Steven E. Laux

Band structure, deformation potentials, and carrier mobility in strained Si, Ge, and SiGe alloys

Using nonlocal empirical pseudopotentials, we compute the band structure and shear deformation potentials of strained Si, Ge, and SiGe alloys. Fitting the theoretical results to experimental data on the phonon‐limited carrier mobilities in bulk Si and Ge, the dilatation deformation potential Ξd is found to be 1.1 eV for the Si Δ minima, −4.4 eV for the Ge L minima, corresponding to a value for the valence band dilatation deformation potential a of approximately 2 eV for both Si and Ge. The optical deformation potential d0 is found to be 41.45 and 41.75 eV for Si and Ge, respectively. Carrier mobilities in strained Si and Ge are then evaluated. The results show a large enhancement of the hole mobility for both tensile and compressive strain along the [001] direction, but only a modest enhancement (approximately 60%) of the electron mobility for tensile biaxial strain in Si. Finally, from a fit to carrier mobilities in relaxed SiGe alloys, the effective alloy scattering potential is determined to be about 0...

Techniques for small-signal analysis of semiconductor devices

Techniques for ascertaining the small-signal behavior of semiconductor devices in the context of numerical device simulation are discussed. Three standard approaches to this problem will be compared: (i) transient excitation followed by Fourier decomposition, (ii) incremental charge partitioning, and (iii) sinusoidal steady-state analysis. Sinusoidal steady-state analysis is shown to be the superior approach by providing accurate, rigorously correct results with reasonable computational cost and programming commitment.

Understanding hot‐electron transport in silicon devices: Is there a shortcut?

Results of a Monte Carlo study of carrier multiplication in silicon bipolar and field‐effect transistors and of electron injection into silicon dioxide are presented. Qualitative and, in most cases, quantitative agreement is obtained only by accounting for the correct band structure, all relevant scattering processes (phonons, Coulomb, impact ionization), and the highly nonlocal properties of electron transport in small silicon devices. In addition, it is shown that quantization effects in inversion layers cause a shift of the threshold energy for impact ionization which is very significant for the calculation of the substrate current in field‐effect transistors. Conservation of parallel momentum, image‐force corrections, dynamic screening of the interparticle Coulomb interaction, and improvements to the WKB approximation are necessary to treat correctly the injection of electrons from silicon into silicon dioxide. The validity of models—analytic or Monte Carlo—which treat hot‐electron transport with oversimplified physical approximations is argued against. In a few words, there is no shortcut.

Quasi-one-dimensional electron states in a split-gate GaAs/AlGaAs heterostructure

Abstract Self-consistent solutions for quasi-one-dimensional electron states in a narrow inversion layer channel at a GaAs/AlGaAs heterointerface have been obtained for a structure with a split gate. A simple model for fixed charge at the exposed surface in the gate opening has been used in the calculation. Energy levels for lateral motion are separated by ∼1–5 meV for the example considered, with a 0.4 μm gate opening.

Comments on "Monte Carlo simulation of transport in technologically significant semiconductors of the diamond and zinc-blende structures. II. Submicrometer MOSFETs" [with reply]

For pt.I see ibid., vol.38, no.3, p.634-49, March 1991. MOSFETs with channel lengths smaller than 0.25 mu m with substrates of four different semiconductors and one alloy of the diamond and zinc-blende structures (n-channel Ge, Si, GaAs, InP, In/sub 0.53/Ga/sub 0.47/As, and p-channel Si) were simulated at 77 and 300 K with a self-consistent two-dimensional Monte Carlo program. With the exception of the In-based materials, the speed of the devices appears to be largely independent of the semiconductor. This universal behavior results from the similarity among the medium-energy-scale features of the band structures of the cubic semiconductors. Low-energy concepts, such as mobility and effective mass, fail to describe charge transport as carriers populate a larger fraction of the Brillouin zone in these small devices driven at reasonably high biases. The assumptions made, the approximations used, and, in particular, the meaning of the words speed and reasonably mentioned above are discussed. >

