Ting Wei Tang

Modeling of electron mobility in gated silicon nanowires at room temperature: Surface roughness scattering, dielectric screening, and band nonparabolicity

We present a theoretical study of electron mobility in cylindrical gated silicon nanowires at 300 K based on the Kubo-Greenwood formula and the self-consistent solution of the Schrodinger and Poisson equations. A rigorous surface roughness scattering model is derived, which takes into account the roughness-induced fluctuation of the subband wave function, of the electron charge, and of the interface polarization charge. Dielectric screening of the scattering potential is modeled within the random phase approximation, wherein a generalized dielectric function for a multi-subband quasi-one-dimensional electron gas system is derived accounting for the presence of the gate electrode and the mismatch of the dielectric constant between the semiconductor and gate insulator. A nonparabolic correction method is also presented, which is applied to the calculation of the density of states, the matrix element of the scattering potential, and the generalized Lindhard function. The Coulomb scattering due to the fixed i...

Modeling of Surface-Roughness Scattering in Ultrathin-Body SOI MOSFETs

A rigorous surface-roughness scattering model for ultrathin-body silicon-on-insulator (SOI) MOSFETs is derived, which reduces to Andos model in the limit of bulk MOSFETs. The matrix element of the scattering potential reflects the fluctuations of both the wavefunction and the potential energy. The matrix element reflecting the fluctuation of the wavefunction is expressed in an integral form which can be considered as a generalized Prange-Nee term-to which it is equivalent in the limit of an infinitely high insulator-semiconductor barrier-giving more accurate results in the case of a finite barrier height. The matrix element reflecting the fluctuation of the potential energy is due to the Coulomb interactions originating from the roughness-induced fluctuation of the electron charge density, the interface polarization charge, and the image-charge density. The roughness-limited low-field electron mobility in thin-body SOI MOSFETs is obtained using the matrix elements that we have derived. We study its dependence on the silicon body thickness, effective field, and dielectric constant of the insulator.

Monte Carlo calculation of strained and unstrained electron mobilities in Si1−xGex using an improved ionized‐impurity model

An improved Monte Carlo (MC) model for ionized impurity scattering developed in a previous work [L. E. Kay and T.‐W. Tang, J. Appl. Phys. 70 1475 (1991)] is used to perform a comprehensive study of majority‐ and minority‐electron mobilities in the Si1−xGex material system for both strained and unstrained cases. This investigation includes calculation of low‐field mobilities for wide ranges of doping and Ge mole fraction at both 300 and 77 K as well as high‐field studies. A significant improvement in mobility (up to 50%) is observed for transport perpendicular to the growth plane in strained Si1−xGex as compared to the unstrained case. The magnitude of the improvement is dependent on doping (both concentration and type) and germanium content, and is somewhat larger at 77 K. High‐field MC simulations show that some strained‐mobility enhancement remains even at an electric field of 100 kV/cm. These studies also suggest there is a temperature‐dependent Ge content for which mobility is maximized at higher dopings.

Simulation of Silicon Nanowire Transistors Using Boltzmann Transport Equation Under Relaxation Time Approximation

An efficient approach for the simulation of electronic transport in nanoscale transistors is presented based on the multi-subband Boltzmann transport equation under the relaxation time approximation, which takes into account the effects of quantum confinement and quasi-ballistic transport. This approach is applied to the study of electronic transport in circular gate-all-around silicon nanowire transistors. Comparison with the nonequilibrium Greens function method shows that the new method gives reasonably accurate terminal characteristics. We study the influence of silicon body diameter and gate length on the terminal current and subthreshold slope (SS). We have found that the calculated ON current is inversely proportional to the gate length to the power 1/2, and that the silicon body diameter should be smaller than roughly 2/3 of the channel length in order to maintain the SS within 80 mV/dec.

