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ournal of the Korean Physical Society, Yol. 53, Nọ 4, October 2008. pp. 1971-'1975
Parametric Resonance of Acoustic and Optical Phonons ¡n a Doped Semiconductor Superiattice ¡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 non- degenerative electrón gas in the presence of a láser field is theoretically predicted by using a set of quantum transport equations for the phonons. Dispersions 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
Ị 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 conditions 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 excitations, such as p l a s m o n - p h o n o n excitations, will arise; ịẹ, 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 frequencỵ 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@yahoọcom; Fax: +84-54-825824
causes the acoustic phonons mentioned abovẹ T h e re- 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 d a m p i n g process for one excitation and 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 versạ 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 en- ergy exchange processes between two different kinds of phonons in d o p e d superlattices, which are driven by a 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- degeneratẹ 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 equa- 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-
foumal of the Korean Physical Society, Vol. 53, Nọ 4, October 2008, pp. 1971~1975
Parametric Resonance of Acoustic and Optical Phonons in a Doped Semiconductor Superiattice 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 non- degenerative electrón gas in the presence of a láser field is theoretically predicted by using a set of quantum transport equations for the phonons. Dispersions 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