Quantum Hydrodynamic Modeling, Numerical Methods, and Applications Semiconductor Transistors

1. 交通大學數學建模與科學計算研究中心 Quantum Hydrodynamic Modeling, Numerical Methods, and Applications Semiconductor Transistors Jinn-Liang Liu 劉晉良 National Hsinchu Univ. of Edu. 新竹教育大學 Jan. 25-27, 2010

2. Classical Computer Microprocessor Microchips MOSFET

3. Transistor The most important invention of the 20th century? A transistor is an electronic device used as a switch or to amplify an electric current or voltage.

4. 1930 First Transistor Patent Filed by J. E. Lilienfeld in 1926

5. The First Transistor Invented at Bell Labs in 1947

6. The original version of the paper was rejected for publication by Physical Review on the referee's unimaginative assertion that it was 'too speculative' and involved 'no new physics.' Received his Ph.D. at University of Tokyo in 1959, Esaki was awarded the Nobel Prize in 1973 for research conducted around 1958 on electron quantum tunneling (Esaki Diode). 假設20歲年輕人之創造力是100%、辨別力是0%，70歲老年人創造力是0%、辨別力是100%，人生分歧點是45歲。分析諾貝爾獎得主獲獎事由和年齡關聯性，會發現得獎人年齡大多集中於35歲至39歲時，而我於44歲發明人造量子結構。

8. MOSFET (Metal Oxide Semiconductor Field Effect Transistor)

9. Semiconductor A semiconductor is a material that can behave as a conductor or an insulator depending on what is done to it. We can control the amount of current that can pass through a semiconductor. Kingfisher Science Encyclopedia

12. Czochralski Crystal Growth

13. Sand Ingot Wafer Doping IC 12吋矽晶圓 Gold Ingots Silicon Ingot

14. Silicon Crystal

15. Si Si Si Extra Si As Si Si Si Si - Doping Impurities (n-Type) Conducting band, Ec Ed ~ 0.05 eV Electron Eg = 1.1 eV Valence band, Ev

16. Conducting band, Ec Si Si Si Hole Eg = 1.1 eV Si B Si Ea ~ 0.05 eV Si Si Si - Valence band, Ev Electron Doping Impurities (p-Type)

17. S. Roy and A. Asenov, Science 2005 MOSFET (Metal Oxide Semiconductor Field Effect Transistor) 2003 L = 4 nm Research 2005 L = 45 nm Production 2018 L = 7 nm Production 3D, 30nm x 30nm

18. Gate Length: 90 nm (2005 In Production) (Device Size) 65 nm (2006 In Production) 34 nm (This Talk)

19. Device Sizes Vs. Models

20. Self-Adjoint Energy Transport Model (Chen & Liu, JCP 2003) Quantum Corrected Energy Transport Model (Chen & Liu, JCP 2005) L=IJ=34nm

21. Doping Concentration

22. Energy Transport Model • electrostatic potential • n electron density • p hole density • J current density • S energy flux • E electric field • R generation- recombination rate

23. Auxiliary Relationships

24. Self-Adjoint Formulation New Variables

25. Bohm’s Quantum Potential

27. Self-Adjoint QCET Model

28. Singularly Perturbed QCET Model(Liu, Lee, & Chen, 2009 Preprint) Dimensionless Scaling • Nano devices extremely singular • Boundary layer • Junction layer • Quantum potential layer

29. Adaptive Algorithm Finite Element Method Monotone Iteration Exponential Fitting

30. The Final Adaptive Mesh

31. Electron Temperature

32. Hole Quantum Potential

33. Electron Current Density

34. Drain Current for MOSFET

35. Alternative Future MOS

36. MOS Scaling Challenges • Technology Scaling Parasitic Effects: Leakage, Capacitance, Risistance • Power Limits: End of Voltage Scaling • Band-Structure Engineering • Scattering: e-insulator, e-imp, e-ph, e-e • Dopant Atom Fluctuations • Non-Equilibrium Electron & Phonon Distrb. • Long Range Coulomb Interactions • Full-Band Bias-Induced Quantization • Phonon Transport Models • Automatic Multi-Scale Computing

37. MOS Simulation Challenges

38. Conclusion • Self-Adjoint QCET Model: More Advanced • Technology Scaling Challenges in Physics and Engineering • Muti-Scaling Modeling and Numerical Methods • High-Performance Architecture, Algorithms, and Coding