Nghiên cứu ảnh hưởng của sóng điện từ mạnh lên một số tính chất động trong bán dẫn thấp chiều

2, Các cóng trinh da cóng ló tren các tap chí khoa hpc Quóc gia: 5 bái t L Nguyén Thi Mai Nhien, Do Manh Hung, Nguyén Quang Bau.. Các cóng trlrih da hoán thánh gái dang tren các lap chí

D.\I HOC QUÓC GIA HA NÜI TRIONG OAI HOC KHOA HOC TI NHIKN

TEN DE TAI:

NGHIÉN Cirv ANH HlfÓNG CÚA SÓNG DÍÉN TI MATsM

LÉN MOT SO TÍNH CHAT DONGTRONG

BÁNDANTHÁPCHIÉL

M A S Ó : Q T - 0 8 - 15

CHU TRI DE TAI: GS.TS NÍ.ÍJVEN Q r A N í , B W

H - NCii - 20'M

DAl HOC QUÓC GIA HA NÓÍ TRUÓNG DAI HOC KHOA HOC TU NHHN

TEN DE TAI:

NGHIÉN CÚU ANH HUÓNG CÚA SÓNG DIÉN TÚ MANÍ!

LÉN MOT SÓ TÍNH CHAT DONGTRONG

BÁN DAN THAP CHIÉU

HA NOÍ - 20(«8

Bao cao tóm tát

í! f í'on de tai:

NGHIÉN CÚU ANH Hl/ÓNG CÜA SÓNG DÍEN TÜ^i:A^H

LÉN MOT SÓ TÍNH CHAT DONGTRONG

BÁN D A N THAP CHIÉU

MA SO:

O T - 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 n i s Lé Dinh.Ths-NCS Hoáng Dmh Trien ,Ths-NCS Trun Thi Hái NCS.l A- JhÁi i bu

NCS Nguyén Bích Ngoc,NCS Dó Manh Hüng,CLr nhán Nguyén 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 nhau ( 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 các dang thé giam cám khác nhau

- Nghién cii'u cóng huang tham só giu'a phonon ám giam cám \á phonon ijiiLinií

g'^.^r-cám Irong bán dan tháp chiéu vái các dang thé giam g'^.^r-cám khác nhau

Tính chai, phuong pliáp luán vá sir pham cao cúa các két qua nghién cú'u IT!:-; ÍÍI^: C

Dé tai cüng góp phán quan trong vao su nghiep dao tao Dai hpc Sau d.M hoc \;Í va} dung dói ngu các nhá khoa hoc cóng nghe tien tién cho dál mróc

e) Các kcl quá dat dupc: 11 cóng trinh da cóng bó tren các lap chi khoj n;x ^i'

hoí nghi khoa hoc:

1 f ac cong trinh da cóng bó tren các tap chí khoa hoc Quóc 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^

2 Các cóng trinh da cóng bó tren các tap chí khoa hpc Quóc 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 1 S.pp.'.MO- ::43(2008)

2 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)

3 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 \^<V -Jouniai ^'í

Science Mathematics-Physics, Vol.24,No 1 S,pp.47o0(2008)

4 Do Manh Hung, Nguyén Quang Bau, Hoang Dinh Trien, and Ngiiycn 'Tu]

í hanh Nhan Caculation of the nonlinear absorption coeffciení of a srí^úig eieciroi^iagnetic vvave by coefined elecírons in the composiíional zuperíatiir^s

\']\V Jouma! of Science, Mathematics-Physics, Vol.24,No.! S,pp-236-239í2í;08 Í

5 Luong Van Tung, Hoang Dinh Trien, NguyenQuang Bau A nuinb;r Higi' íiequency Lftects on Semiconductor Superlattices VNU -Journa; cr-' Sciei c:,

-Mathematics-Physics, Vol.24.No 1 S,pp.228-231 (2008)

3 í ác báu cao khoa hpc tai các Hói nghh (4 bao cao)

- 3 bao cao khoa hpc ó Hói nghi khoa hpc Vát ly trong nuóc:

i Nyuj.en V^an Hieu l e Thi Thu Phuong Do Manh Hung Nguven

Cu-'^M-ih Si'ivsL-n Quang Fiau The 33th National Conference on rhoo.eticj; "

0^ Naiiíz 08/2008

- i-loang Dinh Iricn Nguyén (^uang Bau and Do Manh Hung Calcuiaif P

ú'.jiih'near absorption coefficient of a strong electromagnetic vvavc b> COÍM.I.C^

elecíiX'Hs ]]] rcciongular quantum vviivs v/ith infinite poienía! Tiio 33!i! N:';' ^ i.^

Confcrcncc on rhcoretica! Physics, Da Nang 08G008

3 Nguyén Van Nghia, Nguyén Van Thuan, Tran Thi Nga, Nguyén Qnu\-s I:' i"

Nguyén Vu Nhan Parametric transformation and parametric resonance acoustic phonons and superlattices The 33th National Conferencc on (hcoreiica Physics, Da Nang, 08/2008

ofcciiíiiu^-í háofcciiíiiu^-í) cao a Hói nghi Vát ly Quóc Te:

1 Nguyén Quang Bau, Ha Dang íChoa, Nguyén Bich Ngoc and Ngi¡>'eri Dinii

i • ien Calculation of nonlinear absorption coefficient ofthe strong ei^:cu\vr;;u:iKii^ vvave by coníined electrotis in the composiíional superlattices Proceed.iig ^r cv iTlevenlh Vielnamese - Germán Seminar on Physics and fingineering, Nha íV,;i:^!

C ii}, from March, 31 to April, 5, 2008

4 k Các cóng irinh da hoán thánh gái dang Irén các tap chí khoa ho;

gúi dáng trong tap chí Han Quóc )

5 Kei quá dao tao: Góp phán dao tao 2 Tién sv , 5 Thac sy

j tan do tuoTig tac !

I elecíron-phonon trong

i dáy \uaniz tir bán dan

TS (bao vé 1 Chu nh;vni tháng I dé tai hu"ó'ri 6/2008) ! dánchính

i^^) Cae két quá dat dupc: 11 cóng trinh da cóng bó tren các íap chi khov^ hoc M^

hoi nghi khoa hoc:

Cae cong trinh da cóng bó tren các tap chí khoa hpc Quóc te: (2 bái)

: i^'^" ^"oMu Phc»ng Luong Van Tun,ü Nguyén Quang Bau.Pararncíiic Reseña.>:; v

v•:<>ti^r¡(• ,¡^1 Opiical Phonons in a Doped Semiconductor SunerlaUice.Ko^cai^ ¡-"r^y^u

'-'-i-í.v \'(>! 53 No4 (J^iob-r 2008 pp.i97M975

2 ¡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 các 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 1 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)

3 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 IAIOÍ^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

3 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)

3 Các háo cao khoa hoc lai các Hói nghi: (4 bao cao

3 bao cao kbo:i hoc ó Hói nghi khoa hoc Vát ly trong 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!

i bao cao o Hói nghi Vát ly Quóc Té:

1 Nguyén Quang Bau, Ha Dang ÍChoa, Nguyén Bich Ngoc and Ngi;\'c;i Difjit

1 • ¡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

4 Các cóng trlrih da hoán thánh gái dang tren các lap chí khoa ho:

gu'i dang trong lap chí Han Quóc )

i dáv luaniz tir bán dan

Cap cláo tao

-•i uo'n-^ Van Mót só

1-! tan trong , tna.ng

liéu bán

i'mg dan

cao siéu

TS (bao \ é tháng 12''2008)

/'inh Ivjoúii cua tír

•ruoPü ¡en hé so han thu piíi luyen sóng dien tú trong sicu mang pha tap

ThS {bao vé ' *' in 'V;'v ••: thánií ; de tai iii.c^i 12/2008) ' dancíunh

Bien dói tham só giira phonon ám giam cám

vá phonon quang giam cám trons siéu mang pha tap

ThS (bao vé Chu iihié.n tháng i dé tai huxÍDg 12/2008) ! dl.nchrir

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 trong siéu

I mang pha tap Bien dói tham só güja j>honon ám giam cám

vá phonon quang giam cám trong hó luong tú

ThS (bao vé ¡ Chu nhiem tháng 1 dé tai hiróü 12/2008) • dan chí.-h

ThS (bao vé ¡ Chu nliic;ivi tháno dé lái huon 12/2008) i danch'piT

ThS (bao vé ' Ch:i nhie^n tháns i dé tai h'L'.ón

i

2/2008)

.L

Ngoái ra, dé tai góp phán dao tao 5 Cu nhán Vát ly : Nguyén Hoa; \:.'\,

an Nuuvén lhi Nizoc Ha Nieó lhi Thanh Ha N^iuvéa lhi Thaüh H-^

n i íní) hinh kinh phi cúa dé tai:

1 vij])d V a n

¡ ' j - i

Mót só hiéu úng cao tan troné bán dan siéu nang,

TS (bao v tháng 12/2008)

I thu phi luyen sóng

i dién tú trong SICU

ThS(bao \i

thánií 12/2008)

de tai iu.' dan chür' mang pha íap

LNauvéi)

^^ an Níjuia

Bien dói tham só giúa phonon ám giam cám

vá phonon quang giam

! cám tronü siéu mang

I aiúa phonon ám giam

; cam va phonon quang

I giam cárn trong hó

ThS (bao vé i Chu nh¡en"i

dé tai hu'ó tháne

i giam cám trong siéu

¡ mang pha tap

; Bien dói tham só giúa

i< I

tháng 12/2008)

dé tai huong ; dan ch^r'h

•l'ián Tin N^a • i vlionon am s.iam cam

I vá phonon quang giam

i cám troné hó luone íú

; ThS (bao vé ' Chu nhioni

; tháng i dé tai hiión

i 12/2008) I danchír,!)

