7Covalent Bonding space-symmetric tend to be closer SYM ASYM spatial spinASYM SYMspatial spinspace-symmetric tend to be closerRef: Harris
8Ionic vs Covalent Bond Properties Ionic CharacteristicsCrystalline solidsHigh melting & boiling pointConduct electricity when meltedMany soluble in water, but not in non-polar liquidsCovalent CharacteristicsGases, liquids, non-crystalline solidsLow melting & boiling pointPoor conductors in all phasesMany soluble in non-polar liquids but not water
9Molecular Excitations Rotational Spectra wmoment of inertiarotational A.M.
18Some Molecular Constants MoleculeEquilibrium DistanceRo (Å)Dissociation NRGDo (eV)Vibrational freqv a (cm-1)Moment of InertiaBb (cm-1)H2+1.062.65229729.8H20.7424.48439560.8O21.215.0815801.45N21.099.7523602.01CO1.139.6021701.93NO1.155.319041.70HCl1.284.43299010.6NaCl2.364.223650.190Notes: a) vibrational frequency in table is given as f / cb) moment of inertia in table is given as hbar2/(2I) / hc
22Four Closely Spaced Atoms conduction bandvalence band
23Two atomsSix atomsSolid of N atomsref: A.Baski, VCU 01SolidState041.ppt
24Sodium Bands vs Separation There’s only one band for sodium.An isolated s-orbital can hold 2 electrons. But since each Na only has one electron, the ‘3s’ band would be half full.Suppose we wanted to sketch the function N(e)Rohlf Fig 14-4 and Slater Phys Rev 45, 794 (1934)
25Copper Bands vs Separation An individual copper atom is 3d10 4s1.At the separation in bulk copper, all the band overlap and there is no band gap.Rohlf Fig 14-6 and Kutter Phys Rev 48, 664 (1935)
26Differences down a column in the Periodic Table: IV-A Elements same valenceconfigSandin
36Semiconductors & Insulators Resistivity r increases with increasing TempTemp t but same # conduction e-’s rSemiconductors & InsulatorsResistivity r decreases with increasing TempTemp t but more conduction e-’s r
37Semiconductors ~1/40 eV gap Types Intrinsic – by thermal excitation or high nrg photonPhotoconductive – excitation by VIS-red or IRExtrinsic / Dopedn-typep-type~1 eV gap~1-4 eV gap~0.01 eV gap with adjustable charge carrier density
405A doping in a 4A lattice Almost free, but not quite Sandin, “Modern Physics”5A in 4A lattice3A in 4A lattice
41Bands in n-doped Semiconductor The extra electron is almost free to roam, but not quite because of its weak attraction to the lattice site.Energy available from thermal excitation is enough to break the electron loose and let it roam.9.44
42Bands in p-doped Semiconductor 1. The extra electron is almost free to roam, but not quite because of its weak attraction to the lattice site.9.45
44Superconductivity First observed Kamerlingh Onnes 1911 Groenigen, Netherlands1908 Liquified 4He1911 reached 0.9 KNobel Prize 1913William Thomson (developed Kelvin scale) thought electron motion would cease at 0K, therefore no conduction. Onnes and others thought resistance would gradually decrease to zero.First observed Kamerlingh Onnes 1911
45Note: The best conductors & magnetic materials tend not to be superconductors (so far) Superconductors.orgOnly in nanotubes
47Superconductor Classifications Type Itend to be pure elements or simple alloysr = 0 at T < TcritInternal B = 0 (Meissner Effect)At jinternal > jcrit, no superconductivityAt Bext > Bcrit, no superconductivityWell explained by BCS theoryType IItend to be ceramic compoundsCan carry higher current densities ~ 1010 A/m2Mechanically harder compoundsHigher Bcrit critical fieldsAbove Bext > Bcrit-1, some superconductivity
49Type I Bardeen, Cooper, Schrieffer 1957, 1972 “Cooper Pairs” e- e- 1. Bardeen. 2 Nobels. Transitor & bcse-e-Symmetry energy ~ eVQ: Stot=0 or 1? L? J?
