ENG2000 Chapter 10 Optical Properties of Materials · 2002-11-11 · ENG2000: R.I. Hornsey Optic: 4...

ENG2000: R.I. Hornsey Optic: 1

ENG2000 Chapter 10Optical Properties of Materials


Overview• The study of the optical properties of materials is

a huge field and we will only be able to touch onsome of the most basic parts

• So we will consider the essential properties suchas absorption/reflection/transmission andrefraction

• Then we will look at other phenomena likeluminescence and fluorescence

• Finally we will mention applications, in particularoptical fibres and lasers


Nature of light• Light is an electromagnetic wave:

§ with a velocity given by c = 1/√(ε0µ0) = 3 x 108 m/s

• In view of this, it is not surprising that the electricfield component of the wave should interact withelectrons electrostatically

http://www.astronomynotes.com/light/emanim.gif


• Many of the electronic properties of materials,information on the bonding, material compositionetc. was discovered using spectroscopy, thestudy of absorbed or emitted radiation§ evidence for energy levels in atoms

§ evidence for energy bands and band-gaps

§ photoelectric effect


General description of absorption• Because of conservation of energy, we can say

that I0 = IT + IA + IR§ Io is the intensity (W/m2) of incident light and subscripts refer

to transmitted, absorbed or reflected

• Alternatively T + A + R = 1 where T, A, and R arefractions of the amount of incident light§ T = IT/I0, etc.

• So materials are broadly classed as§ transparent:relatively little absorption

and reflection

§ translucent:light scattered withinthe material (see right)

§ opaque:relatively little transmission

http://www.tekano.pwp.blueyonder.co.uk/tekano/translucent.jpg


• If the material is not perfectly transparent, theintensity decreases exponentially with distance

• Consider a small thickness of material, x

• The fall of intensity in x is I so I = - . x.I§ where α is the absorption coefficient (dimensions are m-1)

• In the limit of x 0, we get

• The solution of which is I = I0 exp(– x)

• Taking “ln” of both sides, we have:

§ which is known as Lambert’s Law (he also has a unit of lightintensity named for him)

dIdx

= − I

x = − lnII0


• Thus, if we can plot -ln(I) against x, we shouldfind from the gradient

• Depending on the material and the wavelength,light can be absorbed by§ nuclei – all materials

§ electrons – metals and small band-gap materials


ATOMIC ABSORPTION• How the solid absorbs the radiation depends on

what it is!

• Solids which bond ionically, show highabsorption because ions of opposite chargemove in opposite directions§ in the same electric field

§ hence we get effectively twice the interaction between thelight and the atoms

• Generally, we would expect absorption mainly inthe infrared§ because these frequencies match the thermal vibrations of

the atoms


• If we think of our atom-on-springs model, there isa single resonance peak:

• But things are more complex when the atoms areconnected – phonons§ recall transverse and longitudinal optical phonons

f0f

absorption


Electronic absorption• Absorption or emission due to excitation or

relaxation of the electrons in the atoms

http://www.nhn.ou.edu/~kieran/reuhome/vizqm/figs/hydrogen.gif


Molecular materials• Materials such as organic (carbon containing)

solids or water consist of molecules which arerelatively weakly connected to other molecules

• Hence, the absorption spectrum is dominated byabsorptions due to the molecules themselves

• e.g. water molecule:

http://www.sbu.ac.uk/water/images/molecul5.jpg


• The spectrum of liquid water

http://www.sbu.ac.uk/water/images/watopt.jpg


• Since the bonds have different “springconstants”, the frequencies of the modes aredifferent§ when the incident illumination is of a wavelength that excites

one of these modes, the illumination is preferentiallyabsorbed

• This technique allows us to measureconcentrations of different gas species in, forexample, the atmosphere§ by fitting spectra of known gases to the measured

atmospheric spectra, we can figure out the quantities of eachof the gases


Optical properties of metals• Recall that the energy diagram of a metal looks

like:

§ EF is the energy below which, at 0K, all electron states arefull and above which they are empty

§ this is the Fermi Energy

• For T > 0, EF is the energy at which half of theavailable energy states are occupied

