The Boltzmann equation for transport in semiconductors is projected onto spherical harmonics in such a way that the resultant balance equations for the coefficients of the distribution function times the generalized density of states can be discretized over energy and real space by box integration. This ensures exact current continuity for the discrete equations. Spurious oscillations of the distribution function are successfully suppressed by stabilization based on a maximum entropy dissipation principle avoiding the H-transformation. The derived formulation can be used on arbitrary grids as long as box integration is possible. The new approach works not only with analytical bands but also with full-band structures in the case of holes. Results are presented for holes in bulk silicon based on a full band structure and electrons in a Si NPN BJT. For the first time the convergence of the spherical harmonics expansion is shown for a device and it is found that the quasiballistic transport in nanoscale devices requires an expansion of considerably higher order than the usual first one. The stability of the discretization is demonstrated for a range of grid spacings in the real space and bias points which produce huge gradients in the electron density and electric field. It is shown that the resultant large linear system of equations can be solved memory efficiently by the numerically robust package ILUPACK.

No abstract

The numerical properties of a deterministic Boltzmann equation solver based on a spherical harmonics expansion of the distribution function are analyzed and improved. A fully coupled discretization scheme of the Boltzmann and Poisson equations is proposed, where stable equations are obtained based on the H-transformation. It is explicitly shown that the resultant Jacobian matrix for the zeroth order component has property M for a first order expansion, which improves the stability even of higher order expansions. The detailed dependence of the free-streaming operator and the scattering operator on the electrostatic potential is exactly considered in the Newton-Raphson scheme. Therefore, convergence enhancement is achieved compared with previous Gummel-type approaches. This scheme is readily applicable to small-signal and noise analysis. As numerical examples, simulation results are shown for a silicon n + nn + structure including a magnetic field, an SOI NMOSFET and a SiGe HBT.

High frequency and noise model of gate-all-around metal-oxide-semiconductor field-effect transistors J. Appl. Phys. 105, 074505 (2009); 10.1063/1.3093884 High-frequency compact analytical noise model for double-gate metal-oxide-semiconductor field-effect transistor A compact quantum model of nanoscale double-gate metal-oxide-semiconductor field-effect transistor for high frequency and noise simulations J. Appl. Phys. 100, 084320 (2006); 10.1063/1.2360379Direct calculation of metal-oxide-semiconductor field effect transistor high frequency noise parametersThe noise characteristics of today's short-channel devices are shown to have a better resemblance to ballistic devices than to long-channel metal oxide semiconductor field effect transistors ͑MOSFETs͒. Therefore the noise characteristics of these devices are best modeled using a ballistic-MOSFET-based noise model. Extensive hydrodynamic device simulations are presented in support of this hypothesis and a simple compact model is introduced. This model is used for predicting the noise behavior of future nanoscale devices. Most of the findings of this work can also be applied to carbon nanotubes and nanowires because of their similarities to MOSFETs.

No abstract