50Popular Bad Visualizations: correlation lengthsSn nmAlPbNbPairs are related by momentum ±p,NOT position.1. Here are some popular visualizations of Cooper pairs, but the are NOT correct.Best conductors best ‘free-electrons’ no e- – lattice interaction not superconducting
51More realistic 1-D billiard ball picture: Cooper Pairs are ±k setsFurthermore:Q: Are 2 e-’s in correlated in position ? A: NO!Wave-particle dualityFrom a particle viewpt pairs are constantly forming & breakingFrom a wave viewpt, the ‘correlation length’ describes the region of space over which the superconducting effects occur about a distortion.“Pairs should not be thought of as independent particles” -- Ashcroft & Mermin Ch 34
52Experimental Support of BCS Theory Isotope EffectsMeasured Band Gaps corresponding to Tcrit predictionsEnergy Gap decreases as Temp TcritHeat Capacity BehaviorIsotope effects – inertia of lattice ions. Heavier atoms are more difficult to accelerate out of position. Superconductivity difficult to achieve when lattice harder to deform.HC shows strong growth from a zero value. Suggests that there’s some sort of threshold that we’ve gone over, such as a band gap - like in a semiconductor.Band Gaps – If do scatter plot of measured band gap energies vs critical temp, discover there is a correlation. Band gaps small and consistent with BCS estimates of KE. The band gap energy is directly related to the “kinetic energy” at the transition temp.Egap as a function of temp. Note that there is a common scaling law indicating some type of universal behaviour. – as approach Tc, thermal energy makes pairing difficult. Thermal agitation hides the correlation structures in the lattice.
53Semiconductor or Superconductor Normal Conductor In a normal conductor, there is no band gap between the filled and unfilled levels. Normal conductors to not exhibit macroscopic quantum features.In a superconducting material, there is a very tiny band gap ~10-4 eV, which is very small compared to the 1-2 eV occurring in semiconductors. This tiny band gap would only be apparent at very low temperatures.
54Superconductors and Semiconductors are the same animal from a band model viewpoint
55Another fact about Type I: -- Interrelationship of Bcrit and Tcrit
56Type II Tc Yr Composition Mar 2011 (Tl5Pb2)Ba2MgCu10O17+ 20 C 293 K Oct2010(Tl4Pb)Ba2MgCu8O13+3C276KMay2006InSnBa4Tm4Cu6O18+1502004Hg0.8Tl0.2Ba2Ca2Cu3O8.331381987YBa2Cu3O7931986(La1.85Ba.15)CuO4301. Type-IIs have mixed sc/normal phases in the sample.Q: does BCS apply ?
63Magnetic Levitation – Meissner Effect 1. One could envision a surface process as diagrammed to explain the Meissner Effect. However the sketched idea for the induced currents is not quite right. If one stacks two type-II disks, the magnet will be raised higher. There’s some sort of bulk process going on.Kittel states this explusion effectis not clearly directly connectedto the r = 0 effectsQ: Why ?
64Magnetic Levitation – Meissner Effect MLX01 Test Vehicle581 km/h mph,000+ riders2005 tested passing trains at relative 1026 km/h
66Maglev in Germany 32 km track 550,000 km since 1984 Design speed 550 km/hRegularly operated at 420 km/hNOTE(061204): I’m not so sure this track is superconducting. The MagLev planned for the Munich area will be. France is also thinking about a sc maglev.
67Maglev FrogA live frog levitates inside a 32 mm diameter vertical bore of a Bitter solenoid in a magnetic field of about 16 Tesla at the Nijmegen High Field Magnet Laboratory.
68Josephson Junction ~ 2 nm Josephson Junction is created by placing a non-superconductor between two different superconductors. If the gap is thin, then electrons can tunnel through the barrier. If the gap is really thin, on the order of “the Cooper-pair correlation length”, then the lattice distortions responsible for the “Cooper pairs” can be transmitted. This current is observable. This is the “DC Josephson Effect”.If a voltage difference is applied btw the two superconductors, the tunneling is modified, the phase difference across the gap increases, and also the effective current. Since our wavefunctions are periodic, the constantly increasing phase difference will result in an oscillating current. This is the “AC Josephson Effect”.NIST in Gaithersburg has a development program to construction more accurate voltage standards using this effect.
69SQUID superconducting quantum interference device The phase of the wfn in left and right branches is differentbecause of the penetrating flux.
