Unusual Diamagnetism in Semiconductor Nano-Objects
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1 Psics Psics Pocedia Pocedia t Intenational Confeence on Naow Gap Seiconducto and Sstes Unusual Diaanetis in Seiconducto Nano-Objects L. M. Tu and O. oskobonikov* National CiaoTun Univesit Ta Hsue d. Hsincu 3 Taiwan.O.C lsevie use onl: eceived date ee; evised date ee; accepted date ee Abstact We teoeticall conside te diaanetic esponse of an InAs/GaAs asetical nano-in and asetical quantu dot olecule wen etenal anetic field is applied in te sste s owt diections. We use te effective one-electonic-band Hailtonian ene-position-dependent electon effective ass and -facto appoiation wit soot full tee-diensional confineent potentials appin actual stain and ateial content in tose nano-objects. Tis appoac allows us to siulate and stud psical popeties of seiconducto nano-objects witin a wide ane of cane in eoet and paaetes. Altou te eoeties of te sstes investiated ae ve diffeent we found fo bot sstes a siila anetic esponse. At low tepeatue te sinle electon diffeential anetic susceptibilit as a positive peak and wit tepeatue inceasin te peak eain Loent-like saped and aduall disappea. PASC: 73..-b; a Kewod: Quantu dots; Nano ins; Diaaetis.. Intoduction Te deand fo new nano-based seiconducto devices stiulates te developent of novel nano-stuctued etaateials []. Possible uent ipleentations in tis field ae lae scale quantu coputation etaateials wit te neative efactin inde in optical ane static and dnaic atificial anetis etc. Te etaateial popeties deive fo popeties of nano-coponents nano-objects ade fo te conventional seiconductos. ecent advance in seiconducto nanotecnolo akes it possible to desin and stud in detail diffeent kinds of seiconducto nano-objects and fabicate atificial seiconducto nano-stuctue suc as quantu dots and nanoins etc. Tose nano-objects ae nano-sied seiconducto stuctues eseblin atificial atos and tei anetic popeties attacted uc inteest in ecent decade [-]. We use a coputational etod wic allows us tee diensionall to ap ealistic eoet stain and ateial coposition of seiconducto nano objects known fo epeients on soot tee diensional potential's and paaete's pofiles fo electons confined in te objects. Teefoe we ae able to copae soe psical popeties of nano-objects wit ve diffeent * Coespondin auto. Tel.: ; fa: ail addess: va@facult.nctu.edu.tw. doi:.6/j.ppo...5
2 Auto nae / Psics Pocedia 9. ˆ H b eoeties witin on appoac. In tis teoetical stud we conside and copae diaanetic esponse in two tpes of te nano-objects: asetical nano-ins AN and asetical quantu dot olecules AQDM.. Metod desciption To siulate InAs/GaAs nano-objects we use te effective one-electonic-band Hailtonian ene and positiondependent electon effective ass and -facto appoiation [8]: wee: A e i is te electonic oentu opeato is te spatial adient A is te vecto potential of te anetic field = cul A is te confineent potential is te vecto of te Pauli atices is te o aneton and e stand fo te fee electon eleenta ass and cae is te ene and position ={ } dependent electon effective ass: and is Landé facto: 3 wee b is te effective ass at te botto of te conductin band is te position dependent band ap and is te spin-obit inteaction splittin. is soot full tee-diensional confineent potential: 5 appin te actual stain and In content in te nano-objects ebedded in te GaAs ati. In quation 5: a is te aiu value of te potential outside of te object C = a - in is te electonic band offset in te sste and in is te iniu value of te potential inside te object te slope of potential and te ane of te potential cane at te boundaies of te object is contolled b te paaete a te potential descibes te ad wall confineent wen a is function pesents te eit of te object in te diection te sste s owt diection. Usin analsis of te epeient stuctual and coposition infoation obtained fo AFM atoic foce icoscop and XSTM coss-section scannin tunnelin icoscop easueent te function can be eadil discoveed and even analticall appoiated fo ost of te objects. Fo te InAs/GaAs AN see Fi. te eit of te in can be obtained fo te epeiental fittin [3]: 6 wee M stand coespondinl fo te eit at te cente of te in at te i of te in wee + = and fa awa fo te cente of te in; espectivel deteine te inne and oute slope nea te i. Te paaete defines te anisotop of te in in te plane. M M ] 3[ a a C tan tan 4 a 34 L.M. Tu O. oskobonikov / Psics Pocedia
![we adopt te lens-saped eoet fo [45] and te eit of te eac dot d can be pesented as d u u b 7 wee u is te adius of te uppe cicle and b is te base adius of te dot. e Fi.](/docs-images/92/111011760/images/3-1.jpg ". Confineent potential of double dot sste.")
