- Email: [email protected]
Recombination effects on electron tunneling into superconducting lead
Volume 20, n u m b e r 4
PHYSICS
RECOMBINATION INTO
LETTERS
1March1966
EFFECTS ON ELECTRON SUPERCONDUCTING LEAD
TUNNELING *
S. M. K H A N N A a n d S. B. WOODS D e p a r t m e n t o f P h y s i c s , University of A l b e r t a , Edmonton, Canada
Received 24 J a n u a r y 1966
A new s t r u c t u r e c a u s e d by r e c o m b i n a t i o n p r o c e s s e s in the n o r m a l i z e d dynamic conductance of an a l u m i n u m - a l u m i n u m oxide-lead tunnel junction, as predicted e a r l i e r [1], has been o b s e r v e d at t e m p e r a t u r e s just below the superconducting t r a n s i t i o n t e m p e r a t u r e of lead.
S c a l a p i n o e t a l . [1] a n d S w i h a r t e t a l . [2] h a v e r e c e n t l y c a l c u l a t e d t h e e n e r g y d e p e n d e n c e of t h e energy gap parameter at non-zero temperatures for Pb which is a strong-coupling superconductor. They have used the same phonon distribution and Coulomb pseudo-potential as used by Schrieffer et a l . [3] w h i c h g a v e r e s u l t s t h a t a r e in g o o d a g r e e m e n t w i t h t u n n e l i n g e x p e r i m e n t s of R o w e l l e t a l . [4]. H o w e v e r , i n P b , S c a l a p i n o e t a l . [1] e s t i m a t e d t h e e l e c t r o n - p h o n o n c o u p l i n g p a r a m e t e r ot ~2 f o r l o n g i t u d i n a l p h o n o n s to b e d o u b l e t h e o t f o r t r a n s v e r s e p h o n o n s , w h e r e a s S c h r i e f f e r e t a l . [3] e m ployed the same coupling parameter for all phonons. S c a l a p i n o e t a l . [1] h a v e d i s c u s s e d t h e o c c u r r e n c e of a s e c o n d p e a k i n t h e e f f e c t i v e t u n n e l i n g d e n s i t y of s t a t e s of P b a t T ~ T c c a u s e d b y r e c o m bination effects. These processes are explained i n t e r m s of r e m o v a l of a n e l e c t r o n f r o m t h e n o r mal metal and a quasi-particle from the supercond u c t i n g P b a n d c r e a t i o n of a g r o u n d s t a t e p a i r i n P b w i t h e m i s s i o n of a p h o n o n . A t n o n - z e r o t e m p e r a t u r e s , t h e r e a r e a r e l a t i v e l y l a r g e n u m b e r of excited quasi-particles and there is a high density of s t a t e s a t t h e g a p e d g e i n P b . A n e l e c t r o n c a n b e injected from a normal metal into Pb across an insulating layer and can then combine with an excited quasi-particle and form a ground state pair. A p h o n o n i s e m i t t e d i n t h e p r o c e s s . B e c a u s e of h i g h d e n s i t y of s t a t e s a t t h e g a p e d g e a n d t h e r e q u i r e m e n t s of e n e r g y c o n s e r v a t i o n , t h i s p r o c e s s i s m o s t p r o b a b l e w h e n v + A o ( T ) = w ;~ w h e r e v i s t h e e n e r g y of t h e i n j e c t e d e l e c t r o n , Ao(T) i s t h e gap parameter at the gap edge at temperature T a n d w ~ i s t h e e n e r g y c o r r e s p o n d i n g to a p e a k in t h e p h o n o n d e n s i t y of s t a t e s . T h e s e r e c o m b i n a t i o n * This work was s u p p o r t e d in p a r t by the National R e s e a r c h Council of Canada.
