1Phy107 Fall 20061From Last Time…Today• Conductors and superconductors• Molecules– Symmetric and anti-symmetric wave functions– Lightly higher and lower energy levels– More atoms more energy levels• Conductors, insulators and semiconductorsDue Friday: Essay outlineHW9: Chap 15 Conceptual: # 2, 4, 14, 24 Problems: # 2, 4Phy107 Fall 20062Energy Levels• Basic n levels,• include l and mlZero energyn=1n=2n=3n=4E1= 13.612 eVE2= 13.622 eVE3= 13.632 eVEnergy axisPhy107 Fall 20063Energy Levels in a Metal1s2s3s2p3pNa = [Ne]3s1empty1 electron6 electrons2 electrons2 electronsFullFullFull3p3s2p2s1sPartially FullThis band notcompletelyoccupied• Include molecular symmetric and anti-symmetricwavefuctionsPhy107 Fall 20064n- and p-type semiconductorsElectrons from donorsn-type semiconductorDonors, one extra electron‘Holes’ from acceptorsp-type semiconductorAcceptors, one fewer electronPhy107 Fall 20065Junctions• Real usefulness comes from combining n and p-type semiconductorsn-type p-typeJunction develops a ‘built-in’ electric field at theinterface due to charge rearrangement.Phy107 Fall 20066Light emitting diode• Battery causes electrons and holesto flow toward pn interface• Electrons and holes recombineat interface (electrondrops down to lower level)• Photon carriesaway released energy.• Low energy use - one color!2Phy107 Fall 20067Electrical resistance• Last time we said that a metalcan conduct electricity.• Electrons can flow through thewire when pushed by abattery.• But remember that the wire ismade of atoms.•Electrons as waves driftthrough the atomic lattice.Phy107 Fall 20068Resistance questionSuppose we have a perfect crystal ofmetal in which we produce anelectric current. The electrons inthe metalA.Collide with the atoms, causingelectrical resistanceB.Twist between atoms, causingelectrical resistanceC.Propagate through the crystalwithout any electrical resistanceIf all atoms are perfectly in place, the electronmoves though the without any resistance!Phy107 Fall 20069Life is tough• In the real world, electronsdon’t have it so easySome missing atoms (defects)Vibrating atoms!Electron scatters from theseirregularities, -> resistancePhy107 Fall 200610Temperature-dependent resistanceSuppose we cool down thewire that carries electricalcurrent to light bulb. Thelight willA.Get brighterB.Get dimmerC.Stay samePhy107 Fall 200611Resistance•As elecron wave propagatesthrough lattice, it facesresistance• Resistance: Bumps from vibrating atoms Collisions with impurities Repulsion from other electrons• Electrons ‘scatter’ from theseatomic vibrations and defects.• Vibrations are less at lowtemperature, so resistancedecreases.• More current flows through wire• Life is tough for electrons,especially on hot dayshttp://regentsprep.org/Regents/physics/phys03/bresist/default.htmPhy107 Fall 200612Why does temperature matter?Temperature is related to the energy of amacroscopic object.• The energy usually shows up as energy ofrandom motion.• There really is a coldest temperature,corresponding to zero motional energy!• The Kelvin scale has the same size degreeas the Celsius (˚C) scale. But 0 K means nointernal kinetic energy.• 0 degrees Kelvin (Absolute Zero) is thecoldest temperature possible– This is -459.67 ˚F3Phy107 Fall 200613Temperature scales• Kelvin (K):– K = C + 273.15– K = 5/9 F + 255.37absolute zero0-273.15-459.67liquid helium boils4.2-268.95-452.11liquid nitrogen boils77.36-195.79-300.42water freezes273.15032water boils373.15100212commentsKelvinCelsiusFahrenheitPhy107 Fall 200614What happens at the lowesttemperature?Kelvin (1824-1907): electrons freeze and resistance increases Onnes (1853-1926):Resistance continues drop,finally reaching zero at zerotemperaturePhy107 Fall 200615Heike Kamerlingh Onnes• 1908 - liquefied helium(~4 K = - 452°F )• 1911- investigated lowtemperature resistance ofmercury• Found resistance droppedabruptly to zero at 4.2 K• 1913 - Nobel Prize in physicsSometimes,something else!Phy107 Fall 200616Superconductivity• Superconductors are materialsthat have exactly zeroelectrical resistance.• But this only occurs attemperatures below acritical temperature, Tc• In most cases thistemperature is far belowroom temperature.Hg (mercury)Not superconducting (normal)SuperconductingCriticalTemperaturePhy107 Fall 200617Persistent currents• How zero is zero?• EXACTLY!• Can set up a persistent current ina ring.• The magnitude of the currentmeasured by the magnetic fieldgenerated.• No current decay detected overmany years!PersistentsupercurrentMagneticfieldPhy107 Fall 200618Critical current• If the current is too big,superconductivity isdestroyed.• Maximum current forzero resistance is calledthe critical current.• For larger currents, thevoltage is no longer zero,and power is dissipated.CurrentVoltageCriticalcurrentNot superconducting (normal)SuperconductingCriticalCurrent4Phy107 Fall 200619Superconducting elements• Many elements are in fact superconducting• In fact, most of them are!Phy107 Fall 200620Critical temperaturesIf superconductivity is so common, why don’t wehave superconducting cars, trains, toothbrushes?Many superconducting critical temperatures are low.-443-2649.25Niobium-453-2693.72Tin-447-2667.2Lead-452-2694.15Mercury-457-2711.75Aluminum(˚F)(˚C)Critical T. (K)ElementPhy107 Fall 200621Higher transition temperatures• Much higher critical temperature alloys havebeen discovered•NbTi 10 K•Nb3Sn 19 K• YBa2Cu3O7, 92 K• BiSrCaCuO, 120 KHigh-temperaturesuperconductorsPhy107 Fall 200622Meissner effect• Response to magnetic field• For small magnetic fields asuperconductor willspontaneously expel allmagnetic flux.• Above the criticaltemperature, this effect isnot observed.Phy107 Fall 200623Meissner effect• Apply uniformmagnetic field.• Superconductorresponds withcirculatingcurrent.•Produces ownmagnetic fieldPhy107 Fall 200624Add these fieldstogetherCancellation:field zeroAddition, fieldenhancedApplied fieldField from screeningcurrents5Phy107 Fall 200625Add these fieldstogetherCancellation:field zeroAddition, fieldenhancedApplied fieldField from screeningcurrentsPhy107 Fall 200626Total magnetic field issuperposition of fieldgenerated bysuperconductor andapplied fieldField is zero insidesuperconductor,enhanced outsidePhy107 Fall 200627QuestionA superconductor has a maximum supercurrent it can carrybefore losing superconductivity.A
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