Photons Và Nguyên Tử

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Photons Và Nguyên Tử

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  • 1

    LI CM T

    Trn thc t khng c s thnh cng no m khng gn lin vi nhng s h tr, gip

    d t hay nhiu, d trc tip hay gin tip ca ngi khc. Trong sut thi gian t khi bt

    u hc tp ging ng i hc n nay, em nhn c rt nhiu s quan tm, gip

    ca qu Thy C, gia nh v bn b.

    Vi lng bit n su sc nht, em xin gi n qu Thy C Khoa Khoa Khoa Hc Vt

    Liu Trng i Hc Khoa Hc T Nhin cng vi tri thc v tm huyt ca mnh

    truyn t vn kin thc qu bu cho chng em trong sut thi gian hc tp ti trng.

    V c bit nht, em xin chn thnh cm n thy Ng Hi ng, Trng PTN Tng hp

    Vt liu Mng mng, ngi tn tnh du dt v cung cp nhng kin thc quan trng

    em hon thnh tt Tiu Lun ny.

    Xin gi li cm n n ba m, Ngi l ch da tinh thn, l ng lc gip con ni

    nhng bc di trn con ng thnh cng. Ngn li cm n Ngi.

    Cui cng, xin chc tt c mi ngi u mnh khe, hnh phc.

    Tp. HCM, ngy 8 thng 11 nm 2013

    Sinh vin thc hin

    Lm Vn K

  • 2

    MC LC

    Li Cm T ................................................................................................................... 1

    Mc Lc ......................................................................................................................... 2

    Danh Mc Hnh nh .................................................................................................... 4

    Li m u .................................................................................................................... 5

    13.1 Cc mc nng lng ............................................................................................. 6

    A.Nguyn t ............................................................................................................... 7

    Hydrogen ................................................................................................................. 8

    Cc nguyn t a in t ......................................................................................... 10

    B.Phn t .................................................................................................................... 14

    Phn t quay hai nguyn t .................................................................................... 15

    Dao ng phn t hai nguyn t ............................................................................ 16

    Dao ng phn t ba nguyn t .............................................................................. 16

    Phn t nhm .......................................................................................................... 17

    C.Cht rn .................................................................................................................. 18

    Mi trng pha tp in mi .................................................................................. 22

    Cht kch thch kim loi chuyn tip ion ............................................................ 23

    Cht bn dn ............................................................................................................ 25

    Nhng khi bn dn ........................................................................................... 25

    Dy lng t ....................................................................................................... 26

    Chm lng t v ging lng t ....................................................................... 27

    13.2 S chim ch ca cc mc nng lng ............................................................... 29

  • 3

    Phn b Boltzmann lng t .................................................................................... 29

    Thng k Fermi-Dirac .............................................................................................. 30

    13.3 Tng tc ca Photon vi nguyn t .................................................................... 31

    A.Tng tc ca nh sng n mole vi nguyn t ............................................ 31

    Bc x t pht .................................................................................................... 31

    Qu trnh hp th ............................................................................................... 32

    Bc x cng bc .............................................................................................. 33

    The lineshape function ....................................................................................... 34

    B.Bc x t pht ..................................................................................................... 34

    Tng bc x t pht vo tt c cc mode .......................................................... 34

    Lin h gia mt ph khi lng v thi gian sng ..................................... 35

    C.Bc x cng bc v hp th ............................................................................ 35

    Qu trnh chuyn tip cm ng bi nh sng n sc ....................................... 35

    Ti Liu Tham Kho ...................................................................................................... 37

  • 4

    DANH MC HNH NH

    Hnh 13.1-1: M hnh nguyn t, obital nguyn t ........................................................... 7

    Hnh 13.1-2: Nguyn t hidro ........................................................................................... 8

    Hnh 13.1-3 : Mc nng lng ca kh hydro .................................................................. 9

    Hnh 13.1-4: Cu hnh cho trng thi c bn ca He ........................................................ 11

    Hnh 13,1-5 : Mc nng lng ca nguyn t He v Ne .................................................. 12

    Hnh 13.1-6 :Bng tun hon cc nguyn t ..................................................................... 13

    Hnh 13.1-7: Cc vng nh sng theo bc song .............................................................. 14

    Hnh 13.1-8: M hnh phn t quay hai nguyn t ........................................................... 15

    Hnh 13,1-9: Mc nng lng dao ng thp nht ca phn t N2 v CO2 .................... 17

    Hnh 13.1-10: Cu trc ca Rhodamine-60 lon................................................................. 18

    Hnh 13.1-11: M rng cc mc nng lng ring bit ca mt nguyn t b c lp vo

    vng nng lng khi nguyn t gn thnh cht rn .......................................................... 21

    Hnh 13.1-12: Cu trc GaAs bn dn .............................................................................. 26

    Hnh 13.1-13: Kch thc ht CdSe .................................................................................. 29

    Hnh 13.3-14: Nguyn t chuyn t trng thi kch thch c nng lng E2 v trng thi

    c bn c nng lng E1, pht ra photon c nng lng h =E2-E1 ................................. 32

    Hnh 13.3-15: Sau khi hp th photon, nguyn t chuyn ln trng thi kch thch ......... 32

  • 5

    Li m u

    Mc ch ca chng ny l gii thiu nh lut chi phi s tng tc ca nh

    sng vi vt cht. Cc nh lut ny gii thch cho tnh cht laser, nhit, v nh sng pht

    quang ca nh sng.

    Chng ny bt u vi mt nh gi ngn gn v cc mc nng lng chung kt

    hp vi cc loi khc nhau ca vt cht (13.1), v s chim ng ca cc mc nng

    lng (13.2). Trong (13.3), chng ta tm hiu v s hp th v pht x ca cc photon bi

    mt nguyn t.

  • 6

    13.1 Cc mc nng lng

    Cc nguyn t ca vt cht c th tn ti trong s c lp tng i, nh trong

    trng hp ca mt nguyn t cht kh long, hoc chng c th tng tc, kt hp vi

    cc nguyn t ln cn to thnh phn t, cht lng v cht rn. Cc thnh phn ca vt

    cht tun theo nguyn l ca c hc lng t.

    Mt ht c khi lng m (VD: mt electron), th nng V (r, t), c biu din bi

    mt hm sng (r, t) tha mn phng trnh Schrodinger:

    22 ( , )( , ) ( , ) ( , )

    2

    r tr t V r t r t j

    m t

    (13.1-1)

    Th nng c trng cho mi trng ca ht, trong c ng gp t cc lnh vc

    quang hc bn ngoi p dng. Phng trnh vi phn tng phn biu din trong (13,1-1)

    ty thuc vo V (r, t). H bao gm nhiu ht nh chng hn nh cc nguyn t, phn t,

    cc cht lng v cht rn, tun theo mt phng trnh khc phc tp hn, trong th

    nng l s cc tng tc gia cc ht.

    Cc tin ca c hc lng t xc nh rng xc sut tm thy ht bn trong mt

    lng dV tng theo cc v tr r, trong khong thi gian gia t v t + dt, l:

    p(r, t) dV dt = | (r, t)2| dV dt. (13.1-2)

    Phng trnh (13,1-2) cho bit xc sut tm thy mt photon trong mt vng theo

    thi gian. Trong trng hp khng ph thuc vo thi gian, cc mc nng lng cho

    php E ca ht c xc nh bng cch s dng k thut tch bin. iu ny dn n

    (r, t) = (r) exp[j(E/ ) t], trong (r) tha mn phng trnh Schrodinger:

    2

    2 ( ) ( () ( )2

    )r V r E rrm

    (13.1-3)

  • 7

    Phng trnh (13,1-3), tng t nh phng trnh Helmholtz (2,2-7), c th c coi nh

    mt gi tr c trng m cc gi tr cho php ca nng lng E l gi tr ring, trong khi

    (r) l hm sng ring

    H gm nhiu ht tun theo phng trnh (13,1-3). Nhng gi tr ny c th l ri rc

    (nh i vi mt nguyn t), hoc lin tc (nh i vi mt ht t do), S c mt ca

    nhit kch thch hoc mt yu t bn ngoi, chng hn nh nh sng chiu ti, c th lm

    h thay i mt trong cc mc nng lng ca n. Bng cc hot ng ny m h trao i

    nng lng vi mi trng bn ngoi.

    Trong cc phn sau, chng ta s s minh ha cu trc mc nng lng in hnh cho

    cc nguyn t, phn t, v cht rn.

    A. Nguyn t

    Mc nng lng ca nguyn t c hnh thnh bi th nng ca cc electron vi ht

    nhn nguyn t v cc electron khc, cng nh cc lc lin quan n Obital v cc xung

    lng spin, hnh (13.1-1)thng l yu hn nhiu so vi tng tc in.

    Hnh 13.1-1: m hnh nguyn t, obital nguyn t

  • 8

    Hnh 13.1-2: nguyn t

    hidro

    Hydrogen

    Mc nng lng ca mt nguyn t ging hydro

    (hnh. 13.1-2) bao gm:

    Ht nhn tch in +Ze

    Electron tch in e, khi lng m

    Z (s nguyn t) c xc nh bng cch p th

    Coulomb, V(r)=-Ze2/r, khng ph thuc vo thi gian

    phng trnh Schrodinger (13,1-3).

    Khi V(r) l mt hm th nng xuyn tm c lp, ton t Laplace

    Hnh13.1-2 c th c vit trong ta cu, phng trnh chia tch thnh ba

    phng trnh vi phn thng thng thng qua tch bin. iu ny cho php chng ta gii

    quyt vn gi tr ring. Cc gi tr ring bao gm mt v hn s mc nng lng ri

    rc vi cc gi tr

    ( 13.1-4)

    trong gim khi lng ca nguyn t Mr thay th khi lng electron m cha khi

    lng hu hn ca ht nhn. Cc mc nng lng trong (13,1-4), c c trng bi mt

    s lng t n c gi l s lng t chnh, c hin th trong hnh. (13,1-3) cho H v

    C5+

    . Cc mc cng c th thu c bng cch cn bng lc Coulomb thu ht lc ly tm

    cn thit gi cc electron trong mt qu o trn,

  • 9

    Hnh 13.1-3 : mc nng lng

    ca kh hydro (Z = 1; trc tung

    tri) v C 5+

    (a hydrogen-like

    atom with Z = 6; trc tung phi).

    Qu trnh n=3 n n =2, c

    ch dn bi mi tn, tng ng

    vi C 5+ chuyn trng thi laser

    cc-t ngoi 18,2 nm. Ti mc

    nng lng zero bt k c di

    trng vi mc n = 1.

    trong khi gi nh rng cc xung lng gc qu o electron l lng t ha bi s

    nguyn ca . Bn knh ca cc qu o Bohr 2 2 20(4 ) n / , 1,2,3,...nr e mZe n ; bn

    knh ca qu o n=1 c k hiu r1 . y l c s ca l thuyt Bohr , l mt phn

    ca " l thuyt lng t c . "

    Cc hm ring ca phng trnh Schrodinger ly t cc kt qu ca ba hm

    lm( , , ) ( ) ( ) ( )nlm nl mr R r , trong n=1 , 2, 3, . . . c gi l s lng t chnh; l

    = 0, 1, 2, 3, , n-1 c gi l s lng t xung lng; v m = 0, 1, 2, , l c

    gi l s lng t t . Trong , Rnl( r ) i din cho hm Laguerre (quan cht ch n a

    thc Laguerre tng qut c tho lun trong cc ch thch trn trang 98 ) , lm ( ) l

    hm Legendre, v ( )m l hm pha.. Kt hp spin ni ti ca in t i hi mt s

    lng t khc gi l s lng t spin: s =

    . S tng tc ca cc spin ca electron vi

    xung lng gc qu o ca n, c gi l s tng tc spin- qu o, dng phn

    chia cc mc nng lng vo khng gian xp cht.

  • 10

    Cc nguyn t a in t

    Nguyn t a in t bao gm mt ht nhn c in tch +Ze bao quanh bi Z

    electron, mi electron tch in -e . Cc mc nng lng ca cc nguyn t a in t c

    th c xc nh bng cch s dng l thuyt ca Schrodinger , min l thay i tng

    i c th c b qua (ngha l ch p dng cho cc nguyn t nh nht ) . V v s

    tng tc Coulomb gia cc electron , gii gn ng phng trnh Schrodinger gi l "

    phng php Hartree . "

    Mi in t c coi l di chuyn mt cch c lp vi nhau thnh m hnh cu

    v cn bng th nng V(r). Theo cc gi nh , cc phng trnh Schrodinger Z-electron

    phn chia thnh Z phng trnh Schrodinger ca mi electron vi mt hm ring tng

    th l mt phn ca hm ring mi electron, v mt tng nng lng l tng ca cc

    ngun nng lng ca cc in t. Cu. Kt qu cc hm ring n in t c biu din

    ging vi nguyn t hydro.

    Mi in t chim ng v tr tun theo nguyn l loi tr Pauli. V nguyn tc,

    quy nh rng khng c hai electron c th c cng bn s lng t. Cc spin in vo

    obital ( theo ch nh ca s lng t chnh n ), biu din c th cc in t .Trong mi

    shell, subshells c xc nh bi cc cp s lng t nl , trong l thng c quy

    nh trong k hiu quang ph ( cc ch s, p, d , f, g , h, i tng ng vi l = 0 , 1, 2 , 3, 4 ,

    5, 6 , tng ng) . Cu hnh electron nlu c trng cho s s sp xp ca cc electron

    trong subshells ; u cho bit s in t hin din trong mi nguyn t.

  • 11

    1s2 1s

    2 2s

    2 2p

    6

    Hnh 13.1-4:(a)cu hnh cho trng thi c bn ca He ( Z = 2) l 1s2, hai electron ca

    n ch cn in n=1 shell ( l = 0). (b) Ne ( Z = 10), trng thi c bn cu hnh l ls2

    2s22p

    6 , 10 electron ch cn n = 1 v n = 2 shell

    Mi cu hnh electron bao gm nhiu mc nng lng xp gn nhau, c gi l a

    manifold, nh biu din trong s hnh. 13,1-4 cho Ne. Chng c gii thiu ch yu

    bi s tng tc spin- qu o, l s tng tc gia tng cc spin v tng xung lng

    gc qu o ca cc nguyn t.. Lin kt ny, c gi l lin kt Russell- Saunders (

    hoc lien kt LS ), ng cho cc nguyn t nng nht . i vi cu hnh electron, cc

    nguyn t khc nhau xung lng gc c tm tt bi k hiu 2+1f , trong l tng

    xung lng gc ca s lng t spin; 2+1 l a spin (v d , singlet, trilet ) ; l tng s

    lng t xung lng gc ca qu o, (ch hoa S , P , D, F , ... i din cho = 0, 1, 2, 3,

    ... , tng ng) , v f l tng s lng t xung lng gc. K hiu mt nguyn t hoc

    ion thng c cung cp ngay sau cu hnh electron. V d, cu hnh thp nht trng

    thi single v triplet ca He c k hiu 1s2s1S0 v 1s2s3S1 , tng ng, nh th hin

    trong hnh (13,1-4). Khi tt c subshells u c in y ( ging trng thi c bn ca

    tt c cc kh him cng vi mt s cc nguyn t khc nh Ca, Cd , Yb , v Hg ), k hiu

    l 1S0

  • 12

    Hnh 13,1-5 : mc nng lng ca nguyn t He v Ne. (cu hnh electron cho nguyn t

    Ne, 1s2 2s

    2, tng ng vi subshells y). Qu trnh chuyn i Ne c nh du bng

    mi tn tng ng vi bc sng 3,39 m v 632,8 m, nh c ch ra. S chuyn i

    ny, nm trong vng hng ngoi v c th nhn thy ca quang ph, tng ng, thng

    c s dng trong laser He-Ne (xem Secs. 14.3E v 15.30).

    Gi tr n cng ln, lc Coulomb ca cc electron vi ht nhn cng yu. Cc lp

    theo th t n = 1 , 2 , 3, 4 , . . .. Tng t nh vy , gi tr l cng ln, cc electron cng

    dn dch chuyn ra xa ht nhn. Do , subshells thng in vo lp s , p , d, f , . . ..

    Nh mt h qu ca cc qu trnh thc hin k tip. Hng k tip ca bng tng ng vi

    gi tr lin tip ca s lng t chnh n . Mi ct ca bng cha cc nguyn t c th cht

    v tnh cht ha hc tng ng nht nh vi nhau v chng c cha cng mt s

    electron trong v ngoi cng (electron ha tr ) .

    Ct VIII , v d, bao gm cc kh him , bao gm c He v Ne ,l nhng nguyn t

    n nguyn t v tr ha hc bi v h lp y lp v bn ngoi

    Ct I v VII , ngc li, bao gm cc nguyn t c hot ng ha hc mnh

    nht,v d dng hnh thnh cc phn t . Mi nguyn t kim loi kim trong ct I, cha

  • 13

    mt in t bn ngoi duy nht n s d dng chia s vi bt k nguyn t halogen gn

    trong ct VII , nhng nguyn t nhu cu ch mt in t t trng thi bn vng

    Hnh 13.1-6 :Bng tun hon cc nguyn t , vi k hiu ca nguyn t v s nguyn t

    Z . Hng k tip ca bng bao gm cc nguyn t c electron ha tr c s lng t

    chnh n ch nh bi cc s rp bn tri. Mi ct ca bng, xc nh bi mt tn gi

    La M - ch s truyn thng, bao gm cc yu t c tnh cht vt l v ha hc tng t .

    nguyn t th kh, cht lng v cc cht rn nhit phng c th hin trong mu

    xanh , vng, v bc , tng ng .

    mc nng lng [Tuy nhin , cng thc nng lng tng t nh ( 13,1-4 )ch tn ti i

    vi cc electron hot ng quang hc nh cc electron ha tr trong nguyn t kim ] .

    Mc d qu trnh chuyn i quang thng ch lin quan n in t ha tr , s a dng

    ca cc mc nng lng ln lt lm to ra c nhiu s khc bit nng lng , nhiu

    trong s nh bc sng tia laser (xem Secs . 14.3E v 15.3D ) . S khc bit gia cc

    mc nng lng nguyn t kch thch ca Ne hin th trong hnh . 13,1-4 , v d, nm ch

    yu vng hng ngoi v nh sang nhn thy ca quang ph.

  • 14

    B. Phn t

    Cc phn t c hnh thnh bi s kt hp ca hai hay nhiu nguyn t . Mc

    nng lng phn t c xc nh mt phn bi cc ngun nng lng th nng kt hp

    vi cc lc gia cc nguyn t lin kt cc nguyn t . Mt phn t hnh thnh khi c

    s gp mt ca cc electron ha tr ca cc nguyn t lm gim tng nng lng. Hai

    loi chnh ca lin kt phn t l lin kt ion v lin kt cng ha tr. i vi cc lin

    kt ion (nh HF), vng in tch dng v m vn cn c vng khng gian tch ri

    xut hin mt momen lng cc in ca phn t. i vi cc phn t lin kt cng ha

    tr ( nh H2 ) , cc nguyn t s tham gia v gp y in t to ra cc kt qu l

    khng c momen lng cc. i vi ht nhn khc nhau , cc lin kt c th l mt phn

    ion v mt phn kt cng ha tr ( v d: NH4Cl). Cc hnh thc lin kt ng mt vai tr

    quan trng trong vic xc nh cu trc mc nng ca phn t . Cc mc nng lng ca

    mt phn t pht sinh t ba tng tc ring bit , v c qu trnh chuyn i trong vng

    bc sng khc nhau : qu trnh chuyn i lun phin nm trong l vi sng v hng

    ngoi xa , qu trnh chuyn i dao ng nm trong vng hng ngoi , v chuyn tip

    in t nm trong vng nhn thy v tia cc tm. Hnh 13.1-6

    Hnh 13.1-7: cc vng nh sng theo bc sng

  • 15

    Phn t quay hai nguyn t

    S quay ca mt phn t hai nguyn t vi momen qun tnh J so vi tm, c th

    c coi nh vng quay ca mt cnh qut v mt trc vung gc vi trc ca n,( hnh

    13.1-7). Nng lng quay c in cho mt h thng nh vy l E == L2/2J, trong L l

    momen ng lng ca h thng v trc quay.do ,Theo c hc lng t, cng

    ca xung lng gc ca mt h thng nh vy c lng t ha theo L2 = ( + 1)2 ,

    trong l s lng t quay. Cc mc nng lng cho php ca phn t quay hai

    nguyn t l:

    21 ( 1) ,2

    EJ

    = 0, 1, 2, 3(13.1-5)

    Nng lng ca cc mc nng lng quay thng nm trong khong 10- 4 -10-2

    eV, tng ng vi cc photon trong l vi sng v hng ngoi xa khu vc ca quang ph.

