The University of Tokyo, The University of Tokyo, The Institute For Solid State The Institute For Solid State

PhysicsPhysicsYasuhiro Yasuhiro IyeIye

November 11, 2005University LectureScience of Material

Lecture 6 What is Condensed Matter Physics?Lecture 6 What is Condensed Matter Physics?Lecture 7 Lecture 7 Quantum Mechanics and Artificial Quantum Mechanics and Artificial

MaterialsMaterials---- HighHigh--tech and the Statetech and the State--ofof--thethe--art Physicsart Physics

Lecture 8Lecture 8 Atom Control and Quantum ControlAtom Control and Quantum Control----NanoNano--science and Quantum Information science and Quantum Information

Lecture 9Lecture 9 Diverse Matter and Physical PropertiesDiverse Matter and Physical Properties

The figures, photos and moving images with ‡ marks attached belong to their copyright holders. Reusing or reproducing them is prohibited unless permission is obtained directly from such copyright holders.

Review of Lecture 6 (1)Review of Lecture 6 (1)

Story about scale.Story about scale.Modern civilization and physics.

Personal computers, cellular phones, satellite communications, GPS, and MRI.Semiconductors, magnetic bodies, dielectric, liquid crystals, gels, superconductors.

Condensed matter physics is the field of physics.Matter and materials.Materials science and materials engineering.Incorporation of the concept with elementary particle physics.The hierarchy structure in the physical world. ⇒ emergent properties.Diversity in matter and physical properties.

Review of Lecture 6 (2)Review of Lecture 6 (2)Quantum mechanics and atomic structure.

Energy level in atoms ⇒ shell structure ⇒ periodic law.The energy scale ~eV in the outermost shell is the most essential to the properties of the element.

The existing forms of matter.Energy versus entropy ⇒ phase transition.

Agglutination mechanism and crystal structure in atom.Crystal structure Crystal structure ⇒⇒ XX--rayray（（electron beam, neutron beam) electron beam, neutron beam) diffraction.diffraction.The bonding force of atoms: Van der Waal bonding, ion bonding, covalent bonding, metal bonding, hydrogen bonding.

⇒ Diversity of matter and physical properties. (Lecture 9)

TodayToday’’s Topicss Topics

Overview of quantum mechanicsOverview of quantum mechanicsQuantum interferenceQuantum interferenceArtificial materials in Artificial materials in mesoscopicmesoscopicsystemssystemsQuantum conductionQuantum conduction

Overview of Quantum MechanicsOverview of Quantum Mechanics

Quantum MechanicsQuantum MechanicsTheoretical description of behaviors in microscopic systems.

Structure of atoms and molecules.The behavior of an electron in a solid state.Visible radiation and matter.

Particle properties: discreteness and separatenesWave properties: superposition and interference

Light: possesses both wave and particle properties.Electron: particle and wave at the same time.

The expressions such as “particle” and “wave” used to refer to everyday phenomena (classical mechanics) is now considered just an analogy that contributes to the phenomena relevant to quantum mechanics.

In Quantum Mechanics, a Particle also Behaves as a Wave

de Broglie wavelength of electron accelerated at 100V:

mEpm

pE 22

2

=⇒=

m1023.1106.11001091.02

1062.62

10

1930

34

−

−−

−

×=×××××

×=

==mEh

phλ

nm12.0=λ

de Broglie wavelength:ph

=λMomentum

de Broglie wavelength in classical particles, e.g., tennis ball is extremely short.

Quantum MechanicsQuantum Mechanics

Time evolution of a wave function follows Schrodinger’s equati

),,,()(2

),,,( 22

2

2

2

22

tzyxrVzyxm

tzyxdtdi ψψ ⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

+∂∂

−=h

h

The existence probability of a particle is given by: 2),,,( tzyxψ

The state of a particle is described by a wave function: ),,,( tzyxψ,,( zyxψ

Linear equation ⇒ superposition principle2121, ψψψψ +⇒ ⇒ Quantum interference

Uncertainty RelationUncertainty RelationThere is uncertainty relation between position and momentum for particle in quantum mechanics. h≥Δ⋅Δ px

x k

f x( ) a k( )

2πk0

e ik x0

0 k

デルタ関数

フーリエ変換

Defined momentum

Plane wave

0kp h=

xikex 0)( =ψ

フーリエ変換

x k

Δx Δk~ /1 Δx

Wave packet∑=

k

ikxekcx )()(ψ

Delta functionFourier transformation

Fourier transformation

QuantumQuantum--mechanical State and mechanical State and Measured ValueMeasured Value

The existence probability of a particle can be obtained by:2),,,( tzyxψ

The exact point of existence can be determined by measuring the position of the particle.

a aEach physical quantity has corresponding operator:

eigenfunction and eigenvalue of operator.

