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Detailed Device Simulators Commercial simulators: EM, semiconductor devices, Comsol Commercial Simulator for Detailed Device Modeling • A lot of very powerful device level tools. • Commercial tools that handle meshing, solution and analysis • Three examples – EM – Finite Difference Time Domain and HFSS – Comsol – multi-physics – Semiconductors – Sentuarus First Example is Maxwell’s Equations The basic set of equations describing the electromagnetic world Gauss’s law Gauss’s law for magnetism Faraday’s law Ampere’s law Constitutive relations D v B 0 B E t D H J t D E and B H Commercial software packages Commercial software packages Finite element method (FEM) Method of Moments (MoM) ADS Momentum HFSS Transmission line matrix (TLM) CST Microstripes Finite-difference time-domain (FDTD) FDTD Overview – Cells A three-dimensional problem space is composed of cells 5/60 FDTD Overview – Material grid A three-dimensional problem space is composed of cells 6/60 Transformation from Time-Domain to Frequency-Domain Results can be obtained for frequency domain using Fourier Transform A low-pass filter S11 S21 Incident plane wave 8/60 Scattering Problems H inc H scat Einc Escat t A dielectric sphere 9/60 H inc 0 Einc t Scattering from a Dielectric Sphere 10/60 Wireless Personal Communications Devices Source: Allen Taflove, “A Perspective on the 40-Year History of FDTD Computational Electrodynamics,” Applied Computational Electromagnetics Society (ACES) Conference, Miami, Florida, March 15, 2006. 11/60 Can be found at http://www.ece.northwestern.edu/ecefaculty/Allen1.html Also for optics: Focusing Plasmonic Lens Source: Allen Taflove, “A Perspective on the 40-Year History of FDTD Computational Electrodynamics,” Applied Computational Electromagnetics Society (ACES) Conference, Miami, Florida, March 15, 2006. Can be found at http://www.ece.northwestern.edu/ecefaculty/Allen1.html Different Methods of Electromagnetic Analysis MOM 13 Example of Adaptive meshing Waveguide Filter at right (symmetry along top face) shows effect of mesh adaptation. The region between posts has a denser mesh, due to the superposition of reflected energy found in the solution process. Post Post 14 Some Typical High-Frequency Electromagnetic Applications Waveguide Components RF Integrated Circuits Antenna EMC 15 EM Summary • Lots of choices – you will use Maxwell-2D • Lots of data – Fields – Terminal currents/voltages – S parameters • Typically slow • Often hard to learn Multi-physics - Comsol • Multi-physics is the combination of several physics phenomena when describing a process • In modeling and simulations, these descriptions are based on the laws of physics • There is one precise way to present the laws of physics, and that is by means of differential equations* * Feynman “Famous Lectures” The description of a loudspeaker involves electromagnetic fields and forces, structural analysis, and acoustic pressure fields in the one model. COMSOL’s Methodology for Modeling Multiphysics Phenomena • Development goals: – To create a software where scientists and engineers can formulate any system of partial differential equations (PDEs) based on the laws of physics – To formulate user interfaces, based on the above methods, for the most common areas in applied physics and engineering Microwave-thermal-structural multiphysics couplings in a waveguide circulator COMSOL’s Methodology for Modeling Multiphysics Phenomena Example: Fully Coupled Physics with Joule Heating and CFD • • • Definition in the graphical user interface Automatic assembly using equation interpretation and then discretization Solution with direct or iterative solvers using a fully coupled system utilizing a damped Newton method Fluid dynamics and heat transfer Thermal analysis in solids Assembling of equations and discretization using FEM Solution of the coupled system Electromagentic fields COMSOL’s Methodology for Modeling Multiphysics Phenomena Example: Fully Coupled Physics with Joule Heating and CFD • • • Temperature field defined in both solid and fluid domains The fluid flow equations are only defined in the fluid domain The static electric field is only defined in the solid domain Outlet Metal wire heated using an electric current Inlet Automatic meshing with tetrahedral elements. Quadrilateral and prism elements are also available as well as manual settings and adaptive meshing. The slice plot shows temperature. The arrows show the velocity field. Note the expansion due to the temperature increase. The boundary plot on the hot wire shows the electric potential. The solution takes 12 minutes on a Toshiba Tecra laptop. It requires about 600 Mb of RAM including a 300 Mb footprint. The deformation and stresses are mostly caused by thermal expansion. The fluid forces have little effect. Other Multiphysics Coupling Examples in COMSOL • Electromagnetic wave propagation and structural analysis – Stress-optical effects After annealing at high temperatures, mismatch in thermal expansion between the silica and silicon layers results in thermally induced stresses at the operating temperature. These stresses influence the refractive index. Other Multiphysics Coupling Examples in COMSOL • Equation-based modeling of semiconductors – Electrons and hole concentration fields coupled to Poisson’s equations Distributed SPICE model of an integrated bipolar transistor. The model couples the electric potential for four different layers (four equations) with a circuit model. Model of a MOS transistor including drift-diffusion of electron (n) and hole (p) concentrations, coupled to the Poisson equation.