Physical Chemistry B

Goals
The course provides a systematic exposition of basic concepts of the solid state of matter and of its properties. The aim is to provide a solid ground for the understanding of the vast and varied phenomenology that accompanies the matter at the solid state, one that can be of help to rationalize the structural, microstructural, thermal, optical and transport properties of materials.

Acquired skills
Mastering electronic band structures and their relation with optical and transport phenomena. Classification of solid-state matter in metals, semiconductors and insulators, and their electric and thermal properties. Comprehension of phase diagrams, phase transition, reactivity and defects thermodynamics in the solid state. Theoretical and practical knowledge of the following experimental techniques: XRPD, SEM/EMPA, TEM/EELS, AFM, EPR, EIS, UV, DSC.


Course content

Simple models of metals. Drude model: DC and AC conductivity, magnetotransport and Hall effect, thermal conductivity, thermopower. Sommerfield model: Fermi sphere, density of states; energy, pressure and entropy of the free-electron quantum gas. Fermi-Dirac statistics: gran-canonical parition function, Fermi function, Sommerfield expansion.
Crystal structure. Lattices, basis vectors and unit cells. Bravais lattices. Reciprocal lattice. Lattice planes, Miller indices. Investigation of crystal structures: Thomson diffusion, X ray diffraction, von Laue vs. Bragg laws, structure factor.
Electrons in periodic potentials. Bloch theorem, Bloch functions, energy bands. Tight-binding method and application to model systems: linear chains, two- and three-dimensional materials. Peirls distortion. Graphene electronic structure: Dirac cones, chiral fermions.
Semiclassical electron dynamics. Wavapackects, uncertainty principle, semiclassical equations of motion, phase-space distribution function. Fundamental properties: inertness of filled bands, electrons and holes, effective mass tensor. Drude-Boltzmann theory of DC and AC charge transport. Optical conductivity. Diffusive vs. balistic motion. Disordered systems.
Semiconductors. Number density of charge carriers in thermal equilibrium, law of mass action, chemical potential. Electron and hole doping. Heterogeneous semiconductors: p-n junction, potential profile, current. Interfaces: metal/semiconductor, semiconductor heterostructures, quantum wells. Delta doping and remote doping. Two-dimensional electron-gases and electrostatic gating. Surfaces and Fermi level pinning.
Phonons. Normal modes, statistical mechanics of harmonic oscillators. Phonon dispersion curves, acoustic and optical phonons. Phonon heat capacitances, Einstein and Debye models. Lattice thermal conductivity, phonon-phonon scattering.
Phase diagrams: one components systems; two components systems with intermediate phases and solid solutions; phase transition by the structural, thermodynamic kinetical point of view.
Defects in solids and reactivity. Point defects in solids; mass and charge diffusion mechanisms. Reactivity at the solid phase.
Experimental Techniques: XRPD, SEM/EMPA, TEM/EELS, AFM, EPR, IS, UV, DSC.


Suggested prerequisites
Attending Chimica Quantistica e Metodi matematici applicati alla chimica.

Reference material
N. W. Ashcroft and D. N. Mermim, Solid State Physics, Saunders College Publishing
T. Ihn, Semiconductor Nanostructures, Oxford University Press,
Anthony R. West, Solid State Chemistry and its applications Wiley India


Prerequisites


Assessment method
Access to the final exam is subjected to the compilation of a short report on the experimental activities performed in the laboratory. The examination is written, 3 hours long, and consists of two open questions on topics discussed in classroom lectures, and two simple exercises aimed at establishing the degree of understanding of the course. The written part is followed by a critical oral discussion of the experimental report.

Language of instruction [required]
Italian

Attendance Policy:
Strongly recommended for the lectures, compulsory for the laboratory course.

Mode of teaching:
The course is organized through a series of lectures on blackboard. The laboratory experiences will be carried out both in the student's labs and in research labs where the instruments are positioned.

Website:
Supporting material will be provided to the students upon request.

Other information:
Teachers are always available for any explanation upon fixing an appointment via email.