... Inc.ThematrixelementjMj2forthetransitionswherewavevectorconservationdoesnotnecessarilyholdisgivenbytheproductofEq.(3.29)andEq.(3.34).Equation(3.34)indicatesthatjMj2islargeintheregionofkwherea2k2issmall.AlthoughEq.(3.34)iseffectivefortransitionsbetweenthebandtailandaextendedband,itdoesnotapplyfortransitionsbetweenparabolicbandswithlargerenergiesandthosebetweenbandtails.Tosolvethedifficulty,Sternexpressedeachconduction-bandelectronandeachvalence-bandelectronintheformofEqs.(3.30 )and( 3.31).ThevaluesofaweredeterminedbyfittingtheeffectiveenergyreductionduetothelocalizationtotheeffectiveenergyreductioncalculatedfromthedensityofstatesintheGHLBTmodel.ThevalueofjMenvj2wascalculatedbyusingthesevaluesinEq.(3.33)andaveragingoverallkdirectionsandthelocalizationsitesri[11].TheresultiswrittenasjMenvj2¼64pb3ðt4Àq4ÞÀ5½ðb4À5b2B2þ5B4Þð3t4þq4Þðt4Àq4Þ2þ8b2B2t2ð3b2À10B2Þðt8Àq8Þþ16b4B4ð5t8þ10t4q4þq8Þð3:35ÞB2¼1acav;b¼1acþ1av;t2¼b2þk2cþk2v;q2¼2kckvwherekcandkvarethewavenumbersofvalence-bandandconduction-bandelectronswiththeeffectiveenergyreductiontakenintoaccount.ThematrixelementjMj2¼jM(E1,E2)j2¼jMBj2jMenvj2usingthisjMenvj2iscalledtheSternenergy-dependentmatrixelement(SME).Figure3.6showsanexampleofjMenvj2calculated ... orbital and consists of a heavy-hole band, a light-hole band and a split-off band [3]. The upper edge of the valence band is at the À point,the center of k space, where the heavy-hole and light-hole ... etc.) and II–VI compoundsemiconductors have a band structure similar to that of Fig. 3.1 and thedirect-transition bandgap. On the other hand, for group IV semiconductorssuch as Si and Ge, and...