• Semiconductors also have a Fermi level§ for an intrinsic material EF is in the middle of the bandgap

§ nearer Ec for n-type; nearer Ev for p-type

fulllevels

emptylevels

T = 0K

EF


• This structure for metals means that almost anyfrequency of light can be absorbed

• Since there is a very high concentration ofelectrons, practically all the light is absorbedwithin about 0.1µm of the surface

• Metal films thinner than this will transmit light§ e.g. gold coatings on space suit helmets

• Penetration depths (I/I0 = 1/e) for some materialsare:§ water: 32 cm

§ glass: 29 cm

§ graphite: 0.6 µm

§ gold: 0.15µm


• So what happens to the excited atoms in thesurface layers of metal atoms?§ they relax again, emitting a photon

• The energy lost by the descending electron is thesame as the one originally incident

• So the metal reflects the light very well – about 95%for most metals§ metals are both opaque and reflective

§ the remaining energy is usually lost as heat

• In terms of electrostatics, the field of the radiationcauses the free electrons to move and a movingcharge emits electromagnetic radiation§ hence the wave is re-emitted = reflected


• The metal appears “silvery” since it acts as aperfect mirror

• OK then, why are gold and copper not silvery?§ because the band structure of a real metal is not always as

simple as we have assumed

§ there can be some empty levels below EF and the energy re-emitted from these absorptions is not in the visible spectrum

• Metals are more transparent to very high energyradiation (x- & - rays) when the inertia of theelectrons themselves is the limiting factor


• Reflection spectra for gold and aluminum are:

blue red

gold reflects lots ofred wavelengths

aluminumspectrum isrelatively flat

http://www.thermo.com/eThermo/CMA/Images/Various/109Image_12275.gif


Electronic absorption in non-metals• Dielectrics and semiconductors behave

essentially the same way, the only differencebeing in the size of the bandgap

• We know that photons with energies greater thanEg will be absorbed by giving their energy toelectron-hole pairs

§ which may or may not re-emit light when they relax

EC

EV

EG

hole


• Hence, the absorption coefficients of varioussemiconductors look like:

0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8Wavelength (µm)

In0.53Ga0.47As

Ge

Si

In0.7Ga0.3As0.64P0.36

InP

GaAs

a-Si:H

123450.9 0.8 0.7

103

104

105

106

107

108

Photon energy (eV)

1.0

(m

-1)

Fig. 9.19: Absorption coefficient ( ) vs. wavelength ( ) forvarious semiconductors (Data selectively collected and combinedfrom various sources.)From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca


• Semiconductors can appear “metallic” if visiblephotons are all reflected (like Ge) but those withsmaller Eg, such as CdS look coloured§ yellow for CdS which absorbs 540nm and above

• The above picture is good for pure materials butimpurities can add extra absorption features

EC

EV

phononhf1

hf2


• Impurity levels divide up the bandgap to allowtransitions with energies less than Eg

• Recombination can be either radiative (photon) ornon-radiative (phonon) depending on thetransition probabilities

• Practical p-n diodes usually contain a smallamount of impurity to help recombinationbecause Si has a relatively low recombination“efficiency”§ for the same reason that Si is inefficient at generating light


Refraction in non-metals• One of the most important optical properties of

non-metallic materials is refraction

• This refers to the bending of a light beam as itpasses from one material into another§ e.g. from air to glass

• We define the index of refraction to be

n = c/v§ where c is the speed of light in a vacuum and v is the speed

of light in the material (which is in general wavelength-dependent)

• A familiar example is the prism where thedifferent amounts of bending separates out thewavelengths


• Refraction is also vital for other applications,such as:§ optical fibres – keeps the light in

§ semiconductor laser – keeps the light in the amplifying cavityof the laser

• Given that

§ where µ and µ0 (= µrµ0) are the permeability of the materialand free space, respectively (a magnetic property)

§ and ε and ε0 (= εrε0) are the permittivity of the material andfree space, respectively (an electrostatic property)

• We find that n = (µr r) ( r for many materials)

v = 1 and c = 1

0 0


• Since light is an electromagnetic wave, theconnection with both the dielectric permittivity ( )and the magnetic permeability (µ) is notsurprising

• The index of refraction is therefore aconsequence of electrical polarization, especiallyelectronic polarization

• Hence, the radiation loses energy to the electrons

+–


• Since E = hv/ , and doesn’t change, the velocitymust be smaller in the material than in free space§ since we lose E to the atoms, v must also decrease

• Electronic polarization tends to be easier forlarger atoms so n is higher in those materials§ e.g. glass: n ~ 1.5

§ lead crystal: n ~ 2.1 (which makes glasses and chandeliersmore sparkly!)