Theoretical Study of Carrier Transport in Silicon Nanowire Transistors Based on the Multisubband Boltzmann Transport Equation

We study electronic transport in silicon nanowire transistors at room temperature based on the self-consistent numerical solution of the multisubband Boltzmann transport equation and Poisson equation. The Schrodinger equation with nonparabolic corrections is solved in order to obtain the multisubband structure. Relevant microscopic scattering mechanisms due to acoustic and intervalley phonons, surface roughness, and ionized impurities are included in the simulation. A flux-conserving discretization scheme based on the uniform total energy grid is employed to avoid excessive numerical diffusion originating from the conventional kinetic-energy-based upwind scheme. We report an interesting kink behavior in the output characteristics and study the electron energy distribution inside the transistor as a function of bias conditions and scattering mechanisms.

Impact ionization coefficient and energy distribution function at high fields in semiconductors

Impact ionization coefficients in semiconductors are numerically calculated following Keldysh’s method [Sov. Phys. JETP 21, 1135 (1965)]. This requires deriving expressions for an energy‐dependent mean free path l(e) and an energy‐dependent impact ionization scattering rate rii(e). In the derivation of rii(e), a nonparabolic e‐k relation as well as a smooth transition from the phonon‐assisted impact ionization to the phononless impact ionization are considered. Numerically calculated impact ionization coefficients for electrons and holes in Ge, Si, and GaAs agree very well with experimental data. The calculated Keldysh energy distribution function is also compared with the standard Maxwellian distribution. The average mean free path l, which is a function of the electric field, has values within the range often quoted in the literature.

Construction of higher‐moment terms in the hydrodynamic electron‐transport model

A critical step in the development of all hydrodynamic transport models (HTMs), derived from moments of the Boltzmann transport equation, is the introduction of accurate closure relations to terminate the resulting infinite set of macroscopic equations. In general, there are a number of resulting integral terms that are highly dependent on the form of the true electron distribution function. The so‐called heat flux term is one very important higher‐moment term that requires attention. Methods for the accurate construction of an improved heat‐flux model are presented. In this construction, a higher‐moments approach is combined with a unique definition of electron temperature (i.e., based upon an ansatz distribution) to investigate the effects of conduction‐band nonparabolicity and distributional asymmetry. The Monte Carlo method has been used to evaluate the resulting model closures and to study microscopic electron dynamics. These investigations have identified an important relationship between a particul...

Differential conductance fluctuations in silicon nanowire transistors caused by quasiballistic transport and scattering induced intersubband transitions

Calculations based on the multisubband Boltzmann transport equation with relevant microscopic scattering mechanisms predict abrupt differential conductance fluctuations (kinks) in the drain current versus drain voltage curves of silicon nanowire transistors at room temperature. The kink originates from the change of series resistance at the drain extension related to the interplay between quasiballistic transport and intersubband transitions of electrons caused by elastic interactions with acoustic phonons, surface roughness, and ionized impurities. The kink occurs when the energy of the second subband in the drain extension is aligned with the peak of the net electron flux distribution in the first subband. This bias condition yields a large series resistance in the drain extension because those quasiballistic electrons in the first subband which reach the drain can scatter isotropically into the second subband.

An improved ionized-impurity scattering model for Monte Carlo simulations

An improved Monte Carlo model for ionized‐impurity scattering is developed and used to calculate majority‐ and minority‐electron mobilities in silicon. The model includes scattering cross sections derived from phase‐shift analysis, implementation of the Friedel sum rule, and a simple phenomenological model for multiple‐potential scattering. This model provides a very good fit to experiment using a single adjustable parameter. Electron mobilities in n‐ and p‐type Si are calculated and fit to experimental data at 300 and 77 K. Experimental results for Si of μn(NA)/μn(ND) ≊ 2 at 300 K are reproduced and a value of 3 < μn(NA)/μn(ND) < 4 is predicted at 77 K.

Anatomy of Carrier Backscattering in Silicon Nanowire Transistors

We study the physics of carrier backscattering in silicon nanowire transistors by using the numerical solution of the multisubband Boltzmann transport equation, where relevant scattering mechanisms by acoustic and intervalley phonons, surface roughness, and ionized impurities are included, accounting for intrasubband and intersubband, and elastic and inelastic transitions. The validity of several assumptions in the virtual source model is checked against the numerical solution. We have found that scattering processes make it difficult to model the macroscopic quantities at the virtual source without self-consistent simulations.