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Submitted on 1 Jan 1981
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PHONONS IN RESONANT SECONDARY EMISSION
OF IMPURITY MOLECULES IN CRYSTALS
L. Rebane, K. Rebane
To cite this version:
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZQment a u n o 12, Tome 42, dQcembre 1981 page C6-505
iJHONONS I N RESONANT SECONDARY E M I S S I O N O F I M P U R I T Y MOLECULES I N CRYSTALS
L.A. Rebane and K.K. Rebane
I n s t i t u t e o f P h y s i c s o f t h e E s t o n i a n SSR Academy of S c i e n c e s , T a r t u , U.S.S.R.
A b s t r a c t .
-
Resonant Raman s c a t t e r i n g (RS), h o t luminescence (H&) and o r d i n a r y luminescence (OL) were s t u d i e d i n t h e s p e c t r a of S2 and Se2 impurity molecules i n K1 a t v a r i o u s f r e q u e n c i e s of l a s e r e x c i t a t i o n and temperatures. C h a r a c t e r i s t i c t i m e s of phase r e l a - x a t i o n i n t h e e x c i t e d e l e c t r o n i c s t a t e caused by phomn s c a t t e r - ing were e s t i m a t e d . I n c o n t r a d i c t i o n w i t h t h e simple v e r s i o n of t h e RSE t h e o r y no resonance i n t h e Raman s c a t t e r i n g c r o s s sec- t i o n was observed when t h e e x c i t a t i o n frequency was c l o s e o r i n resonance w i t h a s h a r p no-phonon a b s o r p t i o n l i n e .1. Model and t h e o r e t i c a l formulas.
-
Theory of RSE of a r a p i d l y r e l a x - ing c e n t e r p r e d i c t s t h r e e components i n t h e spectrum I ( v 1 , v Z ) c o r r e s - ponding t o t h e t h r e e s t a g e s of t h e t r a n s f o r m a t i o n of t h e primary pho- ton v l i n t o t h e emitted secondary phonon v 2 . A model w i t h only one l o - c a l v i b r a t i o n Q i n t e r a c t i n g w i t h l a t t i c e phonons i s considered [ 1 , 2 ] . The anharmonic decayrm
and t h e phase r e l a x a t i o nr 2
due t o phonon s c a t t e r i n g a r e taken i n t o account. Under monochromatic s t e a d y e x c i t a - t i o n i n resonance w i t h t h e v i b r o n i c t r a n s i t i o n v l = v+
"'
( v e-
f r e - quency of t h e e l e c t r o n i c t r a n s i t i o n ; prime r e f e r s t o t h e e x c i t e d e l e c - t r o n i c s t a t e ) i n t h e low-temperature l i m i tHere K ( V ~
-
v e ) i s t h e a b s o r p t i o n spectrum of t h e photon v l . RS i s t h e spectrum of photons v 2 emitted b e f o r e any r e l a x a t i o n has taken place:where i s t h e Franck-Condon f a s t o r . HL
i s
t h e emission from t h es t a t e s where t h e phase memory i s l o s t , b u t t h e p o p u l a t i o n of v i b r a t i o - n a l l e v e l s has n o t y e t reached thermal e q u i l i b r i u m w i t h t h e l a t t i c e :
m-l -1 2 2 2 -1 H L ( V ~
-
v e ) =z
F L n ( r L+
r n )
[ ( v 2-
v e-
"
+
. Q ~ )+
( r L + r n ) 1 ,(3) L=l where q i s t h e p o p u l a t i o n of t h e v i b r a t i o n a l l e v e l L under e x c i t a t i o n mLt o t h e l e v e l m. OL i s t h e emission from v i b r a t i o n a l l e v e l s i n thermal e q u i l i b r i u m w i t h phonons (from = 0 a t low t e m p e r a t u r e s ) :
C6-506 JOURNAL DE PHYSIQUE
where y-l i s t h e r a d i a t i v e l i f e t i m e . I t should b e p o i n t e d o u t t h a t t h e model and f o r m u l a s do n o t t a k e i n t o a c c o u n t t h e phonon s i d e b a n d s and
t h e e x c i t a t i o n v i a them.