3 L.M. Tu O. oskobonikov / Psics Pocedia Auto nae / Psics Pocedia 9 a b e e Fi.. Pojections of te confineent potential on a =5 n and b =5 n planes. Fo bot quantu dots in te InAs/GaAs ADQM see Fi. we adopt te lens-saped eoet fo [45] and te eit of te eac dot d can be pesented as d u u b 7 wee u is te adius of te uppe cicle and b is te base adius of te dot. e Fi.. Confineent potential of double dot sste. Te potential fo 5 is used to define te appin function a M 8 C Te appin function epoduces epeiental infoation about eoet sape and position dependent coposition of te object. Usin M we odel te position dependent band ap spin-obit inteaction splittin and te effective ass at te botto of te conductin band b : b in in M M bin out M out [ M ] [ M ] bout [ M ] 9
4 36 L.M. Tu O. oskobonikov / Psics Pocedia Auto nae / Psics Pocedia 9 To deteine te sinle electon anetic esponse of an isolated nano-object we calculate te total ene of te electon confined in te nano-object in te pesence of te etenal anetic field. Te anetiation M and diffeent anetic susceptibilit DMS of te sstes ae defined b n M M f n n wee f is te Fei-Diac distibution function and is te ceical potential of te sste deteined fo te nube of electons in te nano-object b te followin equation 3. Siulation esults and Discussion N f n n To siulate diaanetic esponse in te AN and ADQM we take ealistic seiconducto paaetes fo InAs/GaAs nano-stuctues wit cople stained coposition accodin to [5-7]: in =.86e out =.59 in =.37 out =.34 bin =.44 bout =.67 in = a = C =.474e. We also accept te eoet paaetes fo AN fo [3] and fo ADQM fo [56]. Te ene states and wave functions of te electons confined in te nano-objects ae found b te nonlinea iteative etod [8] usin te Cosol Multipsics packae Ten te anetic esponse of sinle electon AN and ADQM is calculated see Fi. 3. e.4.36.t T e.5.48.t T.3 a.44 b T T Fi. 3. Manetiation of sinle electon of a AN and b ADQM at tepeatue T =.K Fo bot sstes at eo tepeatue te sinle electon DMS as a positive peak nea T. Wit tepeatue inceasin te peaks eain Loent-like saped and aduall disappea. And fo bot sstes consideed te peaks ae esults of te conveence of two lowest ene levels wen te anetic field inceases. ut fo AN te wave functions ave diffeent set and levels coss. At te sae tie fo ADQM te wave functions ave te sae set and te levels anticoss. Altou te topolo of te sstes is diffeent te conveence leads to about te sae unusual diaanetic esponse fo bot. We can assue tat tis unusual diaanetic esponse can be obseved in nano objects wee te lowest ene states ae close enou and te convee wen anetic field is applied to te sste. 4. Conclusion It follows fo tis teoetical stud tat ou etod can efficientl and econoicall epoduces psical popeties of seiconducto nano-objects of ve diffeent eoeties and ateial paaetes. Te diaanetic esponse followin te seiconducto nano-objects eoet can be ve unusual and even evese te sin. peiental investiations of te diaanetic esponse of nano-objects ade fo conventional seiconductos will ield inteestin esults and can be useful fo fute fabication of etaateials wit pincipall new anetic popeties.
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