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D.\I HOC QUÓC GIA HA NÜI TRIONG OAI HOC KHOA HOC TI NHIKN TEN DE TAI: NGHIÉN Cirv ANH HlfÓNG CÚA SĨNG DÍÉN TI MATsM LÉN MOT SO TÍNH CHAT DONGTRONG BÁNDANTHÁPCHIÉL M A S Ó : Q T - - 15 CHU TRI DE TAI: GS.TS NÍ.ÍJVEN QrANí, B W H - NCii - 20'M DAl HOC QC GIA HA NĨÍ TRNG DAI HOC KHOA HOC TU NHHN TEN DE TAI: NGHIÉN CÚU ANH HUÓNG CÚA SĨNG DIÉN TÚ MANÍ! LÉN MOT SĨ TÍNH CHAT DONGTRONG BÁN DAN THAP CHIÉU MÁSO:QT-08-15 CHU TRI DÉ TAI : GS.TS NGUYÉN QUANíí P.ÁU CÁC CAN B() THAM GIA: 7S Nguyén Vü Nhán TS Trán Cóng Pliong TS, Dinh Quóc Viíctnc 'Jhs - NCS l.,uun¿ v Tung, ^^^s Le Dinh,Th.s-NCS Hoang Dlnli Trien ,Ths-NCS Trán fhi Hai, NCS.L:.- Tlii;; NCS Ngun Bích Ngoc.NCS Dó Manh Hüng.Cir nhán Ngun hi Mai Nhicn, Cú nS.ar Trán Thi Nga.Cú nhán Nguyén Ván Thiián Cú nhán Ngu\én Van Nglua Cif nhán NÍÍIÍX.Thu Híifc*iio HA N - 20(«8 Bao cao tóm tát í! f í'on de tai: NGHIÉN CÚU ANH Hl/ĨNG CÜA SĨNG DÍEN TÜ^i:A^H LÉN MOT SĨ TÍNH CHAT DONGTRONG BÁN DAN THAP CHIÉU MA SO: OT - OS 15 b) N¿ubi chij Irj: (ÍS.TS Nguyén Quang Báu Khoa Vat ly,Dai hoc Khoa hpc Tir nhién ( DHQGHN ) Día chi: 334 Nguyén Trai, Thanh Xuán, Ha Noi Sódien thoai:(C)4)7626547 c) C;k can bo tham gia: TS Ngiiycn Vü Nhán, TS Trán Cóng Phong, TS Dinh Quóc Vucfng, Ths - NCS Luor^^ Van Tíing nis Lé Dinh.Ths-NCS Hống Dmh Trien ,Ths-NCS Trun Thi Hái NCS.l A- JhÁi i bu NCS Ngun Bích Ngoc,NCS Dó Manh Hüng,CLr nhán Ngun Thi Mai Nhién Cu íihai; Trán Thi Nga^Cú nhán Nguyén Ván Thuán, Cu nhán Nguyén Ván Nghía, Cú nhán ^iguycíi Thu Huono d) Miic tiéu vá nói diing nghién cúu: - Nghién ci'm háp thu phi tuyén sóng dien tir bal dien tií giam cám irong bán úhn ihap chiéu vái cae dang thé giam cám khác ( có ké den sir giam cám ci:a phonon ,\ -:'• ké den aiih huang cüa tír tru'ófng - Nghién ciiu bien dói tham só giira phonon ám giam cám vá phonon quang gsam c;\^-; iiong bán dan tbáp chiéu vói dang thé giam cám khác - Nghién cii'u cóng huang tham só giu'a phonon ám giam cám \á phonon ijiiLinií g'^.^rcám Irong bán dan tháp chiéu vái dang thé giam cám khác Tính chai, phuong pliáp luán vá sir pham cao cúa két qua nghién cú'u IT!:-; ÍÍI^: C Dé tai cüng góp phán quan vao su nghiep dao tao Dai hpc Sau d.M hoc \;Í va} dung dói ngu nhá khoa hoc cóng nghe tien tién cho dál mróc e) Các kcl dat dupc: 11 cóng trinh da cóng bó tren lap chi khoj n;x ^i' hoí nghi khoa hoc: f ac cong trinh da cóng bó tren tap chí khoa hoc Qc te: (2 bái) : i'tii! í'.íjMii Ptu»ng Luong Van Tung Nguyén Quang Bau-PararncMic I'CMÍVA.I ^ ' \':o\\^uc ^!i)d (jpiical Phonons in a Doped Semiconductor Suncíi;:üice.Kv'.c;ü^ I'.; -i' ^-ci-y V(;! 53 No4 (.ktober 2008 pp.1971-1975 j Ng'ayen Quami, Bau Nguyén Bich Ngoc, and Do Manh h'ung Tii^: r.oi;hii:o; absorption coefficient of a strong electromagnetic vvave by contíned cloctuwi- ;f rlie quantum v^eíls Journal ofthe Korean Physical Socicty (to be pubü^hed) >iK'V^ Các cóng trinh da cóng bó tren tap chí khoa hpc Qc gia: (5 baii i Nguyén Thi Mai Nhien, Do Manh Hung, Nguyén Quang Bau The paraincirtL iesonatice of conílned acoustic phonons and confined optical phonon> in qucUiíuní vveUs VN(J -Journal of Science, Mathematics-Physics, Vol.24.No S.pp.'.MO::43(2008) Nguven Van Thuan, Do Manh Hung, Nguyén Quang Bau The influenc;.^ o! magnetic tleld on the nonhnear absorption coefficient of a strong eleonomaíir.ciie vvave by confiried electrons in the doping superlattices VNTJ -Journa! oí Scior/.::: Mathematics-Physics, Vol.24,No.lS pp.232-235(2008) Hoang Dinh Trien, Nguyén Quang Bau, Nguyén Thi Thar-h Nhon ¡r;iuení.e *-,r magnetic field on the nonlinear absorption coefficient of a strong e¡ec:roniag!^.:ti: v^^ave by confíned electronis in cylindrical quantum v/ires \^! 53 No4 (J^iob-r 2008 pp.i97M975 ¡Nguyén Ou^ng Bau Nguyén Bich Ngoc, and Do Manii Hung Th¿ nonhn-o: absorption coefficient of a strong electromagnetic vvave by confíned eloclrDUs ;{ vh.e quantum weíls Journal ofthe Korean Physical Society (to be published) JOOV 2, Các cóng trinh da cóng l)ó tren tap chí khoa hpc Quóc gia: (5 bái t L Nguyén Thi Mai Nhien, Do Manh Hung, Nguyén Quang Bau The paramenta loonaucc of confíned acoustic phonons and confíned optical phonons in qucUiluoi weüs VN(J -Journal of Science, Mathematics-Physics, Vol.24.No S.pp.'.:4'»243(20í)8) 2, Nguyén Van Thuan, Do Manh Hung, Nguyén Quang Bau The intluencL^ o! magnetic field on the nonlinear absorption coefficient of a strong elcciiOir>.iL''íC'.!c vvave hy confír¡ed electrons in the doping superlattices VNL' -Journul o! SÍ i:,:.:: -Matheniatics-Physics, Vol.24,No.l S pp.232-235(2008) Hoang Dinh Trien, Nguyén Quang Bau, Nguyén Thi Thanh Nhan iüiue-ice r,\ magneric fíeld on the nonlinear absorption coefficient of a strong eieccroiv.auri.-hL vvave by confíned electronis in cylindrical quantum vvires V?'Jli -Jouriv^i ^'l Science Mathematics-Physics, Vol.24,No.lS,pp.47-50(2008) 4- Do Manh Hung, Nguyén Quang Bau, Hoang Dinh Trien, and Nguycn '¡ ¡li í lianii Nhan Caculation of the nonlinear absoiption coeffcient of i IAI^ÍJ elecíroinagnetic vvave by coefined electrons in the composiíionaí lur'.vririíil; :, \'NC "Jouma! of Science, Mathematics-Physics Vo!.24.No,lS,pp.236-239í2í;08í Luong Van Tung, Hoang Dinh Trien, NguyenQuang Bau A nuinber H.igi' íi-equency Lffects on Semiconductor Superlattices VNU -Jouü-ía; oi' Sciei C: Matiiematics-Physics Vol.24,No.! S,pp.228-231 (2008) Các háo cao khoa hoc lai Hói nghi: (4 bao cao bao cao kbo:i hoc ó Hói nghi khoa hoc Vát ly niróc: :\¿M,rvcn Van Hieu, I e Thi Thu Phuong Do Manh Hung Nguveri li -;i.'i: NiMjjycn Quang íJau The 33rh National Conference on rhi^rverScj! í")- i\ 1 í^ ¡hmm - i-ioanu Dinh iricn N'juven Qínii Bau and Do Manh \h.\r:¿ CaicMÍaiup i\ i-v n.^niinear absorption coefficient of a strong electromagnetic vvavc b> CUIKLV elecírons u] recion^zular quantum vvires vvith infínite oolentíd The 33!!i N':';^^-•' Conferencc or rhcoretica! Physics, Da Nang 08^2008 Nguyén Van Nghia, Nguyén Van Thuan, Tran Thi Nga, Nguyén Qii liig L' : : Nguyén Vti Nhan Parametric transformation and parametric resonance o! ccríiiv,: acoustic phonons and superlattices The 33th National Conferencc on (hooreiicai Physics, Da Nang 08/2008 i bao cao o Hói nghi Vát ly Quóc Té: Nguyén Quang Bau, Ha Dang ÍChoa, Nguyén Bich Ngoc and Ngi;\'c;i Difjit • ¡en Calculation of nonlinear absorption coefficient ofthe strong ei;Xi;\vr;á;:iKi> vvave by coníined electrons in the composiíional superlattices Procccd-ng '-i^(:v Rleventh Vieínainese - Germán Seminar on Physics and Fingineering Nria ¡:.:;:;.: C iiy, from March, 31 lo April, 