6.Optical and electronic properties of Low

Transcription

1 6.Optical and lctonic poptis of Low dinsional atials (I). Concpt of Engy Band. Bonding foation in H Molculs Lina cobination of atoic obital (LCAO) Schoding quation:(- i VionV) E find a,a s.t. E is in a a [ ( H) ( H) ( H )] i, E Eb bonding stat ( a a) b A( ) E Ea antibonding stat ( a a) a A( )

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3 Fo bond to band Hybidization in CH 4 olcul (sp3), 3, 4 s p p p s p p p x y z x y z s p p p s p p p x y z x y z Hybidization in Bnzn (sp) Plana stuctu and lcton dlocalization 3

4 Fo two to any Engy bands. Mtal (Li) (N atos intactn lctons N obitals N stats ) lcton/stat 4

5 F lcton odl (V=) E( k) ( k x k y k z ) 4 n k x, k y, k z,,,, L : lattic constant, L L L i( k ) k A n intg. Fi lvl and wokfunction Fi lvl (E f ) fo tal : th highst ngy lvl filld by lctons at K Wokfunction: E vac E sults fo th foation of sufac dipol f with lcton split off 5

6 Poptis of lctons in a band (und lctical fild). Fo tal: F lcton odl: p k E 6

7 Quantu thoy of tals(v(x)=) 5. Fi-Diac Distibution Function Dtin th # of stats that actually contain - Distibution function f( E) E Ef xp( ) kt n total nub of volu - f( E) g( E) de 7

8 Naly f lcton odl (NFE) V(X) A sipl odl. - : a tavling wav in a solid with a wak potntial distubanc. piodic by ionic co Bagg s diffaction Siconducto (Si) :Foation of band gap. A. Intinsic siconducto * Basic concpts:. Band Gap. Elcton affinity lcton ( ), and hol (h ) 8

9 4. Thal and photon gnation 5. Rcobination. Silicon cystal and ngy band diaga: lcton affinity v.s. wokfunction??. Elctons and hols 9

10 Conduction in Siconducto J nv pv d dh v E, v E d x dh h x, h * h * h n p Elcton and Hol concntation h

11 () Intinsic siconducto Fi lvl is in th iddl of V.B and C.B () n typ siconducto Fi lvl is na to C.B n (3) p typ siconducto Fi lvl is na to V.B p By adding ipuity (doping). n-typ n>p (E c -E f )< (E f -E v ). p-pyp p>n (E c -E f )> (E f -E v ) But np=n i (n i dpnds on T, by ass law) B. Extinsic Siconducto N-typ doping dscibd by H-ato odl. Binding ngy: ( E H 4 n = 3.6 V (4 ) If fo Si: dilctic constant fo Si )

12 n, 3.6 Edoping = (4 ) 4 * * * fo Si:.,.9 d E V * G:., d 5 E V Boh adius 4 a H.53 Å 4 dopnt Boh adius: ad.53 * Fo Si ad 3 Å, G ad 8 Å * Å. Doping and ipuity Shallow dono and accpto: Shallow dono/ accpto: th ngy lvl of dono/accpto is na to C.B/V.B asy to totally ionizd shallow dono: Nd Nd, Nd N d totally ionizd shallow accpto: Na Na, Na Na

13 . Dict v.s. indict band gap dict bandgap: E indict bandgap: E (, q phonon) f k f E (consvation of ngy) f f i k i i (consvation of p) E k k q i Optical absoption: 3

14 B s law I I Ix I( x) I xp( x) I x : absoption ocfficint x: distanc whn =/ : pntation dpth Absoption cofficint dpnds on dnsity of stats ge ( ) Optical poptis of low dinsional atials Quantu confinnt ffct Bulk: no quantu ffct Quantu wll: -D quantu confinnt, f donsions Quantu wi: -D quantu confinnt, f donsions Quantu dot: 3-D quantu confinnt, f donsions Bulk concpt of band 3D band stuctu 4

15 3D cystal Wll D band stuctu (-D confinnt, -D f lcton) D Quantu Wll Wi D band stuctu (-D confind, -D f lcton) -D quantu wi 5

16 Dot 3-D confind Q: whn should w consid quantu confinnt ffcts? Ans: Unctainty Pincipls, x p ( px ) p x ~ Econfinnt ~ x ( x) Classical physics: E classical kt fo D diction if E E, confinnt classical x ~ (oughly) k T At oo tpatu,. x = 5 n Us th concpts of infinit Quantu wll E n k n wh d is th thicknss of th wll d D( E) E 3D constant D E D 6

17 7 Exciton Binding ngy and Boh s adius - + h + xciton f xciton V E b. tightly bound xciton V E b. F xciton H x x H n H x x H h a a a n a n R R wh n R n R n n E * * 3.6 GsAs

18 8 kt V R x h ,.,.67 * *

19 Plasonic Nanopaticls Plasons a th oscillations of f lctons which a th consqunc of th foation of a dipol in th atial du to lctoagntic wavs. Th lctons igat in th atial to sto its initial stat; howv, th light wavs a constantly oscillating lading to a constant shift in th dipol, so th lctons a focd to oscillat at th sa fquncy as th light. This coupling only occus whn th fquncy of th light is qual to o lss than th plasa fquncy and is gatst at th plasa fquncy and is thfo calld th sonant fquncy. 9

20 Nanopaticl plasons hav th additional popty of bing dpndnt on thi goty and siz, th scatting and absobanc coss-sctions dscib th intnsity of a givn fquncy to b scattd o absobd Diffnt Gotis (Gold nanoods) Applications:. Sufac-nhancd Raan scatting (SERS) is a phnonon stongly dpndnt on th sufac Plason xcitations of tal nanostuctus. Raan scatting fo vibational bands of a olcul at o na a nanostucutd sufac is gatly nhancd du to xtly high local lctoagntic filds associatd with localizd sufac Plason sonancs. E-ba lithogaphy can b usd to fabicat nanostuctus with contollabl siz and piod. Figu shows gold nanohol aay fabicatd with -ba lithogaphy (lft) and SERS spcta fo nanohol-aays of th sa hol-siz but diffnt hol-spacing with dtction of 4 M 4-captopyidin olculs.

21 SERS by D. Yuh-Lin Wang, IAMS, Acadic Sinica. Plasonic sola clls: (Mtal Nanopaticl Plasonic Sola Cll) A coon dsign is to dposit tal nanopaticls on th top sufac of th thin fil SC. Whn light hits ths tal nanopaticls at thi sufac plason sonanc, th light is scattd in any diffnt dictions. This allows light to tavl along th SC and bounc btwn th substat and th nanopaticls nabling th SC to absob o light.