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Introduction to Optical Properties BW, Chs 10 & 11; YC, Chs 6-8; S, Chs 11-13

Introduction to Optical Properties BW, Chs 10 & 11; YC, Chs 6-8; S, Chs 11-13. Recall : Semiconductor Bandgaps E g are usually in the range: 0 < E g < 3 eV (up to 6 eV if diamond is included) Also, at equilibrium, at temperature T = 0 , the valence band is full & the

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Introduction to Optical Properties BW, Chs 10 & 11; YC, Chs 6-8; S, Chs 11-13

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  1. Introduction to Optical Properties BW, Chs 10 & 11; YC, Chs 6-8; S, Chs 11-13

  2. Recall:Semiconductor BandgapsEgare usually in the range: 0 < Eg < 3 eV (up to 6 eVif diamond is included) • Also, at equilibrium, at temperature T = 0, the valence band is full & the conduction band is empty. • Now, consider what happens if electromagnetic radiation (“light”) is shined on the material. • In the photon representation of this radiation If hν  Eg, some electrons can be promoted to the conduction band leaving some holes in the valence band.

  3. Now, consider some of the various possible types of spectra associated with this process: Absorption Looks at the number of absorbed photons (intensity) vs. photon frequency ω Reflection Looks at the number of reflected photons (intensity) vs. photon frequency ω Transmission Looks at the number of transmitted photons (intensity) vs. photon frequency ω Emission Looks at the number of emitted photons (intensity) vs. photon frequency ω

  4. A (non-comprehensive) list of Various Spectra Types: Absorption, Reflection, Transmission, Emission • Each of these types of spectra is very rich, complicated, & varied! • Understanding such spectra gives huge amounts of information about: electronic energy bands, vibrational properties, defects, …

  5. Interaction Between Light & Bulk Material Many differentpossible processes can occur! 1. Refraction 2. Transmission 3. Reflection a. Specular b. Total internal c. Diffused 4. Scattering There is also Dispersion where different colors bend differently 3c “Semi- transparent” material Incident light 4 1 3a 3b 2

  6. A Quick Review of “Light” & PhotonsHistory: Newton & Huygens on Light • Light as waves • Light as particles Christiaan Huygens They strongly disagreed with each other! Isaac Newton

  7. Light – Einstein & Planck • 1905 Einstein– Related the wave & particle properties of light when he looked at the • Photoelectric Effect. • Planck – Solved the “black body” radiation problem by making the (first ever!) quantum hypothesis: Light is quantized into quanta (photons) of energy • E = h. Wave-Particle duality. (waves) (particles) • Light is emitted in multiples of a certain minimum energy unit. The size of the unit – the photon. • Explains how anelectron can be emitted if light is shined on a metal • The energy of the light is not spread but propagates like particles .

  8. Photons • When dealing with events on the atomic scale, it is often best to regard light as composed of quasi- particles: PHOTONS Photonsare Quanta of light Electromagnetic radiation is quantized & occurs in finite "bundles" of energy Photons • The energy of a single photon in terms of its frequency , or wavelength  is, Eph = h = (hc)/

  9. Maxwell – Electromagnetic Waves

  10. Light as an Electromagnetic Wave • Light as an electromagnetic wave is characterized by a combinationof atime-varying electric field (E)& a time-varying magnetic field (H) propagating through space. • Maxwell’s Equations give the result that E & H satisfy the same wave equation: 2 (E, H) (E, H)  Changes in the fields propagate through free space with speed c.

  11. Speed of Light, c • The frequency of oscillation, of the fields & their wavelength, oin vacuum are related by:c = o • In any other medium the speed, v is given by: v = c/n =  n  refractive indexof the medium wavelengthin the medium rrelative magnetic permeabilityof the medium r relative electric permittivityof the medium The speed of light in a medium is related to the electric & magnetic properties of the medium. The speed of light c, in vacuum, can be expressed as

  12. The Electromagnetic Spectrum Shorter Wavelengths Increasing Photon Energy (eV) Color & Energy Violet ~ 3.17eV Blue ~ 2.73eV Green ~ 2.52eV Yellow ~ 2.15eV Orange ~ 2.08eV Red ~ 1.62eV Longer Wavelengths

  13. Visible Light • Light that can be detected by the human eye has wavelengths in the rangeλ ~ 450nm to 650nm & is called visible light: 1.8eV 3.1eV • The human eye can detect light of many different colors. • Each color is detected with different efficiency. Spectral Response of Human Eyes Efficiency, 100% 400nm 500nm 600nm 700nm

  14. Visual Appearance of Insulators, Metals, & Semiconductors • A material’s appearance & color depend on the interaction between light with the electron configuration of the material.

  15. Visual Appearance of Insulators, Metals, & Semiconductors • A material’s appearance & color depend on the interaction between light with the electron configuration of the material. • Normally High resistivity materials(Insulators) are Transparent High conductivity materials(Metals) have a “Metallic Luster” & are Opaque Semiconductorscan beopaque or transparent This & their color depend on the material band gap • For semiconductors the energy band diagram can explain the appearance of the material in terms of both luster & color.

  16. QuestionWhy is Silicon Black & Shiny?

  17. To Answer This: • We need to know that the energy gap of Si is: Egap = 1.2eV • We also need to know that, for visible light, the photon energy is in the range: Evis ~ 1.8 – 3.1eV So, for Silicon, Evisis larger than Egap • So, all visible light will be absorbed & Silicon appears black So, why is Si shiny? • The answer is somewhat subtle: Significant photon absorption occurs in silicon, because there are a significant number of electrons in the conduction band. These electrons are delocalized. They scatter photons.

