THE DIPOLE MOMENT INTERACTION OF BOUND EXCITONS IN HIGHLY EXCITED CdS

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THE DIPOLE MOMENT INTERACTION OF BOUND

EXCITONS IN HIGHLY EXCITED CdS

Bao Qingcheng, Dai Rensong, Xu Xurong

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C7, supplément au n°10, Tome *6, octobre 1985 page C7-221

THE DIPOLE MOMENT INTERACTION OF BOUND EXCITONS IN HIGHLY EXCITED CdS

Bao Qingcheng, Dai Rensong and Xu Xurong

Changchun Institute of Physios, The Academy of Sciences of China, Changchun, China.

Résuraé — Nous avons trouvé que la polarisation de la luminescence de 1'ex-ci ton piégé dans CdS dépend de l'intensité d'ex1'ex-citation dans la gamme 1CP W/cm2 à ÎO^ W/cm^. Pour interpréter ce phénomène, un modèle d'interac-tion du moment dipolaire transitoire est proposé. Quand deux excitons sont proches l'un de l'autre, un moment dipolaire induit doit être ajouté à ceux des excitons liés le long de l'axe c. Le moment dipolaire induit croît avec la densité des excitons liés et par conséquent augmente la polarisation de la recombination radiative des excitons liés. Les variations des caractéris-tiques de luminescence du système uniaxe CdS prédites par ce modèle sont en bon accord avec les résultats expérimentaux.

Abstract — The polarization of bound exciton luminescence in CdS is found to be-dependent on the excitation intensity which varies from 10 w/cm2

to 10 w/cm2.To interprete this phenomenon a model of transient dipole

moment interaction is suggested. When two excitons approach each other within a very short distance an induced dipole moment should be added to the ordinary ones of bound excitons along the c-axis. The induced dipole moment increases with the density of bound excitons and consequently incre-ases the polarization of the recombination radiation of the bound excitons. The predicted variations of luminescence characteristics of uniaxial CdS from this model agree well with the experimental data.

I - INTRODUCTION

Bound exciton is an impotant localized excited state in crystal.The charcteristies of it's radiative recombination is wide attractive in the fundamental reseach or in the applications .A large number of papers discussing the profile of spectral lines,the energy positions,the intensities of the emission from bound excitons,esp-ecially, the detailed structure of the spectra under magnitic fied give us a relat-ively clear picture about the constitution and the dynamical processes of the bound excitons.//1-7//.In the paper authors propose a new concept for the interac-tion between bound excitons under high density excitainterac-tion.In our theoretical model the interaction of the bound excitons on neutral donors is considered as that of neutral atoms.//8//.Because the dielectric tensor has different values at different directions in some uniaxial crystals,the dispersion effect and the induced transient dipole moment are quite different along different directions, In general we choose two directions,which are parallel or perpendicular to the C-axis.For a bound exciton system the energy position and the induced dipole moment can be examined by the polarization of the recombination radiation of bound excitons at different extent of applied excitation.

II - EXPERIMENTAL SETUP AND RESULTS

Very pure and fine CdS single crystal was grown by vapour transfer method*.The •The authors are much indebted to professor C.Klingshirn in Frankfurt,West Germany for providing this crystal.

C7-222 JOURNAL

DE

PHYSIQUE

as

grown crystal w a s mounted on the holder in cryustat ESR-900

at

77-llK. (see

Fig. 1)

Fig.2

-The

photolumhscence spectra of CdS under different I-exc (the brief wri$ting of the excitation intensity). FE:the peak due t o the free excitons, BED :the peak due t o the excitons bound t o the ionized donor, BEAo:the peak due t o the neutral a ptor.Now pay attention t o the peak of BED'. @)

.-

the spectrum with 1-c of 3Xl%/cm2; (b).- the spectrum with I-exc of l.lX10 W/an2. Beside the increase of the lmhescence intensity, one can see the longwave s h i f t with the I-excs.

In our e x p e r h n t a beam of 308

nm

l i g h t from Excimer laser -102 excited the sanples with the e l e c t r i c a l f i e l d vector E perpendicular t o the C-axis of the

t a l

(i.e

1C). Using lenses and neutral f i l t e r s we can change the I-exc £ran

y

10

/

&

t o 10

k

/ a 2 easily. A polarizer and a double grating s p e c t r a ~ t e r CSD 50-1 are used t o masure the emission peak due t o the recanbination of BED0in different directions r e l a t i v e t o the C-axis of CdS crystal. Through a photcmutipl- i e r C-31034 with cooling system the l i g h t signal w a s masured by

the

MI62 boxcar and the X-Y recorder. In Fig.3 we s h m the s h i f t of the emission peak of BEDOand the polarizability P (we'll define the mxming of P i n following) of the same one a t different excitation intensities.

Fig.3-The e x p e r h t a l results of the photoluminescence frcin BEDOin CdS crystal. The cross points stand f o r the masurement values of

A

under different I-excs; the dot points stand f o r the m e a s m n t values of P under different I-excs.

The solid lines represent the trial caculation values using the equations ( 7 )

and (8) with adequately chosen parameters A,B,and C.

We consider the A sieres f exciton only//9//.For simplicity

ws4

consid% two bound excitons a t two n e u d a l donors (BED0) with a distance vector

r

=

?

-

r

in

an uniaxial crystal, see Fig.4. In our another essay: which

aims

a t &he

dtexa-

ction between bound excitons we'll do tvm things.