71Finding 'objects of interest' at sea with MAGSAFE Finding 'objects of interest' at sea with MAGSAFEMAGSAFE is a new system for locating and identifying submarines.Operators of MAGSAFE should be able to tell the range, depth and bearing of a target, as well as where it’s heading, how fast it’s going and if it’s diving.Building on our extensive experience using highly sensitive magnetic sensors known as Superconducting QUantum Interference Devices (SQUIDs) for minerals exploration, MAGSAFE harnesses the power of three SQUIDs to measure slight variations in the local magnetic field.MAGSAFE will be able to locate targets without flying close to the surface. Image courtesy Department of Defence.MAGSAFE has higher sensitivity and greater immunity to external noise than conventional Magnetic Anomaly Detector (MAD) systems. This is especially relevant to operation over shallow seawater where the background noise may 100 times greater than the noise floor of a MAD instrument.
731. For studying tiny currents in the working brain.
74SQUID 2 nm 10-14 T SQUID threshold Heart signals 10 -10 T Superconducting Quantum Interference DeviceOne starts with a bias current in the device. If a B-field threads the center, then a vector potential will exist in the ring region, modifying the phases near each junction.Because wavefunctions have to be single valued at any location in the ring, if one were to make a loop around the ring measuring the phase change, one would have to come up with a multiple of 2pi.This constraint and the fact that we’re observing wavefunction phases makes the device incredible sensitive to changes in the central B-field.10-14 T SQUID thresholdHeart signals TBrain signals T
75Fundamentals of superconductors: Basic Introduction to SQUIDs:Detection of SubmarinesFancy cross-referenced site for Josephson Junctions/Josephson:SQUID sensitivity and other ramifications of Josephson’s work:Understanding a SQUID magnetometer:Some exciting applications of SQUIDs:
76Relative strengths of pertinent magnetic fields The 1973 Nobel Prize in physicsCritical overview of SQUIDsResearch ApplicationsTechnical overview of SQUIDs:
80Parts of a LaserPrincipal components: 1. Gain medium 2. Laser pumping energy 3. High reflector 4. Output coupler 5. Laser beam
81Spontaneous Emission Stimulated Emission Population Inversion PUMP
82Energy Level Diagram Three Level System PUMPINGLight AbsorptionElectrical dischargeMolecular collisionsWhen we start the process, all the atoms in our lasing medium will be in the ground state.The pump mechanism will knock a few of them up into the #3 state, which immediately decays into #2.It is extremely difficult to get more atoms in state #2 rather than state #1This requires lots of power input & therefore heat generation is a real problem & the system is very wasteful of energy.Many 3-level laser systems are pulsed.The first laser, ruby laser was pulsed.
83Ruby Laser http://en.wikipedia.org/wiki/Theodore_Maiman A ruby laser is a solid-state laser that uses a synthetic ruby crystal as its gain medium. The first working laser was a ruby laser made by Theodore H. "Ted" Maiman at Hughes Research Laboratories on May 16, 1960.Ruby lasers produce pulses of visible light at a wavelength of 694.3 nm, which is a deep red color. Typical ruby laser pulse lengths are on the order of a millisecond.
84Ruby Laser http://web.phys.ksu.edu/vqm/laserweb/Ch-6/C6s2t1p2.htm This system is a three level laser with lasing transitions between E2 and E1. The excitation of the Chromium ions is done by light pulses from flash lamps (usually Xenon).The Chromium ions absorb light at wavelengths around 545 [nm] ( [nm]). As a result the ions are transferred to the excited energy level E3. From this level the ions are going down to the metastable energy level E2 in a non-radiative transition. The energy released in this non-radiative transition is transferred to the crystal vibrations and changed into heat that must be removed away from the system.The lifetime of the metastable level (E2) is about 5 [msec].Ruby laser has another absorption band which can be used for pumping, in the spectrum range: [nm].It is difficult to achieve continuous operation of a Ruby laser since it is a three level laser. However, in 1962, by using very intensive pump, using arc lamp with high pressure Mercury vapor, a continuous wave Ruby laser was buildRami Arieli: "The Laser Adventure" Section page 2
85Energy Level Diagram Four Level System PUMPINGLight AbsorptionElectrical dischargeMolecular collisionsIt is much easier to maintain a population inversion in a 4-state system.A state is inserted above the ground state.The population inversion is maintained between #3 and #2.This is easy because when state #2 is formed it immediately empties out to #1.
