... Inc. 3 StimulatedEmissionandOptical GaininSemiconductors Thischapterpresentsthebasictheoryandcharacteristicsofstimulated emissionandopticalamplificationgaininsemiconductors.Theformeristhe mostimportantprinciplethatenablessemiconductorlaserstobeimplemented, andthelatteristhemostimportantparameterforanalysisofthelaser performances.First,stimulatedemissioninsemiconductorsisexplained ,and thenquantumtheoryanalysisandstatisticanalysisusingthedensitymatrix oftheopticalamplificationgainaregiven.Stimulatedemissionandoptical gaininsemiconductorquantumwellstructureswillbepresentedinthenext chapter. 3.1BANDSTRUCTUREOFSEMICONDUCTORSAND STIMULATEDEMISSION 3.1.1BandStructureofDirect-TransitionBandgap Semiconductors Semiconductorlasersutilizetheinterbandopticaltransitionsofcarriersina semiconductorhavingadirect-transitionbandgap.Asiswellknowninthe electrontheoryofsolids[1],thewavefunctionofanelectronofwavevector k(momentumhh k )inanidealsemiconductorcrystalcanbewrittenasa Blochfunction j ... Dekker, Inc. 3 StimulatedEmissionandOptical GaininSemiconductors Thischapterpresentsthebasictheoryandcharacteristicsofstimulated emissionandopticalamplificationgaininsemiconductors.Theformeristhe mostimportantprinciplethatenablessemiconductorlaserstobeimplemented, andthelatteristhemostimportantparameterforanalysisofthelaser performances.First,stimulatedemissioninsemiconductorsisexplained ,and thenquantumtheoryanalysisandstatisticanalysisusingthedensitymatrix oftheopticalamplificationgainaregiven.Stimulatedemissionandoptical gaininsemiconductorquantumwellstructureswillbepresentedinthenext chapter. 3.1BANDSTRUCTUREOFSEMICONDUCTORSAND STIMULATEDEMISSION 3.1.1BandStructureofDirect-TransitionBandgap Semiconductors Semiconductorlasersutilizetheinterbandopticaltransitionsofcarriersina semiconductorhavingadirect-transitionbandgap.Asiswellknowninthe electrontheoryofsolids[1],thewavefunctionofanelectronofwavevector k(momentumhh k )inanidealsemiconductorcrystalcanbewrittenasa Blochfunction j ... Inc. ThematrixelementjMj 2 forthetransitionswherewavevectorconservation doesnotnecessarilyholdisgivenbytheproductofEq.(3.29)andEq.(3.34). Equation(3.34)indicatesthatjMj 2 islargeintheregionofkwherea 2 k 2 issmall. AlthoughEq.(3.34)iseffectivefortransitionsbetweenthebandtail andaextendedband,itdoesnotapplyfortransitionsbetweenparabolic bandswithlargerenergiesandthosebetweenbandtails.Tosolvethe difficulty,Sternexpressedeachconduction-bandelectronandeachvalence- bandelectronintheformofEqs.(3.30 )and( 3.31).Thevaluesofawere determinedbyfittingtheeffectiveenergyreductionduetothelocalizationto theeffectiveenergyreductioncalculatedfromthedensityofstatesinthe GHLBTmodel.ThevalueofjM env j 2 wascalculatedbyusingthesevaluesin Eq.(3.33)andaveragingoverallkdirectionsandthelocalizationsitesr i [11].Theresultiswrittenas jM env j 2 ¼ 64pb 3 ðt 4 Àq 4 Þ À5 ½ðb 4 À5b 2 B 2 þ5B 4 Þð3t 4 þq 4 Þðt 4 Àq 4 Þ 2 þ8b 2 B 2 t 2 ð3b 2 À10B 2 Þðt 8 Àq 8 Þ þ16b 4 B 4 ð5t 8 þ10t 4 q 4 þq 8 Þð3:35Þ B 2 ¼ 1 a c a v ;b¼ 1 a c þ 1 a v ;t 2 ¼b 2 þk 2 c þk 2 v ;q 2 ¼2k c k v wherek c andk v arethewavenumbersofvalence-bandandconduction- bandelectronswiththeeffectiveenergyreductiontakenintoaccount.The matrixelementjMj 2 ¼jM(E 1 ,E 2 )j 2 ¼jM B j 2 jM env j 2 usingthisjM env j 2 is calledtheSternenergy-dependentmatrixelement(SME). Figure3.6showsanexampleofjM env j 2 calculated...
Ngày tải lên: 23/10/2013, 20:15
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semiconductors for micro and nanotechnology an introduction for engineers -korvink j. g., greiner a.
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electrochemistry of semiconductors and electronics 1992 - mchardy
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einstein relation in compound semiconductors and their nanostructures, 2009, p.471
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