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Optical transition to the Fermi level in NaxWO3
Volume 38A, n u m b e r 7
PHYSICS
OPTICAL
TRANSITION
TO
LETTERS
THE
27 M a r c h 1972
FERMI
LEVEL
IN
NaxWO
3
G. G I U L I A N I , A. G U S T I N E T T I a n d A. S T E L L A Istituto di Fisica dell'Universit& di Pavia, Gruppo Nazionale di Struttura della Materia del Consiglio Nazionale delle R i c e r c h e , Pavia, Italy Received 4 J a n u a r y 1972 Evidence is given of an optical t r a n s i t i o n to the F e r m i level in metallic NaxWO 3. The t r a n s i t i o n energy depends on the s t o i c h i o m e t r i c index x. The data allow to evaluate an average m *.
The sodium tungsten bronzes are non-stoichiometric compounds, having the basic p e r o v s k i t e s t r u c t u r e ABO3. T h e s t a t i c d i e l e c t r i c a n d o p t i c a l p r o p e r t i e s a r e g o v e r n e d b y t h e BO 6 o c t a h e d r o n [1]. In t a b l e 1 t h e m a i n s t r u c t u r a l , electrical and optical data presently known, conc e r n i n g t h e s e c o m p o u n d s , a r e l i s t e d [2,3]. In t h i s l e t t e r we r e p o r t on s o m e e l e c t r o r e f l e c tance results, obtained at room temperature, using the electrolyte technique, which give evid e n c e of a n o p t i c a l t r a n s i t i o n to t h e F e r m i l e v e l in metallic bronzes. Such a transition can be d e t e c t e d a s a c o n s e q u e n c e of a b a n d p o p u l a t i o n e f f e c t , s i m i l a r l y to w h a t w a s p r e v i o u s l y o b s e r v e d i n d e g e n e r a t e s e m i c o n d u c t o r s [4,5]. R e f l e c t a n c e m e a s u r e m e n t s h a v e s h o w n no r e l e v a n t s t r u c t u r e on t h e l o w e r e n e r g y s i d e of t h e m i n i m u m in t h e m e t a l l i c s a m p l e s , o r at e n e r g i e s l o w e r t h a n 2.8 eV in t h e o t h e r s a m p l e s . In t h e e l e c t r o r e f l e c tance spectra it has been possible to observe the e x i s t e n c e of a s t r u c t u r e in t h r e e s a m p l e s w i t h x = 0 . 0 7 , 0 . 5 1 7 , 0.72 a t ~ 1 eV, 1.35 eV a n d 1.6 eV, r e s p e c t i v e l y . T h i s p e a k m o v e s to h i g h e r energies as x increases. The most important f e a t u r e s of t h e e l e c t r o r e f l e c t a n c e r e s p o n s e a r e the following: 4 5
%
o -10 -15 .20
•;
scale chang%~e~'L.
p,.e -4b -e..|
2%
e'e~l.
IL; ~
2 1=
°°
.4
I; Ii I: 1
=
~
t
3
eV
Fig. 1. E l e c t r o r e f l e c t a n c e of the semiconducting sample. The e x t e r n a l d.c. voltage was z e r o and the a.c. voltage w a s 1 volt peak to peak.
0f
---Na~WO 3 x=0.72
i i
..-_._1
l
Fig. 2. E1ectroreflectance in the two metallic samples at the s a m e conditions specified in fig. 1.
