Decreasing Value of Mechanical Stress in a Semiconductor Heterostructure by Using Modified Materials

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1 Nnoscence n Nnoengneerng (): 57-7 O: 9/nn9 hp://hrpborg ecresng le o Mechncl ress n emconcor eerosrcre b Usng Moe Merls A Ble Pnro * Nhn Nogoro e Uners o Archecre n l ngneerng 5 l'ns ree Nhn Nogoro 95 Rss Nhn Nogoro e Uners grn Aene Nhn Nogoro 95 Rss orresponng Ahor: elp@mlr oprgh oron Reserch Pblshng All rghs resere Absrc n hs pper e presene n pproch o moel n resls o moelng o relon o mechncl sress n heerosrcre h poros epl ler We lso presene n pproch o moel n resl o moelng o mocon o he poros ner nlence o he mechncl sress e o he nlss o relon o mechncl sress n mocon o poros e obn h poros o epl ler les o ecresng o le o mechncl sress n heerosrcre A he sme me ens o he epl ler ncreses ner nlence o mechncl sress eors Poros er PA Nmbers: emconcor eerosrcre Poros er ecresng o Mechncl ress ncresng o ens o e -n r R nrocon A he presen me mncrng o semconcor eces sll bse on sng semconcor heerosrcres () [-] ce spcng ssmes eren les n eren lers o e o he erence one cn obn mechncl sress n o ecrese he sress col be se merls h s smll s possble erence o lce spcng he secon o ecrese he sress s sng ber lers or grll ecresng o erence beeen lce spcng n mn lers o he rmeor he pper e conser lerne pproch o ecrese he mechncl sress n he pproch bse on sng poros lers n A he sme me e obn ecresng o ol olme o poros We lso nroce nlcl pproch o moel relon o mechncl sress n mocon o poros one me We n n recenl pblshe lerre moelng o hs processes nepenenl rom ech oher n n more prclr cses or emple he hors o Re [5] he been consere onl nl sge o mocon o poros hen poros re lmos sphercl On he oher hn hs been epermenll shon n Re [] h pores re no ls sphercl rng her mocon n he Re [7] hs been consere onl nmercl smlon o mechncl sress ho cconng relon o mechncl sress emen o he Problem We conser hch conss o sbsre () h hcness - n poros epl ler () h hcness (see g ) e s eermne splcemen ecor n srbon o cnces n he n hs son e ssme h pores conss o cnces he cnces col mgre n he poros ler n hs son h me (or emple rng nnelng [5]) smll pores col ecompose o cnces n he sme me lrge pores col ncreses e o cprng o he ree cnces We eermne he chrcerscs h ccon emperre epenence hch ges pprecble conrbon rng opng o []

2 5 ecresng le o Mechncl ress n emconcor eerosrcre b Usng Moe Merls gre emconcor heerosrcre h epl ler ( []) n sbsre ( [ ]) Meho o olon We eermne spoemporl srbon o concenrons o cnces b solng he ollong eqon [79] () h he nl n bonr conons ; (); ( ); (); ( ); (); ( ) here s he srces o pores; s he srce o eernl bonr o poros regon; gr s n s re operors o srcl gren n srcl ergence; n s he mols o norml eloc o moemen o srce o grong or ecresng pore []; s he specc srce energ [9]; ω s he omc spcng; s he omc olme; () s he emperre; - / s he Bolmnn consn; s he molr olme; µ () R ln( / ) [9] и s he nl n nl olme o pores R /(mole ) s he molr gs consn; µ ()() [ () ()]/ [] he relon or µ () col be rnsorme o he orm () here s he Posson coecen; ε ( s - )/ s he msmch srn s re lce spcngs or n respecel; s he mols o norm compresson; χ s he coecen o herml epnson; r s he eqlbrm emperre hch { } gr gr µ W W gr µ n ω e e e ω µ δ χ ε δ δ ε

3 Nnoscence n Nnoengneerng (): conce (or or cse) h room emperre; () s he Yong mols; s he sress ensor; s he eormon ensor []; re he componens () () n () o splcemen ecor ; re coornes omponens o splcemen ecor col be obne b solng o he ollong eqons [] () here ; () s he ens o merls; δ s he ronecer smbol Wh ccon o he relon he ls ssem o eqon es he orm () [ r χ δ ] δ 5 χ χ 5 }

