EE 232 Lightwave DevicesEE 232 Lightwave DevicesLecture 16: 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 16-1©2008. University of CaliforniaEnergy Band Structure for Strained GaInAsThe energy-band structure in the momentum space for a bulk Gaxln1-xAs material under (a) biaxial compression, (b) lattice-matched condition, and (c) biaxial tension for different Ga mole fractions x. Th hhl b di b th lihthl b d dit ff tii th t l (thEE232 Lecture 16-2©2008. University of CaliforniaThe heavy-hole band is above the light-hole band and its effective mass in the transverse plane (the kxor kydirection) is lighter than that of the light-hole band in the compressive strain case in (a). The light-hole band shifts above the heavy-hole band in the case of tension in (c).Energy Band Gap for Strained GaInAsThe energy band gap of a bulk In1-xGaxAs vs. the Ga mole fraction x:_._, unstrained In1-xGaxAs; -, transition energies from the conduction band (C) to the heavy-hole(HH) d li hthl (LH)b d f blkIGAdhillIPEE232 Lecture 16-3©2008. University of California(HH) and light-hole (LH) bands for a bulk In1-xGaxAs pseudomorphically grown on InP; ---,the conduction to light-hole transition energy calculated without the spin-orbit (SO) split-offband coupling. E-k Relation and Effective MassesC⎛⎞121112()21(2)12Vxx yy zz VCPa aCCbQbεεεε ε⎛⎞=− + + =− −⎜⎟⎝⎠⎛⎞⎜⎟1211(2)122 : hydrostatic potentialxx yy zzCVCbQbCaa aεεεε ε⎛⎞=− + − =− +⎜⎟⎝⎠=−21 : shear potential ()2HHbEk PQmεεγγ=− − − +=()( )222122tzkkγγ⎡⎤+−⎣⎦02m()( )22212 1 20() 22LH t zEk PQ k kmεεγγ γ γ⎡⎤=− + − − + +⎣⎦=0012 12 2zthh hhmmmmγγ γγ==−+EE232 Lecture 16-4©2008. University of California0012 12 2ztlh lhmmmmγγ γγ==+−EE232 Lecture 16-5©2008. University of CaliforniaBand-Edge Profile and SubbandDispersionUse to longitudial effective mass00calculate the quantum well levelsHH: , LH: 22zzhh lhmmmmγγ γγ==−+12 1222Use to calculate 2-d density of states, gain, etransverse effective mtc.assγγ γγ−+EE232 Lecture 16-6©2008. University of California012 HH: ,thhmmγγ=+012 LH: