Outlines. Part 1 Fundamentals. Atomic Structure---An Overview. The Bohr Model 2/2/2011. PHY5937:ST-Nanofabrication using FIB. v r

Transcription

1 //0 PHY5937:ST-Naofabicaio usig FIB Chow Dp. of Physics Uivsiy of Ca Foia Ouis Pa Fuaas of Io-Soi Iacios Pa Physics of FIB Isu Pa 3 Appicaio of FIB Isu Pa 4 Naofabicaio wih cos a phoos Pa 5 Oh io ba achiqus Jauay 0 cu- Pa Fuaas Aoic Sucu---A Ovviw Aoic Sucu----Ovviw Aoic Coisios---uhfo i Scaig gy oss of igh ios Dph pofi Th Boh Mo----Cassica hoy ay quau hoy of aos Fo aos o Soi Sa Physics Jauay 0 cu- 3 Jauay 0 cu- 4 Th Boh Mo Th basic hypohss cos ov i a sab cicua obis. saioay sa/obi aiaio issio occus oy wh co ovs fo o sa o aoh sa. asiio Agua ou of co is quaiz. = ћ Assu a asss of a ao is i h ucus wih a aius of ~0-3 a cos ov i cicua obi wih aius of ~0-0. Th foc bw co a h ucus is co-saic i au. Z v Jauay 0 cu- 5 Jauay 0 cu- 6

2 //0 Agua ou is quaiz. v Cobi quaios a v Z 3 Jauay 0 cu- 7 Fo quaio 3 w fou Z 4 So h obia aius is quaiz. Fo hyog ao Z= a = Boh aius ao 0.53 Boh vociy vo a c / s Jauay 0 cu- 8 o Th aio of Boh vociy o h vociy of igh is ca fi sucu cosa. v o c c 37 Fi sucu cosa α Z K P v Z Z Z 4 Z Jauay 0 cu- 9 Fo H ao: Dfi Z o c a 4 o c a o c o Copo wavgh of Jauay 0 cu- 0 Hyog gy v iaga Hyog spcu-ba sis ay hoy of QM fo aos Now w wi us hyog as a ap o show how QM vop i h ay 0 h cuy ca b us o scib co ovig i h obi of a ao. Fo fiiio of oa gy P P i i b h ou a gy opao Jauay 0 cu- Jauay 0 cu-

3 //0 3 i This is Schöig quaio. I fos h basis of quau chaics. Fo h i big w assu is ip of i Jauay 0 cu- 3 assu is ip of i. T Us spaaio of vaiabs T T i p i c T Th abov quaio as o wo iffia quaios: T i T Jauay 0 cu- 4 i Fo Couob fi ca fi h is o agua pc so W ca us sphica cooia o sov h Schoig quaio. Jauay 0 cu- 5 Y Yθφ is a sphica haoic fucio a ca b wi as Yθφ = ΘθΦφ I sphica cooias h squa is: si si si Subsiu i io Schoig quaio Jauay 0 cu- 6 Subsiu i io Schoig quaio a w up wih h quaios si si si Th souios of h abov quaio a popoioa o h associa g poyoias P cosθ h aia pa is as foow: Jauay 0 cu- 7 Th souios of h abov quaio a popoioa o hassocia aqu poyoias. Popis of g poyoias a aq poyoias ca b fou i os quau chaics o coyaics books. H a so ga popis of aq poyiias. 0 = = -+ = ½ = /6 I ga oiqus aio is us o ga aq poyoias! Jauay 0 cu- 8! Fo associa aqu poyoias! cuc aio: o

