Luận án tiến sỹ " Tính chất điện và quang của tạp chất và exciton trong dây giếng lượng tử "

80 GIAO DUC vA DAo TAO D~ HQCQuacGIA TP. HCM TRuONG D~I HQC KHOA HQC Tt!NHIEN

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TINH CHAT D~N VA QUANG CUA T~p CHAT VA EXCITON TRaNG DAY GIENG LUQNG TV

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TOM TAT LUhN AN TIEN SI V~T LY

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THANH rHO HO CHI MINH -1999

Lu~n an duqc ho~mthanh t~i ~ mOll V~t 19 L9 thuy€t, Khoa V~t 19, Truemg D~i hQc Khoa hQc 1\r nhien, D~i hQc Qu6c gia TP H6 Chi Minh va Phong V~t 19 L9 thuy€t, Phan vi~n V~t 19 TP H6 Chi Minh, Trung tam Khoa hQCva C6ng ngh~ Qu6c gia.

Tr~n Tho~i Ouy Bao

Ngll'Oi hl16'ng dfin khoa hQc : 1. GSTS

2. PGS PTS Nguy~nNhl)tKhanh

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C6 th~ tlm hi~u lu~n an ~i Thu vi~n Truemg D~i hQc Khoa hQc TV nhien, D~i hQc Qu6c gia TP H6 Chi Minh va Thu vi~n T6ng hqp TP H6 Chi minh.

.-'Z .)..~Y'.I!-~. vao h6i

Md DAU

Trong VIDnam g!in dfiy, sl! ti~n b() trong cac ky thu~t nuOi tinh the cho phep thl!c . .' hi~n cac vi cffu trUc ban dan nho Mn muc ma cac tfnh cMt di~n va quang hQc thay

ddi dang ke so vcri cac v~t li~u ban dAftkh6i. M()t trong cac vi cllu trUc nay la cac

h~ dfiy gi~ng luqng tU (quantum-well wire (QWW». Trong cac h~ nay, cac h~t till bi

giam nMt trong 2 chieu khOng gian, sl! chuyen dQng tinh ti~n theo lr\Ic dfiy thAng

g6c vcrimiJt phAng giam nh6t Iii tl! do.

SI! thanh cOng trong vi~c cM t~o ra cac QWW dii cho phep ngueri ta sir d\mg

chung trong cac d\mg c\l ban dAn, d6ng thCriqUail sat duqc nhieu hi~n tUqng ky I~

obu Hnh cMt phi tuy~n quang hQc, vi v~y, t~o nen mOt sl! qUail tfim dang ke trong

vi~c nghien CUllIy thuy~t cfing nhu thl!c nghi~m ve cac tmh cMt di~n va quang hQc

cua chUng.

Trong lanh VlJcly thuy~t, cac c6ng trinh nghien CUlltrucrc dfiy thuCrngsir d\lng

mO hinh rao thtgiam nh6t vO h~ hoiJc hiiu h~n c6 tfnh d6i XU-figcao nhu QWW tr\l,

QWW chli nh~t vcrirao th~ vO h~n. D6i vcri cac QWW rao tht hiiu h~ c6 Hnh bIll

d6i xU"ngnhu QWW cM nh~t, QWW be m~t..., kh6 khan cClban mang Hnh chIll Iy

thuytt la vi~c giro phuClngtrlnh SchrOdinger 2 chieu de dc djnh tr~g thai Dang luqng

cua h1;lttai. De khiic ph\lc kh6 khan nay, chUng tOi sir d\lng g!in dung TlJa-Hartree dii

dltqc Bastard va Marzin dua ra gan dlly k€t hqp vcriphlfClngphilp bitn thj~n de xac

dinh tr1;lngthai Dang htqng cua h~ t1;lPcMt. Ben c~h do, anh hubng cua di~n truerng

ngoai left t~p chIll va exciton cfing duqc chung tOi xem xet bi'rivi tr~g thai di~n cua

h~ thuerng duqc thiim do bang vi~c sir d\lng mOt tfUerngngoai.

Ducri ki'ch thi'ch laser m~nh trong cac M ban dAfthinh thanh plasma di~n tir-lei

tr6ng d~l.mdiJ.c,khi do do cac hi~u U"ngtlfClngquan-trao ddi va SI!cMn clla tuClnglac

Coulomb, nhieu tinh cMt dClnh~t clla h~ bi Mi chunn h6a nhlf khe dai se bi co I~i

ducri lac dOng clla cac hi~u U"ngnay va vi v~y clAnMn hi~u U"ngphi tuytn quang hQc.

Trong cac h~ ban clAnc6 CI!Cnhu GaAs sl! lien ktt gilia plasmon di~n tU-leitr6ng va

phonon quang hQc dQc (phonon La) cling la mOt hi~u U"ngdang qUail tfim. D6i vcri

QWW, cac. hi~u U"ngnay dii duqc qUail tfim nghien CUlltrong m()t vai flam rIll gall

1

dRy, IllYnhien trong cac cOng trlnh nay, ngum ta thuoog sit d\mg cac glin dung khac

nhall nhu gdn dung tinh, glin dung €o-giA tinh. Ngoai fa, nhu dii bi~t m<)tdiJc tr\1ng

quaD trQng CURcac h~ IMp chi~u la cA'utrUc dAicon CURcac dIDdAnva boa tr!, hi~u

tffig plasmon di~n tit-16 tr6ng vl v~y se anh hm1ng I~n d<)tlii chuAn hoa dAi con va

Himthay d6i pM quang hQc CURh~. Cho Mn nay, d6i vOOcac h~ QWW, d<)tlii chuiIn

h6a d:',i con chi mOOdUng I~i xem xet b gdn dung Hartree"Fock, nghia la bO qua hi~u

lIng chdn va t\1O'ngquaD.

V~ nguy~n tlic, d~ nghi~n cUu hi~u tffig cMn chung ta pbaixac d!fih duge ham

di~n mOi €(q,UJ), co nghia la Anh hufJng cua h~ nhi~u h~t duge xem la m<)t tr\1Ung

trung blnh khi xem xet tuO"ngtic giiia m<)th~t tAi nay vcrim<)th~t tii khae. M<)tsl!

Hnh toaD ehfnh xae ham nay gtin nhu khOng tM thl!c hi~n. M()l vai mO hlnh gtin dung

clIo ham di~n mOi dii duge dua ra nhu mO hlnh RPA (random phase approximation)

va cae mO hlnh mb r<)ngcua no nhu Hubbard, Singwi-Sjolander... clIo eac mall kh6i.

TI1O"ngtl! eac mall kh6i, trong h~ thA'pehi~u, ham di~n mOiRPA co th~ tfnh tl1phuO"ng

plllip tmUng II!hqp ho~e phuO"ngphap ham Green Matsubara k~t hqp vcriky thu~t giAn

do. Trong phuO"ngphap ham Green Matsubara, chUng 18co th~ tlm tM eMn qua vi~c

giiii pll110"ngtrlnh Dyson. Tit do, 18co th~ xae d!nh duge ham di~n mOi theo cae bQ.e

gall dung mong mu6n.

VI lu~n an Ihl!e hi~n v&inhi~u van d~ kh:ic nhau, Den trong ehuO"ngmb datI nay

chung IOj khOng gi&i thi~u nhiIng cOng trlnh cua cae lac giA khac lien quaIl den d~

lai elm III~n an ma se gi&i thi~u trong tUng ehuO"ngcua luQ.nan d~ de dang tha:y r5

hO"nnhUng k~t qua ma chUng tOi dii d~t duge.

LuQ.nan gOm 4 ehuO"ng,mb dllu va k~1luQ.n.Th~m vao do lu~n an duge lam sang

to bai, Iph!,l (!,Ie,I hlnh va 27 dO th!.

