EMT 392/492 Photonic Materials Propagation of Light in Solids (2) Dr. Ala’eddin A. Saif Semester I Academic session 2013/2014

Absorption 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: 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, Evis is larger than Egap So, all visible light will be absorbed & Silicon appears black So, why is Si shiny? 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.

Photon of Wavelength  = 549 nm. GaP Appears Yellow/Orange. 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 = hf > 2.26 eV (i.e. green, blue, violet) are absorbed. Also photons with E = hf < 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.

Colors of Semiconductors Summary 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 than Egap 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). It 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, Why?

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

The Initial Interaction is Absorption Absorption is an important phenomena in the description of the optical properties of materials 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 (> 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 Edge or Absorption Threshold.

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 = hf = Egap Conduction Band, EC If hf > Egap then obviously a transition can happen. Electrons are then excited to the conduction band. hf = Ephoton Egap Valence Band, EV

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) hf Conservation of Energy hf = EC(min) - Ev (max) = Egap Conservation of Momentum Kvmax + Kphoton = kc E A Direct Vertical Transition!

Indirect Band Gap Absorption K (wave number) h

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. This explains why many insulators or wide band gap semiconductors are transparent to visible light, whereas narrow band semiconductors (Si, GaAs) are not.

Some of the many applications Emission: Light emitting diodes (LED) & Laser Diodes (LD) Absorption: Photovoltaic & Photodetector 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

Dispersion Dispersive Prism: Dependence of the index of refraction, n(), on frequency or wavelength of light. When white light passes through a prism, the blue constituent experiences a larger index of refraction than the red component and therefore it deviates at a larger angle, as we shall see. In order to explain the dispersion it is necessary to take into account the actual motion of the electrons in the optical medium through which the light is traveling.

The effect of introducing a dielectric matter changes Maxwell’s equations to the extent that o   and o  . The phase speed in the medium becomes: The ratio of the speed of an E-M wave in vacuum to that in matter is defined as the index of refraction n: Relative Permittivity and Relative Permeability For most dielectrics of interest that are transparent in the visible, these are essentially non-magnetic and to a good approximation  1. To a good approximation also known as Maxwell’s Relation: In reality, and n are actually frequency-dependent, n(), known as dispersion.

Electron is bound to nucleus by a ‘spring’-kind of force: F = -kEx Electron may oscillate at natural resonance frequency: Light  E(t) and produces a classical forced oscillator. x-axis Light wave exerts a force: E(t) + - Using Newton’s 2nd law: Driving Force – Restoring Force = ma, where Rest. Force = -kEx, where kE=

Solution: N electrons per unit volume each contribute dipole moment qx, Electric polarization: But, Therefore

Since n2 = = /o it follows that we obtain the following Dispersion equation  > o  n < 1 (above resonance), n increases with frequency. (Displacement is 180 out-of-phase with driving force.)  < o  n >1 (below resonance), n increases with frequency. (Displacement is in-phase with driving force.) Symbols summery

Note that as   oj, n() gradually increases and the behavior is called “Normal Dispersion.” Again, at  = oj, n is complex and leads to an absorption band. Also, when dn/d < 0, the behavior is called “Anomalous Dispersion.” Electronic resonances usually occur in the UV; vibrational and rotational resonances occur in the IR; and inner-shell electronic resonances occur in the x-ray region.

When white light passes through a glass prism, the blue constituent experiences a larger index of refraction than the red component and therefore it deviates (refract) at a larger angle.

Note the rise of n in the UV and the fall of n in the IR, consistent with “Normal Dispersion.” At even lower frequencies in the radio range, the materials become again transparent with n > ~1. Transparency occurs when  << o or  >> o. When  ~ o, dissipation, friction and therefore absorption occurs, causing the observed opacity.