Quantum Theory of Atoms, Molecules, and Solids


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 …,0,…+l• spin quantum number m s: m s = ± 1 / 2electron is spinning up/down

Angular Momentum Conservationin Radiative TransitionsAbsorption (starting at ‘ground state’)5s4s3s2s1s• A photon is a particular kind of particle called a boson5p4p3p2p• It has an angular momentum of l = ±1• Thus to conserve angular momentum in an electronictransition within an atom where a photon is absorbedor emitted, the electron must go between states wherel = l final – l initial = ±1• Let us look at an example for transitions in a He atom:5d4d3d5f4f5gemission (starting from populated excited states)5s4s3s2s1sX5p4p5d4d5f4f5g3p 3d2p‘meta-stable’ = can’t decay(forbidden transition)• Some electron states can be populated by radiativetransitions that cannot be depopulated by the sameradiative transitions metastableLaserslight amplification by stimulated emission of radiation; metastable because l = ±1; collisions opposite l’ s all in-phase,, highly polarized

Laserslight 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 NaClMolecularvan-der-Waals bonds• Attraction between Molecules with permanentDipole-moments.• Usually quite weak, but somewhatstronger for Hydrogen-bond.• Binding energy around 0.03 – 0.3 eV

Metallic 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 effectPotential Energy in MoleculesDistancebetween Atoms• All sorts of binding lead to a potential energy curve, withan “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 reaction

Band 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 symmetryBand 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) ≤0: Conductor; it requiresessentially no energy to startmoving stationary electrons⇒ move easily!!b) >5eV: Insulator; largeenergy barrier⇒ very difficult!!c) ~1eV Semiconductor;(gap is close to k BT)⇒ could be pushed withvoltage or thermal energy!!• Semiconductors:• Germanium, Silicon, GaAs, ...Conduction bandlowest empty (mobile) stateshighest filled e- statesValence bandlowest empty (mobile) states[No states here]highest filled e- stateslowest empty (mobile) states[No states here]highest filled e- states

Semiconductors 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;• (even though 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 too few electrons (a ‘hole’), which also easily moves around• Extra electrons “n-type” or extra “holes” “p-type”n-typep-type“moving hole”Characteristics of pn- junction• doping a semiconductor p-type puts extra filled electronstates in the band gap just above the normally filled maximumenergy states (called the Fermi energy).• n-type semiconductors also have excess ‘hole’states just below the conduction band.• When a voltage is applied across the junction,electrons will fall into neighboring holes, eachgaining the “band gap” 0.6 eV in energy.• The process stops because the surplus chargecreates an opposing electricfield of 0.6 VConduction bandDiode symbolp+ n-p- - -- - - - -++ + + + + + +nConduction bandband-gap ofsemiconductor=voltsValence bandp-typeValence bandΔV = “band gap” = 0.6 Vn-type• current will flow from p+ to n- when voltage bias in that direction.• But current will not flow in the reverse bias direction until muchhigher voltage.

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–––––––––(bipolar junction) Transistors• 2 pn junctions ‘back-to-back’,BE-forward biased CB-reverse biased• The base is so weakly doped and thin, that only ~1% of theelectrons recombine with a hole in the base.Amplifier:I C~100 I Breverse biased+forward biased––––––––––––––––––+ + + + + ++ +++ + + ++ + + ++ + + + ++ + + +––––––––––––––––––•As minority carriers, the other 99% arenow free to pass the reverse biased BC-junctioncreating an amplifier.•In computers and electronic devices, up to 2.3 billion transistorseach 32nm across perform the computations, each acting like tinyon/off switches to store and move bits of data.+npn

Photo-Diodes, Solar Cells- - - -hf- - - -+ -+ + + + + + + +n• When a photon has energyof a least E γ> 0.6 eV, (and visiblelight is from ~2-5ev)it can lift an electron from the valence into theconductionband. (or push a ‘hole’ in theconduction band into the valence band)• Inside the junction – there is a field; “band gap”=0.6 V both electron, hole gainenergy of at least 0.6 eV,+ current flows• Convert photon E γ= hfinto electric P.E. (energy)-hfpp-typen-typeDiode bridgeinput signalAC signalinputoutputforward biasoutputreverse biasforward biasreverse biasinputadded together

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