The state in quantum mechanics is described in “wave function”, in other words “Hilbert space”, i.e., state vector in abstract space.

λψψ =Linear algebra a

固有ベクトルの場合

a=λa

Eigenvector

Quantum Mechanical MeasuringQuantum Mechanical MeasuringIn general, quantum mechanics can give probability distribution of measurements obtained by repeated measurement of the “same state” physical quantity but, it cannot give the probability distribution of measured values of different and individual states.

Measurement determines the quantum state in a single eigenstateof physical quantity ⇒ “contraction of the state”

The observation problem and interpretation problem of quantum mechanics

Time evolution in Schrodinger’s equation and the contraction of wave function by measurement.

The most common interpretation in quantum mechanics: Copenhagen interpretation.

Characteristic Phenomena in Characteristic Phenomena in Quantum MechanicsQuantum Mechanics

Tunnel effectTunnel effectParticle can pass through Particle can pass through a potential barrier, a potential barrier, something that is something that is inconceivable in inconceivable in classical mechanics. classical mechanics. ?

Quantum interference Quantum interference effecteffect

SuperpositioningSuperpositioning of of different paths.different paths.⇒⇒ quantum quantum interference.interference.

IyeIye, Yasuhiro., Yasuhiro. Alice no Alice no RyoshiRyoshi RikigakuRikigaku.. InIn Parity.Parity. Tokyo: Maruzen, 2006.Tokyo: Maruzen, 2006.

‡

Quantum InterferenceQuantum Interference

Light Wave InterferenceLight Wave InterferenceThe double-slit experiment by Young. (1805)

Image of interfering waves as light passes through each slit.

In phase

Opposite phase

qdIncident wave

Diffracted wav

q

( )⎩⎨⎧

+=

打ち消し合い

強め合い

λλ

θ21

sinn

nd Intensifying

Canceling

‡

出典確認中

For Classical ParticlesFor Classical Particles

)()()( LRtotal yPyPyP +=

Probability of bullets hitting the wall:＝probability of bullets hitting the wall

through the right slit.＋probability of bullets hitting the wall

through the left slit.

Single slit

A double slit

IyeIye, Yasuhiro., Yasuhiro. Alice no Alice no RyoshiRyoshi RikigakuRikigaku.. InIn Parity.Parity. Tokyo: Maruzen, 2006.Tokyo: Maruzen, 2006.

‡

The Incident WaveThe Incident Wave

P y( )

y

Interference pattern

Particles in Quantum MechanicsParticles in Quantum Mechanics

LRtotal Ψ+Ψ=Ψ

Wave function＝Wave function for particles passing thorough the right slit.＋Wave function for particles passing through the left slit.

Probability＝｜Wave function｜2

*LRL

*R

2L

2R

2LR

2total

ΨΨ+ΨΨ+Ψ+Ψ=

Ψ+Ψ=Ψ

Quantum interference term

Electron InterferenceElectron Interference

Dr. Akira Sotomura(Advanced Research

Laboratory, Hitachi, Ltd.）

Electron source

Electron

DetectorElectron beam

bi pri sm

Figure 3. A double-slit experiment of electrons:Electron beam biprisms are used to replace slits. The experiment was so difficult to perform that people used to think that it could berealized only in one’s mind and not in reality.

‡

The DoubleThe Double--slit Experiment of Electron slit Experiment of Electron (Dr. Akira (Dr. Akira SotomuraSotomura))

Electron InterferenceElectron Interference

Electrons individually reach the screen.

Interference pattern appears.

Clear evidence for an electron’s wave properties.

Dr. Akira Sotomura(Advanced Research

Laboratory, Hitachi, Ltd.)

