Tgp chiKhoa hgc TrudngDgi hgc Cdn Tha Phan A: Khoa hgc Tv nhien, Cdng nghe vd Mdi Irudng: 35 (2014): 119-122 ''
Tap chf Khoa hoc Tru'dng Oai hoc Can Thci website: sj.ctu.edu.vn
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ANH HircKNG CUA NHIET ©Q VA DiEN TRlTCXNG D 6 I VCa HIEU ITNG QUANG KICH THICH TRONG BAN DAN SIEU MANG HOP PHAN Luang Van TCing'
' Khoa Su pham Ly — KTCN, Trirang Dgi hoc Dong Thdp Thdng tin chung:
Ngdy nhdn: 02/10/2014 Ngdy chdp nhdn: 29/12/2014 Title-
Effect of temperature and parameters of electromagnetic for optical effects stimulated horizontal in semiconductor superlattices component Tit khda:
Hieu ung quang kich thich, bdn ddn sieu mang, suy bien hodn todn, hdm phdn bo hat ldi, phonon
Keywords:
Optical stimulation effects, semiconductor superlattice, completely degenerate, carrier distribution function, phonon
ABSTRACT
In this study we apply the quantum dynamics equation for the electron distribution function in semiconductor superlattices components under the effect of an electromagnetic field with frequency a), amplitude E and a laser pulse frequency Q, amplitude F. To solve this equation we have obtained analytical expressions for the constant electric field intensity of horizontal stimulation optical effects. Based on numerical computing results by using the Matiab software, we have obtained the dependence of the electromagnetic field on the temperature as well as the parameters of the magnetic field puling on the material
TOM TAT
Trong nghien cvu ndy chung toi dp dung phuang phdp phuang trinh dong lifong til cho hdm phdn bo mat do electron ddn trong bdn ddn siiu mang hop phdn dudi tdc diing cua truong dien tie tdn s6 m, bien do E vd mat xung laser cao tdn tdn sd Q bien dQ F . Gidi phuang trinh ndy chung toi da thu duac bieu thirc gidi tich cua cucmg do diin truong Ididng doi xudt hien trong vdt lieu do hieu ung quang kich thich ngang gdy ra. Khdo sdt tinh so bdng phdn mem todn hoc Matiab da thu du(rc su phu thupc cua dien trudng khong doi nay vdo nhiet do cUng nhu cdc tham so khdc ciia Iruang diin tu- ddt vdo vdt lieu.
1 GIOI THIEU
Hidu dng quang kich thich da dugc nhilu nhi vat 1^ frong nude vd frdn thd gidi quan tim nghien cuu. Cdc nghidn edu ndy ddu dya fren md hinh:
dua vio vat lieu bin din mgt didn td trudng didu hda vdi tin so gde la, bidn do dien trudng E, bidn dd td trudng H v i radt tin hidu Laser mgnh cd tin so O bidn dg F. Dudi tic dung cua eic hat photon, phonon,... vdi electton frong khdi bin dSn dua din kit qud cd sy phdn b l lgi cdc hat elecfron frong vit li$u, tu dd ldm xuit hien mdt didn trudng khdng ddi EQ theo cac phuang xac dinh frong vit lieu ban
ddn. Dd chinh la hidu ung quang kich thich. Nlu didn trudng khdng ddi xuat hidn dgc theo phuong fruydn cua trudng didn td thi dugc ggi la hi?u dng quang kich thich dgc. Ngugc lai nlu didn trudng nay xuat hidn theo phuong vudng gdc vdi phuang truyen cua trudng dien tu thi ggi la hidu ung quang kich thich ngang.
Cic hidu dng kich thich chii ylu mdi dugc nghien euu frong ban din khdi va chi xdt frong trudng hgp khi didn td dugc xem Id suy biln hoin toan (Shmelev et al., 1982; A.L. Tronconi and O.A. Nunces, 1986). Cung da cd mdt sd cdng trinh nghien cdu ddi vdi vat li?u thdp chilu nhu diy
Tgp chi Khoa hgc Trudng Dgi hgc Cdn Tha Phdn A: Khoa hgc Tv nhien, Cdng nghi vd Mdi trudng: 35 (2014): 119-122 lugng tu, hd lugng tu,... nhung cung chi xet cho
tnrdng hgp khi dien tu suy biln hoin toin (Bui Due Hunger a/., 2012).
