Size Effects

how is the bandgap defined

difference between the HOMO and the LUMO

How much energy does each dimension contribute in a cubic NP of size a

n²h²/(8ma²)

De Broglie wavelength, lambda =

h/p

When does electron confinement occur

When NP is smaller than e wavelength

What is a plasmon and are surface or volume plasmons more important

quantised excitation of delocalised e in the conduction band; surface are more important in NPs for light absorption (they can determine colour)

How can the electron mean free path be defined

distance between two successive scattering events; ballistic transport occurs when NM is smaller than mfp

What is electron storage in NPs

NP below the mfp and with charging energy e²/2C > kT, C is capacitance of particle which decreases with smaller particles; occurs for d<10nm at RT in most materials

How is current density quantised

small finite atom width junctions between nanowires causes transverse confinement of e discretising the e momentum states and therefore the current density

How does the electron wavelength in (simple) metals compare to free electrons

about the same due to screening of ionic lattice

How do unsaturated surface bonds affect NPs

forces can act on dangling bonds producing centripetal force (spherical NPs) or distortion/compression effects causing changes to lattice constant; weak affects on properties

How does NP size affect lattice stability

E difference between stable and meta stable phases can be small (especially between close packed), changes in surface energy can change energetics of structure

Why do NPs have fewer defects

increased surface tension term in GFE provides driving force for defect migration to surface where they annihilate, lack of flaws increases toughness; dislocations and loops don’t fit in small NPs; however NP fracture determined by presence of a flaw rather than flaw density

Why do NPs have more defects and how does that affect them

surfaces are defects as they deviate from bulk structure; high SA can lead to: gas diffusion into surface due to looser packing, atom loss generates vacancies and changes stoichiometry, high reactivity (eg water or gas)