The

f i r s t thing is t o give the detailed deduction of following equations and the second Pne is t o show that the dispertion effect betmen BED0 and BEA; between BED0 and BED o r between BED0 and

FE

are neclegtable and the sing frequency approach is resonable. These two points provide

the

basic situation f o r t h i s current paper.

JOURNAL DE PHYSIQUE

Fig.4-The -1 of

the

dispersion action between two nearest BEDo. fitand% represent the transient e l e c t r i c a l - d i p o l e - m n t of BED' localized a t r and

r2,

3

and

.

₂ represent the angles bet-

Xir&

and Y, is the positih vector. According t o t h e theory of c l a s s i c a l electrmagnetism, a transient electrical. f i e l d w i l l

5

Muted a t

Fl

by

'

and

the

dipole m n t w i l l increase along &'vector

.

As the t r d i n t emission i n t e n s i t y

dl1

be proportional t o the square of &&'transient dipole -nt. The l a t t e r quantity w i l l be calcula-

ted. The square of the added transient dipole m n t due t o t h e induction by the nearest BEDo can be integrated along t h e angle 6, t h e

root

of the integrated value is calculated

and

written as M. T h i s quantity M is an incremnt of dipole m n t mainly due t o the mutual- induction between two nearest n e i w u r s of BEDo

Then we represent M i n t o MI1

and

M1. i . e paraller and perpendicular t o t h e C-axis

.

W e can obtain f o l l w i n g equatzons:

&

: t h e &to;; energy of the rea&ination radiation of BED"

we.h

without the m t a n with t h e neighbow one,

K,,:

the o p t i c a l inductivity along

the C-axis,

Kl: that one perpendicular t o the C - a x i s , go: t h e inductivity i n vacuum, U: the energy decremnt of t h e BED' due t o the interaction with the nearest neighburs. The detailed deduction of these equations w i l l appear in our another essay, w h i c h deal with the interaction between bound excitons.

Nm

we d i f i n e the p o l a r i z a b i l i t y P as f o l l w i n g : -

( fl10 +

MilZ

( 4 )

Here, I i n t e n s i t y

or me

p o m i z e d emission of BEDe i n the direction p a r a l l e l l o r cular t o the c-axis respectively, D: a p n q p r t i o n d l constant. w i d e r i n g p l < = fll0 =

p:

M L 1 7 MI andgLj. _M, we obtain:

1 Z M

P = D.(1++) (5)

N

-

H e r e C:

the

l i g h t velocity in the vacuun. The deducenrent of equation (5) is based on the f a c t t h a t t h e value of is smaller than K

.

I f we.

take

account of the o p t i c a l aligranmt of excitons

311

-

N

aolpnnds

f/10//, the value of w i l l

go

,

a storey still higher. t h i s f a c t

can

be used t o understand t h a t

t3l1~a.s~~~-

mt values of P andohare s l i g h t

larger

than

t h e calculated one by using equations

( 1 ) t o ( 3 ) .

Normally t h e density of BED0 i n c r y s t a l is proportional t o the excitqtion intensity I-exc, s o we have the relationship I-excc*

r30c

M, t h e equation ( 5 ) and ( 6 ) m y be expressed as:

Here, A, B and C a r e Constants.

N-The conclusions

1.

-

the p o l a r i z a b i l i t y P of the emission f r a n BEDe in CdS increases with the excitation i n t e n s i t y I-exc, and tlae t h e o r e t i c a l relationship between P and I-exc agrees with the experimmtal results

2.

-

The photo energy £ran BED" in CdS decreases with

I-exc,

and

the theoreticdl relationship between A

and

I-exc

agrees

w i t h t h e experimental r e l u t s w e l l .

3.

-

lhye

two phenarrena appear i n

the

same similarity. When the I-exc

reaches

about 10 W / c m 2 , both processes w i l l be saturated, because of the saturation of the density, which w i l l be limited by the density of

the

defects which

bound

exciton

as

BED". man its

poipg

of view m can evaluate the density of neutral donor, which

is

estimated

as

10 /cm3.

/I/.

-

D.G.ThaMs

and

J.J.Hapfield, Phys. Rev.

128.

2135 (1962) /2/.

-

H.Venghauss and P.L.Dean, Phys.Rev.B22. 1956 (1980)

/3/.

-

R.Ranestain

and

N.

mgnea,

Solid.state.Cannun.32 1201 (1979)

/4/.- P.J.Dean, Excitons in Semiconductors in "Collective Excitons i n Solids" Edited by Baldassare D i Bartolo, Plenun Press-New York and London Published in Coaperation with NAKI Scientic Affairs Division (1981)

/5/.

-

D.G.Thanas, M.Gershenzeo andJ. J. Hopfield, Phys

.

Rev.=. 2397 ( 1963 ) /6/.

-

J.L.Merz, R.A.Faulkner and P.J.Dean, Phys.Rev 188.1228 (1969)

/7/.

-

R.Ranestain, Le S i Dang, A.Nahnani, J.Phys (France).Vo1.45.No.7.1175 (1984) /8/.- M m g Wrong Yan, Yau Xi, "The fundamntal of D i e l e c t r i c d l Physicsn (1979) F ' u b l i s M by The National Defense Industry, China

/9/.

-

C.Klingshirn

and

H.Hang, Phys.Report (Review section of 'Physics Lettersn ) 70.N0.5. 315-398 (1981) North

-

Holland Publishing Canpany

/lo/

.-

C .E. Picks

and

E.L. Ivchenko, @ t i c a l Orientation and Polarized Luminescence of Excitons i n Semiconductor i n "Excitons* Edited by E.L.Rashba and M.D.Sturge,