p r o c e s s e s c a u s e a n e w n e g a t i v e p e a k in t h e i m a g i n a r y p a r t of t h e g a p p a r a m e t e r A 2 ( E , T) w h i c h i s e v e n t u a l l y r e f l e c t e d in t h e e f f e c t i v e t u n n e l i n g d e n s i t y of s t a t e s . T h e c o r r e s p o n d i n g s t r u c t u r e i n the normalized dynamic conductance ~ = (di/dv)s / (di/dv) n versus, v curve for a tunnel junction is, h o w e v e r , s u b j e c t to t h e r m a l s m e a r i n g . T h e y e s t i m a t e t h a t t h e m a x i m u m o b s e r v a b l e s t r u c t u r e due to r e c o m b i n a t i o n p r o c e s s e s s h o u l d o c c u r n e a r T / T c = 0.95 a r o u n d a n e n e r g y v = 3.9 m e V . Results are reported here for the measurement of a : v c h a r a c t e r i s t i c s of two A1 - AlxOy - P b s p e c i m e n s a t v a r i o u s t e m p e r a t u r e s c l o s e to T c for Pb. Each tunnel junction studied here was made by o x i d i z i n g t h e s u r f a c e o£ a n A1 f i l m t h a t h a d b e e n p r e p a r e d b y v a c u u m e v a p o r a t i o n . A c r o s s s t r i p of Pb was then deposited. All evaporations were
I
'
I
I I
,
I ?.
~
'
I
'
I 5
i
I 4
,
I
1.05
O"
1.00
,
V
I 5
,
I 6
,
(mV)
Fig. 1. E x p e r i m e n t a l r e s u l t s for the s p e c i m e n P b - 4 6 . A. T / T c = 0.97; B. Calculated c u r v e [1] at T / T c = 0.95.
335
Volume 20, number 4 '
I
PHYSICS
A
m
•
1.10
"° O-
1.05
I .00
i 0
l
LLIL
I
2
LLL $
4 V
LII 5
6
7
(mV)
Fig. 2. E x p e r i m e n t a l r e s u l t s for the s p e c i m e n Pb-47. T / T c = 0.89; B. T / T e = 0.96; C. T / T c = 0.98.
A.
s t a r t e d a t a p r e s s u r e of a b o u t 3 × 10 -5 m m of Hg. O x i d a t i o n t i m e w a s n e a r l y 1 m i n u t e at a b o u t 200 ° C. T h e (~ : v c h a r a c t e r i s t i c s f o r t h e s e s p e c i m e n s w e r e m e a s u r e d w i t h a c u r v e t r a c e r [5] w h i c h p e r mitted sensitive four terminal resistance measurem e n t s . The t e m p e r a t u r e s w e r e m e a s u r e d with a Ge r e s i s t a n c e t h e r m o m e t e r a n d a r e a c c u r a t e to b e t t e r t h a n one p e r c e n t . T c f o r P b f i l m in s p e c i m e n s P b - 4 6 a n d P b - 4 7 w a s f o u n d to b e r e s p e c t i v e l y 6 . 9 7 ° K a n d 6 . 3 2 ° K . T h e s e f i l m s h a d a b r o a d t r a n s i t i o n , p r o b a b l y due to n o n - u n i f o r m t h i c k n e s s a t the f i l m e d g e s . T h e s e m e a s u r e m e n t s i n d i c a t e t h a t the t r a n s i t i o n t e m p e -
336
1 M a r c h 1966
r a t u r e s of t h i n f i l m s of P b , like T a [6] f i l m s , a r e l o w e r t h a n t h a t of t h e bulk m a t e r i a l in c o n t r a s t to t h e t r a n s i t i o n t e m p e r a t u r e s of t h i n f i l m s of A1, In [7] a n d Sn [8] w h i c h a r e h i g h e r t h a n t h o s e of the c o r r e s p o n d i n g bulk m a t e r i a l s . F i g s . 1 and 2 i l l u s t r a t e t h e ~ : v c h a r a c t e r i s t i c s f o r t h e s p e c i m e n s P b - 4 6 a n d P b - 4 7 at d i f f e r e n t t e m p e r a t u r e s a n d the c a l c u l a t e d c u r v e [1] a t T / T c = 0 . 9 5 . T h e r e is g o o d a g r e e m e n t b e t w e e n t h e t h e o r e t i c a l a n d the e x p e r i m e n t a l l y o b s e r v e d c u r v e s . T h e d e c r e a s e in r e c o m b i n a t i o n r a t e a s the t e m p e r a t u r e w a s l o w e r e d i s e v i d e n t f r o m the d e c r e a s e in t h e f l a t p o r t i o n b e t w e e n the two p e a k s in the a : v c u r v e s . T h e a : v c u r v e f o r s p e c i m e n P b - 4 6 l i e s c l o s e r to the c a l c u l a t e d c u r v e t h a n the c u r v e s f o r s p e c i m e n P b - 4 7 . T h i s i s p r o b a b l y b e c a u s e P b - 4 6 w a s the t h i n n e r of the two s p e c i m e n s .
