CONG SUAT HAP T H U VA DO R O N G PHO PHI TUYEN TRONG DAY LtfdNG TU* THE DAO D O N G
DIEU HOA
LE DINH Tn/dng Dai hoc Sii pham - Dai hoc Hui Hd THI NGOC.ANH Trudng Cao dang nghi Lilama - Ddng .Vai
Tom tat: Trong bai bao nay. chiing toi nghien cihi cong suat hap thu va dp rong phi phi tuyIn trong day lUdng tii thi dao dpng dilu hoa. Tii bi6u thiic giai tich cua teu xd do dan phi tm-eu, chung toi thu dupe bieu thiic cua cong suit hap thy phi tiiyln. ttr do ve d6 thi su phu thuoc cua cong suit nay vao n&ng lugng photon tdi. Tii dudng cong cOng hudng cua cong suit hip thu phi tu}'en. dimg phuOng phap Profile, chiing toi thu dupe su phu thuoc ciia do rong ^-ach phi phi tu>-en Y-ao nhiet do.
Kit qua thu dupc cho thay do rong vach phi ciia dinh cong budng phi tuyIn tang theo nhiet do.
Tii khoa: cong su4t h4p thu, phi tuyIn, phudng phap profile 1 GlOl THIEU
Trong nhiing nam gan day. viec khao sat dp d i n va cdng suat hiip thu (CSHT) phi tuy^n do tUdng tar electron-phonon trong ban dan th^p chigu dugc nhi^u nha vki ly quan tam, trong do thanh tyu Idn nhit thupc vl nhdm tac gia H. J. Lee, X. L. Kang va S D. Choi [1, 2. 3]. Trong cac cdng trinh nay cac tac gia da thu dugc cac thanh phSn tuyen tinh vh, phi tuyIn ciia dp dan. Tuy nhien. kit qua thu duoc ve hieu ling phi tu>'en \-Sn cdn han chi vi chua dua ra dugc bilu thiic ting quat ciia dp d i n chiia ca thanh phln tin'cn tinh va phi tuj'In.
\ ' l \iec nghien cdu dp rdng phd hap thu. da co nhilu tac gia sd dung cac phudng phap khac nhau trong nghiSn cdu trong cac he ban d i n thap chilu [4, 5. 6. 7j. K i t qua ciia cac cong trinh tren cho thay r i n g dp rdng vach phd trong trudng hpp tUdng tac electron-phonon quang dgc tang theo nhiet dp va giam theo kich thudc ciia mSu.
Ket qua nay la dang luu y. tu>- nhien mdi chi dl cap din do rpng vach pho cua dinh T^p chi Khoa hoc va Giao due, Trudng Dai hpc Su pham Hul
ISSN IS59-1612. So 03(27)/2013: tr. 5-13
LE DINH - HO THI NGOC ANH
cong hu6ng electron-phonon tuyIn tinh Vi vay, bai toan v l dp rpng vach ph6 phi tuyIn van can tilp tuc dUdc nghien cdu.
Bai bao nay se nghign ciiu vl CSHT phi tuyIn do tUdng tac ciia electron-phonon quang doc dudi tac dung ciia trudng laser cao tan trong day lupng t^ vdi t h i giam giu dang dao dong dilu hoa Su phu thuoc do rong ph6 cua dinh cong hudng phi tuyIn vao nhiet dp cung dugc khao sat bang phUdng phap Profile nhS phln mim Mathematica.
2 Bieu THtrC CUA CONG S U A T H A P THU PHI T U Y E N TRONG D A Y L U Q N G Tir VCI TRUING HOP TAN XA ELECTRON - PHONON QUANG DOC
Chung toi khao sat mo hinh day ludng tu, trong do dien t d chuyin dpng t u do theo phuong x va bi giam giii theo ca hai phUdng y, z vdi t h i giam giS co dang U{y) ^ mw^yV2 va U{z) ^ mw^z^/2. Bing each giai phUdng trmh Schrodinger cho electron, t a dudc bigu thiic nang luang va ham song tUdng I'mg nhu sau'
^i...n.,{x,y,z) = ^ — J ^ e ' ^ . H j f ) . ^ 2 = e - ^ . H , ( f ] , { l ) t?kl , 1 1
— + ?iu;„(n + -)+fiw.(<+-). (2)
trong do II = 0,1,2,3... va < = 0,1, 2,3...lan luot la cac s6 Imng tii tuong ijng vdi stt Imng ta hoa nang luong tlieo pliuong y va z; t, = J ~ - , 4 = /--A__ k^ )t^ tijjj,ii phin vecto song cua electron tu do theo phuong x; H„{u) la da thilc Hermite bac n cua bien u.
