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POLARONS AND SOLITONS IN TRANS-(CH)x : AN OPTICAL STUDY
S. Etemad, A. Feldblum, A. Macdiarmid, T. Chung, A. Heeger
To cite this version:
S. Etemad, A. Feldblum, A. Macdiarmid, T. Chung, A. Heeger. POLARONS AND SOLITONS IN
TRANS-(CH)x : AN OPTICAL STUDY. Journal de Physique Colloques, 1983, 44 (C3), pp.C3-413-
C3-422. �10.1051/jphyscol:1983383�. �jpa-00222821�
J O U R N A L DE PHYSIQUE
Colloque C3, suppldment au n06, T o m e 44, juin 1983 page '(3-413
POLARONS AND SOLITONS I N
TRANS-(CHI,:
AN OPTICAL STUDYS. ~temad*, A . FeldbludH, A.G. ~ac~iarmid.*
,
T.C. Chung+**and A.J. Heeger***' B e l l L a b o r a t o r i e s , blhippany, NJ 07981, U . S . A.
"'Department o f C h e m i s t r y , U n i v e r s i t y of PennsyZvania, PA 19104, U.S.A.
** I n s t i t u t e f o r Polymer and O r g a n i c S o l i d s , UCSB, CA 93106, U.S.A.
R6sum6
-
Les spectres d'absorption des Polarons et Solitons danstrans-
(CH) ont Bt6 caract6ris6s expgrimentalement par les 6tudes quantita- tiveg d6tailli5es de l'absorption ir proche pendant le processus de dopage 6lectrochimique. L'agrBment quantitatif avec les calculs de l'ab- sorption i mi-gap des solitons est une 6vidence directe que le dopage de trans-(CH) procsde par la formation des solitons. On observe que la transitionXabrupte entre les deux niveaux localis6s d'un polaron donne lieu une s6rie d'absorptions supp16mentaires intenses (:O,leV en largeur), que nous avonsutilis6epour contrbler la concentration des polarons lors du dopage. En conformit6 avec la mgtastabilit6 des pola- rons dans trans-(CH)
,
une ~ a i r e se dGcornposant en la paire soliton- antisoliton d16nergiZ plus basse, on trouve que les Polarons ne sont pr6sents qu'aw taux de dopage trss faibles.Abstract
-
The absorption spectra of Polaron and Soliton excitations in =-(CH), have been characterized experimentally using the detailed quantitative studies of the near-ir-absorption during the electrochemical doping process. The quantitative agreement with the calculations of soliton mid-gap absorption is shown to be a direct evidence for the proposal that doping of trans-(CH), predominantlyproceeds through soliton formation. The intense 6-function
transition between the two localized levels of a polaron is observed to give rise to a series of sharp ( 50.1 eV wide) additional
absorptions which we have used to monitor polaron concentration during the doping process. Consistent with the metastability of polarons in =-(CH),, with a pair decaying into the lower energy soliton- antisoliton pair, polarons are found to be present only at very dilute doping levels.
I. INTRODUCTION
Polyacetylene has been a subject of many theoretical and experimental studies because of its simplicity as the prototype polymeric
semiconductor 111, and because of the fact that the thermodynamically stable --isomer possesses a broken symmetry degenerate ground state.
Recent theoretical studies have demonstrated that addition of a
pair
of charge carriers to a trans-(CH) chain invariably distorts the lattice leading to formation of a soliton-antisoliton pair (See Fig. 1) /2-51. The added charges are then accommodated in the soliton mid-gap electronic levels. Since by
topological constraints solitons can be generated only in pairs, generalized 1-d theories predict that the lowest energy state available to a single added carrier
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983383
i s a 1-d l a r g e p o l a r o n d i s t o r t i o n ( S e e F i g u r e 1) /5-8/. I n t h e a b s e n c e o f e l e c t r o n - e l e c t r o n i n t e r a c t i o n i t h a s been shown t h a t a s s o c i a t e d w i t h a p o l a r o n d i s t o r t i o n t h e r e a r e two e l e c t r o n i c l e v e l s d i s p o s e d s y m m e t r i c a l l y byy,
./+!2
from t h e c e n t e r of t h e e n e r g y g a p , 2 ~ 0 /6-8/. Thus two t y p e s of s i n g l y c h a r g e d l o c a l i z e d e x c i t a t i o n s a r e p r e d i c t e d t o e x i s t i n t r a n s - ( C H ).
