Full Hydrodynamic Simulation of GaAs MESFETs

A finite difference upwind discretization scheme in two dimensions is presented in detail for the transient simulation of the highly coupled non-linear partial differential equations of the full hydrodynamic model, providing thereby a practical engineering tool for improved charge carrier transport simulations at high electric fields and frequencies. The discretization scheme preserves the conservation and transportive properties of the equations. The hydrodynamic model is able to describe inertia effects which play an increasing role in different fields of micro- and optoelectronics, where simplified charge transport models like the drift-diffusion model and the energy balance model are no longer applicable. Results of extensive numerical simulations are shown for a two-dimensional MESFET device. A comparison of the hydrodynamic model to the commonly used energy balance model is given and the accuracy of the results is discussed.Comment: 18 pages, LATE

Dissipative Chaos in Semiconductor Superlattices

We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use the semi-classical balance-equation approach which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free electron lasers, chaos may be observable in SSLs. We clarify the nature of this novel nonlinear dynamics in the superlattice-external field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field and to Josephson junctions.Comment: 33 pages, 8 figure

Accuracy of transfer matrix approaches for solving the effective mass Schr\"{o}dinger equation

The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schr\"{o}dinger equation for arbitrary one-dimensional potentials, is investigated analytically and numerically. Both the case of a constant and a position dependent effective mass are considered. Comparisons with a finite difference method are also performed. Based on analytical model potentials as well as self-consistent Schr\"{o}dinger-Poisson simulations of a heterostructure device, it is shown that a symmetrized transfer matrix approach yields a similar accuracy as the Airy function method at a significantly reduced numerical cost, moreover avoiding the numerical problems associated with Airy functions

A generalized drift-diffusion model for rectifying Schottky contact simulation

We present a discussion on the modeling of Schottky barrier rectifying contacts (diodes) within the framework of partial-differential-equation-based physical simulations. We propose a physically consistent generalization of the drift-diffusion model to describe the boundary layer close to the Schottky barrier where thermionic emission leads to a non-Maxwellian carrier distribution, including a novel boundary condition at the contact. The modified drift-diffusion model is validated against Monte Carlo simulations of a GaAs device. The proposed model is in agreement with the Monte Carlo simulations not only in the current value but also in the spatial distributions of microscopic quantities like the electron velocity and concentratio

Numerical schemes for semiconductors energy- transport models

International audienceWe introduce some finite volume schemes for unipolar energy-transportmodels. Using a reformulation in dual entropy variables, we can show the decay ofa discrete entropy with control of the discrete entropy dissipation

Simulation of INSB Devices using Drift-Diffusion Equations

Silicon technology has for several decades followed Moore\u27s law. Reduction of feature dimensions has resulted in constant increase in device density which has enabled increased functionality. Simultaneously, performance, such as circuit speed, has been improving. Recently, this trend is in jeopardy due to, for example, unsustainable increase in the processor power dissipation. In order to continue development trends, as outlined in ITRS roadmap, new approaches seem to be required once feature size reaches 10 - 20 nm range. This research focuses on using 111-V compounds, specifically indiumantimonide (lnSb), to supplement silicon CMOS technology. Due to its low bandgap and high mobility, lnSb shows promise as a material for extremely high frequency active devices operating at very low voltages. In this research electrical properties of lnSb material are characterized and modeled with special emphasis on recombination-generation mechanisms. Device simulators based on drift-diffusion approach - DESSIS and nanoMOS - are modified for lnSb MOSFET design and analysis. To assess the quality of lnSb MOSFET designs several figures of merit are utilized: lon/loff ratio, 1-V characteristics, threshold voltage, drain induced barrier lowering (DIBL) and unity current gain frequency for different configurations and gate lengths. It is shown that significant performance improvement can be achieved in lnSb MOSFETs through proper scaling. For example, extrapolated cutoff frequencies reach into THz range. Semi-empirical scaling rules that remedy short channel effects are proposed. Finally, quantum mechanical (QM) effects in lnSb MOSFET and their effect on device performance are examined using nanoMOS device simulation program. It is found that nonparabolicity has to be properly modeled and that QM effects have a large effect on threshold voltage and transconductance and should be included when analyzing and designing deca-nanometer size lnSb MOSFETs

Numerical schemes for semiconductors energy- transport models

International audienceWe introduce some finite volume schemes for unipolar energy-transportmodels. Using a reformulation in dual entropy variables, we can show the decay ofa discrete entropy with control of the discrete entropy dissipation

A Multicarrier Technique for Monte Carlo Simulation of Electrothermal Transport in Nanoelectronics

The field of microelectronics plays an important role in many areas of engineering and science, being ubiquitous in aerospace, industrial manufacturing, biotechnology, and many other fields. Today, many micro- and nanoscale electronic devices are integrated into one package. e capacity to simulate new devices accurately is critical to the engineering design process, as device engineers use simulations to predict performance characteristics and identify potential issues before fabrication. A problem of particular interest is the simulation of devices which exhibit exotic behaviors due to non-equilibrium thermodynamics and thermal effects such as self-heating. Frequently, it is desirable to predict the level of heat generation, the maximum temperature and its location, and the impact of these thermal effects on the current-voltage (IV) characteristic of a device. is problem is furthermore complicated by nanoscale device dimensions. As the ratio of surface area to volume increases, boundary effects tend to dominate the transfer of energy through a device. Effects such as quantum confinement begin to play a role for nanoscale devices as geometric feature sizes approach the wavelength of the particles involved. Classical approaches to charge transport and heat transfer simulation such as the drift-diffusion approach and Fourier’s law, respectively, do not provide accurate results at these length scales. Instead, the transport processes are governed by the semi-classical Boltzmann transport equation (BTE) with quantum corrections derived from the Schrodinger equation ̈ (SE). In this work, a technique is presented for coupling a 3D phonon Monte Carlo (MC) simulation to an electron multi-subband Monte Carlo (MSBMC) simulation. Both carrier species are first examined separately. An electron MC simulation of bulk silicon, a silicon n-i-n diode, and an intrinsic-channel fin-field effect transistor (FinFET) structure are also presented. A 3D phonon MC algorithm is demonstrated in bulk silicon, a silicon thin film, and a silicon nanoconstriction. These tests verify the correctness of the MC framework. Finally, a novel carrier scattering system which directly accounts for the interaction be- tween the two particle populations inside a nanoscale device is shown. e tool developed supports quantum size effects and is shown to be capable of modeling the exchange of energy between thermal and electronic particle systems in a silicon FinFET