Trong ehuO"ng1, chUng IOitrlnh bay phudng phap 1\ra-Hartree va sit d!,lngphUO"ng

pIlar nay d~ khao sat sl! AnhhufJng cUa di~n truUng I~n di~n tit va t~p cMt trong eac

QWW co rao the ba:td6i xtffig. Trong ehuO"ng2, chUng tOi sit d!,lngphuO"ngphap bien

(hien d~ I(nh Dang luqng li~n ket exciton Wannier trong QWW ducri tlic d<)ngcua dj~n

InfO-fig.Oll101lg 3, v&ihlnh thuc luQ.nham Green Matsubara, chUng toj xel hj~u tffig

2

cMn dOng hQc do lien k~t plasmon-phonon trong phl;\m vi gttn dung ctfc-plasmon-

phonon de tfnh nang lu

nang lu

ding vm hlnh tMc lu~ ham Green Matsubara, chUng t6i da u6'c lu

chuAn bOa dill con du6'i t

BOi VI cac phu<1JJ.gpMp chUng t6i su d1.lng trong lu~n an la nhUng phu<1JJ.gpMp

quen thuOc cho cac mAll ban dAn kh6i. Do v~y, chUng t6i se kh6ng dua vao lu~n an

mOt chu<1JJ.gve phlin tOng qUaD ma chi diem qua mOt vai hi~n tU

Call trUc kh6i va Call trUc thap chieu trong ma dllu cua lu~n an fibula mOt phlin tOng

qUaD de thll'y ro h<1JJ.ve ,stf khac bi~t trong cac hi~n t\1

kh6i va cac cliu trUc h~ thap chieu.

CHWNG I : HI~U UNGDI~ TRllNG TREN DAY GI~NG Ut;jNG Hi

glin dung thfch hqp.

Trong v~t 19 ban dan va di;i.cbi~t trong cac cliu trUc.ban dan gill mOt chieu stf co

m~t cua t/,\pcMt ion bOa the hi~n mOt vai tro qUaDtrQng trong co cM tlii a nhi~t d()

iMp cling nhu tl;\Ora m()t stf dich chuyen ml,lnhtrong phISquang hQc. Osorio, Degani

va Hipolito dii tfnh nang lu

blft dang hu6'ng cua rao tM hihl hl,\D.Thy nhien, rao th! nay kh6ng cho phep chUng

ta tach bi!n trong vi~c gilli phu<1JJ.gtrmh SchrOdinger de xac djnh trl,\Dgthai Dang

lu

di~n trI1emgding duqc qUaDtam nghien cUu. Narayani va Sukuma da nghien cUu bai

loan v&i stf co ml.\t cua t/,\pcMt lo/,\ihydrogen trong QWW cM nh~t rao tM vO hl,\D

d~t trong di~n truemg dell thang goc v6'i tT1.JcQWW.

Trong chu<1JJ.gnay, chUng t6i su d1.lngphu<1JJ.gpMp Ttfa-Hartree de xem xct Ilnh

hihl h/,\n.

huang cua di~n trI1emgtren cac day lu

1.PhU<1JJ.gphap Tl!a-Hartree

3

Xua't phat ta phuo'l1gtrlnh SchrOdinger cho dAygieng luQ'l1gfir vcritM giam nh6t

V(x, y) :

]

[

n2 - 2m.

{

82 (I) 82 8X2 + 8y2 + V(x, y) w(x, y) = €w(x, y) . }

Theo Bastard va Mazin, phUo'l1gtrinh (1) co the xem nhu phuo'l1gtrinh mO ta 2 di~n

tit tuo'l1glac thOng qua tM V(x, y) thay cho tM Coulomb, cac nghi~m co tM tach

cua phuo'l1gtrinh nay co d~g w(x, y) = a(x)x(y) duge xAyd\!l1gta nghi~m cua cae

~ 2m. 8X2 +

(2)

V(x, Y)X2(y) dy a(x) = €za(x), }

{

V(x, y)a2(x) dx X(y) = €yX(Y), }

(3)

{

- 2m. 8y2 +

phl1o'11gtrlnh Hartree :

Ji2 82 ! n2 82 !

€=€z+€y-! V(x,y)a2(x)x2(y)dxdy. (4) 56 h"Ulgcu6i dIng trong phuo'l1gtrlnh (4) dugc dua vao de tranh vi~e tfnh 2 IAntl1o'11g

2.Anh huang eua di~n tru(mg Jen die mue HAngluqng trong dlly luqng fir b~ m!)t

lac V(x,y).

Bastard va Mazin dii tfnh cae mue Hang luQ'l1geua di~n fir trong day luQ'l1gfir M

(5)

m~t.v(1irao tM V(x, y) co d~lIIg:

V(:1:,y) = V1O[y(y - Ly)] + L~.lIO(y- Ly)O(x2 - L;/4),

(J day O(x) la ham Heaviside. Chung tOi mb r(}ng bai toan eho trui'mg hqp co di~n

trui'mg ngoai. Hamiltonian cua m(}tdi~n fir trong dAydi;}ttrong di~n trui'mg ngoai d~u

(6)

H = --

+ V(x,y) + eF(y - Yo),

n2\J2 2m.

vcri Yo = < Y > F=O la gia tr, trung binh eua y trong tr~\IIgthai kMng co di~n trui'mg.

f-Him song thir eua tr~ng thai co ban va tr~ng thai kfch thfch dati

lien :

(7)

w,,(x,y) = Nnwno(x,y)

4

song song vcrifn;1ey :

Wno(x,y) dugc lay nhu tfch cac nghi~m cua cac phuO'l1gtrinh T1,1a-Hartreecho Mi

(8)

q)n(X,y) = exp[-t1n(Y - Yo)],

Bastard va Mazin. Ham song bie'n thien q)n(x, y) :

Chung t6i thtJc hi~n pMp Hnh bie'n thien d6i v6'i t1n de xac djnh cac muc nang

e

(9)

<1p = -F {(wdylwl)F;lo- (wdylwl)F=O}.

cac Hnh loan s6 dugc thtJchi~n cho dAyhrgng tit be m<}tGa(ln)As

- GaAs

v6'i cac tham s6 dii dugc sit d\mg : m* = 0.06mo, Lv = 50 A, VI = 0.15eV va .6.V = 0.8eV.

lugng cua di~n tit. Khi do, h~ s6 phAn ctJc cua di~n tit dugc dinh nghia nhu sau :

Nang lugng tr~g thai c<1ban va kfch thfch thu nhat El va E2 nhu la ham cua

cuang dO di~n twang dugc bieu hi~n trong hinh 1. G6c tfnh nang lugng fJ dAy dugc

chQn la Dang lugng tr~g thai C<1ban cua QW c6 l~p va bang 69.1meV. Theo ke't

qua ma chUng t6i thu dugc thi cac muc nang lugng cua di~n tit giant khi cuang dO

di~n twang tang. Trong hlnh 2, chUng t6i ve d6 thj h~ s6 phAn clfc <1ptheo Lx. <1p

tang nhy khi Lx tang. Ngoai ra de so sanh, chUng t6i cfing xem xet twang hgp di~n

twang hu6'ng theo phuO'l1gcua trl}c x. Nhu co the thay tru6'c, chung t6i dii thu dugc

<1ptrong twang hgp nay phI} thu<)cml;lnhvao stJ thay dOi cua Lx.

3. T~p eMt trong dAy gieng luQ"ngtir du6i hie dOng eua di~n trub'ng

Trong khu6n kh6 cua g!in dung kh6i lugng hi~u dl}ng, Hamiltonian cua mOt di~n

IiI baa quanh tl;lPchill trong QWW chii nh~t raa the' hiiu hl;lndl}.ttrong di~n tnrcmg

H = --

ngoai thfing goc v6'i tfl}c dAy:

~~. 2 m*

~ f r - ro + V(x,y) + eF(xcosB+ ysinB)- 1- -I'

00)

a2

a2

(11)

,

b2 V(x,y) = VO 8(X2 - 4) + 8(4 - x2)8(y2- 4)

]

trang do 8 la goc giUa hu6'ng di~n twang va trl}Cx. Rao the' V (x, y) co d~g :

5

[

Ham song thu tr~g

th:ii eC1ban e6 d~g

dem gian sau :

a va b la cae kfch tll\16'e eua QWW.

(12)

Ham iIlo(x,y) e6 the Iffy nhl1 tfeh cae nghi~m eua h~ phl1emgtrlnh 1Va-Hartree :

82

ft2

a2

a2

(13)

. - 2m" 8X2 + Vo B(X2- ""4)+ B(""4- X2)p"

lex) = Exf(x),

W(x, y, z) = NWo(x, y)4J(x, y, z) .

] }

[

Ti,2 82

(14)

[

{

{

(15)

b2 - 2m" 8y2 + Vo Pl,xB(y2 - "4) + P2,x Bey) = E"g(y), Eo = Ex + E" - VO[P2,x+ P1,xP,,] ,

b2

B(y2 -

"4)g2(y)dy,

a2

] }

B(""4- x2)f2(x) dx,

a2

P2,x =

B(X2 -

""4)f2(X)

dx.

P" = J J P1,x = J

(16)

bt'1i Osorio

nhl1 dii n6i

t'1tren. Ham thlt 4J(x,y,

z) dl1qe eho dl1ai d;.tng:

(17)

Neu d~\tPI,x := 1 va P2,x := P" := 0, chUng ta se nMn dl1qe nghi~m dii dl1qe su dl;mg

4J(x, 1('z) = exp[-'x1f - rolJexp[-,B(xcosB + ysinB)] ,

(18)

Eb = E(,B,'x = O)min- E(,B, 'x)min .

Nang Il1qng lien k~t t;.tpeMt Eb :

(19)

a" = - ~ {(iIllxcosB+ ysinBIW) Ji'ofO - (iIllxcosB+ ysinBliII)F=O}.

F

H~ s6 pMn Qre eua t;.tpeMt dl1qe dinh nghia :

va f = 12.53.

Niing Il1qnglien k~t Eb (hinh 3) eua m<)tt;.tpeMt tro'ngm<)tQWW ran th€ hiIu

Cae k€t qua bfuIg s6 th1!ehi~n eho QWW GaAs : Vo = O.4eV, m" = O.067mo

6

h~ dii duQ'c ve va so sanh voi cac ket qua cua QWW vO h~. ChUng tOi tha"yrang

rao tM hiiu hip} dii lam giam nang luqng lien ket ml)t cach dang k~, d~c bi~t b cac

Trong hlnh 4, chUng tOi trlnh bay M s6 pMn qrc ap nhu ml)t ham cua goc (). H~

klch thuac day nho.

s6 pMn cgc giam khi tang. () vi trong truOng h

theo trvc y. R5 rang rao tM hiiu h~ dii khuech d1Psg ph1,lthul)c cua h~ s6 phAn cgc

vao huang di~n truC1ng.

Ifmh 5 trlnh bay nang Iuqng lien kef Eb theo vi trl ~p cMt Yo.Ct!c dl:\icua duOng

cong Dang Iuqng lien kef dOi di khi co m~t cua di~n truOng. VUi QWW vO hip}, sg

dOi di cua cgc dl:\iIa It hem so vUiQWW rao the hiiu hip}.

canst. Khi khOngco di~n truOng,Eb It thay ddicho cac QWW co kfch thuac g~

bang Mali. V6i sg co m~t cua di~n truOng,no bUydi tfnh d6i xfutg va cho chUng

ta mOt QUaDsat d~ng chU y ; Trong khi sg co cua klch thuac cl;\nh theo huang di~n truOng(tr1,lcy) 11;\0ra ml)tthay ddi nho trongEb thl sg mb rl)ngkfchthuac theo huang

doll:\ilam giiun nhanhnang luqng lien ket. D6i vUicac QWWco kich thuac Ian, cgc

dl;\icua nang luqng lien ket b cac Cl:\nhbang nhau bi oboe di.

Hinh 6 bieu hi~n nang luqng lien kef Eb theo kich thuac a cua QWW cho a x b =

Ket lu~n : Trong chuemg nay, bilng phuemg pMp Tga-Hartree, chung tOi dii giai

quy€t vfu1de co tfnl,tphuemg pMp lu~n cho vi~ giai phucrng trlnh SchrOdinger trong mO hlnh QwW chu nh~t rao tM hiiu hip}. Chung tOi dii xem xet sg Anh hul1ng cua

di~n truOng leD cac muc nang luqng trong day gieng luqng fir be m~t va xac djnh h~

s6 phfin cgc cua di~n fir. D6i vai cac QWW chu nh~t, chUng tOi tfnh Dang luqng lien

ket va h~ s6 phAn cgc cua ml)t 1I;\pcMt trong sg co m~t cua di~n tfUOng. Chung tOi

Om th1fychung ph1,lthul)c m~h vao tM giam nMt, vi trl cua tl:\PcMt, huang cua di~n

CHWNG 2 : EXCITONDuJi TAc DONGCUA DI~N TRtf1NG NGOAI

1. Giai thi~u

7

tfUOngva tiel di~n khOng vuOng.

Ngltai ta dii chtffig to ph6 Mp tho va ph6 phat quang cM yeu gAy Mi hi~u tffig

exciLon. Hau h~1cac nghien CUll1:9thuyet trltac dAy ve QW cling nhu cac QWW sir

lh.HlgmO h111hrao Lhechii nh~t. Brum va Bastard dii nghien cuu hi~u tffig di~n twang

I~n nung lulJng lien kef cua tr~ng thai CC1ban cua mQt exciton trong mQt QW. Brown

va Spector dii.tlnh nang luqng lien kef tr~g thai CC1ban cua mQt exciton bi giam nMt

Lrong mQLQWW hlnh tf\! rao the vf:Jh~ va hlIu h~.

Glin dlly, Clk QWW rao tM bell parabol dii dltC;tcnhieu nha 1:9thuyet va thlfc

nghi~m nghien CUllMi vi mO h1nh nay dii mf:Jta t6t han cac kef qua tht!c nghi~m.

Trung chuang nay, chUng tf:Jise trlnh bay cac ketqua Hnh loan cua chUng tOi ve nang

luqng lien kef tr~ng thai CC1ban cua mQt exciton Wannier trong mQt QWW rao tM

bell parabol d~t trong di~n trltCrngngoai thAng goc vui tf\Ic QWW.

Vui Sl!hi~u biet ve exciton va cac ham song lien t\Jc va cac tri rieng nang Iuqng,

chung la co lh~ giai phuang trlnh phfin cl!c c~p di~Ii tir-IOtr6ng d~ nh~ du<;1cdQphfin

qrc gHi'ncac d{1iva VI v~y co the Hnh du<;1Cph6 quang hQc cua cMt ban dan trong

vllllg mep duj. D~ dan Mn phuang trlnh pMn clfc c~p di~n tir-IO tr6ng, chung ta co

Lhesir d\lI1gcach tiep c~ ti':tphuC1ngpMp twCrngit! hqp ho~c tier c~n ti':tphuang phap hum Green.

Trong Ln1lmghqp gall dung ban clan 2 vimg, bo qua st! chin va xct h~ trong dieu

X(w) = -2ldcvl2 ~IY!/(r= oW [n(w + i8)~ Eg - E/

ki~n ghi ca.n bhng, ta co dQ carn quang hQcc~p di~n tU- 10tr6ng trong gan dung RPA:

(

20) ] 1 - n(w + i8) + Eg + E/'

Lrongdo dcv la y~u t6 ma tr~n luO'ngcl!c. Y!/(f) la ham song tr~g thai c~p di~n tU-IO

trOng, E/ wang tffig la tri rieng nang luqng (ila t~p cac s6 Iuqng fir) va chung thoa

1i2"V2

pl1l1l1ngtrlnh Wannier :

[

]

the Coulomb V(f)

ta con

21lr +V(r) - (21)

Y!/(f)=E/Y!/(f). Luu y dIng trung twCrng hqp QW, ho~c QWW, ngoai

phiii LhemVllOLh€ giam nh6t trong phuang trmh (21).