5, 2008 Các cóng trlrih da hốn thánh gái dang tren lap chí khoa ho: gu'i dang lap chí Han Qc ) K q dao tao: (íóp phán dao tao lio vá ten NCSJiioc vién Tién sv , Cap cláo tao Ten luán vñn Ghi cht^ " TS/Ths" Mót só hiéu li'ns cao l^S (bao vé tan tucnig tac ! thán2 I elecíron-phonon 6/2008) i dáv luaniz tir bán dan I I Lé Dinh Thac sS * I C h u nh-vín ' dé lái huoivj ! danchíni-^ i [ S^U -•i uo'n-^ Van i:'p; en V an í hn •LNauvéi '' an NL'íiia :.Ngun Lhi Ma.i Nhién ó.Ngun Thu Huaim Trán Thi No^a Mót só 1-liéu i'mg cao TS (bao \ é ! tan bán dan siéu tháng , tna.ng 12''2008) /'inh Ivjii cua tír •ruoPü ¡en so han thu piíi luyen sóng dien tú sicu mang pha tap Bien dói tham só giira phonon ám giam cám vá phonon quang giam cám trons siéu mang pha tap i Cóng hiróníi tham so i giúa phonon ám giam I cáin vá phonon quang I í2Íam cám ti'onu hó j liranií tu I :—^ ^ I C'ónu hiróim tham so ! gura phonn am giam ; cám vá phonon quang j giam cám siéu I mang phatham tap só güja Bien dói ' Cí \ii nh: • • ; íái \'\o ' d jn Ch!:* • ThS {bao vé thánií 12/2008) ' *' in 'V;'v ••: ; de tai iii.c^i ' dancíunh ThS (bao vé tháng 12/2008) Chu iihié.n i dé tai huxÍDg ! dl.nchrir ThS (bao vé tháng 12/2008) ¡ Chu nhiem dé tai hiróü • dan chí.-h ThS (bao vé tháno 12/2008) ¡ Chu nliic;ivi dé lái huon i danch'piT ThS (bao vé j>honon ám giam cám tháns vá phonon quang giam 2/2008) cám hó luong tú ' Ch:i nhie^n i dé tai h'L'.ón i L Ngối ra, dé tai góp phán dao tao Cu nhán Vát ly : Nguyén Hoa; \:.'\, an Nuuvén lhi Nizoc Ha Nieó lhi Thanh Ha N^iuvéa lhi Thẵh H-^ n i íní) hinh kinh phi cúa dé tai: Mót só hiéu úng cao TS (bao v tan troné bán dan siéu tháng 12/2008) nang, vij])d V a n ¡ 'j-i 'ji! V íin I hn LNauvéi) ^^ an Níjuia I Anh hng cua tú i '.rM' >'ng só háp I thu phi luyen sóng i dién tú SICU mang pha íap Bien dói tham só giúa phonon ám giam cám vá phonon quang giam ! cám tronü siéu mang I :.Nguyén Lhi Mai Nhién o ' Chu nhio:» i tai !";LIĨ íLíU chí ThS(bao \i thánií 12/2008) de tai iu.' dan chür' ThS (bcio vé j Chu nhiém ^ • thánu 2/2008) I ! dé ta: luiwrz dan chivui o I P^i'- tap i Cóng hirón¿: tham so I aiúa phonon ám giam ThS (bao vé ; cam va phonon quang tháne I giam cárn hó 12/2008) i Chu nh¡en"i dé tai hu'ó dan iro'ne tu O.N^uvén Thu Huanu •l'ián Tin N^a tCóníi hirón^i tham so \ i * ' I giúa pliónn ám giam ¡ ThS (bao ve | Chu nSiiéi< I dé tai huong ; ¡ cám vá phonon quang tháng dan ch^r'h i giam cám siéu 12/2008) ¡ mang pha tap ; Bien dói tham só giúa ; ThS (bao vé ' Chu nhioni • i vlionon am s.iam cam ; tháng i dé tai hiión I vá phonon quang giam i 12/2008) I danchír,!) i cám troné hó luone íú Ngối ra, dé tai góp phán dao tao Cu nhán Vát ly : Nguyén Hoai XiLi an Nguyén lili Ngoc Ha NgO lhi Thanh Ha Nguyén thi Thai^.h H ^ fí \)nh hmh kinh phi cüa dé tai: - Kmh ¡>hí d w c cap: 20 iriéu dóng VN irong nárn 2006 G'ái irinh nhúng khoiui chi lón: 18 iriéu VND thué chuyén p:\ uorv.^ 'VJ •'=• -v ' i hj! bao va bao cao khoa hpc (4 cóng trinh nghién cúu trony ^o i I -IL •:::.: Í''"j ' ' í n i i c r í KHOAQLANLV (Kv ^a ^ni ró ho tin) Ha Noi, Ngay 2'h [\:1:)-: i :u:.; CHL ! H ! i i L LU íKv \ j5 ^t^ rv ho U:i-) ^h^ív^^i J'jz¿:)i^ (íS.TS.Nguyet5 Quanií B.iu TRCONC OAI HOC KHOA HOC Til NHIEN MIEU T R U O N G pesJS.