Magic film thicknesses Magic terrace widths Magic ...rocca/Didattica/Fisica Superfici/8 Quantum size...

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Quantum size effects Magic film thicknesses Magic terrace widths Magic terrace widths Magic adatom distances

Transcript of Magic film thicknesses Magic terrace widths Magic ...rocca/Didattica/Fisica Superfici/8 Quantum size...

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Quantum size effects

Magic film thicknesses

Magic terrace widthsMagic terrace widths

Magic adatom distances

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Let’s consider a film of uniform thickness D and

otherwise infinitely extended along x and y.

The electronic states are confined along z:

With k⊥ wavevector along z and ϕ phase shift

upon reflection at the film surface

The number of states and its density read for a square quantum well :

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The Shockley surface state is absent for Ag/Si because of the

strain in the Ag film which pushes it above the Fermi level

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The dependence of N(E) and of D(EF) on film thickness cause the

oscillation of the total energy of a thin film.

Since the electrons which are squeezed out of the quantum well end up

in bulk states of the substrate at the Fermi level, the appropriate free

energy is the one of an open system (Gibbs free energy)

which integrating by parts becomes:

The oscillating part of G reads then:

In 3Dim the calculation is similar except that we have to integrate over k||

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The result is similar in 3Dim except that the oscillations are less pronounced.

The energy oscillation is, however still large enough to make films of given

thickness stable or unstable: e.g. Ag(100) on Fe(100) and Pb on Cu(111)

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Ag/Fe

Magic film thickness

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Pb/Cu(111)

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Quantum confinement of electronic states by Defects:

Fe quantum corral on Cu(111). The Surface Shockley state

of Cu is confined within the corral

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The same effect causes the confinement on nanosized terraces.

The energy excess causes an additional step – step interaction

ϑππ

ϑβ

γγ tan3

4

2

1tan/ 2

0||h

EkEk

hLLG FF

FFp +−=+== ⊥projected surface tension

Magic terrace widths

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Quantum confinement causes the repulsion between adatoms

δF phase factor

D distance between the adatoms

Magic adatom distances

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Magic adatom distances

The interaction is oscillatory, attractive at d=π/kF

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Quantum size effects on phonons: Na films on Cu(100)

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Inelastic He atoms scattering data:

The vibration corresponds to

the vertical motion of the film

layers

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Fuchs – Kliever mode: counterphase vibration of odd and even layers of the film.

Surface mode derived from the tranverse optical bulk mode.

Strongly dipole active due to the ionic character of the MgO bond

TheoryExp

Wallis mode

FK mode

MgO island

border mode