Mathematical Simulation and Michael D ohler Zheng He Optimization - PowerPoint PPT Presentation

Mathematical Simulation and Optimization of Semiconductor Devices Mathematical Simulation and Michael D¨ ohler Zheng He Optimization of Semiconductor Devices Maike Lorenz Philipp Monreal Aleksandra Rakic Sapna Sharma Instructor: Marie-Therese Michael D¨ ohler Wolfram Zheng He Physics Maike Lorenz Semiconductor Devices Philipp Monreal Drift-Diffusion Aleksandra Rakic Equation (DDE) Sapna Sharma Solving DDE & Results Inverse Problem Instructor: Marie-Therese Wolfram Optimization Algorithm for Inverse Problem 20th ECMI Modeling week @DTU, Denmark Numerical Results Conclusions 24th August 2006

Mathematical Physics Simulation and Optimization of Semiconductor Devices Solid states material can be grouped into three classes: Michael D¨ ohler Zheng He ◮ Insulators Maike Lorenz Philipp Monreal Aleksandra Rakic ◮ Semiconductors Sapna Sharma ◮ Conductors Instructor: Marie-Therese Wolfram Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Physics Simulation and Optimization of Semiconductor Devices Solid states material can be grouped into three classes: Michael D¨ ohler Zheng He ◮ Insulators Maike Lorenz Philipp Monreal Aleksandra Rakic ◮ Semiconductors Sapna Sharma ◮ Conductors Instructor: Marie-Therese Wolfram Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Physics Simulation and Optimization of Semiconductor Devices ◮ Electrons occupy different energy levels Michael D¨ ohler Zheng He Maike Lorenz Philipp Monreal Aleksandra Rakic Sapna Sharma Instructor: Marie-Therese Wolfram Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Physics Simulation and Optimization of Semiconductor Devices ◮ Electrons occupy different energy levels Michael D¨ ohler Zheng He ◮ Conduction/Valence Band Maike Lorenz Philipp Monreal Aleksandra Rakic Sapna Sharma Instructor: Marie-Therese Wolfram Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Physics Simulation and Optimization of Semiconductor Devices ◮ Electrons occupy different energy levels Michael D¨ ohler Zheng He ◮ Conduction/Valence Band Maike Lorenz Philipp Monreal ◮ Different conductivities result from different ’Band Gaps’ Aleksandra Rakic Sapna Sharma Instructor: Marie-Therese Wolfram Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Physics Simulation and Optimization of Semiconductor Devices ◮ Electrons occupy different energy levels Michael D¨ ohler Zheng He ◮ Conduction/Valence Band Maike Lorenz Philipp Monreal ◮ Different conductivities result from different ’Band Gaps’ Aleksandra Rakic Sapna Sharma ◮ Semiconductors typically have a gap size of about 1eV Instructor: Marie-Therese Wolfram Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Physics Simulation and Optimization of Semiconductor Devices ◮ Electrons occupy different energy levels Michael D¨ ohler Zheng He ◮ Conduction/Valence Band Maike Lorenz Philipp Monreal ◮ Different conductivities result from different ’Band Gaps’ Aleksandra Rakic Sapna Sharma ◮ Semiconductors typically have a gap size of about 1eV Instructor: Marie-Therese Wolfram Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Physics Simulation and Optimization of Semiconductor Devices Michael D¨ ohler ◮ To achieve a desired band gap, ’doping’ is used Zheng He Maike Lorenz Philipp Monreal ◮ Doping means adding impurities (different elements); Aleksandra Rakic Sapna Sharma donors (n-type) or acceptors (p-type) Instructor: Marie-Therese Wolfram Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Physics Simulation and Optimization of Semiconductor Devices Michael D¨ ohler ◮ To achieve a desired band gap, ’doping’ is used Zheng He Maike Lorenz Philipp Monreal ◮ Doping means adding impurities (different elements); Aleksandra Rakic Sapna Sharma donors (n-type) or acceptors (p-type) Instructor: Marie-Therese Wolfram Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse (a) intrinsic (b) n-type (c) p-type Problem Numerical Results Figure: Doping Conclusions