    Khong cch nng lng gia cc mc nng lng lun phin lin tip tng vi s gia

    tng s lng t , tri ngc vi khong cch gia cc mc nng lng in t k tip

    ca nguyn t hydro, m gim vi s gia tng s lng t theo (13,1-4). Phn t hai

    nguyn t vi

    ht nhn ging

    ht nhau (nh

    N2 ) khng

    Hnh 13.1-7

    c men lng

    cc in; do

    khng th

    hin ph quay

    Hnh 13.1-8: m hnh phn t quay hai nguyn t

  • 16

    hon chnh.

    Dao ng phn t hai nguyn t

    Nhng dao ng ca mt phn t hai nguyn t (nh N 2, CO, hoc HCI) do gia

    cc phn t b ht bi lc n hi, lc ny t l thun vi vic tng khong cch lin ht

    nhn x, hnh 13.1-8. H ny c th c m hnh ha nh hai khi M1 v M2,vi khi

    lng rt gn M = M1M2 / (M1 + M2).

    Th nng l 21

    ( )2

    V x x , trong k l hng s lc. Do dao ng phn t c

    cc mc nng lng ca mt dao ng iu ha c hc lng t.

    Hnh 13.1-8 Cc mc nng lng c lng

    t ha theo:

    1( )

    2E , = o, 1, 2, 3, (13.1-6)

    trong / M l tn s gc dao ng v 1

    2 l nng lng ban u. Gi tr ca

    cho dao ng phn t nm trong khong 0,05-0,5 eV, tng ng vi vng hng

    ngoi ca quang ph.

    Dao ng phn t ba nguyn t

    Mt phn t ba nguyn t c tm quan trng ln trong lng t nh sng l carbon

    dioxide , bi v n nh l mt mi trng laser rt hu ch .

  • 17

    Hnh 13,1-9: mc nng lng dao ng thp nht ca phn t N2 v CO2 (nng lng

    ban u chn ti = 0). Qu trnh bin i c ch dn bi cc mi tn i din cho s

    trao i nng lng gia cc dng khc nhau, tng ng vi 0 = 10,6 m v 0 = 9. 6

    m. S chuyn i ny c s dng trong laser CO2 (xem n. 14.3E v I5.3D). Mi

    mc dao ng ca CO2 c nhiu mc nng lng quay

    V n bao gm ba nguyn t l tuyn tnh, cc phn t CO2 c th dao ng c

    lp ba kiu ( nh minh ha trong hnh. 13,1-9): bt i xng Ko di(AS), i xng ko

    di (SS), v un (B). Mi phng bnh thng c cc c tnh ca mt lng t dao ng

    iu ha, vi ngun khng i ca ring n v do gi tr ring ca . Cc mc nng

    lng cho php ca phn t l nh vy, c trng bi mt trong ba iu kin, mi

    kiu(13,1-6), tng ng vi ba s lng t (1,2, 3) c trng cho dao ng (xem hnh.

    13,1-9). Nh vi phn t hai nguyn t, mi mc dao ng c chia thnh nhiu mc

    lun phin nhau cht ch, m nng lng c cung cp xp x (13,1-5).

    Phn t nhum

    Thuc nhum hu c l cc phn t ln v phc tp. Kt qu l, n c th l qu

    trnh, dao ng, v quay, v thng c mt lot cc mc nng lng. Mc tn ti

  • 18

    trong c hai trng thi singlet(S) v triplet(T) (xem Sec. 13.1 A). trng thi singlet u

    c mt electron b kch thch m spin nm bt song song vi cc phn cn li ca phn t

    thuc nhum; trng thi triplet c spin song song.

    S khc bit gia cc mc nng lng tng ng vi bc sng vng nh sng

    nhn thy v vng cc tm. Hnh 13,1-5 l mt minh ho s ca mt phn ca c cu

    mc nng lng cho Rhodamine-6G, n s tr thnh mt ion khi ha tan trong mt dung

    mi nh nc hoc ru. Thuc nhum c bit ny i khi c s dng nh mt

    phng tin pht laser trong khu vc mu vng ca quang ph. (Laser nhum hu c

    c trnh by ngn gn trong Sec. 15.3C.)

    C. Cht rn

    Cc phn t ( hay nguyn t ) ca cc cht rn nm gn nhau v thng hp li thnh 1

    cch sp xp tun hon bao gm mt mng tinh th. ln ca cc lc gi cc nguyn t

    vi nhau l xp x cng ln nh cc lc lin kt cc nguyn t thnh cc phn t . Do

    , cc mc nng lng ca cc cht rn c xc nh khng ch bi th kt hp vi cc

    nguyn t ring l , m cn bi nhng th lin quan n nguyn t mng ln cn. Cht

    rn Noncrystalline , chng hn nh knh v nha, c cu trc c trt t nh nhng tinh

    th , nhng trong mt phm vi ngn .

  • 19

    Hnh 13.1-10: Cu trc ca Rhodamine-60 lon, trong c cc cng thc ha hc

    C28H31N203+ .Bn tri l mt minh ho s ca mt chuyn trng thi laser gia hai a

    tp lt vi cu hnh hi khc nhau, nh c ch ra ng ngang ca chng b p. Mc

    nng lng rung ng v quay c i din bi cc ng dy v mng, tng ng.

    Ba loi lai lin kt chnh thng gp : ion , cng ha tr, v kim loi. Cht rn ion ( nh

    CaF2 ) bao gm mt mng tinh th ca cc ion dng v m vi hnh cu v kn i

    xng. V khng c cc electron t do mang dng in, cc vt liu ny l cht cch in .

    Chng ni chung l trong sut trong vng nhn ph kh kin v nng lng vng cm ca

    chng thng nm trong vng t ngoi. Nhng cht rn lin kt cng ha tr , nh cc

    phn t hp cht lin kt ha tr, bao gm cc nguyn t b lin kt bng cch gp cc

    electron ha tr . Chng thng l cht cch in v c th trong sut ( nh kim cng )

    hoc c ( nh than ch ) trong vng nhn thy c . Cht rn kt cng ha tr c th l

    cht bn dn ( GaAs nh vy) , m m trong vng nhn thy v trong sut trong vng

    hng ngoi. Cht rn bng kim loi c cc electron ha tr v tt c c dng chung bi

    tt c cc ion dng , v di chuyn trong th ca chng . Kh nng ca cc electron

    thay i v tr theo mun thng qua tinh th kim loi chu nhim v v tnh dn in cao

    ca chng . Kim loi mnh phn chiu nh sng v c trong vng nhn thy .