Ngoái ra, dé tai góp phán dao tao 5 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

2 hj! bao va 2 bao cao khoa hpc (4 cóng trinh nghién cúu trony ^o i I -IL •:::.:

TRCONC OAI HOC KHOA HOC Til NHIEN

MIEU T R U O N G

pes JS.^üi lili uOs'/n

J

VÍETNAM NATIONAL UNIVERSÍ^'V C{ji LEGE OF NATURAL SCIE'V^:í:.>,

HA NOI - 2008 DAI HOC QUÓC GIA HA NÓÍ

1 RLÓNG DAI HOC KHOA HOC TI NHÍLN

:íí 5i> Í:< ; K ?•-• -ií ^ ^ ;ií

PROFECT:

INVESTIGATION OF THE INFLUENCE OF STRONí ELECTROMAGNETIC WAVE ON THE TRANSÍ OR I PROPERTIES 0FSEMIC0NDUC70R LOW DíMENSIONAi

SYSTEMS CODE: QT - 08 - 15

DIRECTOR OF PROJECT: PROF.DR NííL'YÉN Ql AN« í UÁl PARTICIPANTE:

Ür Nguyén Vü Nli;\n Dr Trán Cóng Phong, Dr Dinh Quóc Vuong M- Luon^^ Vá;! ILÍP.L

Ms Lé Dinh Ms Hoáng Dinh Trien Ms Trán Thi Hái NCS vTs Le Thái Hunp Ms,' {)• Manii !-ii¡n;:, and Bachelors: Nguyén Bích Ngoc, Nguyén Thi Mai Nhién Trán Tiii NV.Í

^suyén Ván Thuán, Nguyén Ván Nghía, Nguyén Thu Huang

NGHIÉN CÚU ANH HUÍONG CÜA SÓNG DIÉN TU M \NH LÉN MÓT s ó TÍNH CHAT DÓNGTRON(; BÁN DAN

THAP CHIÉU

Má só: QT - 0 8 - 15

HA NÓI-2008

Report on the situation and the results of the project

a) Titleof t h e P r o j e c t :

IN V KSTK;ATION OF THE INFLUENCE OF STRONG ELECTRON! \ < ; N E T Í ( ^^ V \ l »^^

1 llE TRANSPORT FROPERTIES OF SEMICONDUCTOR LOW OIMKNSÍONAL

SYSTEMS Cốc:

^.>T' - 08 - i ^

h) í)irtc!oí oí project:

Fror.l~).- Nguyén Quang Báụ

FChoa Val lỵDai hoc K W I hoc Ttr nhién ( DHQGHN )

Dia chi: ^34 Nguyén Tráị Thanh Xuán Ha Noị

Só dién lhoai:í04)7626547

c) Parlicípanlii:

iJị Ny,u>én Vü Nhán, Dr Trán Cóng Phon^\ ür Dinh Quóc Vuong Ms Laon^' Vj^; íuiv::

>N LcOiiih, Ms Hoáng Dinh TriliKMs Trán Thi Háị NCS vis LéliuM H-^.2 N!^ Ọ 'í.iníi Hur.s and Bachelors: Nguyén Bích Ngoc, Nguyén Thi Mai Nhién Ti/

!v;:!ij\cii Ván Tluián Nguyén Ván Nghiạ Nguyén Thu Hirong

di Aini and content of researches:

- Sradying the Absorption Coefficent of a strong eleclromagnêic ^

cicclions in semiconductor \o\\ dimensional syslems

- Siudying tlie Parametric transformation coefficient of conlnL

contincd optical phonon in semiconductor low dimensional systenr•^

- Siudying the Parametric resonace of confined Acoustic and confín

iT: Quantum vires

T'i i ; ^ N

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W ; L1V, J t P

•^»'KJV'!J-I¿I tíjc U,^{^ of Phonon hxciíatinn and Cnndiüons in: :1v

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:•-•.'• uíici ị;:' /[:, )!i '^i!ý.i^-¿i! !:iU:rn:'li -^nal and Natioñii :;';n' ic^.:::

'.';V.)n C:.ní: Phong Luon? Van Tung Nguyén Quang BauPai-anietric Resop.ancc oí Á oụ-;íụ and Oplical Phonons in a Ị>o¡x^d Semiconductor Siiperiatíicc.Korean Píiv-ícs

:v)c;-lỵ Vof 5''K N O 4 , Ocli^ber 2008 p p i 9 7 M 9 7 5

2 i^'giij'c'n Oịiii:íg Bau, Kguyen Bich Ngoc, and Do Mí'/ih 'iiu^'j 1 he nc:Jí;íc:^r

r*i/:"ir;''-';in cocnicíTti :^f a ^nong electroniagnetic \va\:; b^' • on':Pcd elecí^'t:-/- ¡M íí' qiviniíü^i v/oils Joiirnr;! o f t h e Koiean Physical S^'Citi) íu h ;-ị''l?^'ied i 2{)('->

^ J utvr- s»í I!K Nă¿03ial Journals: (5 papcrs)

:, ,^}g'!\'en Tí'i Mai Nliicn Do Manh Hung Nguven í)Lian'^: \'''dh ' i h o j)níairK:í'ị

•\ <•!' ;'>.c oí coíínicd ậ()usti>: phonons and cc»n+!'icd opíic^^i ;^!:in¡ị;n': ÜI ii!:'r;iÜVÍ

\' iis \ ' N U -JoM-i^a! of Sciencẹ N4athejTiaíics l^hys¡'js, X o l M Nọ¡S.pp.2Mí

2 iyguyen \'ar! Tihu-Hi, Do Manh Hung Nguven O u a n g I^au, 'ÍÍVJ i n ü u c n c e oí

!iia; iK^iiL licki '.Mi ííic iionlinear absorption coefficiení ol :i SỊTMI;: e!v:;:ú.>ínav[;') [í.:

V u\': b; conHucd elecírons in the doping superlattices Xí^íC - JOU*M:'! of SLU::"-:'::

-' 'JO rA\[\ú\ H;!!ig, N g a } e n Q u a n g Baụ H o a n g Dinli Trié:, '^nd '\>;iut^íi íi^

'^' ":(:•';;vị:iu;dc \vp'.^e ^v; coeíined electrons in roe coP1p^.^iii^^:^r spper:atii:;e:;

juiiniai oíScivJipc Matliematics-Ph)'sic¿ \ ' o f 2 4.NọlS.cr).2'-;i-2'^^':200Ñ;

|-¡;eh Liioiig Van i lüig Hoat'ig Dinh Trien Ngü}'?nk)pang Baụ A isiiribc

,- ,|(:;;i-;ry rjjp^r? -.«p ^emicôd'Jc^or Spppriauicp^-, \':<.'' -íôí": í ^P Scị^r-p

';=i-í iị.::tH::-PÍPp.:: v i 2 1 ! A :

íS„pp.22c-22U.:p'2.::-) t

' ' t

2% Ri poris in Physicíii conferencc: Í4 reports)

3 reports in Ihe National Physical conference:

! Ngnven Van Hieu., Le Thi Thu Phuong, Do Manh Hung Ng^ivcn i

Nhan Nguyén Quang Bau The 33th National Conference o\-\ Theopr.ioa

f)a Nang, 08/2008

2 Hoang Dinh Trien Nguyén Quang Bau and Do Manh Hung CalcjíPti'.ps ^ "i '.'PP nonlinear absorption coefficient of a strong electromagnetic ^'VP've b\ coprpc-.: electrons in reciangular quantum wires with infinite pótenla! The 33':!! Nali^piaí Conference on Iheoretical Physics, Da Nang, 08/2008

3 Nguven Van Nghia, Nguyén Van Thuan, Tran Thi Nga Nguyén Quang Bap Nguyén Vu Nhan Parametric transformation and parametric resonance of con lineo acoustic phonons and superlattices The 33th National Conference on Theorelical IMnsics, Da Nanu, 08/2008

1 reports in the Internationa! Physical conference:

1 Nguyén Quang Bau, Ha Dang Khoa, Nguyén Bich Ngoc and Ngp>éP. DPVP Trien Calculation of nonlinear absorption coefficient ofthe strong clcctri;iMappe[¡« vvave by confíned electrons in the composiíional superlattices Proccecing of the tieventh Vietnamese - Germán Seminar on Physics and Fn?ineerin9 Nna 1 ;papp City, from March 31, to April, 5, 2008

4 Papers (to ho published): (] paper JKPS )

5 Resulís of edncation: 5 Bachelors, 5 Masters, 2 Docíors

- 5 Bachelors: Nguyén Hoai Anh Mai thi Lan Nguyén thi Ngoc Ha

NP-HíP Nguyén thi Thanh Ha

-5 ¡Masters 2 Doctors:

rán do tuong tac

cleclron-pl'ionon trong dáy luong tu bán dan Mót só hiéu úng cao tan trong bán dan siéu

T S ( b a o vé tháng

Bien dói tham só giúa phonon ám giam cám

vá phonon quang giam cá!n trong siéu mang pha tap

TS (bao ve tháng

ThS (bao ve tháng

12/2008) u'O'ng tu

Cóng íiU'óng tham só giúa phónn ám giam

I vá phonon quang giam

! can) trong hó luOTg tú

ThS (bao vé tháng

12/2008)

