Computational Solid State Physics 計算物性学特論 Akiko Natori 名取晃子 Purpose To understand fundamental solid state physics in nanostructures with computer simulation 計算機シミュレーションを用いて、ナノスケール原子構造の物性の基礎を理解する。 Nanotechnology for electronics  How to make nanometer-scale structure?  What features of electronic properties are expected in nanometer-scale structure?  How to use the electronic properties for creating novel devices? Study  Atomic structure: Interaction between atoms Homogeneous structure: Gas, liquid and solid Solid: crystal, quasi-crystal and amorphous Heterogeneous structure: growth mode of thin films, quantum well, superlattice  Electronic properties in nanometer-scale structure: Electronic structure Transport properties Recommended textbooks  The physics of low-dimensional semiconductors, J.H. Davies, Cambridge University press  Mesoscopic electronics in solid state nanostructures, T.Heinzel, WILEY-VCH  Physics and applications of semiconductor microstructures, M.Jaros, Oxford Science Publications  Simulation for solid state physics, R.H.Silsbee and J.Drager, Cambridge University press Acknowledgements My students, M. Hirayama, J. Ito, H. Masu and S. Wakui, helped to shape this e-Learning text. I am grateful for their help. I would also like to thank Prof. K. Natori in Tsukuba University for permitting me to use CASTEP. It is a pleasure to thank Prof. T. Okamoto and Prof. K. Nakayama in The University of ElectroCommunications for giving me a chance and various convenience to make e-Learning text. CONTENTS 1. Introduction: What is nanotechnology? 8. Many-body effect II: Quantum Monte Carlo method 2. Interactions between atoms and the lattice properties of crystals 9. Transport properties I: Diffusive transport 3. Covalent bond and morphology of crystals, surfaces and interfaces 10.Transport properties II: Ballistic transport 4. Electronic structure of crystals A1. Solutions 5. Band offsets at hetero-interfaces and effective mass approximation A2. Electronic properties of crystals: Calculation results by CASTEP 6. Pseudopotential A3.Simulation for solid state physics 7. Many-body effect I: Hartree approximation, Hartree-Fock approximation and density functional method Computational Solid State Physics 計算物性学特論第１回 1. Introduction What is nonotechnology? What is nano?  10-3 : m  10-6  10-9  10-12  10-15  10-18  10-21 (Milli) : μ (Maicro) 微（び） : n (Nano) 塵（じん） : p (Pico) 漠（ばく） : f (Femto) 須臾（しゅゆ） : a (Atto) 刹那（せつな） : 清浄（せいじょう） What is nanotechnology? Nanometer scale control of materials which requires to manipulate atoms and molecules. 1nm=10-9m Size of atoms： a spread of electron cloud 0.1nm structure control in atomic scale： Top-down method、bottom-up method Expected effects for electrons in nanostructures  Quantum confinement effect  Charge discreteness and strong electron-electron Coulomb interaction effects  Tunneling effects  Strong electric field effects  Ballistic transport effects Application fields of nanotechnology Miniaturization of electron devices  High integration  High speed  Low consumption electric power  Low cost Miniaturization by top-down method Application to electronic devices Ge transistor 1950 Quantum Carbon Point corral nanotube contact LSI 1970 1980 L.L.Sohn, Nature 394(1998)131 2000 Roadmap for Si Microelectronics Moor’s Low: M.Schulz, Nature 399(1999)729 Moor’s law and number of electrons per device Moor’s Law: Device size 2/3, Chip size 1.5, Integration 4-times / new chip（3 years） I-V Charactaristics of resonanttunneling diodes Resonant tunneling diode resonant tunneling quasi-bound state Fermi sea of electrons Profile through a three-dimensional resonant-tunneling diode. Quantum point contact GaAs/AlGaAs interface : two-dimensional electron gas Quantum conductance Conductance of a quantum point contact STM images of electron flow close to a quantum point contact ・Electrons are wave with wave vector ・Interference stripe with 1  2k F kF [110] gold contact TEM image Quantized conductance atomic switch (QCAS) Nature, 433(’05)47 Switching results of the QCAS Quantum conductance of QCAS Si single-electron CCD Electron device using Coulomb blockade caused by electron-electron Coulomb interaction SEM image Manipulation of elementary charge Sensing of a single hole Kondo corral STM image Bottom-up method Interference pattern of twodimensional electron gas on Co/Cu(111) D.M.Eigler et al. PRL 86(2001)2392 Molecualr abacus STM image of molecules Quantum computer Computer which uses principles of “superposition” in quantum mechanics Classical bit：１ or 0 Quantum bit： superposition of 0 and 1 N qubit： express 2n states simultaneously Examples of qubit： electron spin, nuclear spin Quantum computer by Kane’s model STM image Qubit: Nuclear spin of 31P in Si Controlled not gate qubit:superconducting Cooper pairs SEM image T.Yamamoto et al. Nature 425 (2003) Spin coupling in a double-dots Qubit: electron spin in a dot TEM image