• n can be anisotropic for crystals which have non-cubic lattices


Reflection in non-metals• Reflection occurs at the interface between two

materials and is therefore related to index ofrefraction

• Reflectivity, R = IR/I0, where the I’s are intensities

• Assuming the light is normally incident to theinterface:

§ where n1 and n2 are the indices for the two materials

• Optical lenses are frequently coated withantireflection layers such as MgF2 which work byreducing the overall reflectivity§ some lenses have multiple coatings for different wavelengths

R = n2 − n1

n2 + n1

2

n1 n2


Spectra• So we have seen that reflection and absorption

are dependent on wavelength§ and transmission is what’s left over!

• Thus the three components for a green glass are:

Callister Fig. 21.8


Colours• Small differences in composition can lead to

large differences in appearance

• For example, high-purity single-crystal Al2O3 iscolourless§ sapphire

• If we add only 0.5 - 2.0% of Cr2O3 we find that thematerial looks red§ ruby

• The Cr substitutes for the Al and introducesimpurity levels in the bandgap of the sapphire

• These levels give strong absorptions at:§ 400nm (green) and 600nm (blue)

§ leaving only red to be transmitted


• The spectra for ruby and sapphire look like:

• A similar technique is used to colour glasses orpottery glaze by adding impurities into the moltenstate:§ Cu2+: blue-green, Cr3+: green

§ Co2+: blue-violet, Mn2+: yellowhttp://www.valleydesign.com/images/sapp.jpghttp://home.achilles.net/~jtalbot/glossary/photopumping.gif


Translucency• Even after the light has entered the material, it

might yet be reflected out again due to scatteringinside the material

• Even the transmitted light can lose information bybeing scattered internally§ so a beam of light will spread out or an image will become

blurred

• In extreme cases, the material could becomeopaque due to excessive internal scattering

• Scattering can come from obvious causes:§ grain boundaries in poly-crystalline materials

§ fine pores in ceramics

§ different phases of materials


• In highly pure materials, scattering still occursand an important contribution comes fromRayleigh scattering

• This is due to small, random differences inrefractive index from place to place

• In amorphous materials such as glass this istypically due to density or compositionaldifferences in the random structure

• In crystals, lattice defects, thermal motion ofatoms etc. also give rise to Rayleigh scattering


• Rayleigh scattering also causes the sky to beblue. The reason for this is the wavelength-dependence of Rayleigh scattering§ scattering goes as λ-4

§ so since λred ~ 2λblue blue light is scattered ~16 times morethan red light

• This mechanism is of great technologicalimportance because it governs losses in opticalfibres for communication

• But before we get onto fibres, we will mention acouple more basic effects


Scattered waves

Incident wave Through wave

A dielectric particle smaller than wavelength

Fig. 9.21: Rayleigh scattering involves the polarization of a smalldielectric particle or a region that is much smaller than the lightwavelength. The field forces dipole oscillations in the particle (bypolarizing it) which leads to the emission of EM waves in "many"directions so that a portion of the light energy is directed away from theincident beam.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca


Dispersion• Dispersion is a general name given to things

which vary with wavelength

• For example, the wavelength-dependence of theindex of refraction is termed the dispersion of theindex

• Another important case arises because the speedof the wave depends on its wavelength

• If a pulse of white light is transmitted through amaterial, different wavelengths arrive at the otherend at different times§ this is also called dispersion


Luminescence• Luminescence is the general term which

describes the re-emission of previously absorbedradiative energy

• Common types are photo- , electro-, and cathodo-luminescence, depending on whether the originalincident radiation was§ light of a different wavelength – e.g. fluorescent light

§ electric field – e.g. LED

§ electrons – e.g. electron gun in a cathode ray tube (CRT)

• There is also chemo-luminescence due tochemical reactions which make the glowing ringsseen at fairgrounds!