ThS (bao vé tháng

! r-i

MPi

; dé tai huá!;u dan CíPoh

Chu nípcn'^

dó íái faivVi dánchpih

• CíiU nh'vi'P

I dé íái huár

i dan chính

PHAN CHINH BAO CAO:

M n c h i

-1 ' í] iP.o d u

2 : ipt duPig nglncn cúu chúih cua dé lái

•' i'pu'pne phán mihiép cúu kv Ihuál sú duns

•i ' ac kcl i\U'd dat duoc

3 Kei luán

w Tai liéu ihappi kháo

L íM íwj dáu

lófig quan tinh hinh nghién cúu vá luán giai sn can ihi.T phat UÍÍÍP.'P, LU de ÍLU

Tinh hinh nghién cúu ngoái nuóc {phán lich dáíih LLÍ)

- Nhóm nghién cúu cüa các nhá khoa hoc ]s<i:.\ íShik A.Y SÍPi!.;í':\ ( L \ P

!{|>síein E.M., Romant)v lu.A ), các nhá khoa hoc Dúc fl'iooí.' K LHMP r (i.íí >, -.;•- nn::i khoa hoc Pháp, y, l'>lhál Trung Quóc M\' (Mann j C Cfi.tpp i.» i^siúví L

1 sp R ) da nghién cúu thánh cóng mol so tính chát val ly ciuan íioi;u < P;Í Í"PP Ur iháp

-i¡u;t.! iiéíi quan den các ván dé chính sau :

¡ Can irúc tinh ihé dóng luc hoc man*í^

1 Ti'nh chíít dién tú

-'r TínU chai quang, tính chai ám

•i- Các hieu úng phi tuyén vá luong tú

-i- úng dung irong ky ihuát vá cóng nghe val liéu mói

Tinh hinh nghién cúu trong nuóc (phán lích, dánh giáj

- Các can bó nghién cúu cúa Trung lám Vái ly Ly thuNcP VÍPP. \ al Iv íHá NOÍ ; 'A.íS.TSKH Nguyén ái Viet va các cóng su), các can bó nghicn cúu cu;i i han vicn Vái

Iv l^hánh phó Hó Chí Minh, (GS.TSKH Trán Thoai Duy P>áo vá cJ^c c')|'Í. ' PÍ- C^IP i^Á}^

hó jphién cúu giáng day cua Bó món Vat ly ly thuyél Truong Oai ¡PP; Khna h<)P VP

pippn (F)ai hoc Quoc gia Ha Nói) (GS.TS Nguyén Quang Báu -pi ca^: c-pp: su» da tinív

!ppp pp kéi (.mi cá^- hoai dong nghién cúu khoa hoc vh dao íao dc;^' á\Hv: ohun¡i hiéu

ÍPCÍ: ^ ái! :,ác ó iíliih dó Quóc ce Irén các huúug cínnh hiú qu.tn -JéP =:)•: PP n^hicn aai

;ppi d a y

-;- Ly Ihuyét Fxciton trong chám luong íú

-^ Do lái chuán hoá khe dái írong dáy - giéng krong tú

p- f.y thu} el \c các hiéu úng dóng vé các tính chát quang - c-m - iipr; ur CU;Í các

P • •.iip'i iu ciiipui hai chicu inót chiéu

! MPí ¡"ppb nghién cúu cúa chu nhiém dé iái irong lính vire náy va PÍIÍJU;:: van do mó¡ diu

•.: p;?ni^ n cuu

:\I.Í;P^ lujiien cuu cua chu nhiém dé tai da páy dung 'y d\u\ét ¡'P/PP -P ^.'"

- Do dan cao (fin

- Mé Svó háp thu sópig dién tú

- C'oíTg huáng IhaiTi só bícíi dói íhaní só elíp' nh'iúcn P:P :.' niv,;)M,i i.|M;np'

irong siéu mang hó luang tú, dáy luong tú nhirng chtra xéi dáy du các \ PU m anh

huang nhu giam cám cúa phonon, tú trirang, các dang thé vá các co che lán \a LPÍ ca hiéu ú'ng ké tren

Luán cú lính cap thícl, y nghia tám quan trong cúa dé tai doi xói kh.^a ín^c v •

kha náng úng dung két quá nghién cúu váo sir hinh thánh, phát trien ngánh khoa hoc

\ a váo ihuc tién

De tai nghién cffu nám trong huóng nghién cúu các tính ciial \ di i\ cu:i ^ \i<- íp bán dan tháp chiéu vá các he có cáu truc nano, la huóng nghién cúu óaiv¿ dj-.p I'IPP

trien rát manh me hién nay trong nuóc vá Quóc té do khá náng úng duipi: ui ioi : i:)

loai v¿)i liéu có lính náng dac biét náy trong cóng nghiep dién tu tin lioc thé b^.^ PP); (siéu nhó vá da náng) Viec trien khai Dé tai tao diéu kien cho các nhá khoa hoc \ ; ;i Nam hiéu sáu sác han các lính chát vat ly cüa các he bán dan tháp chiéu vá cae be cp -

cáu truc nano, tao diéu kien dé ho có thé' truc tiép tham gia giái quyét nhúng ván ác khoa hpc vá cóng nghe có tính thói su cao má thé gioi dang quan tám dap úng mvc

tiéu tiép can trinh dó nghién ciru khoa hoc vá cóng nghe cao cúa Ihé giói, chuan bi khá náng hgp lác ky thuat vá dáu tu nuóc ngoái

el)*-Các nghién cúu mói thuóc Dé tai góp phán hoán thien các phuong pháp hicn dai

nghién cúu vát ly ly ihuyét các mói trudng dam dác Tính chát, phuong pháp \iuu\ \a

su pham cao cüa các nghién cúu mói thuoc Dé tai cüng góp phán quan trong váo su nghiep dáo tao Dai hoc, Sau dai hoc va xáy du'ng dói ngú các nhá khoa hoc cong nghe tién lien cho dál nuóc

2 Nói dung nghién cúfu chính cüa dé tai:

- Nghién cúu háp thu phi tuyén sóng dién tú hói dien tú giam cám trong bán dan iháp chiéu vó'i các dang thé giam cám khác nhau ( có ké den sir giam cám cua plioi^on p Í.Í)

ké den ánh huóng cúa tú truang

- Nghién ciru bien dói tham só giúa phonon ám giam cám vá phonon quang giam can^ tiong bán dan tháp chiéu vói các dang thé giam cám khác nhau

- Nghién cúu cóng huóng tham só giúa phonon ám giam cám vá phonon quang gíaui cám trong bán dan tháp chiéu vói các dang thé giam cám khác nhau

Tính chát, phirang pháp luán vá su pham cao cüa các két quá nghién cúu rní7] iliuóc

Dé tai cüng góp phán quan trong váo sir nghiep dáo tao Dai hoc Sau dai ínyz \ii ay

dung dói ngü các nhá khoa hoc cóng nghe tién tién cho dál nuóc

3 Phua^ng pháp nghién cúu, ky thuat súrdung:

- Phuang pháp Kubo-Mori cho Tenxa dó dan cao tan vá Kubo - Morí nio von^

cíio truang hap ngoái sóng dien tú yéu có thém truang Láser va tú truóng

- Phirang pháp phirang trinh dong luong tú, phuang truih chuyén dóng t bw ppj irán mal dó vá các dai só toan tú can Ihiél

Dáy lá các phtrong pháp vúa hién dai vúa duae sú dung róng rái tron<? v.:^^ Iv p irp;v._M nay ap dung cho các hé bán dan tháp chiéu

4 (Vic kct quá dat diruc: Các két quá dat diíoc: 11 cónj? trinh da ró SLÍ » > í ' n

các lap chi khoa hoc va hói nghi khoa hoc trong nuóc vá Quóc íe:

j Các cóng trinh da cóng bo Irén các tap chí khoa hoc Quóc le; í2 f'.ní)

L'íían Cong Phi^ng Luong Van Tung, Nguyén Quang BaụPararneínc Rộ>n rP-: P Acoustic and Optical Phonons in a Doped Semiconductor SupeiiüUiLC.Korc.:rí Í'P\MV Socíclv Vo! 53 No4 Oclober 2008 pp.1971-1975

2 Nguven (^)uang Bau, Nguyén Bich Ngoc, and Do Man.h MPÍPÍ' 'AL ip:pp:ír:'; absoiption coefficient of a strong electromagnetic wave by confíned elccrí ns P the quantinn wells Journal ofthe Korean Physical Societ}' (to be published p 2009

2, Các cóng trinh da cóng bó tren các tap chí khoa hpc Quóc gia: (5 bái)

ị Nguyén Lhi Mai Nhien Do Manh Hung, Nguyén Quang Baụ Ihe pprp¡)icp>p, resonance of confíned acoustic phonons and confíned óptica! phonons ịn quppTip-p v/elis VNU -.loumal of Science, Mathematics-Physics, Vol.24.Nọ 1 S.np 240- 243(2008)

2 Nguven Van Thuan, Do Manh Hung, Nguyén Quang Baụ fhc injíuepce oí magnetic fíeld on the nonlinear absorption coeffícient of a sírong e¡ectj':'rnpp::pii • wave by confíned electrons in the doping superlattices VNTJ -Jounial ol^ Scienct- Mathematics-Physics, Vol.24,NọlS.pp.232-235(2008)

3 Hoang Dinh Trien, Nguyén Quang Bau, Nguyén Thi Thanh Nhapu hfiụ^n.P: ^ú magnetic fíeld on the nonlinear absorption coefficient of a sírong e!eci»-ornagní.r;.:

Vvave by confíned electronis in cylindrical quantum v.ires VNL - iounpii of

Science, Mathematics-Physics, Vol.24,Nọ 1 S,pp.47-50(2008)

4 Do Manh Hung, Nguyén Quang Bau, Hoang Dinh Trien, and Nipuyen Tir Thanh Nhan Caculation of the nonlinear absorption coeffcient of a slronu electromagnetic vvave by coefíned electrons in the compositional suoeríanices VNL' -Journal of Science, Mathematics-Physics, Voị24,NọlS,pp.236-2"-^9:200p:

3 Luong Van Tung Hoang Dinh Trien, NguyenQuang Baụ /\ nui^iber M'p:: tcequency Efíécts on Semiconductor Superlattices VNlí -Journoi <A S :ÍP Mathematics-Physics, Vol.24,Nọ 1 S,pp.228-231 (2008.)

3 C ác bao cao khoa hoc tai các Hoi nghi: (4 bao cao

- 3 bao cao khoa hpc a Hói nghi khoa hoc Vát ly trong mróc:

1 Nguyén Van Hieu, Le Thi Thu Phuong, Do Manh Hung Ngu>eri fhi Tlvap^ Nhan, Nguyén Quaní^ Bau The 33th National Conference on íhcoreticpi PPVPP:

Da Nang, 08/2008

2 Hoang Dinh Trien, Nguyén Quang Bau and Do Manh Hung Ca'icuia0ípi> (p Í'PP nonlinear absorption coeffícient of a strong electromagnetic wave b\ coníined electrons in rectangular quantum wires with infínite potental The 33th NaiiOípp Conference on Theoretical Physics, Da Nang, 08/2008

3 Nguyén Van Nghia, Nguyén Van Thuan, Tran Thi Nga, Ngu\en Qimvj Bap

Nguven Vu Nhan Parametric transformation and parametric resonance OÍ r.pmipkd

acoustic phonons and superlattices The 33th National Conference on Theorepcr-i

Physics, Da Nang, 08/2008

- 1 bao cao a Hoi nghi Vát ly Quóc Té:

J Nguyén Quang Bau, Ha Dang Khoa, Nguyén Bich Ngoc and Nguven fJinh Trien Calculation of nonlinear absorption coeffícient ofthe strong eleclromagneOc v/ave by confíned electrons in the compositional superlattices Proceeding c»! IÍP: Eleventh Vietnamese - Germán Seminar on Physics and Engineering, Nlía i rang City, from March 31, to April, 5, 2008

4 Các cóng trinh da hoán thánh gufi dang tren các tap chí khoa hoc: í! ha gúi dang trong tap chí Han Quóc )

5 Két quá dáo tao: Góp phán dáo tao 2 Tién sv , 5 Thac s\

I dáy luong tu bán dan : 2.Lirang Ván

mang pha tap

ThS (bao vé tháng

12/2008)

ThS (bao vé tháng

12/2008)

Cóng huong tham so giúa phonon ám giam cám vá phonon quang giam cám trong hó

ThS (bao vé tháng

12/2008) luong tú

Cóng huóng tham só giúa phónn ám giam cám vá phonon quang giam cám trong siéu mang pha tap

ThS (bao vt:

tháng 12/2008)

- Ngoái ra, dé tai góp phán dáo tao 5 Cú nhán Vát ly : Nguyén Hoai Ai

Lan, Nguyén thi Ngoc Ha, Ngó lhi Thanh Ha, Nguyén íhi Thanh Há

V 1 ir

6 Két luán:

cu; !

I 11 C ^- i ; '

i c r

Các két quá thu duac có khá náng úng dung trong cóng ngh¿ san \pa

vát liéu mai có tính náng dác biét Dira tren ca só các hé bán dan thá|) ciucu L(

tao các ioai linh kién dién tú thé hé mói trang thiél bi dién lú cón^ nghe nn hoc,

thóng hién dai siéu nhó vá da náng

Viéc trien khai Dé tai tao diéu kien cho cá nhán vá tap thé khoa IÍ.'C ppp Í

-r-sac han các tính chát vat ly cüa các he bán dan tháp chiéu vá các hé có can \iú: n;pp\

tao diéu kién dé ho có thé trirc tiép tham gia giái quyét nhúng ván dé khoa hoc \ a c* íp; nghe có tính thai su cao má thé giói dang quan tám, dáp úng muc tiéu tiéj> can trinh do nghién cúu khoa hoc vá cóng nghe cao cüa thé giái, chuán bi cho khá náng hop tac k^ thuát vá dáu tu mróc ngoái

Két quá nghién cúii cüa dé tai:

I 1 cóng trinh da cóng bó tren các tap chí khoa hoc vá hói nghi khoa hoc trong dó: Hai cong trinh da cóng bó tren các tap chí khoa hoc Quóc té

- Nám cóng trinh da cóng bó tren các tap chí khoa hoc Quóc gia

Bón bao cao khoa hoc tai các Hói nghi, trong dó:

+ 3 bao cao khoa hpc ó Hói nghi khoa hoc Val ly trong nuóc:

+ i bao cao ó Hói nghi Val ly Quóc Té:

- Mót cóng trinh dá hoán thánh gúi dáng tren các tap chí khoa hoc cúa Han Quoc

- Két quá nghién cúu cüa dé tai góp phán dáo tao: 5 Cú nhán 5 Thac sy 2 Tien sv

7 Tai lien tham kháo

1 A.Y Shik ''Quantum wells - Physics on Electronics (>f lUi''Dn}:c!¡sio:iul

Sysrcms^\ World Scientifíc Publishing, 1997

2 M.J Kelly " L m v - Dimensional Semiconductor'' Ciarendon Press.! 99.5

3 Woggon U ^'Optical Properties of Semiconductor Oua/innn /)/-*s"2

Springlcr- Verlag 1997

4 Ng:uven Ouan!¿ Bau Tran Cong Phong

'^Calculations of the Absorption Coeffícient of of a Weak ElectrornagneOc V/a-^ b\ irce Carriers m Quantum Wells by the Kubo-Mori Method'*

Journal ofthe Physical Society of Japan, VoL67, NI 1(1998)3875-3880

-'V Nguven Quang Bau Nguyén Vu Nhan.Tran Cong Phong

"The Absorption of a weak Electromagnetic wave by free electrons in quinnup' vr!i>

in the presence of quantum magnetic field"

Journal of Communications in Physics, v8, K ' l , (1998)1-6

6 Nguven Quang Bau, Chhoumm Navy, Shmelev G.M

^'Influence of Láser Radiation on the Absorption of a vvcak EVÍV/ b^ bcp J Í P L P U P P

Semiconduclors Superlattices"

Optics for Science and New Technology ( Taejon, Korea-Augusí 1996 ) Piocecéings

n.814 The 17'^ Congrcss ofthe International Commission for Optics

7 Nguven Ouang Bau, Nguven Vu Nhan, Tran Cong Phong

"'Calculations of the absorption coefficienl of a weak eleciromagnenc •\:P j '.v

:'\.-carriers in doped superlattices by using the Kubo - Morí method" Journpi o\ I\K

Korean Physical Society, Vol 4L No I, July 2002 ppT49 - 1.^4

8 Tran Cong Phong, Nguven Ouang Bau

"Parametric Resonance or Acoustic and Optical Phonons in a Quantum \Ve!r\ Journal

of the Korean Physical VoL42, No.3, May 2003, pp 647 - 65 L

9 Nguyén ái Viet

"Ly thuyét các hé tháp chiéu vá các he có cáu truc Nano"

Hói tháo Khoa hoc vá Cóng nghé Nano, Há Nói, (2003) tr 198

10 Tran Thoai D.B., Cao H.T., Subband renormalizaiion of highl> photoexcited quantum-well wires, Solid State Commum V.l 11 (1999) p.67

PHIÉU DÁNG KY KÉT QUÁ NGHIÉN CÚtJ KH-CN

Ion dé tai (hoác duán): ?

Nghién cúu ánh huóng cüa sóng dién tir manh lén mót só tínli chát dóng ti <>ng Uán í

dan tháp chiéu y

GS.TS Nguyén Quang Báu

Í V l á s ó : Q T - 0 8 - 15

Co quan chú tri de tai (hoác dir án):

Khoa Vat ly,Dai hoc Khoa hoc Tu nhién ( DHQGHN )

Dja chí: 334 Nguyén Trái, Thanh Xuan, Há Noi

Tel: (04)7626547

H

Co quan quán ly dé tai (hoác dir án);

fj)ai hoc Quóc gia Llá Noi

Dia chi:

Tel:

Tóng kinh phi thirc chi: 20 triéu

Thoi gian nghién cúu: 12 tháng

I hói gian bát dáu: 1/2008

Thoi ííian két thúc: 12/2008

TS Nguyén Vu Nhán, TS Trán Cóng Phong, TS Dinh Quóc Vuang, Ths - NCS Lu.í>n*: Van j

Tung, Ths f,é Dinh.Ths-NCS Hoáng Dinh Trien ,Ths-NCS Trán fhi Hái, NCS.Lé Th;ú Hing

NCS Nguyén Bích Ngoc,NCS Dó Manh Hüng,Cú nhán Nguyén Thi Mai Nhién, Cu nlvpo Jrin I

Thi Nga.Cu nhán Nguyén Ván Thuan, Cú nhán Nguyén Ván Nghia, Cú nhán Nguycii Thu

fíüou!.: \

Só dáng ky dé tai

Nip

So chúng nhán dáng ky két quá nghién cúu:

Bao mal: Phó bien roña rá¡

»4>

-1

s

• - » t - (

1 óm lát két quá nghién cúu:

- Nghién cüii háp thii phi tuyén sóng dien tú bái dién tú giam cám troné bín dan ihip

chiéu vai các dang thé giam cám khác nhau ( có ké den su gpim cám avd phoípp; K :r

ke den ánh hiróne cúa tú truang

' Nghién cúu bien dói tham só giúa phonon am giam cám vá phonon quang eia p

trong bán dan tháp chiéu vói các dang thé giam cám khác nhau

- Nghicn cúu cong huóng tham só giúa phonon ám giam cám vá phonoíi i uanp ::

cám trong bán dan tháp chiéu vói các dang thé giam cám khác nhau

í

Các kéi quá nghién cúu cüa dé tai :l 1 cóng trinh dá cóng bó tren các tap clu kippi h e |

vá hói nghi khoa hoc, trong dó:

- Hai cóng trinh dá cóng bó tren các tap chí khoa hoc Quóc lé

- Nám cóng trinh dá cóng bó tren các tap chí khoa hoc Quóc gia

- Bón bao cao khoa hoc tai các Hói nghi, trong dó:

+ 3 bao cao khoa hoc ó Hoi nghi khoa hoc Val I y trong mróc:

+ 1 bao cao ó Hoi nghi Vát ly Quoc Té:

- Mót cóng trinh dá hoán thánh gúi dáng tren các tap chí khoa hoc cúa Han Quóc

- Két quá nghién cúu cúa dé tai góp phán dáo tao: 5 Cú nhan 5 7 hac sy 2 Tin\ sv

Kién nghj vé quy mó vá dói tirong áp dung nghién cúu:

Sú dung trong nghién cúu khoa hoc vá dáo tao

Giáo s!.r, Tién sy

Thu truómgcaquan chú tri dé tai

Chú tich Hói dóng dánh giá chính thúc

Thu íruonii co '.jisiin quan Iv dé Í;ÍÍ

— — LLJ GIAM O Ó C

ífí ; 7 - ; c F < ^ ' ^ ' Í ^ ^

t'G5J$M7¿3uy^'^am

ournal of the Korean Physical Society, Yol 53, No 4, October 2008 pp 1971-'1975

Parametric Resonance of Acoustic and Optical Phonons

¡n a Doped Semiconductor Superiattice

TVan Cong PHONG*

Department of Physics, CoUege of Education, Hue University, 32 Le Loi, Hue, Vietnam

Luong Van T U N G

Department of Physics, Dong Thap University of Education,

783 Pham Huu Lau, Cao Lanh, Dong Thap, Vietnam

Nguyén Q u a n g B A U

Department of Physics, Hanoi National University, 334-Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

(Received 23 January 2008, in final form 3 September 2008)

The parametric resonance of acoustic and optical phonons in a doped superiattice with a degenerative electrón gas in the presence of a láser field is theoretically predicted by using a set

non-of quantum transport equations for the phonons Dispersions non-of the resonant phonon frequency and the threshold amplitude of the field for parametric amplification of the acoustic phonons are obtained The amplitude is also estimated for realistic semiconductor models

PACS numbers: 63.20.Kr, 63.20.+m, 68.65.Cd, 73.63.Hs, 78.67.Pt Keywords: Pau"ametric resonance, Acoustic phonon, Optical phonon, Doped semiconductor superiattice

I I N T R O D U C T I O N

In t h e presence of a n external electromagnetic field

( E E F ) , a n electrón gas is well known to become

non-s t a t i o n a r y W h e n t h e conditionnon-s of t h e p a r a m e t r i c

resonance ( P R ) a r e satisfied, p a r a m e t r i c interactions

a n d t r a n s f o r m a t i o n s ( P I T ) of t h e s a m e kind of

excita-tions, such as p h o n o n - p h o n o n a n d plasmon-plasmon

ex-citations, or of diíTerent kinds of exex-citations, such as

p l a s m o n - p h o n o n excitations, will arise; i.e., energy

ex-change processes between these excitations will occur [1]

T h e P I T of acoustic a n d optical p h o n o n s have been

con-sidered in bulk s e m i c o n d u c t o r s a n d in q u a n t u m wells [2,

3] T h e physical p i c t u r e can b e described as follows:

Due t o t h e e l e c t r o n - p h o n o n interaction, p r o p a g a t i o n of

a n acoustic p h o n o n w i t h a frequency a;^ is accompanied

by a density wave w i t h t h e same frequency W h e n a n

E E F w i t h a frequency Q is presented, a charge density

waves ( C D W ) w i t h a c o m b i n a t i o n frequency ujg ± iü

(i = 1,2,3 ) will a p p e a r If a m o n g t h e C D W t h e r e

exists a c e r t a i n wave having a frequency t h a t coincides,

or a p p r o x i m a t e l y coincides, with t h e frequency of t h e

optical p h o n o n , u^, optical p h o n o n s will a p p e a r T h e s e

optical p h o n o n s cause a C D W w i t h a combination

fre-quency of i / ^ i ^ n a n d when i/q±ifl = a;^-, a certain C D W

"E-mail: congphong2000@yahoo.com; Fax: +84-54-825824

causes the acoustic phonons mentioned above T h e sult of t h e s t u d y shows t h a t t h e P I T can speed u p t h e

re-d a m p i n g process for one excitation anre-d t h e amplification process for a n o t h e r excitation; namely, acoustic p h o n o n s are amplified while optical phonon are decreased or vice versa For low-dimensional semiconductors, t h e r e have been several works on t h e generation a n d amplification

of acoustic phonons [4] However, in our opinión, t h e ergy exchange processes between two different kinds of phonons in d o p e d superlattices, which are driven by a

en-P R of a two-phonon kind, have not yet been r e p o r t e d It should be n o t e d t h a t t h e mechanism for P I T is diíTerent from t h a t for phonon amplification u n d e r a láser field [5]

a n d from t h e P R of a defect m o d e [6]

In Ref 3, we studied t h e P I T in a q u a n t u m well w i t h non-degenerative electrón gases In order to continué

t h e ideas of Refs 2 a n d 3, t h e p u r p o s e of this p a p e r is

to also s t u d y t h e p a r a m e t r i c resonance of acoustic a n d optical p h o n o n s , b u t in a d o p e d semiconductor super- iattice (DSSL) T h e electrón gas is assumed to b e non- degenerate Because t h e analytic calculation process in

t h e present p a p e r is similax t h a t in Ref 3 a n d because

t h e main differences are expressions of form factor and

t h e energy s p e c t r u m of electrón in t h e models, only a brief description of t h e calculation will be given in this

p a p e r In Sec II, we introduce t h e dispersión tion o b t a i n e d from t h e q u a n t u m t r a n s p o r t e q u a t i o n s for 1971-

equa-foumal of the Korean Physical Society, Vol 53, No 4, October 2008, pp 1971~1975

Parametric Resonance of Acoustic and Optical Phonons

in a Doped Semiconductor Superiattice

Tran Cong P H O N G *

Department of Physics, College of Education, Hue University, 32 Le Loi, Hue, Vietnam

Luong Van TUNG

Department of Physics, Dong Thap University of Education,

783 Pham Huu Lau, Cao Lanh, Dong Thap, Vietnam

Nguyén Quang B A U

Department of Physics, Hanoi National University, 334-Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

(Received 23 January 2008, in final form 3 September 2008)

The parametric resonance of acoustic and optical phonons in a doped superiattice with a degenerative electrón gas in the presence of a láser field is theoretically predicted by using a set

non-of quantum transport equations for the phonons Dispersions non-of the resonant phonon frequency and the threshold amplitude of the field for parametric amplification of the acoustic phonons are obtained The amplitude is also estimated fot realistic semiconductor models

PACS numbers: 63.20.Kr, 63.20.+m, 68.65.Cd, 73.63.Hs, 78.67.Pt Keywords: Parametric resonance, Acoustic phonon, Optical phonon, Doped semiconductor superiattice

I, I N T R O D U C T I O N

In the presence of an external electromagnetic field

(EEF), an electrón gas is well known to become

non-stationary When the conditions of the parametric

resonance (PR) are satisfied, parametric interactions

and transformations (PIT) of the same kind of

excita-tions, such as phonon-phonon and plasmon-plasmon

ex-citations, or of different kinds of exex-citations, such as

plasmon-phonon excitations, will arise; i.e., energy

ex-change processes between these excitations will occur [1]

The P I T of acoustic and optical phonons have been

con-sidered in bulk semiconductors and in quantum wells [2,

3j The physical picture can be described as follows:

Due to the electron-phonon interaction, propagation of

an acoustic phonon with a frequency uj^ is accompanied

by a density wave with the same frequency When an

EEF with a frequency Q is presented, a charge density

waves (CDW) with a combination frequency ujg ± iQ

{i = 1,2,3 ) will appear If among the CDW there

exists a certain wave having a frequency that coincides,

or approximately coincides, with the frequency of the

optical phonon, u^, optical phonons will appear These

optical phonons cause a CDW with a combination

fre-quency of í/g-±^n and when ¡/q±iQ = u;,-, a certain CDW

E-mail: congphong2000@yahoo.com; Fax: +84-54-825824

causes the acoustic phonons mentioned above The sult of the study shows that the PIT can speed up the damping process for one excitation and the amplification process for another excitation; namely, acoustic phonons are amplified while optical phonon are decreased or vice versa For low-dimensional semiconductors, there have been several works on the generation and amplification

re-of acoustic phonons [4] However, in our opinión, the ergy exchange processes between two different kinds of phonons in doped superlattices, which are driven by a

en-P R of a two-phonon kind, have not yet been reported It should be noted that the mechanism for PIT is different from that for phonon amplification under a láser field [5] and from the P R of a defect mode [6]

