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Quantum and kinetic simulation tools for nano-scale electronic devices

A. Fedoseyev, V. Kolobov, R. Arslanbekov, A. Przekwas, and A. Balandin
CFD Research Corporation,, US

Keywords: Boltzmann transfer equation, quantum, kinetic, semiconductor, MOSFET, nano-scale

The progress in LSI technologies has resulted in scaling down semiconductor devices to nano-scale dimensions where kinetic and quantum effects in the carrier transport become crucial for the device performance. The transistor counts on the high-end microprocessor is rushing toward the 400-million mark and the feature dimensions are shrinking toward the nanometer scale. As a result, the kinetic and quantum effects in the carrier transport and thermal conductivity in semiconductor nanostructures are beginning to attract significant attention. Designing an efficient simulation tool for nano-scale and quantum devices involves a trade-off between efficiency and accuracy. We have developed a novel simulation tool for nano-scale quantum devices based on deterministic solution of the classical Boltzmann equation with quantum corrections proposed in Ref [1]. Using two-term spherical harmonic expansion in velocity space reduces the Boltzmann equation for electrons to a Fokker-Planck equation in a four-dimensional space (3 spatial and 1 energy dimensions). The Fokker-Planck equation is coupled to the Poisson and hole-continuity equations as described in Ref. [2]. We describe the details of numerical implementation of the 4-dimensional Fokker-Planck solver using kinetic and total energy domains. The effect of quantum corrections on spatial distribution of carriers will be analyzed. This solver provides a substantially lower computational cost than the Monte Carlo method, and resolves all points in phase space with equal accuracy. We will present simulation results for an ultra-small 2D NMOSFET [3], compared well with experimental data. We work on software that will provide a practical simulation tool for nano-scale semiconductor devices. Two numerical methods are employed, the finite volume technique with time-splitting factorization of spatial and energy space transport, and a meshless multiquadric technique [4]. References 1. H. Tsuchiya and T. Miyoshi, IEICE Trans. Electron E82-C, (1999) 880. 2. W. Liang, N. Goldsmann, I. Meyergoyz, P.J. Oldiges, IEEE Trans. Electron Devices, 44, (1997) 257. 3. D.A.Antoniadis et all. MIT "Well-Tempered" Bulk-Si NMOSFET Device, MIT, MS, 1999, 4. E.J. Kansa, Comput. Math. Applic., 19, No.8/9 (1990), 147-161.

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