Electron states in narrow gate‐induced channels in Si

Self‐consistent numerical solutions of the Poisson and Schrodinger equations have been obtained for the states of electrons under a narrow gate or under a narrow slit in a metal‐oxide‐silicon structure with an inner and an outer gate. For the cases considered (30‐nm‐wide gate and 80‐nm‐wide slit), the states of motion parallel to the Si‐SiO2 interface are more closely spaced than the states for motion perpendicular to the interface. It should be possible, for the structures considered, to achieve a dynamically one‐dimensional system with an electron density ≲106 cm−1.

Long-range Coulomb interactions in small Si devices. Part I: Performance and reliability

In the ever smaller silicon metal–oxide–semiconductor field-effect transistors of the present technology, electrons in the conductive channel are subject to increasingly stronger long-range Coulomb interactions with high-density electron gases present in the source, drain, and gate regions. We first discuss how two-dimensional, self-consistent full-band Monte Carlo/Poisson simulations can be tailored to reproduce correctly the semiclassical behavior of a high-density electron gas. We then employ these simulations to show that for devices with channel lengths shorter than about 40 nm and oxides thinner than about 2.5 nm, the long-range Coulomb interactions cause a significant reduction of the electron velocity, and so a degradation of the performance of the devices. In addition, the strong “thermalization” of the hot-electron energy distribution induced by Coulomb interactions has an effect on the expected reliability of the transistors.

Monte-Carlo simulation of submicrometer Si n-MOSFETs at 77 and 300 K

Monte Carlo simulation results for small silicon n-MOSFETs at 77 and 300 K are presented. A complete description of the silicon band structure including consistent scattering rates, electron-electron scattering, and plasma effects is included in the calculation for the first time. The dependence of transconductance on channel length is in excellent agreement with the experiments of G.A. Sai-Halasz et al. (see ibid., vol.EDL-8, p.463-6, Oct. 1987 and ibid., vol.EDL-9, p.464-6, Sep. 1988) and serves to support the expectation of significant velocity overshoot in these devices. For extremely short channels (<or=0.1 mu m) at 77 K, electron-electron scattering plays a significant role in determining the electron energy distribution, while at drain biases exceeding about 1.5 V, band structure effects can play an important role.<<ETX>>

Effective barrier heights of mixed phase contacts: Size effects

Computer simulations of mixed phase Schottky contacts have been performed to gain insight into the effects of lateral dimensions upon device behavior. As expected, lateral dimensions comparable to the Debye length of the semiconductor result in strong modification of the device characteristics that would result from independent, parallel diodes. We suggest that such effects can play a role in most experimentally obtained contacts. Current models of Schottky barrier formation typically invoke kinetics‐limited chemical interactions at the metal‐semiconductor interface; such effects are unlikely to be laterally uniform over macroscopic dimensions, and may well provide strong sensitivity to seemingly minor variations in preparation techniques used by different groups. We demonstrate that mixed phase contacts, with size effects, can affect ideality factors, and can also cause disagreement between C‐V and I‐V barrier heights.

Analysis of quantum ballistic electron transport in ultrasmall silicon devices including space-charge and geometric effects

A two-dimensional device simulation program which self consistently solves the Schrodinger and Poisson equations with current flow is described in detail. Significant approximations adopted in this work are the absence of scattering and a simple six-valley, parabolic band structure for silicon. A modified version of the quantum transmitting boundary method is used to describe open boundary conditions permitting current flow in device solutions far from equilibrium. The continuous energy spectrum of the system is discretized by temporarily imposing two different forms of closed boundary conditions, resulting in energies which sample the density-of-states and establish the wave function normalization conditions. These standing wave solutions (“normal modes”) are decomposed into their traveling wave constituents, each of which represents injection from only one of the open boundary contacts (“traveling eigencomponents”). These current-carrying states are occupied by a drifted Fermi distribution associated wi...