Mixed-Mode Device/Circuit Simulation Tibor Grasser Institute for Microelectronics Gußhausstraße 27–29, A-1040 Wien, Austria Technical University Vienna, Austria http://www.iue.tuwien.ac.at OOuuttlliinnee Circuit simulation and compact models Numerical models instead of compact models Challenges in numerical modeling Mixed-mode device/circuit simulation Examples Conclusion 2 CCiirrccuuiitt SSiimmuullaattiioonn Circuit simulation fundamental Development of modern IC To understand and optimize the way a circuit works 3 CCiirrccuuiitt SSiimmuullaattiioonn Circuit simulation fundamental Development of modern IC To understand and optimize the way a circuit works For circuit simulation we need Lumped elements: R, C, L, etc. Current and voltage sources, controlled sources Semiconductor devices Thermal equivalent circuit (coupling and self-heating) 3 CCiirrccuuiitt SSiimmuullaattiioonn Circuit simulation fundamental Development of modern IC To understand and optimize the way a circuit works For circuit simulation we need Lumped elements: R, C, L, etc. Current and voltage sources, controlled sources Semiconductor devices Thermal equivalent circuit (coupling and self-heating) Electrical/thermal properties of semiconductor devices Characterized by coupled partial differential equations 3 CCiirrccuuiitt SSiimmuullaattiioonn Circuit simulation fundamental Development of modern IC To understand and optimize the way a circuit works For circuit simulation we need Lumped elements: R, C, L, etc. Current and voltage sources, controlled sources Semiconductor devices Thermal equivalent circuit (coupling and self-heating) Electrical/thermal properties of semiconductor devices Characterized by coupled partial differential equations For the simulation of large circuits we need compact models Obtained from simplified solutions of these PDEs or empirically Must be very efficient (compact!) 3 CCoommppaacctt MMooddeelliinngg Derivation of compact models based on fundamental equations Often the drift-diffusion framework is used Simplifying assumptions on geometry, doping profiles, material parameters ⇒ Compact model It is becoming increasingly difficult to extract main features 4 CCoommppaacctt MMooddeelliinngg Derivation of compact models based on fundamental equations Often the drift-diffusion framework is used Simplifying assumptions on geometry, doping profiles, material parameters ⇒ Compact model It is becoming increasingly difficult to extract main features Ongoing struggle regarding Number of parameters Physical meaning of these parameters Predictiveness difficult to obtain, calibration required 4 CCoommppaacctt MMooddeelliinngg Derivation of compact models based on fundamental equations Often the drift-diffusion framework is used Simplifying assumptions on geometry, doping profiles, material parameters ⇒ Compact model It is becoming increasingly difficult to extract main features Ongoing struggle regarding Number of parameters Physical meaning of these parameters Predictiveness difficult to obtain, calibration required Compact modeling challenges (ITRS) Quantum confinement Ballistic effects Inclusion of variability and statistics 4 SSiimmuullaattiioonn wwiitthh CCoommppaacctt MMooddeellss Advantages of using compact models Very fast execution (compared to PDEs) 5