CA LCU LA TIO N O F T H E ABSO RPTIO N C O E F F IC IE N T O F A W EAK ELE C T R O M A G N E T IC W AVE BY F R E E C A R R IE R S IN QUANTUM
W IR E S BY U SIN G T H E KUBO -M O RI M ETHO D
N g u y e n Q u a n g B a u , D i n h Q u o c V u o n g , N g u y e n B a L a m , L u u B i c h L in h
D epartm ent o f Physics, College o f Science, V N U
A b s t r a c t : A n a ly tic e x p re s s io n s fo r th e h ig h -fre q u e n c y c o n d u c tiv ity te n s o r
fre e c a rrie rs fo r th e c a s e o f e le c tro n -a c o u s tic p h o n o n s c a tte rin g in Q u a n tu m
a b s e n c e o f a m a g n e tic fie ld a n d th e p re s e n c e o f a m a g n e tic fie ld In
c o m p a ra tio rt w ith b u lk s e m ic o n d u c to rs , d iffe re n t d e p e n d e n c e o f th e h ig h - fre q u e n c y c o n d u c tiv ity te n s o r a n d th e a b s o rp tio n c o e ffic ie n ts o n th e
c y c lo tro n fre q u e n c y Í Ì (w h e n a m a g n e tic fie ld is p re s e n t) a n d c h a ra c te ris tic
n u m e ric a lly e v a lu a te d , p lo tte d a n d d is c u s s e d fo r a s p e c ific Q u a n tu m W ire s o f
th e G a A s / G a A sA I
1 I n t r o d u c t io n
T h e c a p tio n o f e le c tr o n s in the lo w -d im e n s io n a l system s ig n if ic a n t ly re d uce d the
v e r s a ltilit y o f th e electron s T h is le a d s to s ev era l o p t ic a l a n d e le c tr ic a l p ro pe rties,
d iffe r in g to tho se o f u s u a l sem icon d uctors[l-5] T h e c a lc u la t io n s o f th e ab sorp tion
c o e ffic ie n t o f w e a k e le c tr o m a g n e tic w a ve in q u a n tu m w e lls [6], a n d in th e doped
s u p c r la tic c s [7] w e re stu d ied
In th is p a p e r w e s tu d y th e h ig h -freq u en cy c o n d u c tiv ity te n so r a n d th e ab sorp tion
c o e ffic ie n t o f a w e a k e lec tro m a g n e tic w a ve (E M W ) (w eak e le c tr o m a g n e tic w a ve h a s the form : E = Eoe'wt) d u e to fre e c a r rie r s c o n fin e d in q u a n tu m w ừ e s in th e cases o f the absence o f m a g n e tic fie ld a n d the p resen ce o f a m a g ne tic f ie ld a p p lie d p e rp e n d ic u la r to its b a rrie rs T h e e le c tro n - a co u stic pho n on s ca tte rin g m e c h a n is m is a ssu m e d to be
d om in a nt T h e r e s u lts w e re c a lc u la te d n u m e ric a lly fo r a t y p ic a l q u a n tu m w ir e
G a A s / G a A s A l
2 H i g h - f r e q u e n c y c o n d u c t iv i t y t e n s o r a n d t h e a b s o r p t io n c o e f f i c i e n t o f w e a k
e le c t r o m a g n e t ic w a v e b y f r e e c a r r i e r s i n q u a n t u m w i r e s i n th e ' c a s e o f th e
a b s e n c e o f a m a g n e t ic f ie ld
A c y lin d r ic a l q u a n tu m w ire: th e ra d iu s R 0, the le n g th L , th e in f in it e con fin ed
p ote n tia l: V ( r ) = 0 in s id e th e w ir e a n d V ( r ) =co elsew here
B a sed on th e K u b o - M o r i m eth od w it h th e fra c tio n s c u t-o ff w it h in second order
a p p ro x im a tio n o f th e in te ra c tio n , w e o b ta in e d fo llo w in g fo r m u la fo r th e a b sorp tion
c o e ffic ie n t o f w e a k e le c tr o m a g n e tic w a ve in th e q u a n tu m w ir e s w it h e lectron -acou stic
Trang 2H e re , N* is th e in d e x o f re fra c tio n and c is the lig h t ve lo city , ƠXX(<I>) is the
p e r p e n d ic u la r co m p o n e n t o f th e h igh - frequen cy c o n d u c tiv ity te n so r in th e absebce o f
m a g n e tic file d w h ic h is a fu n c tio n o f fre q ue n cy Ü) o f th e e le c tr o m a g n e tic field ,
te m p e r a tu re T a n d p a ra m e te rs o f q u a n tu m w ires, w h ic h is n o n -lin ea r
3 H ig h f r e q u e n c y c o n d u c t iv i t y t e n s o r a n d t h e a b s o r p t io n c o e f f i c i e n t o f w e a k
e le c t r o m a g n e t ic w a v e b y f r e e e le c tr o n s in q u a n t u m w ir e s in p r e s e n c e o f
m a g n e t ic f i e l d
In the case o f p resence o f m agnetic fie ld (m agnetic fie ld B //O Z ), u sin g K u b o-M o ri method, th e c om pon ents o f th e absorption coefficient o f electrom agnetic w a ve in qua ntum
w ires w ith electron-acoustic phonon s catterin g m echanism in presence o f externa] m agnetic field:
o f the h ig h frequen cy con d u ctiv ity tensor in presence o f e xtern al m agnetic fie ld w h ich is a
fu nction o f frequen cy (Ứ o f the electrom agnetic field, c yclotron frequen cy Q o f external
m agnetic field, tem p era tu re T an d p aram eters o f q ua ntum w ires, w h ic h is non-linear
4 N u m e r ic a l c a l c u l a t io n a n d d is c u s s io n
a xx((ũ,Q)= - ^ - R e ơ xx(ci),Q),
W h ere Q = -^- is the frequency cyclotron, o^m.q) is th e p e rp e n d icu la r com ponents
F ig u r e 1 Dependence o f the absorption
coefficient of E M W on the energy o f E M W and
temperature in the case of the Absence o f a
F ig u r e 2 Dependence o f the absorption coefficient o f E M W on the energy o f E M W and radius in the case o f the presence o f a
Trang 310 Nguyen Quctng Bau, Dinh Quoc Vuong
B a s e d o n t h e a n a ly t ic a l e x p re ss io n s fo r th e p e rp e n d ic u la r co m p o n e n ts o f th e h ig h fre q u e n cy c o n d u c t iv ity te n so r, th e a b s o rp tio n c o e ffic ie n t o f w e a k e le c tr o m a g n e tic wave
b y fre e e le c tr o n s in q u a n t u m w ir e s w it h e le c tro n -a c o u s tic p h o n on s c a t te r in g m ech anism
in th e c a se s o f p re se n ce (2) a n d a b sen ce (1) - (3) o f e x te r n a l m a g n e tic fie ld fo r a ty p ic a l
q u a n tu m w ir e G a A s / G a A s A l w it h values: n = 0.01m eV;m = 0.067m 0 ,e = 2.07e0 ; r = 5 0 A °
a n d th e sy s te m is a s su m e d to be a s ro om te m p e r a tu re (T = 300°K)
A c k n o w le d g m e n t s :
T h is w o rk is c om p le te d w it h fin a n c ia l su p p o rt from the P ro g ra m o f B a sic Research in
N a tu r a l S cie n ce 411204
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