2. R e s u l t s .
-
The i m p u r i t y m o l e c u l e s S; and ~ ei n i K 1 were chosen be- c a u s e of t h e i r s i n g l e l o c a l ( i n t r a m o l e c u l a r ) v i b r a t i o n of a r e l a t i v e l y h i g h f r e q u e n c y and t h e p r e s e n c e of a long series of s h a r p no-phonon l i n e s i n t h e i r low t e m p e r a t u r e luminescence s p e c t r a [3,41. I t e n a b l e s u s t o c o n s t r u c t t h e p o t e n t i a l c u r v e s and t o c a l c u l a t e t h e Franck-Con- don f a c t o r s . The RSE spectrum of~ e i
c o n t a i n i n g a l l t h r e e components-
RS, HL and OL, i s shown i n f i g u r e 1 ( s e e a l s o 153 ) . The dependence oft h e i n t e n s i t i e s of RS o v e r t o n e s on t h e i r o r d e r ( v e r t i c a l l i n e s i n t h e lower p a r t of f i g u r e 1) i s n o n - m o n o t o n i c i n a c c o r - dance w i t h c a l c u l a t e d Franck-Condon f a c - t o r s ( c u r v e 1)
.
The e x p e r i m e n t a l HL spec- trum ( s o l i d l i n e ) i s i n accordance w i t h t h e t h e o r e t i c a l one (dashed l i n e ) obtained from ( 3 ) as a smoothed sum of many HLso0 600
,,A,
t r a n s i t i o n s . From t h e r e l a t i o n of t h e lF,: summary i n t e n s i t y of RS l i n e s t o t h a t of
t h e OL t h e phase r e l a x a t i o n t i m e ';'l was found t o be 10' t i m e s s h o r t e r t h a n t h e o p t i c a l l i f e t i m e y - l . The a b s e n c e of no- phonon l i n e s i n t h e HL spectrum of
se;
may b e caused by r e l a t i v e l y s h o r t l i f e -1 2 3 4 5 6 7 8 t i m e s of t h e e x c i t e d l o c a l modes: t h e r e
F i g . 1 i s n o t enough t i m e f o r t h e r m a l i z a t i o n of t h e phonon e x c i t e d a t t h e i m p u r i t y . So, when t h e HL t r a n s i t i o n t a k e s p l a c e , t h e phonons a t t h e c e n t r e a r e s t i l l h o t ( t h e Debye-Waller f a c - t o r i s c o n s i d e r a b l y s m a l l e r t h e n f o r O L ) . For t h i s i n t e r p r e t a t i o n
(1) no-phonon l i n e s a r e a b s e n t i n t h e OL a l r e a d y a t 30 K; ( 2 ) t h e l o c a l mode of ~ ec a n decay i n t o o n l y two l a t t i c e phonons. i
I 1 1 , F i g . 2 m,, ,4 I.1 1 0 .I, R I . 211 00 21200 +,,,cm-' F i g . 3 ( 3 + O ) l i n e i s 4.2, 2.8 and 2.3 a t T = 2 , 10 and 1 5 K, r e s p e c t i v e l y . I t i n d i c a t e s t h a t t h e phase r e l a x a t i o n r a t e i n c r e a s e s w i t h t e m p e r a t u r e more r a p i d l y t h a n t h a t of t h e energy r e l a x a t i o n .
Both RS and OL i n t e n s i t i e s should f o l l o w t h e a b s o r p t i o n spectrum when t h e e x c i t a t i o n f r e q u e n c y i s v a r i e d ( s e e formula (1) )
.
F i g u r e 3 shows t h a t it i s t h e c a s e w i t h t h e p u r e l y - e l e c t r o n i c l i n e of OL f o r e x c i t a t i o n f r e q u e n c i e s i n t h e v i c i n i t y of t h e no-phonon l i n e L = 3 ( t h e OL e x c i t a t i o n spectrum i s shown), b u t n o t s o w i t h t h e RS1 l i n e . D e f i - n i t e l y , t h e r e i s no r e s o n a n c e i n t h e RS c r o s s s e c t i o n , i.e. t h e v e r y s i m p l e f o r m u l a s ( l ) , (2) f o r RS a r e i n a d e q u a t e . A more e l a b o r a t e d v e r - s i o n of t h e t h e o r y t a k i n g a c c o u n t t h e non-resonant l e v e l s , phonon wings and t h e dependence of t h e e l e c t r o n i c m a t r i x e l e m e n t s on v i b r a - t i o n s i s needed.References
1. V.Hizhnyakov and I.Tehver, phys. s t a t . s o l . (b)
82
(1977) K89. 2. K.Rebane, P.Saari, J. Luminescence,16
(1978) 223.3 . C.J.Vella, J . R o l f e , J. Chem. Phys.
61
(1974) 41.4 . K.Rebane, L.Rebane, J. Pure and Appl. Chem.
37
(1974) 161.5. L.A.Rebane, T.J.Haldre, ZhETP P i s . Red. 26 (1977) 674; (JETP L e t t . 26 (1973) 515).