  18. Why is GaP Yellow? To Answer This: • We need to know that the energy gap of GaP is: • Egap= 2.26 eV • This is equivalent to a • Photon of Wavelength  = 549 nm. • So photons with E = h > 2.26 eV(i.e. green, blue, violet)are absorbed. • Also photons with E = h < 2.26eV (i.e. yellow, orange, red) are transmitted. • Also, the sensitivity of the human eye is greater for yellow than for red, so • GaP Appears Yellow/Orange.

  19. Colors of Semiconductors Evis= 1.8eV 3.1eV I B G Y O R If the Photon Energy is Evis > Egap Photons will be absorbed If the Photon Energy is Evis < Egap Photons will transmitted If the Photon Energy is in the range of Egap those with higher energy thanEgapwill be absorbed. We see the color of the light being transmitted. If all colors are transmitted the light is White

  20. Why is Glass Transparent? • Glass is an insulator (with a huge band gap). Its is difficult for electrons to jump across a big energy gap:Egap >> 5eV • Egap >> E(visible light) ~ 2.7- 1.6eV • All colored photons are transmitted, with no absorption, hence the light is transmitted & the material is transparent. • Define transmission & absorption by • Lambert’s Law: I = Ioexp(-x) • Io = incident beam intensity, I = transmitted beam intensity • x = distance of light penetration into material from a surface • total linear absorption coefficient(m-1) • takes into account the loss of intensity from scattering centers & absorption centers.approaches zero for a pure insulator.

  21. What happens during the photon absorption process? Photons interact with the lattice Photons interact with defects Photons interact with valence electrons Photons interact with …..

  22. Wavelength (m) Vis UV IR Absorption coefficient (, cm-1) Eg ~ Evis Photon Energy (eV) Absorption spectrum of a semiconductor. Absorption Processes in Semiconductors Important region: Lllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllll

  23. Absorption An Important Phenomena in the Description of the Optical Properties of Semiconductors • Light (electromagnetic radiation) interacts with the electronic structure of the material. • The Initial Interaction is Absorption • This occurs because valence electrons on the surface of a material absorb the photon energy & move to higher-energy states. • The degree of absorption depends,among many other things,on the number of valence electronscapable of receiving the photon energy.

  24. The photon-electron interactionprocess obviously depends strongly on the photon energy. • Lower Energy Photonsinteract principally by ionization or excitation of the solid’s valence electrons. • Low Energy Photons (< 10 eV)are in the infrared (IR), visible&ultraviolet (UV)in the EM spectrum. • High Energy Photons (> 104 eV) are in the X-Ray&Gamma Ray region of the EM spectrum. • The minimum photon energy to excite and/or ionize a solid’s valence electrons is called the Absorption Edgeor Absorption Threshold.

  25. Valence Band – Conduction Band Absorption (Band to Band Absorption) Conduction Band, EC h = Ephoton Egap Valence Band, EV

  26. Valence Band – Conduction Band Absorption (Band to Band Absorption) This process obviously requires that the minimum energy of a photon to initiate an electron transition must satisfy EC - EV = h = Egap Conduction Band, EC h = Ephoton Egap Valence Band, EV

  27. Valence Band – Conduction Band Absorption (Band to Band Absorption) This process obviously requires that the minimum energy of a photon to initiate an electron transition must satisfy EC - EV = h = Egap Conduction Band, EC If h > Egapthen obviously a transition can happen. Electrons are then excited to the conduction band. h = Ephoton Egap Valence Band, EV

  28. After the Absorption Then What? 2 Primary Absorption Types Direct Absorption & Indirect Absorption • Allabsorption processes must satisfy: Conservation of Total Energy Conservation of Momentum or Wavevector • The production of electron-hole pairs is very important for electronics devices especially photovoltaic & photodetector devices. • The conduction electrons produced by the absorbed light can be converted into a current in these devices.

  29. A Direct Vertical Transition! E Conservation of Energy h = EC(min) - Ev (max) = Egap K (wave number) h The Photon Momentum is Negligible Conservation of Momentum Kvmax + qphoton = kc Direct Band Gap Absorption

  30. K (wave number) h Indirect Band Gap Absorption E

  31. Another Viewpoint • If a semiconductor or insulator does not have many impurity levels in the band gap, photons with energies smaller than the band gap energy can’t be absorbed • There are no quantum states with energies in the band gap • This explains why many insulators or wide band gap semiconductors are transparent to visible light, whereas narrow band semiconductors (Si, GaAs) are not

  32. Some of the many applications • Emission: light emitting diodes (LED) & Laser Diodes (LD) • Absorption: • Filtering: Sunglasses, .. Si filters (transmission of infra red light with simultaneous blocking of visible light)

  33. If there are many impurity levels the photons with energies smaller than the band gap energy can be absorbed, by exciting electrons or holes from these energy levels into the conduction or valence band, respectively • Example: Colored Diamonds

  34. Charge carriers (electrons or holes or both) created in the corresponding bands by absorbed light can also participate in current flow, and thus should increase the current for a given applied voltage, i.e., the conductivity increases This effect is calledPhotoconductivity Want conductivity to be controlled by light. So want few carriers in dark → A semiconductor But want light to be absorbed, creating photoelectrons → Band gap of intrinsic photoconductors should be smaller than the energy of the photons that are absorbed Photoconductivity

  35. Refraction, Reflection &Dispersion Light, when it travels in a medium can be absorbed and reemitted by every atom in its path. High n Small n n1 = refractive index of material 1 n2 = refractive index of material 2 Defined by refractive index; n

  36. Total Internal Reflection

  37. Mechanism & Applications of TIR Optical fiber for communication What kinds of materials do you think are suitable for fiber optics cables?

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