6 C. Carbon-based materials. Graphene. Graphene applications. Ηλεκτρικές και οπτικές και ιδιότητες γραφενίου

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1 Unvs o Ionnn Dpmn o Mls Sn & nnn Compuonl Mls Sn Cbon-bs mls Ηλεκτρικές και οπτικές και ιδιότητες γραφενίου 6 C los Los Mls Sn & nnn, Unvs o Ionnn, G Gphn Gphn pplons on-om-h pln sh o sp -bon bon oms Pu om:.k. Gm n K.S. Novoslov, Th s o phn, N. M. 6, 8 7

2 Gphn omp hp://phn-lshp.u/wponn/uplos///smplshow_n_gphn_4-646.mp4 Som o phn s opolon pplons G pops o opolons h mobl -opl nspn lbl nvonmnl sbl. onoso, l., N. Phoons 4, 6 Gown phn ow os phn loo l? snl phn l o hnss =.5 nm s vsbl o h n!! h l mosop D l mosop Ims b Slv Mln, Unv. Cmb

3 Cbon: 6 C=s s p, oup IV Gphn om suu obl hbzon sp hbzon: mon sp sp sp hbzon: ph σ bon sp π bon pz sp Gphn lon suu: p z obls Gphn: D honl l wh bss l vos,, ns nhbo vos,,, Shön uon wvunon unnowns h n s unon o nvlu poblm

4 Th-bnn ppoh nvlu poblm Inls n nhbos, ohws = n nhbos, ohws = W om pmn =, ohws = W, om pmn <<, hus w onl ssum hoppn V ˊ. V Th-bnn ppoh nvlu poblm s Soluon o h nvlu poblm os 4os os Gphn bn suu Rlon bwn wvvo momnum n n zo-p smonuo zo p smonuo ln bn ossn, M, K K, K D pon pn oun K-pon K, K n oun K-pon p / 6 m/s 6 m m p 4

5 Msslss D mons Opl pops pl smonuo phn D opl nsons nson m s oln ul M D ħ σ p D ns o ss Tnson m lmn D ns o ss D 4 Chn no n D Th jon ns o ss s DOS ħ/ ħ mlonn wh mnml oupln σ p Vo ponl s unon o l l M lmn σ 6 M ħ D l l s unon o nn pow M I

6 Opl pops Unvsl opl onun D opl nsons nson m s oln ul M D nson m lmn M I D ns o ss ħ Rl p o onuv υ D D υ 4 ħ D bsopon on I Dl onsn 4 Gphn opl nsmsson Gphn opl nsmsson R hn lm lm =.5nm<<... pmnl von o bsopon p l pmns on phn suspn n T... vhn s unon o l unon, n hus o h onun Lh nsmsson n h hn lm lm 4 T Lh lon n h hn lm lm R n suu onsn Lh bsopon = -R-T = πα unvsl bsopon πα p phn l..% N l., Sn, 8 8

5 4.4.... 5 6 l l ls l N=.9 lsl 6 ls l l p pmn ls p ho ls p 6 ls p -. 45 55 65 75 85 95 wvlnh nm nh nm wvln R / R SO hnss nm Csh l., Nno Ls 7, 7 7 J SLG ρ ρ ρ Rlh sn n h lln ρ obsvon pon onn po..8.6 4.

7 Gphn vsbl I phn os no l, how om s vsbl? onl n sp subss u o nn hoos subs wh smll nl lon phn s s hn mml Conon o smll lon: nlon sp hnss = /4 sp n = subs n D l vsbl In l mo, onl h s o phn lh up Numl smulons n ho p hs bhvo / SLG pmnl von ons lv l l ls l N=.9 lsl 6 ls l l p pmn ls p ho ls p 6 ls p wvlnh nm nh nm wvln R / R SO hnss nm Csh l., Nno Ls 7, 7 7 J SLG ρ ρ ρ Rlh sn n h lln ρ obsvon pon onn po I phn SO nl sn.u. on S 6 nm 4 nm num Collon nl Conun n mpu n opn Gphn onun m-d sbuon unon : hml ponl u o opn T: mpu K / T : olzmnn onsn Inbn nsons n h D on n υ D nh nh 8 4T 4T Inbn nsons o s n υ υ 4 4 / T ln osh T / -/ T= T=.5..5 / T.5..5 / [ /4ħ] un Con Th ull spum o phn Vn ov p n UV Unvsl onun n VIS Pul blon u o opn n NIR Du lon onun n IR 4 Phoon n V V.G. Kvs l., Phs. Rv. 8, 554 Z.Q. L l., Nu Phss 4, 5 8 Phoon wvlnh m T= K, V = V, = V T= K, V = V, =.8 V T= K, V =4 V, =.4 V T= K, V =7 V, =.5 V T= K, V = V T= K, V = V T= K, V =4 V T= K, V =7 V