~ l , l , l ~ l ~ I r l
,
LETTERS
RefC~CnCCS 1. D. J. Scalapino, Y. Wada and J . C . S w i h a r t , Phys. Rev. L e t t e r s 14 (1965) 102. 2. J . C . S w i h a r t , D . J . S c a l a p i n o and Y.Wada, Phys. Rev. L e t t e r s 14 (1965) 106. 3. J . R . Schrieffer, D . J . Sealapino and J. W. Wilkins, Phys. Rev. L e t t e r s 10 (1963) 336. 4. J . M . R o w e l l , P . W . Anderson and D . E . T h o m a s , Phys. Rev. L e t t e r s 10 (1963) 334. 5. J . S . R o g e r s , J . G . A d l e r and S . B . W o o d s , Rev. Sci. I n s t r u m . 35 (1964) 208. 6. J . J . H a u s e r and H . C . T h e u e r e r , Rev. Mod. Phys. 36 (1964) 80. 7. R . D . C h a u d h a r i and J . B . B r o w n , Phys. Rev. 139 (1965) 1482. 8. M.Strongin, O . F . K a m m e r e r and A. Paskin, Phys. Rev. L e t t e r s 14 (1965) 949.
PHYSICS
RECOMBINATION INTO
LETTERS
1March1966
EFFECTS ON ELECTRON SUPERCONDUCTING LEAD
TUNNELING *
S. M. K H A N N A a n d S. B. WOODS D e p a r t m e n t o f P h y s i c s , University of A l b e r t a , Edmonton, Canada
Received 24 J a n u a r y 1966
A new s t r u c t u r e c a u s e d by r e c o m b i n a t i o n p r o c e s s e s in the n o r m a l i z e d dynamic conductance of an a l u m i n u m - a l u m i n u m oxide-lead tunnel junction, as predicted e a r l i e r [1], has been o b s e r v e d at t e m p e r a t u r e s just below the superconducting t r a n s i t i o n t e m p e r a t u r e of lead.
