固体材料宏观光学性质

1、第四章 固体材料的宏观光学性质OverviewThe study of the optical properties of materials is a huge field and we will only be able to touch on some of the most basic partsSo we will consider the essential properties such as absorption/reflection/transmission and refraction Then we will look at other phenomena like lu

2、minescence and fluorescenceFinally we will mention applications, in particular optical fibres and lasersNature of lightLight is an electromagnetic wave:with a velocity given by c=1/(00) = 3 x 108 m/sIn view of this, it is not surprising that the electric field component of the wave should interact w

3、ith electrons electrostaticallyMany of the electronic properties of materials, information on the bonding, material composition etc. was discovered using spectroscopy, the study of absorbed or emitted radiationevidence for energy levels in atomsevidence for energy bands and band-gapsphotoelectric ef

4、fectGeneral description of absorptionBecause of conservation of energy, we can say that I0 = IT + IA + IRIo is the intensity (W/m2) of incident light and subscripts refer to transmitted, absorbed or reflectedAlternatively T + A + R = 1 where T, A, and R are fractions of the amount of incident lightT

5、 = IT/I0, etc.So materials are broadly classed astransparent:relatively little absorption and reflectiontranslucent:light scattered within the material (see right)opaque:relatively little transmissionIf the material is not perfectly transparent, the intensity decreases exponentially with distanceCon

6、sider a small thickness of material, xThe fall of intensity in x is I so I = -a.x.Iwhere is the absorption coefficient (dimensions are m-1)In the limit of x 0, we getThe solution of which is I=I0exp(x)Taking “ln” of both sides, we have:which is known as Lamberts Law (he also has a unit of light inte

7、nsity named for him)Thus, if we can plot -ln(I) against x, we should find from the gradientDepending on the material and the wavelength, light can be absorbed bynuclei all materialselectrons metals and small band-gap materialsATOMIC ABSORPTIONHow the solid absorbs the radiation depends on what it is

8、!Solids which bond ionically, show high absorption because ions of opposite charge move in opposite directionsin the same electric fieldhence we get effectively twice the interaction between the light and the atomsGenerally, we would expect absorption mainly in the infraredbecause these frequencies

9、match the thermal vibrations of the atomsIf we think of our atom-on-springs model, there is a single resonance peak:But things are more complex when the atoms are connected phononsrecall transverse and longitudinal optical phononsf0fabsorptionElectronic absorptionAbsorption or emission due to excita

10、tion or relaxation of the electrons in the atomsMolecular materialsMaterials such as organic (carbon containing) solids or water consist of molecules which are relatively weakly connected to other moleculesHence, the absorption spectrum is dominated by absorptions due to the molecules themselvese.g.

11、 water molecule:The spectrum of liquid waterSince the bonds have different “spring constants”, the frequencies of the modes are differentwhen the incident illumination is of a wavelength that excites one of these modes, the illumination is preferentially absorbedThis technique allows us to measure c

12、oncentrations of different gas species in, for example, the atmosphereby fitting spectra of known gases to the measured atmospheric spectra, we can figure out the quantities of each of the gasesOptical properties of metalsRecall that the energy diagram of a metal looks like:EF is the energy below wh

13、ich, at 0K, all electron states are full and above which they are emptythis is the Fermi EnergyFor T 0, EF is the energy at which half of the available energy states are occupiedSemiconductors also have a Fermi levelfor an intrinsic material EF is in the middle of the bandgapnearer Ec for n-type; ne

14、arer Ev for p-typefulllevelsemptylevelsT = 0KEFThis structure for metals means that almost any frequency of light can be absorbedSince there is a very high concentration of electrons, practically all the light is absorbed within about 0.1m of the surfaceMetal films thinner than this will transmit li

15、ght e.g. gold coatings on space suit helmetsPenetration depths (I/I0 = 1/e) for some materials are:water: 32 cmglass: 29 cmgraphite: 0.6 mgold: 0.15mSo what happens to the excited atoms in the surface layers of metal atoms?they relax again, emitting a photonThe energy lost by the descending electron

16、 is the same as the one originally incidentSo the metal reflects the light very well about 95% for most metalsmetals are both opaque and reflectivethe remaining energy is usually lost as heatIn terms of electrostatics, the field of the radiation causes the free electrons to move and a moving charge

17、emits electromagnetic radiationhence the wave is re-emitted = reflectedThe metal appears “silvery” since it acts as a perfect mirrorOK then, why are gold and copper not silvery?because the band structure of a real metal is not always as simple as we have assumedthere can be some empty levels below E

18、F and the energy re-emitted from these absorptions is not in the visible spectrumMetals are more transparent to very high energy radiation (x- & - rays) when the inertia of the electrons themselves is the limiting factorReflection spectra for gold and aluminum are:blueredgold reflects lots of red wa

19、velengthsaluminum spectrum is relatively flatElectronic absorption in non-metalsDielectrics and semiconductors behave essentially the same way, the only difference being in the size of the bandgapWe know that photons with energies greater than Eg will be absorbed by giving their energy to electron-h