    N cung cp d liu kim tra xem cc mc nng lng ca mt nguyn t b c lp

    c thay i nh n tip xc gn vi cc nguyn t ln cn trong qu trnh hnh thnh

    mt mng tinh th. Cc nguyn t b c lp v phn t (v d , nhng trong kh ) c

    biu hin mc nng lng ring ( xem hnh 13.1-1-13.1-5 ) . Mi nguyn t ring l

    trong mt tp hp nh vy cc nguyn t b c lp ng nht c mt b ng nht ca

    cc mc nng lng ring . V cc nguyn t mang trng thi gn mt cht rn , tng

    tc trao i (Xut pht t yu cu c hc lng t ca indistinguishability cho ht ng

    nht) , song song vi s hin din ca trng mnh khc nhaut cc nguyn t ln cn ,

    tr nn cng quan trng . Cc mc nng lng ban u sc nt kt hp vi cc electron

  • 20

    ha tr ca cc nguyn t b c lp dn dn m rng thnh tp hp ca nhiu mc nng

    lng khong cch ng hnh thnh vng nng lng . Qu trnh ny c minh ha

    trong hnh 13.1-6 , ni m mc nng lng electron c minh ha bng s cho hai

    nguyn t b c lp ( a) , mt phn t c cha hai nguyn t nh vy ( b ) , v cho mt

    mng ID th s bao gm nm nguyn t nh vy ( c ) . Cc mc nng lng thp nht ,

    vng vn cn sc nt bi v cc electron trong cc phn v bn trong c bo v khi

    nh hng ca cc nguyn t gn trong khi cc mc nng lng sc nt kt hp vi

    cc electron nguyn t bn ngoi tr thnh vn giao thoa nh cc nguyn t tham gia ln

    cn.

    Hnh ny c b sung trong hnh 13.1-7 , s so snh cc mc nng lng ca mt

    nguyn t b c lp v ba loi khc nhau ca cc cht rn bao gm mng tinh th ca

    nguyn t nh : kim loi , cht bn dn, v mt cht cch in . Cc mc nng lng thp

    nht ca nhng cht rn ny , biu hin bng cc cu hnh electron 1s , 2s v 2p, ging

    nh ca cc nguyn t b c lp v cc in t bn trong c bo v t cc lc lin

    nguyn t. Ngc li, cc ngun nng lng ring cao hn ca cc electron ha tr

    nguyn t , k hiu l 3s v 3p , c chia thnh vng nng lng dy c trong cc cht

    rn . Mc thp nht vng trng(vng khng b chim), hoc mt phn b chim, vng

    nng lng c gi l vng dn trong khi vng nng lng hon ton b chim cao nht

    nm c bit n nh vng ha tr . Hai vng ny c ngn cch bi vng cm , vi

    mt mc nng lng E 9 c gi l nng lng vng cm (bandgap) . Nh vi cc

    electron trong nguyn t ring bit , nguyn l loi tr Pauli p dng cho cc in t

    electron trong cht rn cc vng nng lng thp nht l vng ang b chim u tin .

  • 21

    Hnh 13.1-11 M rng cc mc nng lng ring bit ca mt nguyn t b c lp vo

    vng nng lng khi nguyn t gn thnh cht rn. y cc vng ang b chim gi

    l bng ti, cc vng khng b chim gi bng sng, v mt phn vng b chim gi u

    bng ti v bng sng. Vng cm c hin th nh mu trng. Gi tr tiu biu ca kim

    loi dn in, cht bn dn, v cch in l 108 (-m)-1, 1 - 4 -105 (-m)-1, v 10- 10 (-

    m)-1, tng ng, nhit phng.

    Kim loi c mt phn vng dn b chim gi mi nhit (nh sng v khu vc bng

    m trong hnh 13.1-7). S sn c ca nhiu trng thi khng b chim gi trong vng ny

    l nhim v v tnh dn in cao ca chng. Kim loi gm cc cc nguyn t u th ln

    trong bng tun hon (xem hnh 13.1-3). Cht bn kim loi, mt khc, chng cho ha

    tr v vng dn.

    Cht bn dn bn trong c mt vng ha tr b chim ng (bng ti) v mt vng dn

    khng b chim ng (bng sng) ti T = 0 K. V khng c trng thi t do c sn trong

    vng ha tr, v khng c cc electron trong vng dn, dn in ca mt cht bn dn

    bn trong l tng l khng ti T = 0 0 K. Khi nhit ca cht bn dn tng ln trn

    khng tuyt i, mt s lng ngy cng tng ca cc electron t vng ha tr thu

  • 22

    c nng lng nhit vo vng dn, v do gp phn vo s dn in ca vt

    liu.

    Cht cch in cng c mt vng ha tr hon ton b chim gi v mt vng dn khng

    b chim gi. Chng c phn bit vi cc cht bn dn bi nng lng bandgap ca

    ln hn (thng l Eg > 3 e V). V d, nng lng bandgap cho silicon (mt cht bn dn)

    l Eg 1,1 eV trong khi i vi kim cng (mt cht cch in) c Eg 5,5 eV.

    Mt vi electron trong cch in c nng lng nhit cn thit vt qua nhng nng

    lng bandgap v ng gp vo s dn in ca vt liu. N s c ch ra, tuy nhin,

    cc vn nh mc ca vng chng cho ng mt vai tr trong vic xc nh mt

    vt liu l mt kim loi, cht bn dn, hoc cch in.

    Vt liu trng thi rn ng mt lot cc vai tr quan trng trong lng t nh sng. Kim

    loi phn chiu cao trong vng kh kin v vng hng ngoi ca quang ph, chng

    thng c s dng ch to cc thnh phn quang hc nh gng. Nhiu loi khuch

    i laser v laser da trn vt liu in mi pha tp. Cht bn dn pha tp, trong cc dng

    lin kt p-n, heterostructures, v ging lng t, cng c s dng rng ri nh l tia

    laser v detectors.

    Chng ti tin hnh kim tra cc mc nng lng ca mt biu din mi trng pha tp

    in mi v vt liu bn dn c s dng nh hot ng ca laser.

    Mi trng Pha tp in mi

    Cht rn lin kt ion hoc cng ha tr c cch in v trong sut trong mt vng ring

    bit ca quang ph c gi l mi trng in mi trong sut . Vi iu kin l chng

    c tnh cht quang hc , nhit v c hc thch hp , nhng vt liu ny thng dng ch

    yu cho cc tia laser ion hot ng . Cc tnh cht quang hc ca cc cc vt liu chnh

    ny c xem xt trong Sec. 5.5C trong hon cnh ca m hnh dao ng Lorentz . Mc

  • 23

    d m hnh ny l c in , n l thch hp cho c trng cho vt liu chnh t cc vt

    liu trong sut trong vng c bc sng quan tm ( cng hng ca n nm bn ngoi

    khu vc ). Cng hng ca cc cht kch thch ion , ngc li, phi c thit lp

    thng qua cc tnh ton c hc lng t , hay nh l thng xuyn hn cc trng hp

    trn thc tin, theo kinh nghim . Kim loi chuyn tip v nhm Lantan ion kim loi l

    nhng cht ph gia ph bin nht.

    ln m cc mc nng lng ca cc ion tia laser hot ng b nh hng bi mi

    trng chnh c xc nh ch yu bi s chuyn ng quang hc ca chng c bo

    v t cc nguyn t mng ln cn. N s tr nn r rng rng mc nng lng ca cc

    ion kim loi chuyn tip c thay i ng k do tc ng trng-tinh th trong khi

    nhng ion nhm Lantan - kim loi ( t him ) kh b nh hng . Bng mt v d ,

    chng ta xem xt cc mc nng lng ca bn h thng tia laser c nhiu ngi bit

    n : Cr3+ : AI2O3 ( ruby ) , Cr3+

    : BeAI2O4 ( alexandrite ) , Nd3+

    : Y3AI5O12( Nd3+

    : YAG

    ) , v Nd3+

    : glass .