92Laser Diode http://zone.ni.com/devzone/cda/ph/p/id/249 4.7 PRINCIPLE OF THE LASER DIODE18 Consider a degenerately doped direct bandgap semiconductor pn junction whose band diagram is shown in Figure 4.14 (a). By degenerate doping we mean that the Fermi level EFp in the p-side is in the valence band (VB) and that EFn in the n-side is in the conduction band (CB). All energy levels up to the Fermi level can be taken to be occupiedFIGURE 4.14 The energy band diagram of a degenerately doped pn junction with no bias. (b) Band diagram with a sufficiently large forward bias to cause population inversion and hence stimulated emission.by electrons as in Figure 4.14 (a). In the absence of an applied voltage, the Fermi level is continuous across the diode, EFp = EFn. The depletion region or the space charge layer (SCL) in such a pn junction is very narrow. There is a built-in voltage Vo that gives rise to a potential energy barrier eV0 that prevents electrons in the CB of n+-side diffusing into the CB of the p+-side. There is a similar barrier stopping hole diffusion from p+-side to n+-side.Recall that when a voltage is applied to a pn junction device, the change in the Fermi level from end-to-end is the electrical work done by the applied voltage19, that is EF = eV. Suppose that this degenerately doped pn junction is forward biased by a voltage V greater than the bandgap voltage; eV > Eg as shown in Figure 4.14 (b). The separation between EFn and EFp is now the applied potential energy or eV. The applied voltage diminishes the built-in potential barrier to almost zero which means that electrons flow into the SCL and flow over to the p+-side to constitute the diode current. There is a similar reduction in the potential barrier for holes from p+ to n+-side. The final result is that electrons from n+ side and holes from p+ side flow into the SCL, and this SCL region is no longer depleted, as apparent in Figure 4.14 (b). If we draw the energy band diagram with EFn – EFp = eV > Eg this conclusion is apparent. In this region, there are more electrons in the conduction band at energies near Ec than electrons in the valence band near Ev as illustrated by density of states diagram for the junction region in Figure 4.15 (a). In other words, there is a population inversion between energies near Ec and those near Ev around the junction.FIGURE 4.15 (a) The density of states and energy distribution of electrons and holes in the conduction and valence bands respectively at T 0 in the SCL under forward bias such that EFn – EFp > Eg. Holes in the VB are empty states. (b) Gain vs. photon energy.This population inversion region is a layer along the junction and is called the inversion layer or the active region. An incoming photon with an energy of (Ec – Ev) cannot excite an electron from Ev to Ec as there are almost none near Ev. It can, however, stimulate an electron to fall down from Ec to Ev as shown in Figure 4.14 (b). Put differently, the incoming photon stimulates direct recombination. The region where there is population inversion and hence more stimulated emission than absorption, or the active region, has an optical gain because an incoming photon is more likely to cause stimulated emission than being absorbed. The optical gain depends on the photon energy (and hence on the wavelength) as apparent by the energy distributions of electrons and holes in the conduction and valence bands in the active layer in Figure 4.15 (a). At low temperatures (T 0 K), the states between Ec and EFn are filled with electrons and those between EFP and Ev are empty. Photons with energy greater than Eg but less than EFn – Efp cause stimulated emissions whereas those photons with energies greater than EFn – EFp become absorbed. Figure 4.15 (b) shows the expected dependence of optical gain and absorption on the photon energy at low temperatures (T 0 K). As the temperature increases, the Fermi-Dirac function spreads the energy distributions of electrons in the CB to above EFn and holes below EFp in the VB. The result is a reduction in optical gain as indicated in Figure 4.15 (b). The optical gain depends on EFn – EFp which depends on the applied voltage and hence on the diode current.It is apparent that population inversion between energies near Ec and those near Ev is achieved by the injection of carriers across the junction under a sufficiently large forward bias. The pumping mechanism is therefore the forward diode current and the pumping energy is supplied by the external battery. This type of pumping is called injection pumping.In addition to population inversion we also need to have an optical cavity to implement a laser oscillator, that is, to build up the intensity of stimulated emissions byFIGURE 4.16 A schematic illustration of a GaAs homojunction laser diode. The cleaved surfaces act as reflecting mirrors.means of an optical resonator. This would provide a continuous coherent radiation as output from the device. Figure 4.16 shows schematically the structure of a homojunction laser diode. The pn junction uses the same direct bandgap semiconductor material throughout, for example GaAs, and hence has the name homojunction. The ends of the crystal are cleaved to be flat and optically polished to provide reflection and hence form an optical cavity. Photons that are reflected from the cleaved surfaces stimulate more photons of the same frequency and so on. This process builds up the intensity of the radiation in the cavity. The wavelength of the radiation that can build up in the cavity is determined by the length L of the cavity because only multiples of the half-wavelength can exists in such an optical cavity as explained above, i.e.[+] Enlarge Imagewhere m is an integer, n is the refractive index of the semiconductor and is the free space wavelength. Each radiation satisfying the above relationship is essentially a resonant frequency of the cavity, that is, a mode of the cavity. The separation between possible modes of the cavity (or separation between allowed wavelengths) m can be readily found from Eq. (1) as in the case of the He-Ne gas laser previously.
