NanophysicsNanophysics

Michael Hietschold

Solid Surfaces Analysis Group &

Electron Microscopy Laboratory

Institute of Physics

Portland State University, May 2005

Content of the Whole Course

1st Lecture

• 1. Introduction

• 2. The Nanoscale in 2,1,0, and 3 Dimensions

• 3a. Surfaces and Interfaces – Geometrical Structure

Intermediate Lecture – SPM Nanoanalysis

I. Nature of Resolution Limits – Near-Field Principle

II. Scanning Tunneling Microscopy / Spectroscopy / Manipulation

III. Scanning Force Microscopies

IV. Other Near-Field Microscopies

2nd Lecture

• 3b. Surfaces and Interfaces – Electronic Structure

• 4. Semiconductor Heterostructures

3rd Lecture

•5. 2-Dimensional Electron Gas

•6. Quantum Interference, Molecular Devices, and Self-Assembling

•7. Outlook

1.IntroductionHistory:

Richard Feynman 29th December 1959 (APS Meeting at Caltech):

„There is plenty of room at the bottom“

Fiction : Molecular electronics (F.L.Carter 1982)

Reality: Daily-life nanotechnology (e.g. ultrathin films,ultra-precision manufacturing, self-organizedand -assembled structures, ...)

Breakthrough: Scanning probe techniques

Nanotechnology needs Nanoscience !!!

Dimensional Considerations

1 nm = 10-9 m = 0.001 µm

Fe (bcc): d = 0.25 nm

A few nearest-neighbor distances in solids

1/1000 extension of a malaria bacterium

1 nm

A / V = 6a2 / a3 = 6 / a = 6 V-1/3

V = a3 (2a)3 = 8 a3 (5a)3 = 125 a3 (10a)3 = 1000 a3

Percentage of „surface atoms“:

100% 100% 78,4% 48,8%

Macroscopic: V = (108a)3 = 1024 a3 A = 6 (108a)2 = 6 1016 a2

Percentage of surface atoms: 6 10-8 % !!! (negligible)

Role of surface effects increases with decreasing dimensions

Behavior of extensive physical quantities

Classical macroscopic physics (thermodynamics):

E = ε V = e N

Geometry-dependent mesoscopic quantities:

Sphere:

E = ε V + εSurface(R) A = e N + eSurface(R) N2/3

 Cube:

E = ε V + εSurface A + εEdge L + εCorner 8

≈ e N + eSurface N2/3 + eedge N

1/3 + eCorner N0

 

εSurface = εSurface (∞)

Application of Basic Physical Theories –

Classical vs. Quantum Physics:

 mesoscopic phenomena (quasiclassical regime) 

Classical MechanicsElectrodynamicsThermodynamics

Quantum MechnicsQuantum Electrodynamics

Quantum Statistics

Bottom-up and top-down

approaches

• Top-down:

classical approach of miniaturization (scaling down from the macroscopic world)

• Bottom-up:

„chemical/syntheti-cal approach“ (scaling-up from the atomic entities)

2. The Nanoscale 1, 2, 3 Dimensions

Number of Nano-Dimensions:

1 – Nanofilms

2 – Nanowires

3 - Nanodots

One can start by creating Nanofilms on a substrate and proceed to Nanowires and Nanodots by lateral lithography

Other Nanoobjects

Nanocomposites

Nanoporous Systems

High-velocity deformed nanostrucutred Nihttp://www.nanodynamics.com/ndMaterials.asp

Nanoporous luminescent Sihttp://www.chem.ucsb.edu/~buratto_group/PorousSilicon_1.htm

Supramolecular Architectures

J.-M.Lehnhttp://www.iupac.org/publications/pac/1994/pdf/6610x1961.pdf

C.J.Kuehlhttp://www.iupac.org/news/prize/2002/Kuehl-essay.pdf

3-dimensional functional structures according to the molecular geometri-cal and electronic structures

3. Surfaces and Interfaces 3.1. Macroscopic Description

Surface Energy:

Classical cleavage

Relaxation

„frozen“ surface relaxestowards equilibrium

E = ε0 V < 2 [ ε0 (½ V) + εSurface A ] 

εSurface > 0

Wulff‘s Construction

Surface tension γ:

γ = ∂ F / ∂ A  ∫ γ(n) dA Min.(whole surface)

γ-plot: inner enveloppe of γ(n) determines crystalshape in equilibrium

Phase Boundaries

Interfacial tensions

Young‘s equation: γS = γS/F + γF cos Ф

determines modes of thin film growth: Frank - van der Merwe (complete wetting) Vollmer-Weber (islands)

Frank-van der Merwe Stranski-Krastanov Vollmer-Weber

Ф = 0; γS > γS/F + γF Ф > 0; γS < γS/F + γF

Atomic interactions:

Sub-Ads > Ads-Ads Ads-Ads > Sub-Ads

only valid in equilibrium supersaturation changes conditions

3.2. Structure and Crystallography

of Surfaces

TLK model

(terraces, ledges,kinks)

Burton, Frank,Cabrera 1935

Fundamental Surface Lattices

5 Bravais lattices in 2 dimensions belonging to 10 point groups

in 3 dimensions: 14 Bravais lattices, 32 point groups

Miller Indices

Sections cutted from the axis

Take inverse of them

Multipy to get the smallest Integers

Axes parallel to surface – index 0

(1-10) (211)

x

y

z

• Surface Relaxation

varying distances between lattice planes

(metals)

• Surface Recon-struction

Change of (lateral) atomic arrangement on the surface

(semiconductors)

z

Adsorbate Structuresz

Description of superstructures:

R = m a1 + n a2

 Adsorbate / Rec. Surface Lattice: b1 = m11 a1 + m12 a2

b = M ab2 = m21 a1 + m22 a2

 Area of new unit cell:  |b1 x b2| = det M |a1 x a2|

 integer simple

det M rational coincidence superlatticeirrational incommensurate

Exemples:

Real space diffraction image

Structure of interfaces

crystallinity and sharpnesscharacterize solid-solid interfaces

z