    Cht kch thch kim loi chuyn tip ion .

    Thng c s dng nht cht kch thch kim loi chuyn tip ion cho laser l Cr3+ v

    Ti3+

    . Cc cu hnh electron v s hng biu tng nhng yu t ny , v cc ion ha tr

    ba ca chng , c cung cp trong Bng 13.1-1 . Ni2+ v Co2+ cng thng c s

    dng nh l cht ph gia .

    Chng ti xem xt cc mc nng lng ca hai mi trng pha tp in mi vi Cr3+ , c

    th l ruby v alexandrite (Hnh 13.1-8 ) . Ruby c t chc bi v n c s dng

    lm cho laser u tin , trong khi alexandrite nhn c s ch ng k v u ra

    cng sut ca n l mt dy iu hng c trn mt lot cc bc sng . Cc mc

    nng lng ca Ti : sapphire , mt vt liu laser chuyn tip -ion quan trng , s c

    xem xt trong Sec. 15.3A .

  • 24

    Ruby ( Cr 3+

    : AI2 O3 ) l oxit crom nhm . N l mt mi trng in mi vi ch s

    khc x n 1,76 c lp ch yu ca sapphire ( Al2 O3 , cng c gi l oxit nhm ,

    nhm, v corundum ) , trong mt phn nh ca cc ion Al3+ ( ~0,05%) c thay th

    bng ion Cr3+ . Alexandrite ( Cr 3+ : BeAI2O4 ) l hnh thnh bng cch pha mt lng

    nh oxit crom ( rv 0,1% ) vo mt chrysobery ( BeA1 2 0 4 ) . Ti liu ny c mt ch s

    khc x l gn vi ruby n 1.74 , tuy nhin Chrysoberyl l hai trc trong khi sapphire l

    n trc .

    Khi cc electron 3d ca Cr 3 + trong c hai vt liu tip xc vi cc ion ln cn, cc mc

    nng lng ca cc vt liu c xc nh trong phn ln do s bao quanh cc trng

    tinh th v do ph thuc rt ln vo vt liu chnh.

    c bit, mi ion crm c bao quanh bi cc nguyn t oxy trong mt cu hnh vo

    mt th khng gian khc nhau ng k. Biu din tt nht trong trng hp ca l thuyt

    tinh th trng (hoc l thuyt ligand trng), th ny, cng vi cc ht nhn Cr 3+, xc

    nh mc nng lng ca hng ngc v alexandrite qua phng trnh Schrodinger. Kt

    qu l, cc mc nng lng ca cc ion kim loi chuyn tip trong mt in mi thng

    c xc nh bi cc k hiu l thuyt nhm hn l k hiu s hng.

    Kt qu cc ngun nng lng l mt hn hp ca cc mc ring bit v vng nng

    lng, mt s trong c th hin, cng vi cc biu tng nhm l thuyt ca chng,

    trong hnh 13.1-8. Cc mc nng lng ca hai cht liu l kh khc bit ngay c khi chia

    s chia s cng mt cht kch thch. c bit, vng nng lng 4A2 trong alexandrite bao

    gm mt tp hp cc trng thi vibronic, kt qu t khp ni gia cc mc nng lng

    in t v cc dao ng mng ca tinh th, thc s, cc trng thi ny hi ging nh 1

    phn t thuc dye (xem hnh 13.1. -5). Do , alexandrite lases trn mt phm vi ln ca

    cc bc sng m khng c sn trong ruby (xem n. 14.3E v 15.3D). Tuy nhin, c hai

  • 25

    vt liu lase cc bc sng c trng ring m khng phi l qu xa nhau (cho ruby v

    alexandrite, tng ng 694 v 680 nm).

    Cht bn dn

    Cht bn dn tm thy s dng rng ri trong lng t nh sng. Chng c s dng

    nh ngun nh it pht sng v n laser, v cc my d, v c nhiu vai tr quan trng

    khc. Chng ti cung cp mt gii thiu ngn gn cc mc nng lng ca nhng

    khi bn dn, ging lng t, dy lng t, v chm lng t. Mt s trnh by rng ln

    hn lin quan n cc mc nng lng ca cht bn dn c cung cp trong Chng 16.

    Nhng khi bn dn.

    Cht bn dn GaAs sm tm thy l hu ch trong lng t nh sng. Vt liu ny c

    dng ca mt cu trc mng tinh th lp phng bao gm hai mt lm trung tm khi,

    mt trong nhng nguyn t Ga v nguyn t As khc, khong cch mi nguyn t bng

    chiu di ca mt ng cho (Hnh 13,1-10). Bn phn t ca GaAs c mt trong cc

    pin thng thng, l mt khi lp phng. Mi nguyn t c bao quanh bi bn

    nguyn t ca cc loi i din, cch nhau bng nhau v nm cc gc ca mt t din

    thng xuyn.

  • 26

    Hnh 13.1-12: Cc GaAs bn dn c dng ca mt cu trc tinh th zincblende bao gm

    hai mng tinh th lp phng tm mt, mt trong Ga v khc ca As. Cc mc nng

    lng cao rt gn nhau v di dng nhng vng. nng lng khng l (ty ) quy c

    ti cc cnh trn ca vng ha tr. Cc diode laser GaAs hot ng v vic chuyn i

    in t gia cc vng dn v vng ha tr, trong khu vc cn hng ngoi ca quang ph

    (xem Chng 17).

    Cht bn dn c nhiu mc nng lng electron cho php gn nhau m di dng cc

    vng, nh hin th trong hnh. 13,1-10 cho GaAs. Nng lng vng cm Eg l nng lng

    tch vng ha tr v vng dn, l 1.42 e V ti nhit phng. Cc cp chnh Ga v As

    (3D) l kh sc nt, r rng l nh trong hnh 13.1-10. Vng ha tr ca GaAs c hnh

    thnh t mc 4s v 4p (nh minh ha bng s hnh 13.1-7). Cc tnh cht ca cht

    bn dn c kim tra chi tit hn trong Chng 16.

    Dy lng t .

    Mt vt liu bn dn c dng ca mt si dy mng bao quanh bi mt vt liu ca

    bandgap rng hn c bit n nh l mt dy lng t. Dy hot ng vi th n nh,

    giam hm in t theo hai hng bn nhng khng phi theo hng dc theo trc ca

  • 27

    dy . Dy lng t c th d dng c lm t nhng vt liu nhm III - V v II -VI ,

    chng hn nh InP v CdSe , tng ng , chng c th c mt ct ngang hnh ch nht

    hoc hnh trn . ng nano v dy nano , ch to t mt lot cc vt liu , c th vn hnh

    nh dy lng t . c bit, cc ng nano carbon , phn t carbon hnh tr vi ng

    knh ca mt hoc mt vi nm , hin th cc thuc tnh ng ch . Cc phn t carbon

    t t chc thnh si dy mng rng vi nhau bi lc van der Waals . n hoc a cc

    ng nano c tng bao quanh biu hin tnh cht quang hc, c kh , in v c o .

