M1 nanosciences

Cnrs/Lcmi

Description

Niveau: Supérieur, Master, Bac+4
M1-nanosciences 1 Nanophysics CHAPITER I. Orders of magnitude in nanophysique CHAPITER II. Conductance of nanowires and circuits CHAPITER III. Nanoelectronics, transistors, mosfets, one-electron devices CHAPITER IV. Nanomagnetism an spintronics CHAPITER V. Quantum computing CHAPITER VI. Molecular motors and wratchets Outline

• zyx


• box size


• physical radius minimize


• quantum computing


• atomic scale


• coulomb potential


• nanophysique chapiter


• kinetic coulomb

Sujets

• Quantum computer
• Electric potential

Informations

• Publié par: larec
• Nombre de lectures: 39
• Langue: Español

Extrait

Nanophysics

Outline

CHAPITER I.Orders of magnitude in nanophysique CHAPITER II.Conductance of nanowires and circuits CHAPITER III. Nanoelectronics, transistors, mosfets, oneelectron devices CHAPITER IV.Nanomagnetism an spintronics CHAPITER V.Quantum computing CHAPITER VI.Molecular motors and wratchets

http://www.ujf-grenoble.fr/PHY/intra/Formations/M1/Physique/UEs/2-5fois3ECTS/PHY425i/Planducours/

M1-nanosciences

1

Chapiter 1: Orders of magnitudes for nanoscale objects

a) Atomic scale (1Å) 1Å=0.1 nm

-9 1 nanometer=1 nm=10 m

Bohr radius of the hydrogen atom

+Ze

-e r

2 |Ψ(r)|

r

2 2 r r p Ze E=H(p,r)= − 2m4πεr 0

kinetic

Coulomb attraction

Quantum uncertainty

ΔpΔr~h

h p ~Δp= Δr

2 2 hZe E= − 2 2m ( Δr ) 4πε 0 Δr M1-nanosciences

2

Atomic Bohr radius, angular momentum

2 2 hZe E= − 2 ( ) r 2mΔr 4πε 0 Δ

Physical radius minimize E

2 2 ∂E2hZe =0= − + 3 2 ∂Δr 2m ( Δr ) 4πε ( Δr ) 0

kinetic 1 α 2 ( Δr ) a 0

1 Coulomb α Δr potential

2 |Ψ(r)|

2 4πεh 0 a Δr=a= =0.5A=0.05nm 0 0 2 mZe r Angular momentum L Ze h Electron velocity L = L mva 0 pa 0 p≈ 2 a v p hZe Z 0 = = = = c mc mca4πεhc137.37 ≈h 0 0 8 C=3 10 m/sec M1-nanosciences 3

Energy-length

ψ

L

x

relation: quantum confinement

(x,y,z) k,k,k x y z

Asink xsinksink z x y z

2 m n p h 2 2 2 k=,k=,k= E= ( k+k+k ) x y z x y z Energy L L L 2m 2 2 h3π Ground state energy (m=n=p=1) E= 0 2 2m L -19 E =1.8 V L=1nm 0 e10 J~1.13

L=100nm E =0.113 meV~1K 0 3 4 ⎛ k L ⎞ 1 3 3 F Metal box (N electrons) Fermi energy E↔N=n max N=π= ⎜ ⎟ 2 k F L F π π 3 ⎝ 2 ⎠ 6 2 h 1/ 3 2 p n ⎛ N ⎞ 1/ 3 E=k=2e F 10max 2 π F F Level spacing: 1D =k F = = ( 6 ) ≈ ⎜ ⎟ 1.610 2m hL ⎝ V ⎠ 2 2 πh Δ =E(n)−E(n−1)=2n In a 1nm box, there is only 4 electrons (spin) 2 max 2mL 2 πhv F = M1-nanosciences L 4

Coulomb interaction in a nano-box

2 electrons in a nanobox

2 e E= =1.4eV c 4πεL 0

Big box: many electrons⇒screening

2 ⎛ ⎞ e L E=exp ⎜ − ⎟ c 4πεLλ 0 ⎝ s ⎠

Decreases exponentially with box size

M1-nanosciences

5

Example: spectroscopy of a quantum box

eV/2

E + n ) i2g

E n ) i+1g

E n ) i g

eU

eV/

A gate voltage allows to shift energy levels uniformly

Color map of tunnelling Current trough the box

Mendeleev table of quantum box as artificial atom

Hund rule holds for large boxes

M1-nanosciences

6

E corr

M1-nanosciences

) E0 ) i

E i

Energy-length

relation:spectral rigidity

v F

impurities

Energy-time uncertainty E h

L

(x=0)

(L)

v F

L τ= v F

(0) expi )

2 h hvh F E== = 2π corr τL mL

7

Sensitivity to boundary condition Diffusive motion « Spectral rigidity » of the electron Random walk L h hD 2 L v l e E= = F τ= D= 2 corr τL D 3

Energy scales

Level spacing

2 2π h Δ = 2 D mS 2 3 8π h Δ = 3 D 3/ 2 ( 2m ) Vε F

Level width

⎡ ⎤ hhD γ = ⎢ , ⎥ 2 τL ⎢ ϕ γ ⎥ ⎣ ⎦

LOW ENERGIES

Diffusive regime

E c

hv F l e

Correlation diffusive/ballistic (Thouless) (spectral rigidity) hD E =, c 2 L hv F E = c L HIGH ENERGIES

Universal regime (indep. of box shape, disorder, etc.)

M1-nanosciences

nonuniversal regime

8

Elastic mean free path

l e

Diffusive regime

l e

Fermi wavelength

F

F

hv F l e

L ϕ

L ϕ

Box size

L ε

Energies/lengths scales

E c

HIGH ENERGY

LONG LENGTH

régime diffusif 2 D ω≈Dk≈ 2 L ω hD 9 ε=hω= 2 L ε

F

LOW ENERGY

Phase coherence Energy length relaxation length Ballistic regime 2 h 2 2 ε≈ ( k−k ) k F 2m k h v 2 F F ε≈h ( k−k ) ≈hvδk= k F F m L ε

M1-nanosciences

Nano-capacitance

d

L

2 εL 0 C= =εL 0 d

Lithography today

-20 1nm⇒C=10 F

2 e E= =2eV Coulomb 2C

L=10nm d=0.1nm

-17 C=10 F

2 e E= =2meV Coulomb 2C Large energies: major effect on nanoscale transistors

M1-nanosciences

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Magnetic moments: Bohr magneton

Magnetic momentμ

a 0

v

Μ=current x surface

e e ea v e he 2 2 0 μ= ⋅π a = ⋅πa= = =L 0 0 2 π a τ 0 2 2 m 2 m v

Bohr magneton

−24−5 μ=9,2741⋅10J/Tesla=6⋅10eV/T=0.67K/T 0

1eV=11400K 4 1Tesla=10 Gauss

M1-nanosciences

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