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
CAO BUY THll;N
, ,.:' A'" 7 ,.:'
TINH CHAT D~N VA QUANG CUA T~p CHATVA
A K 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
1!:):~ ;, H~:rl!-Nt>:-"~
\
T
UE?'\!'r-~' (
'
1
n 1 1 ;,-, ;", ' it j
C
. - ,, ,
I
-~-_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 19L9 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 19L9 thuy€t, Phan vi~n V~t 19TP H6 Chi Minh, Trung tam Khoa hQCva
C6ng ngh~ Qu6c gia.
Ngll'Oi hl16'ng dfin khoa hQc : 1. GSTS

Tr~n Tho~i Ouy Bao
2. PGS PTS Nguy~nNhl)tKhanh
~ I
Phan bi~n 1 : .(;, ~IS N~.~ A,: ':J;e}
\1 '(\ \r<' r ~ r -H-N,n.,
". h~ "" '10.: ~ A (t)
,. /', ';)'-
N
' ~~ N . /L '
Phan bl~n 2: .ti$ t.I.S .
~
eoo at:)c ':'C1~o ,
J\ ' I <,,' Q-7~TP II~"'" 1'14' J
t"R(.l t\~( uo.:: c11a rm ht'ltl ,.I,".J.h
'. : ) O' r
Ph~mbi~n 3 : ./>.4<;.p.rS N ~':f/ll. .11-hJ.c Nl.f-!l?"""":j
4}ai h.f?( ~. .~~.'IM Tt ffi clu.MI.~J,
.,' .
LU~11an se duqc bao ~e ~i H<)id6ng C
~
'mlu~nancapnhanuac hop~i
'Z , -'\ P. ,/ M,'
.) ~Y'.I!-~. J~Qf Kbc<~ J C1 J!" N ~ 7 ' {-J;; clv .'!t.h
vao h6i f! giG &1> ngay 2 thang.l~ nam 199~.
C6 th~ tlm hi~u lu~n an ~i Thu vi~n Truemg D~i hQc Khoa hQc TVnhien, D~i
hQc Qu6c gia TP H6 Chi Minh va Thu vi~n T6ng hqp TP H6 Chi minh.
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 vcricac 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 vcrimiJtphAng 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
mOhinh rao thtgiam nh6t vOh~ hoiJc hiiu h~n c6 tfnh d6i XU-figcao nhu QWW tr\l,
QWW chli nh~t vcrirao th~ vOh~n. D6i vcricac 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 Dangluqng
cua h1;lttai. De khiic ph\lc kh6 khan nay, chUng tOisir 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
Mban 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-giAtinh. 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 hQcCURh~. Cho Mn nay, d6i vOOcac h~ QWW, d<)tlii chuiIn
h6a d:',icon chi mOOdUng I~i xem xet b gdn dung Hartree"Fock, nghia la bOqua 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<)ttr\1Ung
trung blnh khi xem xet tuO"ngtic giiia m<)th~t tAinay 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 mOhlnh 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~ephuO"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 giAkhac lien quaIl den d~
lai elm III~nan ma se gi&ithi~u trong tUng ehuO"ngcua luQ.nan d~ de dang tha:y r5
hO"nnhUng k~t qua ma chUng tOidii d~t duge.
LuQ.nan gOm4 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 dOth!.
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~ndi~n tit va t~p cMt trong eac
QWW co rao the ba:td6i xtffig. Trong ehuO"ng2, chUngtOisit d!,lngphuO"ngphap bien
(hien d~ I(nh Dang luqng li~n ket exciton Wannier trong QWW ducritlic 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;\mvi gttn dung ctfc-plasmon-
phonon de tfnh nang lu<JI1grieng trong glin dung b~cd!iu lien va tll do tinh ham pM

nang lu<JI1grieng, ham m~t d<)phISva dO t<iichuAn bOa khe dill. Trong chu<1JJ.g4,
ding vm hlnh tMc lu~ ham Green Matsubara, chUng t6i da u6'c lu<JI1gduqc dO t<ii
chuAn bOa dill con du6'i t<icdOng cua hi~u li'ngchAodOng hQc nhieu dlli con v6'icac
glin dung thfch hqp.
BOi VIcac 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<JI1gco ban trong cac
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<JI1gv~t 19 cua cac mAll ban dAn
kh6i va cac cliu trUc h~ thap chieu.
CHWNG I :HI~U UNGDI~ TRllNG TRENDAY GI~NG Ut;jNG Hi
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 mOtvai 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<JI1glien k~t cua t/,\pchlft trong day cM nh~t vui tfnh cMt
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<JI1gcua di~n tu. Glin day h<1JJ.,bai toan tI,lpcMt trong QWW du6'i tlic d()ng cua
di~n trI1emgding duqc qUaDtam nghien cUu.Narayani va Sukuma da nghien cUu bai
loan v&i stf co ml.\tcua 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
huang cua di~n trI1emgtren cac day lu<JI1gtUbe ml.\tva dlly lu<JI1gtUchii nh~t rao tM
hihl h/,\n.
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

