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 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  E g, some electrons can be promoted to the conduction band leaving some holes in the valence band.

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

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, …

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

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

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) Light is emitted in multiples of a certain minimum energy unit. The size of the unit – the photon. Explains how an electron can be emitted if light is shined on a metal The energy of the light is not spread but propagates like particles. (particles)

Photons When dealing with events on the atomic scale, it is often best to regard light as composed of quasi- particles: PHOTONS Photons are 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, E ph = h = (hc)/

Maxwell – Electromagnetic Waves

Light as an electromagnetic wave is characterized by a combination of a time-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: Changes in the fields propagate through free space with speed c. Light as an Electromagnetic Wave (E, H) 22 

Speed of Light, c The frequency of oscillation, of the fields & their wavelength, o in vacuum are related by: c = o In any other medium the speed, v is given by: v = c/n = n  refractive index of the medium  wavelength in the medium  r  relative magnetic permeability of the medium  r  relative electric permittivity of 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

The Electromagnetic Spectrum Shorter Wavelengths Longer 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

Visible Light Light that can be detected by the human eye has wavelengths in the range λ ~ 450nm to 650nm & is called visible light: The human eye can detect light of many different colors. Each color is detected with different efficiency. 3.1eV 1.8eV Spectral Response of Human Eyes Efficiency, 100% 400nm600nm700nm500nm

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

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 Semiconductors can be opaque 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.

Question Why is Silicon Black & Shiny?

To Answer This: We need to know that the energy gap of Si is: E gap = 1.2eV We also need to know that, for visible light, the photon energy is in the range: E vis ~ 1.8 – 3.1eV So, for Silicon, E vis is larger than E gap 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.

Why is GaP Yellow? We need to know that the energy gap of GaP is: E gap = 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. To Answer This:

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

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: E gap >> 5eV E gap >> E (visible light) ~ eV 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 = I o exp(-  x) I o = 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.

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

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

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 electrons capable of receiving the photon energy.

The photon-electron interaction process obviously depends strongly on the photon energy. Lower Energy Photons interact 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 (> 10 4 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 Edge or Absorption Threshold.

Valence Band – Conduction Band Absorption (Band to Band Absorption) Conduction Band, E C Valence Band, E V E gap h = E photon

Conduction Band, E C Valence Band, E V E gap h = E photon This process obviously requires that the minimum energy of a photon to initiate an electron transition must satisfy E C - E V = h = E gap Valence Band – Conduction Band Absorption (Band to Band Absorption)

Valence Band – Conduction Band Absorption (Band to Band Absorption) Conduction Band, E C Valence Band, E V E gap h = E photon This process obviously requires that the minimum energy of a photon to initiate an electron transition must satisfy E C - E V = h = E gap If h > E gap then obviously a transition can happen. Electrons are then excited to the conduction band.

After the Absorption Then What? 2 Primary Absorption Types Direct Absorption & Indirect Absorption All absorption 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.

Direct Band Gap Absorption K (wave number) h Conservation of Energy h = E C(min) - E v (max) = E gap Conservation of Momentum K vmax + q photon = k c E A Direct Vertical Transition! The Photon Momentum is Negligible

Indirect Band Gap Absorption E K (wave number) h

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 Another Viewpoint

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)

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

Photoconductivity 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 called Photoconductivity 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

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

Total Internal Reflection

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