Electron source

Electr on b eam b ip r is m

Electron

Detector ‡

AharonovAharonov--BohmBohm Effect (AB Effect)Effect (AB Effect)

eh

de

de

de

de

==

⋅=⋅=

⋅−⋅=Δ

∫∫

∫∫

00

loop

RL

2

)()(

)()(

φφφπ

θ

SrBrrA

rrArrA

hh

hhThe magnetic field（vector potential）changes the phase of the electron. ∫⇒

⋅ rrA deie

)(hψψ

Electron source

Electron beam biprism

Coil

Phase difference

出典確認中

‡

How Large Can a Particle Be in Order How Large Can a Particle Be in Order to Interfere?to Interfere?

C60

A.ZeilingerVienna University of Technology ‡

Same Observation for LightSame Observation for Light

Photomultiplier tube catches faint light.

A single photon can be detected.

Light is more likely to be regarded as a wave but it has particle properties as well.

⇒ photoelectric effect

http://crd.search.yahoo.co.jp/MMSIMG/Q=%B8%F7%C5%C5%BB%D2%C1%FD%C7%DC%B4%C9/U=http%3A%2F%2Fwww.matsusada.co.jp%2Fproduct%2Fopt%2Fpmt3852hd%2Fimg%2Fpmt3852hd.jpg/O=7b7b149948a5fdf8/P=84/C=ckh59tsuor7ho&b=2/F=f/I=yahoojp/T=1129680208/*-http://www.matsusada.co.jp/product/opt/pmt3852hd/img/pmt3852hd.jpg

Topics we have covered up to now only deal Topics we have covered up to now only deal with quantum interference in a vacuum state.with quantum interference in a vacuum state.Do electrons in matter perform quantum Do electrons in matter perform quantum interference too?interference too?Quantum interference properties: coherence.Quantum interference properties: coherence.DecoherenceDecoherence makes for a loss of coherence in makes for a loss of coherence in the system.the system.

Artificial Materials and Artificial Materials and MesoscopicMesoscopic SystemsSystems

The Microscopic Universe１ ｍ１０-3 ｍ１０-9 ｍ１０-12 ｍ １０-6 ｍ

１ ｐｍ

Picometer１ ｎｍ

Nanometer１ μｍ

Micro-meter(micron)

１ ｍｍ

Millimeter

Optical microscope

Electron microscope

Scanning probe microscope

O-157

Needle hole and hum

an hair

Bacteria

Wavelength of visible light

Virus

Size of atom

Size of atomic nucleus

The The MesoscopicMesoscopic SystemSystem

Macroscopic scale

Microscopic scale

Mesoscopic scale

It is an intermediate scale between microscopic and macroscopic systems.

12 inch (30 cm)

Silicon wafer

MicroMicro--processing for processing for Semiconductor DevicesSemiconductor Devices

The first transistor invented by Bell Labs in the U.S.A. (1946)

50 yearsPicture removed due tocopyright restrictions

Magnetic Recording MediaMagnetic Recording Media

Hard discMO disc

Information recording method that takes advantage of magnetization directions in a small magnetic body.Recording unit (bit) of a high capacity HD is:0.1mm×1mm

Track

One bit interval

Disk

Interval of tracks

The latest HDD is composed of 2,700 tracks per width 1mm and 28,000 recording bits per length 1mm in circumferential direction. For higher capacity, the track density is increased because there ismore room allowed in filling out the tracks.

28,000 recording bits per length 1mm.

2,700 tracks per width 1mm.

Silicon Silicon MonocrystalMonocrystal ⇒⇒ Wafer Wafer ⇒⇒Super LSISuper LSI

Cutting out of the monocrystal. Wafer

Super LSI （Large Scale Integration)

Micro-processing

http://www.um.u-tokyo.ac.jp/DM_CD/DM_CONT/SILICON/SILI07.JPGhttp://www.um.u-tokyo.ac.jp/DM_CD/DM_CONT/SILICON/SILI22.JPGhttp://www.um.u-tokyo.ac.jp/DM_CD/DM_CONT/SILICON/SILI08.JPGhttp://www.um.u-tokyo.ac.jp/DM_CD/DM_CONT/SILICON/SILI19.JPG

UltraUltra--large Scale Integration large Scale Integration Semiconductor (ULSI)Semiconductor (ULSI)

A prediction of Gordon Moore that the number of transistors (degree of integration) on a semiconductor chip doubles every one and half to two years.

It is clear that there is a limit to the micro-processing technique because semiconductor devices have already reached submicron scale (less than１μm) .