4 ecresng le o Mechncl ress n emconcor eerosrcre b Usng Moe Merls onons or he splcemen ecor col be ren s ; ; ; ; ; ; ; ; poemporl srbon o emperre col be escrbe b he secon l o orer [] (5) h he nl n bonr conons ; ; ; ()()r ere λ s he he concon coecen le o he coecen epens on merls o n emperre emperre epenence o he concon coecen n mos neres re col be pprome b he ollong ncon: λ()λ ss ()[ µ / ()] (see or emple []) c()c ss [-ϑ ep(-()/ )] s he he cpcnce; s he ebe emperre [] he emperre () s ppromel eql or lrger hn ebe emperre or mos neresng or s emperre nerl n hs son one cn ppromel se: c() c ss p() s he olmerc ens o he hch escpes n he rs o ll le s esme spoemporl srbon o emperre o me he esmon e rnsorm he eqon (5) h ppropre conons o he ollong negrl orm 5 χ n { } p gr c λ µ φ A ss ss µ

5 Nnoscence n Nnoengneerng (): 57-7 A ere Ag ss ( ) ( ) ( ) µ B µ ss ( ) ( ) h p ( ) P φ c We obn solon o he q() b he meho o ergng o nconl correcons [-5] Whn he rmeor o he meho o ergng o nconl correcons he spoemporl srbon o emperre hs been replce b s erge le M / ollong resl he replcemen les o he here P ere ( ) ( ) he secon-orer ppromon o he emperre col be obn b he ollong replcng () () n he rgh pr o he q() he relon s presene n he Appen enon o he prmeer (M -M )/ les o obnng eqon o clcle he prmeer he eqon s presene n he Appen We se he secon-orer ppromon or qle nlss n o obn some qne esmon n hs son e obn mn phscl epenences n n some cses e lso obn enogh goo ecness o qne resls [5] rher he srbon hs been mene nmercll rhermore le s esme componens o splcemen ecor n he common cse ec solon o q () s nnon o obn pprome solon e se meho o ergng o nconl correcons [-5] e s preosl rnsorm he eqons o he ssem () o he ollong negro-erenl orm rhermore le s eermne he rs-orer ppromons o componens o he splcemen ecor o me he procere e replce he componens on her erge les n he rgh ses o qs() e β () β β he erge les cn be eermne s here ( ) ( ) ( ) B h [ ( ) µ ] ( ) ss B P M ss ( ) ( ) ( ) P φ ( ) ( ) p P ( ) ( ) c M β β ( ) ss ( ) M β β g () (7) he replcemen ges s possbl o obn ( ) φ ( ) ( ) ( ) Φ

6 ecresng le o Mechncl ress n emconcor eerosrcre b Usng Moe Merls bson o he obne relons n he qs (7) ges s possbl o obn he prmeers β he obne resls col be ren s Χ ( ) here β he secon-orer ppromons o he componens o he splcemen ecor cn be obne b replcng o he ncons β () on he ollong sms: β β here β (M β -M β )/ Resls o he replcemen n clclons o prmeers β re moe n he Appen becse he resls re bl o eermne he spoemporl srbon o cnces le s rnsorm he q () o negrl orm he negrl orm o he q() s presene n he Appen rhermore e se meho o ergng o nconl correcons o sole he eqons he rs- n he secon-orer ppromon o cnc concenron re lso s presene n he Appen n he ollong secon e nle relon o mechncl sress n spoemporl srbon o cnces n he he obne relons ge s possbl o nlse he relons emonsrbl Usng nmercl pproches ges s possbl o men he obne resls scsson ( ) ( ) ( ) ( ) φ ( ) φ ( ) ( ) ( ) Φ Φ [ Χ ( ) Χ ( ) ] [ Χ ( ) Χ ( ) ] ( ) [ Χ ( ) Χ ( ) ] ( ) ( ) ( ) χ ( ) n hs secon e nle relon o mechncl sress n spoemporl srbon o cnces ner he nlence o he mechncl sress n rng he nlss e obn h or ε > ol olme o pores n ecreses A he sme me olme o mechncl sress ecreses Probbl he ecresng o olme o pores s conseqence o compresson o he ner nlence o he mechncl sress A he sme me h compresson o he he mechncl sress lso ecreses Probbl he ecresng s conseqence o ncresng o ens o oms o he he g shos epenences o componen o splcemen ecor on coorne or poros n nonporos epl lers he g shos epenences o cnc concenrons on coorne n sresse n nsresse epl lers he g shos h mechncl sress n h poros epl ler ecreses Reson o he ecresng s ncresng o ens o poros epl ler n hs son s possble ecresng o erence beeen lce spcng n lers o he consere he g shos ncresng o ens o poros epl ler (e ecresng o ol olme o pores) ner nlence o relon o mechncl sress Possble reson o he ncresng o ens o he epl ler s mgron o nersls ner nlence o mechncl sress s ner eernl orce β