• Luminescence is further divided intophosphorescence and fluorescence

• Fluorescence and phosphorescence aredistinguished by the electron transitionsrequiring no change or a change of spin,respectively§ hence fluorescence is a faster process because no change

of spin is required, around 10-5 – 10-6s

§ phosphorescence takes about 10-4 – 101s

• Thus the energy diagram might be like:E2

E1

E3

phosp.

phosp.

fluor.

incident

flip

flip


• If the energy levels are actually a range ofenergies, then:

• So the light emitted by fluorescence is of longerwavelength than the incident light§ since the energy is smaller

§ and phosphorescent light is typically longer wavelength thanfluorescent light

phonon emission~10-12s per hop

fluorescence, ~10-5s


• In fluorescent lights, the plasma generates UVlight, and a fluorescent coating on the walls of thetube converts this to visible light§ these lights have a visible flicker because (60Hz)-1 > 10-5s

• Rather confusingly, materials that do this aregenerally called phosphors

• To obtain a white light, a mixture of phosphorsmust be used, each fluorescing at a differentwavelength

• TV tubes usually use materials doped withdifferent elements to give the colours:§ ZnS doped with Cu+ gives green

§ ZnS:Ag gives blue

§ YVO4:Eu gives red


Optical fibres• Fibre-optic technology has revolutionised

telecommunications owing to the speed of datatransmission:§ equivalent to >3 hrs of TV per second

§ 24,000 simultaneous phone calls

§ 0.1kg of fibre carries same information as30,000kg of copper cable

• Owing to attenuation in the cable, transmission isusually digital and the system requires severalsections:

encoder conversionto optical

repeater detection decoder

optical optical

http://www.ngflscotland.gov.uk/connected/connected5/images/fibreoptic.jpg


• Obviously, the loss in the cable is importantbecause is determines the maximumuninterrupted length of the fibre

• We know that losses depend on the wavelengthof the light and the purity of the material§ recall the penetration depth for glass was ~30cm

• In 1970, 1km of fibre attenuated 850nm light by afactor of 100

• By 1979, 1km of fibre attenuated 1.2µm light by afactor of only 1.2§ this light is infrared

• Now, over 10km of optical fibre silica glass, theloss is the same as 25mm of ordinary windowglass!


0.05

0.1

0.5

1.0

5

10

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Latticeabsorption

Rayleighscattering

Wavelength (µm)

OH-absorption peaks

1310 nm

1550 nm

Fig. 9.22: Illustration of a typical attenuation vs. wavelength characteristicsof a silica based optical fiber. There are two communications channels at1310 nm and 1550 nm.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Atte

nuat

ion

dB k

m-1

• For such high-purity materials, Rayleighscattering is the dominant loss mechanism:

water


• The Rayleigh scattering results from minute localdensity variations which are present in the liquidglass due to Brownian motion and become frozeninto the solid

• The really clever part about optical fibres is thatthe light is guided around bends in the fibre

• This is achieved by total internal reflection at theboundary of the fibre


• Thus, the cross section of the fibre is designed asfollows

http://www.datacottage.com/nch/images/fibreconstruct.gif


• The light is transmitted in the core and totalinternal reflection is made possible by thedifference in the index of refraction between thecladding and the core

• A simple approach is the “step-index” design:

• The main problem with this design is thatdifferent light rays follow slightly differenttrajectories

n


• So different light rays from an input pulse willtake slightly different paths and will thereforereach the output at different times

• Hence the input pulse is found to broaden duringtransmission:

• This limits the data rate of digital communicationin out

signal

t t

signal


• Such broadening is largely eliminated by using a“graded-index” design:

• This is achieved by doping the silica with B2O3 orGeO2 parabolically as shown above