[
82 82
] }
- 2m. 8X2 + 8y2 + V(x, y) w(x, y) = €w(x, y) .
(I)
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'11gtrlnh Hartree :
{
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 Jendie 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'l1gfir M
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),
(5)
(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
song song vcrifn;1ey :

n2\J2
H = + V(x,y) + eF(y - Yo),
2m.
(6)
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 :
w,,(x,y) = Nnwno(x,y)<P,,(x,y),n = 1,2
(7)
4
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) :
q)n(X,y) = exp[-t1n(Y - Yo)], (8)
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
<1p = -F {(wdylwl)F;lo- (wdylwl)F=O}.
(9)
cac Hnhloan s6 dugc thtJchi~n cho dAyhrgng tit be m<}tGa(ln)As - GaAs
v6'icac tham s6 dii dugc sit d\mg : m* = 0.06mo, Lv = 50 A, VI = 0.15eV va
.6.V = 0.8eV.
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 fJdAydugc
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 mOtdi~n

IiI baa quanh tl;lPchill trong QWW chii nh~t raa the' hiiu hl;lndl}.ttrong di~n tnrcmg
ngoai thfing goc v6'i tfl}c dAy:
~~. ~
H =
2
+ V(x,y) + eF(xcosB+ ysinB)- 1- -I'
m* f r - ro
00)
trang do 8 la goc giUa hu6'ng di~n twang va trl}Cx. Rao the' V (x, y) co d~g :
[
a2 a2 b2
]
V(x,y) = VO 8(X2- 4) + 8(4 - x2)8(y2- 4) ,
(11)
5
a va b la caekfch tll\16'e eua QWW.
Ham song thu tr~g th:ii eC1ban e6 d~g dem gian sau :
W(x, y, z) = NWo(x, y)4J(x, y, z) . (12)
Ham iIlo(x,y) e6 the Iffy nhl1 tfeh cae nghi~m eua h~ phl1emgtrlnh 1Va-Hartree :
{
. ft2 82
[
a2 a2
] }
- 2m" 8X2+ Vo B(X2- ""4)+ B(""4- X2)p" lex) = Exf(x),
(13)
{
Ti,2 82
[
b2

] }
- 2m" 8y2 + Vo Pl,xB(y2 - "4) + P2,x Bey) =E"g(y),
Eo = Ex+ E" - VO[P2,x+ P1,xP,,] ,
(14)
(15)
P" =
J
b2
B(y2 - "4)g2(y)dy,
J
a2
B(""4- x2)f2(x) dx,
J
a2
B(X2 - ""4)f2(X) dx.
(16)
P1,x =
P2,x =
Neu d~\tPI,x := 1 va P2,x := P" := 0, chUng ta se nMn dl1qe nghi~m dii dl1qe su dl;mg
bt'1i Osorio nhl1 dii n6i t'1tren. Ham thlt 4J(x,y, z) dl1qe eho dl1ai d;.tng:
4J(x, 1('z) = exp[-'x1f - rolJexp[-,B(xcosB + ysinB)] ,
(17)
Nang Il1qnglien k~t t;.tpeMt Eb :
Eb = E(,B,'x = O)min- E(,B,'x)min.
(18)
H~ s6 pMn Qre eua t;.tpeMt dl1qedinh nghia :
a" = - ~ {(iIllxcosB+ysinBIW)Ji'ofO - (iIllxcosB+ ysinBliII)F=O}.
F
(19)
Cae k€t qua bfuIg s6 th1!ehi~n eho QWW GaAs : Vo = O.4eV, m" = O.067mo

va f = 12.53.
NiingIl1qnglienk~tEb (hinh 3) eua m<)tt;.tpeMt tro'ngm<)tQWW ran th€ hiIu
6
h~ dii duQ'cve va so sanh voi cac ket qua cua QWW vOh~. 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.
Trong hlnh 4, chUng tOi trlnh bay Ms6 pMn qrc ap nhu ml)t ham cua goc (). H~
s6 pMn cgc giam khi tang. () vi trong truOng h<Jpnay dl) giam nh6t la Ian nha"tdQc
theo trvc y. R5 rang rao tM hiiu h~ dii khuech d1Psg ph1,lthul)c cua h~ s6 phAncgc
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 vOhip}, sg
dOidi cua cgc dl:\iIa It hem so vUiQWW rao the hiiu hip}.
Hinh 6 bieu hi~n nang luqng lien kef Eb theo kich thuac a cua QWW cho a x b
=
canst. Khi khOngco di~ntruOng,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 xfutgva cho chUng
ta mOt QUaDsat d~ng chU y ; Trong khi sg co cua klch thuac cl;\nhtheo huang di~n
truOng(tr1,lcy) 11;\0raml)tthayddi nho trongEb thl sg mb rl)ngkfchthuac theohuang
doll:\ilamgiiunnhanhnang luqnglien ket. D6ivUicac QWWco kich thuac Ian,cgc
dl;\icua nang luqng lien ket b cac Cl:\nhbangnhau bi oboe di.
Ket lu~n : Trong chuemg nay, bilng phuemg pMp Tga-Hartree, chung tOidii giai
quy€t vfu1de co tfnl,tphuemg pMp lu~n cho vi~ giai phucrngtrlnh SchrOdinger trong
mO hlnh QwW chu nh~t rao tM hiiu hip}. Chung tOi dii xem xet sg Anhhul1ng cua
di~n truOng leDcac 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 tOitfnh 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
tfUOngva tiel di~n khOng vuOng.
CHWNG 2 : EXCITONDuJi TAc DONGCUADI~N TRtf1NG NGOAI

1. Giai thi~u
7
Ngltai ta dii chtffig to ph6 Mp tho va ph6 phat quang cM yeu gAyMi hi~u tffig
exciLon. Hau h~1cac nghien CUll1:9thuyet trltac dAyve QW cling nhu cac QWW sir
lh.HlgmO h111hrao Lhechii nh~t. Brum va Bastard dii nghien cuu hi~u tffigdi~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 mQtexciton bi giam nMt
LrongmQLQWW 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 tOive 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~Iitir-IOtr6ng d~ nh~ du<;1cdQphfin
qrc gHi'ncac d{1iva VIv~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-IOtr6ng, 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
ki~n ghi ca.nbhng, ta co dQcarn quang hQcc~p di~n tU- 10tr6ng trong gan dung RPA:
X(w) = -2ldcvl2 ~IY!/(r=oW [n(w+ i8)~ Eg - E/
1
]
20)
- 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
pl1l1l1ngtrlnh Wannier :
[

