EE 232 Lightwave DevicesEE 232 Lightwave DevicesLecture 15: Strained Quantum Well LaserReading: Chuang, Sec. 10.4(There is also a good discussion in Coldren, Appendix 11)Instructor: Ming C. WuUniversity of California, BerkeleyElectrical Engineering and Computer Sciences DeptElectrical Engineering and Computer Sciences Dept.EE232 Lecture 15-1©2008. University of CaliforniaReduction of Lasing Threshold Current Density by Lowering Valence Band Effective Mass11Bernard-Duraffourg Condition:CV e hFF EEω−≥ ≥ −=**Ordinary Semiconductor6 High transparenchemm≈**Ideal Semiconductor Lo transparenchemm≈• Yablonovitch, E.; Kane, E., "Reduction of lasing threshold current density by the lowering of valence band effective mass"LightwaveTechnology Journal ofvol 4 no 5 pp 504-506 May 1986High transparency carrier concentrationLow transparency carrier concentrationEE232 Lecture 15-2©2008. University of Californiaeffective mass, LightwaveTechnology, Journal of, vol.4, no.5, pp. 504506, May 1986• Yablonovitch, E.; Kane, E.O., "Band structure engineering of semiconductor lasers for optical communications," Lightwave Technology, Journal of , vol.6, no.8, pp.1292-1299, Aug 1988Bernard-Duraffourg Condition in Quantum Well1Bernard-Duraffourg Condition:CV hFFEE−=−**11(a) (as in most semiconductors) > heVhCemmFEFE>1*2112() ()Large High threshold currentCedetr e C e C ezmNFE FELNρπ=−= −→=**Large High threshold current(b) (Ideal semiconductor)trheNmm→= VF11*= hCeEFEm∞=∫EE232 Lecture 15-3©2008. University of California12( ) is loweetr CzEmNfEdELπ=∫=Transparency Carrier Concentration for Ordinary Semiconductor**11(b) Ideal Semiconductor = he VhCemm FE FE=⇒ =11*211eeBetrEEzEkTmNdELeπ∞−=+∫=*20111BexzekTmdxLeπ∞+=+∫=()*20*ln(1 )xBezkTmeLkTπ∞−=−+=Transparency Condition:*2*ln 2For=0 067BezkTmLmmπ==11pyCV e hFFEE−= −EE232 Lecture 15-4©2008. University of California017 3For 0.067 4.6 10etrmmNcm−≈×Transparency Carrier Concentration for Ordinary Semiconductor*2(a) Ordinary Semiconductor()demNFEρΔ12()To estimate , note that etr e C ezNFELNPρπ=−=ΔΔ==*22*BBkT kTdBhVzkTmPNe eLπ−Δ−Δ−Δ===Transparency Condition:**** For 6 (in 1 55 m laser)BkTeBhmNP ekTmmmμΔΔ=⇒ =≈11Transparency Condition:CV e hFFEE−= −*For 6 (in 1.55 m laser), 1.43143heBBemmkTkTmNμ≈Δ=EE232 Lecture 15-5©2008. University of California1.43BetrNπ==2zLEffective Mass Asymmetry Penalty1.432ln 2OrdinarytrIdealtrNN==Threshold current density reduction is more than a factor of 2:trJJ J J23 23th nonrad rad AugerthJJ J JJNAN BN CN BN CNqdτ=++=+ + =+ +: Shockley-Read-Hall nonradiative recombination lifetimeqdJττ is greatly reduced when is lowered AugerN3(1) is reduced by 8x(2) C is also reduced due to band structure change by strainNEE232 Lecture 15-6©2008. University of CaliforniaBandgap-vs-Lattice Constant of Common III-V SemiconductorsCompressive StrainTensile StrainLattice MatchedIn0.53Ga0.47AsEE232 Lecture 15-7©2008. University of CaliforniaQualitative Band Energy Shifts Under StrainHd ttiBi i lHydrostatic StrainBiaxialStrainBiaxialStrainHydrostatic StrainCCCCCHH LHLHCEδHH, LHHH, LHHHHH, LHLHHHSOSOPε−Qε−SOSOSOLHSOSOTilStiQε+EE232 Lecture 15-8©2008. University of CaliforniaSOSOCompressive StrainTensile StrainStrain and Stress0()aaxεε ε−===11 12 12xxxxCCCCCCσεσε⎡⎤⎡ ⎤⎡ ⎤⎢⎥⎢ ⎥⎢ ⎥=⎢⎥⎢ ⎥⎢⎥00: lattice constant of InP0: compressive strainxxyyaaεε εε===<⎧12 11 1212 12 11yy yyzzzzCCCCCCσεσε=⎢⎥⎢ ⎥⎢⎥⎢⎥⎢ ⎥⎢ ⎥⎣⎦⎣ ⎦⎣ ⎦120: compressive strain0: tensile strain2Cεε<⎧⎨>⎩Biaxial stress:xx yyσσσ==12112: Compliance TensorzzijCCεεε⊥==−12 12 110 0zzxx yy zzCCCCσεεε=⇒++=12 110.5CC≈12112zzCCεε=−EE232 Lecture 15-9©2008. University of CaliforniaBand Edge Shift()Cg CHHEEx EEPQεεδ=+=− −LHEPQCεε=− +⎛⎞1211()21C C xx yy yy CCEa aCCδεεε ε⎛⎞=++=−⎜⎟⎝⎠⎛⎞121112()21()12Vxx yy yy VCPaaCCbQbεεεε εεεε ε⎛⎞=− + + =− −⎜⎟⎝⎠⎛⎞=++=+⎜⎟11()122 : hydrostatic potentialxx yy yyCVQbCaa abεεεε ε=−++ =−+⎜⎟⎝⎠=−hilEE232 Lecture 15-10©2008. University of California :b shear potentialStrain Parameters in III-V(Coldren, p.535)EE232 Lecture 15-11©2008. University of CaliforniaBand-Edge Profile and SubbandDispersionEE232 Lecture 15-12©2008. University of