i) In t h e b e s t c a s e s o b s e r v e d , A R / R i n c o r r e s p o n d e n c e of t h e l o w - e n e r g y p e a k w a s e v e n two o r d e r s of m a g n i t u d e h i g h e r in t h e s e m i c o n d u c t o r t h a n in t h e m e t a l s a n d r e a c h e d v a l u e s a s h i g h a s 0.2 (fig. 1). We k n o w f r o m t h e l i t e r a t u r e t h a t Es .~ 103 in W O 3 1 6 ]. If e s r e m a i n s h i g h w h e n d e a l i n g w i t h s m a l l v a l u e s of x, we m a y e x p e c t a n e f f e c t due to l a t t i c e p o l a r i z a t i o n , w h i c h i s r e s p o n s i b l e f o r t h e l a r g e s i g n a l s o b s e r v e d , a s in t h e c a s e of K T a O 3 [7]. ii) In m e t a l l i c b r o n z e s , a p e a k s h o w s up at 1.35 eV a n d a t ~ 1.6 eV in t h e s a m p l e s w i t h x = 0.517 a n d x = 0 . 7 2 , r e s p e c t i v e l y . As s h o w n in fig. 2 t h e s e p e a k s a r e o n t h e l o w e r e n e r g y s i d e of t h e s t r o n g e l e c t r o r e f l e c t a n c e p e a k s o b s e r v e d in c o r r e s p o n d e n c e of t h e r e f l e c t i v i t y m i n i m a due to p l a s m a o s c i l l a t i o n s , a l r e a d y r e p o r t e d f o r o t h e r m e t a l s [8]. W e r e c a l l t h a t a s t r u c t u r e at 515
Volume 38A, number 7
Lattice structure x ~ 0.35 tetragonal
x > 0.35 cubic
PHYSICS
27 March 1972
Table 1 Structural, electrical and optical properties of NaxWO3 Y Electrical I Optical properties ! properties
f
I
x =0
x =0
insulator
RT optical gap = 2.8 eV
0,- x< 0.25 semiconductor
0 < x< 0.25 under investigation
0.25 ~: x < 1 metallic
0.25 : x ~ 1 MOp. > 2 eV i n c r e a s i n g function of x
a b o u t 1.5 eV h a s b e e n p r e v i o u s l y o b s e r v e d in a m e t a l l i c s a m p l e of N a x W O 3 with x= 0.6, u s i n g a d i f f e r e n t t e c h n i q u e [9]. W h e n d e a l i n g with m e t a l s , t h e p e n e t r a t i o n d e p t h of t h e e l e c t r i c field is much s m a l l e r than the p e n e t r a t i o n depth of l i g h t . H o w e v e r , t h e e l e c t r o r e f l e c t a n c e s i g n a l s a p p e a r to b e r e l a t e d to t h e i n t r i n s i c o p t i c a l p r o p e r t i e s of t h e c r y s t a l s i n v e s t i g a t e d . P r o s t a k and Hansen have shown that the electroreflectance p e a k in c o r r e s p o n d e n c e of t h e r e f l e c t i v i t y m i n i m u m c o u l d b e fully e x p l a i n e d a s s u m i n g a s h i f t of t h e p l a s m a f r e q u e n c y due to a s u i t a b l e c h a n g e of t h e e l e c t r o n c o n c e n t r a t i o n in a v e r y t h i n l a y e r at t h e s u r f a c e [10]. iii) T h e e l e c t r o r e f l e c t a n c e l o w - e n e r g y p e a k s o b s e r v e d in b o t h m e t a l l i c s a m p l e s e x h i b i t e d a b l u e s h i f t , of the o r d e r of 0.1 eV, when the e x t e r n a l b i a s w a s v a r i e d f r o m - 0 . 5 V to + 0 . 5 V. which is about the flat band position. M o r e o v e r , t h e s h i f t s h o w e d no i n v e r s i o n when c r o s s i n g t h e f l a t b a n d p o s i t i o n in t h e b i a s s c a l e . A c c o r d i n g to s o m e r e c e n t w o r k m a d e on d e g e n e r a t e s e m i c o n d u c t o r s [4,5], s u c h a b e h a v i o u r is r e l a t e d to t h e f a c t t h a t t h e F e r m i l e v e l i s t h e f i n a l l e v e l of t h e t r a n s i t i o n . In o u r c a s e t h i s i n t e r p r e t a t i o n i s in a g r e e m e n t with t h e f a c t t h a t , f r o m the g e n e r a l l y a c c e p t e d viewpoint [1-3,11] that the l o w e r e n e r g y band s t r u c t u r e d o e s not change when x c h a n g e s , t h e F e r m i l e v e l a p p e a r s to b e i n v o l v e d in t h e t r a n s i t i o n a s t h e o n l y p l a u s i b l e c a u s e of the e n e r g y s h i f t of t h e p e a k a s a f u n c t i o n of x. iv) T h e l i n e s h a p e of o u r l o w - e n e r g y s t r u c t u r e s i s q u a l i t a t i v e l y s i m i l a r to t h e one of t h e p e a k s due t o b a n d p o p u l a t i o n e f f e c t s in d e g e n e r a t e s e m i c o n ductors. If it i s t r u e t h a t t h e e n e r g y gap of t h e c o m p o u n d s h a v i n g the ABO3 s t r u c t u r e i s ~ 3 eV, we a r e c l e a r l y dealing with a t r a n s i t i o n f r o m a l o c a l i z e d l e v e l o r f r o m t h e c o n d u c t i o n b a n d to t h e Fermi level. 516
LETTERS
O u r r e s u l t s m a y be u s e d to e v a l u a t e the d e n s i t y of s t a t e s e f f e c t i v e m a s s , s u p p o s e d to b e c o n s t a n t b e t w e e n x = 0 . 5 1 7 a n d x = 0 . 7 2 . We c a n write AE F =
(3//8n)2/3 (h2/2rn ,) ~n2'2/3 _ nl"2/3,p
(1)
w h e r e t h e e x p e r i m e n t a l v a l u e 0.25 eV is s u b s t i t u t e d f o r E F a n d the v a l u e s f o r n 2 a n d n 1 a r e t a k e n f r o m the l i t e r a t u r e [12]. In t h i s way one g e t s rn* ~ 1 . 1 t o o , w h i c h c a n b e c o m p a r e d w i t h t h e v a l u e s , r a n g i n g f r o m 1 rn o to 3 rn o, r e p o r t e d in r e f . [13].
R ere ten ces [1] M. Di Domenico J r . and S. tt. Wemple, J. Appl. Phys. 40 (1969) 720. [2] F. Consadori and A. Stella, L e t t e r e al Nuovo Cimento, Serie I, 3 (1970) 600. [3] J. Feinleib, W. J. Scouler and A. F e r r e t t i , Phys. Rev. 165 (1968) 765. [4] R. Glosser and B. 0. Seraphin, Phys. Rev. 187 (1969) 1021. [5] R. G l o s s e r , J. P. F i s h e r and B. O. Seraphin, Phys. Rev. 1B (1970) 1607. [6] B . T . M a t t h i a s , Phys. Rev. 76 (1949) 430. [7] A. Frova and P. J. Boddy, Phys. Rev. L e t t e r s 16 (1966) 688; Phys. Rev. 153 (1967) 606. [8] J. Feinleib, Phys. Rev. L e t t e r s 16 (1966) 1200. [9] P. G. Dickens, R. M. Quilliam and M. S. Whittingam, Mat. Res. Bull. 3 (1968) 941, P e r g a m o n P r e s s , Inc. printed in the U. S. [10] A. P r o s t a k and W. N. Hansen, Phys. Rev. 160 (1967) 600; 174 (1968) 500. [11] A. H. Kahn and A. J. Leyendecker, Phys. Rev. 135 (1964) A1321. [12] W.R. Garner and G. C. Danielson, Phys. Rev. 93
i(1954) 46.
[13] B. L. Crowder and M. J. Sienko, J. Chem. Phys. 38 (1963) 1576.
PHYSICS
OPTICAL
TRANSITION
TO
LETTERS
THE
27 M a r c h 1972
FERMI
LEVEL
IN
NaxWO
3
G. G I U L I A N I , A. G U S T I N E T T I a n d A. S T E L L A Istituto di Fisica dell'Universit& di Pavia, Gruppo Nazionale di Struttura della Materia del Consiglio Nazionale delle R i c e r c h e , Pavia, Italy Received 4 J a n u a r y 1972 Evidence is given of an optical t r a n s i t i o n to the F e r m i level in metallic NaxWO 3. The t r a n s i t i o n energy depends on the s t o i c h i o m e t r i c index x. The data allow to evaluate an average m *.
The sodium tungsten bronzes are non-stoichiometric compounds, having the basic p e r o v s k i t e s t r u c t u r e ABO3. T h e s t a t i c d i e l e c t r i c a n d o p t i c a l p r o p e r t i e s a r e g o v e r n e d b y t h e BO 6 o c t a h e d r o n [1]. In t a b l e 1 t h e m a i n s t r u c t u r a l , electrical and optical data presently known, conc e r n i n g t h e s e c o m p o u n d s , a r e l i s t e d [2,3]. In t h i s l e t t e r we r e p o r t on s o m e e l e c t r o r e f l e c tance results, obtained at room temperature, using the electrolyte technique, which give evid e n c e of a n o p t i c a l t r a n s i t i o n to t h e F e r m i l e v e l in metallic bronzes. Such a transition can be d e t e c t e d a s a c o n s e q u e n c e of a b a n d p o p u l a t i o n e f f e c t , s i m i l a r l y to w h a t w a s p r e v i o u s l y o b s e r v e d i n d e g e n e r a t e s e m i c o n d u c t o r s [4,5]. R e f l e c t a n c e m e a s u r e m e n t s h a v e s h o w n no r e l e v a n t s t r u c t u r e on t h e l o w e r e n e r g y s i d e of t h e m i n i m u m in t h e m e t a l l i c s a m p l e s , o r at e n e r g i e s l o w e r t h a n 2.8 eV in t h e o t h e r s a m p l e s . In t h e e l e c t r o r e f l e c tance spectra it has been possible to observe the e x i s t e n c e of a s t r u c t u r e in t h r e e s a m p l e s w i t h x = 0 . 0 7 , 0 . 5 1 7 , 0.72 a t ~ 1 eV, 1.35 eV a n d 1.6 eV, r e s p e c t i v e l y . T h i s p e a k m o v e s to h i g h e r energies as x increases. The most important f e a t u r e s of t h e e l e c t r o r e f l e c t a n c e r e s p o n s e a r e the following: 4 5
%
o -10 -15 .20
•;
scale chang%~e~'L.
p,.e -4b -e..|
2%
e'e~l.
IL; ~
2 1=
°°
.4
I; Ii I: 1
=
~
t
3
eV
Fig. 1. E l e c t r o r e f l e c t a n c e of the semiconducting sample. The e x t e r n a l d.c. voltage was z e r o and the a.c. voltage w a s 1 volt peak to peak.
0f
---Na~WO 3 x=0.72
i i
..-_._1
l
Fig. 2. E1ectroreflectance in the two metallic samples at the s a m e conditions specified in fig. 1.
i) In t h e b e s t c a s e s o b s e r v e d , A R / R i n c o r r e s p o n d e n c e of t h e l o w - e n e r g y p e a k w a s e v e n two o r d e r s of m a g n i t u d e h i g h e r in t h e s e m i c o n d u c t o r t h a n in t h e m e t a l s a n d r e a c h e d v a l u e s a s h i g h a s 0.2 (fig. 1). We k n o w f r o m t h e l i t e r a t u r e t h a t Es .~ 103 in W O 3 1 6 ]. If e s r e m a i n s h i g h w h e n d e a l i n g w i t h s m a l l v a l u e s of x, we m a y e x p e c t a n e f f e c t due to l a t t i c e p o l a r i z a t i o n , w h i c h i s r e s p o n s i b l e f o r t h e l a r g e s i g n a l s o b s e r v e d , a s in t h e c a s e of K T a O 3 [7]. ii) In m e t a l l i c b r o n z e s , a p e a k s h o w s up at 1.35 eV a n d a t ~ 1.6 eV in t h e s a m p l e s w i t h x = 0.517 a n d x = 0 . 7 2 , r e s p e c t i v e l y . As s h o w n in fig. 2 t h e s e p e a k s a r e o n t h e l o w e r e n e r g y s i d e of t h e s t r o n g e l e c t r o r e f l e c t a n c e p e a k s o b s e r v e d in c o r r e s p o n d e n c e of t h e r e f l e c t i v i t y m i n i m a due to p l a s m a o s c i l l a t i o n s , a l r e a d y r e p o r t e d f o r o t h e r m e t a l s [8]. W e r e c a l l t h a t a s t r u c t u r e at 515
Volume 38A, number 7
Lattice structure x ~ 0.35 tetragonal
x > 0.35 cubic
PHYSICS
27 March 1972
Table 1 Structural, electrical and optical properties of NaxWO3 Y Electrical I Optical properties ! properties
f
I
x =0
x =0
insulator
RT optical gap = 2.8 eV
0,- x< 0.25 semiconductor
0 < x< 0.25 under investigation
0.25 ~: x < 1 metallic
0.25 : x ~ 1 MOp. > 2 eV i n c r e a s i n g function of x
a b o u t 1.5 eV h a s b e e n p r e v i o u s l y o b s e r v e d in a m e t a l l i c s a m p l e of N a x W O 3 with x= 0.6, u s i n g a d i f f e r e n t t e c h n i q u e [9]. W h e n d e a l i n g with m e t a l s , t h e p e n e t r a t i o n d e p t h of t h e e l e c t r i c field is much s m a l l e r than the p e n e t r a t i o n depth of l i g h t . H o w e v e r , t h e e l e c t r o r e f l e c t a n c e s i g n a l s a p p e a r to b e r e l a t e d to t h e i n t r i n s i c o p t i c a l p r o p e r t i e s of t h e c r y s t a l s i n v e s t i g a t e d . P r o s t a k and Hansen have shown that the electroreflectance p e a k in c o r r e s p o n d e n c e of t h e r e f l e c t i v i t y m i n i m u m c o u l d b e fully e x p l a i n e d a s s u m i n g a s h i f t of t h e p l a s m a f r e q u e n c y due to a s u i t a b l e c h a n g e of t h e e l e c t r o n c o n c e n t r a t i o n in a v e r y t h i n l a y e r at t h e s u r f a c e [10]. iii) T h e e l e c t r o r e f l e c t a n c e l o w - e n e r g y p e a k s o b s e r v e d in b o t h m e t a l l i c s a m p l e s e x h i b i t e d a b l u e s h i f t , of the o r d e r of 0.1 eV, when the e x t e r n a l b i a s w a s v a r i e d f r o m - 0 . 