EE 529 Semiconductor Optoelectronics – Optical Processes and LED EE529 Semiconductor Optoelectronics Optical Processes and Light Emitting Diodes 1. Band-to-band optical transitions 2. Absorption spectrum and mechanisms 3. Spontaneous emission 4. LED principles and efficiency 5. Frequency response and modulation bandwidth Reading: Liu, Sec. 13.2, 13.4-13.5, 13.7 Reference: Bhattacharya, Sec. 3.1-3.4, 5.4-5.5, 5.8 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Schrödinger’s Equation and Probability Schrödinger’s Equation: Position operator: x ∂ ∂Ψ ∂ Ψ 2 2 = − + Ψ Momentum operator: i V ∂ i x ∂ ∂ 2 2 t m x ∂ Potential energy Energy operator: i Total energy Kinetic energy ∂ t Ψ ( , ) x t : Wave function of a matter wave Ψ b ∫ 2 | ( , ) | x t dx : Probability of finding the particle between a and b at time t a 2 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Solving Schrödinger Equation Assume time-independent potential V ( x ). 1. Solve the time-independent Schrödinger Equation. ψ 2 2 d − + ψ = ψ V E 2 2 m dx Obtain ψ n ( x ) with associated energy E n . 2. Initial wave function: ∞ Ψ = ψ ∑ ( ,0) ( ) x c x n n = n 1 C n can be obtained by matching initial conditions. 3. Wave function at subsequent time t: ∞ ∞ Ψ = ψ = Ψ − ∑ ∑ / iE t ( , ) ( ) ( , ) x t c x e c x t n n n n n = = n 1 n 1 3 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Infinite Square Well Potential V(x) Eigenfunction: π 2 sin n E 3 ψ = ( ) x x a a E 2 Quantized energy: E 1 π 2 2 2 2 2 k n x = = n E 0 a n 2 2 2 m ma Wave function: π 2 n ∞ Ψ = ∑ − 2 π 2 2 ( /2 ) i n ma t ( , ) sin x t c x e n a a = 1 n Expectation value of the energy: ∞ = ∑ 2 1 | | H c E n n = n 4 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Direct Bandgap vs. Indirect Bandgap Direct bandgap E • Recall that photon momentum is very small, CB compared to electron momentum. = ( ) p k E c Direct Bandgap Photon E g • Momentum conservation can be satisfied in E v direct bandgap semiconductors. VB • Can be good photon absorbers and emitters. – k k (a) GaAs Indirect bandgap E E • Momentum conservation cannot be satisfied with Indirect Bandgap, Eg photon-only process in CB indirect bandgap CB E c E c E r Phonon semiconductors. k cb E v E v • Can be good photon VB k vb VB absorbers, but not good k – k – k k photon emitters. (c) Si with a recombination center (b) Si 5 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Band-to-Band Absorption and Recombination Momentum of photons and electrons p = h/ λ → Photon momentum << Electron Momentum Absorption and emission Emission in Absorption in in direct bandgap indirect bandgap indirect bandgap Defect center ω = ε + ε e g p ε = ω ph ω = ε − ε a g p Involves emission of a phonon Involves absorption or e.g. GaAs, InP e.g. Si, Ge emission of a phonon 6 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Exercise: Determine bandgap and phonon energies from absorption experiment The figure below shows the absorption for Ge at 300K and 77K. Analyze the 300K data to obtain the value of the direct bandgap, the indirect bandgap, and the phonon energy participating in the indirect transitions. Note: The band structure of Ge shows possibilities of indirect and direct transitions. The values we obtain from this exercise will be different from the calculated data at 0K. (Source: Kittel, “Introduction to Solid State Physics”) 7 Lih Y. Lin
EE 529 Semiconductor Optoelectronics Absorption Spectrum of a Typical – Optical Processes and LED Semiconductor (Source: Wolfe, Holonyak, and Stillman, “Physical Properties of Semiconductors) 8 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Exciton Absorption Q: Exciton absorption peaks are normally seen in very pure semiconductors at low temperatures. Higher degree of confinement in the semiconductors also greatly helps observing these, e.g., quantum wells. Why? 9 Lih Y. Lin
EE 529 Semiconductor Optoelectronics Calculated Absorption Spectrum due to – Optical Processes and LED Franz-Keldysh Effect 10 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Quantum-Confined Stark Effect (QCSE) 11 Lih Y. Lin
EE 529 Semiconductor Optoelectronics Relation between Absorption and – Optical Processes and LED Spontaneous Emission π ν α ν 2 2 8 ( ) n ν = 0 0 ( ) R Roosbroeck-Shockley relation e ν − sp 2 h / k T 1 c B Spontaneous emission spectrum of GaAs at 300K 12 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Light Emitting Diodes A p-n junction diode typically made from a direct bandgap semiconductor. Principles Electron-hole pair recombination results in the emission of a photon. Spontaneous emission; emitted photons in random direction. Electron energy n + n + p p E c eV o E c E g E F E g (a) E F (b) h υ - E g E v eV o E v Distance into device V Electron in CB Hole in VB Device Structures L ig h t o u tp u t L ig h t o u tp u t In su lato r (o xid e ) p p E p itax ial la ye rs E p itax ial la ye r n + n + n + n + S u b strate S u b strate (b) (a) M etal ele ctro de 13 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Heterojunction LEDs n + p p Avoid re-absorption of photons along the emission path. (a) AlGaAs AlGaAs GaAs ~ 0.2 µ m E c ∆ E c (a) A double Electrons in CB No bias heterostructure diode has 2 eV eV o 1.4 eV two junctions which are E F E F between two different E c E v bandgap semiconductors (GaAs and AlGaAs) (b) 2 eV Holes in VB (b) A simplified energy E v band diagram with exaggerated features. E F must be uniform. With (c) Forward biased simplified energy band forward diagram. bias (c) (d) Forward biased LED. Schematic illustration of photons escaping reabsorption in the AlGaAs layer and being n + p p emitted from the device. (d) AlGaAs GaAs AlGaAs 14 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Exercise: LED Efficiency An AlGaInP/GaP LED with peak emission wavelength of 636 nm has an external quantum efficiency of 25%. (a) To achieve 5 mW of output optical power, what should be the injected current? (b) If this corresponds to forward-biasing the device at 2 V, find its power conversion efficiency. (c) Find its luminous efficiency and luminous flux. 15 Lih Y. Lin
EE 529 Semiconductor Optoelectronics – Optical Processes and LED Photon Escape Efficiency The intensity distribution of the LED radiation is Lambertian. At the semiconductor-air interface, if the incident angle is greater than the critical angle 𝜄 𝑑 = sin −1 ( 𝑜 𝑏𝑏𝑏 𝑜 𝑏 ⁄ ) , total internal reflection occurs and the light is trapped inside the semiconductor. Possible solutions: (a) Shape the semiconductor surface as a hemisphere (expensive). (b) Encapsulate the LED in a transparent dome with higher refractive index than air to increase 𝜄 𝐷 . 16 Lih Y. Lin
Recommend
More recommend
