EE 232 Lightwave DevicesLecture 21: Light-Emitting Diode (LED)Instructor: Ming C. WuUniversity of California, BerkeleyElectrical Engineering and Computer Sciences DeptElectrical Engineering and Computer Sciences Dept.EE232 Lecture 21-1©2008. University of CaliforniaSpontaneous Emission Spectra12 213221 2121338()rBBBAnENEπ====CBE2()1sponCVRff∝−Spontaneous Emission[]213321 21 21 21 2 121 2 1 21()() (1 )() ()spon sponabs absNEBhcRrEdEAffRrEdEBffPE==−==−hν[][]21 2 1 2121() ()Absorption coefficient:()() ()net netabsnetrRrEdEBffPErEdEnEdE Bf f gEdEα==−=−VBE1[]21 1 2 212121 21() ()()(/)()()rsponEdE Bf f gEdEPE c n crEgEα==−=−=21 2 1(1 )Af fnff−CBE2()stimnet C VRff∝−Stimulated Emission21()gE21222121 21 2132 381111() () []rsponrEFnffBcnErEgEhπΔ−=CBhνEE232 Lecture 21-2©2008. University of California2121 21 2132 3() () [ ]1BEFkTghcsmeVe−Δ−VBE1Spontaneous Emission and Gain Spectra for Various Temperatures21044×31044×41044×51044×JointDOS21044×31044×41044×51044×)JointDOS1 1.2 1.4 1.6 1.8011044×hvieV1.5V)1 1.2 1.4 1.6 1.8011044×hvieV1.5V)15−0V)eV)5eV)EmissionProbability150V)eV)5eV)FermiInversionFactor1 1.2 1.4 1.6 1.81.5−hvieV1.5 106×T=1KSpontaneous1 1.2 1.4 1.6 1.81.5−hvieV1.5 106×Gain0T 1 KT= 77KT = 300KSpontaneousEmissionSpectra0GainSpectraEE232 Lecture 21-3©2008. University of California1 1.2 1.4 1.6 1.81.5−106×hvieV1 1.2 1.4 1.6 1.81.5 106×hvieVSpontaneous Emission and Gain Spectra for ΔF (T = 300 K)21044×31044×41044×51044×i)JointDOS21044×31044×41044×51044×i)JointDOS1 1.2 1.4 1.6 1.8011044×hvieV1.5)1 1.2 1.4 1.6 1.8011044×hvieV1.55eV)05eV)55eV)6eV)ΔF= 1 5eVEmissionProbability15−05eV)55eV)6eV)FermiInversionFactorΔF= 1 5eV1 1.2 1.4 1.6 1.81.5−hvieV1.5 106×ΔF= 1.5eVΔF= 1.55eVΔF= 1.6eVSpontaneous1 1.2 1.4 1.6 1.81.5hvieV1.5 106×GainΔF= 1.5eVΔF= 1.55eVΔF= 1.6eV0SpontaneousEmissionSpectra0GainSpectraEE232 Lecture 21-4©2008. University of California1 1.2 1.4 1.6 1.81.5− 106×hvieV1 1.2 1.4 1.6 1.81.5−106×hvieVTotal Spontaneous Emission RateTotal number of photons emitted per unit volume of idtibtidbit tith ti()3/2semiconductor is obtained by integratingover the entire spontaneousemission spectrum:()()3/2*3/23/2 30() exp2rfCfVgsprmEEErvdv kTVkTπτ∞−−⎛⎞Φ==⎜⎟⎝⎠∫=0expVΦ=fC fVEEkT−⎛⎞⎜⎟⎝⎠3Unit : [1/ cm ]EE232 Lecture 21-5©2008. University of CaliforniaPhoton Flux vs Bias Voltage• In a p-n junction, the separation of quasi-Fermi levels is equal to the applied voltage:ECEfCEΔEf= EfC-EfVEVEfVV• The spontaneous emission photon density is an exponential function of applied voltage to the p-n junction:qV⎛⎞ΦΦ⎜⎟EE232 Lecture 21-6©2008. University of California0expqkT⎛⎞Φ=Φ⎜⎟⎝⎠Light-vs-Current (L-I) Characteristics2.1083.108ntI-V characteristics of p-n junction:exp 1 expqV qVII I⎛⎞⎛⎞ ⎛⎞=≈⎜⎟ ⎜⎟⎜⎟01.108CurrenIV()exp 1 expSSII IkT kT=−≈⎜⎟ ⎜⎟⎜⎟⎝⎠ ⎝⎠⎝⎠0.5 0 0.51.108V00expSqVIIkT I⎛⎞Φ⎛⎞Φ=Φ = ∝⎜⎟⎜⎟⎝⎠⎝⎠ensityCtLightLight InteCurrentLight IntensityEE232 Lecture 21-7©2008. University of CaliforniaCurrentDynamic Response