1i2"V2
]
- 21lr +V(r) Y!/(f)=E/Y!/(f). (21)
Luu ydIng trung twCrng hqp QW, ho~c QWW, ngoai the Coulomb V(f) ta con
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
phO hfip tllU :
fiuJ
[
00 471" 1 7I"e"/ !li.
]
a(w)=ag-
R
L.:30(~+2)+8(~). VIS. ,
n=l n n smh(7I"/ ~)
trongd6n la s61uqngtitchfnh,~ = (fiuJ- Eg)/R, R laDangluqngRydberg3-chieu
(22)
va ag la h~ s6 ph\l thu~c s6 chieu va dcv
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
li~n) va mOt phO hap thu Ii~n t\lc do cae tqU1gthai ion h6a (s6lwng cu6i).
2. Ly thuyet
Trong mO hlnh QWW chUng tOi sir d\lng, trong d6 di~n tit bi giam nh6t trong
II1l.\.tpilling yz (crx = 0). Trong huO'ngy 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 tOisir d\lng h~ thac d6i xUng cua khOng gian
dili con di~n tir va 16tr6ng ma dii duqc sir d\lng b(JiBenner 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 10tr6ng. 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 10tr6ng trong the giam nh6t parabol. Tn;mg khuOn khO cua gau dung kh6i hrqng
hi~u d\lng, Hamiltonian cua h~ cho bcri
11,'1.82 r,,2 82 n2 82 mew~ 2 m"w~ 2
- 2me 8y~ - 2m" 8y~ - 2f L8Z2 + ~Ye + ~y"
e2
+eF(Ye - y,,)- I- -,.
Ere - rh
H =
(24)
Ham song thii trlplg thai C(Jban cua exciton:
\l!(r-;,r-;') = N (P(Ye)1>(y,,)exp{-Alr-; - 1'7,I} ,
(25)
9
b day tjJ(Ye)va tjJ(y,,)la ham song cuadi~n tit va 10tr6ng d<1nIe trong di~n tr\1ang.
Nang l\1qngIi~n ke'ttr:;mgthai co ban cuaexciton:
Eb = Eo - (wIHlw}min
,
(26)
trong do Eo la tOngHang l\1qngtr~mgthai co ban cua di~n tir va 16tr6ng d<1nIe trong
di~n twang.
Chung ta nh~ d\1C;1CHang Iuqng trl;lngthai co ban cua
exciton 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
Cac tfnh loan b5.ngs6 thvc hi~n cho QWW GaAs, vm cac tham s6 dii duqc sir
d~ng : me = O.O67mo,mh = O.45mova €= 12.53.
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:;mhtranh giiIa sVphiln Iy
cam (rng bbi di~n twang, tU<1ngtac Coulomb giiIa di~n tir va 16tr6ng va sv giam nMt
cam (rng biJi rao the'. M<)tcach 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
phOnlydo cU111trngbbi di~ntrUangkhi do chi€111\1UtM. VcriF Ian, Hangluqngli~n
kef giam ch~m Il;li,di~u nay ra rang do sv cam trng bbi rao the giam nh6t co khuynh
huang can sVphiln Iy cua di~n firva 10tr6ng 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 tangtuung trng vcrisVtang cua tM giam nh6t.
Ket Iui;tn : Trong chu<1ngnay chung tClidii nghi~n Clruhi~u trng di~n tr\1ang I~n
nang hIQ'ngIi~n'ketcua exciton trongQWW.ChungtClidiitlm tMy hi~utrngnay th~t
sV Iiil6'nva ph~ thu<)cml;lnhvao the'giam nMt Mn parabol.
CHUaNG 3 : S{/CHAN DONG HQC TRaNG cAc DAY GIENG LUQNGTV
KICHTHICH QUANGHQC.MO HINHMOTDAI CON
10
Dll<1i.kfch thfch laser m1p1h,nhi~utfnh chA'tdan h~tcua h~ bi tliichua.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 dankh6iva QW.Olioday,co m()tvwnghien
cUlltren 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) 10tr6ng
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 phOniing Illqng rieng di~n tit, ham m~t dOpM, dOtai 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)
(28)
:Ho= ~ at n>,ak,n,>,Ek,n,>,, \= c,v
L J "
k,n,>'
tmng do, niing luqng cua di~n fir trong dui con thu n thuOc
daidan( \=c) :
1i,2k2
Ek,n,c = Eg + En,e + _
2
= Eg + Ce,n,k ,
me
(29)
Ilung Illqng cua 16tr6ng trong dill con thu n thul)c dillh6a trj ( \=v) :
Ti,2k2
E
k n v = -E n v - - = -c" n k
.
, , '2m" ' ,
(30)
11

56 h~U1gCoulomb:
H - 1 '" V. ~+ ~+ ~ ,
c - "2 L , qak+q,nttAakl-q,n2,Alak',n3,,\,ak,n.,A,
k,kl,q,N,A,A'
(31) .
trong d6 N = {nt,n2,na,n4} va
!
dz
d
I I
Vq = y;dxdy x dy
<I>~1,A(x, y)<I>~2Y (x'y')<I>n3N (x', y')<I>n.,A(x, y)eiqz
e2
X EOV(X - x')2 + (y - y')2 + Z2 .
(32)
2. S,! cMn d()ng hQcbm phonon va plasmon Ii~nk€t
Xuat phat tU mOhlnh 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 :
e2
[
q2
] (
q2
)V(q)= Eooexp 4fL11 1(0 4{111 '
(33)
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<mghqp cae mau kh6i, tM ch1in Coulomb dOng hQe V5(q, ivrn)
trang gall dung RPA :
EooV(q) - EooV(q)

115(q,ivrn) = Eoo+ n~,(ivtn) + n~l(q, ivrn) - E(q,ivrn) ,
(34)
trong d6 iv", lit tftn s6 Matsubara cho boson. Ham phall clfc m~g duge eho bbi :
EO- Eoo
nO (UJ)= W2'
L 1-;;;r.
(35)
Trong gall dllng PPA ham pIlau clfe di~n :
2
UJpl
n°
(q
UJ) = Eoo 2 - UJ2: zj2 '
el , UJq pi
(36)
2 nq2
UJpl= -V(q),
II
(37)
12
2 2
{
1
}
q4
CJJq = CJJpl 1+ V(q)I>- On. + 4p2'
,-e,h 7fiii
vUin Him~tdOdai plasrna.Khi do, ham di~nm6i :
(38)
2

]
2 - CJJ2 CJJpl
CJJL T .
E(q,CJJ)=Eoo [1- CJJ2_CJJ} - CJJ2+CJJ;,-CJJ~
(39)
Ole mode ri~ng cila cac phonon, plasmon li~n ket CJJiva cUC1ngdO dao dOng tlr
Ui(i = 1,2) duge cho bc:'1icac cVcva th~ng du cila c1 (q, CJJ):
-1 1
[
U1 U2
]
E (q,CJJ)=- 1+ 2 2+ 2 2.
Eoo CJJ- CJJI CJJ- CJJ2
(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 thuGlu~ ham Green Matsubara, phOnang lugng ri~ng dan h~t trong
gan dung b~c 1:
~i(k,z) = -~L Vs(k',z')G?(k - k',z - Zl),
k',z'
(41)
trong do z, Z' tl1anglIng Iiicac 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
q J-00 7r CJJ+~b- ei(k - q) + Pi - CJJI . ( )
~iX(k) = - L V(q)/;(k - q),
q
(43)

g(CJJ)= ell:-l la ham pMn b6 boson
Ham m~tdOph6 dun h1;lt:
A.(k ) = 2Iml~i(k,CJJ)1
"CJJ (CJJ+ Pi - ei(k) - Re~i(k,CJJW+ [Im~i(k,CJJW .
(44)
13
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 tOichi ra phlin thl!c cua nang lu<JI1grieng 1:. (O,UJ)ciia di~n
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
duO'l1gchung ta co Cl!cdliu lien It s!\c net, dUc;1cgQi Iiiplasmaron. 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
xem xet them lien ket phonon ta nhQ.n them dUc;1c2 cl!c t:;1ivi trl :!:UJL- M. ttrO'l1g
t\! nhu ph6 cua nang lu<JI1grieng, chi CI!Ccrvi trf -UJL - It. Iii.s!\c net, con ClfCa
+UJr, - It. chi co the thlly ro hO'l1crnhi~t d() caD.Ngoai ra khi nhi~t d() tang lien ket
phonon lam cl!cghi h~t giam d() snc net.
4. Ht) tai chu:\n h6a khe dai
Cho UJ-t ei(k) - Mi trong (46) ta thu dUc;1cbieu thuc cho nang lu<JI1grieng dO'l1
h:;1t:
1:.(k e.(k» = 1:~"'(k)- "
/
00 rid ImVs(q,UJ' + i8)[l + g(UJ/)- fi(k - q)]
, , , , ~ -00 7T ei(k) - ei(k - q) - UJI+ i8 .
q
. (45)

N€u bo qua nang lu<JI1ggiQ.tIj)i ei(k) - ei(k - q), ta.duc;1cbieu thuc cho nang
lu<JI1grieng dO'l1h:;1ttrong glin dung gia tinh, neu dOng thai d~t Eoo = EO ta nhQ.n duc;1C
glin dung EOgill tinh vii dii dUc;1cnghien CUubbi Benner vii.Haug. Luu yriing, trong
glin dung EOta phai them viio d() dich chuyen polaron d~ so sanh v(1itruang hqp tmh
tuang minh lien k€t phonon-plasmon.
DO tai chudn hoa khe dai (BGR) dUc;1cdinh nghia :
fj,Eg = 1:.(k = O,e.(O» + 1:h(k = O,eh(O».
(46)
14
Trong hlOO11chUng 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'ngqUaDva k~t
qua dii lam Ulnggia trj tuy~t d6i cua BGR.
Trong hlOO12 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(). TAtca 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)tdang 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()nghQCday 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() phOcua di~n tit va dii tlm thAym()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 rIftt6t
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 NHIEUDAI CON
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 dMcon 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 dMcon 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! diitfnh
BGR cho nhieu dlli nhung chi trong gan dung Hartree-Fock, bO qua hi~u U'ngchiin
cua tvoog ruc Coulomb.
1. Cae yell t6 ma tr~n di~n m6i
Cling xuat pIlat tit m<')h'inh QWW rao th€ Mn parabol, y€u t6 ma tr~ cua tUO11g
ruc CoulombtraIl giiiacac h!;}ttIliduqc cho Mi trungb'inhtren cac ham rieng ~I(X)
cua the giam nh6t :
V(q)lmn = 2(;:2
/dx /dxl~i(x)~;(XI)~s(X')~m(x)KO(lq(x - Xl}!).
(47)
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),
r',s'
(48)
trong do P:~(q,UJ) la phan thl!c cua ham Lindhard l-chieu :
f rj rj

