Quantum Theory of Atoms, Molecules, and Solids

L20—Ch29Spring 2008PHY 2054C – College Physics BElectricity, Magnetism, Light, Optics and Modern PhysicsWÜA Wtä|w `A _|ÇwToday’s Lecture: purpose & goalsQuantum Theory of Atoms,Molecules, and Solids1) Atomic Orbitals2) Heisenberg UncertaintyPrinciple3) Lasers4) Molecular bonds5) Semiconductors: Diodesand TransistorsReview:Quantum numbers• Principal quantum number n:describes the electron’s radial behaviour.• Angular momentum number l:describes the electron’s angular position• magnetic quantum number m l :describes the electron’s orientationn =1,2,3…∞l =0,1,2,3…(n-1)m l = -l …+l• spin quantum number m s: m s = ± 1 / 2electron is spinning up/down

Laserslight amplification by stimulated emission of radiation; metastable because l = ±1; collisions opposite l’ s all in-phase,, highly polarizedLaserslight amplification by stimulated emission of radiatione.g. HeNe laser (red light)• we all have a holograph in our pocket (thetiny iridescent images on right of VISAand Mastercard credit cards)• very complex interference pattern created byinterference of laser light off the 3-dimensional object.

Covalent Molecular BondsS=0S=1++- + +-+ +-• Covalent bonds form by sharing of electronsbetween atoms. Spin becomes very important;• Each electron must have different quantumnumbers, which favours ↑↓ over ↑↑.• Allows identical spacial distribution, true “sharing”of electrons• Binding comes from +- electric attraction.• Binding Energy large! e.g. 7.4 eV (Diamond)Ionic Molecular Bonds• Ionic Bonds are covalent bonds, where electrons‘prefer’ one of the atoms.• Na, 3 valence e - , wants to be Ne with 2 e -• Cl, 7 valence e - ,wants to be Ar with 8 e - ,• Cl can “borrow” an electronfrom Na and both becomequasi-noble gases• Binding comes from electric attraction between the Na +and Cl -• Very Strong binding!! Energy 7.8 eV NaCl

Molecularvan-der-Waals bonds• Attraction between Molecules with permanentDipole-moments.• Usually quite weak, but somewhatstronger for Hydrogen-bond.• Binding energy around 0.03 – 0.3 eVMetallic Bond• Metals have free moving electrons, which areshared by all the atoms.• Electrons between positiveIons lead to electricattraction.• Binding Energy:1 to 3 eV• Compare Binding Energy to “Work Function”in photo-electric effect

Potential Energy in MoleculesDistancebetween Atoms• All sorts of binding lead to a potential energy curve, with an“optimum” distance between atoms at the lowestpotenial energy• Most atoms need to overcome a P.E. barrier to form aMolecule –this is the activation energy for reactionBand Theory of Solids• Every state in a Single Atom leads to two states ina Molecule, one S=0, one S=1.• Many Atoms Many states.• Solid State crystal energy bands• “Energy gap” will be found between bands of differentatomic symmetry

Band Gap and Conductivity• Valence Band: band created from valence (bound) electrons• Conduction Band: electrons in conduction band are not tiedto individual atoms, but are free to move around.• Band gap:a) 5eV: Insulator⇒ very difficult!!c) ~1eV Semiconductor⇒ could be pushedwith voltage or kT!!• Semiconductors:• Germanium, Silicon, GaAs, ...Conduction bandlowest empty (mobile) stateshighest filled e- statesValence bandlowest empty (mobile) stateshighest filled e- stateslowest empty (mobile) stateshighest filled e- statesSemiconductors and Doping• You can “dope” semiconductors (i.e. add extra chargecarriers) by adding a small concentration of impurities tobecome conductors of either positive or negative charges;• (No net charge is added;• e.g. Arsenic has extra e - ,extrap + , but the electron easily moves around,‘acts like’ a silicon atom with one extra electron• e.g. Gallium has one fewer e - ,one fewerp + , ‘acts like’ a silicon atom withone to few electrons (a ‘hole’), which also easily moves around• Extra electrons “n-type” or extra “holes” “p-type”n-typep-type“moving hole”

Semiconductor Diodes• The simplest application of dopedsemiconductors is the pn-junctiondiode.• Contact between regions of p-dopedand n-doped Silicon.• a) apply voltage p+ n-: + holes movetoward n-zone - electrons toward p-zone→ brought closer together and thusrecombine → current flow+ + + ++ + + +––––––––––––––––––• b) apply voltage opposite direction:holes and electrons are pushed fartherapart → cannot recombine → nocurrent flow+ region + + of ++ ––––– + + +no charge–––– carriers–––––Characteristics of pn- junction• At the junction, the electrons will fallinto the neighboring holes, each gainingthe “band gap” 0.6 eV in energy.• The process stops because the surpluscharge creates an opposing electricfield of 0.6 Vp- - -- - - - -++ + + + + + +np+ n-Diode symbolPE (e - )band-gap ofsemiconductor=p-type• Notice that current will ΔV = “band gap”flow from from p+ to n-=0.6 V n-typewhen voltage bias is in that direction.• But current will not flow in the reverse bias direction.

Photo-Diode, Solar Cell• When a photon has energyE γ> 0.6 eV, (and visible light isfrom ~2-5ev)it can lift an electron from thevalence into the conductionband.• Inside junction-field;electron, hole gainenergy of at least 0.6 eV, current flows• Convert photon E γinto electric U (energy)p-typep- - - - - - - -+ -+ + + + + + + +n“band gap”=0.6 VPE (e - )+-n-typeDiode bridgeinput signalAC signalinputoutputforward biasoutputreverse biasforward biasreverse biasinputadded together

(bipolar junction) Transistors• 2 pn junctions ‘back-to-back’,BE-forward biasedCB-reverse biasedAmplifier:I C~100 I Breversebiasedforwardbiased++npn-• The base is so weakly doped and thin, that only ~1%of the electrons recombine with a hole in the base.• As minority carriers, the other 99% are now free topass the reverse biased BC-junction creating anamplifier.