8 l l : opn b n l l : m lvl sh Gphn/o/smonuo ssm Conuo/l/onuo po l ppl b boom n wh vol V Q C V n C V / Th sl pn C / ws msu o phn C So w n us n / m - - nmso/s 7. m V - 7. nm.9 V V : sp hnss : sp l onsn Numb o hs n m lvl T= n 4 sv 4 4 So w n l h m n o opn T= n / C V / n V n CV / n C V / V V Z.Q. L l., Nu Phss 4, 5 8 K.S. Novoslov l., Sn 6, K. Gm n K.S. Novoslov, N. M. 6 7 Z.Q. L l., Nu Phss 4, 5 8 Dopn b on Gphn on b ml wh n m lvl Lol sh o phn s m lvl Con o ll l Sho junon Gphn phooos G. Govnn, l., Phs. Rv. L., 68 8 Gphn s hs Th onun n T ln osh T / hh opn l m n o hml ponl, h onun boms mpu npnn. So w us h T= ppomon: n / Ths s hv n v mss : lon m h / 4 = p =. =.6 =.. =. 4 Tmpu K m m / Th mobl s l o h lon m om h Du omul: m T. Mull l., N. Phoons 4, 97 Tpl mobl vlus m / V s o hh. o =. V w pl vlus o nobl mls 4 s s Gphn v pomsn o IR plsmons!!

9 Gphn plsmon pplons Su Plsmon Polons v plsmons: nmll moul ml plsmon Gphn plsmons: Wvus n us Ch ns osllons oupl wh lh oun o pop lon h ml su Gnl om o ll ls bov h n nsulo wh l unon z z,, / z u J. Chsnsn l., CS Nno 6, 4 In plsmon bosnsn: bo-unonlzon n nm moulon blow h n ml wh l unon z z,, / oun onons Su Plsmon Polon SPP.5 / p.5.5 /. /..5 SPPs J. Km l., Nno L., 5598 J.C. R l., Nno L.,,, V.G. Kvs l., Nu M.,, DOI:.8/NMT / K p Plsmons on phn SPP onons Lh oupl wh D h ns osllons oun o pop lon h phn su W wo n SPP lons Gnl om o ll ls bov phn nsulo wh l unon z,, / z blow phn nsulo wh l unon z z,, / z nsulo phn nsulo pl ml/l SPP pl l/phn/l plsmon ns phn whh hs onun w hv un I oun onons Gnl SPP onon I I / hn usn w lso D l un non V D l un non phn V V

10 Cmpson bwn SPPs on o SPPs.5. /S SPP. /phn/s plsmon Su plsmon polons s blow h lh-on momnum onsvon os no llow on spl s n o hm.5 V..5 Kshmnn Oo TIR V. 4 6 V 5.5. popon lnh.4 / popon lnh / V..5. wv lolzon / SP wv lolzon / SP SNOM Don n Don Zs, Smolnnov n Mun, Phs. Rp. 48, 5 In n on: m, m,,,... Msun phn plsmons J. Chn l., Nu 487, 77 Z. l., Nu 487, 8

Appendix. In the absence of default risk, the benefit of the tax shield due to debt financing by the firm is 1 C E C

Appendix. In the absence of default risk, the benefit of the tax shield due to debt financing by the firm is 1 C E C nx. Dvon o h n wh In h sn o ul sk h n o h x shl u o nnng y h m s s h ol ouon s h num o ssus s h oo nom x s h sonl nom x n s h v x on quy whh s wgh vg o vn n l gns x s. In hs s h o sonl nom xs on h x shl