Optical properties of solids: an introductory textbook

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Electromagnetic Waves in Medium J isthe current density. How should the cycled-averaged intensity of the Poynting vectorof an electromagnetic wave in a medium be? Electromagnetic Potential This transformation of potentials iscalled gauge transformation. This invariance of fields is called gaugei nvaFrrioamnceE. The vector potential previously explained in Section 8. We impose the periodicboundary conditions in a cube of volume L3 as follows: 2p n j a. Problems 93 c. They alsocorrespond to the classical field amplitudes. Also show that a linearly polarized light wave is the superposition of two circularly polarized light waves.

Describe how a half wave plate operates. Explain the electromagnetic potential and gauge transforma- tion, including Lorentz and Coulomb gauges. This relation indicates that the strengths of electric and magnetic fields are not zero even if there is no photon, but they fluctuate around the value zero. This fluctuation is called the zero-pointvibration. Many useful theories of optical properties of matter, such as theKramers—Kronig relation, can be proved in the classical framework. The interactionof light with materials is reflected by a dielectric function. Scatteringand absorption of light occur due to the dielectric response from thematerial, as shown in Fig.

Hence, we describe the effect of free electrons in terms of thedielectric function. Suppose that the effect of the magnetic field oflight becomes small and that we have no true charge. In addition, when w reaches zero, we adopt only thereal part of e. Lower currentdensityFigure 9. The light polarized perpendicular to the incident plane is called s-polarization, whereas the light polarized parallel to the incident plane is called p-polarization. The incident plane is the plane that contains the incident and reflected lights.

Figure 9. For a normal incidence of light as shown in Fig. The square root terms of Eqs. Kramers—Kronig Relations In Fig.

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When this complex function is an optical response function,the relations are called Kramers—Kronig K—K relations. Multiplying theexpressions in Eqs. The K—K relation can be applied to the complex refractiveindex n w. Finally, the electrical conductivity can be analyzed. Verify that for a sufficiently large electrical conductivity s, the skin depth is. Suppose that light is incident on a prism of refractive index n and of isosceles triangular shape with an apex angle b.

When the angle of deviation d is at the minimum d0, the optical path is symmetric as shown in the figure below. Prove that the power of an electromagnetic wave is absorbed when the phase of the vibration of the induced polarization is delayed compared to that of the electric field during its travel in a medium.

This phenomenon is called dielectric loss. Let f be the phase shift. Calculate the loss of the cycle-averaged power of the electromagnetic wave per unit time and unit volume.

Problems 7. Apply K—K relations in a complex dielectric function. First, we will learn the Lorentz model of insulators i. We will then learn light emissionfrom an electric dipole. When we assume a solution to Eq. The fi is the oscillatorstrength. Thus, the dielectric function of this group of oscillatorsfrom Eq. Equation In the remaining region, the material istransparent T.

Then a totalreflection is observed. A and T denote absorption and transparent, respectively. This leads to a plasma-like behavior. Below this energy region, real metals behave like an ideal metaland their optical reflectivity tends to be close to unity. By contrast,beyond this energy, free carriers in the metals cannot follow avariation of the electric field and then the electromagnetic wavetends to penetrate and propagate freely into the metals.

This corresponds to a collective excitation calledplasmon Fig. Furthermore, at sufficiently high frequencies, the Drude modelcan also be applied to all materials. When w become infinite, ebecomes e0 and the refractive index becomes unity. This is why wedo not have good mirrors or lenses in X-ray or Gamma-ray regions.

Figure T denotes transparent. Supposewe have a void sphere instead of an atom and a macroscopic field Eis applied to the whole medium, as shown in Fig. These charges will enhance the internal electric fieldat the center of the sphere, in addition to the average macroscopicfield.

This model of thelocal electric field by Lorentz can be applied to the case of the local. Theory of Local Field electrons of insulators. It is noted that in the case of the carrierstraveling freely in the whole crystal, just as in the case treated bythe Drude model, the average macroscopic field directly acts onthe electrons. Fields radiated from these mutipoles arecalled the electric dipole field, the magnetic dipole field, and theelectric quadrupole field, respectively.

The magnetic dipole fieldand the electric quadrupole field are weaker than the electric dipolefield by a factor of ak 2, where a is the size of an atom.

