Gerhard Karlowatz

The Effect of General Strain on the Band Structure and Electron Mobility of Silicon

A model capturing the effect of general strain on the electron effective masses and band-edge energies of the lowest conduction band of silicon is developed. Analytical expressions for the effective mass change induced by shear strain and valley shifts/splittings are derived using a degenerate kldrp theory at the zone-boundary X point. Good agreement to numerical band- structure calculations using the nonlocal empirical pseudopotential method with spin-orbit interactions is observed. The model is validated by calculating the bulk electron mobility under general strain with a Monte Carlo technique using the full-band structure and the proposed analytical model for the band structure. Finally, the impact of strain on the inversion-layer mobility of electrons is discussed.

Full-Band Monte Carlo Analysis of Electron Transport in Arbitrarily Strained Silicon

Full-band Monte Carlo simulations of electron transport in bulk silicon under several strain conditions are performed. The band structures of Si for arbitrary stress and strain conditions are calculated using the empirical non-local pseudopotential method. To restrict the EPM calculation to the smallest possible domain the symmetry properties for a given stress condition are taken into account. Results for biaxially strained Si grown on a [001] oriented Si1-x Gex substrate and for uniaxial tensile stress in [110] direction exhibit a high mobility enhancement. The effective masses and the energy splitting of the valleys extracted from the band structure explain the mobility gain observed in the simulation results. It is shown that the effective masses can change considerably under certain stress conditions

High-Field Electron Mobility Model for Strained-Silicon Devices

The application of mechanical stress to enhance the carrier mobility in silicon has been well established in the last few years. This paper probes into the electron conduction in biaxially and uniaxially stressed silicon in the nonlinear transport regime. The electron behavior has been analyzed for different field directions and stress/strain conditions using full-band Monte Carlo simulations. An analytical model describing the velocity components parallel and perpendicular to the electric field has been developed. The model includes the effect of strain induced valley splitting and can be applied for arbitrary directions of the electric field. The extension to different field directions has been performed using a Fourier series interpolation and a spherical harmonics interpolation for transport in two and three dimensions, respectively. The model can be implemented in a drift-diffusion-based device simulator

A Tensorial High-Field Electron Mobility Model for Strained Silicon

Application of stress to Si causes a deviation of its lattice constant from the equilibrium value, thereby modifying the electronic band structure. A phenomenological approach to calculate the mobility tensor for electrons in strained Si at high electric fields has been proposed. The model is intended for implementation in drift-diffusion based device simulators

Analysis of Hole Transport in Arbitrarily Strained Germanium

Full-band Monte Carlo simulations are performed to study the properties of hole transport in bulk Germanium under general strain conditions. The band structures are calculated with the empirical non-local pseudopotential method. For Monte Carlo simulations acoustic and optical phonon scattering as well as impact ionization are taken into account. Results for biaxially strained Ge grown on a [001] oriented Si1 xGex substrate and for uniaxial compressive stress in [110] exhibit a high mobility enhancement. These results are compared to experimental and theoretical results from literature.

Numerical and Analytical Modeling of the High-Field Electron Mobility in Strained Silicon

We have performed a detailed analysis of the electron transport at high electric field in strained Si for different field directions and stress/strain conditions using Full-band Monte Carlo simulations. A phenomeno-logical model describing the velocity-field relationship for electrons in biaxially or uniaxially strained Si has been developed. The model is suitable for incorporation into any device simulator for performing TCAD tasks.

Effect of band structure discretization on the performance of full-band Monte Carlo simulation

Full-band Monte Carlo simulation offers a very accurate simulation technique, but is often limited by its high demand on computation time. The advantage of a numerical representation of the band structure over an analytical approximation is the accurate representation of the energy bands in the high energy regime. This allows accurate treatment of hot carrier effects in semiconductors. In this work we outline an efficient full-band Monte Carlo (FBMC) simulator and investigate the accuracy of simulation results for different meshing approaches for the Brillouin zone.

Influence of Uniaxial [110] Stress on the Silicon Conduction Band Structure: Stress Dependence of the Nonparabolicity Parameter

An alytical expression for the dependence of the nonparabolicity parameter on shear stress is presented. At 3 GPa the nonparabolicity parameter is shown to increase by a factor of 1.7. Stress dependence of the nonparabolicity parameter is verified by comparing the density-of-states obtained analytically and from the empirical pseudopotential method, and good agreement is found. Increase in the nonparabolicity parameter increases the after-scattering density-of-states and hence the scattering rates, which results in a 25% suppression of the mobility enhancement due to effective mass decrease in a 3 nm thin body FET at 3 GPa [110] stress.