Moore’s law

Chip area

Transistor amount (10,000)

Smallest processing size (gate length) (nm)

Clock frequency (MHz)

Figure 1. Development of LSI (Microprocessor)Year

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Size of the system Land

The lengths that are characteristic of physical phenomenade Broglie wavelength

Free mean pathPhase relaxation length

The The MesoscopicMesoscopic SystemSystem

lλ

The behaviors are different from those of a microscopic system; strong effects of quantum mechanics can be observed.

Region of submicron-scale

φL

Conditions Necessary for Conditions Necessary for MesoscopicMesoscopicPhysics and Physics and NanoscienceNanoscience

Artificial materialsMicro-processingExtreme environments (extreme low temperatures and strong magnetic fields)High-sensitivity, high-resolution, and high-accuracy measurements

Artificial Artificial SuperlatticeSuperlattice

Dr. Leona Esaki (1972) ‡

Semiconductor Artificial Semiconductor Artificial SuperlatticeSuperlattice ProductionProductionMolecular beam epitaxy

GaSi As Be

Al

RHEEDpattern

E-gunScreen

Substrate

Accumulate each layer of atoms inside ultra-high-vacuum in a clean environment.

The artificial superlattice can be obtained by accumulating different types of atomic layers.

‡Iye Laboratory, The Institute for Solid State Physics, University of Tokyo.

Potential of Artificial Potential of Artificial SuperlatticesSuperlattices

Electrons get caught

here.GaAs/AlGaAs

Gap

Valence electron band

Conduction band

TwoTwo--dimension Electron System at dimension Electron System at Semiconductor InterfaceSemiconductor Interface

The electron is confined by potential in the direction perpendicular to the interface while it is freely traveling in the direction parallel to the interface.

The electron density can be changed by applying electric voltageto the gate electrode.The potential for the electron is artificially induced by using an appropriate form of gate electrode.

Gate electrodeSource electrode

Si impurity

Drain electrode

Two-dimension electron system

Two-dimension electron system

Examples of Examples of MesoscopicMesoscopic SamplesSamples

Two-dimension modulat（antidot lattice）

1mm

Single-dimension modulation （washboard potential)

1mm

Quantum point contactQuantum dot

Variety of artificial structures are produced by micro-processing of two-dimensional electron system samples.

Ⓒ Yasuhiro Iye

‡

Scanning electron microscopeElectron beam lithography

Optical microscope

Dustproof suit

Operation image in clean room.

Clean Room OperationClean Room Operation

Iye Laboratory, The Institute for Solid State Physics, University of Tokyo.

‡

Scanning electron microscopeElectron beam lithography

Emission vent of electron beam

Sample holder

Controller

Electron Beam Lithography SystemElectron Beam Lithography System

Iye Laboratory, The Institute for Solid State Physics, University of Tokyo. ‡

ターゲット

基板イオンソース

Ion beam spattering system

Metal Vapor DepositionMetal Vapor Deposition

Ion source

Target

Foundation base

Iye Laboratory, The Institute for Solid State Physics, University of Tokyo.

‡

Ⓒ Yasuhiro Iye ‡

① Cleansing the foundation.

② Resist coating ④ Exposure ⑥ Development

③ Mask alignment ⑤ After exposure

Formation of MicroFormation of Micro--patternspatterns

Ⓒ Yasuhiro Iye ‡

Vapor deposition

Lift-off

Etching

Resist removal

Vapor Deposition and LiftVapor Deposition and Lift--offoff

Ⓒ Yasuhiro Iye ‡

Production of Quantum Structures by Production of Quantum Structures by UltraUltra--micromicro--processingprocessing

Electron lithography system The quantum dot was produced by micro-processing of the electron lithography.

The antidot lattice of two-dimension electron system in a semiconductor:Artificial superperiodicstructure. Ⓒ Yasuhiro Iye ‡

Iye Laboratory, ISSP, University of Tokyo.

‡

The example for the micro-structure sample observed by an optical microscope. A single quantum dot is formed both above and below in the structure.

1.2 mm

Gold deposited electrodeEtching-treated part

5μm

MicroMicro--structure Samplestructure Sample

Ⓒ Yasuhiro Iye ‡

Quantum ConductionQuantum Conduction

Conduction Electrons in MetalsConduction Electrons in Metals

Free electron model

In metals, there is an electron (conduction electron) that can move around in the entire crystal.

