Abstract
In this article we address the numerical study of 3D semiconductor devices for applications in electronics industry including charge generation phenomena due to impact ionization. With this aim, we propose two novel 3D finite element (FE) models (methods A and B), for electron and hole Drift-Diffusion (DD) current densities. Method A is based on a primal-mixed formulation of the DD model as a function of the quasi-Fermi potential gradient, while method B is a modification of the standard DD formula based on the introduction of an artificial diffusion matrix. Method A is a Galerkin FE approximation of the density current (written in generalized ohmic form) where the harmonic average of the electrical conductivity is used instead of the standard average while method B is a genuine 3D extension of the classic 1D Scharfetter-Gummel difference formula interpreted as a stabilized Galerkin FE approximation with the use of an ‘optimal’ artificial diffusion. The proposed methods are compared in the 3D simulation of a p-n junction diode and of a p-MOS transistor in the on-state regime. Results show that method A outperforms method B in physical accuracy and numerical stability. Method A is then used in the 3D simulation of a n-MOS transistor in the off-state regime including impact ionization. Results demonstrate that the model is able to accurately compute the I-V characteristic of the device until drain-to-bulk junction breakdown.
Highlights
Introduction and motivationSemiconductor technology is undergoing a continuously increasing advancement in the aggressive scaling of device length [ ]
In the present work we extend the FEMOS computational platform in the study of the Drift Diffusion model (DD) [, ] and focus on the issue of endowing the simulation tool of a consistent, stable and accurate procedure for the approximation of electron and hole current densities in the device
3.3 Method B In the previous section the discrete form of the current density is constructed by starting from the equivalent ‘ohmic’ representation in terms of the quasi Fermi potential, and by performing a suitable approximation of the electrical conductivity over the finite element K
Summary
Introduction and motivationSemiconductor technology is undergoing a continuously increasing advancement in the aggressive scaling of device length [ ]. In the case of novel memory devices, due to the different undergoing physical phenomena, a self-consistent multiphysics approach is preferred with respect to the simulation of independent phenomena such as chemical reactions, electrical conduction and material properties modification To respond to this need the software FEMOS (Finite Element Modeling Oriented Simulator) has been designed: FEMOS is a general-purpose modular numerical code based. In the present work we extend the FEMOS computational platform in the study of the Drift Diffusion model (DD) [ , ] and focus on the issue of endowing the simulation tool of a consistent, stable and accurate procedure for the approximation of electron and hole current densities in the device This is of utmost importance in: (i) visualization and post-processing; (ii) evaluation of conduction currents at device terminals; and (iii) inclusion in the DD model of generation phenomena due to Impact Ionization (II). Our attention is devoted to (iii), because of the critical role of II in the convergence and numerical stability of the iterative algorithm used to solve the DD system (see [ ], Chapter and [ ]), the methods we propose for the treatment of (iii) can be profitably employed for (i) and (ii)
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