^üi lili J uOs'/n SAO bulk sei niconductc IS seen that there a re di erences betweei n th because ofthedccr case cfsize leto anc ri O res o/" í'íírc rth metáis is itistical //leíií method cale ulate tlu^ Helmholtz free leííí /í at a íJc rangge of tais can be etcrmined by per e.t he phase that id that lower bcc Dy metal of Dy metal ^ trinh báy: Hoá ng Dinh Trié Qo Ci Interf ace-rou ghn ess Paranáeters D termiinatío from 1Mobility Rat a re rtre re o g a a o re The pre studied S 7^ re jiperatu (—1 ^ "§^ Vi a -^ re pr Q 3" energy tempera examini gives th than 17 n c ;:: N EL ;r ^ ~— H n rt -— **- '.A rt a" A 3 z^ > 55 E fif H Z ni> :r Zz z fij c " ff rt 3* v O -1 5: Ti r- ^ C "1 < p( a re OQ o" z^ re o' ~^ re re" = re A C fif n rt re" re -N 3 e dependence of t ííie/íí) 1^ temperat g the equation of st esder ivedfrom MM studies were carri ed ou t in order cp and bcc Dy a fcc a nd bcc C s Tlie síab/e pha f and Ce he Helmholtz free nergy a t a given west free energy w ill best able For the hcp Dy metal s stable At highe Thus 1750K marks e phase transit gs are in greemen ith previous ex¡ tr These fi p- X re a s a- en re o rti P s^I^^ 3^ *« P Ci •** a OQ OQ ^ ^ 12 rt es CA -t A P- S^ rt a Z •0 m> ^ H p >• rt X n 3, p' XCÍ g^^i 3 A sy o> o OQ QT^ H 3- rt rt en -• ^ r s- tr OQ A Vi g- 3A fif tr « o p, r- H rt EC c a 5: = V) p- o A p ^y* 5i" 9l •> o> ^^Z rt ?r 5"" o- a H 3- A t£3 n A V) •P í OQ Q Ts H n 3H rt rt rt •P 03 "^ 3- OQ rt CA CA u fil C3 r^ qQ i^ 3 03 O p< Qua 3- o> 3.rt en' a p' 2' 3- n OQ fil rr 3 Nguyé n Huyen" rt -I *o rt L3 is 11 OQ P' a 1= 3cr X S" tr ztr p- § ^ ^ lo, rt O ta a p( a en Cn Co en ^ re 3 re OQ o ?^ o " H a3 re ^js^+^^ - e,,jjj^ +- huj^-khn) (2) NONLINEAR ABSORPTION COEFFICCIENT Eqs is the general expression for the nonlinear aborption of electromagnetic wave in a C Q W In this paper, we will consider the case of non-degenerative electrón gíis and consider it with different electron-phonon scattering me( Iwuiisnis In t h e c a s e of e l e c t r o n - o p t i c a l p h o n o n s c a t t e r i n g 1.1 T h e a b s o r p t i o n far away from i t s t h r e s h o l d The interaction coefficient of electron-optical phonon scattering C5 takes the form [14] In this case, to happen the absorption of electromagnetic wave in a C Q W the condition ¡khü - HLOQ] > e must be satisfied Here e i^ the average energy of an electrón hi a CQW, we have the nonlinear absorption coeíhcient of a strong electromagnetic wave in a C Q W for the case of the absorption far away from its threshold is obtained 7T'^e'^kBTnoR'^.costc(2n) l2SeoCy/x^7nñ^Q^ / \x^ I\ XQ J w i t h B — 5r,',/' — £,í,/ -I- hiu'Q — hí^j cosecix) = ^ -\- Zlfcli "(2/)'^^ ^ ' ^^^ ^^ ^^ BernouUi number 1.2 T h e a b s o r p t i o n cióse t o i t s t h r e s h o l d In this case, the condition \kM}, - HUJQI ' C £ is needed We obtained tlie explicit formula for the nonlinear absorption coefficient of a strong electromagnetic wave in a C Q W (electrón gas is non-degenerative) "^ 7re^kBTnQR^.cosec{27r) / I 2r>6eQC,/5—nih^9? \x^ B 1xr XQJI £nj r x e r c p ( - r r - ; p exi^í —-7) - exp( 2kBl ksl L B ^^2kBT^ IB.e'EJ _e mK^Ü'^ "^4/,-^ í^Q-9 ksl (4) K-ni^) is the Bessel function of 2ad order I n t h e c a s e e l e c t r o n - a c o u s t i c p h o n o n s c a t t e r i n g T h e interaction coefficient of electron-acoustic phonon scattering C~ [14] q^,n,l,n'J' íó) III N U M E R I C A L R E S U L T S A N D D I S C U S S I O N S In order to clarify the mechanism for the nonhnear absorption of electromagnetic wave in a cylindrical quantum wires, we will evalúate, plot and discuss the expression of the nonlinear absorption coefficient for the case of a specific NGüYEN VAN HIEU GaAsIGaAsAl cylindrical quantum wires The parameters used in the caictila- tions are as follow [8, 9, 10, 11]: The foiiowing numerical results are obtained íor the cases in which n = n ' = and l = r = l Electron-optical p h o n o n s c a t t e r i n g DaalMd Line II.14 S o l i d l i n a K.aona T-27)K Oaahed Ii.ne T'100í< S o l i d l i n " T.103X R-:Orun 20 Fig Dependence of the absorption coefficient on photon energy at different valúes ofthe wire's radius (The absorption far away from its threshold) 30 40 Photon enefgv(meV) Fig Dependence of the absorption coefficient on photon energy at different values of the lattice temperature (The absorption far away from its threshold) 4.5 _ 3.5 c ü S o l i d l i n e r-2';0 Qaebed l i n e T-)DC R-20nB 1' I" fr o • I ^-5 c í , 60 80 100 120 Photon energyfmeV) 140 160 05 60 80 100 120 Photon efiergylTieVl I-IO O Fig Dependence of the absorption co- Fig -4 Dependence of tho absorption coefficient on photon energy at different val- efficient on photon oiirrgy diíTrrcni valúes of the wire's radius (The absorption ues of the lattice temperature (Tho absorpclose to its threshold) tion close to its threshold) Figure and present ^he dependence of the absorption ^^^"^f^"^^^^^ E M W energy at different valúes of the wire's radius and at different lemperature valúes It is noted t h a t in the >w range of E M W energ>- appear resonant p c k NONLINEAR ABSORPTION COEFFICCrENT '> at fi = U;Ü (the absorption close to its threshold, figm-e 3, 4) In addition ÍL can SÍ.ÍC from figure 1,2 that the peak move to th;.» right when thf» temperature and wire's rises In contrast, figure 3, shows that the positions of the míixinnmi is nearly unchangcd when the wire's radius and latticcs temperaturíí are varied This means that resonance condition is determaned mainly by the photon's energy This has been investigated and resulted in [12, 14] for the case absorption electromagnetic wave with small amplitude Comparing Figm'C 1, 2, 3, 4, wc sec that when tho tcmpcratiu-cs or tho wire's radius is constant, there is a resonance point, corresponds to varioiis photon cncrgies, in each curve This exprcsses the fact that the energy spectra of electrons in CQR are quantized and bring about complicated selection rules From figures and 4, we also see that máximum corresponded to the same photon energy and was independent of the temperature and the wire's radius Because tho intrasubband transitions n=n'=0 and l = r = l are considered Different with acoustic phonons, in the case of optical phonons not observe amplification of the EMW Tliis conforms to our consideration of phonon generation and can be explained by the great significance of optical phonon energy Electron-acoustic phonon scattering 0.2 ' ' ' " ' 0.2S /'' i -0* 1 c 1^-0.6 / ' // s Daahed lina T.2/3X Solid line T.J'/OK /' 01 ft -0.6 -1 • -1,2 -I.4L 1i A/' / M 0.2 0.4 0.6 Radius (rf quantum wire(in] 100 120 140 Tempe rarure(K) 160 IBO 200 Fig Dependence ofthe absorption co- Fig Dependence of the absorption coefficient on the wire's radius at different efficient ou the temperature at ditiererit valúes of the radius valúes of the lattice temperature Figure shows the dependence of the absorption coefficient on the wire s radius at different valúes of the lattices temperature The dependence of the absorption coefficient on the wire's radius at different valúes of temperatur(í shows that the absorption coefBcient has same máximum valué (peaks) at R -^ 15 nm, but with valué ranges of the wire's from 50nm to 70nm, the absorption coefficient has a máximum increases a^ the temperature rises For example, at T-273K T=270K, the peaks correspond to R ^ 60 nm, R 65 nm, respectively This means that absorption coefficient dependences significantly on the lattice temperature It can see from figure that there exist valué range of the wire s radnas at NGUYÉN VAN HIEU which the absorption coefncient has negative valúes In this case, we can say t hat we has an amphfieation of the electromagnetic wave (acoiLSti(^ wave)- This has been investigated aud resulted in [12, 14] for the case absorption electromagnetic wave with small amplitude It can see from figure that has a peak at T-6ÜK for R~20 nm, which corresponds to the strongest absorption It is worth noting that a quantum wire with the abovc-mentioned radius was fabricated cxperinientally [13] IV CONCLUSIONS In the present paper, wc have obtained analytical expressions for the absorption coefficient of a strong EMWs in a cylindrical quantum wire for both mechanisms of electron-phonon scattering The dependences of the absorption coefficient on the EMW energy ftfi, the temperature T, and the wire's radius R aie complex and dififerent compared to those obtained in cyclindrical and rectangular quantum wires for the absorption electromagnetic wave with small auiplitude[12,14] In addition the results show a geometrical dcpcnd(;nces of the absorption coefficient due to the differeces in the energy spectra, the wave fmi(.'tions and the form factors for different samples The numerical results obtained for a GaAs/GaAsAl wire show that when the momentum-energy of electrons compiles with specific conditions m^ixiinuin peaks will appear in the EMW absorption spectra These results also can consider numcricfdly wires with any radius Specially, for a wire with a radius R - 20 nm, which was fabricated experimentally, the results show that the absorptitm of EMWs becomes more powcrful at T~60 K in the case of electron-acoustic phonon scattering For electron-optical phonon scattering, absorption spectrum lias a peak correspoding to a frequency íl = LJQ ACKNOWLEDGMENT This work is completed with financial support from the Program of Basic Research in Natural Science QT-08-15, 405906 REFERENCES N Mori and T Ando, phys Rev, B 40 (1989) 6175 H Rucker, E Molinari and R Lugli phys Rev B 45 (1992) 6747 J Pozelar and V Juciene, Sov Phys Tech, Semicond.40 (1995) 459 ' R Yasilopoulos M Charbonneau and C M Van Vlict Phys Rev B 35 (1987) 13-34 A Suzuki, phys Rev B 45 (1992) 6731 N Nishiguchi, Phys Rev B 52 (1995) 5279 ^ ,^^, ^,,,,, RZhao,P/ií/5.fíeí;.I349(1994) 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