s p i n l e s s c h a r g e dx '
( t o p o l o g i c a l ) s o l i t o n s and p o l a r o n s w i t h s = 1/2. It s h o u l d be emphasized t h a t p o l a r o n s i n t r a n s - ( C H ) x a r e m e t a s t a b l e s t a t e s ; i - e . , f i n i t e o v e r l a p of
F i g . 1 ( a ) The a r r a n g e m e n t o f t h e d o u b l e and s i n g l e bonds of
trans
(CH), i n t h e p r e s e n c e o f a s i n g l e ( P ) and a p a i r ( S -- g-)
of added c h a r g e . ( b ) S c h e m a t i c o f t h e e n e r g y d i a g r a m f o r (P-) and(S--
?) s t a t e s n o t i n g t h e v a r i o u s t r a n s i t i o n s i n v o l v i n g t h e gap s t a t e s . ( c ) The s p a t i a l v a r i a t i o n o f o r d e r p a r a m e t e r s u ( x ) f o r ( P - ) and (S-- &) s t a t e s .t h e wave f u n c t i o n of two p o l a r o n s on t h e same c h a i n l e a d s t o t h e f o r m a t i o n of a s o l i t o n - a n t i s o l i t o n p a i r . T h i s c a n r e a d i l y be s e e n from e n e r g e t i c c o n s i d e r a t i o n s s i n c e 2E > 2Es, where E = ( 2
/FA
.)/l:and Es = 2 A o / ~ r a r e t h e p o l a r o nP P
and s o l i t o n r e s t mass e n e r g i e s /6-8/. Thus one e x p e c t s t h a t c h a r g e d s o l i t o n s t o be t h e p r i m a r y e l e c t r o n i c e x c i t a t i o n s i n t r a n s - ( C H ) x .
I n t h i s r e v i e w we p r e s e n t t h e h i g h l i g h t s of a r e c e n t e x p e r i m e n t a l s t u d y of t h e a b s o r p t i o n s p e c t r a o f p o l a r o n s and s o l i t o n s i n t r a n s - ( C H ) x /9-lo/. C o n s i s t e n t w i t h t h e t h e o r e t i c a l p r e d i c t i o n s we p r i m a r i l y f i n d t h a t upon t h e e l e c t r o c h e m i c a l i n j e c t i o n o f c h a r g e o n t o t h e polymer c h a i n s a n i n t e n s e a b s o r p t i o n a p p e a r s n e a r mid-gap. ?he i n t e g r a t e d o s c i l l a t o r s t r e n g t h of t h i s a b s o r p t i o n band i s i n
agreement w i t h t h e t h e o r e t i c a l c a l c u l a t i o n s f o r t h e s o l i t o n mid-gap a b s o r p t i o n ,
(.! ( S e e F i g u r e 1 ) /11-12/. F u r t h e r m o r e , t h e r e a r e a l s o s h a r p a d d i t i o n a l
a b s o r p t i o n bands below t h e 1-d gap t h a t a r e o n l y p r e s e n t a t t h e i n i t i a l s t a g e (y - <
1 % ) o f doping. Using t h e r e s u l t of a r e c e n t t h e o r e t i c a l c a l c u l a t i o n s / 1 0 , 1 3 / we
h a v e p l a u s i b l y a r g u e d t h a t t h e s e s h a r p a d d i t i o n a l a b s o r p t i o n s a r e due t o t h e t r a n s i t i o n between t h e two l o c a l i z e d l e v e l s of t h e p o l a r o n d i s t o r t i o n (a
2 in Fig. 1 ) .
C a l c u l a t i o n s of t h e v a r i o u s o p t i c a l t r a n s i t i o n s ( s e e Fig. 1 ) i n v o l v i n g t h e s o l i t o n /11,12/ and t h e p o l a r o n /10,13/ gap s t a t e s have been r e p o r t e d i n t h e l i t e r a t u r e . The i n t e g r a t e d o s c i l l a t o r s t r e n g t h f o r t h e s e t r a n s i t i o n s a r e reproduced i n t a b l e 1 and compared w i t h t h a t of t h e i n t e r b a n d t r a n s i t i o n , n i
.
TABLE 1: S t r e n g t h of t r a n s i t i o n s i n v o l v i n g g a p - s t a t e s of S o l i t o n s and P o l a r o n s .
With t h e e x c e p t i o n of a3, a l l t h e o t h e r t r a n s i t i o n s have o s c i l l a t o r s t r e n g t h s which a r e enhanced by more t h a n a n o r d e r of magnitude compared t o ai. As shown e l s e w h e r e /lo-131, c o n c u r r e n t w i t h t h e a p p e a r a n c e of t h e s e a b s o r p t i o n s i n s i d e t h e g a p t h e i n t e r b a n d a b s o r p t i o n i s reduced u n i f o r m l y and t h e o s c i l l a t o r sum r o l e i s p r e s e r v e d .
n = r e f r a c t i v e i n d e x 2 x f a s d ~
1 ~
=~
t r a n s i t i o n m a t r i x element1
\ ~ ~ d ' f i t o = t r a n s f e r i n t e g r a l (2-3 eV) 2dw 5, = 2t o / A o-
7 c o h e r e n c e l e n g t h 3xla 3dmD e t a i l e d c a l c u l a t i o n s show t h a t t h e a b s o r p t i o n s a s s o c i a t e d w i t h a s and (<,/Na)
.
(2.82)A(C,/Na)
.
(1.76)A(Co/Na)
.
(1.72)A( C , / N ~ )
.