In Ref 3, we studied the PIT in a quantum well with non-degenerative electrón gases In order to continué the ideas of Refs 2 and 3, the purpose of this paper is

to also study the parametric resonance of acoustic and optical phonons, but in a doped semiconductor super- iattice (DSSL) The electrón gas is assumed to be non- degenerate Because the analytic calculation process in the present paper is similar that in Ref 3 and because the main differences are expressions of form factor and the energy spectrum of electrón in the models, only a brief description of the calculation will be given in this paper In Sec II, we introduce the dispersión equa- tion obtained from the quantum transport equations for 1971-

-1972- Journal ofthe Korean Physical Society, Vol 53, No 4, October 2008 phonons In Sec III, we present the results of an ana-

lytical approximation for the resonant acoustic phonon

frequency and the threshold amplitude of the field for

parametric amplification of acoustic phonons

Conclu-sions are shown in Sec IV

II G E N E R A L D I S P E R S I Ó N E Q U A T I O N

The superiattice potential in DSSLs is created solely

by using the spatial distribution of the charge A

sub-stantial improvement in spatial (on an atomic scale)

monitoring of the doping during film growth by means

of molecular-beam epitaxy enabled the growth of doped

superlattices-periodic alternation of thin ( ~ l - 2 rma)

lay-ers of GaAs of the n (GaAs:Si)-and p (GaAs:Be)-types,

separated in many cases by layers of intrinsic GaAs We

consider a DSSL, in which the electrón gas is confined by

a superiattice potential along the z direction (the axis of

the superiattice) and in which electrons are free on the

X — y plañe The motion of an electrón is well known

confined in each layer of the DSSL and its energy

spec-trum is quantized into discrete levéis in the z direction

The electrón state, a, is defined by the quantum number

n in the z direction and the wave vector A;j_ on the x — y

plañe perpendicular to 2-axis, o = (n, fc_L), P = ¿j^ 4-A:f

The structure of the DSSL also modifies the

disper-sión relation of optical phonons, which leads to interface

modes and confined modes [7] However, the

contribu-tion from these two modes can be approximated well by

calculations with bulk phonons [8] Thus, in this paper,

we will deal with bulk (3-dimensional) phonons and

con-sider a compensated n-p DSSL with equal thicknesses

dn = dp ~ d/2, of the n-doped and the p-doped layers

and equal constant doping concentrations, no = TIA, in

the respective layers

A láser field irradiates the sample in the z direction,

the electric field of the láser wave is polarized in the x —y

plañe and E = EosinQt, where ^ o ^-^d Q, are the

am-plitude and the frequency of the láser field, respectively

The vector potential of the field is A{t) = ytocosfií If

the FVohlich electron-acoustic and optical phonon

inter-action potential is used, the Hamiltonian for the system

of the electrons and the acoustic and optical phonons in

the láser field is H{t) = Ho{t) -I- He-ph^ where:

w i t h €ait) = £ „ (Jc± - (e/ch)Á(tyj, £n{k±) = £a, £a

and a j being the energy spectrum and the creation

op-erator of an electrón for state a and 6 t ( c í ) is the

cre-ation operator of an ax:oustic (optical) phonon for

en-ergy hujq (tWq) In this paper, we will deal with bulk

(3-dimensional) phonons; therefore, the electron-acoustic and -optical phonon interaction constants take the forms

Gnn'ií) = G^Mnn'(gz) a n d Drxn'iq) = Dq^fnn'iQz)

where [9]

|G,f = 2pVaV ' l ^ ' l 2Vq^

Xoo XoJ (3) Here, V, /?, Va and ^ are the volume, the density, the

acoustic velocity and the deformation potential constant, respectively; xo and Xoo are the static and the high- frequency dielectric constants, respectively The electrón form factor, M„„'(g¿), is written as [10]

Mnn'iqz)

3o fd

''''^n(z-jd)^n'(z-jd)dz,{4)

where d is the periods of the DSSL and SQ is the number

of periods of the DSSL ^ n í ^ ) is the eigenfunction of the electrón for an individual potential well

In most cases, the interaction between neighboring quantum wells in the DSSL can be neglected; t.e., the

dependence of the energy on the wave vector k^ can be

neglected The energy spectrum of an electrón in the

DSSL for the state a takes the forra [11,12]

h^kl

where m and e are the effective mass and the charge

of the electrón, respectively, no is the concentration of

the donor impurities and £„ are the energy levéis of an individual well

In order to establish a set of quantum transport tions for acoustic and optical phonons, we use the general

equa-quantum distribution functions for the phonons, {b^)t and {c^)t, where (tp)t denotes a statistical average at the moment t: {ij)t = Tr{W7p), where W is the density matrix operator and Tr denotes the trace Using the Hamiltonian H(t) and realizing the operator algébrale

calculations as in Ref 3, we obtain a set of coupled quantum transport equations for the acoustic phonons:

Parametric Resonance of Acoustic and Optical Phonons

It can be noted t h a t T^UJ H- sil) is t h e polarization

op-erator of t h e electrón d i s t r i b u t i o n function in t h e n - t h

miniband [13] a n d t h a t t h e q u a n t i t y S is infinitesimal

and a p p e a r s due t o t h e a s s u m p t i o n of a n a d i a b a t i c

in-teraction of t h e E E F

R e p e a t i n g t h e above processes, we c a n also o b t a i n a n

equation for t h e Fourier t r a n s f o r m a t i o n B^Juj) of {b'tff)t

and t h e relative expression between Bq{uj) a n d B'^Juj)

In t h e s a m e way, b u t for optical p h o n o n s , we o b t a i n a

Drxn'io) a n d v^ are replaced w i t h i/^, Cg(cj), C^uj - ÍH),

Dnn'{q), Gnn'io) a n d w^, respectively In t h e

equa-tions, B^üj) a n d C^uj) a r e t h e Fourier t r a n s f o r m a t i o n s

of (b^)t a n d {c^)t, respectively In these coupled

equa-tions, t h e first t e r m s describe t h e interactions between

phonons t h a t belong t o t h e s a m e kind (acoustic-acoustic

or optical-optical p h o n o n s ) while t h e second t e r m s

de-scribe interactions between p h o n o n s t h a t belong to

dif-ferent kinds (acoustic-optical p h o n o n ) We can p u t ^ = O

in the first t e r m s of t h e coupled e q u a t i o n s because we are

now focusing on t h e P I T of t h e acoustic a n d t h e optical

phonons Solving t h e set, we o b t a i n a general

disper-sión e q u a t i o n for t h e P I T of t h e acoustic a n d t h e optical

tion to t h e case of t h e first-order resonance (i = 1),

t h e electron-phonon interaictions satisfy t h e condition

\Gnn'{q)\^\Dnn'{q)\^ « 1 W i t h these Hmitations, if

we write t h e dispersión relations for acoustic a n d optical

phonons as ujadq) =^a + ira and ujop(q) = Ü;O + ITQ, we

o b t a i n t h e resonant acoustic phonon modes

where Va a n d uja {VQ a n d UJQ) are the group velocity a n d

t h e renormalization (by t h e electron-phonon interaction) frequency of the acoustic (opticail) phonon, respectively,

^q = q - qo, qo being t h e wave n u m b e r for which t h e

resonance is maximal a n d

In Eq (11), t h e signs ( ± ) in t h e subscript of u^^^

correspond to t h e signs ( ± ) in front of t h e root a n d t h e signs ( ± ) in t h e superscript of w ¿ correspond to t h e

o t h e r sign pairs T h e s e signs depend on t h e resonance

condition u>q±i/q-= Q For instance, the existence of

a positive imaginary p a r t of u;;." iraplies a p a r a m e t r i c amplification of t h e acoustic phonon In such cases t h a t

A < < 1, t h e maximal resonance and q = q±, qz = O, we

o b t a i n

Imbi ^1 = 1 r

13)

where TQ a n d TQ are t h e imaginary p a r t s of t h e

frequen-cies o f t h e acoustic and t h e optical p h o n o n s a n d take t h e

-1974- Journal of the Korean Physical Society, Vol 53, No 4, October 2008 forms

with 0 — l/iksT), kB being the Boltzmann constant

and T the temperature of the system ep is the Fermi

level, S is the área of the sample and

FVom Eq (13), the condition for the resonant acoustic

phonon modes to have a positive imaginary part leads

to |A|2 > ázaTo Using these conditions and Eqs

(14)-(16) yields the threshold amphtude for the EEF for a

non-degenerate electrón gas:

\/l{^q)l{^q)

y/[e{uj^) - e{uj^ - n)]2 + [7(0;,-) - 7(^9- - m''