3
Xet day hiong tu dat trong dien trudng ngoai co dang E(t) = V Boi.e"'"'4, khi do xiy ra trudng hop he h i p thu nhilu photon. Lee va cong su da ap dung ky thuat chilu phu thuoc trang thai d l thu dugc bilu thiJc cua mgt do dong trong do bao gSm ca so hang phi tuyIn co dang sau |1] :
Wens = ^ ( T „ ( u ) B j ( i ^ ) + J2 <^«i('^i,aJ2)£j(u,)£)j(a;2) + ., (3)
Cac dai luong (T,,(a)) va i7„t(ui,aj2) Un luot Ik tenxo do d b i tuyIn tinh ling vdi song tdi cd tan s5 u, va tenxo do dfa phi tuyin bac nhfa Ung vdi cac sdng tdi t i n sd Wj va 1^2- .. Ta xet trudng hgp h i p thu hai photon cd cung t i n s6, nghia la oJi = Wj = u),
DO TIM C Q N G H U 6 N G E L E C T R O X - P H O N O N B A N G Q U A N G H O C . . 7
ttt (3) ta cd:
vdi a^^"{u) tenxd dd dan phi tuj'In.
Gia su: song dien tit dat vao he phan cue theo phUdng giam giii z, liic do bieu thiic cua cong suit hap th\i phi tuyen cd d^ng:
= PoM + ftM-
^ {Re[o,M\ + Re[o,,MEaM\) , (5) Trong mpt bai bao tnfdc da\-. chiing toi da khao sat so hang tuyen tinh PQ{IJJ) = Re[a^2{(jj)] [9]. 0 bai bao nay chung toi tap trung tinh toan so hang phi tuyIn cua cong suit h i p thu, PI{LO) — /ie[<7;,j(a))£oi('^)]'
Sii dung phUdng phap chilu phu thudc trang thai vh thuc hien cac phep tinh tUOng tu nhu phln do d i n tuyIn tinh. chung tdi cung thu dUdc bieu thiic ciia tenxd dp d i n phi tuyIn bac nhlt:
a,,,{uj) c= lim T '^'°'''''*
- i - . o - ' ^ t o - £ 3 „ Y ^ {z)-,a{3z)^l
^ 9 f i , T i F... r?^1l')
-/») - r f (^)
~A ^ V
{Z)ps{jz)5a 2fiw-E6^-rf{2u))
trong do r°^''(2tj), Fj"^ (2aJ) la cac ham dang pho doi vdi tenxo dp din phi tuyen;
^ = u — ib, vdi 6 —>• 0. Sd dung dilu kien gin dung Lorentz [6], ta cd the ^'ilt lai thanh phln ciia tenxd do d i n phi tuyIn (J„,(tj) nhu sau:
7;^.-(w)
E E
flh) - E,^a - lBo{uj)
r E
(Z)IM{JJ(C 2fiw - £to - iB2{2ui) ' 2fiaj - Ef,^ - !Bi(2a))Cac ylu td ma tran sau trong (6) cd dang
(6)
eA....=.Jn.
ieh 1 ,
LE DlNH - HO T H j N S S - 4 ^ ieh 1
trong dd ta da ky hieu
lis + 1 , ./<7r -,
(7)
D,.i,.i, = iy-^^'s-'^
D,.,a.
(\/-f *<..«.-!-
2
£-, + 1 2 4 + 1
2
* 3 i - + i ) . (8)
-0(5,(1+1 + y ywj.fi-iJ-
Thay cac dai luong vCta tinh dugc vao (6) t a thu dugc thanh p h l u phi tuyIn ciia tenxd do din, sau dd thuc hien tudng tU nhu phan tuyIn tinh, t a cd dUdc bilu thiJc tdng quat thanh phan phi tuyIn bac nhfa cua cdng suit h i p thu sdng dicn tit do car electron bi giam giO trong day lugng tii hinh tru nhu sau:
P i H a , ^-Re[a„MEoM\
e'hE^J, v ^ \ p \r^ Y ^ fl»,(„,(j(/t...n„,(. ~ /t,a,nj,(,) ';;r- 2^ 1^ 1^ 2^ (^^ _
^^^y
+ BI(U) 2m' tu ,1a ng ,(a ni.(, ns ,UBilu thiic giai tich ciia ham dd rpng phd plii tuyIn i?i{2w), i?2(2u;) cd dang sau:
f ; ^ v , L'D-^\ s r \ i \ 1 . 1 1 ^ "
B I
H S - . , + M 2 F fe, -Afi2)2JMi2 Hfc., + Wl3F (fcx, - Mi3)^J M s
.Wi5 H - t . . + - W i » ) ^ ( t , + M i 6 ) ' - ' M i 6 r ^ » - ^ '
DO TIM C Q N G HUClNG ELECTRON-PHONON BANG QUANG HOC...
r 2 • V''^
i l - - ^ ( 2 f i a , ± f c i o - £ » , . ( . + £ » „ , ( , ) ; r 2777* 1 ^^^
M5,16= U i + - ^ ( 2 & ^ ± f e j L O - £ - , . ( , + B n . , < J ; F i u 3 = (1 + Af.j/A^ [1 - (1 + exp [l){^§^ + £^-„,(„ - B F ) ] ) " ' ]
- A',(i - h . ) { i -oxp [ e ( ^ - ^ + £„,.(, - E,)])-\
Fi214 = (1 + -V,)(l - /5..)(1 + exp :»(^^^^|^^ + £ „ , ( . - E F ) ] ) " ' + N,U.. [1 - {1 - exp [ e ( ^ ^ ^ + £ „ „ ( , - E F ) ; ) " ' ] ; Fi, = {1 + A',)(l - /<,)(1 + exp [ 9 ( ^ ^ + «.„,(„ - Eri]r'
- W,A [1 - (1 + exp ; f l ( ^ + £ . „ ( , - £ p ) ] ) - ' ] ; fi6 = (1 + Af,)/„ [1 - (1 + exp [ » ( ^ - £»,. .<„ - £ F ) ] )""]
- N,{1 - U){1 + exp [ # ( ^ + £„„,, - £p)])-'
, 1 (ni>!)^(A7ii - l)!(7ii< - iy.
' " N / 2 « , V ? Hi<!Ari,!
X3 i^2{-ni<, AT!, + - , - ; Ani + 1, - - 77i<; 1),
^ 1 ( f i > ! ) - ( A C i - l ) ! ( ( i < - i ) ' '-' y 2 < . 0 f «i<!A<i!
X3 F2(-f i< A<i - i i : A<, + 1, i - £r<; 1), , 1 (n2>!)^(A>r2-l)!(n2<-i)!
"' ^ f , y f n2<!Ai72!
X3 f2(-'i2<, A712 + :^- :j; A772 + 1 , ^ - >i2<; 1);
v / 2 / , v ^ / 2 < ' A 7 3 ' X3 f2(-<:2<. A<2 - i . i . Af2 + 1. i _ (,^. 1);
LE DINH - HO THJ NGOC AXH
vdi TiK = max{Ti^,7l^}, 7ii< = min{77.j,n^}, ATII ^ 77> - n<, n2> = max{77,.,7i^}, 7i2< = inin{n^,n3}. An2 = n2> — 'i2<-
B2(2w) = 1 7 ^
167r3/i2(/3 - U) ^^ l^H-k.,'^ -1/21)= (K + A/2,)2J A/21 1 1 7 i"22 r 1 , 1 ' ( - * : , , +A/22)2 ' fe,+A42PJAf22 ^(-fc., + A/23P (fr«-.W23)2- f23 , r 1 , 1 7 ^ 2 4 ' , ,
-1/23 H-fcx, + Af2<,)^ (fe, + Af24)^-' -V2J * "
^ r 1 1 7 ^ 2 5
V Hfe. +Afe)= ( t , -M25)2'A#25
Cac s6 hang trong (10) la
fc|.--^(2fi^±fia;to-£«,.(„+£•»..£,) ;
M23,24 = [fc., + ^ ( Z S " ± So^io - £ „ „ , , + £ „ „ ( , ) | ; (11)
.1/.3 26 = \l% - ^ { 2 & . ^ ± ^LO - £„,.(., + £•„,.(.)!
7 1/2
f2i,23 = ( 1 + - V , ) ( 1 - / . , 3 ) ( 1 + e x p [ e ( ^ ^ + £ „ , , , , - £ ^ ) ] ) - '
- % A 4 l - (1 + exp P { ^ ^ + £,.,(, - -BF)])-'];
i^22.24 = (i + .v,)/<.,,[i-(i + e x p [ e ( 5 ! ^ + £„„<,-i;F)])^']
--V,(l - /a.s){l + exp [ 9 ( ^ ^ + £„„.(, - E,)\y\
F2S = {l + A - , ) / 4 l - ( l + e x p [ e ( ^ + £ „ „ , ^ - £ ^ ) ] ) - ' ]
--V,(l - /s)(l + exp [ 9 { ^ + En,.,, - £ F ) ] ) " ' ;
f26 (1 + iV,)(l - /5)(1 + exp [ e { ^ + En,.,, - £ F ) ] ) ' '
--V,/.[1 - (1 + exp [ S ( ^ + En,.i, - £ F ) ] ) - ' ] ;
DO TIM CONG H C O N G ELECTRON-PHONON BANG QUANG HQC...
( n 3 > ! ) - ( A n 3 - ^ ) ! ( n 3 < - i } !
\ / 2 4 v ^ n3<!A7i3!
X sFii-Tii^, Aui + - - - . ^n3 - 1- 2 ^ "3<; 1), 1 ( ^ 3 ^ 1 ) 2 ( ^ ^ 3 - i ) ! ( 4 < - i ) !
X sF2{-e3<,^(2 + ^,\ A / 3 - l , ^ - ^ 3 < ; l ) , y/2£,^ ^3<!A/3!
^ 1 ( n 4 > ! ) ^ ( A n 4 - ^ ) ! ( n 4 < - ^ ) !
X 3^2(-n4<, An4 + - . - : An4 + 1, - - 7i4<: 1),
'^ V 2 4 V ^ 4<'A^4!
X 3F2(-^4<.Ar4 + ^=^;A^4 + U ^ - 4 < ; l ) .
vdi n3> = max{n^,T7^}. n3< = niin{n^,nj}, A^s = n3> - 7i3<; ra4> = max{no,n^}, ri4< = min{na, n^}, An4 = n4> — n4<.
3 KET QUA TINH SO VA THAO L U A N
D i lam ro hdn kit qua thu dUdc tii nhiing lap luan tren da;-, chung toi su dung phUdng phap tinh sd va ve dd thi ddi vdi cong suit h i p thu phi tuyIn /*Ai.n(-^') cho m5 hinh day lUdng td GaAs/AIAs. Su chuyln miic nang lUdng ciia electron (theo phudng z) duoc xet gida hai trang thai o va j3 ling vdi ria = /^ = 0 va ng = 1. ^^ = 1.
Hinh l a mo ta sii phu thudc ciia cong suit h i p thu nhu ham nang luang ciia photon tai cac gia tri khac nhau cua nhiet dp. vdi tan s6 giam giii w^ = J^'; — 0.4 ULO-, vdi jJio II t i n s6 phonon quang dpc ling vdi nang luoiig 36,25 meV. D6 thi cbo thiy cac dudng cong deu co dinh ciic dai tai ciing mot vi tri 14.5 meV. Tuy nhien. khi nhiet dp tang thi do cao cua dinh cong hudng giam. Cac dinh nay mo ta qua trinh electron d trang thai |a) h i p thu ddng thdi hai photon d l dich chuyin len tr9,ng thai cuoi I/?). Qua trinh dich chuyen nay thoa man dilu kien 2ho ^ E^ — Ea- D§ tim duoc su phu thudc do rdng pha vao nhiet dp. dau tien chiing tdi \-e dS thi md ta sir phu thudc cua CSHTPT liiig vdi mot s6 gia tri nhiet do khac nhau, sau do sii dung phuong phap Profile [8, 9, 10] chiing toi thu dudc d6 thi m5 t a sU phu thupc dd rdng \'ach ph6 phi tuyIn vao nhiet dp nhu hinh l b . Da thi cho thl>- ring, dp rpng vach phd phi tuyen tang theo nhiet dp. Dieu na-v dUdc giai thich la do do rong vach ph6 cd lien qiau mat thiet den t6c dp hoi phuc, chung phu thupc \'ao tinh chit cu t h i cua cd chi tan xa, khi nliiet do tang thi xac suit tan xa ciia electron-phonon
LE DINH - HO THJ NGOC ANH
Nang luoDg photon <meV)
Hinh 1. aJSiC phy. thuoc cua cong sudt hap thu phi tuyin vao nang lugng photon tai cdc gia tri khdc nhau cua nhiet do. T=250K (dudng liin net), T = 300K (dudng dM nit), T = 350K (dudng chdm cham). b) Suphu thuoc cua do rgng phd phi tuyin vao nliiet do.
tang, do do dp rdng vach ph6 tang.
4 KETLUAN
Trong bai bao nay. dila tren gia tlmji-lt he dien td hap thu d6ng thdi hai photon cimg tan s6 u, chung toi da thu dupc bilu thiic tU&ng minh ciia cdng suat hap thu phi tuj'ln theo phudng giam giii trong day lUdng tii t h i dao d5ng dieu boa. Chiing tdi da tinh sd va ve d6 thi CSHT phi tuyin phu thupc vao nang ludng photon cho m l u day lupng tii GaAs/AlAs. Sii phi; thupc CSHT phi tuyin vao cac gia tri khac nliau cua nhiet dp da dUdc khao sat. Chiing toi da su; dung dinh cdng hudng tUdng ling vdi qua trinh h i p thu hai photon dl khao sat dp rdng pho. Tit do thi su phu thuoc ciia CSHT phi tuyin vao nang lupng photon, chiing toi thu dUdc sU phu thupc do rpng phd theo nhiet dp. Kit qua thu dUdc cbo t h i y dp rpng phd phi tuyin tang theo nliiet dp. Kit qua nay phu hdp vdi du doan vl mat ly thuyet va y ugliia vat ly cua nd cd the dudc giai thich mot each tudng minh.
TAI LIEU THAM KHAO
[1] Kang N. L., Lee H. J. and Choi S. D. (2004), J. Kor. Phys. Soc. 44, pp. 938-943.
[2] Lee H. J.. Kang N. L.. Sug J. Y., Choi S. D. (2002), Phys. Rev. B 65, pp. 195113- 195117
[3] Kang N. L., Lee Y. J. and Choi S. D. (2011), J. Kor. Phys. Soc. 58, pp. 538-544 [4] Kang X. L., Ji Y. S., Lee H. J. and Choi S. D. (2003), J. Kor. Phys. Soc. 42, pp.
379-385.
5] Kang X, L.. Lee V J. and Choi S. D. (2004), J. Kor. Phys. Soc. 44, pp. 1535-1541.
[6] Kang X. L. and Choi S. D. (2002), J. Phys.: Condens. Matter 14. pp. 9733-9742.
DO TIM COXG HUCiXG ELECTRON-PHOXOX B A N G QUANG HOC.
[7] Yu S. G., Pevzner V. B., Kim K. W. and Stroscio M. A. (1998), Phys. Rev. B 58. pp.
3580-3583.
[8] Huyuh Vinh Phuc, Lugu an tiln sT vat ly, Dai hoc Hul, 2012.
[9] La Dinh, Hi Thi Ngoc Anh (2012), Tap chi Khoa hoc va Giao due, Trudng Dai hoc Su pham Hul, S6 03 (23), trang 5- 12.
[10] Tran Cong Phong. Huynh Vinh Phuc (2011), Modern Physics Letters B 25. pp. 1003- 1011.
Title: XOXLIXEAR ABSORPTIOX POW^R AXD LIX&WIDTHS IN QUANTUM \MRES WITH HARMONIC OSCILLATOR POTENTIALS
Abstract: In this paper, we considered the first order nonlinear absorption power and linewidths. Prom the analytical expressions of the nonlinear conductivity tensor, we ob- tained the expression of nonlinear absorption power (X.A.P) and plotted the graphs showing the dependence of X'^AP on the incident photon energy. Prom curves on graphs of the X'.\P with different temperature, using profile method we obtained the dependence of line-widtlis on temperature. The obtained results show that the nonlinear resonant peak line-widths increase with temperature.
Keywords: absorption power, nonlinear, profile method
PGS. TS. LE DINH
Khoa Vat ly, Trung tam Vat ly ly thuylt & \"at ly tinh toan, Trudng Dai hpc Su pham - Dai hpc Hul
ThS. HO THI NGOC ANH
Trudng Cao ding nghl Lilama - Ddng Xai