(0.06)Aa l a r e r e l a t i v e l y s h a r p a s s y m e t r i c bands /lo-131. I n t h e a b s e n c e of
inhomogeneous b r o a d e n i n g t h e y d i v e r g e a t a t h r e s h o l d on t h e i r low e n e r g y s i d e and have a n e x p o n e n t i a l l y d e c r e a s i n g t a i l on t h e i r h i g h energy s i d e . A most
s i g n i f i c a n t r e s u l t i n t a b l e i s t h e l a r g e i n t e g r a t e d o s c i l l a t o r s t r e n g t h of a 2 , which i s supposed t o have z e r o i n t r i n s i c width. T h i s c h a r a c t e r i s t i c p o l a r o n a b s o r p t i o n i s e x p e c t e d t o o c c u r n e a r a 2 a s a n e x t r e m e l y s h a r p s t r u c t u r e , and should be o v s e r v a b l e a t v e r y low c o n c e n t r a t i o n s .
11. EXPERIMENTAL RESULTS
The d e t a i l e d e x p e r i m e n t a l s t u d y of t h e a b s o r p t i o n s p e c t r a of t h e p o l a r o n and s o l i t o n g a p - s t a t e s i n trans-(CH) h a s been c a r r i e d o u t u s i n g t h e r e c e n t l y d e v i s e d
X
o p t o - e l e c t r o c h e m i c a l s p e c t r o s c o p y 191 f o r t h e f o l l o w i n g r e a s o n s . F i r s t , t h e c o n t r o l of d o p a n t c o n c e n t r a t i o n h a s e n a b l e d u s t o m o n i t o r t h e a d d i t i o n a l a b s o r p t i o n s p e c t r u m q u a n t i t a t i v e l y and r e p r o d u c i b l y . S e c o n d l y , t h e u n i f o r m i t y of t h e dopant
c o n c e n t r a t i o n i n o u r e l e c t r o c h e m i c a l doping e x p e r i m e n t s h a s ensured t h a t t h e s i n g l y i n j e c t e d c a r r i e r s a r e uniformly d i s t r i b u t e d . F i n a l l y t h e p o s s i b i l i t y of doing t h e e x p e r i m e n t s i n s i t u h a s enabled u s t o monitor t h e a d d i t i o n a l a b s o r p t i o n a t very low dopant c o n c e n t r a t i o n s w i t h h i g h accuracy. This t e c h n i q u e , which i s d e t a i l e d
e l s e w h e r e /9/, u s e s a t h i n (g 1000 A t h i c k ) f i l m of Shirakawa (CH)x /14/
polymerized d i r e c t l y on a t r a n s p a r e n t conducting g l a s s a s a n e l e c t r o d e i n a t r a n s p a r e n t e l e c t r o c h e m i c a l c e l l . Since t h e amount of c h a r g e on t h e f i l m i s d i r e c t l y c o n t r o l l e d by t h e v o l t a g e d i f f e r e n c e between t h e (CH);electrode and a c o u n t e r - e l e c t r o d e ( L i m e t a l i n t h i s c a s e ) , any d e s i r e d dopant l e v e l can be achieved by m a i n t a i n i n g a predetermined v o l t a g e a c r o s s t h e c e l l .
Fig. 2 I n s e t shows t h e change i n t h e a b s o r p t i o n spectrum of p-type doped ( a ) compared t o t h a t of a s grown ( a o ) w - ( C H ) , . The f i g u r e shows t h e d i f f e r e n c e s p e c t r a 6 a o = (a
-
a o ) .F i g . ( 2 ) shows t h e change i n t h e a b s o r p t i o n spectrum of p-type doped E-(CH)~
u s i n g t h e e l e c t r o c h e m i c a l procedure d e s c r i b e d above. The i n s e t t o Fig. ( 2 ) shows t h e s p e c t r a l dependence of u f o r an undoped f i l m and t h e c o r r e s p o n d i n g s p e c t r a l dependence a f t e r l i g h t doping. A t a l l c o n c e n t r a t i o n s t h e main e f f e c t s a r e t h e a p p e a r a n c e of a broad dopant induced a b s o r p t i o n n e a r mid-gap c o n c u r r e n t w i t h t h e uniform s u p p r e s s i o n of t h e e n t i r e i n t e r b a n d t r a n s i t i o n f o r photon e n e r g i e s a s high a s 4.0eV /9,11/ ( n o t shown h e r e ) . J u s t below t h e i s o s b e s t i c p o i n t i n a c u r v e s
t h e r e i s a weak and s h a r p s h o u l d e r which a p p e a r s t o grow w i t h doping a t t h i s l e v e l , Both t h e mid-gap a b s o r p t i o n and t h i s s h o u l d e r a r e s e e n more c l e a r l y i n t h e d i f f e r e n c e c u r v e , & a , shown i n Fig. (2). T h e s a c u r v e i s t h e a d d i t i o n a l a b s o r p t i o n due t o doping; i . e . , t h e d i f f e r e n c e between t h e a b s o r p t i o n s p e c t r a of t h e doped and as-grown f i l m . The i s o s b e s t i c p o i n t , where t h e r e i s no change i n a b s o r p t i o n , i s s e e n t o be a t -1.6 eV. The mid-gap a b s o r p t i o n i s s e e n a s a peak i n ba a t r 0.7 eV f o r ~ ~ 0 . 2 % . The s u p p r e s s i o n of t h e i n t e r b a n d t r a n s i t i o n i s s e e n a s a n e g a t i v e p l a t e a u i n t h e 6 2 p l o t . Near t h e i s o s b e s t i c p o i n t we n o t e t h e p r e s e n c e of a v e r y s h a r p a b s o r p t i o n a t 1.47 eV t o g e t h e r w i t h a second s h a r p a b s o r p t i o n peak
o f l e s s i n t e n s i t y a t 1.6 eV. These r e s u l t s a r e from p-type doping w i t h (C104) i o n s , but i d e n t i c a l r e s u l t s can be observed w i t h o t h e r p- o r n-type dopants.