Eq (20) means that the parametric amplification of the

acoustic phonons is achieved when the amplitude of the

EEF is higher than some threshold amplitude

To numerically estímate the threshold ampUtude, Eth^

for parametric amplification of acoustic phonons, we use

the n-i-p-i superiattice of GaAs:Si/GaAs:Be with the

pa-rameters [9,11]: (, = 13.5 eV, p = 5.32 gcm-^, Va = 5370

ni"^, Xoo = 10.9, Xo = 12.9, m = 0.067mo, mo being the

mass of free electrón and huq' c:^ huQ = 36.25 meV

In Figure 1, we show the threshold amplitude, Eth, as

a function of the wave number for three different

temper-atures The figure shows that the curves have maximal

valúes and are non-symmetric around the máxima This

is due to the fact that a fixed EEF with an amplitude

greater than the corresponding threshold amplitude can

induce parametric amplification for acoustic phonons in

two regions of the wave number corresponding to the

two signs in (JJ^± Uq = fi The máximum increases as

K (dashed line) and 300 K (solid line) Here, the frequencies

of the láser field are O = 4.5 x 10^^ Hz (the figure above) and

n = 5.0 X 10^^ Hz (the figure below)

the temperature increases A consequence of the symmetric behavior of the curves is that at fixed tem- perature (for example, 77 K) an EEF having a small amphtude (for instance, smaller than 10 kVcm~^) can amplify only acoustic phonons with wave numbers that are smaller than 0.85 x 10^ cm~^ while an EEF having

non-a lnon-arge non-ampUtude (for instnon-ance, lnon-arge thnon-an 15 kVcm~^) can amplify acoustic phonons with wave numbers that are either smaller than 0.9 x 10^ cm"^ or greater than 2.0X 10^ cm~^ These characteristics are similar to those

in a quantum well [3]

The dependence of the threshold amplitude on the temperature is presented in Figure 2 WTien the temper- ature is decreased, the threshold amplitude for paramet-

ric amplification of acoustic phonons in which uj^i/q- = SI

decreases; the threshold amplitude, however, increases

for the case of 0;^ — i/^- = Q We can see that the

thresh-old amplitude is sensitive to the temperature change and that it is more sensitive to the temperature change for the case in which the resonant frequency is smaller than

it is for the case in which the resonant frequency is larger (in Figure 1, in the región to the left of the máximum,

Eth is more sensitive to temperature than it is in the

re-gión to the right of the máximum) We can also realize that the threshold amplitude satúrate as the tempera- ture increases This characteristic is also manifested in Figure 1 in which three lines for three different temper-

Parametric Resonance of Acoustic and Optical Phonons Tran Cong PHONG et al

Fig 2 Threshold amplitude (kVcm ^) as a function of the

temperature at wave numbers of 0.75 x 10® cm~^ (doted line),

1.0X 10® cm"^ (dashed Hne) and 1.25 x 10® cm~^ (solid line)

Here, the frequencies of the láser field are Q = 4.5 x 10*^ Hz

(the figure above) and f) = 5.0 x 10^^ Hz (the figure below)

atures begin to coincide as the wave number increases

The sensitivity of Eth to temperature change, which is

a behavior of acoustic phonons, is clearly present in this

mechanism SaturabiUty of Eth with temperature the

change in región of high temperatures, which is a

be-havior of optical phonons, can be explained by the

non-dispersion of optical phonons

I V C O N C L U S I O N S

In this paper, we analytically investigated the

possi-bility of parametric resonance of acoustic and optical

phonons in DSSLs We obtained a general dispersión

equation for parametric amplification and

transforma-tion of phonons However, an analytical solutransforma-tion to

the equation could only be obtained within some

lim-itations Using these limitations for simplicity, we

ob-tained dispersions ofthe resonant acoustic phonon modes

and the threshold amplitude of the field for acoustic

phonon parametric amplification Similarly to the

mech-anism pointed out in previous papers for bulk

semicon-ductors and for quantum wells, parametric amplification

for acoustic phonons in a doped superiattice could occur

under the condition that the amplitude of the external

electromagnetic field was higher than some threshold plitude Analytical expressions showed that the thresh- old amplitude depended on the field, the material and the physical conditions

am-Numerical results for the n-i-p-i superiattice of GaAs:Si/GaAs:Be clearly showed the predicted mech- anism Parametric amplification for acoustic phonons and the threshold amplitude depended on the physical parameters of the system and were sensitive to the tem- perature in the región of low temperature but saturated

in the región of high temperatures These characteristics are similar to those in quantum wells and maybe they are common properties of quasi-two-dimensional systems

[1] V P Silin, Parametric Action of the High-Power

Radi-ation on Plasma (Nauka Publisher, Moscow, 1973)

[2] E M Epshtein, Sov Phys Semicond 10, 1164 (1976);

M V Vyazovskii and V A Yakovlev, Sov Phys cond 11, 809 (1977)

Semi-[3] T C Phong and N Q Bau, J Korean Phys Soc 42,

647 (2003)

[4] S M Komirenko, K W Kim, A A Dimidenko, V A Kochelap and M A Stroscio, Phys Rev B 62, 7459 (2000); J Appl Phys 90, 3934 (2001); N Nishiguchi, Phys Rev B 52, 5279 (1995)

[5] A L Troncoin and O A C Nunes, Phys Rev B 33,

4125 (1986); P Zhao, Phys Rev B 49, 13589 (1994); Feng Peng, Phys Rev B 49, 4646 (1994); J Phys.: Con- dens Matter 11, 4039 (1999)

[6] V Konotop and V Kuzmiak, Phys Rev B 64, 125120 (2001)

[7] N Mori and T Ando, Phys Rev B 40, 6175 (1989) [8] H Rucker, E Molinari and P Lugli, Phys Rev B 45,

6747 (1992)

[9] Y He, Z Yin, M S Zhang, T Lu and Y Zheng, Mat Sci Eng B 75, 130 (2000); N Mori, H Momose and C Hamaguchi, Phys Rev B 45, 4536 (1992)

[10] V V Pavlovic and E M Epstein, Sol Stat Phys 19,

1760 (1977)

[11] A P Silin, Sov Phys Usp 28, 972 (1986); K Ploog and

G H Dohler, Adv Phys 32, 285 (1983)

[12] N Q Bau, N V Nhan and T C Phong, J Korean Phys Soc 41, 149 (2002)

[13] G M Shmelev, 1 A Chaikovskii, V V Pavlovich and

E M Epshtein, Phys Stat Sol (b) 80, 697 (1977); ibtd

82, 391 (1977)

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T H E N O N L I N E A R A B S O R P T I O N C O E F F I C I E N T O F A S T R O N (

E L E C T R O M A G N E T I C W A V E BY C O N F I N E D ELEC T R O N S í > T H I

O t A N T U M W ELLS

Nguyén Quang Bau, Nguyén Bich Ngoc, Do M a n h íluu¿

Facuky of Physics College of Natural Sciences Vietnam Naiionai i.inp cts-iv

334 Nguyén Trai, Thanh Xuan, Hanoi Vietnam

A B S T R A C T

.Aniilytic expressions for the nonlinear absorption coefficient of a strong cicctrornaun^^ic v\u^c

íLaser radiation) by coníined electrons for the case of electron-optical phonon scnítí.*riuu -MUÍ electron-acoustic phonon scattering in quantum wells are calculated by usin*: lY.c quantum kinciü

equation for electrons The problem is also considered for both cases of ihe an.scncc aiiv! ÍIÜ presence of an external magnetic field The dependence ofthe nonlinear absoiprion cocfiícíciv

on the intensity £", and frequency Q of the external strong electromagncíi^ v,a\c lUt temperature T of the system and the cyclotron frequency Q^ for case of the proseni;o OÍ o.n

external magnetic fíeld is obtained The analytic expressions are numerically exaluj.icd ;i:oi;c(' and discussed for a specific quantum well AlAs/GaAs/AlAs The compLia-i-.it^ >^ >^' t^vi t'-^o

nonlinear absorption coefficient in quantum wells is much more greaier rbon in n:.írnii r^^nv semiconductor The appearence of an external magnetic fíeld causes surprisíng c^an^ios lo i'r^r

nonlinear absorption All the results are compared with the normal bulk scniicondiicfPiS i*- ^'^i^v' the difference

1 I N T R O D U C T I O N

In recent times, there are more and more interests in studying and discovering the behaviuur oí low dimensional system, in particular, of two dimensional systems, such as ctn''ipí)'^ir¡''nu! superlattices doping superlattices and quantum wells The confinement of cieciron- iü \iv: :s: syslems considerably enhances the electrón mobility and leads to their unusuai beÍ!a\ ¡our>. UÍ;-:!:;'

external stimuli As the results the properties of low dimensional systen-is eípeciaü.} opiic:;]

properties are very different in comparison with normal bulk semiconductors [1 2| Th<- pronU i-ns

of optical properties in normal bulk semiconductors [3-7], as well as, low dimensiívaai s s^cm^ [10.13] have ever been enthusiastically investigated The nonlinear absorpiior o! : >n•,>:!•.: electromagnetic wave by free electrons in normal bulk semiconductors has been rtudiod bv u-^i;\_ quantum kinetic equation mediod [4] while the linear absorption of a weak clecuoirüi.^nvti' \ av v

by confíned electrons in low dimentional systems has been invesligaíed b> u:^\i\¿ i^iii.'v'-.xirr;

method [3,5-7]

However the nonlinear absorption problem of an electromagnetic o.i,\c 'xhic:' ¡VJ- :=•;

