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. Designing an efficient simulation tool for quantum devices involves a trade-off between efficiency and accuracy.

We are developing a novel simulation tool for design of 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 shall 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 MOSFET.

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 [3].

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. E.J. Kansa, Comput. Math. Applic., 19, No.8/9 (1990), 147-161.

Figure 1. I-V curves for 2.5 nm GaAs/AlGaAs single tunneling barrier (2.5 nm 0.22V single barrier in 40 nm GaAs/AlGaAs device, T = 300K, doping density 1018 cm-3 , bias up to 0.35 V). Classical and quantum BTE solutions with CFD-ACE+ compare well with ones from [1](upper diagram). Electric field: classical and one with quantum correction for bias 0.2 V (lower diagram).