pL
( )
- 2 ""' k - Hq . - h
rs q,UJ - L j
(
k
)
j
(
k
)
,J - e,
i,k UJ- es + q + er
(49)
vai fkj va e{(k) tl1O11gU'ngla ham phan b6 va Bang luqng cua h!;}ttlli tren muc nang
111qngdai con thu l.
, tt2k2
(
1
)
E
eJ=-+ l+- UJ,+2.
I 2m' 2 J 2
J
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
(50)
16
t6t iJ vung DOngdOplasmacaD.Theo dinh nghia cua ham di~n mOif/m,,(q,lJJ) =
1~r8rn(q)[v,~8m(q, IJJ)]-l, ta duQ'c:

flr8m(q,W) = 1- 2:= ~r'8'm(q)V8'r8r'(q) pl,
r',8' ~r8m(q) r'8,(Q,W).
(51)
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 :
E{(k,z) = -~ L Vz~lm(k-k/,z-z')G~m(k,z'),
k',z',m
= E{,HF(k,z) + Ef.corr(k,z),
(52)
E{'JlF(k,z)=-~ L ~mlm(k-k')G~m(k'z'),
k',z',m
IIInfmg ItrQ'ngrieng Hartree-Fock khOng chfin,
(53)
.i - 1 ~ - I
)
[
1 - 1
]~I,con(k,z) - -73 L., Vtmlm(k k f (k -k' z - Zl)
k',z',rn /mlm,
xG~m(k'z'), (54)
Iii nfmg luqng rieng tucrngqUaD.
Phan Hartree-FockkhOng chfin elJa Dang luqng rieng dcrnh~t trong delicon thu l:
~f.IlF(k,C{(k))= - L~m'm(q)f;;lq'
(55)
q,m
D6i vai ham di~nmOinh~ duQ'ctlr(51) :
fh"lm(q,lJJ) =
1 - ~ ~rrm(q)Vrmlr(q) pL
(
)

L u
( )
rr q,w
Ylmlm q
r
- ~ ~r8m(q)V8mlr(q) pL
( )
L., 11
( )
r8 q,1JJ ,
-I- IIlmlm q
r,8-rr
(56)
m = l cho s6 hlplg cheo va m i- l cho s6 hlplgtrao dOLDo dong gop nho cua s6
hlplgtan x~ giUacae dai con, chung tOise hlpleM xem xet chi 2 s6 hlplgdau lien
17
!rung cOngthtk (56) ca cho s6 h~ngch~ova IraQd6i cila ham di~nmoL
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 :
2 - '" v,;rm(q) njq2
wpl,lmlm - L t 1T
(q)
-
m
' '
. "Imlm J
r,J
(57)
,2 - 2
(3

Lr,j,k v,;rm(q)f;j(l- frj) 2
Xlml1ll - 2 n~ Wpl,lmlm .
Lr,j v,rrm(q);;;
D~ dan gillll trong vi~c tmh loan bilng s6 chUngtCliSlrd1}nggill dung c1!c-plasmon
(58)
2
wpl,lmlrn ~- ,
( )
- 1 - 2 W2
IOlmlrn q, W - W2 + Wpl,lrnlm - q,lrnlrn
(59)
W;,lmlm = W;"lm'm
(
1+ -1-
)
+
(
~2
)
2 .
X'mlm It
Khi d6, chung ta nh~n dugc pMn nang lugng rieng tl1<mgquan :
(60)
2',f.corr (k, e{(k))
'" . wfmlm
L t v,mlm(q)-
2
Wq,lmlm
q,m
[

