1. Detailed Device Simulators Commercial simulators: EM, semiconductor devices, Comsol

2. 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

3. First Example is Maxwell’s Equations  The basic set of equations describing the electromagnetic world Constitutive relations Gauss’s law Gauss’s law for magnetism Ampere’s law Faraday’s law

4. Commercial software packages  Commercial software packages Finite-difference time-domain (FDTD) Method of Moments (MoM) Finite element method (FEM) Transmission line matrix (TLM) CST Microstripes HFSS ADS Momentum

5. 5/60 FDTD Overview – Cells  A three-dimensional problem space is composed of cells

6. 6/60 FDTD Overview – Material grid  A three-dimensional problem space is composed of cells

7. Transformation from Time-Domain to Frequency-Domain  Results can be obtained for frequency domain using Fourier Transform A low-pass filterS11 S21

8. 8/60 Incident plane wave

9. 9/60 Scattering Problems A dielectric sphere

10. 10/60 Scattering from a Dielectric Sphere

11. 11/60 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. Can be found at http://www.ece.northwestern.edu/ecefaculty/Allen1.htmlhttp://www.ece.northwestern.edu/ecefaculty/Allen1.html

12. 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.htmlhttp://www.ece.northwestern.edu/ecefaculty/Allen1.html

13. 13 Different Methods of Electromagnetic Analysis MOM

14. 14 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

15. 15 Some Typical High-Frequency Electromagnetic Applications Waveguide Components Antenna RF Integrated CircuitsEMC

16. 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

17. 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.

18. 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

19. 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 Assembling of equations and discretization using FEM Solution of the coupled system Thermal analysis in solids Fluid dynamics and heat transfer Electromagentic fields

20. 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 Inlet Outlet Metal wire heated using an electric current

21. Automatic meshing with tetrahedral elements. Quadrilateral and prism elements are also available as well as manual settings and adaptive meshing.

22. The solution takes 12 minutes on a Toshiba Tecra laptop. It requires about 600 Mb of RAM including a 300 Mb footprint. 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.

23. The deformation and stresses are mostly caused by thermal expansion. The fluid forces have little effect.

24. 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.

25. 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.

26. Semiconductor solvers Solve basic equations Plus many additions – Quantum effects – Energy conservation – Thermal distribution – Photon and particle fluxes As an example Sentaurus (Synopsis) for a radiation detector.

27. 3D detectors 3D detector – photodiode detector with electrode columns passing through substrate – Small electrode spacing gives fast collection, low V dep – Radiation hardness Planar 3D

28. Sentaurus Device Editor New feature of Sentaurus TCAD Start with sde Can work in 2D and 3D modes Has functions for complicated shapes like circles, spheres etc. – In command files or MDraw, these must be built up point- by-point, which is very inconvenient Has a built-in command line, and can be controlled with scripts – In 3D, easier than using mouse! – Possible to insert parameters using Workbench

29. Sentaurus Device Editor

30. Mesh tool noffset3d can be run using command files or through Structure Editor, just like mesh Other mesh tool produce axis aligned meshes This tool produces unstructured meshes – More effective for creating curved structures Input command files more complicated – see “Mesh Generation Tools User Guide”

31. Sentaurus Device Takes mesh, applies semiconductor equations and boundary conditions (in discrete form) and solves Physics models: Works by modelling electrostatic potential (Poisson’s equation) and carrier continuity Different versions of physics models available – Different models of mobility, bandgap… – Generation and recombination rates may include avalanche effects, charge generation by high-energy particles… Poisson Electron continuity Hole continuity where See Fichtner, Rose, Bank, “Semiconductor Device Simulation”, IEEE Trans. Electron Devices 30 (9), pp1018, 1983

32. 3D detectors Electric field pattern in a new device structure

33. Semiconductor Device Summary A few choices Lots of Data – n, p and V – Currents, charges – Heat generation – Etc. Typically slow Hard to Use Lots of physical insight if are smart enough Remember all “models are wrong”