S c a l a p i n o e t a l . [1] a n d S w i h a r t e t a l . [2] h a v e r e c e n t l y c a l c u l a t e d t h e e n e r g y d e p e n d e n c e of t h e energy gap parameter at non-zero temperatures for Pb which is a strong-coupling superconductor. They have used the same phonon distribution and Coulomb pseudo-potential as used by Schrieffer et a l . [3] w h i c h g a v e r e s u l t s t h a t a r e in g o o d a g r e e m e n t w i t h t u n n e l i n g e x p e r i m e n t s of R o w e l l e t a l . [4]. H o w e v e r , i n P b , S c a l a p i n o e t a l . [1] e s t i m a t e d t h e e l e c t r o n - p h o n o n c o u p l i n g p a r a m e t e r ot ~2 f o r l o n g i t u d i n a l p h o n o n s to b e d o u b l e t h e o t f o r t r a n s v e r s e p h o n o n s , w h e r e a s S c h r i e f f e r e t a l . [3] e m ployed the same coupling parameter for all phonons. S c a l a p i n o e t a l . [1] h a v e d i s c u s s e d t h e o c c u r r e n c e of a s e c o n d p e a k i n t h e e f f e c t i v e t u n n e l i n g d e n s i t y of s t a t e s of P b a t T ~ T c c a u s e d b y r e c o m bination effects. These processes are explained i n t e r m s of r e m o v a l of a n e l e c t r o n f r o m t h e n o r mal metal and a quasi-particle from the supercond u c t i n g P b a n d c r e a t i o n of a g r o u n d s t a t e p a i r i n P b w i t h e m i s s i o n of a p h o n o n . A t n o n - z e r o t e m p e r a t u r e s , t h e r e a r e a r e l a t i v e l y l a r g e n u m b e r of excited quasi-particles and there is a high density of s t a t e s a t t h e g a p e d g e i n P b . A n e l e c t r o n c a n b e injected from a normal metal into Pb across an insulating layer and can then combine with an excited quasi-particle and form a ground state pair. A p h o n o n i s e m i t t e d i n t h e p r o c e s s . B e c a u s e of h i g h d e n s i t y of s t a t e s a t t h e g a p e d g e a n d t h e r e q u i r e m e n t s of e n e r g y c o n s e r v a t i o n , t h i s p r o c e s s i s m o s t p r o b a b l e w h e n v + A o ( T ) = w ;~ w h e r e v i s t h e e n e r g y of t h e i n j e c t e d e l e c t r o n , Ao(T) i s t h e gap parameter at the gap edge at temperature T a n d w ~ i s t h e e n e r g y c o r r e s p o n d i n g to a p e a k in t h e p h o n o n d e n s i t y of s t a t e s . T h e s e r e c o m b i n a t i o n * This work was s u p p o r t e d in p a r t by the National R e s e a r c h Council of Canada.
p r o c e s s e s c a u s e a n e w n e g a t i v e p e a k in t h e i m a g i n a r y p a r t of t h e g a p p a r a m e t e r A 2 ( E , T) w h i c h i s e v e n t u a l l y r e f l e c t e d in t h e e f f e c t i v e t u n n e l i n g d e n s i t y of s t a t e s . T h e c o r r e s p o n d i n g s t r u c t u r e i n the normalized dynamic conductance ~ = (di/dv)s / (di/dv) n versus, v curve for a tunnel junction is, h o w e v e r , s u b j e c t to t h e r m a l s m e a r i n g . T h e y e s t i m a t e t h a t t h e m a x i m u m o b s e r v a b l e s t r u c t u r e due to r e c o m b i n a t i o n p r o c e s s e s s h o u l d o c c u r n e a r T / T c = 0.95 a r o u n d a n e n e r g y v = 3.9 m e V . Results are reported here for the measurement of a : v c h a r a c t e r i s t i c s of two A1 - AlxOy - P b s p e c i m e n s a t v a r i o u s t e m p e r a t u r e s c l o s e to T c for Pb. Each tunnel junction studied here was made by o x i d i z i n g t h e s u r f a c e o£ a n A1 f i l m t h a t h a d b e e n p r e p a r e d b y v a c u u m e v a p o r a t i o n . A c r o s s s t r i p of Pb was then deposited. All evaporations were
I
'
I
I I
,
I ?.
~
'
I
'
I 5
i
I 4
,
I
1.05
O"
1.00
,
V
I 5
,
I 6
,
(mV)
Fig. 1. E x p e r i m e n t a l r e s u l t s for the s p e c i m e n P b - 4 6 . A. T / T c = 0.97; B. Calculated c u r v e [1] at T / T c = 0.95.
335
Volume 20, number 4 '
I
PHYSICS
A
m
•
1.10
"° O-
1.05
I .00
i 0
l
LLIL
I
2
LLL $
4 V
LII 5
6
7
(mV)
Fig. 2. E x p e r i m e n t a l r e s u l t s for the s p e c i m e n Pb-47. T / T c = 0.89; B. T / T e = 0.96; C. T / T c = 0.98.