g(Wq,lrnlm)+ 1 - f~~q
x e{(k)-e!n(k-q)-Wq,lrnlm+i<'i
g(Wq,lmlm)+ f;~q
]
+ e{(k) - e!n(k - q) + Wq,lrnlm+ i<'i .
(61)
3. Dc)(:Iichuiln hoa dai con
D\) I<lichudn h6a diii con (subband renormalization (SBR» dugc dinh nghia :
llE;
= 2',/(k =O,e,(O)) + 2',:'(k= O,e:'(O)).
(62)
Ok tham s6 st'rd1}ngcho tmh s6 gi6ng nhu chu<1ng3 . Chung !Oichi xem xet
Info-nghlJp :I d,li can.
I-nnh 14 chi ra d\) tai chudn h6a khe dlli cho 3 dlli can nhula mQtham cua nOng
dO plasma loan phan Irong gan dung ch~n dQnghQc va glin dung Rartree-Pock. Ri~u
18
li'ng nOibf:\.tla sl! kMc bi~t 16'0gifta SBR trong gan dung chlln dQng hQCva gan dung
Hartree-Fock. Trong vUngn6ng dQplasma thap, gall dung Hartree-fock cho SBRnho
do vi~c bo qua niing luqng ri~ng tuo'ng quan. LUll
yriingdau cua niingluQ'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 lUllykhac trong hinh
14 la s,!kt!ac nhau cua dQtach 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 dQtach nho.
Tmng hinh 15 chUng tOrdii ve SBR theo nhi~t dQtmng 2 g!1ndung. 010 dIDcon
l
= 0, sl!ch:in gay nen mQtsv thu nho ml;1nhgiatr, tuy~t d6i cua SBRtrongvting
nhi~t d() IMp. Thy nhi~n, Val cac dai con cao ho'n (l = 1 va l = 2) S1,tch:in khOng th~
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 chUngto rang g!1ndung Hartree- Fock
kha di co th~ si'1dl:mgtrong cac h~ ban clankh6i.
Ket lui),n: Trong chuO'J1gnay, chung tOrdii danh gia duQ'cSBR tmng QWW cho
2 gAn dung va dft tim tMy mOt SIfkhac bi~t 16'0giiia gAn dung cMn dQng hQc va
g!1ndung Hartree-Fock, d~c bi~t lJ vUng n6ng dQplasma cao va tM gram nh6t 16'0.
Chung tOi dietsi'1d\lng mQt Valg!1ndung: g!1ndung cl!c-plasmon, gall dung Parle va
bo qua s6 hl;lngtan XI;lgiUa cac d,!i con. 01ung tOrdietchung 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 dQplasma cao, lJdo 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 CalltrUe 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 mOhlnh 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~ mOth~t, trong cac ca'u trUcQWW co rao the!b1ftd6i xUng, bilng
phuang phap 1Va- Hartree chUng tOi dii giro quye!tvan d~ mang tfrih phuang pMp
luQ.ntrong vi~c sit d~ng phuang pMp bie!nthien de giro phuang trlnh SchrOdinger,
danh gia duQ'Chi~u Ungdi~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
hQcelm dlc hl,lttai trong cac d~ng c~ di~n tit sit d~ng ca'u trUcQWW. CluIng tOicling
Om tha'y mOtslf 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 dOpM cua di~n tit, BGR cua Qww
trong ph':lm vi gan dung PPA cua slf chiin dOng hQc, ma nhu dii bie!ttrong ca'u truc
kMi va QW, dOco cua khe dai dii giai thfch duQ'Cban GMtdich 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 tOidii 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 tOicling 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
plasma. chung tOicling 11mtha'y duQ'cmOt diJcdiem kM nOi b~t v~ niing luqng tuang
quan do la d~cdiem doi da'ucila no trong vitngbu6'csong dai ma nhu chung ta dii .
bic!ttrong cac sach giao khoa v~h~ nhieu h~t, nguui ta diitrmh bay ni\.ngluqng wang
quan t':lik, 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 tOidii co nhUng
dang gap nh!\'tdinh vilo slf hieu bi!t ve tfnh GMt di~n va Quang h<;>ccua h~ ban clan
QWW d(\ng thai hoan thi~n ban cac tfnh loan cila cac GOngtrlnh trucrc day.
20
"
;-
I
~
~ '" "
F(kW",,}
tnnh I : IIn; nuk nAngl"\1I1gIMp nM! nhlt IAhAmeun wOng
dQdj~nInJln'gF. NAngIltQ11gt"",g !hIlico bAn: dltOngIi~neho
0 0
D. = 300 A, dltOngg~eheho L. = 600 A. NAngl"\1I1g
0
klch Ihleh ddu li~n : dttbng gleh-ehd ehn L. = 300 A.
0

dltOngehd eho D. = 600 A.
30
~, ,
;-
I
;1
w
,
""'"
~ ~"'~"'"
~- "'"
""
II
.~
'30
""
'"
100
a(:J
tnnh 3 : NAnglUQ11gIi~nk€i Eb nhlt hAmcu. kfeh thlt"" a
0
cu. QWW ehii nhA'v(ri kfeh Ihlt"" b = 150 A, ',p eMI b
:1:0 = YO= OvAeltOngdQdj~ntrttbngF = JOOkV!em.
8 = 45°. DltOngl;~nehorAolh€hiillh"Vo = 0.4eV.
dltOng g,eh eho rAo Ih€ vO h".
"
"
,//
/'
////

