Planeamento

Aulas

T1-Introduction to Nanophysics

1

Course presentation: syllabus, bibliography and evaluation method.
The role of technological development in the evolution towards the nanoscale.
The scope of Nanophysics.

T2 - Revisiting some important concepts in Solid State Physics

2

Nanosystems as an intermediary between classical and quantum systems.
Relevant modifications at the Nanoscale compared with Macroscale systems..Electronic structure of materials. Formation of energy bands in a solid.
The free and nearly-free electron model for describing electrons in a metal.
The density of states in 3d and 2d.
From metals to semiconductors.

T2 - Revisiting some important concepts in Solid State Physics

3

Electronic structure of materials. Formation of energy bands in a solid.
The free and nearly-free electron model for describing electrons in a metal.
The density of states in 3d and 2d.
From metals to semiconductors.

T3 - Diffusive transport

4

Classification of materials into conductors, insulators and semiconductors and relationship with their electronic structure. Hole definition and its characteristics. Pure semiconductors and doped semiconductors. The tight binding approach for electronic states in semiconductors.
Transport by electronic states. Contribution to the transport of a filled band. Electrical transport in macroscopic  materials using semi-classical model. Boltzmann equation. Approximation of relaxation time. Diffusive transport. Transport on a two-dimensional conductor. Relaxation of confinement in a two-dimensional gas and transition to a three-dimensional gas. Einstein relations between mobility and diffusion constant.

T4 - Surface and interface electronic states

5

Surfaces and interfaces. p-n junction as the example of an interface between semiconductors. surface states.
Modification of surface electronic states: band adjustment and "band-bending"."Pinning" of the Fermi energy. Semiconductor metal junctions. Schottky barrier. Rectifier contacts and ohmic contacts.
MOS interface and two-dimensional electron gas formation (2DEG). Production of 2DEG using junctions of two different semiconductors. Triangular potential well

T - Optical properties of nanoparticles

6

Optical properties of materials. Plasma frequency. Dielectric constant as a function of frequency. Dielectric constant of metallic nanoparticles. Clausius-Mossotti relationship. Surface plasmon. Metallic nanoparticles with diameters smaller than 20 nm. Quantum effects: redshift and resonance broadening.
Optical properties of semiconductors. Direct and indirect gap. Optical properties of semiconductor nanoparticles. Exciton binding energy versus confinement. Semiconductor laser.
Applications of nanoparticles.

T3 - Diffusive transport

7

Classification of materials into conductors, insulators and semiconductors and relationship with their electronic structure. Hole definition and its characteristics. Pure semiconductors and doped semiconductors. The tight binding approach for electronic states in semiconductors.
Transport by electronic states. Contribution to the transport of a filled band. Electrical transport in macroscopic  materials using semi-classical model. Boltzmann equation. Approximation of relaxation time. Diffusive transport. Transport on a two-dimensional conductor. Relaxation of confinement in a two-dimensional gas and transition to a three-dimensional gas. Einstein relations between mobility and diffusion constant.

T4 - Surface and interface electronic states

8

Surfaces and interfaces. p-n junction as the example of an interface between semiconductors. surface states.
Modification of surface electronic states: band adjustment and "band-bending"."Pinning" of the Fermi energy. Semiconductor metal junctions. Schottky barrier. Rectifier contacts and ohmic contacts.
MOS interface and two-dimensional electron gas formation (2DEG). Production of 2DEG using junctions of two different semiconductors. Triangular potential well

T5 - 1d conductivity

9

Confinement in a gas d=2 ("Quantum point contact"). Ballistic transport.
Landauer formula for non-reflecting contacts. Contact resistance. Contribution of one or more sub-bands. Coherent transport through a one-dimensional conductor with a scattering center . Associated resistance. Coherent transport through a one-dimensional conductor with two centers of dispersion. Landauer formula extended to non-reflecting contacts and presence of scattering centers.
Important lengths in the mesoscopic system. Conclusions for the behavior of the system based on the relationship between the characteristic lengths.

T6 - Landauer-Buttiker formalism

10

What conductivity is experimentally measured in mesoscopic systems. Influence of contacts.
Landauer-Buttiker formalism.
Application example.

T7 - Coherent Transport

11

Coherent transport through a one-dimensional conductor with two scattering centers. Scattering matrix (S) and transfer matrix (T). Relationship between both matrices. Difference between the electrical resistances obtained with coherent transport and with incoherent transport. Diffusive coherent transport. Weak localization effect.
Electrons with trajectories enclosing magnetic flux. Phase variation. Aharonov-Bohm effect. Explanation of the destruction of the weak localization effect by the magnetic field. Weak localization and Aharonov-Bohm effect h/2e.

T9 - Quantum Hall Effect

12

Multiplicity of Landau levels. Magnetic length. Relationship with magnetic flux. The chemical potential of two-dimensional electron gas with applied magnetic field.
Electrons in a parabolic confinement potential and subject to an intense magnetic field. charge transport along the boundaries. Localization of Landau states by impurities. Synthesis of the main aspects involved in Quantum Hall Effect. Presentations of the fractional quantum Hall effect.

T10 - Coulomb blockade. Single electron transistor.

13

Transference through a barrier. Tunnel effect. A tunnel effect barrier seen as balli sticconductance with small transmission. Limit for barrier resistance to exist tunnel effect. Electrostatic energy and Coulomb blockade effect. Orthodox condition for an electron to be transfer across the barrier. Metallic island between two barriers in a canal - double barrier. Single electron tunneling. Asymmetric double barrier. Single electron transistor (SET). Representation Vgate as function of Vsource-drain- stability diagram (diamond diagram).

T2

14

x

T11 - Nanoparticles and nanostructures

15

"Quantum dots" - Stability diagram showing "magic numbers". Comparison with results in metallic aggregates. Application of the Jellium model for the calculation of electronic states. Behavior of small aggregates as "giant atoms". Nanoparticles: importance of surface contribution, thermodynamic properties. Crystalline metallic nanoparticles in thermodynamic equilibrium: Wulf polyhedron. Nanoparticles with directional bonds. Cage aggregates. The carbon allotropes. Fullerenes. Carbon nanotubes. Single-walled and multi-walled nanotubes. Winding vector and electronic structure. Relationship with physical properties.