Khi nghien cuu hidu dng quang kich thich vdi gia thilt khi didn hi suy biln hoan todn thi bdi todn frd nen don gidn hon rat nhieu nhung chung ta chi thu dugc kdt qud gan dung vi him phdn bd elecfron ddi vdi trudng hgp khi dien tu suy biln hoin hodn thudng dugc sd dyng theo him budc nhiy. Chinh vi ly do niy, hieu iing thu dugc chi phu thugc vdo cic thdng sd dac trung eho vat lieu vd ^dn tu trudng dat vdo mi khdng thu dugc sy phy thudc vio nhiet dd ii mdt ydu td vd cung quan frgng. Cho
% ^ . ( e % ) . . „ [ p . h ( l ) ] , £ ^ ) .
nen cdc ket qui tinh toan cho trudng hgp khi dien tu suy bien rdt khd ed thd kiem chung bdng thuc i^hi^in. Trong bdi bdo nay, chiing tdi nghien cuu hidu ling kich tiiich ngai^ trong bdn ddn sidu mgng hgp phin ddi vdi trudng hgp khi didn tir khdng suy bidn.
2 BIEU THU'C GIAI TICH CUA HIEU inVG QUANG KfCH THICH
Vdi md hinh bai toin nhu vua frinh biy, theo (Ephshtem, Vuzov, 1975), ta cd till vilt dugc phuong frinh dgng lugng td cho hdm phin bd hgt tai (electton) frong ban ddn sieu mgng la:
( - ^ ) =
2 1 ^ 2 M(q) ^ lF(I.q)[f(Px + q)~f(Px.t)]6[e„,5^. - / n ] , (1) Trong dd: Jj li him Bessel ddi vdi sd thyc; q li
xung lugng cua phonon (li chudn hat eua nang lugng dao ddng mang tinh thi ban din); f(px, t) la him phin bl hgt tdi dien; p^ la thdnh phdn xung lugng hat elecfron theo phuang vudng gdc vdi tu trudng; M(q) li hd sd dang, ddi vdi tuong tac electton - phonon frong bdn ddn sidu mang he s6 dgng la (Shmelev et ai, 1982):
M(q) e^fioi;
L x\t^^ + <^lf)
! n , p j . = - ^ + £ n ( p J ; En(Pj)
= 5;;^-A„cos(p,d)
(2)
. (3) Trong do En.pj.l3 phd ning lugng cua elecfron ttong bin dan sidu mang hgp phan; d la hang sd sidu mgng; Aj, li nda dg rgng vung ning lugng mini; ft Id hing sd Planck nit ggn; n li chi sd mini viing nang lugng (n = 1, 2, 3,...); pj li thinh phin xui^ lugng bgt tii theo phuang truyen cua didn tu trudng ngodi; e la didn ti'ch elecfron; cog Id tin sd plasma; Vii till tich mdu; Xeo.Xo la hdng sd didn mdi cao tin vi hdi^ sd dien mdi tmh; q^ li n^ich dao do dai chdn Debye; m li khdi lugng hieu dung cda electton. Trong phuong trinh (1) ta da sd dyng
eH -. H(t) ^
" « = ; : : : : ; h(t) = ——; a =
eP (4)
Dg giai phuong trinh (1) tim ham phan bd hat tai ta dat theo tai li?u (Ephshtein. Vuzov. 1975):
f(Pi.t) = fo(En,pJ + fi(p±.t) (5) vdi fo(£n,Pi) i^ thanh phin ham phan bd khdng phu thupc thoi gian dupe gpi la ham phSn b6 c§n bang. Ddi vdi khi di$n tijr khdng suy bien ham phan bd can bang la:
fo(En.Jij.) = Hoe •^ • n .? j
'_;_. ''BT^ (.6) HQ li m^t dd hgt tii; T la nhidt dg; kg Id hdng sd Bonzman.