Fig. 3 The h i g h r e s o l u t i o n a b s o r p t i o n s p e c t r a w i t h a uniform smooth background s u b t r a c t e d .
The s h a r p a d d i t o n a l a b s o r p t i o n f e a t u r e s a r e s e e n i n g r e a t e r d e t a i l i n t h e h i g h r e s o l u t i o n ( 2 0.01 eV) p l o t s shown i n Fig. (3). The procedure f o r p l o t t i n g t h e s e r e s u l t s which a r e t a k e n a t l a r g e r dopant c o n c e n t r a t i o n i s s i m i l a r t o t h e 6 a p l o t . For t h e s e p l o t s a uniform background Kao, which i s a c o n s t a n t f r a c t i o n (K 1 0.9) of t h e undoped a b s o r p t i o n s p e c t r u m a o , i s s u b t r a c t e d from t h e a b s o r p t i o n s p e c t r a a f t e r doping i n o r d e r t o a l l o w a q u a n t i t a t i v e comparison of t h e s e s h a r p f e a t u r e s . These c u r v e s a r e p l o t t e d on t h e same o r d i n a t e s c a l e b u t s c a l e d a s shown. Fig. ( 3 )
r e v e a l s two i m p o r t a n t p o i n t s about t h e s e s h a r p dopant induced a b s o r p t i o n s . The s h a r p a b s o r p t i o n band a r e n o t l i m i t e d t o t h e two observed i n t h e low r e s o l u t i o n d a t a of Fig (2). A t l e a s t f o u r uniformly spaced s h a r p a b s o r p t i o n bands a p p e a r t o be p r e s e n t i n t h e c u r v e which c o r r e s p o n d s t o a dopant c o n c e n t r a t i o n of 2 0.4%. We n o t e t h a t t h e f i r s t two a b s o r p t i o n s a r e w e l l i n s i d e 2A3d = 1.5 eV. The
semiconducting gap 2A3d, d e f i n e d a s where t h e g e n e r a t i o n of f r e e c a r r i e s o c c u r s , 115,161 i s s m a l l e r t h a n 2 4 because of t h e i n t e r c h a i n coupling. Secondly, t h e s e s t r u c t u r e a p p e a r t o s t a y a s s h a r p a t a l l c o n c e n t r a t i o n s , t h e r e b y p e r m i t t i n g a q u a n t i t a t i v e e v a l u a t i o n of t h e i r a b s o l u t e i n t e n s i t y by simply s u b t r a c t i n g a smooth
background a s done i n Fig (3). D e t a i l e d s t u d y of t h i s behavior shows t h a t t h e i r maximum i n t e n s i t y o c c u r s n e a r y = 0.01 and t h e y a r e n o t o b s e r v a b l e a t y
5
0.04/lo/.
lhis u n u s u a l n o n l i n e a r dependence of t h e i n t e n s i t y w i t h dopant c o n c e n t r a t i o n i n d i c a t e s t h a t t h e s e s h a r p peaks a r e n o t a n a r t i f a c t of a dopant induced modulation of s h a r p s t r u c t u r e s on t h e band edge; i.e., a B u r s t e i n s h i f t of t h e band edge due t o t h e e l e c t r i c f i e l d of t h e added charged species.1171 We, however, n o t e t h a t t h e s h a r p s t r u c t u r e on t h e band edge of trans-(CH)x ( s e e i n s e t t o Fig. 2) can be accounted f o r by t h e s m a l l amount I161 of a c c i d e n t a l doping of t h e polymer d u r i n g t h e s y n t h e s i s .The sharp absorption at 1.47 eV results in photogeneration of free carriers. This conclusion is the result of our parallel photoconductivity experiments carried out as a function of chemical doping and compensation. Fig.
(4)
shows the spectral dependence of the photoconductivity in E-(CH)~, obtained in a manner similarto the results reported previously 1181. The observation of primary interest here is the presence of a rather sharp peak in the photo-response of trans-(CH) at
X
the same energy as the sharp additional absorptions discussed earlier. The size of this sharp peak relative to the smoothly rising background is sample dependent, and can be varied upon doping or compensation of the sample as shown in Fig.
(4).
-
t+ AS-GROWN
I- 2 5 W (L
0.5 1.0 1.5 2.0 2.5
a
E (eV)Fig.
4
Photoconductivity of (+) as-grown =-(CH), and (x) after compensation with ammonium.111. DISCUSSION
The in situ optical studies during electrochemical doping provide detailed quantitative information on the absorption spectra of the soliton and polaron excitations in trans-(CH)
.
First, the main dopant induced absorption band near mid-gap is a direct evidence for the proposal that doping of trans-(CH)X
primarily proceeds through formation of charged solitons (see Fig. 1). This absorption corresponds to the transition between the soliton mid-gap level and either the conduction or the valence band. Since the exact value of the dopant concentration is determined in these experiments, detailed quantitative comparison with the theoretical predictions of the soliton model can be carried out. Using the results from Fig. ( 2 ) and Table (1) one estimates E, /a
-
6+
2 in goodagreement with the parameters of the 1-d coupled electron lattice model used to characterize the soliton excitation in trans-(CH) 12-41.
X
Second, the characteristic features of the sharp additional absorption that we have observed can be understood if we assume that injection of a single charge onto a tran~-(CH)~ chain results in formation of a large 1-d polaron distortion. On the experimental side, the sharpness of the additional absorption is a strong
indication that it originates from a transition between two localized levels inside
t h e gap. The f a c t t h a t t h e t r a n s i t i o n i s i n d u c e d upon d o p i n g i n d i c a t e s t h a t t h e two l o c a l i z e d l e v e l s a r e r e l a t e d t o a c h a r g e d e l e c t r o n i c s t a t e . F i n a l l y ,
d i s a p p e a r a n c e of t h i s s h a r p a b s o r p t i o n a t h i g h e r d o p i n g l e v e l s ( a few p e r c e n t ) i s i n d i c a t i v e o f t h e m e t a s t a b i l i t y of i t s a s s o c i a t e d e l e c t r o n i c s t a t e . On t h e t h e o r e t i c a l s i d e , a s s o c i a t e d w i t h t h e l a r g e 1-d p o l a r o n d i s t o r t i o n t h e r e a r e
two
l o c a l i z e d s t a t e s p u l l e d i n t o t h e gap from t h e c o n d u c t i o n and v a l e n c e bands. Due t o t h e p r e s e n c e of t h e b r o k e n symmetry d e g e n e r a t e ground s t a t e , a p o l a r o n i n
trans-(CH) i s a m e t a s t a b l e e x c i t e d s t a t e w i t h a p a i r o f p o l a r o n s e v e n t u a l l y
X
d e c a y i n g i n t o t h e l o w e r e n e r g y s t a t e o f a c h a r g e d s o l i t o n - a n t i s o l i t o n p a i r ( b u t s e e t h e d i s c u s s i o n of r e c o m b i n a t i o n b a r r i e r below). F i n a l l y , r e c e n t c a l c u l a t i o n s i n d i c a t e t h a t t h e t o t a l s t r e n g t h o f t h e o p t i c a l t r a n s i t i o n between t h e s e two l o c a l i z e d s t a t e s i s enhanced by more t h a n a n o r d e r of magnitude o v e r t h e t r a n s i t i o n s between t h e band s t a t e s , and t h e & - f u n c t i o n c h a r a c t e r of t h i s t r a n s i t i o n i m p l i e s t h a t i t s h o u l d be v e r y s h a r p and o v s e r v a b l e e v e n a t e x t r e m e l y low c o n c e n t r a t i o n s . Thus, t h e s h a r p a d d i t i o n a l a b s o r p t i o n a t - 1 . 5 eV i s
i n t e r p r e t e d a s t h e s i g n a t u r e of p o l a r o n f o r m a t i o n i n t r a n s - ( C H ) x and r e s u l t s from t h e t r a n s i t i o n between t h e two p o l a r o n bound s t a t e s i n s i d e t h e gap.
The s h a r p a b s o r p t i o n p e a k s d e t a i l e d i n F i g . ( 3 ) and t h e s h a r p peak i n t h e p h o t o r e s p o n s e of t r a n ~ - ( C H ) ~ ( s e e Fig. 4) a r e n o t a b s o r p t i o n due t o e x c i t o n f o r m a t i o n which u s u a l l y a p p e a r s below t h e o n s e t of t h e i n t e r b a n d a b s o r p t i o n . T h i s f o l l o w s s i n c e e x c i t o n s a r e a n i n t r i n s i c f e a t u r e of t h e e l e c t r o n i c s t r u c t u r e and a r e t h e r e f o r e e x p e c t e d t o h a v e a s p e c i f i c a b s o r p t i o n c r o s s s e c t i o n . We f i n d , however, t h a t t h e i n t e n s i t y of t h e s h a r p s t r u c t u r e c a n be v a r i e d by d o p i n g and compensation i n d i c a t i n g t h a t i t i s r e l a t e d t o a c h a r g e d e l e c t r o n i c s t a t e . Thus, c o n t r a r y t o a p r e v i o u s a s s e r t i o n , /15/ t h e peak i n t h e p h o t o r e s p o n s e d o e s n o t a r i s e from t h e t h e r m a l d i s s o c i a t i o n o f e x c i t o n s . The o b s e r v a t i o n t h a t t h e s h a r p a d d i t i o n a l a b s o r p t i o n l e a d s t o t h e g e n e r a t i o n of f r e e c a r r i e r s i s i n t e r p r e t e d t o be a r e s u l t o f t h e p r e s e n c e o f p o l a r o n s i n t h e as-grown f i l m s . F i r s t , t h e peak i n t h e
p h o t o r e s p o n s e can be quenched by compensation ( s e e Fig. 4 ) . Second, t h e t r a n s i t i o n between t h e two l e v e l s l e a v e s t h e p o l a r o n i n a n e x c i t e d s t a t e which by e n e r g e t i c c o n s i d e r a t i o n s i s u n s t a b l e t o decay i n t o a s o l i t o n - a n t i s o l i t o n p a i r (p'
+
hv +s'+
S o ) . S i n c e t h e r e a r e c l e a r i n d i c a t i o n s t h a t s o l i t o n s a r e t h e p h o t o g e n e r a t e d c a r r i e r s i n trans-(CH) / 5 , 1 6 / , t h e s h a r p p o l a r o n a b s o r p t i o n t h u s s e n s i t i z e s t h e p h o t o r e s p o n s e of t r a n s - ( C H ) i n a n a r r o w band c e n t e r e d n e a r 1 . 5 eV.
The c a l c u l a t i o n f o r o p t i c a l a b s o r p t i o n i n v o l v i n g p o l a r o n l o c a l i z e d l e v e l s c o n s i d e r s t h e t r a n s i t i o n s a s p u r e l y e l e c t r o n i c /10,13/. W i t h i n t h i s a p p r o x i m a t i o n phonon a s s i s t e d t r a n s i t i o n s a r e i g n o r e d . However, i n t h e p r e s e n c e o f t h e s i z e a b l e e l e c t r o n - p h o n o n c o u p l i n g i n (CH)x t r a n s i t i o n s between t h e two l o c a l i z e d l e v e l s a r e d e t e r m i n e d by a c o m b i n a t i o n of t h e e l e c t r o n i c and phonon c o o r d i n a t e s . A s a
r e s u l t , t h e a b s o r p t i o n s p e c t r u m o f t r a n s i t i o n s b e t w e e n 5 - and
<+
l e v e l s i s e x p e c t e d t o c o n s i s t of a s e r i e s o f s h a r p b a n d s , a ( w ) , s e p a r a t e d by a n i n t e g r a lv, 0
m u l t i p l e ( v ) of t h e o p t i c a l phonon e n e r g y (5 w ) from t h e p u r e l y e l e c t r o n i c a b s o r p t i o n , i . e . , a o , o ( u ) . T h e s e s i d e b a n d s a r e d u e t o t r a n s i t i o n s i n w h i c h t h e f i n a l s t a t e is l e f t i n a n e x c i t e d v i b r a t i o n a l s t a t e . T h i s i n d e e d a p p e a r s t o be t h e c a s e f o r t h e t r a n s i t i o n between t h e t v o l o c a l i z e d p o l a r o n l e v e l s . A s d e t a i l e d i n F i g . ( 3 ) , t h e r e a r e a t l e a s t f o u r a d d i t i o n a l a b s o r p t i o n b a n d s s e p a r a t e d by 0.13 eV ( 1 0 3 0 cm -1 ) from e a c h o t h e r . T h i s s e p a r a t i o n i s c l o s e t o t h e l o w e s t o p t i c a l phonon (A mode) f r e q u e n c y of t h e u n p e r t u r b e d t r a n s - ( C H ) x . As a r e s u l t t h e
P
s t r o n g e s t a b s o r p t i o n band a t 1.47 eV i s n o t a o S o ( w ) .
I n g e n e r a l t h e e n v e l o p e which d e t e r m i n e s t h e i n t e n s i t y o f t h e v i b r o n i c a (,,,) V ? O
a b s o r p t i o n b a n d s d e p e n d s on t h e d i f f e r e n c e i n t h e c h a r g e d e n s i t y v a v e p a t t e r n i n t h e e l e c t r o n i c g r o u n d s t a t e a n d e x c i t e d s t a t e i n a c c o r d a n c e w i t h t h e Prank-Condon p r i n c i p l e . S i n c e t h e t r a n s i t i o n a 2 ( s e e F i g . 1 ) i n v o l v e s o n e e l e c t r o n o u t o f t h r e e , t h e concommitant c h a n g e i n t h e c h a r g e d e n s i t y p a t t e r n i s e x p e c t e d t o be l a r g e i.e., t h e s e t r a n s i t i o n s f a l l i n t h e s t r o n g c o u p l i n g regime
/lo/.
Due t o t h e l i m i t e d number o f t h e o b s e r v e d v i b r o n i c b a n d s we must r e l y o n o t h e r r e s u l t s t o a s s i g n t h e U ~ , ~ ( W ) a b s o r p t i o n . We n o t e t h a t from t h e r e c e n t e l e c t r o c h e m i c a l v o l t a g e s p e c t r o s c o p y e x p e r i m e n t s 1 1 9 1 , t h e d i f f e r e n c e b e t w e e n t h e t h r e s h o l d f o ri n j e c t i o n o f a n e g a t i v e and p o s i t i v e c h a r g e upon i n i t i a l d o p i n g is 1.35 eV. S i n c e t h e c h a n g e i n j e c t i o n p r o c e s s r e q u i r e s m a t c h i n g o f a n e l e c t r o n i c l e v e l i n t h e
polymer a n d t h e Permi l e v e l i n t h e e l e c t r o d e , t h i s d i f f e r e n c e i n v o l t a g e t h r e s h o l d s d e t e r m i n e t h e d i f f e r e n c e between t h e p o s i t i o n o f 5+ and 5- l e v e l s ( s e e F i g . 1 ) . Thus t h e z e r o t h o r d e r a b s o r p t i o n band i s t h e s t r u c t u r e n e a r 1.33 eV and t h e s t r o n g band a t 1.47 eV i s a (w) a s i d e n t i f i e d i n F i g . ( 3 ) . S i n c e w i t h i n t h e s i n g l e
O , O
e l e c t r o n - l a t t i c e r e p r e s e n t a t i o n o f trans-(CH)
,
p o l a r o n s t a t e s a r e s i t u a t e d a t+
~ ~ / d F f r o m t h e g a p c e n t e r t h e l - d g a p c a n be e s t i m a t e d t o be 2 Ao:1.9 e V . T h i s i s i n good a g r e e m e n t v i t h t h e r e s u l t o b t a i n e d from t h e a n a l y s i s o f t h e p r e s s u r e
d e p e n d e n c e of t h e a b s o r p t i o n e d g e 1201.
The d e c a y o f a p a i r o f p o l a r o n s o n a t r a n s - ( C H ) c h a i n i n t o t h e more s t a b l e
s o l i t o n - a n t i s o l i t o n p a i r i s p o s s i b l e o n l y i f a p a i r of p o l a r o n s on a c h a i n a r e f r e e t o g e t c l o s e enough f o r a s u b s t a n t i a l o v e r l a p o f t h e i r wave f u n c t i o n s . Such a c a s e can happen i f we p h o t o g e n e r a t e a m o b i l e p a i r o r i n j e c t them t h r o u g h a t u n n e l b a r r i e r . I n o u r e l e c t r o c h e m i c a l i n j e c t i o n e x p e r i m e n t s , t h a t i s n o t n e c e s s a r i l y t h e c a s e b e c a u s e a p o l a r o n is bound t o t h e d o p a n t s p e c i e s o f o p p o s i t e c h a r g e by a r e l a t i v e l y l a r g e b i n d i n g p o t e n t i a l o f t h e o r d e r o f 0.3 eV. C o n s e q u e n t l y ,
n e g l e c t i n g d i f f u s i o n o f t h e d o p a n t s p e c i e s , t h e r e i s a b a r r i e r f o r r e c o m b i n a t i o n o f a p a i r o f p o l a r o n s f a r a p a r t , e v e n i f t h e y a r e on t h e
same
c h a i n . One c a n e n v i s i o n t h i s b a r r i e r i n t h e c a s e of two f a r a p a r t bound p o l a r o n s by t h e f o l l o w i n g d e s c r i p t i o n : S i n c e a P s t a t e c a n be c o n s i d e r e d a s t h e bound s t a t e o f a S ' a n d S os o l i t o n - a n t i s o l i t o n p a i r ( s e e F i g . I ) , t h e b a r r i e r a r i s e s from t h e s e p a r a t i o n of t h e bound p a i r i n t o a two bound S 'and two f r e e S o which can recombine by moving c l o s e t o each o t h e r 1181. The e n e r g y r e q u i r e d f o r t h e f o r m a t i o n of t h i s
i n t e r m e d i a t e s t a t e ( 2 ~ ' -2s'
+
2s') i s t h e d i f f e r e n c e between t h e e n e r g y of f o u r i s o l a t e d s o l i t o n s ( 4 x 2Ao/n) l e s s t h a t of two i s o l a t e d p o l a r o n s ( 2 x 0 . 9 ~ ). A s a r e s u l t two i s o l a t e d p o l a r o n s would n o t r e a d i l y recombine a t room t e m p e r a t u r e . When two p o l a r o n s g e t c l o s e t o each o t h e r t h e b a r r i e r i s lowered due t o t h e i r o v e r l a p . Bredas e t a 1 / 8 / show t h a t t h e b a r r i e r s f o r r e c o m b i n a t i o n d i s a p p e a r s i f two p o l a r o n s which a r e bound t o t h e i r d o p a n t s a r e s e p a r a t e d by l e s s t h a n-
25s i t e s ; i - e . , i f t h e a v e r a g e dopant c o n c e n t r a t i o n i s l a r g e r t h a n y z 4%. T h i s i s c o n s i s t e n t w i t h o u r e x p e r i m e n t a l r e s u l t s
/ l o / .
