Drift-Diffusion Models for Transport in Semiconductor Devices, J. Comp. Phys. 204 (2) (2005) 533–561] for the decoupled solution of the Quantum Drift-Diffusion (QDD) model. The solution of the problem is characterized as being a fixed point of the GGM, which permits the establishment of a close link between the theoretical existence analysis and the implementation of a numerical tool, which was lacking in previous non-constructive proofs [N.B. Abdallah, A. Unterreiter, On the stationary quantum drift-diffusion model, Z. Angew. Math. Phys. 49 (1998) 251–275, R. Pinnau, A. Unterreiter, The stationary current–voltage characteristics of the quantum drift-diffusion model, SIAM J. Numer. Anal. 37 (1) (1999) 211–245]. The finite element approximation of the GGM is illustrated, and the main properties of the numerical fixed point map (discrete maximum principle and order of convergence) are discussed. Numerical results on realistic nanoscale devices are included to support the theoretical conclusions.
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    • "Quantum transport models that involve the solution to the Schrödinger wave equation can be used to study current flow over small scales where the transport can be either ballistic or can involve some type of scattering. The main models used to model ballistic transport are Quantum Transmitting Boundary Model (QTBM) [5] and the Quantum Device Analysis by Mode Evaluation (QDAME) [6]. QTBM involves formulating the boundary conditions for a given problem by calculating the transmission and reflection coefficients for a known boundary potential. "
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