20、ole pairswhich may or may not re-emit light when they relaxECEVEGholeHence, the absorption coefficients of various semiconductors look like:Semiconductors can appear “metallic” if visible photons are all reflected (like Ge) but those with smaller Eg, such as CdS look colouredyellow for CdS which abs

21、orbs 540nm and aboveThe above picture is good for pure materials but impurities can add extra absorption featuresECEVphononhf1hf2Impurity levels divide up the bandgap to allow transitions with energies less than Eg Recombination can be either radiative (photon) or non-radiative (phonon) depending on

22、 the transition probabilitiesPractical p-n diodes usually contain a small amount of impurity to help recombination because Si has a relatively low recombination “efficiency”for the same reason that Si is inefficient at generating lightRefraction in non-metalsOne of the most important optical propert

23、ies of non-metallic materials is refractionThis refers to the bending of a light beam as it passes from one material into anothere.g. from air to glassWe define the index of refraction to ben = c/vwhere c is the speed of light in a vacuum and v is the speed of light in the material (which is in gene

24、ral wavelength-dependent)A familiar example is the prism where the different amounts of bending separates out the wavelengthsRefraction is also vital for other applications, such as:optical fibres keeps the light insemiconductor laser keeps the light in the amplifying cavity of the laserGiven thatwh

25、ere and 0 (= r0) are the permeability of the material and free space, respectively (a magnetic property)and e and e0 (= ere0) are the permittivity of the material and free space, respectively (an electrostatic property)We find that n = (rer) ( er for many materials)Since light is an electromagnetic

26、wave, the connection with both the dielectric permittivity () and the magnetic permeability () is not surprisingThe index of refraction is therefore a consequence of electrical polarization, especially electronic polarizationHence, the radiation loses energy to the electrons+Since E = hv/, and doesn

27、t change, the velocity must be smaller in the material than in free spacesince we lose E to the atoms, v must also decreaseElectronic polarization tends to be easier for larger atoms so n is higher in those materialse.g. glass: n 1.5lead crystal: n 2.1 (which makes glasses and chandeliers more spark

28、ly!)n can be anisotropic for crystals which have non-cubic latticesReflection in non-metalsReflection occurs at the interface between two materials and is therefore related to index of refractionReflectivity, R = IR/I0, where the Is are intensitiesAssuming the light is normally incident to the inter

29、face:where n1 and n2 are the indices for the two materialsOptical lenses are frequently coated with antireflection layers such as MgF2 which work by reducing the overall reflectivitysome lenses have multiple coatings for different wavelengthsn1n2SpectraSo we have seen that reflection and absorption

30、are dependent on wavelengthand transmission is whats left over!Thus the three components for a green glass are:Callister Fig. 21.8ColoursSmall differences in composition can lead to large differences in appearanceFor example, high-purity single-crystal Al2O3 is colourlesssapphireIf we add only 0.5 -

31、 2.0% of Cr2O3 we find that the material looks redrubyThe Cr substitutes for the Al and introduces impurity levels in the bandgap of the sapphireThese levels give strong absorptions at:400nm (green) and 600nm (blue)leaving only red to be transmittedThe spectra for ruby and sapphire look like:A simil

32、ar technique is used to colour glasses or pottery glaze by adding impurities into the molten state:Cu2+: blue-green, Cr3+: greenCo2+: blue-violet, Mn2+: yellowTranslucencyEven after the light has entered the material, it might yet be reflected out again due to scattering inside the materialEven the

33、transmitted light can lose information by being scattered internallyso a beam of light will spread out or an image will become blurredIn extreme cases, the material could become opaque due to excessive internal scatteringScattering can come from obvious causes:grain boundaries in poly-crystalline ma

34、terialsfine pores in ceramicsdifferent phases of materialsIn highly pure materials, scattering still occurs and an important contribution comes from Rayleigh scatteringThis is due to small, random differences in refractive index from place to placeIn amorphous materials such as glass this is typical

35、ly due to density or compositional differences in the random structureIn crystals, lattice defects, thermal motion of atoms etc. also give rise to Rayleigh scatteringRayleigh scattering also causes the sky to be blue. The reason for this is the wavelength-dependence of Rayleigh scatteringscattering

36、goes as l-4so since lred 2lblue blue light is scattered 16 times more than red lightThis mechanism is of great technological importance because it governs losses in optical fibres for communicationBut before we get onto fibres, we will mention a couple more basic effectsDispersionDispersion is a gen

37、eral name given to things which vary with wavelengthFor example, the wavelength-dependence of the index of refraction is termed the dispersion of the indexAnother important case arises because the speed of the wave depends on its wavelengthIf a pulse of white light is transmitted through a material,

38、 different wavelengths arrive at the other end at different timesthis is also called dispersionLuminescenceLuminescence is the general term which describes the re-emission of previously absorbed radiative energyCommon types are photo- , electro-, and cathodo-luminescence, depending on whether the or