8

Voi nghi~m q[, va E, trong ban dAn kMi ta dl1c;fctOng thU'cElliot 3-chi~u cho

00 471"

1

7I"e" /...!li.

phO hfip tllU :

(22)

,

n=l n

VIS. smh(7I"/ ~)

a(w)=ag- R L.:30(~+2)+8(~). n [

]

trong d6 n la s61uqngtit chfnh, ~ = (fiuJ- Eg)/ R, R la DangluqngRydberg3-chieu va ag la h~ s6 ph\l thu~c s6 chieu va dcv

fiuJ

Chung ta tMy tir phu<1ngtrlnh (22) phO Mp thu exciton 3-chieu bao g6m cac

duOng siic net vm cuOng d~ duo d~ng giam nhanh ch6ng tY I~ vm n -3 (s6 hlplg dliu

2. Ly thuyet

li~n) va mOt phO hap thu Ii~n t\lc do cae tqU1gthai ion h6a (s6lwng cu6i).

Trong mO hlnh QWW chUng tOi sir d\lng, trong d6 di~n tit bi giam nh6t trong

II1l.\.tpilling yz (cr x = 0). Trong huO'ng y chUng ta ghi djnh tM giam nh6t parabol

V (y) = mw2y2/2, vui m la kh6i luqng h~t tii va fiuJla be TOngdw con cua h~t till.

De don gian cho vi~c tinh loan, chUng tOi sir d\lng h~ thac d6i xUng cua khOng gian

dili con di~n tir va 16tr6ng ma dii duqc sir d\lng b(Ji Benner va Haug :

mewe = m"w" = pJJ .

(23)

Trang do, f..Lla kh6i hrqng thu gQn cua ci;ipdi~n tir-IOtr6ng, me va mh tuang t1'ngla

kh6i hrqng hi~u d\lng cua di~n tir va 10 tr6ng. no. la be TOngcua khOng gian dai con toan phau (0. = We + w,,), voi fiuJeva fiuJ" tuang t1'ngla be TOngdai con cua di~n tir va 10 tr6ng trong the giam nh6t parabol. Tn;mg khuOn khO cua gau dung kh6i hrqng

hi~u d\lng, Hamiltonian cua h~ cho bcri

+ ~y"

11,'1.82 r,,2 82 n2 82 mew~ 2 m"w~ 2 H =

Ere

+eF(Ye - y,,)-

- 2me 8y~ - 2m" 8y~ - 2f..L8Z2 + ~Ye e2 I- - rh

-,.

(24)

Ham song thii trlplg thai C(Jban cua exciton:

9

(25) \l!(r-;,r-;') = N (P(Ye)1>(y,,)exp{-Alr-; - 1'7,I} ,

b day tjJ(Ye)va tjJ(y,,) la ham song cua di~n tit va 10tr6ng d<1nIe trong di~n tr\1ang.

Nang l\1qngIi~n ke't tr:;mgthai co ban cua exciton:

(26) Eb = Eo - (wIHlw}min ,

trong do Eo la tOng Hang l\1qng tr~mgthai co ban cua di~n tir va 16tr6ng d<1nIe trong

di~n twang.

bilng cach qrc lieu theo ). tr,

trung blnh cua nang Iuqng b trl;lng thai

thir w.

3. Cae kef qua bang 86

Chung ta nh~ d\1C;1CHang Iuqng trl;lngthai co ban cua exciton trong di~n twang

d~ng : me = O.O67mo,mh = O.45mova € = 12.53.

Cac tfnh loan b5.ng s6 thvc hi~n cho QWW GaAs, vm cac tham s6 dii duqc sir

Nang luqng lien ke't Eb nhu la ham cua cuang d<)di~n tr\1ang duqc the hi~n trong

hlnh 7. Trong hlnh nay chung ta co the tha:y ra.ng co sv c:;mh tranh giiIa sV philn Iy

cam (rng bbi di~n twang, tU<1ngtac Coulomb giiIa di~n tir va 16tr6ng va sv giam nMt

phOnly do cU111trngbbi di~n trUangkhi do chi€111\1UtM. VcriF Ian, Hangluqng li~n

cam (rng biJi rao the'. M<)t cach dinh tfnh, khi cuang d<)di~n twang tang, trong liln c~n F = 0 t\1ung tac Coulomb chie'm \1Uthe' VIv~y nang luqng li~n ke't giam ch~m. Nang Iwmg li~n k€t giam cang nhanh vcrisVtang cuang d<)di~n twang Mi VIsV

kef giam ch~m Il;li,di~u nay ra rang do sv cam trng bbi rao the giam nh6t co khuynh

huang can sV philn Iy cua di~n fir va 10 tr6ng lien g1illden mer rao tM.

Trong hlnh 8, chung tClive nang luqng li~n kef theo o. Nang luqng Ii~n ke't tang

khi n tang tuung trng vcrisV tang cua tM giam nh6t.

nang hIQ'ngIi~n'ketcua exciton trong QWW.Chung tClidiitlm tMy hi~u trngnay th~t

Ket Iui;tn : Trong chu<1ngnay chung tClidii nghi~n Clruhi~u trng di~n tr\1ang I~n

CHUaNG 3 : S{/CHAN DONG HQC TRaNG cAc DAY GIENG LUQNG TV

KICH THICH QUANGHQC. MO HINH MOT DAI CON

10

sV Iii l6'n va ph~ thu<)c ml;lnhvao the' giam nMt Mn parabol.

Dll<1i.kfch thfch laser m1p1h,nhi~u tfnh chA'tdan h~t cua h~ bi tlii chua.nhoa do

mil hll«'m.gcua tuang quan-trao d6i va S1!chdn cua tllang lac Coulomb. Ml)t trong

cac tfnh chA'td6 la dl) tai chua.n hOakhe dai (band-gap renormalization (BOR» dii dllqc nghien cUllnhi~u trong cac Mban dan kh6i va QW.Olioday, co m()tvw nghien cUll tren BOR trong cac QWW. Benner va Haug dii nghien CUllBGR trong glio dung

c1!c-plasmon gill tinh, Thnata tfnh BOR trong glio dung RPA tinh , Hu va Das Sarma

du xac dinh n6 trong gan dung RPA nhung I~i bO qua d6ng gop cua m~t dl) 10 tr6ng

trong ham di~n mOL Trong cac cOng trlnh nay, cac lac gia chi xac dinh BOR trong

glio dung EO.

Trong cac v~t Ii~u (ITI-V), tuang lac h~t tai-h~t tai va h~t till-phonon xay ra va

unh hll«'m.glen ca h~. Cho cac QWW, Ouven va Tanata dii xem xet hi~u U"ngtai chu!ln

h6a elm lien k~t c1)pdi~n tU-IOtr6ng vcriphonon trong glio dung chilD tmh. Vl v~y,

hQ dii daub gill qua caD d6ng gop cua phonon trong BOR.

Dl!u trell h11lhthuc lulplham Green Matsubara, trong chuang nay chung tOise

xem xci phO niing Illqng rieng di~n tit, ham m~t dO pM, dO tai chua.n h6a khe dui va

chi h~nch~ iJd6nggop cuadill con tr~ng thai C<1ban trong ph~

vi g1indung PPA

bao g6m cu hi~u U"ngtUang lac h~t tai-phonon.

1. Hamiltonian cua h~ di~n tit-IO trong trong dAy gi€ng luqng tit

Toan tit Hamiltonian cho h~ di~n tUbi giam nh6t trong m~t phAng (x, y) cho biJi Bcnllcr:

H = Ho +Hc.

