Optical properties of materials Flashcards
Which are the 4 broad categories of solid state materials based on their optical properties?
- Metals
- Glasses
- Crystalline insulators & Semiconductors
- Molecular materials
Crystalline insulators and SC optical properties
- Insulators, e.g. Al2O3 tend to be colourless and transparent in the visible spectral region. If they are coloured, this is most likely caused by impurities. For these reasons the materials are useful for making optical windows and lenses. However, insulators are not transparent in the UV and IR regions.
- SC conceptually similar to those of insulators, except that the electronic transitions giving rise to absorption occur at larger wavelength (lower energy). The band gap Eg determines the lowest energy for inter band transitions and the corresponding lower bound of the transparency range, given by λg = hc/Eg . The upper Eg
limit is determined by lattice absorption, as for insulators, and also by free carrier absorption. Free carriers are present in SC due to thermal excitations across the Eg or doping of impurities. Free carriers cause IR absorption.
Glasses optical properties
Glasses are usually transparent in the visible, as
insulators. However, because they are amorphous, they lack the optical anisotropy properties (birefringence, optical activity, etc) that are found in certain crystalline solids. Most types of optical glasses are made by fusing sand (silica: SiO2) with other chemicals to tune the refractive index.
Metals optical properties
They are shiny. This is why metals like Ag and Al are used for making mirrors. The high reflectivity is due to the interaction of light with free electrons. We have seen in Sect. 7 that an electric field cannot exist inside a metal, because the conduction electrons follow the field until they have compensated it. This is also true for an electromagnetic wave, where electrons respond to the changing external field so as to cancel the field inside the metal, which causes reflection of the incident wave –> plasma frequency
Where does plasma frequency quantity come from?
Metals can be treated as plasmas,
i.e., an ensemble of charged particles composed by an equal number of positive ions and free electrons. If the electrons in the plasma are displaced from the uniform background of ions, electric fields are built up in such a direction as to restore equilibrium by pulling the electrons back to their original positions.
Because of their inertia, the electrons will overshoot and oscillate around their equilibrium positions with a characteristic frequency ωp, typically around 10-30 eV (deep UV region), known as the plasma frequency. As a result, electromagnetic waves with frequency ω < ωp cannot enter a metal and are totally reflected, whereas electromagnetic waves with frequency ω > ωp are transmitted.
Molecular materials optical properties
large organic molecules that may form crystals or amorphous ag- gregates and are held together by relatively weak van der Waals forces, such that the optical properties of the solid tend to be very close to those of the individual molecules.
- Saturated compounds: the valence electrons are incorporated into strong, localised bonds between neighbouring atoms –> these electrons feel strong restoring forces when exposed to EM radiation and can only respond at high frequencies in the UV range –> e.g. PMMA or PE.
- Conjugated compounds: have delocalised π orbitals that spread over the whole molecule, such as benzene (C6H6), aromatic hydrocarbons, dye molecules, and conjugated polymers. π electrons are less tightly bound than the electrons in the saturated bonds and interact with light at lower frequency, often in the visible range –> e.g. OLEDS applications
Which interband absorptions exist? What are they?
Are the mechanism that drive the optical properties of crystalline SC materials.
- Direct band gap SC: energy conservation must be fulfilled, e.g. only photons with energy ℏω ≥ Eg are absorbed. Emission = recombination of e/h producing a photon.
- Indirect band gap SC: energy conservation must include photon energy + phonon energy (as well for momentum conservation with phonon momentum q). –> 2nd order process since requires both photon+phonon absorption –> less probability to occur!
What is the joint DOS?
It tells the energy states that fulfill the energy conservation, i.e. the number of possible interband transitions, i.e. how many states have energy difference of minimum ℏω across the band gap.
- g(ℏω) = 0 for ℏω < Eg
- g(ℏω) ≠ 0 for ℏω ≥ Eg
What is the parallel band effect? (example of Si)
Si semiconductor have an indirect Eg = 1.1eV; the joint DOS, i.e. the abs. coeff, is low at such energy; however interband transitions can take place for energies greater than Eg since the curvature of the valence and conduction band is similar, such that the bands run nearly parallel to each other –> large DOS since dE/dk = 0 –> “Hove singularities”
What is luminescence?
Which type exists?
Spontaneous light emission in solids.
* Photoluminescence: optical excitation, light absorbed and emitted at a different λ.
* Electroluminescence: electrical excitation, electron injected into a SC (pn junction) where they recombine and emits a photon.
* Cathodeluminescence: electro-beam excitation
What is fluorescence?
Spontaneous emission of light during a transition of a molecule from the lowest vibrational energy level to an excited singlet state S1, back to the ground state S0
–> fluorescent material cease to glow upon removal of excitation source
–> emitted light at lower energy
–> time scale approx. nano seconds)
What is phosporecence?
Decay into a intermediate state called “trap state” and it decays very slow
–> from a singlet state S1 (spin = 0) to a triplet state T1 (spin = 1) –> forbidden transition ∆S = 1 available to return to lower energy state –> altough forbidden they occur but at a slower time scales (µs to ms)
What is the skin effect? What is the skin depth?
The exponential decay of an E-field inside a conductor as exp(-α/2 z); the skin depth δ is the distance that the E-field can penetrate inside the conductor.
- Note that if the thickness d of the metal is comparable or smaller than δ, the evanescent field will not fall to zero within the medium, and some fraction of the fields will be transmitted. Conservation of energy demands then that the reflected EM field decrease, and the reflectivity R must drop accordingly. Thus R depends on d when d ≤ δ
