Lecture_11-Simulation

Lecture_11-Simulation - Lecture 11 Process and Device...

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Process and Device Simulation Lecture 11 Carl-Mikael Zetterling bellman@kth.se www.ict.kth.se/courses/IH2655
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH • Motivation • Analysis vs Simulation • Simulation types (hierarchy) • How does it work? • Process simulation – MOSFET example • Device simulation – examples • How long does it take? • Further studies
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Processing Characterization Simulation Motivation 1 $imulation saves time and Mon€y!
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Motivation 2 Simulation shows what happens inside!
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Analysis vs Simulation 1D problems Simple doping (analytic) Constant mobility, temp. Linear Low electric fields Exact solutions (May be series solutions) Special cases Any geometry Any doping Varying mobility, temp. Nonlinear High and low fields No equations, only numbers May be incorrect May not converge
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Simulation types (hierarchy) One or more simulators may be needed: Hierarchy: System – Circuit – Device - Process
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH System simulation High level description of system May use VHDL or circuit libraries Design and simulation phase coupled Input: circuit specifications input signals (test vectors) Output: mask layout or programming info
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Circuit simulation Circuit level description Spice is a common tool, uses node analysis Circuit design for circuit board or ASIC Input: circuit layout + input signals component specifications (models, measured or simulated) Output: node voltages vs time or frequency
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Device simulation Usually single device level Physics based tools Device design, usually coupled to Process simulation Input: device geometry (cross-section, doping) applied voltages/currents, temperature Output: terminal voltages vs time or frequency electric fields, temperatures internal potential, electron/hole concentration
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Process simulation Usually single device level Physics based tools (+ empirical models) Recipe design or device design Input: starting geometry (doping, material) process run sheet (time, gases, temp, masks) Output: device geometry (cross-section, doping profiles)
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH How does it work? Physics based simulation is based on solving partial differential equations, making sure that charge, particle number, energy, momentum etc is conserved. Three basic equations: Parabolic (diffusion) Elliptic (Poisson) Hyperbolic (Wave) () 2 2 x C D t C u D t u = = ρ ε = = 2 2 dx u d u 2 2 2 2 2 2 x u c t u u c t u = =
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Discretization 1 Derivatives are replaced by differences
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Discretization 2 Derivatives are replaced by differences
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Discretization 3 The device geometry is gridded in 1D, 2D or 3D
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Discretization 4 Poisson’s equation in 1D:
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IH2655, Spring 2009 Carl-Mikael Zetterling KTH Discretization 5 Set up equations for each node:
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This note was uploaded on 03/09/2009 for the course EE 300 taught by Professor Y during the Spring '09 term at CUNY City.

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Lecture_11-Simulation - Lecture 11 Process and Device...

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