(27)

:Ho = ~ at n >,ak,n,>,Ek,n,>,

,..\= c,v

L...J " k,n,>'

(28)

1i,2k2

tmng do, niing luqng cua di~n fir trong dui con thu n thuOcdaidan(..\= c) :

= Eg + Ce,n,k ,

Ek,n,c = Eg + En,e + _2 me

(29)

Ti,2k2

Ilung Illqng cua 16 tr6ng trong dill con thu n thul)c dill h6a trj (..\= v) :

= -c" n k . '

(30) E k n v = -E n v - - , , '2m" ,

11

56 h~U1gCoulomb:

V. ~+

~+

~

,

H - c -

1 "2

qak+q,nttAakl-q,n2,Alak',n3,,\,ak,n.,A,

'" L , k,kl,q,N,A,A'

trong d6 N = {nt,n2,na,n4}

va

I

(31) .

~1,A(x, y)~2Y (x'y')n3N (x', y')n.,A(x, y)eiqz

Vq =

y;dxdy x dy

! dz

d I

e2 X EOV(X - x')2 + (y - y')2 + Z2 .

2. S,! cMn d()ng hQcbm phonon va plasmon Ii~n k€t

(32)

Xuat phat tU mO hlnh QWW rao th~ Mn parabol, xem eae h~t uii djnh xu trong

diii con thap nhaL Khi d6, tUO'ngtac Coulomb hi~u d\lng giUa cae h~t tai :

q2

(33)

4fL11 1(0 ]

e2

V(q)= Eooexp

(

q2 ) 4{111 '

[

1(0 IIIham Bessel bi~n d~ng b~e O.

Chung tOj ehi xem xet lien k€t cila plasma di~n tu-lO tr6ng vai eae phonon La

kh6i. TuC1ngtlf trt1

trang gall dung RPA :

- EooV(q) (34) EooV(q) 115(q,ivrn) = Eoo+ n~,(ivtn) + n~l(q, ivrn) - E(q,ivrn) ,

trong d6 iv", lit tftn s6 Matsubara cho boson. Ham phall clfc m~g duge eho bbi :

nO (UJ) =

EO- Eoo W2'

L

1-;;;r.

(35)

2 UJpl

(36)

n° (q , el

UJ) = Eoo 2 - UJ2: zj2 ' UJq

pi

2

Trong gall dllng PPA ham pIlau clfe di~n :

UJpl= -V(q),

nq2 II

(37)

12

2

q4

(38)

On. + 4p2 '

1 2 CJJq = CJJpl 1 + V(q) I>-

{

} ,-e,h 7fiii

vUin Him~tdOdai plasrna.Khi do, ham di~nm6i :

2 CJJpl

T

.

E(q,CJJ)=Eoo

[1-

2 - CJJ2 CJJL CJJ2_CJJ} - CJJ2+CJJ;,-CJJ~ ]

(39)

Ui(i = 1,2) duge cho bc:'1icac cVc va th~ng du cila c1 (q, CJJ):

Ole mode ri~ng cila cac phonon, plasmon li~n ket CJJiva cUC1ngdO dao dOng tlr

E

(q,CJJ)=-

1+

2

2+

2

Eoo

2. CJJ - CJJI CJJ - CJJ2 ]

U1 U2 -1 1 (40) [

Gan dung dOng hQc EOla gan dungma chUng ta xet dong gop cila phonon vao

hi~u lIng chao Ia tinh va nh~ dugc bang cach d~t Eoo= EO.

3. Ph6 nang h1Q"11gri~ng va ham m~t di) ph6 daD h~t

Trang h1nh thuG lu~ ham Green Matsubara, phO nang lugng ri~ng dan h~t trong

(41)

- k',z - Zl),

~i(k,z) = -~L Vs(k',z')G?(k

k',z'

gan dung b~c 1:

trong do z, Z' tl1ang lIng Iii cac t11ns6 Matsubara cho fermion va boson, G? (k', z') Iii ham Green b~c o.

~i(k,CJJ)=~r"(k)-L

42

7r

. (

)

roo dCJJ'ImVs(q,CJJ:+ib)[l+g(CJJ')-J;(k-q)] CJJ+ ~b- ei(k - q) + Pi - CJJI

I-HimphO nang lugng ri~ng :

q

la ham pMn b6 boson

g(CJJ)= ell:-l Ham m~tdOph6 dun h1;lt:

A.(k

) =

(44)

(43) q J-00 ~iX(k) = - L V(q)/;(k - q),

2Iml~i(k,CJJ)1 (CJJ+ Pi - ei(k) - Re~i(k,CJJW + [Im~i(k,CJJW .

13

"CJJ

Xet truCmghqp cua QWW GaAs v6i cac tham s6 dUc;1csir dl;mg : m. = O.O67mo,

mh = O.45mo, EO= 13.1, Eoo= 11.1, UJL= 36meV va n = lOR.

Trong hlnh 9, chUng tOi chi ra phlin thl!c cua nang lu

tir. De so sanh, chung tOi ding trlnh bay cac ket qua cua glin dung EO.Ngoai 2 c()ng

hubng quell thu()c cua plasmon, chUng tOi nh~ duc;1cthem 2 c()ng hubng trong Ian

cQ.n:!:UJr,- It. khi tlnh den sl! ph1,lthu()c tlin s6 ciia ham phan cl!c m!p1g.

Ham mQ.td() phd cua di~n tit duc;1ccho trong hlnh 10. Cho tfUang hqp kMng co

dong gop cua phonon chung ta co 2 cl!c quen thu()c dii dUc;1cnghien cUu trong cac

mati 3-chieu, 2-chieu ding nhu l-chieu. Neu dem theo cpieu tang cua UJtit am den

ttrO'l1g

xem xet

duO'l1gchung ta co Cl!cdliu lien It s!\c net, dUc;1cgQi Iii plasmaron. a,c thu 2 rllt s!\c

net dUc;1cgQi Iii.m()t gia h~t, Iii m()t kfch thlch rllt ro rang cua h~. Trong trtrang hqp them lien ket phonon ta nhQ.n them dUc;1c2 cl!c t:;1ivi trl :!:UJL- M.

t\! nhu ph6 cua nang lu

4. Ht) tai chu:\n h6a khe dai

phonon lam cl!cghi h~t giam d() snc net.

Cho UJ-t ei(k) - Mi trong (46) ta thu dUc;1cbieu thuc cho nang lu

rid ImVs(q,UJ' + i8)[l + g(UJ/)- fi(k - q)]

,

,

,

-00 7T

1:.(k ,

h:;1t:

~ q

e.(k» = 1:~"'(k)- " / 00

. (45)

ei(k) - ei(k - q) - UJI+ i8 .

N€u bo qua nang lu

- ei(k - q), ta.duc;1cbieu thuc cho nang lu

tuang minh lien k€t phonon-plasmon.

(46)

fj,Eg = 1:.(k = O,e.(O» + 1:h(k = O,eh(O».

14

DO tai chudn hoa khe dai (BGR) dUc;1cdinh nghia :

Trong hlOO11 chUng t6i trlnh bay BGR OOula ham cua m~t d() plasma cho 3 gful

dung. Hi~u tffig niSib~t Om thlfy l:Jddy la Sl! khac bi~t 000 giii'a BGR oo~ duQ'cMi

gful dung cMn d()ng hQc tfnh Mn ca tuo'ng Mc h~t tm-phonon ma chUng t6i ~ gQi

la gan dung cMn d()ng hQCday du va giin dung d()ng hQc £0. Trong vilng n6ng d()

000, gan dung d()ng hQc £0 lam vi~c rift t6t. Vi~c bo qua nang Iugng gi~t lui trong

giin dung ghl tmh dADMn m()t sl! ucrc Iugng cao ve Dang Iugng tUo'ng qUaDva k~t

qua dii lam Ulng gia trj tuy~t d6i cua BGR.