Mathematical Semiconductors devices Simulation and Optimization of Semiconductor Devices Michael D¨ ohler Zheng He Maike Lorenz Philipp Monreal Aleksandra Rakic Advantages Sapna Sharma ◮ Very small length (e.g. ≈ 10nm for a transistor used in a Instructor: Marie-Therese CPU) Wolfram ◮ Controlable conductivity Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Semiconductors devices Simulation and Optimization of Semiconductor Devices Michael D¨ ohler Zheng He Maike Lorenz Philipp Monreal Aleksandra Rakic Advantages Sapna Sharma ◮ Very small length (e.g. ≈ 10nm for a transistor used in a Instructor: Marie-Therese CPU) Wolfram ◮ Controlable conductivity Physics Semiconductor Devices Applications of semiconductor devices Drift-Diffusion Equation (DDE) ◮ Camcorders, solar cells (Photonic devices) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Semiconductors devices Simulation and Optimization of Semiconductor Devices Michael D¨ ohler Zheng He Maike Lorenz Philipp Monreal Aleksandra Rakic Advantages Sapna Sharma ◮ Very small length (e.g. ≈ 10nm for a transistor used in a Instructor: Marie-Therese CPU) Wolfram ◮ Controlable conductivity Physics Semiconductor Devices Applications of semiconductor devices Drift-Diffusion Equation (DDE) ◮ Camcorders, solar cells (Photonic devices) Solving DDE & Results ◮ LEDs (Optoelectric emitters) Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Semiconductors devices Simulation and Optimization of Semiconductor Devices Michael D¨ ohler Zheng He Maike Lorenz Philipp Monreal Aleksandra Rakic Advantages Sapna Sharma ◮ Very small length (e.g. ≈ 10nm for a transistor used in a Instructor: Marie-Therese CPU) Wolfram ◮ Controlable conductivity Physics Semiconductor Devices Applications of semiconductor devices Drift-Diffusion Equation (DDE) ◮ Camcorders, solar cells (Photonic devices) Solving DDE & Results ◮ LEDs (Optoelectric emitters) Inverse Problem ◮ Flat panel displays Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Semiconductors devices Simulation and Optimization of Semiconductor Devices Michael D¨ ohler Zheng He Maike Lorenz Philipp Monreal Aleksandra Rakic Advantages Sapna Sharma ◮ Very small length (e.g. ≈ 10nm for a transistor used in a Instructor: Marie-Therese CPU) Wolfram ◮ Controlable conductivity Physics Semiconductor Devices Applications of semiconductor devices Drift-Diffusion Equation (DDE) ◮ Camcorders, solar cells (Photonic devices) Solving DDE & Results ◮ LEDs (Optoelectric emitters) Inverse Problem ◮ Flat panel displays Optimization Algorithm for Inverse ◮ Integrated circuits (MOSFETs) and many more... Problem Numerical Results Conclusions

Mathematical Semiconductor devices Simulation and Optimization of Semiconductor Devices Michael D¨ ohler Zheng He ◮ We consider the following (called diode) Maike Lorenz Philipp Monreal Aleksandra Rakic Sapna Sharma Instructor: Marie-Therese Wolfram Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions

Mathematical Semiconductor devices Simulation and Optimization of Semiconductor Devices Michael D¨ ohler Zheng He ◮ We consider the following (called diode) Maike Lorenz Philipp Monreal Aleksandra Rakic Sapna Sharma Instructor: Marie-Therese Wolfram Physics Semiconductor Devices Drift-Diffusion Equation (DDE) Solving DDE & Results Inverse Problem Optimization Algorithm for Inverse Problem Numerical Results Conclusions