of LEDRate Equations for LED:dN I N N⎧11 1 ; /( )rnrinjneVolieVolωττττ=− =+⋅⋅rnrdt e VoldP Nττ⎧=−−⎪⋅⎪⎨⎪=⎪/( )11ieVolnjiωτ=+⎛⎞⎛⎞⎛⎞rdtτ⎪=⎪⎩11rrnipjeVolτττ ωτ⎛⎞⎛⎞⎛⎞==⎜⎟⎜⎟⎜⎟+⋅⎝⎠⎝⎠⎝⎠0Small-signal response:jtNN neω=+⋅AC quantum efficiency:1()prωη⎛⎞==⎜⎟00jtjtIIiePP peωω=+⋅=+⋅()1irijeVolωηωττ==⎜⎟+⎛⎞⎝⎠⎜⎟⋅⎝⎠⎛⎞EE232 Lecture 21-8©2008. University of Californiawhere is internal quantum efficiencyirτητ⎛⎞=⎜⎟⎝⎠Dynamic Response of LED (Cont’d)50e1.596−se Slope =20 dB / decadeirτητ⎛⎞=⎜⎟⎝⎠1510ResponseriRespons(dB)πτ213=dBf20 dB / decade1.1071.1081.10920Frequency (Hz) 16.119−1109×1107×wi2 π⋅Frequency (Hz)• ηiis a measure of material quality–Defects or dopants can reduce τnrand lead to lower internal Frequency (Hz)pnrquantum efficiency• Typical τ ~ 1 nsec3dB frequency ~ 160 MHzEE232 Lecture 21-9©2008. University of California–3-dB frequency ~ 160 MHzBandwidth-Efficiency Product• τris generally fixed for a given material• Bandwidth-efficiency product is constant:• τnrdepends on material quality–Sensitive to defects or31122dB irrfτηπττ πτ⎛⎞⎛⎞×= =⎜⎟⎜⎟⎝⎠⎝⎠Sensitive to defects or dopants• LED speed can be increased by intentionally01010riincreased by intentionally introduce defects or dopants to shorten τnr2010Responseri0,ri1,ri2,• Shorter lifetime also leads to lower internal quantum efficiency1.1071.1081.1091.1010302030−5109×1107×wiEE232 Lecture 21-10©2008. University of CaliforniaFrequency (Hz) 2 π⋅Radiation Pattern• Light is generated in the active layer isotropicallyθ• Only a small fraction of light can escape from the semiconductor due to total internal reflection– Refractive index of semiconductor ~ 3.5 )cos()(θθ∝P• Optical refraction at semiconductor-air interfaceTh lti di ti• Usually the LED is packaged with an lens cap, which narrows the width of the •The resulting radiation pattern is Lambertian:– θFWHM= 120°radiation patternEE232 Lecture 21-11©2008. University of CaliforniaExternal Quantum Efficiency• Not all photons generated in the active layer of an LED will be collected by an external detectorEscape Conecollected by an external detector– Reflection at semiconductor-air interface21n⎛⎞θC•Total internal reflection limit the130%1nRn−⎛⎞=≈⎜⎟+⎝⎠1⎛⎞Total internal reflection limit the amount of photons that can escape from the semiconductor– Escape cone is determined 121sin16i()CCndπθθθθ−⎛⎞=⎜⎟⎝⎠∫∫by total internal reflection angle, θc– Typical semiconductor 35()006sin()4621cos()4TIRCdηθθππθπ=⋅=⋅ −∫∫EE232 Lecture 21-12©2008. University of Californian ≈ 3.5θC ≈ 16.6°412.5%π≈Transparency SubstrateSource: http://www.lumileds.com/pdfs/techpaperspres/intertch2000.PDF• Photons trapped by TIR bounce around inside the semiconductor– If substrate is absorptive, the trapped photons will mostly be absorbed by the substratepppppby the substrate• TIR trapping can be reduced by– Rough surfaceTransparent substrateEE232 Lecture 21-13©2008. University of California–Transparent substrate– Non-cubic shape chipHB-LED