4 //0 Fo hyog ik aos o ios h poia gy = -Z / =-Z ε o / wh ε o = 4 /ћ²= /a o =7.. Th souio is giv by Y Wh a quau ubs = picip quau ub = obia quau ub = agic quau ub W s ha gy is ga aig ha iff sas cou hav h sa gy. Fo = = 0 = 0 his is S sa = = 0 = 0 his is S sa = = = - his is P sa = 0 his is P sa = his is P sa. Dgacy of gy 0 Jauay 0 cu- 9 Jauay 0 cu- 0 Sphica haoics wih = 0 Sphica haoics wih = Th shaps of aoic obias Sphica haoics wih = Jauay 0 cu- Jauay 0 cu- aia copos: k = Z/a o k S S 3/ k / p k 3/ k p k / 3/ k k P k / p 3 k 3/ k k k 3 S [ ] p Assig # iv pssios fo 3p a 3. pcaio vaus W assu ha vy obsvab ca b associa wih a opao. Such ha: * A A Wh is oaiz. If is a igfucio of A A a Jauay 0 cu- 3 Jauay 0 cu- 4 4

5 //0 Th w ca wi h pcaio vau of a opao as: * A A * a a W ca show ha Assig # ao [3 ] Z ao [5 3 ] Z Z a o Jauay 0 cu- 5 Spi-Obi Iacio This is h iacio bw h spi of h co wih h agic fi ca by h obiig co. This is a aivisic ffc ivovig spi a is sposib fo h fi sucus i aoic spcu. Th fi sucu gy is of h fo: B B o ZB o ZB B ; B 3 3 M 4 4 ao Z Z Z 4o ao Jauay 0 cu- 6 Wh c S P Boh o 37 is h fi sucu cosa. ~ 0.36 c - P 3/ S / P / Fo aos o ocus o soi Th buiig bocks of soi is ach iiviua aos. Fo aos w show how o cacua h gy vs of hyog a h bgiig of his cu. Fo soi h a ypicay 0 3 aos p c 3. So i is o vy pacica o cacua h. W wi show i h foowig wha happs wh w big wo aos cos a h iac wih ach oh. W sa ou wih wo aos a ifii apa. Th is o iacios bw h. Spi-obi iacio Th S / P / gacy is fuh sov a is ca ab shif. Ao A has a Haioia H A a a sa of a Ao B has a Haioia H B a a sa of b. Jauay 0 cu- 7 Jauay 0 cu- 8 Wh hs wo aos a w spaa h oa gy of h cobi sys is jus H = H A + H B Wh wo aos a cos ough h Haioia bcos H = H A + H B + H AB Wh H AB is h Haioia of h iacio Th wavfucio b h ia cobiaio of h oigia sas = c a + c b a H = H = Assu A a B a h sa ao a H a = H = b H b a H b = b H a = a a b = s Th q. o pvious pag ca b sov. Assig # a h souio is giv by: H s A h wavfucio is giv by: a b s 3 So w ca s ha if w sa wih wo iica paics wih h sa gy oc hy sa o iac wih ach oh hi gy a wavfucio wi chag sighy. Jauay 0 cu- 9 Jauay 0 cu- 30 5

6 //0 H a so his o how o obai quaios a 3 fo. Fo quaio w hav: Th boig a ai-boig sas a hi gy vs a H = 0 b H = 0 Subsiu = c a + c b io h abov quaios a us h iiis fi a h of pag 9 w up wih h foowig quaios: H -c + -sc = 0 -sc + H -c = 0 Sovig h abov quaios assuig ha c a c hav o b o-zo wi aiv a quaio of pag 9. Jauay 0 cu- 3 Jauay 0 cu- 3 This is h saig poi fo soi sa physics. Wh w hav 0 aos iacig wih ach ohs. Ba picu sas o g. Cysa Sucu aic Bas a cipoca spac. Coo aic sucus Mi Iics fo Cysa Dicios a Pas Th cipoca aic Jauay 0 cu- 33 Cassificaio A sois a ih sig cysai poy-cysai o aophous pig o hi cysai sas. Sig cysai: gua aic o h who sap. Poycysai: cosiss of ay sig cysais has a gai siz of a fw icos. Aophous: os o hav ay gua aic sucu o fi spaia aioship bw ocaios of aos. Sig cysa Poy-cysa Aophous soi Quasicysa 6

7 //0 Cysa sucu basics Cysa sucu = aic + basis May as hibi coss packig -- quiisioa objcs a aag so o fi spac fficiy Packig fficicy = vou occupi by aos oa vou of h cysa Th vou o occupi by aos is voi spac o vois Th siz of h voi is iica by h ags sph ha ca b fi isi i Th cooiaio ub of a voi is h ub of aos ha iiay suou i aic Basis a Ui C A ia cysai soi is a ifii piio of iica sucua uis i spac. Th pa ui ay b a sig ao o a goup of aos. A ipoa cocp: cysa sucu = aic + basis = + aic: a pioic aay of pois i spac. Th vio suouig ach aic poi is iica. basis: h ao o goup of aos aach o ach aic poi i o ga h cysa sucu. Ths wo choics of aic vcos iusa wo yps of ui cs: ap: a -D aic Th asaioa syy of a aic is giv by h bas vcos o aic vcos a b c. Usuay hs vcos a chos ih: o b h shos possib vcos o o cospo o a high syy ui c b a Covioa cysaogaphic ui c: b ag ha piiiv c; chos o ispay high a syy ui c Piiiv ui c: has iiu vou a coais oy o aic poi 4 Bavais aics i Th Disios 7

8 //0 Coo cysa sucus Fac-c cubic FCC -- ao/aic poi 4 aos p ui c FCC asaios: 000 ½½0 ½0½ 0½½ Coo cysa sucus Boy-c cubic BCC -- ao/aic poi aos p ui c; o a cos-pack sucu covioa ui c spac-fiig o covioa ui c spac-fiig o aps: Cu Ni Au Ag Pb aps: a-f C M Coo cysa sucus Hagoa cos pack HCP -- ao/aic poi aos p ui c Sackig squc i h FCC a HCP sucus covioa ui c spac-fiig o aps: Z Mg B a-ti HCP -- ABABAB FCC -- ABCABC Oh cysa sucus Th iao cysa sucu Th iao cysa sucu is FCC wih a wo-ao basis 000 a FCC asaios ach ao is suou by fou iica as ighbos i a aha aag aps: Si 50 c-3 G a-s goup I s CsC -- vaia o h piiiv cubic Cs+ a 000 C- a ½½½ NaC -- vaia o h fac-c cubic Na+ a 000 C- a ½00 8

9 //0 Th zicb cysa sucu ik iao h zicb sucu is FCC wih a wo-ao basis bu h aos a iff yps ach A-ao is suou by fou B-ao as ighbos i a aha aag Cooy s i soichioic copou sicoucos; GaAs CT ZS Th wüzi sucu igh is a hagoa vaia of h zicb sucu i which h sackig o of h A-B aha is vai aps: GaN CS ZO AgI Th wüzi cysa sucu aic pas a icios. Jus ik ui cs a iica by syy so a icios a pas i a cysa. Cysaogaphic icios a asy: a i passig fo a oigi 000 hough a poi u v w wi hav a icio iica by [uvw] Poi A: cooias Poi B: cooias / 0 i AB: icio [½0] o ca facios: [0] Poi C: cooias 0 0 o i h ui c Poi D: cooias /3 o /3 w/ oigi a C i CD: icio [ /3 ] o ca facios: [33] Spcific icio: [uvw] Faiy of icios: <uvw> Cysaogaphic pas. Pas i a cysa a o i s of h Mi iics which a h cipocas of h facioa icps ha h pas ak wih h cysaogaphic as. If a pa is paa o a ais h icp is ak o b a ifiiy ; h cipoca of ifiiy is / = 0 a b c Th icps 3 Th cipocas /3 / / Th Mi iics /3 / / uipy by Spcific pa: hk Faiy of pas: {hk} Mi iics of coo pas Iics i hagoa sucus. Hagoa syss a copica by h fac ha w wou ik syicay-a pas a icios o hav siia iics. This ca b avia by goig o a 4-i sys: hk hki wh h+k+i=0 9