Trong hlOO 12 chUng t6i dii ve BGR theo OOi~td() cho gful dung d()ng hQc diiy

du, gan dung d()ng hQc £0 va gful dung £0 gia tinh. (j n6ng d() plasma iMp, gia trj

tuy~t d6i cua BGR giam gful OOutuy~n tfnh vm sl! tang cua OOi~td(). (j n6~g d()

plasma cao, truuc Mt BGR tang va r6i giam OOyvcrisl! tang cua OOi~td(). TAt ca 3

giin dung chung t6i trlnh bay trong hlnh nay cho tMy m()t Sl!ph\l thu()c nhi~t d() cua

BGR tUo'I1gtI! OOau.

T-nnh 13 tr'lnh bay d6 thj cua BGR theo the giam nh6t cho ca 3 gan dung. Tift ca .

dell cho mc)t dang di~u nhu dii chb dQ'i,d6 la gia tr, tuy~t d6i cua BGR tang khi tM

giam nh6t Ulng.SI! khac bi~t giUa BGR trong gful dung d()ng hQCday du va gful dung

gill tinh tang khi tM giam OO6ttang. Trong \TUngtM giam OO6t000, BGR cho gan

dung gia tinh co the sit d\lng duQ'cva ta co the k~t lu~ ding trong cac ban dADkh6i

k~t qua elm gan dung gia tinh su d\lng kha t6t.

Ket lu!)" : Trong chuo'ng nay, vm vi~c xem xet them lien ket giiIa plasma di~n

tit-16 tr6ng va phonon LO kh6i, chung t6i dii tfnh duQ'cphO nang lugng rieng, ham

m~t d() phO cua di~n tit va dii tlm thAy m()t dang di~u quell thu()c nhu trui'1nghQ'pv~t

li~u kh6i va QW. Chung t6i dii chUng to rAng gful dung £0 gia tinh chi th~t Sl! lam

vi~c t6t n€u th~ giam OO6t000 va nhu v~y gful dung nay co the t6t trong cae v~t li~u

kh6i. Ngoili ra chung t6i cling chUng to duQ'cgful dung £0 d()ng hQc lam vi~c rIft t6t

CHWNG 4 : HI~U UNGCHANDONGHQC. MO HlNH NHIEU DAI CON

trong trui'1nghQ'pQWW. VI v~y chung t6i se sit d\lng gful dung nay trong chuo'ng 4.

Trong cac QWW, do hi~u tffig giam OO6thlOOthanh cac dai con nang Iugng trong

15

dlii dfin cling nl1l1dlii hmi trioDo Sl!tach giG'acae dM con thl1C1ng1611trong cac QWW,

VIv~y chung ta thl1C1ngxem xct m6 hlnh chi m<)tdlli con. Thy nhien, trong cac dieu

ki~n thl!c nghj~m nhl1b nhi~t d<)cao, SI!kfch thfch laser m~h, nhieu dill con bi chi€m

gill. 51! phfin b6 cac h!;}tt!\i tren cac dM con khllc nhau phill d6ng m<)tvai tro quaIl

trQng trong d<)tai chuAn h6a cae dM con nhu dii duqc tlm tMy trong QW. Trong Wc

nhieu lac gill nghien cuu BGR cho m<)tdlii, Benner va Grcus dIng cac c<)ngsl! dii tfnh

BGR cho nhieu dlli nhung chi trong gan dung Hartree-Fock, bO qua hi~u U'ngchiin

1. Cae yell t6 ma tr~n di~n m6i

cua tvoog ruc Coulomb.

ruc Coulomb traIl giiia cac h!;}ttIliduqc cho Mi trung b'inhtren cac ham rieng ~I(X)

Cling xuat pIlat tit m<')h'inh QWW rao th€ Mn parabol, y€u t6 ma tr~ cua tUO11g

cua the giam nh6t :

(47) - Xl}!). V(q)lmn = 2(;:2/ dx / dxl~i(x)~;(XI)~s(X')~m(x)KO(lq(x

1M' chan cua tl1O11gruc Coulomb dl1qc cho trong ph!;\ffivi gan dung RPA nha

phl1O11gtrlnh Dyson:

~~srn(q,UJ)= ~rsm(q) + L ~r's'm(q)P::s,(q,UJ)Vs~rsr,(q,UJ),

(48) r',s'

rj

trong do P:~(q,UJ) la phan thl!c cua ham Lindhard l-chieu :

pL ( rs q,UJ -

(k)

f rj k - Hq ) - 2 ""' j L.. (k i,k UJ- es

h (49) . - ,J - e, j ) + q + er

vai fkj va e{(k) tl1O11gU'ngla ham phan b6 va Bang luqng cua h!;}ttlli tren muc nang

l+-

111qngdai con thu l.

, eJ=-+ I

2

E UJ,+2. 2

J

tt2k2 2m' J

( 1)

T~p d,c phl1O11gtrlnh lien k€t

(48) co th~ gilli trong gan dung Fade ma da

dl1qcSlrdl,lngcho cac h~ kh6i va QW dong thai dii duqc chUngto lam vi~c rat

16

(50)

t6t

iJ vung DOng dOplasma caD. Theo dinh nghia cua ham di~n mOif/m,,(q,lJJ) =

1~r8rn(q)[v,~8m(q, IJJ)]-l, ta duQ'c:

2. Niing luQ'ngri~ng nhi~u dai con

(51) flr8m(q,W) = 1- pl, 2:= ~r'8'm(q)V8'r8r'(q) r',8' ~r8m(q) r'8,(Q,W).

k',z',m

(52)

E{(k,z) = -~ L Vz~lm(k-k/,z-z')G~m(k,z'), = E{,HF(k,z) + Ef.corr(k,z),

Nllng luQ'ngrieng dill con tM l trong glin dung cMn dOng hQc b~c nhllt :

E{'JlF(k,z)=-~ L ~mlm(k-k')G~m(k'z'),

(53) k',z',m

.i

1 ~

-

- 1 ]

~I,con(k,z)

- -

-73 L., Vtmlm(k

I ) k

f

1 (k -k'

z - Zl)

[

IIInfmg ItrQ'ngrieng Hartree-Fock khOng chfin,

k',z',rn /mlm,

(54) xG~m(k'z'),

Iii nfmg luqng rieng tucrng qUaD.

(55)

~f.IlF(k,C{(k)) = - L~m'm(q)f;;lq'

Phan Hartree-FockkhOng chfin elJa Dang luqng rieng dcrnh~t trong delicon thu l:

D6i vai ham di~n mOinh~ duQ'ctlr (51) :

)

rr q,w

fh"lm(q,lJJ) =

~rrm(q)Vrmlr(q) pL ( u ( ) Ylmlm q

1 - ~ L r

q,m

(56)

) r8 q,1JJ ,

m = l cho s6 hlplg cheo va m i- l cho s6 hlplg trao dOLDo dong gop nho cua s6 hlplg tan x~ giUacae dai con, chung tOise hlpl eM xem xet chi 2 s6 hlplg dau lien

- ~ ~r8m(q)V8mlr(q) pL ( 11 ( ) IIlmlm q L., -I- r,8-rr

17

!rung cOngthtk (56) ca cho s6 h~ngch~ova IraQd6i cila ham di~n moL

Ok kfch thfch t~p th~ dugc cho bOi €(q,w) = O.T~n s6 plasma bell trong diUva s6 s6ng duln hen trong dai :

(57)

'

- v,;rm(q) njq2 m ' (q) J

. "Imlm

r,J

2 '" - wpl,lmlm - L t 1T

(58)

2

n~

Wpl,lmlm .

Lr,j,k v,;rm(q)f;j(l- frj) 2 ,2 Xlml1ll - 2(3 - Lr,j v,rrm(q);;;

2

(

D~ dan gillll trong vi~c tmh loan bilng s6 chUng tCliSlrd1}nggill dung c1!c-plasmon

,

2

~- W2

) - 1 -

q,lrnlrn

IOlmlrn

q, W -

wpl,lmlrn -

W2 + Wpl,lrnlm

(59)

X'mlm

It

W;,lmlm = W;"lm'm(1 + -1- ) + (~2 )2 .