5 V to + 0 . 5 V. which is about the flat band position. M o r e o v e r , t h e s h i f t s h o w e d no i n v e r s i o n when c r o s s i n g t h e f l a t b a n d p o s i t i o n in t h e b i a s s c a l e . A c c o r d i n g to s o m e r e c e n t w o r k m a d e on d e g e n e r a t e s e m i c o n d u c t o r s [4,5], s u c h a b e h a v i o u r is r e l a t e d to t h e f a c t t h a t t h e F e r m i l e v e l i s t h e f i n a l l e v e l of t h e t r a n s i t i o n . In o u r c a s e t h i s i n t e r p r e t a t i o n i s in a g r e e m e n t with t h e f a c t t h a t , f r o m the g e n e r a l l y a c c e p t e d viewpoint [1-3,11] that the l o w e r e n e r g y band s t r u c t u r e d o e s not change when x c h a n g e s , t h e F e r m i l e v e l a p p e a r s to b e i n v o l v e d in t h e t r a n s i t i o n a s t h e o n l y p l a u s i b l e c a u s e of the e n e r g y s h i f t of t h e p e a k a s a f u n c t i o n of x. iv) T h e l i n e s h a p e of o u r l o w - e n e r g y s t r u c t u r e s i s q u a l i t a t i v e l y s i m i l a r to t h e one of t h e p e a k s due t o b a n d p o p u l a t i o n e f f e c t s in d e g e n e r a t e s e m i c o n ductors. If it i s t r u e t h a t t h e e n e r g y gap of t h e c o m p o u n d s h a v i n g the ABO3 s t r u c t u r e i s ~ 3 eV, we a r e c l e a r l y dealing with a t r a n s i t i o n f r o m a l o c a l i z e d l e v e l o r f r o m t h e c o n d u c t i o n b a n d to t h e Fermi level. 516
LETTERS
O u r r e s u l t s m a y be u s e d to e v a l u a t e the d e n s i t y of s t a t e s e f f e c t i v e m a s s , s u p p o s e d to b e c o n s t a n t b e t w e e n x = 0 . 5 1 7 a n d x = 0 . 7 2 . We c a n write AE F =
(3//8n)2/3 (h2/2rn ,) ~n2'2/3 _ nl"2/3,p
(1)
w h e r e t h e e x p e r i m e n t a l v a l u e 0.25 eV is s u b s t i t u t e d f o r E F a n d the v a l u e s f o r n 2 a n d n 1 a r e t a k e n f r o m the l i t e r a t u r e [12]. In t h i s way one g e t s rn* ~ 1 . 1 t o o , w h i c h c a n b e c o m p a r e d w i t h t h e v a l u e s , r a n g i n g f r o m 1 rn o to 3 rn o, r e p o r t e d in r e f . [13].
R ere ten ces [1] M. Di Domenico J r . and S. tt. Wemple, J. Appl. Phys. 40 (1969) 720. [2] F. Consadori and A. Stella, L e t t e r e al Nuovo Cimento, Serie I, 3 (1970) 600. [3] J. Feinleib, W. J. Scouler and A. F e r r e t t i , Phys. Rev. 165 (1968) 765. [4] R. Glosser and B. 0. Seraphin, Phys. Rev. 187 (1969) 1021. [5] R. G l o s s e r , J. P. F i s h e r and B. O. Seraphin, Phys. Rev. 1B (1970) 1607. [6] B . T . M a t t h i a s , Phys. Rev. 76 (1949) 430. [7] A. Frova and P. J. Boddy, Phys. Rev. L e t t e r s 16 (1966) 688; Phys. Rev. 153 (1967) 606. [8] J. Feinleib, Phys. Rev. L e t t e r s 16 (1966) 1200. [9] P. G. Dickens, R. M. Quilliam and M. S. Whittingam, Mat. Res. Bull. 3 (1968) 941, P e r g a m o n P r e s s , Inc. printed in the U. S. [10] A. P r o s t a k and W. N. Hansen, Phys. Rev. 160 (1967) 600; 174 (1968) 500. [11] A. H. Kahn and A. J. Leyendecker, Phys. Rev. 135 (1964) A1321. [12] W.R. Garner and G. C. Danielson, Phys. Rev. 93
i(1954) 46.
[13] B. L. Crowder and M. J. Sienko, J. Chem. Phys. 38 (1963) 1576.