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- 80 GIAO DUC vA DAo TAO
D~ HQCQuac TP. HCM
GIA
TRuONG D~I HQC KHOA HQC Tt!NHIEN
CAO BUY THll;N
, ,.:' A'" 7 ,.:'...
TINH CHAT D~N VA QUANG K
CUA T~p CHAT VA A 7
EXCITON TRaNG DAY GIENG LUQNG TV
A" "', A' ,
Chuyen nganh: V~T LY LY THUYET VA V~T LY TOAN
Ma 56 : 1.02.01
H~:rl!-Nt>:-"~
1!:):~ ;,
TUE?'\!'r-~'
' (
n.---- .--,, ,-..---- j
1..1 ;,-, ;", ' it
1
I
C -~-_J
, -!: A' '" -A'
TOM TAT LUhN AN TIEN SI V~T LY
-
, '" '" ,
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
~ I
Phan bi~n 1 : .(;,..~IS...N~.~..A,:..':J;e}............................
-
r
~ r - H N,n .,
\1 '(\ \r
- Md DAU
Trong VID nam 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-figao nhu QWW tr\l,
c
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;lt ai. De khiic ph\lc kh6 khan nay, chUng tOi sir d\lng g!in dung TlJa-Hartree dii
t
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;lP
cMt. 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.
M ban
Ducri ki'ch thi'ch laser m~nh trong cac dAfthinh thanh plasma di~n tir-lei
tr6ng d~l.mdiJ.c,khi do do cac hi~u U"ng
tlfClngquan-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"ng tuytn quang hQc.
phi
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-giAtinh. Ngoai fa, nhu dii bi~t m
- cMn dOng hQc do lien k~t plasmon-phonon trong phl;\m vi gttn dung ctfc-plasmon-
phonon de tfnh nang lu
- Xua't phat ta phuo'l1gtrlnh SchrOdinger cho dAygieng luQ'l1g vcritM giam nh6t
fir
V(x, y) :
n2 82 82
(I)
{ - 2m. [ 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
phl1o'11grlnh Hartree :
t
Ji2 82
!
2m. 8X2 + V(x, Y)X2(y) dy } a(x) = €za(x), (2)
{ ~
n2 82
!
{ - 2m. 8y2 + V(x, y)a2(x) dx } X(y) = €yX(Y), (3)
€=€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
lac V(x,y).
2.Anh huang eua di~n tru(mg Jen die mue HAngluqng trong dlly luqng fir b~ m!)t
Bastard va Mazin dii tfnh cae mue Hang luQ'l1geua di~n fir trong day luQ'l1g M
fir
m~t.v(1irao tM V(x, y) co d~lIIg:
(5)
- Ly)] + L~.lIO(y Ly)O(x2 - L;/4),
-
V(:1:,y) = V1O[y(y
(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;}t rong di~n trui'mg ngoai d~u
t
song song vcrifn;1ey :
n2\J2
(6)
H = -- 2m. + V(x,y) + eF(y - Yo),
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)
- Wno(x,y) dugc lay nhu tfch cac nghi~m cua cac phuO'l1gtrinh T1,1a-Hartreecho Mi
Bastard va Mazin. Ham song bie'n thien q)n(x, y) :
= exp[-t1n(Y - Yo)], (8)
q)n(X,y)
Chung t6i thtJc hi~n pMp Hnh bie'n thien d6i v6'i t1n de xac djnh cac muc nang
lugng cua di~n tit. Khi do, h~ s6 phAn ctJc cua di~n tit dugc dinh nghia nhu sau :
e
(9)
- a va b la cae kfch tll\16'e eua QWW.
dem gian sau :
Ham song thu tr~g th:ii eC1ban e6 d~g
(12)
W(x, y, z) = NWo(x, y)4J(x, y, z) .
Ham iIlo(x, y) e6 the Iffy nhl1 tfeh cae nghi~m eua h~ phl1emgtrlnh 1Va-Hartree :
. ft2 82 a2 a2
(13)
= Exf(x),
{ - 2m" 8X2 + Vo [B(X2 - ""4)+ B(""4- X2)p" ] } lex)
Ti,2 82 b2
(14)
+ Vo [ Pl,xB(y2 - "4) + P2,x] } Bey) = E"g(y),
{ - 2m" 8y2
(15)
Eo = Ex + E" - VO[P2,x + P1,xP,,] ,
b2
P" = J B(y2 - "4)g2(y)dy,
a2
J
P1,x = (16)
B(""4- x2)f2(x) dx,
J a2
P2,x = B(X2 - ""4)f2(X) dx.
su dl;mg
Neu d~\tPI,x := 1 va P2,x := P" := 0, chUng ta se nMn dl1qe nghi~m dii dl1qe
nhl1 dii n6i t'1tren. Ham thlt 4J(x,y, z) dl1qe eho dl1ai d;.tng:
bt'1i Osorio
(17)
+ ysinB)] ,
4J(x, 1('z) = exp[-'x1f - rolJexp[-,B(xcosB
Nang Il1qng lien k~t t;.tp eMt Eb :
E(,B,'x = O)min - E(,B, 'x)min . (18)
Eb =
H~ s6 pMn Qre eua t;.tpeMt dl1qe dinh nghia :
a" = - ~ {(iIllxcosB + ysinBIW) Ji'ofO - (iIllxcosB + ysinBliII) F=O}. (19)
F
Cae k€t qua bfuIg s6 th1!e hi~n eho QWW GaAs : Vo = O.4eV, m" = O.067mo
va f = 12.53.
Niing Il1qnglien k~t Eb (hinh 3) eua m
- 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
klch thuac day nho.
M s6
Trong hlnh 4, chUng tOi trlnh bay pMn qrc ap nhu ml)t ham cua goc (). H~
s6 pMn cgc giam khi tang. () vi trong truOng h
- 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 h111h Lhechii nh~t. Brum va Bastard dii nghien cuu hi~u tffig di~n twang
rao
I~n nung lulJng lien kef cua tr~ng thai CC1an cua mQt exciton trong mQt QW. Brown
b
va Spector dii.tlnh nang luqng lien kef tr~g thai CC1an cua mQt exciton bi giam nMt
b
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 CC1 an cua mQt exciton Wannier trong mQt QWW rao tM
b
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
- Voi nghi~m q[, va E, trong ban dAn kMi ta dl1c;fc
tOng thU'cElliot 3-chi~u cho
phO hfip tllU :
fiuJ 00 471" 1 7I"e" /...!li.
(22)
a(w)=ag- R [ n=l n
L.:30(~+2)+8(~). smh(7I"/VIS. ] ,
n ~)
-
trong d6 n la s61uqngtit chfnh, ~ = (fiuJ Eg)/ R, R la Dang
luqngRydberg3-chieu
va ag la h~ s6 ph\l thu~c s6 chieu va dcv
Chung ta tMy tir phu
- b day tjJ(Ye)va tjJ(y,,) la ham song cua di~n tit va 10tr6ng d
- kfch thfch laser m1p1h,
nhi~u tfnh chA't an h~t cua h~ bi tlii chua.nhoa do
d
Dll
- 56 h~U1gCoulomb:
H -1 '" V. ~+ ~+ ~ , (31) .
c - "2 L, qak+q,nttAakl-q,n2,Alak',n3,,\,ak,n.,A,
k,kl,q,N,A,A'
trong d6 N = {nt,n2,na,n4} va
dz
! I I
d ~1 (x, y)~2Y (x'y')n3N (x', y')n.,A(x, y)eiqz
,A
= y;dxdy x dy
Vq
e2
(32)
- x')2 + (y - y')2 + Z2 .
X EOV(X
2. S,! cMn d()ng hQcbm phonon va plasmon Ii~n k€t
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
e2 q2
(33)
( 4{111) '
V(q) Eooexp [ 4fL11 1(0
= ]
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
- 1 q4
2 2
(38)
CJJq = CJJpl { 1 + V(q) I>-
,-e,h 7fiii} + 4p2 '
On.
vUin Him~tdOdai plasrna.Khi do, ham di~nm6i :
2
-
2 .
CJJ2 CJJpl
CJJL T (39)
[1- CJJ2_CJJ} - CJJ2+CJJ;,-CJJ~]
E(q,CJJ)=Eoo
Ole mode ri~ng cila cac phonon, plasmon li~n ket CJJi cUC1ng dao dOng tlr
va dO
Ui(i = 1,2) duge cho bc:'1i cVc va th~ng du cila c1 (q, CJJ)
cac :
U1 U2
-1 1
(40)
E (q,CJJ)=- 1+ 2 2+ 2 2.
Eoo [ CJJ - CJJI CJJ - CJJ2
]
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"11g
ri~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
gan dung b~c 1:
-~L Vs(k',z')G?(k (41)
- k',z -
~i(k,z) = Zl),
k',z'
trong do z, Z' tl1ang lIng Iii cac t11ns6 Matsubara cho fermion va boson, G? (k', z') Iii
ham Green b~c o.
