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 Electro- Communications for giving me a chance and various convenience to make e-Learning text.

CONTENTS 1. Introduction: What is nanotechnology? 2. Interactions between atoms and the lattice properties of crystals 3. Covalent bond and morphology of crystals, surfaces and interfaces 4. Electronic structure of crystals 5. Band offsets at hetero-interfaces and effective mass approximation 6. Pseudopotential 7. Many-body effect I: Hartree approximation, Hartree-Fock approximation and density functional method 8. Many-body effect II: Quantum Monte Carlo method 9. Transport properties I: Diffusive transport 10.Transport properties II: Ballistic transport A1. Solutions A2. Electronic properties of crystals: Calculation results by CASTEP A3.Simulation for solid state physics

Computational Solid State Physics 計算物性学特論 第１回 1. Introduction What is nonotechnology?

What is nano? : m (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 -9 m 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 L.L.Sohn, Nature 394(1998)131 Ge transistor LSI Quantum corral Carbon nanotube Point contact

M.Schulz, Nature 399(1999)729 Roadmap for Si Microelectronics Moor’s Low:

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 resonant- tunneling diodes

Resonant tunneling diode Profile through a three-dimensional resonant-tunneling diode. Fermi sea of electrons resonant tunneling quasi-bound state

GaAs/AlGaAs interface : two-dimensional electron gas Quantum conductance Quantum point contact

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

[110] gold contact TEM image

Quantized conductance atomic switch (QCAS) Nature, 433(’05)47

Switching results of the QCAS

Quantum conductance of QCAS

Electron device using Coulomb blockade caused by electron-electron Coulomb interaction Si single-electron CCD SEM image

Manipulation of elementary charge

Sensing of a single hole

Kondo corral D.M.Eigler et al. PRL 86(2001)2392 Interference pattern of two- dimensional electron gas on Co/Cu(111) Bottom-up method STM image

Molecualr abacus STM image of molecules

Quantum computer Classical bit ： １ or 0 Quantum bit ： superposition of 0 and 1 N qubit ： express 2 n states simultaneously Examples of qubit ： electron spin, nuclear spin Computer which uses principles of “ superposition ” in quantum mechanics

Quantum computer by Kane ’ s model Qubit: Nuclear spin of 31 P in Si STM image

Controlled not gate qubit:superconducting Cooper pairs T.Yamamoto et al. Nature 425 (2003) SEM image

Spin coupling in a double-dots TEM image Qubit: electron spin in a dot