    Chng c th hot ng nh cht bn dn hay kim loi dn in cao , ty thuc vo cu

    trc chnh xc ca chng . C v s s dng cho cc ng nano carbon trong lng t nh

    sng , t si cc ngun n si t d quang in.

    Chm lng t v ging lng t

    Nhng ht vt cht chng hn nh ht kim loi c th nhn thy c bng mt (kch

    thc ~1 mm3) vn cn c nhng di nng lng in t gn nh lin tc v s nguyn

    t cu thnh cn rt ln. Thm ch, mt ht c th tc h 1 m3 ch c th nhn thy qua

    knh hin vi cng cha 1010 (10 t) nguyn t. Con s to ln ny cho bit di nng

    lng vn khng khc g ht kch c mm3, cm3. V vy, cc c tnh ca ht 1 m3

    vn l c tnh khi (bulk properties). Nu tip tc thu nh, mi vic s khc i th

    nguy n nanomt. Gi d nu ta c mt ht kim loi h nh lp phng c cnh di 5 nm

    (nanomt) c th tch 125 nm3, ht kim loi s cha trn di 1.000 nguyn t. th

    nguyn cc nh ny v con s 1.000 nh lm gia tng khong cch gia cc bc

    nng l ng in t. Ni mt cch khc, di nng lng khng cn nh mt quyn sch

    dy m tr thnh nhng trang giy ri rc. S "lin tc" ca di nng lng biu hin

    c tnh khi ti u biu bin mt v c thay th bi nhng bc nng lng ring bit

    khi vt cht tin v th nguyn nanomt. Ta gi y l s "km ta lng t" (quantum

    confinement) hay l s lng t ha nng lng trong mt khng gian cc nh. T th

  • 28

    gii i thng ca c hc Newton ta bc vo th gii sa m ca c hc lng t. V

    trong ci th gii sa m ny vt liu tr nn "thin bin vn ha" kch c nano v cho

    ta bit bao ng dng cc k th v.

    hiu r s lng t ha nng lng trong mt khng gian cc nh ta h y xem p n

    phn Ph lc ca bi ton "ging lng t" (quantum well) ca phng trnh sng

    Schrdinger. Trong bi ton ny, khi kch th c tin n mt tr s cc nh nng l ng

    ca in t khng cn l mt di lin tc m nhng mc ri rc t thp n cao. "Ci

    ging" tht ra l hnh nh ca nguyn t ni m in t b km gi trong vng cng ta

    ca nguyn t.

    ng knh "ci ging" cng l ng knh ca nguyn t. Phi ni y l bi ton n

    gin nhng cho ra mt kt qu cc k quan trng c tm thu bi cng thc sau (Ph

    lc),

    E = n2h2/8ma2 (n= 1, 2, 3, .)

    vi E l nng lng bc n, h l hng s Planck, m l khi lng in t v a l ng

    knh ging hay chm lng t.

    T phng trnh sng Schrdinger v vi li gii ca bi ton "ging lng t", cc nh

    khoa hc ngh ra ci ging lng t thc s bng cch to ra

  • 29

    Hnh 13.1-13: Kch thc ht CdSe gim t 5,5 nm n 2,3 nm (t phi sang tri) khin

    s pht hunh quang ca dung dch n c thay i t mu n mu xanh bao ph

    ton b ph nh sng thy c [10]

    nhng "nguyn t" nhn to. "Nguyn t" ny tc l chm lng t (quantum dot).

    Thut ng nghe hi l tai nhng n rt c ng v chnh xc trong vic din t hnh

    dng v chc nng ca n. "Chm lng t" biu hin mt vt cc nh chu nh h ng

    ca cc qui lut lng t. Trn thc t, chm lng t l cc ht nano cha vi nguyn

    t n vi ngn nguyn t c th c thnh hnh t dung dch colloid.

    Chm l ng t cng c th c kch hot pht quang. C ng nh vt liu khi, s

    pht quang ca chm lng t cng ty thuc vo tr s khe di. Nhng khc vi vt

    liu khi, chm lng t pht ra nhiu mu sc khc nhau bng cch thay i kch thc

    ca n. Nhng phn k tip s gii thch c ch khc bit trong s pht quang gia vt

    liu khi v ht nano (chm lng t).

    13.2 S CHIM CH CA CC MC NNG LNG:

    A. Phn B Boltzmann lng t:

    Kho st h cc ht khng tng tc. Nng lng ca h bng tng nng lng ca cc

    ht ring l: E=i . Khi xc sut h trong trng thi vi nng lng E bng:

    W(E)=

    = exp

    = Wi (1)

    Trong Wi l xc sut mt ht bt k trong trng thi vi nng lng i:

    Wi= a

    (2)

  • 30

    iu kin chun ha: 1= Wi = a

    , t Z =

    , ta c a=

    . Trong trng hp

    mc nng lng i suy bin bi g(i ) th Z= g(i )

    . Trong (2) tr thnh :

    Wi=

    (3)

    y chnh l hm phn b lng t Boltzmann.

    B. Thng k Fermi- Dirac:

    Kho st h cc Fermion ( cc ht c spin bn nguyn) khng tng tc. Gi E v N l

    nng lng v s ht ca c h, i v ni l nng lng v s ht trng thi I, ta c:

    E= nii v N=ni

    Tng thng k ca h l:

    V cc fermion tun theo nguyn l Pauli nn s ht ni ch c th nhn hai gi tr 0 v 1.

    Do ta c:

    Vy tng thng k ca h cc fermion l:

    Th nhit ng ca h bng:

  • 31

    S ht trung bnh ca h:

    Mt khc t N=ni , so snh biu thc ny vi biu thc ngay trn ta c kt qu:

    y l chnh l thng k Fermi-Dirac.

    13.3 Tng tc ca photon vi nguyn t

    A.Tng tc ca nh sng n mode vi nguyn t

    Xt cc mc nng lng E1 v E2 ca mt nguyn t t trong b cng hng quang. Ta

    quan tm n tnh c th s tng tc gia cc nguyn t v cc photon ca bc x vi

    tn s =o , ti ho= E2- E1 ,cc photon c nng lng bng vi chnh lch ca cc

    mc nng lng nguyn t

    C 3 hnh thc tng tc c th xy ra l bc x t pht , bc x cng bc v hp th

    Bc x t pht

    Nguyn t b kch thch c th chuyn v trng thi c nng lng thp hn mt cch t

    pht bng cch pht ra photon c cng tn s vi photon kch thch,qu trnh ny gi l

    bc x t pht

  • 32

    E1

    E2

    E

    Hnh 13.3-14: trong qu trnh ny, nguyn t chuyn t

    trng thi kch thch c nng lng E2 v trng thi c

    bn c nng lng E1,pht ra photon c nng lng h

    =E2-E1

    Bung cng hng c th tch V, h s t l psp ph thuc vo kh nng dch chuyn gi

    2 mc nng lng gi l mt xc sut, c cng thc tnh:

    psp=

    () (13.3-1)

    Hm () l Tit din chuyn tip ca bc x in t l i lng c trng cho nng

    lng ca bc x truyn qua mt n v din tch trong mt n v thi gian c ng vi

    mt tn s xc nh . Tit din chuyn tip th hin cng v s phn b nng lng

    theo tn s bc x.

