The progress of semiconductor fabrication technology, particularly the heteroepitaxial technology (MOCVD, MBE, etc.) has permitted the fabrication of structures and devices whose…
Abstract
The progress of semiconductor fabrication technology, particularly the heteroepitaxial technology (MOCVD, MBE, etc.) has permitted the fabrication of structures and devices whose behaviour is dominated by ballistic and/or quantum‐interference effects through heterojunctions.
P. DEGOND, F. DELAURENS, F.J. MUSTIELES and F. NIER
This paper is devoted to the numerical study, using the deterministic particle method, of the parallel transport of a bidimensional electron gas confined in a potential well near…
Abstract
This paper is devoted to the numerical study, using the deterministic particle method, of the parallel transport of a bidimensional electron gas confined in a potential well near a heterojunction interface. The geometry makes it possible to solve independently the transport under the electric field and the well shape. We simulate the electronic transport with a kinetic model and use the deterministic particle method. As for the description of the potential well, we use different models and compare their influence on the thermodynamic equilibrium and on the transport properties of the electron gas.
Presents a simplified mathematical model of electron transport in a one‐dimensional semiconductor device of N+ ‐ N ‐ N + type. The model is based on a singular perturbation…
Abstract
Presents a simplified mathematical model of electron transport in a one‐dimensional semiconductor device of N+ ‐ N ‐ N + type. The model is based on a singular perturbation approach of the kinetic equation which describes the transport processes. This so‐called Child‐Langmuir asymptotics is obtained by assuming that the injected electrons at the N + ‐ N junction on the source side have a very weak energy compared with what they are able to gain under the influence of the electric field. Formally establishes the limit model when a realistic collision model for electron‐phonon interaction is considered. Compares the results with both experiments and particle simulations.
Details
Keywords
A. Domaingo, M. Galler and F. Schürrer
To present a new direct solution method for the Boltzmann‐Poisson system for simulating one‐dimensional semiconductor devices.
Abstract
Purpose
To present a new direct solution method for the Boltzmann‐Poisson system for simulating one‐dimensional semiconductor devices.
Design/methodology/approach
A combination of finite difference and finite element methods is applied to deal with the differential operators in the Boltzmann transport equation. By taking advantage of a piecewise polynomial approximation of the electron distribution function, the collision operator can be treated without further simplifications. The finite difference method is formulated as a third order WENO approach for non‐uniform grids.
Findings
Comparisons with other methods for a well‐investigated test case reveal that the new method allows faster simulations of devices without losing physical information. It is shown that the presented model provides a better convergence behaviour with respect to the applied grid size than the Minmod scheme of the same order.
Research limitations/implications
The presented direct solution methods provide an easily extensible base for other simulations in 1D or 2D. By modifying the boundary conditions, the simulation of metal‐semiconductor junctions becomes possible. By applying a dimension by dimension approximation models for two‐dimensional devices can be obtained.
Practical implications
The new model is an efficient tool to acquire transport coefficients or current‐voltage characteristics of 1D semiconductor devices due to short computation times.
Originality/value
New grounds have been broken by directly solving the Boltzmann equation based on a combination of finite difference and finite elements methods. This approach allows us to equip the model with the advantages of both methods. The finite element method assures macroscopic balance equations, while the WENO approximation is well‐suited to deal with steep gradients due to the doping profiles. Consequently, the presented model is a good choice for the fast and accurate simulation of one‐dimensional semiconductor devices.