Optical Properties, Lecture 1

The suffix Trepresents the transverse component with respect to the direction r. That is, when theelectromagnetic field forces a bound electron to oscillate and thuscreates an oscillating electric dipole with the same frequency asthat of the incident field, then this dipole radiates a light field. Thisphenomenon is called Rayleigh scattering.

Explain the dispersion relation in a transparent region. Explain the relation between the momentum scattering time t and the damping constant G0. Prove that the Lorentz field is. Prove the Clausius—Mossotti relation. In the previous chapter, we learned anumber of theories within the classical framework. Now we will learnhow they are treated in the quantum theory and see the distinctionbetween quantum mechanical treatment and the classical one.

Quantum Theory of Matter From Eq. This equationis also called the eigenvalue equation in which W is the eigenvalue ofthe system constant and y is the eigenfunction wavefunction. We next calculate theintensity of the second term of Eq. In Coulomb gauge, the perturbation Hamiltonian is. In addition, if we expand the exponent part ofEq. As a generalized form of Eq. Fully Quantum Mechanical Treatment in which I and M are initial and intermediate states, respectively. Theprobability of induced photon emission of light is equal to that ofinduced photon absorption if the initial state and the final state haveno degeneracy.

Spontaneous emission can be explained only by atheory, including quantization of the radiation field. It is an inducedemission of light triggered by a zero-point vibration of the radiationfield. The damping constant of an energy levelis proportional to the speed of its damping by definition. If an atomicelectron system interacts with the radiation field, a level shift andbroadening occur.

Due to this effect, the energy of the 2s state of ahydrogen atom is higher than that of the sp state by Prove that the transition probability is.

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Calculate the possible momentum matrix element of a particle. Prove that the probabilities of the emission and the absorption of electromagnetic waves by the two-level electronic system are the same. Chapter 12Electron—Nuclei Interaction Especially, wewill study the optical spectra from localized electronic states and theelements determining the spectral shapes. Hence, frequencies of their motions are quite different. The ratio of the frequencies of the motion of electrons to those ofmolecular vibration and molecular rotation is In sucha case, we can consider their motions separately.

For instance,suppose a lot of bees are flying around a lion, as shown in Fig. The motions of the bees are so quick that the bees feel that the lionis not moving. In this way, we can separately deal with the motions of the bees and the lion. This does not mean that the motion of the bees has no effect on the motion of the lion. The average density distribution of the bees determined by their motions indeed influences the emotion and thus the motion of the lion. For example, the lion may be nervous enough to start moving. This effect of average distribution of light particles on heavier particles is seen in the electron—lattice e-L interaction in molecules and solid-state materials.

Lattice Vibrations small. In Fig. Let us also suppose that these atoms move only on the x-axisand that the equilibrium distance between the two atoms is a. Also called an internal coordinate,q describes the internal motion of the molecule. When q describesa harmonic oscillator after the transformation of the coordinationsystem, as in the above case, q is also called a normal coordinate. Anormal coordinate is the basis of the eigenenergy of the equationof the vibrational motion. The eigenfrequency wv and the quantummechanical eigenenergy Wn of the harmonic oscillation described byEq.

In crystals, we treat lattice vibration inthe same way as we treat the vibration of molecules, except that alot of vibrating atoms make the mode density high and the vibrationtravels as a wave. When a three-dimensional unit cell of a crystalcontains more than two atoms, there exist longitudinal L andtransverse T modes as well as optical O and acoustic A modes.

As seen in Fig. Absorption Spectrum For this reason, we insert the term —cQ1 in Eq. To discuss the optical transition under theBorn—Oppenheimer approximation mentioned in the previoussection, we first consider a molecular system embedded in a solid-state matrix as a typical example Fig. On one hand, in the case of high temperature, the electronictransition occurs vertically in the potential energy diagramindependently of the temperature according to the Franck—Condonprinciple, as seen in Fig.

Subscripts g and e denote the ground and the excited electronic states, respectively. The peak energy W0 is equal to the averagevalue of Ue-Ug, and the energy width comes from the fluctuation ofUe-Ug. On the other hand, in the case of an intermediate temperature,vibrational structures within the electronic transition appear inthe absorption spectrum, and the optical transition will then bein a quantized potential system, as shown in Fig. The normalcoordinate in the horizontal axis is generalized into a configurationcoordinate representing atomic distances, bond angles, and generaldisplacements of nuclei.

This fact shows thevalidity of the Condon approximation. It is noted that in the case of the second- and higher-orderperturbation by the interaction of electrons with nuclei, we canassume that Ug is not necessarily equal to Ue. Origin of Spectral Profile Equation TheUrbach tails are associated with the absorption bands of manylocalized electronic centers in solids and liquids such as ioniccrystals, organic crystals, and semiconductor crystals.

If the phase factor f jumps atrandom at the rate g, the energy spectrum of the level is a Lorentzianwith a full width at half maximum FWHM of 2g. When the gas molecules collide and electronic transition occursor the molecules decompose or dissociate, there is a broadening of. When there is no electronic transition or no molecular decomposition or dissociation, but there is an effect of phase disturbance, the spectral line also broadens.

This effect is enhanced in proportion to the gas pressure. The former effect is called collision broadening, and the latter effect is called pressure broadening. On the other hand, in inhomogeneous broadening, when there is a distribution of crystal fields due to lattice imperfection or impurities, the energy of localized electronic states has a distribution, and consequently energy broadening of the levels occurs. This is called stress broadening.

A molecule approaching and going away from an observer emits luminescence photons at different wavelengths. This leads to a Doppler broadening of the photon emission of gas molecules. If a molecule emits photons at different wavelengths depending on the surrounding fields, the linewidth of the emitted photons becomes sharp when the molecule begins to move. This is because all the moving molecules see the same averaged surrounding field. This effect is called motional narrowing. Explain the definition of electronic, vibration, and rotation energy level. Discuss the Frank—Condon principle.

Explain the concepts of Born—Oppenheimer approximation and Condon approximation. Problems 6. Show that the curvatures of the adiabatic potentials of the electrons of ground state and excited state are not necessarily the same if the interaction between the electrons and the nuclei has terms higher than the square of q. Draw roughly the spectrum of any solid material affected by the vibration of the molecules.

Discuss why lifetime energy is broaden based on the uncertainty principle, and also discuss the phenomenon called motional narrowing in NMR and ESR. Chapter 13Optical Spectra of Materials A solution to Eq. We will now discuss an atom with more than one electron, asseen in Fig. When the electrons form the closed shells of orbitals, only oneconfiguration of electrons is present.

In the case of open shells whereorbitals are partly occupied, several eigenstates are associated withone configuration of electrons. These eigenstates take differenteigenenergies and are specified by their angular momentumquantum numbers, which we will discuss in two cases. First, in the case of a light atom with atomic number Z less than30, the spin—orbit interaction is small and so it is not taken intoconsideration.

Then we specify the electronic states by the totalorbital angular momentum of electrons. As an example, here we study the case of H atom. The 2p orbital with one electron is split into sublevels by spin—orbit coupling, as shown in Fig. Second, in the case of a heavy atom with atomic number Z morethan 30, the LS coupling scheme becomes worse approximation. The splitting by J value is small for small atomic numbers, so theyare called fine structures. This splitting becomes large for largeatomic numbers, and they are no longer fine structures. It is more. Such a way of specification of electronicconfiguration is called JJ coupling.

In the case of electronic spectra of molecules Fig. Subscripts g and u aresymmetric and antisymmetric, respectively. Here are some examples. Methane molecule CH4 has only s bonds,. Thebonding strength of the s electron is strong, whereas that of the pelectron is weak. The overlap of the bonding p electrons is smallerthan that of the bonding s electrons, so the former has smallerbinding energy than the latter. Hence, the p electron system has acontribution in the visible range of the optical spectrum. In other words, the lifetime of an electron atone atom becomes small and the band broadens.

Wecall the band gap Wg as the direct band gap. In the direct transition,the optical transition occurs almost vertically. CB and VB stand for conduction and valence bands, respectively. We call the band gap the indirect band gap. The opticalabsorption is associated with phonon absorption or creation. Theabsorption coefficient will be. At highertemperature, absorption is associated with phonon emission andoptical absorption is observed at the energy greater than Wg — Wp.