V,-mtensily and high frequenc) in quantum wells still opens for studying In tíli:^ p^P'^v y-: 'JÍ'1

lile nonlinear absorption of a strong electromagnetic wave by confíned electrons ¡n qiianl ÍD^ weíls The electron-optical phonon scattering mechanism as well as electrón-'^icouvtic ÍVIVMK^ÍI

scauerinia mechanism are all considered The nonlinear absorption coeifícieni r- -aicu-M^^'-: '^

both case ofthe presence of a magnetic fíeld applied perpendicular to its baiTiers and liu- iihs-i;.,

'A ii magnetic fíeld by using the quantum kinefíc equation [5.13] for eiectron^ in a L\I\IÂ\UVU

•Acils Then we esnmate numerical valúes for the specifíc quantum weü Al.\s üạ\:v \'Â ; ciarify our results

2, T H E N O N L I N E A R A B S O R P T I O N C O E F F I C I E N T ! \ TIU CXSf r V

T H E A B S E N C E O F AN E X T E R N A L MAGNETIC FÍEÍAJ

2.1 In the case of electron-optical phonon scattering

It is well known that the motion of an electrón in a quantum weüs ¡s eoniuied anJ i:- riiduv spectrum is quantized into discrete levéis We assume that the quanti/atiun dircLlioi is íi^ : direction The Hamiltonian ofthe electron-optical phonon system in a quantum weüs in >cci^nJ quantization representation can be written as:

where n denotes quantization ofthe energy spectrum in the z direction (n=l.I: ) iv k - á-o '•

k^ -vcjy) are electrón states before and after scattering, k^{cj^)-X\\t in plañe (x.\i wa\e ^o

electrón (phonon) ấ^- and a,^- (/?|and h-) the creation and annihilation operaiars o!'t'h.vti<M¡ (phonon) respectively, q ={q^.q.), A{t) is the vector potential of an external eiectioniâ^ịcnc wa\e Ăt) ^ — Ê,sin{Q.l), hcô, is the energy of optical phonon ; C^ is a constant m the case oí

electron-optical phonon interaction '^

1 2nẽtía)a , 1 1

c„r=-v ^v^^(

I

here V and ¿',^ are the normalization volume and electronic constant (often consider V

and x.r ^^^ Ae static and the high-frequency dielectric constant, respectivelỵ

The electrón form factor, ¡„„{q.) is written as:

ít is well known that to obtain the explicit solutions from Eqs.(8) is very difíicuií If> IIM-> naprr

we use ihe fírst order tautology approximation method to solve this equation

The expression of electrón distribution function can be written as:

s - - ^ -, - fico - kfiQ + i(Si £ _ - ^ - + tioj, - ktíQ -r ic!í

Where ^?^^ - (A\-) is the time independent component ofthe electrón (phonoa > Ji aríbup' -i^

lunction: ¿,, Q are the intensity and frequency of electromagnetic vvavc: / úv) isBcsscí

function

The carrier current density formula in quantum wells takes the form:

— i^Ti - í^ —

Because the motion of electrons is confíned along z direction in a quantuní weíív

consider the in plañe (x.y) current density vector of electrons / (/)

í Jsing Kqs.(9) we find out the e.Kpression for current density vector :

i>\ using the electron-optical phonon interaction factor C\ in Eqs.{4) and the I-^ess

¡H.9J from the expression of current density \ector we established the rionlinea! ai-sorpií -!

coefficient of electromagnetic vvave in quantum wells

j(j,(nE,smQi)^= ^—{ - ) Z I L ! ^'••' • (-\!x E; ^u^^JK E- -v A, „ ,,, , , ^

_ _

A/-Eqs.(]3j is the general expression for the nonlinear absorption of a strong eiceuomaaueíif w-w^:

in a quantum wells In this paper, we will consider two limited cases for the abso:píioa: oiosc lo

the absorption threshold and far away from this, to fínd out the explicii !orm

absorption coeffícient a

ala !or \\y<

2.Í.I The absorption far away from its threshold

ín this case, to happen the absorption of a strong electromagnetic wave in a quantum well^ iho

condition \kQ.-co^^ \»£ must be satisfied Here, e is the average energ> o í a n electrón in a

quantum wells Because 6 function does not depend on wave \ector p aa^i noic líu'!

Z n = n (/?,, is the electrón density in quantum wells) we can easiK períbiPi [he adda.i.:;i

foiiowing vector p^ and q^ in Eqs.(13) As the result, we have íhe explicit Ir.rraaia íV: M^j

nonlinear absorption coeffícient of a strong electromagnetic wave in quantum welis t:v¡ ti

ofthe absorption far away from its threshold

O mtiQ 2mLÍ'

[k'cause the motion of electrons is confíned along z direction in a quaritum ^^e!^ \^':

consider the in plañe (x.y) current density vector of electrons / (/)

I 'sing Kqs.{9) we fínd out the expression for current density vector :

l i ^ r c

m IQ'íi^^t-'^ , ^ , mO niQ mí, , i

l'>\ using the electron-optical phonon interaction factor C-^ in Eqs.(4) and the Besi.:l iuiiCiioa

¡K.'>j from the expression of current density vector we established tiie nonhne.ir ¡lí^sorpü.va

cocificient of electromagnetic vvave in quantum wells

8 ^ - 7^ ^ ^ ]67r^e~QkS , 1 1 v - 'c- v - , ,

^ -—^-TÜjnE.smQiX- -^^yi )ZSIiA :

kJ-Eqs.(13) is the general expression for the nonlinear absorption of a strong eiceiuanaanefir \ \ a \ c

in a quantum wells In this paper, we will consider two limited cases for the ahsuipíioii: CJOSC a»

the absorption threshold and far away from this, to fínd out the explicit tormula ¡or ihc

absorption coeffícient a

2.Í.I The absorption far away from its threshold

¡n this case, to happen the absorption of a strong electromagnetic wave in a quantuiri wells the

condition \kQ.-co^^ \»'£ must be satisfied Here, s is the average energ} o í a n electrón in a

quantum wells Because 6 function does not depend on wave vectoi" p and noíc 'Ju!

X , '^'' /' ^ "'» ^ ^í' ^^ ^^^ electrón density in quantum wells), we can easily perfoini {he adJiSiori follovving vector p^ and q^ in Eqs.{13) As the result, we have the expjicil íonani:' far \Y,-:

nonlinear absorption coetfícient of a strong electromagnetic wave in quantum vvelís trii riva cas.,

o f t h e absorption far away from its threshold

2.1.2 The absorption cióse to its threshold

in this case, the condition \kn~co,,\«£ is needed Thereforẹ we i:.:ín aộ I-MOV. '!^

prc:-.uice of vector /"> in the formula of ó funcfíon This also means that ihc caicalrrao- ra ,;!:

Ú^pcüd on ihc form of electrón distribution function Ả,, -, We restricl ilie rrohiciạ la a!=, c r^^ >•

one pnolon absorption [\íl- cọ, \« E ) and consider electrón gas is non-deaencrutí ^

Using ihe electrón distribution function /?,,,, we do the ađiíion foilowa"^ v;;.: i- '•':

in Eqs.(13) Finally, the expression o f t h e absorption coeftkient of a strong ci-caainauaLU wave in quantum wells for the case ofthe absorption cióse to its threshold is oiiuaneo:

2.2 In the case of elctron-acoustic phonon scattering

Por this case, the quantum kinetic equation takes the similar formula witíi ihc cr-.^ ' i cí.'auáv optical phonon scattering Eqs.(8) However, the electron-optical phonon interacia i L-ị-j^a s

is replaced by electron-acoustic phonon interacfíon constant Z)^- and freqaenacN /;:, oj ('piica

phonon is replaced by frequency (O- of acoustic phonon

' 2pvy,

hete pJ\^4 sre the density, the acoustic velocity and the deformation potcniaM co¡v-:a!r':

respective]}'

hi tiiii case, the condition \kD.-(')^- \«e is needed Follovving similarly the cạ-^r abr.w \^ • c-:^:

calcúlate the absorption coeffícient for the case of electron-acoustistic phorion scaac! ai-j

2/;;!-3.THE NONLINEAR ABSORPTION COEFFICIENT IN THE CASF OF

THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD

We assume that the quantization direction is the z direction As well as we con>¡üo: uiiantun!

wells vvith a magnetic field B applied perpendicular to its barriers The KamiliDniaii el riic

electron-optical phonons system in a quantum wells in the presence of the external raaiinetic

lleld B in second quantization representation can be written as:

n,n\l< I ^q

where N is the Landau level index (N=0.1,2 ), n denotes quantization ofthe energy spectrinn ia

the z direction (n=l,2, ), (n, N, k^) and (n', N', k^^-q^) are electrón states before and afro! scattering A") (q^ )-the in plañe (x.y) wave vector of electrón (phonon) c/T , and a , ii-r and

!\,) tfiC creation and annihilation operators of electrón (phonon) respectively cj'^-[q q/) /Va,

is ihc energy of optical phonon ;

In quantum wells in the presence of an external magnetic fíeld, the electrón energy takes ti-'iC simple form :

y.'nere, f\ !S me posiuon vector ot el-eiron a is the orhit radius in íha v.-^, p^üic -,

• >

and O represenis the harmonic vvave function

SíUithig ívom ílamiíoiaa;-' u_-,qs.i2 2)-í24)) anj realh^ing opcialov :iiucra:

vi'U'í:! t!;c taa-ntum kiaeix cC:aaí'On Icr the case ofthe prescíice or vr c.^ ^ • • • ; I

SáhvTig the equation abíjvv' b}' usnig tlie fí'"St order tautology apnroxinaaiio"'

Í:K-.warcssíon •ov the aívsf»rolior¡ coefrcicnt in this cai^e: