Quantum Physics Lecture 14

Interatomic bonding electron exchange and forces s & p bonds, hybridisation

Bonds & bands Semiconductors, metals, insulators

The laser

Physics of the nucleus

Bonds between atoms (cont.) Bonding

Antibonding

ψ orbital is ‘periodic’ inside atom & decaying outside

At finite separations there is a ‘barrier’ between atoms

but electrons move between atoms by tunnelling….

➞ Exponential variation of energy of interaction with separation – Interatomic forces

Expect relationship between forces and current between atoms…

Scanning Tunneling Microscope (STM)

Sharp point (tip) close (~ 1 nm) to surface; under bias electrons tunnel across the gap (barrier potential width z) Because of exponential dependence on z (factor of ~10 for 1Å change when Uo ~ 4 eV), tunnel current is very sensitive to variations in z as tip is scanned across surface. Keep current constant ⇒ z const. ⇒ tip height = image Also, exponential dependence restricts to narrow region of tunneling, giving “atomic” resolution. ⇒ Imaging atoms…

Ge on Si

Atomic Force Microscope Uses Forces (e.g. covalent)

→Atom manipulation TiO2

Eigler et al

Morita et al

Overlapping orbitals - beyond 1s

Add the wavefunctions, noting signs!

one lobe of p-orbital is +ve the other –ve

p-orbital bonds (cont.)

Hybrid orbitals

Combine p & s states to give sp hybrid

Hybrid orbitals (cont.)

Carbon ground state

↑↓ ↑↓ ↑ ↑ 1s 2s 2p 2p 2p

C*

↑↓ ↑ ↑ ↑ ↑ 1s 2s 2p 2p 2p

Methane CH4

Bonds & Bands

A solid contains many atoms interacting, with different interaction strengths (e.g. due to separation etc.)

As a result, many bonding and anti-bonding type states, very close together. Forms ‘bands’ of energy These are the possible energy states of an electron in a solid

The band energies, and whether they are occupied by electrons is determined by the elements (i.e. Z number)

Metal or insulator or….

Semiconductors

Adding impurity (dopant) atoms with more or less electrons than semiconductor (eg. P or Ga in Si) adds electrons or holes to the bands, forming p-type and n-type.

Important for electronic devices….

The Laser

Stimulated emission produces coherent light (Bosons!) Requires population inversion & Mirror cavity

Now mostly Semiconductor lasers….

The atom nucleus

Binding energy per nucleon vs Z

Energies involved are very large…. consider via uncertainty principle!

Terms in the ‘liquid drop’ model of the nucleus Used to evaluate stability with composition - such as number of neutrons

Stability of the nucleus

Only some nuclei are stable Others decay – ‘radioactivity’

Isotopes

Same Z (number of protons) may have different number of neutrons

– isotopes of an element

Segré plot shows number of neutrons and protons for stable elements and isotopes

Radioactive decay can be spontaneous or induced