EE 232 Lightwave Devices Lecture 14: Quantum Well and Strained Quantum Well Laser. Quantum Well Gain
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1 EE 3 Lightwav Dvics Lctur 14: Quantum Wll and Saind Quantum Wll Lasr Rading: huang, Sc (Thr is also a good discussion in oldrn, Appndix 11) Insuctor: Ming. Wu Univrsity of alifornia, rkly Elcical Enginring and ompu Scincs Dpt. EE3 Lctur 14-1 Quantum Wll Gain QW Maial Gain: g(!ω)!!" Pcv d ρr (!ω) f g (!ω) π n r c m ω!!" m Pcv 6 E p m r ρ d r (E) H(E E π! n ) L n x i V EE3 Lctur 14-1
2 EE3 Lctur 14-3 Advantags of Quantum Wll Lasrs (1) Low thrshold currnt dnsity: ompar fundamntal maial proprty Transparncy currnt dnsity J J bulk QW Sinc `1% q τ q τ bulk QW d L activ QW bulk QW bulk J dactiv J 1 nm ~ 1 nm ( ) Highr diffrntial gain Largr bandwidth: Rsonanc frquncy: (3) Lowr chirp: ω Smallr wavlngth shift whn th lasr is dirctly modulatd L v as g g R a τ p V EE3 Lctur 14-4 Transparncy arrir oncnation in ulk E E V F F V Transparncy ondition (rnard-duraffourg Invrsion ondition) Δ F F FV Eg At ansparncy: Lt or V V V V V V F F E E F E F E F E F E Δ kt kt Elcon concnation: Q F 3/ n h kt Q FV > Eh 1 π mkt 4 F E 4 Δ π 3 π 3 π Hol concnation: 3/ F E > E V V π mkt h kt P V π h 3/ 4 3/ m h Δ P 3 π m Δ Solv Δ 3/ For GaAs ( m.67 m, m.5 m ) h Δ.15, 9 1 cm 17 3 Δ 3/
3 Transparncy arrir oncnation in QW At ansparncy: F F V E 1 E h1 V E E V F F V Transparncy ondition (rnard-duraffourg Invrsion ondition) Δ F F FV Eg Lt Δ F E 1 k T or F E 1 F V E h1 F V E h1 k T Elcon concnation: F > E 1 m k T! F E $ 1 π! # L " k T & % d Δ Hol concnation: F V > E h1 P m k h T F V E h1 k T d π! V Δ L P Δ m h m Δ Solv Δ For GaAs (m.67m,m h.5m ) Δ 1.56, d Δ 1 18 cm 3 EE3 Lctur 14-5 ot: is indpndnt of L Rduction of Lasing Thrshold urrnt Dnsity by Lowring Valnc and Effctiv Mass rnard-duraffourg ondition: F F hω E E V 1 h1 Ordinary Smiconductor m 6 m h High ansparncy carrir concnation Idal Smiconductor m m h Low ansparncy carrir concnation Yablonovitch, E.;; Kan, E., "Rduction of lasing thrshold currnt dnsity by th lowring of valnc band ffctiv mass," Lightwav Tc hnology, J ournal of, vol.4, no.5, pp , May 1986 Yablonovitch, E.;; Kan, E.O., "and suctur nginring of smiconductor lasrs for optical communications," Lightwav Tc hnology, Journal of, v ol.6, no.8, pp , Aug 1988 EE3 Lctur
4 rnard-duraffourg ondition in Quantum Wll rnard-duraffourg ondition: F F V E E h1 (a) m h > m (as in most smiconductors) F V > E h1 F E 1 ρ d (F E 1 ) m (F π! E 1 ) L Larg High thrshold currnt (b) m h m (Idal smiconductor) F V E h1 F E 1 m f π! (E)dE is low L E 1 EE3 Lctur 14-7 Transparncy arrir oncnation for Ordinary Smiconductor Transparncy ondition: F F E E V 1 h1 (b) Idal Smiconductor m m F E F E h V h1 1 E1 For m.67 m π h L π h L E E1 kt x ( ln(1 )) ln dx x 1+ + π h L π h L m cm 17 3 de EE3 Lctur
5 Transparncy arrir oncnation for Ordinary Smiconductor Transparncy ondition: F F E E EE3 Lctur 14-9 V 1 h1 (a) Ordinary Smiconductor m F E Δ d ρ ( 1) π h L To stimat Δ, not that P Δ d kt h V π h L P h For mh 6 m (in 1.55µ m lasr), Δ 1.43kT 1.43 π h L Δ kt Δ kt Δ m P Effctiv Mass Asymmy Pnalty Ordinary Idal 1.43 ln Thrshold currnt dnsity rduction is mor than a factor of : J J + J + J th nonrad rad Augr Jth A qd τ 3 3 τ : Shockly-Rad-Hall nonradiativ rcombination liftim J Augr is gratly rducd whn is lowrd 3 (1) is rducd by 8x () is also rducd du to band suctur chang by sain EE3 Lctur
6 andgap-vs-lattic onstant of ommon III-V Smiconductors omprssiv Sain Tnsil Sain Lattic Matchd In.53 Ga.47 As EE3 Lctur Qualitativ and Enrgy Shifts Undr Sain iaxial Sain Hydrostatic Sain Hydrostatic Sain iaxial Sain δ E LH HH HH, LH HH, LH P HH, LH Q +Q HH LH Tnsil Sain EE3 Lctur 14-1 omprssiv Sain 6
7 Sain and Sss a a( x) xx yy a a : lattic constant of InP < : comprssiv sain > : tnsil sain 1 11 ij : omplianc Tnsor σxx xx σ yy yy σ iaxial sss: σ σ σ xx σ yy xx 1 yy EE3 Lctur and Edg Shift E E ( x) + δ E g E P Q HH E P + Q LH 1 δe a ( xx + yy + ) a 1 11 P a + + a xx + yy 1 Q b( ) b a a a : hydrostatic potntial 1 V ( xx yy ) V 1 11 V b : shar potntial EE3 Lctur
8 Sain Params in III-V (oldrn, p.535) EE3 Lctur and-edg Profil and Subband Disprsion EE3 Lctur
EE 232 Lightwave Devices Lecture 14: Quantum Well and Strained Quantum Well Laser. Quantum Well Gain
EE 3 Lightwav Dvics Lctur 4: Quantum Wll and Saind Quantum Wll Lasr Rading: huang, Sc..3-.4 (Thr is also a good discussion in oldrn, Appndix ) Insuctor: Ming. Wu Univrsity of alifornia, rkly Elcical Enginring
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