39、iginal incident radiation waslight of a different wavelength e.g. fluorescent lightelectric field e.g. LEDelectrons e.g. electron gun in a cathode ray tube (CRT)There is also chemo-luminescence due to chemical reactions which make the glowing rings seen at fairgrounds!Luminescence is further divided

40、 into phosphorescence and fluorescenceFluorescence and phosphorescence are distinguished by the electron transitions requiring no change or a change of spin, respectivelyhence fluorescence is a faster process because no change of spin is required, around 10-5 10-6sphosphorescence takes about 10-4 10

41、1sThus the energy diagram might be like:E2E1E3phosp.phosp.fluor.incidentflipflipIf the energy levels are actually a range of energies, then:So the light emitted by fluorescence is of longer wavelength than the incident lightsince the energy is smallerand phosphorescent light is typically longer wave

42、length than fluorescent light phonon emission10-12s per hopfluorescence, 10-5sIn fluorescent lights, the plasma generates UV light, and a fluorescent coating on the walls of the tube converts this to visible lightthese lights have a visible flicker because (60Hz)-1 10-5sRather confusingly, materials

43、 that do this are generally called phosphorsTo obtain a white light, a mixture of phosphors must be used, each fluorescing at a different wavelengthTV tubes usually use materials doped with different elements to give the colours:ZnS doped with Cu+ gives greenZnS:Ag gives blueYVO4:Eu gives redOptical

44、 fibresFibre-optic technology has revolutionised telecommunications owing to the speed of data transmission:equivalent to 3 hrs of TV per second24,000 simultaneous phone calls0.1kg of fibre carries same information as 30,000kg of copper cableOwing to attenuation in the cable, transmission is usually

45、 digital and the system requires several sections:encoderconversionto opticalrepeaterdetectiondecoderopticalopticalObviously, the loss in the cable is important because is determines the maximum uninterrupted length of the fibreWe know that losses depend on the wavelength of the light and the purity

46、 of the materialrecall the penetration depth for glass was 30cmIn 1970, 1km of fibre attenuated 850nm light by a factor of 100By 1979, 1km of fibre attenuated 1.2m light by a factor of only 1.2this light is infraredNow, over 10km of optical fibre silica glass, the loss is the same as 25mm of ordinar

47、y window glass!For such high-purity materials, Rayleigh scattering is the dominant loss mechanism:waterThe Rayleigh scattering results from minute local density variations which are present in the liquid glass due to Brownian motion and become frozen into the solidThe really clever part about optica

48、l fibres is that the light is guided around bends in the fibreThis is achieved by total internal reflection at the boundary of the fibreThus, the cross section of the fibre is designed as follows The light is transmitted in the core and total internal reflection is made possible by the difference in

49、 the index of refraction between the cladding and the coreA simple approach is the “step-index” design:The main problem with this design is that different light rays follow slightly different trajectoriesnSo different light rays from an input pulse will take slightly different paths and will therefo

50、re reach the output at different timesHence the input pulse is found to broaden during transmission:This limits the data rate of digital communicationinoutsignalttsignalSuch broadening is largely eliminated by using a “graded-index” design:This is achieved by doping the silica with B2O3 or GeO2 para

51、bolically as shown aboveNow, waves which travel in the outer regions, do so in a lower refractive index materialand their velocity is higher (v = c/n)nTherefore, they travel both further and fasteras a result, they arrive at the output at almost the same time as the waves with shorter trajectoriesAn

52、ything that might cause scattering in the core must be minimisedCu, Fe, V are all reduced to parts per billionH2O and OH concentrations also need to be very lowVariations in the diameter of the fibre also cause scatteringthis variation is now 1m over a length of 1kmTo avoid dispersion of different w

53、avelengths, lasers are used as the light sourcesmany data channels are possible using wavelength division multiplexing (WDM)A convenient fact is that compound semiconductor lasers can emit IR light close to the 1.55m wavelength where the fibre absorbs leastReferring back to the system diagram, it wo

54、uld be advantageous to integrate the encoder and transmitterso the circuits and the light emitter can be integratedThis is why there is so much interest in getting light out of porous silicon or Si compoundswhere thin strands of material exhibit quantum-mechanical effects which adjust the Si band st

55、ructure to facilitate efficient light emissionLasersLASER stands for Light Amplification by the Stimulated Emission of RadiationThe key word here is “stimulated”All of the light emission we have mentioned so far is spontaneousit happened just due to randomly occurring “natural” effectsStimulated emi

56、ssion refers to electron transitions that are “encouraged” by the presence of other photonsEinstein showed that an incident photon with E Eg was equally likely to cause stimulated emission of light as to be absorbedThe emitted light has the same energy and phase as the incident light (= coherent)Under normal circumstances, there are few excited electrons and many in the ground-state, so we get predominantly absorptionIf we could arrange for more excited than non-excited electrons, then we would get mostly stimulated emissionequally likelyasSince we get more photons out than we p