7 Nnoscence n Nnoengneerng (): 57-7 U gre Normle epenences o componen o splcemen ecor on coorne or nonporos (cre ) n poros (cre ) epl lers ere re ε shol be noe h e o no conser n concree merl We conser some prmeers o es or solon () gre Normle epenences o cnc concenrons on coorne n nsresse (cre ) n sresse (cre ) epl lers ere re ε shol be noe h e o no conser n concree merl We conser some prmeers o es or solon 5 onclson n hs pper e nle relon o mechncl sress n semconcor heerosrcre hs been shon h sng o poros epl ler ges s possbl o ecrese le o mechncl sress n he srcre A he sme me h ecresng o he le o he mechncl sress ol olme o pores ecreses ner specl conon he conon hs been eermne n he pper Appen he secon-orer ppromon o he emperre col be ren s { µ } ( ) ( ) φ [ ( )] [ ( )] ( ) ss A ( ) A ( ) B ( ) B ( )

8 ecresng le o Mechncl ress n emconcor eerosrcre b Usng Moe Merls here B h µ ss g h qon or clclon he prmeer col be ren s here ss { } ( ) ( ) [ ( )] µ ( ) [ ( )] ss ( ) Bh ( ) ss he negro-erenl eqons or componens o splcemen ecor {[ ( )] µ } ( ) ss A g ( ) ( ) ( ) P ( ) ( ) ( ) [ ( ) ] {[ ( )] µ } ss [ ( ) ] [ ( ) ] { } ( ) µ ( ) ( ) ( ) [ ( ) ] µ ( ) ss { } ( ) ( ) [ ( ) ] {[ ( )] } µ P A A Ag ( ) ( ) B B {[ ( ) ] µ } ( ) h ( ) g ( ) 5 ( ) ( ) ( ) ( ) ( ) 5 µ ( ) ( ) ( ) ( )

9 Nnoscence n Nnoengneerng (): ere s he erge le o he Yong molshe negrl orm o he q() col be ren s } φ Φ 5 φ 5 Φ Φ 5 5 φ bc egh c h g b e bce e c b χ φ Φ β β {

10 ecresng le o Mechncl ress n emconcor eerosrcre b Usng Moe Merls here he rs-orer ppromon o cnc concenron col be ren s here s he erge le o cnc concenron he erge le col be eermne b he ollong relon bson o he rs-orer ppromon o cnces ges s possbl o obn he erge le n he nl orm ] } l µ W W µ { ] } l µ l

11 Nnoscence n Nnoengneerng (): he secon-orer ppromon o cnces concenron rmeor he meho o ergng o nconl correcon es he orm here he prmeer col be eermne b sng he ollong relon ] } 7 { ] ( ) } ( l lm ) m m l n lm n W W µ

12 ecresng le o Mechncl ress n emconcor eerosrcre b Usng Moe Merls he secon-orer ppromons o componens o splcemen ecor re ( ) ] ( ) [ ] } φ } Φ Φ { 5 φ 5 5 } Φ Φ { 5 φ 5 5 Φ Φ }

13 Nnoscence n Nnoengneerng (): here lclon o he prmeers β les o he ollong resl here bc egh c h g b e 5 5 Χ Χ Φ 5 Χ 5 Χ Φ Φ 5 5 Χ Φ } Φ Χ Φ β β

14 7 ecresng le o Mechncl ress n emconcor eerosrcre b Usng Moe Merls RRN [] Wng ghr Oron Appl Phs e 7 7 (999) [] Y e eng Y o Z o Appl Phs e 95 5 (9) [] sropo Y Zhle M hme N Nro emconcors 5 (997) [] nl'cheno orol'o Y oleno emconcors 9 (9) [5] P heremso leso Beehn Pore n sol boes (nergoom Mosco 99 n Rssn) [] M Mnbe N Moho AA ren'e Mnbe echn Phs e (7) () [7] YW Zhng A Boer Mech n Phs ols 7 7 (999) [] chn N elo lecroncs (Phoen Roso-n-on ) [9] M m Nrshm W rer RM nnon AM leser Am erm oc 5 (); M m Nrshm AM leser Am erm oc 57 () [] Pnro ornl o Nnoelecroncs n Opoelecroncs () [] Pnro Moern Phscs eers B (9) 7 () [] Pnro n Nnoscence 7 (-5) 7 () [] Y oolo Apple Mechncs (955) [] Pnro Appl Phs () [5] Pnro omp heor Nnoscence ()