Electron is filled from lower energy level

⇒Fermi levelFermi surface

and sphere

Quantum Mechanics: Particles in a Box Quantum Mechanics: Particles in a Box

rkr ⋅= ieL31)(ψ

Fε

Fε

),2,1,0(2 L±±== xxx nnLk π

The permitted wave number of an electron.

Permissive state of wave number space.

Lm2

22 kh=ε

Electric ConductionElectric Conduction

EEv μτ ==me

E

EJ

σ

τ

=

=m

ne2vJ ne=

τv

Ev

medt

dm −=

Electric currentSemi-classical equation of motion

“Friction” term due to scattering.

Acceleration due to electric field.

Electron mobility

mne τσ

2

=

Drude formula

Electric field Electric field

Velocity of ElectronsVelocity of ElectronsMake s current of one ampere Make s current of one ampere

into lead wire with cross into lead wire with cross section area 1 mmsection area 1 mm22

26 A/m10== vJ ne

mm/s0.06m/s106

C106.1m105

19329

=×≈

××−

−−

Am10 26=

=

−

neJv

m/s106F ≈vThe velocity of an electron at the Fermi level is: For ordinary metals:(one hundredth the speed of light)

329 m10 -n =Conduction electron density of metal:

Speed of snails??

kvk k ∂

∂==

εεh

h 1,2

22

m

If there is no electric field, electrons travel in both directions positive and negative to cancel each other out, and as a result, the net electric current is zero.

Even a subtle loss of balance can create very large electric current.This is the average speed.

TwoTwo--dimension Electron System at dimension Electron System at Semiconductor InterfaceSemiconductor Interface

Electron density

HEMT (High Electron Mobility Transistor)

21613 m10~10 -n =

Two-dimension electron system

Two-dimension electron system

Gate electrodeSource electrode

Drain electrode

Si impurity

High MobilityHigh Mobility

Vsm1000 2>μ

m100 μ>l

Electron mobility

Mean free path

Ballistic conductivityL>l （Ｌ： sample size）

Micro-processing lets us to make samples that are smaller than those shown in the figure. M

obili

ty

Bulk

Temperature

Clean bulk

MesoscopicMesoscopic CircuitCircuit

G=GR+GL

Classical parallel circuitMesoscopic ring

G≠GR+GL

Quantum ResistanceQuantum ResistanceThe quantity of the dimension where the electric resistanbelongs is made of physical constants.

eh

Magnetic fluxΦ ＝voltage×time

e Electric charge e ＝electric current×time

2eh

Magnetic flux/electric charge＝ voltage/electric current ＝ electric resistance

Ω= k813.252eh

Quantum resistance

S7.38k813,25

12 μ=Ω

=he

Quantum conductance

Conductance QuantizationConductance Quantization

heN

RG

221==Ω

=k813.25

12

he

Quantum point contact

２次元電子系量子ポイントコンタクト

ソース　電極

ドレイン　　電極

VG

Drain electrodeSource electrode

Two-dimensional electron systemQuantum point contact

Negative bias voltageⒸ Yasuhiro Iye ‡

Hall EffectHall Effect

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛⇒=

y

x

yyyx

xyxx

y

x

EE

JJ

σσσσ

σ EJ

B

B

E

vd

Behavior of electrons in an electrostatic magnetic field.

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛⇒=

y

x

yyyx

xyxx

y

x

JJ

EE

ρρρρ

ρ JE

V

VH

I

W

ρ

ρ

xx

xyL

B

0

ρxx

ρxy

0

∝B/neρxy

ρxx

B

neBBxy =)(ρ ρρ =)(Bxx

( )k

vBvEk kkk ∂∂

=×+=εe

dtd

h

Lorentz force

Quantum Hall EffectQuantum Hall Effect

Ω= k813.252eh

2

10

eh

Nxy

xx

=

=

ρ

ρ

B00

ρxx

ρxyρxy

ρxx

h/e2

h/ e2 2

h/ e32

With accuracy of more than eight digits, agrees with h/e2.

⇒ International standard of resistance

AharonovAharonov--BohmBohm Effect (AB Effect)Effect (AB Effect)

eh

de

de

de

de

==

⋅=⋅=

⋅−⋅=Δ

∫∫

∫∫

00

loop

RL

2

)()(

)()(

φφφπ

θ

SrBrrA

rrArrA

hh

hhPhase change in electron occurs due to the magnetic field (vector potential).