In the discussion of optical properties of solids, one of the mostimportant elementary excitations is exciton. This is because it hasa large optical transition probability and dominates the opticalspectra at low temperatures. In this case, interband transition leavesan electron on the conduction band and a hole on the valence band. The electron and the hole bind each other by Coulomb attraction. They form hydrogen-like energy levels. The exciton absorption bandis observed on the lower energy side of the absorption edge. Thefirst exciton level is located at an energy lower than the absorptionband by the energy of the exciton binding energy.

The relative dielectric constant k is large. Thebinding energy Wex is much smaller than that of hydrogen and theBohr radius is much smaller. Excitons behave as electrically neutralparticles. The exciton absorption series begins with 1s exciton. Notethat the 1s absorption of hydrogen atom is not observed. This Wannierexciton is observable only at low temperature because it has smallbinding energies. This exciton can be regardedas an excitation within an atom. The difference between a Frenkelexciton and a simple electronic excitation within an atom is that theformer is mobile.

In addition, when an electron or a hole can be confined under astructure called quantum well, as shown in Fig. In additionto quantum wells, super-lattices and quantum wires are also muchstudied topics. Discuss the relations between principle quantum number, azimuthal quantum number, and magnetic quantum number. Explain the selection rules for multiple atoms taking into account the spin—orbit coupling. Discuss the difference between LS and JJ coupling. Explain the optical spectra of the energy levels of Na, Ca, and Sn.

Suppose that there are N atoms of the same species aligned in a straight line with constant spacing of a. Explain the direct and indirect band transition. Discuss the difference between Wannier exciton and Frenkel exciton. Chapter 14Some Interesting Phenomena We will also deal with current topics onthe optical second-harmonic spectroscopy of solid surfaces.

Thenonlinear optical response of materials enables us to performsurface-sensitive spectroscopy. Fluorescencehas a lifetime of several nanoseconds, whereas phosphorescence hasa lifetime longer than that of fluorescence ms-ms. There are manytypes of luminescence: cathodoluminescence, electroluminescence,and chemiluminescence. Cathodoluminescence is induced byelectron beam excitation, while electroluminescence is induced byapplying electric field to the material.

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Chemiluminescence is inducedby chemical reaction. The luminescence intensity with respect to the photon energyof exciting light is called the excitation spectrum. The luminescence peak in Fig. Luminescence The line shapes of luminescence and absorption are mirrorimages of one another.

At low temperatures, the electron transfer from point B to pointC becomes slow and an electronic transition can occur before theelectron reaches point C. The energy of the luminescence becomeshigher when the temperature becomes lower. This phenomenonis called dynamic Stokes shifts.

On the other hand, the quantumefficiency of the photon emission according to the scheme shown inFig. At high temperatures,the electron does not follow the path from C to D, but goes to pointE and returns to point A. This is called nonradiative transition. Actually the crossing at E in Fig. In this case, the electron makes anonradiative transition by tunneling to the lower electronic state.

In a semiconductor, a crystal of high purity luminescence froma free exciton is observed; however, luminescence is normallyobserved from a bound exciton. The free exciton is trapped by someimpurity centers in a crystal and becomes the bound exciton. Thisbound exciton disappears radiatively and emits luminescent light. The bound exciton shows stronger luminescence than the freeexciton. Thus, the intensity of this bound exciton can be the measureof the purity of the crystal. When the impurity element and one of the elements constitutingthe bulk material belong to the same column in the periodic table,this impurity becomes a trap of excitons.

For example, GaP:N is asemiconductor with an indirect band gap, but the electrons trappedin N centers are localized and have an ambiguity of wave vector. Light Scattering k. Hence, the direct transition is allowed at the indirect gap andluminescence is observed. In the case of GaP:ZnS, luminescenceoccurs due to the overlap of the wave functions of the donor and theacceptor.

Light scatters whenthere is an inhomogeneity in a medium. The conservation laws canbe graphically described in Fig. In Eqs. For Raman scattering, w is large, and this scattering is caused bymolecular vibration, optical phonon, or electronic level in a crystal. Some of the scientists who contributed to the developmentof laser Fig. For understanding the interaction of electromagnetic radiation light with matter atom , at least two subjects in physics areneeded. One is the structure of atom nucleus consisting of protonsand electrons and its energy states, as shown in Fig.

Excited state Ground stateFigure This formula shows that theenergy of each photon is inversely proportional to its wavelength. Possibly interactions between electromagnetic radiation and matter cause changes in the energy states of the electrons in matter, which can be explained with three mechanisms Fig. First, stimulated absorption is an interaction between the incident photon and atom. Second, spontaneous emission is the random emission of photon by the decay of excited state to a lower level.

