EE 232 Lightwave Devices Lecture 14: Quantum Well and Strained Quantum Well Laser. Quantum Well Gain

Transcription

1 EE 3 Lightwav Dvics Lctur 4: Quantum Wll and Saind Quantum Wll Lasr Rading: huang, Sc (Thr is also a good discussion in oldrn, Appndix ) Insuctor: Ming. Wu Univrsity of alifornia, rkly Elcical Enginring and ompu Scincs Dpt. EE3 Lctur 4- Quantum Wll Gain QW Maial Gain: g( ω) P ρ ( ω) f ( ω) π nc r m m cv 6 P d cv 6 r g ω E p d mr ρr ( E) H( E E ) n n x i V EE3 Lctur 4-

2 Advantags of Quantum Wll Lasrs () Low thrshold h currnt dnsity: ompar fundamntal maial proprty Transparncy currnt dnsity bulk QW q τ q τ bulk QW d L activ QW bulk QW L nm Sinc % bulk d nm activ ( ) Highr diffrntial gain Largr bandwidth: Rsonanc frquncy: (3) Lowr chirp: ω vas g g R a τ p Smallr wavlngth shift whn th lasr is dirctly modulatd EE3 Lctur 4-3 Transparncy arrir oncnation in ulk V F E F V E V Transparncy ondition (rnard-duraffourg Invrsion ondition) ΔF F F F E EE3 Lctur 4-4 V g At ansparncy: F F V E E V or F E F E Lt F E F E Δ V V V V Elcon concnation: F 3/ π m Fn E FV > Eh 4 4 Δ π 3 π 3 π Hol concnation: 3/ F E > E V V π m h P V π 3/ 4 3/ m h P 3 π m Δ Solv Δ 3/ For GaAs ( m m, mh 5.5 m ) Δ.5, 9 cm 7 3 3/

3 V Transparncy arrir oncnation in QW F E F V E V Transparncy ondition (rnard-duraffourg Invrsion ondition) ΔF F F F E EE3 Lctur 4-5 V g At ansparncy: F FV E Eh or F E F E Lt F E F E Δ V h V h Elcon concnation: F m F E Hol concnation: F d Δ h L FV E h m d P V π h V > E > E h m P Δ Solv Δ m For GaAs ( m.67 m, m.5 m ) h Δ.56, Δ cm d 8 3 ot: is indpndnt of L Rduction of Lasing Thrshold urrnt Dnsity by Lowring Valnc and Effctiv Mass rnard-duraffourg ondition: F F ω E E V h Ordinary Smiconductor mh 6 m High ansparncy carrir concnation Idal Smiconductor mh m Low ansparncy carrir concnation Yablonovitch, E.; Kan, E., "Rduction of lasing thrshold currnt dnsity by th lowring of valnc band ffctiv mass, " Lightwav Tchnology, ournal of, vol.4, no.5, pp , May 986 Yablonovitch, E.; Kan, E.O., "and suctur nginring of smiconductor lasrs for optical communications," Lightwav Tchnology, ournal of, vol.6, no.8, pp.9-99, Aug 988 EE3 Lctur 4-6

4 rnard-duraffourg ondition in Quantum Wll rnard-duraffourg ondition: F FV E Eh (a) mh > m (as in most smiconductors) FV > Eh F E d m ρ ( F E ) ( F E ) Larg High thrshold currnt (b) m m h FV Eh F E (Idal smiconductor) m f ( ) is low EdE E EE3 Lctur 4-7 Transparncy arrir oncnation for Ordinary Smiconductor (b) Idal Smiconductor m m F E F E h V h m E + m dx x + m ln( + x ) Transparncy ondition: m F ln FV E Eh For m m cm E E ( ) de EE3 Lctur 4-8

5 Transparncy arrir oncnation for Ordinary Smiconductor Transparncy ondition: F F E E EE3 Lctur 4-9 V h (a) Ordinary Smiconductor d m ρ ( F E ) Δ To stimat Δ, not that P d m h V π L P P For mh 6 m (in 55 μm lasr) Δ m m For 6 (in.55 m lasr), Δ.43 m π L h Effctiv Mass Asymmy Pnalty Ordinary Idal.43 ln Thrshold currnt dnsity rduction is mor than a factor of : + + th nonrad rad Augr th qd A τ 3 3 τ : Shockly-Rad-Hall nonradiativ rcombination liftim Augr is gratly rducd whn is lowrd 3 () is rducd by 8x () is also rducd du to band suctur chang by sain EE3 Lctur 4-

6 andgap-vs-lattic onstant of ommon III-V Smiconductors omprssiv Sain Tnsil Sain Lattic Matchd In.53 Ga.47 As EE3 Lctur 4- Qualitativ and Enrgy Shifts Undr Sain iaxial Sain Hydrostatic Sain Hydrostatic ti iaxiali Sain Sain δ E LH HH HH, LH HH, LH P HH, LH Q +Q HH LH Tnsil Sain EE3 Lctur 4- omprssiv Sain

7 Sain and Sss σ xx xx a a( x) xx yy a σ yy yy σ a : lattic constant of InP < : comprssiv sain iaxial sss: > : tnsil sain σxx σ yy σ σ ij : omplianc Tnsor xx + yy +.5 EE3 Lctur 4-3 E E ( x) +δ E and Edg Shift g E P Q HH LH E P + Q δ E a ( xx yy ) a + + P av( xx + yy + ) av xx + yy Q b ( ) b + a a a : hydrostatic potntial V b : shar potntial EE3 Lctur 4-4

8 Sain Params in III-V (oldrn, p.535) EE3 Lctur 4-5 and-edg Profil and Subband Disprsion EE3 Lctur 4-6