Electron source

CoilElectron beam biprism

Phase difference

出典確認中

‡

AharonovAharonov--BohmBohm Oscillation (AB Oscillation (AB Oscillation)Oscillation)

The above shows the interference of electron waves that pass through the paths in both sides of the ring.Electric resistance periodically oscillates for the ring penetrating magnetic fluxΦ.

Wb1014.4 150−×==

heφ

eh

de

de

de

de

==

⋅=⋅=

⋅−⋅=Δ

∫∫

∫∫

00

loop

RL

2

)()(

)()(

φφφπ

θ

SrBrrA

rrArrA

hh

hh

Magnetic flux quantum

h/e oscillation and h/2e oscillation

Electron Locality as Quantum Electron Locality as Quantum InterferenceInterference

h/2e Oscillation

Φ

−+ Ψ+Ψ=ΨThe pair is in a relationship of inverse symmetry of time. 0

22

2D ln TT

heP

mne

πτσ −=

Classical conductivity

Quantum correction

−+−+−+

−+

ΨΨ+ΨΨ+Ψ+Ψ=

Ψ+Ψ=Ψ**22

22

Quantum interference term

For non-ring structures:

Conductance fluctuation~e2/h

MonoMono--electron Tunnel Effectelectron Tunnel Effect

Coulomb blockadeElectrostatic potential of island is increased due to tunneling of a single electron.⇒ the following electron cannot go in.

Micro tunnel junction

Coulomb island(quantum dot)

Quantum Dot (Artificial Atom)Quantum Dot (Artificial Atom)

Prof. Tarutya, Seigo., School of Science, University of Tokyo ‡

Quantum Physics in Quantum Physics in MesoscopicMesoscopic SystemSystemMono-electron tunnel effect Quantum interference effect

Particle properties Wave properties

Wave-particle duality of electrons

SummarySummaryMesoscopic physics

Artificially-designed system＋state-of-the-art observation

and measuring methods

Visible quantum mechanics:wave properties quantum interference effectparticle properties mono-electron tunnel effect

Magic number e2/h＝（25.813ｋW）-1

Incorporation of fundamental physics and high-tech

Review of Lecture 6 (1)Review of Lecture 6 (2)Today’s TopicsOverview of Quantum MechanicsQuantum MechanicsIn Quantum Mechanics, a Particle also Behaves as a WaveQuantum MechanicsUncertainty RelationQuantum-mechanical State and Measured ValueQuantum Mechanical MeasuringCharacteristic Phenomena in Quantum MechanicsQuantum InterferenceLight Wave InterferenceFor Classical ParticlesThe Incident WaveParticles in Quantum MechanicsElectron InterferenceThe Double-slit Experiment of Electron (Dr. Akira Sotomura)Electron InterferenceAharonov-Bohm Effect (AB Effect)How Large Can a Particle Be in Order to Interfere?Same Observation for LightArtificial Materials and Mesoscopic SystemsThe Microscopic UniverseThe Mesoscopic SystemMicro-processing for Semiconductor DevicesMagnetic Recording MediaSilicon Monocrystal ⇒ Wafer ⇒ Super LSIUltra-large Scale Integration Semiconductor (ULSI)The Mesoscopic System Conditions Necessary for Mesoscopic Physics and NanoscienceArtificial SuperlatticeSemiconductor Artificial Superlattice ProductionPotential of Artificial SuperlatticesTwo-dimension Electron System at Semiconductor InterfaceExamples of Mesoscopic SamplesClean Room OperationElectron Beam Lithography SystemMetal Vapor DepositionFormation of Micro-patternsVapor Deposition and Lift-offProduction of Quantum Structures by Ultra-micro-processingMicro-structure SampleQuantum ConductionConduction Electrons in MetalsQuantum Mechanics: Particles in a Box Electric ConductionVelocity of ElectronsTwo-dimension Electron System at Semiconductor InterfaceHigh MobilityMesoscopic CircuitQuantum ResistanceConductance QuantizationHall EffectQuantum Hall EffectAharonov-Bohm Effect (AB Effect)Aharonov-Bohm Oscillation (AB Oscillation) Electron Locality as Quantum InterferenceMono-electron Tunnel EffectQuantum Dot (Artificial Atom)Quantum Physics in Mesoscopic SystemSummary