Khi d6, chung ta nh~n dugc pMn nang lugng rieng tl1

.

2',f.corr (k, e{ (k))

'" wfmlm L t v,mlm(q)- 2Wq,lmlm q,m

g(Wq,lrnlm)+ 1 - f~~q x e{(k)-e!n(k-q)-Wq,lrnlm+i<'i

[

(60)

g(Wq,lmlm)+ f;~q + e{(k) - e!n(k - q) + Wq,lrnlm+ i<'i .

]

3. Dc)(:Iichuiln hoa dai con

(61)

(62)

D\) I

llE; = 2',/(k = O,e,(O)) + 2',:'(k= O,e:'(O)).

Ok tham s6 st'r d1}ngcho tmh s6 gi6ng nhu chu<1ng3 . Chung !Oi chi xem xet

Info-nghlJp :I d,li can.

I-nnh 14 chi ra d\) tai chudn h6a khe dlli cho 3 dlli can nhula mQt ham cua nOng

dO plasma loan phan Irong gan dung ch~n dQng hQc va glin dung Rartree-Pock. Ri~u

18

li'ng nOi bf:\.tla sl! kMc bi~t 16'0gifta SBR trong gan dung chlln dQng hQCva gan dung

Hartree-Fock. Trong vUng n6ng dQplasma thap, gall dung Hartree-fock cho SBR nho do vi~c bo qua niing luqng ri~ng tuo'ng quan. LUlly riing dau cua niing luQ'Ilgri~ng tuo'ng quail thay dOi khi n6ng dQ plasma loan phan dl;1tMn mQt gia tr, naG ~ 1 cho dIDcon l = 0 va naG ~ 3 cho dIDcon l = L MQt di~m dang lUlly khac trong hinh

14 la s,! kt!ac nhau cua dQ tach gifta cac dai con (hi~u gifta tlE~ va tlE~) : trong lUc dQ tach gifta cac dai con trong gall dung Hartree-Fock 100, glin dung cMn dQng hQc

Il;1igay nen dQ tach nho.

Tmng hinh 15 chUng tOr dii ve SBR theo nhi~t dQ tmng 2 g!1ndung. 010 dIDcon

th~

nhi~t d() IMp. Thy nhi~n, Val cac dai con cao ho'n (l = 1 va l = 2) S1,tch:in khOng

l = 0, sl! ch:in gay nen mQtsv thu nho ml;1nhgiatr, tuy~t d6i cua SBR trong vting

hi~n m()t val tro quan trQng nao va dong gap cua niing luqng rieng tUO'J1gquan gay ra

mQt sl! kMc bi~t 16'0trong SBR cua cac diii con nay.

mnh 16 bi~u hi~n SBR theo n. K€t qua chUng to Sl! khac bi~t qua 16'0giiia gall

dung Hartree-Fock va gall dung ch:in dQng hQc khi tM gram nh6t 16'0.SI! khac bi~t

giiia 2 gAndung chi nho khi tM gram nh6t nM chUng to rang g!1ndung Hartree- Fock

kha di co th~ si'1dl:mgtrong cac h~ ban clan kh6i.

Ket lui),n: Trong chuO'J1gnay, chung tOrdii danh gia duQ'cSBR tmng QWW cho

2 gAn dung va dft tim tMy mOt SIf khac bi~t 16'0giiia gAn dung cMn dQng hQc va

g!1ndung Hartree-Fock, d~c bi~t lJ vUng n6ng dQ plasma cao va tM gram nh6t 16'0.

Chung tOi dietsi'1d\lng mQt Val g!1ndung: g!1ndung cl!c-plasmon, gall dung Parle va

bo qua s6 hl;lng tan XI;lgiUa cac d,!i con. 01ung tOr dietchung to duQ'cdong gap cua

Bang Itrqng ri~ng tl1o'ngquan vao SBR la quan trQng va no khOng duQ'cbo qua, d<)c

bi~t tmng vung n6ng dQ plasma cao, lJ do SI!eh:in tr<'1n~n quan trQng.

KliT LU~N

Chung tor dii trinh bay tmng lu~n an nay 2 10l;1ibar loan trong Call trUe QWW la

bar loan h~ mQt hl;1tva h~ nhieu hl;ltma chUng th~ hi~n tfnh chat di~n va quang hQc

cua QWw. Chung tOrdii tlwc hi~n vi~c Hnh loan tr~n cac mO hlnh QWW khac nhau

19

: QWW be miJt, QWW cM nh$t va mO h1nh QWW vm rao tM ben parabol.

V6'i biii loan h~ mOt h~t, trong cac ca'u trUc QWW co rao the!b1ftd6i xUng, bilng

phuang phap 1Va- Hartree chUng tOi dii giro quye!t van d~ mang tfrih phuang pMp

luQ.ntrong vi~c sit d~ng phuang pMp bie!n thien de giro phuang trlnh SchrOdinger,

danh gia duQ'Chi~u Ung di~n IrUUngIen cac mUGnang Iuqng cua di~ri tit, nang Iuqng

lien k!t vii h~ s6 pMn clfc cua t~p GMt, tUdo cho chUng ta tha'y duQ'cdang di~u dOng

hQc elm dlc hl,lttai trong cac d~ng c~ di~n tit sit d~ng ca'u trUcQWW. CluIng tOi cling

Om tha'y mOt slf arm hubng m~ cua di~n IrUUngIen nang luqng lien ke!tcua exciton

trong cac QWW rao tM ben parabol.

Cho bili loan h~ nhi~u h~t, vm mO h1nh QWW rao the!ben paraboI, chUng tOi

dii tfnh duQ'cham phO niing luqng rieng va m~t dO pM cua di~n tit, BGR cua Qww

trong ph':lm vi gan dung PPA cua slf chiin dOng hQc, ma nhu dii bie!t trong ca'u truc

kMi va QW, dO co cua khe dai dii giai thfch duQ'Cban GMt dich chuyen v~ vitng xanh

cila phO Quang hQc h~ ban clan. ChUng tOi dii chi ra bilng tfnh loan Iy thuye!t dong

gap cila phonon LO kh6i trong BGR khOng I6'n vi v~y co the sit d~ng mO hlnh glin

dung chilil EOdOng h<;>c,ding nhu dii chi ra rAng glin dung chiin dOng h<;>cphai duQ'c

su dl)ng trong vi~c danh gia BGR v1mO h1nh gan dung chiin gia tinh danh gia BGR

trong QWW qua 16'n.Ngoai fa, v6'i kc!tqua Om duQ'cchUng tOi dii chUng to duQ'ccac

gan dung ghl tlnh va Hartree-Fock kha ill chi co the sit d~ng trong cac v~t li~u ban clan kh6i.

Trong lu~n an nay, chUng tOi cling dii u6'c luqng duQ'cSBR trong QWW, do Ia mOt

di.!-ctrung quan trQng cua h~ tha'p chi~u. Ngoai ra vm vi~ xem xet anh hubng cua

quan do la d~c diem doi da'ucila no trong vitng bu6'csong dai ma nhu chung ta dii .

plasma. chung tOi cling 11mtha'y duQ'cmOt diJc diem kM nOi b~t v~ niing luqng tuang

bic!ttrong cac sach giao khoa v~ h~ nhieu h~t, nguui ta dii trmh bay ni\.ngluqng wang

quan t':li k,.. va dii khOng Om tha'y d~c diem nay.

N6i t6m I~i, vcricac kc!tqua d~t duQ'ctrong lu~n an nay, chUng tOi dii co nhUng

dang gap nh!\'tdinh vilo slf hieu bi!t ve tfnh GMt di~n va Quang h<;>ccua h~ ban clan

20

QWW d(\ng thai hoan thi~n ban cac tfnh loan cila cac GOngtrlnh trucrc day.