A.
s t a r t e d a t a p r e s s u r e of a b o u t 3 × 10 -5 m m of Hg. O x i d a t i o n t i m e w a s n e a r l y 1 m i n u t e at a b o u t 200 ° C. T h e (~ : v c h a r a c t e r i s t i c s f o r t h e s e s p e c i m e n s w e r e m e a s u r e d w i t h a c u r v e t r a c e r [5] w h i c h p e r mitted sensitive four terminal resistance measurem e n t s . The t e m p e r a t u r e s w e r e m e a s u r e d with a Ge r e s i s t a n c e t h e r m o m e t e r a n d a r e a c c u r a t e to b e t t e r t h a n one p e r c e n t . T c f o r P b f i l m in s p e c i m e n s P b - 4 6 a n d P b - 4 7 w a s f o u n d to b e r e s p e c t i v e l y 6 . 9 7 ° K a n d 6 . 3 2 ° K . T h e s e f i l m s h a d a b r o a d t r a n s i t i o n , p r o b a b l y due to n o n - u n i f o r m t h i c k n e s s a t the f i l m e d g e s . T h e s e m e a s u r e m e n t s i n d i c a t e t h a t the t r a n s i t i o n t e m p e -
336
1 M a r c h 1966
r a t u r e s of t h i n f i l m s of P b , like T a [6] f i l m s , a r e l o w e r t h a n t h a t of t h e bulk m a t e r i a l in c o n t r a s t to t h e t r a n s i t i o n t e m p e r a t u r e s of t h i n f i l m s of A1, In [7] a n d Sn [8] w h i c h a r e h i g h e r t h a n t h o s e of the c o r r e s p o n d i n g bulk m a t e r i a l s . F i g s . 1 and 2 i l l u s t r a t e t h e ~ : v c h a r a c t e r i s t i c s f o r t h e s p e c i m e n s P b - 4 6 a n d P b - 4 7 at d i f f e r e n t t e m p e r a t u r e s a n d the c a l c u l a t e d c u r v e [1] a t T / T c = 0 . 9 5 . T h e r e is g o o d a g r e e m e n t b e t w e e n t h e t h e o r e t i c a l a n d the e x p e r i m e n t a l l y o b s e r v e d c u r v e s . T h e d e c r e a s e in r e c o m b i n a t i o n r a t e a s the t e m p e r a t u r e w a s l o w e r e d i s e v i d e n t f r o m the d e c r e a s e in t h e f l a t p o r t i o n b e t w e e n the two p e a k s in the a : v c u r v e s . T h e a : v c u r v e f o r s p e c i m e n P b - 4 6 l i e s c l o s e r to the c a l c u l a t e d c u r v e t h a n the c u r v e s f o r s p e c i m e n P b - 4 7 . T h i s i s p r o b a b l y b e c a u s e P b - 4 6 w a s the t h i n n e r of the two s p e c i m e n s .
~ l , l , l ~ l ~ I r l
,
LETTERS
RefC~CnCCS 1. D. J. Scalapino, Y. Wada and J . C . S w i h a r t , Phys. Rev. L e t t e r s 14 (1965) 102. 2. J . C . S w i h a r t , D . J . S c a l a p i n o and Y.Wada, Phys. Rev. L e t t e r s 14 (1965) 106. 3. J . R . Schrieffer, D . J . Sealapino and J. W. Wilkins, Phys. Rev. L e t t e r s 10 (1963) 336. 4. J . M . R o w e l l , P . W . Anderson and D . E . T h o m a s , Phys. Rev. L e t t e r s 10 (1963) 334. 5. J . S . R o g e r s , J . G . A d l e r and S . B . W o o d s , Rev. Sci. I n s t r u m . 35 (1964) 208. 6. J . J . H a u s e r and H . C . T h e u e r e r , Rev. Mod. Phys. 36 (1964) 80. 7. R . D . C h a u d h a r i and J . B . B r o w n , Phys. Rev. 139 (1965) 1482. 8. M.Strongin, O . F . K a m m e r e r and A. Paskin, Phys. Rev. L e t t e r s 14 (1965) 949.