At d i l u t e c o n c e n t r a t i o n s , t h e t o t a l number of p o l a r o n s i n c r e a s e s w i t h d o p i n g , a l t h o u g h t h e r a t i o of p o l a r o n s t os o l i t o n s i s d e c r e a s i n g . Thus, w h i l e r e c o m b i n a t i o n t o form s o l i t o n p a i r s i s t h e overwhelmingly dominate p r o c e s s , enough s i n g l e i n j e c t e d c h a r g e s remain t o i n c r e a s e t h e t o t a l number of p o l a r o n s . A t t h e maximum of p o l a r o n c o n c e n t r a t i o n , y
'
0.01,f o r e a c h two p o l a r o n s i n j e c t e d one p o l a r o n p a i r c o n v e r t s t o a s o l i t o n p a i r l e a v i n g t h e t o t a l number of p o l a r o n s c o n s t a n t . For h i g h e r c o n c e n t r a t i o n , t h e t o t a l number o f p o l a r o n s d e c r e a s e s , r e a c h i n g z e r o , by y 2 0 . 0 4 .
The d e t a i l e d q u a n t i t a t i v e i n t e r p r e t a t i o n of t h e a b s o r p t i o n s p e c t r a l p r e s e n t e d above s u g g e s t s t h a t p o l a r o n s a s w e l l a s s o l i t o n s a r e formed i n trans-(CH)x. S i n c e t h e
p o l a r o n c h a r g e - s p i n r e l a t i o n i s s t a n d a r d ( c h a r g e =
+
e and s p i n = 1 / 2 ) i n p r i n c i p l e one s h o u l d be a b l e t o g e n e r a t e u n p a i r e d s p i n s t h r o u g h p o l a r o n f o r m a t i o n a t d i l u t e doping. However, t h e l a r g e c o n c e n t r a t i o n of So s t a t e s i n as-grown f i l m s ( a few 100 ppm) overshadows d e t e c t i o n of p o l a r o n s ( a few 1 0 ppm) by magnetic measurements. On t h e o t h e r hand, t o quench t h e s p i n of a s u b s t a n t i a l f r a c t i o n of n e u t r a l s o l i t o n s ( S o+
e S ' j we r i s k t h e m u t u a l d e s t r u c t i o n of t h e p o l a r o n s . Thus d e t e c t i o n of t h e s p i n of a p o l a r o n i n trans-(CH)x r e q u i r e a d e l i c a t e b a l a n c e . In p r e l i m i n a r y e x p e r i m e n t s , u s i n g homogeneously and s l o w l y doped samples 1 2 1 / w i t h AsF5 a s dopant we have been a b l e t o c o n t r o l t h e b a l a n c e between t h e c o n c e n t r a t i o n of p o l a r o n s and n e u t r a l s s o l i t o n s and d e t e c t e d t h e s i g n a t u r e s of p o l a r o n s p i n . I n a s e r i e s of e x p e r i m e n t s t o be d e t a i l e d e l s e w h e r e we f i n d two d i s t i n g u i s h a b l e ESR s i g n a l s f o r s a m p l e s doped t o y 2 0.2%. The two ESR l i n e s have t h e same g-value and a r e s e p a r a b l e a t low t e m p e r a t u r e s ( 100 K ) due t o t h e d i f f e r e n c e i n t h e t e m p e r a t u r e dependence of t h e i r l i n e w i d t h . The f a c t t h a t t h e y c o r r e s p o n d t o two s e p a r a t e s p i n s p e c i e s i s a l s o s e e n i n t h e d i f f e r e n t v a l u e s of t h e i r e l e c t r o n i c TI. Ourassignment of t h e second ESR l i n e t o t h e s p i n of p o l a r o n s r e l i e s on t h e o b s e r v a t i o n t h a t o n l y a t a n i n t e r m e d i a t e c o n c e n t r a t i o n of y
-
0.02% have we o b s e r v e d two s e p a r a b l e l i n e s . N e i t h e r i n t h e undoped samples nor i n samples doped i n t h e same manner t o a somewhat h i g h e r l e v e l of Y 7 1% c a n two l i n e s be d e t e c t e d . T h i s o b s e r v a t i o n i s c o n s i s t e n t w i t h t h e m e t a s t a b i l i t y of a p a i r of p o l a r o n s and t h ed i a m a g n e t i c n a t u r e o f t h e c h a r g e d s o l i t o n - a n t i s o l i t o n p a i r i n t o which t h e y d e c a y .
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