"

,//

"

1.1,-

/'

"

////

,/

..

;- I ~

~:," ... 'if

,//

/,/

1.4L//

~

'"

100

"

1.1 '"

'"

..

F(kW",,}

" '" ..

tnnh I : IIn; nuk nAngl"\1I1gIMp nM! nhlt IAhAmeun wOng

tnnh

2 : II~ s6 pMn e~ <>p nhlt IAhAm eun L..

ettbng dQ dj~n

dQdj~n InJln'g F. NAngIltQ11gt"",g !hIlico bAn: dltOngIi~neho

0

0

tnJOng F = 50k V! em : dltOng Ii~ eho di~ trttbng "'ng ,ong

D. = 300 A, dltOngg~eheho L. = 600 A. NAngl"\1I1g

trye Y (lhang Wi) vAdttbng g~eh eho di~n trubng ,ong "'ng trye

klch Ihleh ddu li~n : dttbng gleh-ehd.. ehn L.

0 = 300 A.

:I: (Ihang phil).

0 dltOngehd.. eho D. = 600 A.

30

0."

~,

,

0.11L

"'"

,

""'"

1,(:J

w.-

~ ~"'~"'"

II

f om,

';J- 01"

~-

"'"

""

om

;- I ;1

~ "---~

'30

.~

'"

100

""

w.

------ Qj

..

a(:J

IJ(degrees)

tnnh 3 : NAnglUQ11gIi~n k€i Eb nhlt hAmcu. kfeh thlt"" a

0

mnh

cu. QWW ehii nhA'v(ri kfeh Ihlt"" b = 150 A, ',p eMI b

0

.

trltOngvAtrye:l:choa

:1:0 = YO = OvAeltOngdQdj~ntrttbngF

= JOOkV!em.

8 = 45°. DltOngl;~nehorAolh€hiillh"Vo

= 0.4eV.

4 : H~ s6 phAn eye <>p nhlt hAm CURg6c 8 g;iin dl~n 0 = 100 A,b = 50 A.:l:O = YO = O. vAF = 200kV!cm. Dttbngli~n:rAothl!hiillh,,(Vo = O.4eV), dltOngg,ch:rAnthl!vOh".

dltOng g,eh eho rAo Ih€ vO h".

21

'" "

"

~

'"

'--',

/

"

>'

,

I //'~--------- i,, -- --- ,-,---

, ';~-~'"

,I

'-'

;;!

..

""

'00

----. ", I ""., "" \ // ' \ , '" "1

..

a(;)

.n

"

,.,

Y.(;)

0

0

0

0"/n1g li~n:

rAo thEMu

H1nb 5 : NOng1"<;1I1glito kEt Eb nh" him CUBvi tr! t~p ch

0

0

d"lmg

Koch

: Ibo IhE v~ h~n

0

mob 6 : NOng1"<;1I1glito kt"1Eb nb" him theo kich th""" a CUBQWW eM nh~t do thE biJub", Vo = O.4e V tho a X li~n : a X b = b = eonst vA"'0 = 110 = O. I)~g g~eb-ehlin : a X b = 100 A X 100 A vAF = 0; d~g 1001 X1001. F = 100kV!em vAe = 90°; d"lmg g~ch : a X b = 200 A X200 A vA F = 0; d"lmg ohlin 0 : a X b = 200 A x200 A vAF = 100kV!em vii

e = 90° . Inoh btn tmng : khu6:h d~ CUBd"lmg g~ch.

"

" !

.r

.", "

/////

/"

,/

....

,- ! .r

/. .

..

F~V'~

In(R)

8 : Nilng 1"<;1I1glito kEt Eb nh" him CUBn. O"lmg Ii~n

mnh

7 : NOog 1"<:JOgli~o kEt Eb nh" him cUa C"lmg d~ dj~n

d"lmg g~ch tho F = 75kV!cm

vii

tnrlmg /0'. O"I"'g li~ntho n = 15R. d"lmg g~ch tho n = 20n vild"/n1gchJimtho n = 20R.

mob tho F = lOOk V lorn. d"lmgehlin tho F = 50kV!em,

22

~

r,

a: a <5 .a: ;:;.

/1

a:- 2 a <5 ~

ji

10

15

10

10

.15

mfR

0 .15

.10

.5

10

15

mob 9 : Phl!nIh~c CUOOo.ngI"QIIgri~og E. (0, "') oh" hAm

mfR

cUa '" cho k = O. DUOnglib> r:r = 00 K) vAd"lmg g,ch

mob 10: HAmm,' dQph6 di~ tit A.(O,

"') nhllbAm cuo '"

cook = O.cac tbarn s6 gi6ng ohll hlnh 3.1.

(T = 500 K) !rang gl!n dung ~ng hQCday diL DUOngg,ch. chdin (T = 00 K) vAd"lmg chdin (T = 500 K) troog gl!n dung '0.

.10

.IS

..

;;.E ~."

,

~.........................

.35

"""'"""""""""""""""""""""""""""""""""""""

!

-..',

~

..,L .

w

150

3JO

2W

300

100

1.5

20

D.5

1.0

'0

T(K)

'a,

mob

12 : DQ lAi chul!n h6o kJ1c do !:>.Eo

nhlliA mQl hAm cuo

mob

II

: DQ I.i chul!n hOOkJ1c do !:>'Eo nIl" IAmQI hAm cUa

nhi~tdQchon = 10Rbdco6ngdQplasm.kh4cnhoILDlllmg

n6ngdQplasmochoT = 3000K vAn = lOR. Dlllmglil!n:

lil!o : gl!n dung d<)ng hQC day du, dlllmg g~h

: gl!n dUng d<)ng

gl!n dUng d<)ng hQC day du, d"lmg g,ch : gl!n dung dQng hQC '0

hQC '0

vA d"lmg chdin : gl!n dUng '0 giA-tinh. cac d"lmg nh,t

vA dulmg ch(m : gl!n dUng '0 giA'linh.

chn nao = 0.1, cAcdlllmgdAmcho naO = I.

23

w 0.0

'"

'"

i;:;~.::~:>~<.:::~

'"

~ .to w' ~

.IS

OJ. m ~

co

.20

0

na,

10

10 0

40

30

:;.5.

mob

'" a(R)

14 : D~ tAl chui\n h6n dRi con (t;,.E~)

nhu lA hAm CUR

mob

13 : D~ Ini chui\n h6n khe dM t;,.Eg

nhuU m~I h~m CUR

1M ginm nh61n cho T = 3000 K vi noo = 1.5. Duling

liln , giln dung d~ng hoc ddy du, dulmg g~ch : gdn dUng dUng

hoc <0 vi dui'mg ehnm : gdn dUng <0 gi.'liM.

m~t d~ di~n tit toiln phi\n trong QWW cho T = 500 K v~ n = lOR. Dulingliln d~ : I = 0 SUR,dullngg~ch~ : I = 1 SURv~ dulmg chlfmd~m : I = 2 SURtroog gtln duoS chAod~ng hOC.Dui'mgliln nh~t : I = 0 SUR,dulmg g~ch nh~t : I = 1 SUR v~ dui'mg chlm nh~1 : I = 2 SUR troog gdo dung lIartree.Fock.

"""""""":,:.::,:.::,:.::.:.::.:.::,:,::.:,::.:,

a:

............................................

a:

:;::.:~:

w ~

w' , ~

.12

12

.16

10

40

""

"'"

200

100

1m

30

",

T("K)

mob 16: D~ tM chui\n hOOd.i con (t;,.E~)

nhu lA hAm CURtM

tllrch

giam nh6t n b nhi~1d6 T = 500 K vi noo = 2. 01.

mnh IS :f)~I'ichlldnh6ndRicon(t;,.E~)nhUIAhAmeun nhi~1d~ cho n = lOll b m~1 d~ toiln phtln noO = 2, all! thleh CURcnc

CURde dulmg gi6ng nhu h1nh 4.5.

24

'" a/A