,/
,//
/,/
1.4L//
1.1,-
"
~
:,
"
'if

100
1.1
'"
'"

'"
1,(:J
tnnh 2 : II~ s6 pMn e~ <>p nhlt IAhAm eun L ettbng dQdj~n
tnJOng F = 50k V! em : dltOng Ii~ eho di~ trttbng "'ng ,ong
trye Y (lhang Wi) vAdttbng g~eh eho di~n trubng ,ong "'ng trye
:I: (Ihang phil).
0."
~
" ~
'"

w. "
Qj
IJ(degrees)

mnh 4 : H~ s6 phAn eye <>p nhlt hAm CURg6c 8 g;iin dl~n
. 0 0
trltOngvAtrye:l:choa = 100 A,b = 50 A.:l:O =YO =O.
vAF = 200kV!cm. Dttbngli~n:rAothl!hiillh,,(Vo =
O.4eV), dltOngg,ch:rAnthl!vOh".
21
0.11L "'"
f om,
';J- 01"
om
~
,
I
;;!
' ',
/ "
,
,
';~-~'" ",
// ""
\
' \
,
'"
"1
.",
.n
"
Y.(;)
H1nb 5 : NOng1"<;1I1glito kEt Eb nh" him CUBvi tr! t~pch<it

0
110.chn xo = O.a = b = 100 A. F = 100kV!em
vile = 900. 0"/n1g li~n: rAo thEMu h~ (Vo = OAeV),
d"lmg Koch : Ibo IhE v~ h~n
,-
!
.r
F~V'~
mnh 7 : NOog 1"<:JOgli~o kEt Eb nh" him cUa C"lmg d~ dj~n
tnrlmg /0'. O"I"'g li~ntho n = 15R. d"lmg g~ch tho n =
20n vild"/n1gchJimtho n = 20R.
"
'"
//'~
I
i
,
,
>'
I "
"
.,
,-,
'-'
.
.
'00 ,., ""

a(;)
"

mob 6 : NOng1"<;1I1glito kt"1Eb nb" him theo kich th""" a
CUBQWW eM nh~t do thEbiJub", Vo = O.4eV tho a X
b = eonst vA"'0 = 110 = O. I)~g li~n : a X b =
0 0
100 A X100 A vAF = 0; d~g g~eb-ehlin : a X b =
1001 X1001. F = 100kV!em vAe = 90°; d"lmg
0 0
g~ch : a X b =200 A X200 A vAF = 0; d"lmg ohlin
0 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
/
. . /////
/"
,/

.
.
In(R)
mob 8 : Nilng 1"<;1I1glito kEt Eb nh" him CUBn. O"lmg Ii~n
tho F = lOOk V lorn. d"lmg g~ch tho F = 75kV!cm vii
d"lmgehlin tho F =50kV!em,
22
~
a:
a

<5
;:;. r,
.
a:
10
.15
10 10
mfR
mob 9 : Phl!nIh~cCUOOo.ngI"QIIgri~ogE. (0, "') oh" hAm
cUa'" cho k = O. DUOnglib> r:r = 00 K) vAd"lmg g,ch
(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.

;;
.
E
~."
'0
', ~
w
0.0 1.0
1.5
D.5
'a,
mob II : DQ I.i chul!n hOOkJ1c do !:>'Eo nIl" IAmQI hAm cUa
n6ngdQplasmochoT =3000K vAn =lOR. Dlllmglil!n:
gl!n dUng d<)ng hQCday du, d"lmg g,ch : gl!n dung dQng hQC'0
vAdulmg ch(m : gl!n dUng '0 giA'linh.
a:

-2
a
<5
~
/1
ji
15
0
.15
.10 .5 10 15
mfR
mob 10: HAmm,' dQph6 di~ tit A.(O, "') nhllbAmcuo '"
cook = O.cac tbarn s6 gi6ng ohll hlnh 3.1.
.10
.IS
, ~
.35
"""'""""""""""""""""""""""""""""""""""""" !
,L
. w
100 150 3JO 2W 300
20
T(K)
mob 12 : DQ lAi chul!n h6o kJ1c do !:>.Eo nhlliA mQl hAm cuo
nhi~tdQchon =10Rbdco6ngdQplasm.kh4cnhoILDlllmg
lil!o : gl!n dung d<)ng hQCday du, dlllmg g~h : gl!n dUng d<)ng
hQC'0 vAd"lmg chdin : gl!n dUng '0 giA-tinh. cac d"lmg nh,t
chn nao =0.1, cAcdlllmgdAmcho naO = I.
23