Tidp tuc dit:
fi(p±. t) = fioCPx) + fiCPx)e-'"^ + fi'(Px)e-' (7) d diy fi(px) va fi(px) la lien hiep phuc ciia nhau.
Him phin bd fioCpx) se tao ra ddng didn mdt chidu, cdn fi(px)e~'"' sd tgo ra ddng dien bien ddi vdi tan so (0 nen ta cd the tfnh mat do ddng didn frong v|t lieu dang xet theo cdng thde:
= j ( 0 + To = |[RCe)e-*<-' + R-(£)e"^' + RoC£)jd£ (8)
Tgp chi Khoa hgc Trudng Dgi hgc Cdn Tha
Trong dd:
Px
RoC£) = - - y M o ( p ± M ( £
Px
n.Px.
P/wn A: Khoa hgc Tv nhien, Cdng ngh4 vd Mdi trudng: 35 (2014): 119-122^
TT^ay (6), (7) vdo (1) dl giii phuong trinh, sau do tilp tyc thay vio (8) dd tinh ta se tiiu dugc bilu thuc mit do ddng didn mdt chilu frong vat Hdu dang xet Id:
)de (9) :,,5Jd£ (10)
:V^T{£p)e^no -. S^f2me^noF^a}^^ZT(£p) _
^wid^ { ; — : ^ EQ
4?r3/? 265n^m^h*a.'^XPjp '
T^ie,)f'^
0 nen ta cd:
a day T(£F) la thdi gian hdi phuc miic Fermi. Khi tuong tac dat trang tliai cSn bang thi jg SVlme^nof ^6i,irr(£r) ,
(11)
n2.zU^ / gt^ a'^\
Hay:
47rV
X e ' 2 + e ' T
8^/2me^n^,F^c^}.T(£p) _o2..^
= • £ ' ' " 8
4 i r 3 ; S ( l + w Z T 2 ( £ , ) ) ,[E,h\ - (12) Chu ^ rang:
,^ - , eH r . ff
-i^^- -Am
Matiab vg dd thj ta tim duge quy luit phu thudc eua didn trudng khdng dii EQX vdo nhiet dd T, tin sd trudng laser fl va bien do trudng laser F.
Vdi W Ii vee to mgt do ddng ning lugng frudng didn td. Neu ta chgn tryc Oz trung vdi chilu cua IV thi tu (12) ta cd.- the;suj^rci^ttS5rphin hinh chidu cua vec ta cudng dd didn trudng khdng ddi frdn cic fryc tga dg Id:
265V^7im^ll*n*X^fP
T{£F)eW
~ {l + ai^T2{£p))n - vh EOV
J (13) (14)
^' ,-'->.
J ^
r
_,--'' _. ,
^'' - _, .-" _ .-"
..--—
p - " __
2 0 0 (K)
Bilu tilde (13) chdng td cd tdn tai hidu dng quang kfch thfch ngang trong ban ddn sidu mang tiidnh phan vd gid frj didn trudng khdng ddi dgc theo fryc Ox phy thugc nhidt dd cung nhu cac tiidng sd cua didn tu trudng ddt vio.
3 TINH SO VA THAO LUAN KET QUA Dya vao bilu tiiuc (13), su dyng phdn mdm
Hinh 1: Sy phy thugc cua EQ^ vao nhi|t dg dng vdi tan so laser Q. = 10^^//z (duomg cham),
£1 = 1,05.10^^ Hz (dudng ggch) v i a = 1.1.10"Hz (dudtig liln) Dd thi Hinh 1 cho thdy didn trudng khdng doi theo phuang cda tryc Ox phy thugc manh vao nhi^t dd, d§c bidt khi nhidt dg thap (khodng dudi lOOK) sy phy thudc cing mgnh. Nhidt dd tang ldn (khoang fren 300K) thi sy phy thuOc ndy ylu din.