Last, stimulated emission is the coherence emission of radiation, stimulated by the photon absorbed by the atom in its excited state. This increase in photon density is called light amplification. Table Laser Action Figure Suppose a thermal equilibrium at temperature T of matter atoms between two energy levels and radiation photons. That is,the total number of atoms N2 N1 at E2 E1 and photon number willremain constant in time.

N2 N2 N1 N1 a b Figure Here B21 relates to stimulated emission, leading tophoton amplification. By contrast, A21 relates to spontaneousemission, leading to little photon amplification. Hence, laser withshort wavelength radiation i. A laser device consists of three elements, as shown in Fig. First is the external energy source or pump. Second is the lasermedium or amplifying medium. The last is the optical cavity orresonator. Pump is the source of energy that excites atoms in an active medium to their excited state to create population inversion. Many pumping methods can be used.

One is the electric pumping method used in gas laser, for instance in He—Ne laser A high-voltage power supply causes electrons to accelerate from the cathode toward the anode. Another one is the optic pumping method used in solid or liquid laser, for example in Ruby laser A laser medium is a collection of atoms or molecules stimulatedto population inversion.

Doped material is trivalent Neodymium ions as shownin Fig. These allow each photon to pass back and forth many times through the active medium so that enough amplification of light results. They result in the beam waist W and divergence angle f depending on the mirror distance and the cavity design of radius.

We have so far learned the basic principle of laser. Now how alaser operates? We consider two cases of laser operation: first interms of energy cycle and second in terms of atom and photon incavity. Second is rapid nonradiative transition in which atoms from E4 decay and pile up at E3. Third is light amplification in which photons reflect axially mirror pairs to stimulate other atoms, thus to emit their photons from E3 to E2. Fourth is rapid nonradiative transition in which atoms from E2 decay to E1. N2 N3 N2 N1Figure Second is spontaneous emission in which random emissions of photons leave through the sides of the cavity.

In the meantime, stimulated emission also exists. Seed photons along the optical axis of laser reflect off the mirrors to stimulate other atoms to emit their photons. Third is external laser beam in which a fraction of photons with enough intensity pass out through the output mirror. The laser behavior can be explained in terms of monochroma- ticity wavelength, frequency , coherence phase , direction- ality parallel beam , intensity brightness , and focusability a tiny spot. Light from the flash tube excites atoms in the ground state top.

Excited atoms emit light waves moving parallel to the mirror axes middle. Laser light bursts via permeable mirror bottom. The laser behavior can be explained in terms of monochromaticity wavelength, frequency , coherence phase , directionality parallelbeam , intensity brightness , and focusability a tiny spot. Monochromaticity: Laser radiation is almost one wavelength onecolor , as can be measured by the very narrow linewidth Fig.

Line shape of laser radiation in theory middle and reality right. Coherence: Beams are in phase in both time and location Fig. Coherence time tc is the average time interval over which one cancontinue to predict the correct phase of laser beam at a given pointin space. Coherence length Lc is the average length of the light beamalong which the phase of wave remains unchanged. Directionality: Beam is almost a parallel beam and moves in onedirection in space as can be measured by the very small divergence Fig.

Intensity: Intensity can be explained in terms of output rate andirradiance. Focusability: Focusability is ability of the beam to be focused downto a small point via positive lens Fig. Laser Action Laser applications can be classified into two divisions: 1 laserand interaction and 2 laser and information. They are summarizedin Table The laser energy is absorbed bythe materials, which raises the local temperature so that the mattercould be cut and welded Fig.

The laser energy absorbed by the biologicaltissue raises the local temperature, so the tissue can be coagulatedor cut. Thermal changes depend on temperature level. Many kindsof changes can occur in biological systems, as shown in Table Laser types with specific uses are summarized in Table Laser Action Table First, energies from the laser beams i. Third, a temperature rises at a center ofthe target. Last, enormous energy releases from the target on timescale of ms-ps. For data storage, laser such as GaAslaser creates pits on a photoreactive surface.

Data pattern is thenkept in binary digit bit as 1 land or 0 pit. Eight bits is 1 byte or 1letter or 2 numbers. Bytes and may representA and B, respectively. For data readout Fig. Light is reflected back from pit and land to the detector into original data pattern. Reflection Data pattern is exists if read as laser is 1 reflection or incident 0 transmission. Lasers also have a key role in printing systems, as shown inFig. Traditional printers typewriter or dot printer createmechanical image by pressing ink ribbon from a formed characterof typewriter or from a set of pins of dot printer onto paper.

Laserprinters create electrostatic images by laser beam scanning acrossthe selective discharge of a photoconductive drum. Toner withcharges of opposite polarity adheres to the photoconductive surfaceand is then transferred onto paper. Optical Second-Harmonic Generation When an electronis in a nonparabolic potential, its response to the external field isnonlinear.

In a nonlinear optical effect, the magnitude of a generatedpolarization is not proportional to the magnitude of the incidentelectric field. The fundamental photon energy is 1. I2y z is an increasing functionof z when z is small. This is because the phase velocities ofnonlinear polarization wave and electromagnetic wave at 2w aredifferent, and the harmonic waves radiated by various points ofpolarization wave cancel each other by negative interference.

In this case, we can say that the phase-matching condition is satisfied. SHG occurs in a medium whose structure lacksinversion symmetry. If this potential is asymmetric, as shown in Fig. Discuss the difference between normal population andpopulation inversion. Explain the concept of laser oscillation. Discuss the inversion symmetry of any nonlinear media.

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Chapter 15Optics of Eyes Iris allows lightinto the eye. Cornea, lens, and humors focus light on the retina. Thelight striking the retina is converted into action potentials relayedto brain. Aroundthis area, there is an iris giving an eye pigment and controlling lightintensity via an adjustable pupil. At the retina,there are two photoreceptors, as summarized in Table Accommodation existsfor young adults, whereas accommodation loss occurs in the early40s.

Ocular Problems and Their Corrections Figure NNP is normal near point. Visual acuity is the ability to see detailed image eye resolution—thesmallest readable letter on an eye chart. Visual acuity is measured in terms of the Snellen fractionobtained by dividing the testing distance of defective eyes by thetesting distance of normal eyes.

Normal vision AstigmatismFigure For object from near point NP , partially tensed eyes form a clear vision on retina. Astigmatism Asymmetry Generally blurred Using sphero- of two axes vision comes from cylindrical lens of cornea astigmatism mixed with myopia or hyperopia.

When optometrists prescribe corrective glasses for myopic orhyperopic astigmatism Fig. Not all ocular problems can be corrected with glasses. Someexamples are summarized in Table Next, radial cut by CO2 laser to get flattenPosterior Regrowth of cells on back cornea. Next, remove opacified lens. Last, replace with implant lens.

Explain the components of the eyes along the optical axis. What power of eye glasses is needed to correct MFP from infinity object? What is the new NNP by using this eye glass? A hyperopic person has HNP of cm. What is the power of eye glasses needed to clearly see an object at NNP of 25 cm? Discuss any ocular problem and its correction. Since the differencebetween sine and cosine functions is a relative translation of 0. For a sine wave of amplitude, as shown in Fig. Waves Equation The initial phase j0 is generally set equal to zero for simplicity.

Figure A. Waves Equation Figure A. E and B travel with a constant propagation vector kand frequency w, and thus with a constant wavelength l and velocityc. Superposition of Waves Figure A. In Section A. If N sources are coherent or of difference phase i. Inthe case of the back-and-forth wavesalongthesametransmittingmedium two sine waves traveling in opposite directions with anidentical amplitude and frequency, we get standing waves as shownin Fig.

Superposition of waves of different frequency Fig. Chapter 16Solid Surface The surface is the interfacebetween the vacuum even in a gas phase and the solid in which itsproperty will be remarkably different from those in the interior ofthe matter. The interface is a part of the contact between two piecesof matter. By contrast, the arrangement in the clean surface is differentfrom that in a contaminated or dirty surface due to the relaxationand reconstruction processes. After getting the surface reconstruction, the position vector canbe modified as.

This can be measured from the photoelectric effect, as shown in Fig. The work function is usually in the eV scale. One can then plot the relation between the work function and thephoton energy, as shown in Fig. Problems The work functions for single crystals at different planes aregiven in Table In general, the highest value of the work functionappears on the closed packed surface.

Discuss the rumpling effect in an ionic crystal. Discuss the differences between the Bravais lattices in two and three dimensions. What is a primitive cell? Why the crystal surface is determined by the surface density? Explain the relation between the Jellium model and the work function. Explain the electron distribution at the surface based on the Jellium model. Discuss a more realistic model based on the muffin-tin potential.

Discuss the model of photoelectron emission from the bulk. Explain the potential energy near the surface. Chapter 17Scanning Tunneling Microscopy In general, the probe—specimen gap isabout a few nanometers. Fermi levels shift once one supplies thebias voltage to the specimen. Electron then transfers from high tolow potential, producing an electrical signal. While scanning, theprobe is moved up and down over the specimen to reach a constantelectrical signal and sample—tip separation.

Tungsten is commonlyused as a conductive tip because a sharp tip can be easily producedwith tungsten by electrochemical etching techniques. Creating a voltage dropbetween the two metals allows the tunneling current to flow fromone metal to another [Fig. EF represents Fermi energy and j is the work function eV. The simple potential model of Eq. Therefore, this shows that when the tip closes. Implementation enough to the sample surface, we can simply create the tunnelingcurrent, although there is a break in the circuit between the barriergap.

It consists oftwo main components: a tip and a feedback system. It is then placed very close to the sample. Themotion of the probe—specimen in the xy-axis is mostly manipulatedby a piezoelectric crystal tube. This system is used to control thegap of the probe—specimen in the z-direction. PiezoSample FeedbackFigure For example, an atomof iron can stick on the copper surface. The other iron atoms canthen be dragged along the copper surface to form a circle. Assume the local barrier height to be 4 eV. Write the one-dimensional potential diagram for STM. Give some examples of STM feedback circuits.

Explain the typical piezoscanner. Problems 5. Why do we need coarse positioning and the vibration isolation stage for STM operation? Explain the main components of STM. Discuss the relation between the electron transfer and the gap of probe—specimen.

Optical Properties of Solids / Edition 2

Discuss the atom manipulation in STM. How can we measure the separation and deformation of STM? Chapter 18Atomic Force Microscopy Thistechnique uses the repulsive and attractive forces between the tip mounted on a soft cantilever and the sample. The movement ofthe cantilever frequency shift and damping can be detected by theinput laser and the output photodiode systems. If we assume that the oscillation of the cantilever is harmonic,the solution to Eq. Separation s Potential Force Frequency shiftFigure On the other hand, the specimen is fixedon a piezoelectric crystal tube xy-plane.

After that the cantilevermoves during specimen scanning. The laser light hits around the topof the cantilever end where the probe is set. Next, the displacementsensor detects any reflected light. Thissystem is used to control a constant force at the gap of the probe—specimen in the z-direction. Which forces relate in AFM? Explain the concept of the piezomodulator. Write the equation of the cantilever in contact AFM. Show the schematic of AFM operation. Explain the damping term. Demonstrate the noncontact AFM control system in a block diagram.

Discuss the van der Waals force integrated over the whole volume of the tip and sample. Give some applications of AFM in medical uses. The cantilever dimensions are 30 and microns, respectively. It is held 2 mm above the sample. The work function of the cantilever is 5. Chapter 19Electron Microscopy in Scanning Mode Theelectron—specimen interaction produces an SEM image showingatomic structure and orientation.

Field electron emission relies onthe tunneling effect when we use a strong electric field to induceelectrons at the surface of the tip. Thermionic emission is based onthe heat effect when we rise the temperature of the filament till theemission of electrons at the surface of the filament. Then a primaryelectron beam dislocates the secondary electron deep below thesurface and the backscattered electron in a deeper region.

The current density from the probe indicates the amount ofdislodged electrons.

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That is, the secondary electron released mostlyfrom specimens of low atomic density, i. Above thislimit, the secondary electron disappears although the probe energygets bigger. The probe also produces the backscattered electron releasedmostly from specimens with high atomic density, i. Principle energy of the backscattered electron is higher than that of thesecondary electron. An emission above 50 eV is categorized asthe reflected or backscattered electron. This electron is directlyproportional to the atomic number of elements. If the differenceof the atomic numbers of two elements is more than 3, oneelement can be distinguished from the other.

In addition, since the backscatteredelectron reflects from a certain path of travel, another detector isrequired in addition to the secondary electron detector. Implementation We first vent the chamber using the nitrogen line. Then weintroduce a well-prepared specimen into the chosen holder withinthe chamber. The specimen up to 15 cm height must be electricallyconductive and small enough to fit in the vacuum chamber. Next we can turn the beam source on 5—10 kV. Finally, we can look for the image.

At the end, we turnthe beam off and vent to remove the specimen. Then we close thechamber door and re-pump. Thegenerated electron with high energy appears after we apply a highvoltage from the electron gun. Then the anode position allows theelectrons to interact with the specimen. There are two types ofelectron guns: thermionic and field emission Table A fieldemission gun is generally better than a thermionic one in termsof brightness, monochromatic electron source, and resolution.

Inthermionic emission, we can use tungsten or lanthanum hexaboride LaB6 served as a filament. In terms of performance, as the workfunction of LaB6 is lower than that of tungsten, LaB6 has more abilityto emit electrons than tungsten when equal energy is used. If werequire a high-resolution power, LaB6 is preferred. This is becausesince the tip of LaB6 is smaller than that of tungsten, the electronbeam crossover has a smaller diameter than tungsten. The scanning coils move the focused beam across the sample in the raster scan pattern.

The scan speed is controllable. After that the objective lens focuses the beam spot onto the specimen. In addition, backscattered electrons are also emitted from the sample. Problems Table Many detectors are required. Shows three-dimensional images. Sample dimension is limited. Discuss the difference between conventional microscopy and SEM. How to prepare a sample for SEM? Explain the mechanism of electron when the electron beam strikes the sample surface.

How do you avoid charging issues in an insulated sample in SEM? What is the suitable method to obtain the lattice spacing and chemical composition of a 10 nm diameter InN nanowire? Chapter 20Electron Microscopy in TransmissionMode Theelectron—crystal interaction produces a TEM image to distinguishthe neighboring microstructural features of the material, calledresolution.

Field electronemission relies on the tunneling effect when we use a strongelectric field to induce electrons at the surface of the tip. Thermionicemission is based on the heat effect when we rise the temperatureof the filament till the emission of electrons at the surface of thefilament. After the diverging beam from the electron gun is released by anaccelerating voltage, the beam flows to the anode aperture and theelectromagnetic condensed lens, respectively, to compress the beamspot before it passes through the thin sample.

After passing through the condensed lens, the beam passesthrough the well-prepared specimen. The illuminated beam is thendirected onto the objective lens before the electron distributionsends the TEM image to the CCD camera. By manipulating the opticalaperture behind the objective lens at the appropriate position, thediffraction beam dark-field image , transmission beam bright-field image , and diffraction pattern are then created with the highresolution power. If we substitute Eq. Wecan also adjust the current of the lens to vary the focal length.

Thisresults in the image resolution. Implementation If we cannot use a razor blade, ultramicrotomy is a goodtool for slicing the samples. The prepared slices should be of lessthan 3 mm width and nm thickness before placing them on agrid served as a support material, as shown in Fig. In general, TEM gridoften uses in between and mesh. For ultramicrotomy, the specimen is encapsulated in a thermo-setting polymer e.

This sandwiched specimen isfixed and cleaved over the sharp knife of ultramicrotomy. The thinslices drift off on the surface of the medium e. We can thenpick up these prepared slices and fit them on a grid. If you are the author of this article you still need to obtain permission to reproduce the whole article in a third party publication with the exception of reproduction of the whole article in a thesis or dissertation.

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Optical properties of solids: an introductory textbook Optical properties of solids: an introductory textbook
Optical properties of solids: an introductory textbook Optical properties of solids: an introductory textbook
Optical properties of solids: an introductory textbook Optical properties of solids: an introductory textbook
Optical properties of solids: an introductory textbook Optical properties of solids: an introductory textbook
Optical properties of solids: an introductory textbook Optical properties of solids: an introductory textbook
Optical properties of solids: an introductory textbook Optical properties of solids: an introductory textbook
Optical properties of solids: an introductory textbook Optical properties of solids: an introductory textbook
Optical properties of solids: an introductory textbook Optical properties of solids: an introductory textbook
Optical properties of solids: an introductory textbook Optical properties of solids: an introductory textbook

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