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 . 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. .
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 , 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 .
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NSTI Nanotech 2003 Conference Technical Program Abstract