    Qu trnh hp th

    Nguyn t t trang thi c nng lng thp chuyn ln trng thi kch thch c nng

    lng cao hn di tc dng ca trng ngoi sau khi hp th mt photon c nng lng

    bng hiu nng lng ca hai mc

    Hnh 13.3-15: Sau khi hp th photon, nguyn t chuyn ln trng thi kch thch E2 >

    E1

    Mt xc sut cho qu trnh hp th photon t mode c tn s xc nh , trong bung

    cng hng c th tch V, c tnh tng t nh bc x t pht :

    pab=

    () (13.3-2)

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    Tuy nhin nu c n photon trong mode , mt xc sut nguyn t hp th 1 photon ln

    hn n ln ta c cng thc :

    Pab=

    () (13.3-3)

    Bc x cng bc

    Nguyn t trng thi kch thch, di tc dng ca trng bc x (photon kch thch) c

    th chuyn tr v trng thi c trng thi c nng lng thp

    Trong bc x cng bc, photon pht ra c cng tn s, cng phng truyn v cng pha

    vi photon kch thch.

    Hnh 13.3-16

    Mt xc sut pst cho bc x cng bc c xc nh tng t bc x t pht v hp

    th:

    pst =

    () (13.3-4)

    Nu cc mode ban u mang n photon,th mt d xc sut ca bc x cng bc nh

    trng hp ca hp th:

    Pst=

    () (13.3-5)

    Khi Pst = Pap , t Wi l k hiu chung dai din cho mt xc sut ca bc x cng bc

    v hp th , khi : Wi =

    () (13.3-6)

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    The lineshape function

    Tit din chuyn tip () m ta s tng tc ca nguyn t vi bc x . din tch ca no

    tnh bng cng thc :

    S=

    13.3-7)

    S c n v l cm2.-Hz c gi l cng dao ng hay cng chuyn tip c

    trng cho cng tng tc. Hnh dng ca n nh hng n ln tng i khi

    tng tc vi cc photon c tn s khc nhau.Hm g()= ()/S c gi l hm

    lineshape c n v l Hz-1, din tch :

    =1. Mi lin h gia v

    cho bi cng thc :

    S (13.3-8)

    B. Bc x t pht

    Tng bc x t pht vo tt c cc mode

    Phuong trnh (13.3-1) cho bit mt xc sut psp ca bc x t pht, nh bit mt

    ca mode trong bung cng hng 3D tng theo hm bc hai M()=

    .Mt nguyn t

    c th t pht ra 1 photon vi tn s vo cc mode bt k nh hnh 13.3-6

    Ta c Tit din chuyn tip c tnh bng cng thc :()= max.cos2

    Trong l gc gia moment lng cc ca nguyn t vi phng ca trng .Khi

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    =

    (< . > ly gi tr trung bnh trong khng gian 3D), hm Tit din chuyn tip

    trung bnh l: =

    max

    Khi tng mt xc sut bc x t pht tr thnh:

    Psp =

    ()] [VM()] d = c

    ()M()d (13.3-9)

    V hm () t gi tr ng k so vi hm bc hai M() , khi ()= 0 hm M() khng

    i vi gi tr M(0) do ta c th b du tch phn

    Psp = M(0)c =

    (13.3-10)

    T xc nh c thi gian sng ca bc x t pht t E2E1 l

    Psp =

    (13.3-11)

    T phng trnh trn ta suy ra:

    (13.3-12)

    Lin h gi mt ph khi lng v thi gian sng

    T cng thc ()= v

    ta tm c Lin h gi mt ph khi lng

    trung bnh vi thi gian sng v hm lineshape l:

    () =

    (13.3-13)

    C. Bc x cng bc v hp th

    Qu trnh chuyn tip cm ng bi nh sng n sc

    Xt tng tc ca nh sng n mode vi nguyn t di tc dng ca dng photon. Cho

    nh sng n sc c tn s , cng I,v mt dng photon (photon/cm2-s):

    (13.3-14)

    Tng tc vi nguyn t c tn s cng hng 0,mt xc sut chung cho bc x

    cng bc v hp th l Wi

    S photon n tham gia trong qu trinh tng tc c xc nh bng cch dng 1 khi

    hnh tr c din tch c s A,chiu cao c,th tich V=cA ,phng truyn nh sng k song

    song vi truc ca hnh tr . Thng lng photon qua hnh tr =A(photon/s) v photon

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    di chuyn vi tc c, tt c cc photon m xuyn qua th tch hnh tr rong khoang

    thi gian 1 s .ta c tr cha n=A=V/c photon :

    = n

    (13.3-15)

    Xc nh c : Wi =() (13.3-16)

    Qu trnh chuyn i cm ng bi dy ph nh sng

    Xt 1 nguyn t trong bung cng hng c th tich V ch nh sng a sc ca mt

    ph nng lng () (l phn nng lng cha trong mt n v th tch ca chum bc x

    trong mt n v quang ph). S photon trung bnh trong dy tn s t +d l

    ()Vd/h , mi mt xc sut

    () bt u 1 qu trnh chuyn i nguyn t do

    xc sut tng th ca bc x cng bc v xc sut l

    Wi =

    [

    ()] d (13.3-17)

    Do bc x l dy ph , hm () bin thin chm hn so vi hm () ,do c th thay

    th hm ()/h trong tch phn thnh (0)/h0

    Wi =

    (13.3-18)

    T cng thc (13.3- 12)ta c

    Wi=

    () (13.3-19)

    Ti =c/ ta c : ==

    (0) (13.3-20)

    i din cho trung bnh s photon mi mode cong thc( 13.3- 19)c vit thnh

    Wi=

    (13.3-21)

    H s Einstein

    Einstein thc hin phn tch vic trao i nng lng gia cc nguyn t v bc x

    c biu thc chung ca mt xc sut t pht v cng bc . Gi nh rng cc

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    nguyn t tng tc vi dy ph bc x c mt ph nng lng () ,trong iu kin

    cn bng nhit, ongc cc biu thc:

    Psp = A (13.3-22)

    Wi =B (0) (13.3-23)

    Cc hng s A v B l h s Einstein . So snh vi cng thc (13.3-11)v (13.3-19) th A

    v B l:

    A =

    (13.3-24)

    B =

    (13.3-25)

    Vy mi quan h gia qu trnh chuyn di t pht v cng bc l t s :

    =

    (13.3-26)

    TI LIU THAM KHO

    Fundamentals of PHOTONICS, B.E.A. Saleh M.C. Teich

    C s vt l cht rn, o Trn Cao

    Vt l in t, L Vn Hiu

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