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?

10-3 : m (Milli) 10-6 : μ (Maicro) 微 （び） 10-9 : n (Nano) 　 　塵　 （じん） 10-12 : p (Pico) 　　 漠　 （ばく） 10-15 : f (Femto) 　 須臾　（しゅゆ） 10-18 : a (Atto) 　 　刹那 （せつな） 10-21 : 　 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 effectCharge discreteness and strong

electron-electron Coulomb interaction effects

Tunneling effectsStrong electric field effectsBallistic 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

1950 1970 1980 2000

M.Schulz, Nature 399(1999)729

Roadmap for Si MicroelectronicsMoor’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 gasQuantum conductance

Quantum point contact

Conductance of a quantum point contact

STM images of electron flow close to a quantum point contact

Fk2

1

Fk・ 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 2n 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 31P 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