• Now, waves which travel in the outer regions, doso in a lower refractive index material§ and their velocity is higher (v = c/n)

n


• Therefore, they travel both further and faster§ as a result, they arrive at the output at almost the same time

as the waves with shorter trajectories

• Anything that might cause scattering in the coremust be minimised§ Cu, Fe, V are all reduced to parts per billion

§ H2O and OH concentrations also need to be very low

• Variations in the diameter of the fibre also causescattering§ this variation is now <1µm over a length of 1km

• To avoid dispersion of different wavelengths,lasers are used as the light sources§ many data channels are possible using wavelength division

multiplexing (WDM)


• A convenient fact is that compoundsemiconductor lasers can emit IR light close tothe 1.55µm wavelength where the fibre absorbsleast

• Referring back to the system diagram, it would beadvantageous to integrate the encoder andtransmitter§ so the circuits and the light emitter can be integrated

• This is why there is so much interest in gettinglight out of porous silicon or Si compounds§ where thin strands of material exhibit quantum-mechanical

effects which adjust the Si band structure to facilitateefficient light emission


http://porous.silicon.online.fr/images/poreux.jpg

http://ghuth.com/Porous%20silicon.jpg


Lasers• LASER stands for Light

Amplification by the StimulatedEmission of Radiation

• The key word here is “stimulated”

• All of the light emission we have mentioned so faris spontaneous§ it happened just due to randomly occurring “natural” effects

• Stimulated emission refers to electron transitionsthat are “encouraged” by the presence of otherphotons

• Einstein showed that an incident photon with E Eg was equally likely to cause stimulatedemission of light as to be absorbed

http://www.007sdomain.com/gf_laser.jpg


• The emitted light has the same energy and phaseas the incident light (= coherent)

• Under normal circumstances, there are fewexcited electrons and many in the ground-state,§ so we get predominantly absorption

• If we could arrange for more excited than non-excited electrons, then we would get mostlystimulated emission

equally likelyas


• Since we get more photons out than we put in,this is optical amplification§ hence lAser

§ this system was first used to amplify microwaves forcommunications (maser)

• Such a condition is called a population inversion

• This stimulated emission is what gives the laserits coherent output§ which is what makes it useful for holography, for example

• Clearly, random spontaneous emission “wastes”electron transitions by giving incoherent output§ so we minimise them by using transitions for which the

spontaneous emissions are of low probability

§ so-called metastable states


• The energy levels of a laser material thereforelook like:

• Ruby is a common laser material, which we sawwas Al2O3 (sapphire) with Cr3+ impurities

http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter4a_files/image022.gif


• So all we need to make a laser is to achieve§ (i) a population inversion

§ (ii) enough photons to stimulate emission

• The first is achieved by filling the metastablestates with electrons generated by light from axenon flash lamp

• The second condition is achieved by confiningthe photons to travel back and forth along the rodof ruby using mirrored ends§ next slide

• The ruby laser has an output at 694.3 nm


http

://w

ww

.rep

airf

aq.o

rg/s

am/la

sero

p.gi

f


• In order to keep the coherent emission, we mustensure that the light which completes the roundtrip between the mirrors returns in phase withitself

• Hence the distance between the mirrors shouldobey 2L = N§ where N is an integer, λ is the laser wavelength and L is the

cavity length

• Semiconductor lasers work in just the same wayexcept that they achieve the population inversionelectrically§ by using a carefully designed band structure


• Some laser characteristics are given in thefollowing table:

Callister


Summary• We have looked at how the electronic structure of

atoms and their bonding leads to varying opticalbehaviours in materials

• In particular, properties such as absorption andemission are closely related to the electrons

• Applications of this knowledge include§ anti-reflective coatings for lenses

§ fibre-optic communications

§ lasers


Closing remarks• this first half of ENG2000 is an introduction to a

subject area that is very subtle, and the coursecovers a huge range of subjects

• As you gain more experience, the pieces of thejigsaw will fit better and better

• So, if all the connections etc are not crystal clearright now, have patience!

• For me, the success of the course is how oftenyou say “oh yes, we saw that in ENG2000” !


THE END

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ENG2000 Chapter 10 Optical Properties of Materials · 2002-11-11 · ENG2000: R.I. Hornsey Optic: 4...

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