93Green Laser Pointer http://en.wikipedia.org/wiki/Laser Green Laser PointerA frequency-doubled green laser pointer, showing internal construction. Two AAA cells and electronics power the laser module (lower diagram) This contains a powerful 808 nm IR diode laser that optically pumps a Nd:YVO4 crystal inside a laser cavity. That laser produces 1064 nm (infrared) light which is mainly confined inside the resonator. Also inside the laser cavity, however, is a non-linear KTP crystal which causes frequency doubling, resulting in green light at 532 nm. The front mirror is transparent to this visible wavelength which is then expanded and collimated using two lenses (in this particular design).
94CO2 LasersThe carbon dioxide laser (CO2 laser) was one of the earliest gas lasers to be developed (invented by Kumar Patel of Bell Labs in 1964), and is still one of the most useful. Carbon dioxide lasers are the highest-power continuous wave lasers that are currently available. They are also quite efficient: the ratio of output power to pump power can be as large as 20%.The CO2 laser produces a beam of infrared light with the principal wavelength bands centering around 9.4 and 10.6 micrometers.Because of the high power levels available (combined with reasonable cost for the laser), CO2 lasers are frequently used in industrial applications for cutting and welding, while lower power level lasers are used for engraving. They are also very useful in surgical procedures because water (which makes up most biological tissue) absorbs this frequency of light very well. Some examples of medical uses are laser surgery, skin resurfacing ("laser facelifts") (which essentially consist of burning the skin to promote collagen formation), and dermabrasion. Also, it could be used to treat certain skin conditions such as hirsuties papillaris genitalis by removing embarrassing or annoying bumps, podules, etc. Researchers in Israel are experimenting with using CO2 lasers to weld human tissue, as an alternative to traditional sutures.The common plastic poly (methyl methacrylate) (PMMA) absorbs IR light in the 2.8–25 µm wavelength band, so CO2 lasers have been used in recent years for fabricating microfluidic devices from it, with channel widths of a few hundred micrometers.Because the atmosphere is quite transparent to infrared light, CO2 lasers are also used for military rangefinding using LIDAR techniques.
98Free Electron LasersA free-electron laser, or FEL, is a laser that shares the same optical properties as conventional lasers such as emitting a beam consisting of coherent electromagnetic radiation which can reach high power, but which uses some very different operating principles to form the beam. Unlike gas, liquid, or solid-state lasers such as diode lasers, in which electrons are excited in bound atomic or molecular states, FELs use a relativistic electron beam as the lasing medium which moves freely through a magnetic structure, hence the term free electron. The free-electron laser has the widest frequency range of any laser type, and can be widely tunable, currently ranging in wavelength from microwaves, through terahertz radiation and infrared, to the visible spectrum, to ultraviolet, to X-rays.Free-electron lasers were invented by John Madey in 1976 at Stanford University. The work emanates from research done by Hans Motz who proposed the wiggler magnetic configuration which is at the heart of a free electron laser. Madey used a 24 MeV electron beam and 5 m long wiggler to amplify a signal. Soon afterward, other laboratories with accelerators started developing such lasers.
100Chemical oxygen iodine laser, or COIL, is an infrared chemical laser. As the beam is infrared, it cannot be seen with the naked eye. It is capable of output power scaling up to megawatts in continuous mode. Its output wavelength is 1.315 µm, the wavelength of transition of atomic iodine.The laser is fed with gaseous chlorine, molecular iodine, and an aqueous mixture of hydrogen peroxide and potassium hydroxide. The aqueous peroxide solution undergoes chemical reaction with chlorine, producing heat, potassium chloride, and oxygen in excited state, singlet delta oxygen. Spontaneous transition of excited oxygen to the triplet sigma ground state is forbidden giving the excited oxygen a spontaneous lifetime of about 45 minutes. This allows the singlet delta oxygen to transfer its energy to the iodine molecules injected to the gas stream; they are nearly resonant with the singlet oxygen, so the energy transfer during the collision of the particles is rapid. The excited iodine then undergoes stimulated emission and lases at 1.315 µm in the optical resonator region of the laser.