Anh-Tuan Pham

Stable discretization of the Boltzmann equation based on spherical harmonics, box integration, and a maximum entropy dissipation principle

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 spaces by box integration. This ensures exact current continuity for the discrete equations. Spurious oscillations of the distribution function are 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 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 bipolar junction transistor. The convergence of the spherical harmonics expansion is shown for a device, and it is found that the quasiballistic transport in nanoscale devices require...

Physics-Based Modeling of Hole Inversion-Layer Mobility in Strained-SiGe-on-Insulator

The hole inversion-layer mobility of strained-SiGe homo- and heterostructure-on-insulator in ultrathin-body MOSFETs is modeled by a microscopic approach. The subband structure of the quasi-2-D hole gas is calculated by solving the 6times6koarrldrpoarr Schrodinger equation self-consistently with the electrostatic potential. The model includes four important scattering mechanisms: optical phonon scattering, acoustic phonon scattering, alloy scattering, and surface-roughness scattering. The model parameters are calibrated by matching the measured low-field mobility of two particularly selected long-channel pMOSFET cases. The calibrated model reproduces available channel-mobility measurements for many different strained-SiGe-on-insulator structures. For the silicon-on-insulator MOS structures with unstrained-Si channels, the silicon-thickness dependence resulting from our model for the low-field channel mobility agrees with previous publications.

Comparison of (001), (110) and (111) uniaxial- and biaxial- strained-Ge and strained-Si PMOS DGFETs for all channel orientations: Mobility enhancement, drive current, delay and off-state leakage

Using the non-local empirical pseudopotential method (bandstructure), full-band Monte-Carlo simulations (transport), self-consistent Poisson-Schrodinger (electrostatics) and detailed band-to-band-tunneling (BTBT) (including bandstructure and quantum effects) simulations, the effect of surface/channel orientation, uniaxial- and biaxial-strain, band-structure, mobility, and high-field transport on the drive current, off-state leakage and switching delay in nano-scale, strained-Si and strained-Ge, p-MOS DGFETs have been presented and the optimum strain and channel/surface orientations for highest drive-lowest delay-lowest leakage have been obtained.

Deterministic solvers for the Boltzmann transport equation

Introduction. - Electron transport in the 3D k-space: The Boltzmann transport equation and its projection onto spherical harmonics. - Device simulation. - Band structure and scattering mechanisms. - Results. - Transport in a quasi 2D hole gas: Coordinate systems and systems of equation. - Efficient k . p SE solver. - Efficient 2D k-space discretization and non-linear interpolation schemes. - Deterministic solver for the multisubband stationary BTE. - Poisson equation. - Iteration methods. - Results. - References.

Deterministic multisubband device simulations for strained double gate PMOSFETs including magnetotransport

The authors present, for the first time, deterministic 2D multisubband device simulations based on the self consistent solution of SE-PE-BTE for PMOSFETs including the Pauli principle, magnetic fields, and without any simplification of the subband structure. The deterministic method yields truly stationary solutions and can resolve small changes in the solution due to magnetic fields or small changes in the bias conditions. The magnetoresistance mobility extraction method is investigated and compared to the conventional mobility extraction technique for short channel devices.

Solving Boltzmann Transport Equation without Monte-Carlo algorithms - new methods for industrial TCAD applications

The Drift-Diffusion model is still by far the most frequently used numerical device model in industry today. One important reason for this success is the robust numerical implementation of this model providing CPU efficient DC, AC, transient, and noise simulations with high accuracy and high convergence reliability. On the other hand, many of todays design applications vary strain, crystal and channel orientation, material composition, and the carrier confinement. Such applications certainly require the solution of the Boltzmann Transport Equation in order to be predictive. It will be demonstrated in this paper that with new alternative discretization and solution methods avoiding the Monte-Carlo algorithm many of the favorable numerical properties of the traditional Drift-Diffusion model can be transferred to numerical device models that include the solution of the Boltzmann Transport Equation.

Modeling of hole inversion layer mobility in unstrained and uniaxially strained Si on arbitrarily oriented substrates

The hole inversion layer mobility of in-plane uniaxially strained Si is modeled by a microscopic approach. For an arbitrary crystallographic surface orientation the two dimensional hole gas subband structure is calculated by solving the 6 times 6 koarr ldr poarr Schrodinger equation self-consistently with the electrostatic potential. Three important scattering mechanisms are included: optical phonon scattering, acoustic phonon scattering and surface roughness scattering. The model parameters are calibrated by matching the measured low-field mobility of relaxed Si on (001) Si wafers. The calibrated model reproduces available channel mobility measurements for unstrained and uniaxially strained Si on (001), (111) and (110) substrates.

Modeling of piezoresistive coefficients in Si hole inversion layers

A mobility model for hole inversion layers based on the self-consistent solution of the 6 × 6 k⃗ ⋅ p⃗ Schrödinger equation (SE) and Poisson equation (PE) has been developed. The mobility variation due to uniaxial stress and biaxial strain is simulated and the simulation results reproduce available measurements. The piezoresistive coefficient extraction technique based on the mobility variation due to uniaxial stress is generalized for general diamond crystal lattice material. The new derivation is applicable for arbitrary surface and channel orientations.

A Convergence Enhancement Method for Deterministic Multisubband Device Simulations of Double Gate PMOSFETs

odinger equation is employed for the calculation of the derivative of the Boltzmann transport equation w.r.t the electrostatic potential. The simulation results show that the new approach is efficient for both near-equilibrium and nonequilibrium situations.

A Full-Band Spherical Harmonics Expansion of the Valence Bands up to High Energies

The valence bands of silicon can be expanded exactly by spherical harmonics only up to the energy, where the bands reach the surface of the Brillouin zone (BZ). For higher energies an approximation is required. Therefore an anisotropic extension of the band structure is presented which is determined by matching the density of states (DOS) and moments of the inverse group velocity of the exact full-band (FB) structure. The Boltzmann equation (BE) based on the exact FB at low energies and the approximation at high energies is solved by the spherical harmonic expansion (SHE) method for bulk silicon including impact ionization. The results are compared to Monte Carlo (MC) data based on the exact FB structure