Basic Principles of Light Emission in Semiconductors
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1 Basic Principles of Light Emission in Semiconductors Class: Integrated Photonic Devices Time: Fri. 8:00am ~ 11:00am. Classroom: 資電 06 Lecturer: Prof. 李明昌 (Ming-Chang Lee) Model for Light Generation and Absorption Photon Figures (Particle Nature of Light) (1) mass of photon hv h E = hv= mc m = = c cλ c= vλ 0 0 () Momentum of photon p = mcu u : unit vector in the direction of travel of the photon h p = u = k λ 0
2 Model for Light Generation and Absorption Electron Figures in crystals (1) Crystal momentum of electron is defined as p = k where = h π and h = (Planck s constant) k is the wavevector of the electron state and p is not the classic momentum of a free electron mv () Effective mass of electron in cystals 0 E C 0 E V E g electron hole E E CB VB 0 k = EC + m 0 k = EV + m * e * h 1 * m k Ek ( ) Direct Absorption (Photon-Electron scattering) Direct Bandgap Material Indirect Bandgap Material Energy Conservation Momentum Conservation Ei + hvphoton = Ef pi + pphoton = p f k i + π u = k or λphoton ki k f f
3 Indirect Absorption (Photon-Electron-Phonon scattering) Direct Bandgap Material Indirect Bandgap Material Energy Conservation Momentum Conservation E + hv ± hω = E i photon phonon f k i + π u ± q = k λ photon f Indirect transition rate is much smaller than direct transition rate Intraband absorption (Microscopic View) E-K Diagram E-Space Diagram Both direct and indirect transitions also can take place within a band (intraband) or between energy states introduced by dopant atoms and/or defect. The principles of conservation of energy and momentum apply.
4 Light Emission in Semiconductor Direct Bandgap Material Indirect Bandgap Material Energy Conservation Momentum Conservation Ei Ef = hvphoton ± hω phonon k π i k f ± q = u λ photon Under the thermal equilibrium condition, the emitted light is usually re-absorbed Thermal-Equilibrium Carrier Density Fermi Level Fermi-Dirac distribution 1 f( E) = exp[( E E ) / k T] + 1 f ( E) 1 f ( E) f B : probability of occupancy of electron : probability of occupancy of hole State density of conduction band ne ( ) = σ ( E) f( E) C pe ( ) = σ ( E)[1 f( E)] V State density of valance band
5 Quasi-Equilibrium Carrier Density Fermi Level is split! Fermi level is split due to optical pumping or current injection The electron and hole density changes due to the shift of Fermi- Dirac distribution p-n Junction Light Emitter Electrons and holes are injected and recombined when a forward bias voltage V 0 is applied. (Electroluminescence) Compared with gaseous sources, semiconductor lighters usually have single emission peak (corresponding to the band edge) and wide spectrum
6 A p-n junction light-emitting Diode (LED) Internal Quantum Efficiency η = int number of photons generated number of hole - electron pair injected External Quantum Efficiency number of photons emitted in desired direction η ext = number of hole - electron pair injected Actually, much of light is reabsorbed (due to reflection) before it leaves the diode Making the layer of material between the junction and the surface very thin Choosing the a material with a very small absorption coefficient Interband Light-Matter Interaction hv hv hv hv Spontaneous Emission Stimulated Absorption Stimulated Emission Spontaneous emission mostly depends on the temperature, which affects the electron and hole distribution. (Fermi-Dirac distribution) Stimulated emission relies on the intensity of external photon flux
7 Band-to-Band Light Matter Interaction φ( v ) 1 B1N1φ ( v1) : (stimulated) absorption A1N : spontaneous emission B N φ( v ) : stimulated emission 1 1 stimulated emission rate B N ( v ) B N = φ = absorption B N φ( v ) B N stimulated emission rate B N ( v ) B = φ = spontaneous emission rate A N A φ( v ) N is much smaller than N 1 under thermal-equilibrium condition. Therefore, the stimulated emission is very inefficient 1 Population Inversion Boltzmann Distribution Thermal Equilibrium After Population Inversion Boltzmann Distribution: N N 1 [ E E kt] exp ( ) / 1 Population inversion is essential to let the stimulated emission larger than absorption
8 Stimulated Emission To get the stimulated emission, N has to be much larger than N1 (population density inversion) E hv ( E E ) g Fn Fp Population Density Inversion Direct Bandgap Material Indirect Bandgap Material Pump sec Pump 0.5sec Population density inversion is applicable either by optical pumping or current injection The life time of an indirect recombination is long, resulting in nonradiative process such as lattice vibration Quantum efficiency: ~1(direct bandgap materials) but ~0.001(indirect bandgap materials)
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