Tgp chiKhoa hoc Trudng Dgi hgc Cdn Tha Phdn A: Khoa hgc Tu nhien, Cdng ngh4 va Moi Irudng: 35 (2014): 119-122
tuyy
C
i3 n t\
^
Hinh 2: Sy phu thugc ciia EQX vio tin s i laser ung vdi nbi|t dg T= lOOK (dudng chim), T=250K (duomg ggch) vd T=400K (dudng liln)
Dudng dd thj Hinh 2 chi ra ring tin sd laser cing ting thi hidu dng quang kich thich ngang cing giim. Tdc do giim d midn tin s6 thdp ldn ban rat nhieu so vdi mien tdn sd cao. Khi tin sd kha cao (frdn 10^*//z) thi tdc dd bidn ddi dd cdn giam ding kl, dudng dd tiij gin song song vdi tryc hoanh.
Dang didu ciia dudng dd thi nay li phu hgp vdi khio sit ddi vdi trudng hgp khi didn tii suy bidn hodn todn, dgc biet hau nhu gidng nhau trong mien nhi?t do tiiip (E.M. Ephshtein, Izv. Vuzov, 1975;
Bui Due Hung at al., 2012).
BTSSST'-
^ X , ' --'"
_,.''' '-''
F (V/m)
Hinh 3: Sy phu thuoc ciia Eo^ vdo bien d$ laser ihig vdi tan sd laser ft = lO^^Hz (dudng cham),
n = 1, OS. lO^^Hz (dudng gach) va fl = 1 , 1 . 1 0 " H z ( d u ^ g iiln)
Dudng dd thi thu dirge d Hinh 3 chung td hieu ung quang kfch thich ngang phy thudc phi tuyen vao bidn dd laser. Khi bidn do cdng tang, sy phy thudc niy cing rd. Khdo sat vdi mien bien do rgng hon Cling khdng tim thiy sy bao hda. Dudng dd thi md ta sy phyc thugc cua hi^u dng quang kich thich ngang vdo bidn dg trudng laser thu dugc frong trudng hgp khi didn td khdng suy biln cung cd dang dien bien ddi tuang tu nhu trudng hgp khi didn td suy bien hoan toin frong day lugng tu.
I KETLU4.N
Bang vide gidi phuong ttinh ddng lugng tu cho him phin bd hgt tii frong bin ddn sieu mang hgp phdn dudi tdc dung cua didn tu trudng, ehiing tdi di thu dugc bieu thdc giii tich cua hidu dng quang kieh thieh frong ban ddn sieu mgng hgp phdn ttong trudng hgp khi didn tu khdng suy biln. Khio sit sd chi rd sy phy thudc ciia hidu iing quang kich thich ngang ttong ban din sieu mgng vdo nhiet dg ciing nhu cdc tham sd cda dien td frudng. Nhdng ket qui nay khd trdng khdp vdi mdt sd cdng trinh trudc ddy di nghien euu doi vdi ttudng hgp khi dien tu suy bien hoin toan cho mdt sd vat lieu bdn ddn khdc nhu ddi vdi ban dan khdi da dugc khdo sdt bdi (E.M. Ephshtein, Izv. Vuzov, 1975), diy Iugng tu dugc khio sdt cua nhom tdc gid (Bu! Due Hung at ai, 2012).
AI LI|:U THAM KHAO
1. A.L. Tronconi and O.A. Nunees, 1986.
Theory of the excitation and amplification of longitudinal-optical phonons in degenarate semiconductors under an intense laser field, i'/iy^, .Rev. B (33), pp4125-4131.
2. Bui Due Hung, Nguyen Vu Nhan, Luong Van Tung, and Nguyen Quan Bau, 2012.
Photostimulated quantum effects in quantum wells with a parabolic potenial. Proc. Nati.
Conf Theor. Phys. 37, pp. 168-173 3. E.M. Ephshtein, Izv. Vuzov, 1975.
Radiofizika. Fiz. Tekb. Poluprov.
4. G.M.Shmelev, G.I. Tsuukan, and E.M.
Ephshtem, 1982. Photostimulated Radioelecfrical Transverse Effect in Semiconductors. Phys. stat. sol. (b) 109, K53.