I-HimphO nang lugng ri~ng :
~i(k,CJJ)=~r"(k)-L roo dCJJ'
ImVs(q,CJJ: ib)[l+g(CJJ')-J;(k-q)]
+ 42
J +
CJJ ~b- ei(k - q) + Pi - CJJI .( )
q 7r
-00
L V(q)/;(k - (43)
~iX(k) = - q),
q
= la ham pMn b6 boson
g(CJJ) ell:-l
Ham m~tdOph6 dun h1;lt
:
)= 2Iml~i(k,CJJ)1
A.(k (44)
- ei(k) - Re~i(k,CJJW + [Im~i(k,CJJW .
"CJJ (CJJ Pi
+
13
- Xet truCmghqp cua QWW GaAs v6i cac tham s6 dUc;1c dl;mg : m. = O.O67mo,
sir
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
- 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'I1g OOau.
tI!
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 \TUng giam OO6t000, BGR cho gan
tM
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
trong trui'1nghQ'pQWW. VI v~y chung t6i se sit d\lng gful dung nay trong chuo'ng 4.
CHWNG 4 : HI~U UNGCHANDONGHQC. MO HlNH NHIEU DAI CON
Trong cac QWW, do hi~u tffig giam OO6thlOOthanh cac dai con nang Iugng trong
15
- dlii dfin cling nl1l1 hmi trioDo Sl!tach giG'acae dM con thl1C1ng 611
dlii 1 trong cac QWW,
VIv~y chung ta thl1C1ng em xct m6 hlnh chi m
- t6t iJ vung DOng dOplasma caD. Theo dinh nghia cua ham di~n mOi f/m,,(q,lJJ) =
1~r8rn(q)[v,~8m(q, IJJ)]-l, ta duQ'c:
(51)
flr8m(q,W) = 1- 2:= ~r'8'm(q)V8'r8r'(q) pl,
r',8' ~r8m(q) r'8,(Q,W).
2. Niing luQ'ngri~ng nhi~u dai con
Nllng luQ'ngrieng dill con tM l trong glin dung cMn dOng hQc b~c nhllt :
L
-~ k',z',m Vz~lm(k-k/,z-z')G~m(k,z'),
=
E{(k,z)
(52)
= E{,HF(k,z) + Ef.corr(k,z),
L (53)
E{'JlF(k,z)=-~ ~mlm(k-k')G~m(k'z'),
k',z',m
IIInfmg ItrQ'ngrieng Hartree-Fock khOng chfin,
-1
.i - 1~ - I) 1
~I,con(k,z) - -73 k',z',rn Vtmlm(k k [ f /mlm,(k -k'
L., z - Zl) ]
xG~m(k'z'), (54)
Iii nfmg luqng rieng tucrng qUaD.
Phan Hartree-FockkhOng chfin elJa Dang luqng rieng dcrnh~t trong deli con thu l:
(55)
~f.IlF(k,C{(k)) = - L~m'm(q)f;;lq'
q,m
D6i vai ham di~n mOinh~ duQ'ctlr (51) :
1- L
~ ~rrm(q)Vrmlr(q) pL (q,w )
fh"lm(q,lJJ) = rr
uYlmlm ( q )
r
-~ ~r8m(q)V8mlr(q) pL (q,1JJ , (56)
)
r8
L., 11 ()
-I- IIlmlm q
r,8-rr
= l cho s6 hlplg cheo va m i-
m 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
17
- cOngthtk (56) ca cho s6 h~ngch~ova IraQd6i cila ham di~n moL
!rung
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 :
v,;rm(q) -
2 - '" njq2
(57)
wpl,lmlm - L t 1T m J' '
(q)
r,J. "Imlm
- 2 (3Lr,j,k v,;rm(q)f;j(l- frj) 2
,2 (58)
.
Xlml1ll - 2 n~ Wpl,lmlm
Lr,j v,rrm(q);;;
D~ dan gillll trong vi~c tmh loan bilng s6 chUng tCliSlrd1}nggill dung c1!c-plasmon
2
,
( ) - 1- (59)
wpl,lmlrn ~-
2 W2
+ Wpl,lrnlm
W- -
IOlmlrn q, W2 q,lrnlrn
( )+ ( ) .
2
= W;"lm'm 1 + -1- (60)
W;,lmlm ~2
X'mlm It
Khi d6, chung ta nh~n dugc pMn nang lugng rieng tl1
nguon tai.lieu . vn
