Simulation Of Submicron Devices Research Articles

Stabilized mixed finite elements for fluid models in semiconductors

In this article we deal with the numerical simulation of semiconductor devices using the Energy-Balance (EB) transport model. This accounts for hot electrons behaviour and nonlocal effects which are of utmost relevance in the simulation of submicron devices. We propose an efficient and accurate solver for the EB equations based on the well-known Gummel’s decoupled algorithm to handle iteratively the full system, while the discretization employs cell-centred Mixed Finite Volume (MFV) methods. These are derived from the standard Raviart-Thomas (RT) finite elements of lowest degree through a suitable quadrature formula which diagonalizes the element mass matrix. Numerical results to validate the newly proposed stabilized method are reported including the simulation of a model curved p-n diode, a one-dimensional p-n diode and a realistic state-of-the-art 1 μm-channel nMOS transistor.

Assessment of approximate balance equation transport models used for submicron silicon device modelling

The common approximations found in literature for the balance equation method used for non-stationary submicron device simulation are presented and discussed. To assess different approximations, the full balance equation model is solved numerically solved for the n+-i-n+ submicron silicon structure where nonstationary transport effects eventually take place. The results obtained from the derived approximate models applied to the same silicon structure are compared with those obtained from the full model. In all cases, empirical formulae for momentum and energy relaxation times are used to clarify only the effect of approximations on the simulation results.

Carrier Thermal Conductivity: Analysis and Application to Submicron-Device Simulation

Within a correlation-function (CF) formalism, the kinetic coefficientsof charge carriers in semiconductors are studied under different conditions. For the case of linear response in equilibrium, thetransitions from the non-degenerate to the degenerate regimes as wellas from ballistic to diffusive conditions are discussed within ananalytical model. Generalizing the method to high-field transport innondegenerate semiconductors, the CFs are determined by Monte Carlo (MC) calculations for bulk silicon from which the appropriate thermalconductivity has been obtained and included into the hydrodynamic code HEIELDS. For an n+nn+ submicron structure the temperatureand velocity profiles of the carriers have been calculated with HFIELDS.

Transport effects and characteristic modes in the modeling and simulation of submicron devices

This paper has two major goals: (1) to study the effect of the common practice of neglecting the convective terms (inertial approximation) in the hydrodynamic model in the simulation of n/sup +/-n-n/sup +/ diodes and two dimensional MESFET devices; and (2) to test analytical criteria, formulated in terms of characteristic values of the Jacobian matrix, as a method of determining the impact of first derivative perturbation terms in this model, and in related energy transport models. This characteristic value analysis can be thought of as generalizing the usual analytical solution of first order linear systems of ordinary differential equations with constant coefficients. Concerning (1), we find that the inertial approximation is invalid near the diode junctions, and near the contact regions of the MESFET device. In regard to (2), we find a proper arrangement of terms, expressing the flux, such that the first derivative part of the system is hyperbolic, both for the hydrodynamic model and the energy transport model. For the hydrodynamic model, two forms of the heat conduction term are studied, including the case of a convective term. This suggests and validates the use of shock capturing algorithms for the simulation. >

Effective potential for moment-method simulation of quantum devices

In the simulation of submicron devices, complete quantum descriptions can be extremely computationally intensive, and reduced descriptions are desirable. One such description utilizes a few low-order moments of the momentum distribution that are defined by the Wigner function. Two major difficulties occur in applying this moment method: (i) An independent calculation is required to find quantum mechanically accurate initial conditions. (ii) For a system in a mixed state, the hierarchy of time evolution equations for the moments does not close. We describe an approach to solve these problems. The initial distribution is determined in equilibrium by means of a new effective potential, chosen for its ability to treat the sharp potential features which occur in heterostructures. It accurately describes barrier penetration and repulsion, as well as quantum broadening of the momentum distribution. The moment equation hierarchy is closed at the level of the second-moment time evolution equation, using a closure that is exact for a shifted Fermi distribution. Band-bending is included by simultaneous self-consistent determination of all the moments.

A new set of semiconductor equations for computer simulation of submicron devices

A new set of semiconductor equations is proposed here which will be suitable for the numerical study of the carrier transport effects in submicron devices. With simplified models and comprehensive numerical techniques, the relative importance (on the device behavior) of several physical effects, such as velocity overshoot, intracollisional field effect, avalanche breakdown, carrier generation and temperature effect can be determined. The program that is capable of solving this set of equations will become an indispensible CAD tool if the current trend of the decreasing of the device dimensions continues.