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Time variation of the interisland spacing at liquid nitrogen temperature for copper and silver island films
Thin Solid Films, 159 (1988) L61-L64
L61
LeRer Time variation of the interisland spacing at liquid nitrogen temperature for copper and silver island films MANJUNATHA PATTABI AND M. S. MURALI SASTRY Thin Film Laboratory, Department of Physics, Indian Institute of Technology, Madras 600036 (India) (Received January 20, 1988; accepted March 8, 1988)
Aging in island metal films has been explained by researchers as due to various causes 1-3. It is generally accepted that the mobility of islands followed by coalescence is responsible for the change in post-deposition resistance in such films and this has been supported by electron microscopy studies 3. In our earlier papers on the aging of copper 4 and silver 5 island films at near liquid nitrogen temperature, an agglomeration rate based on the functional dependence of the film resistance on time was defined to quantify the aging process. In this letter, we report on a new agglomeration rate with the evaluation of the tunnelling length (interisland spacing) and its time dependence by making use of Andersson's approach 6 with slight modifications. The data are taken for a few initial resistance films as an illustration from an earlier study which gives the experimental details 4' ~. The time variation of resistance of island metal films based on the quantum mechanical tunnelling model (after Hill 7) is given by R(t) - R°{d(0}2 exp{1.025(m*q~) / d(t)} exp
q~
(1)
where d(t) is the time-dependent interisland spacing, Ro is a constant, ~ois the mean tunnelling barrier for the tunnelling electron, m* is the effective mass of the tunnelling electron and 5E is the activation energy for charge carrier creation. If we assume that d(t) varies logarithmically with time, a good fit is obtained for the resistance vs. time data. In Andersson's case, he found an exponentially varying tunnelling length with time. Keeping this difference in mind, following Andersson 6, d(t) = dl + dsA In(t + 1)
(2)
where ds = dF-- dl
(3)
d~ is the interisland spacing immediately after stoppage of deposition and de the interisland spacing at the end of aging. The constant A is such that A In t = 1 for t = tmax where tmax is the interval of aging. This condition has to be satisfied as can be seen from eqns. (1)-(3). Substituting eqn. (2) in eqn. (1) and neglecting time-dependent changes in {d(t)} 2 and 0040-6090/88/$3.50
© ElsevierSequoia/Printedin The Netherlands
L62
LETTERS
exp(6E/kT) terms compared with the exp{ 1.025(m*~p)l/2d(t)} term, we obtain lnR(t) = l n R , + l n ( ~ )
A In t
(4)
where R~ is the initial resistance and R F is the final resistance at the end of aging for a period of time tm,x which is calculated by the method of least squares. The slope of the In R(t) vs. In t curves gives the agglomeration rate as defined in the earlier studies 4'5 and is equal to Aln(RF/RI). From eqns. (1) and (3), the change in the interisland spacing is evaluated to be ds = 1.54(1n R v - l n RI)
(5)
assuming m* = 0.4 and q~ = 1 eV. If RF and R~ are known, the change in the interisland spacing can be calculated. From eqn. (1) and for typical values of activation energies and interisland spacings, a reasonable approximation would be In Rv/ln R1 ~ dv/dl
(6)
From eqns. (5) and (6), dr and d~ can be calculated. The agglomeration rate may be now defined as (in hngstr6ms per minute) (dr- dO/tm,x. Figure 1 shows the variation of the tunnelling length with In t for some copper and silver films at 125 K and at room temperature. The change in tunnelling for the films at room temperature is considerably larger than for films at 125 K. In Fig, 2 the variation in normalized resistance with time is shown. Here also one can see that the change in resistance with time at room temperature is much more rapid than at 125 K. The linear dependence can be clearly seen from Fig. 1. The points in the figure cu
%
• Ro=I.3MD-/D • Ro=40MQ/D • Ro= 60Mr~/O
O Ro= 10MD-/D A RO= 21MD-/D I3 Ro= 60MP,/D
R=6~Mn/U
0 Ro= ~Mn/U
---------II
°.<
/
26.~
/
2Z,,.I
Z / ~-~
22.1
0
O
± 1.0
,O I 2.0
0 1 3.0
"
0
L.O
In t
Fig. 1. Variation in the interisland spacing with In t for some copper and silver island films at 125 K ( and 300 K ( - - ) .
LETTERS
L63
Cu
Ag
• P~= 3 M ~ #
o % ° IoM~/o
• Ro= 40M~/o • RO= 60Mi]/o 4) Ro= 61MCl/O(300K)
ZS Ro= 21M£~/o [] Ro= 60MD./o 0 Ro= }MCI/o
(30OK) 28.C
0 16.C
0
o
5
0
0
5
0 o
4C
2.
$ # ¢
1.E "•@
•
•
•
g
•
).0 'ol3C~n Ci~O C~ 20
~ a 0
40 t ime (mini
60
Fig. 2. Variation in normalized resistance with time for copper and silver island films at 125 and 300 K. are d e t e r m i n e d from the e x p e r i m e n t a l d a t a , using the expression d(t) = dv -- 1.54{In Rv -- In R(t)}
T a b l e ! gives the m o d i f i e d a g g l o m e r a t i o n rates for c o p p e r island films at 125 K a n d for a film at r o o m t e m p e r a t u r e for c o m p a r i s o n . I n t e r i s l a n d spacings at the b e g i n n i n g (dl) a n d after 20 m i n (dr) are also given. F o r c o m p a r i s o n tma~ was cut o f f a t 20 m i n for all the films. It can be seen that, as one goes to higher initial resistance films (thinner films), the a g g l o m e r a t i o n rate is higher. As the thickness increases, the island size d i s t r i b u t i o n b e c o m e s c o a r s e a n d the density of larger, less m o b i l e islands increases s. Less m o b i l e islands coalesce m o r e slowly a n d hence the slow rate of TABLE I MODIFIED A G G L O M E R A T I O N RATE D A T A FOR C O P P E R ISLAND FILMS AT
Initial resistance
d I (A)
d F (A)
(Mfl/D)
125 K A N D ROOM T E M P E R A T U R E Agglomeration rate
(A min - l)
At 125 K 1.3 40.0 60.0
22.24 26.25 27.38
22.41 26.48 27.68
0.0085 0.0116 0.0146
At room temperature 61.0
27.54
28.57
0.0515
L64
LETTERS
change of interisland spacing with time (agglomeration rate) is expected for low resistance films, as is observed. Also, since the mobility of islands is a thermally activated process, one would expect a slower rate of change of interisland spacing with time at lower temperatures. As can be seen from Table I, and Fig. 1 for almost same initial resistance films, the change in interisland spacing with time is larger at r o o m temperature than at 125 K. This shows the applicability of the thermally activated mobility coalescence model in explaining the post-deposition resistance increase in island copper films. Table II gives the modified agglomeration rate data for silver films at 125 K. In this case, tmax was 55 min for all the films. In the case of silver films, there was an initial fall in resistance for a m a x i m u m period of 5 min followed by an increase in resistance with time. The instant of resistance increase was taken as t = 0 for the calculations. The same functional dependence of d(t) on time was found for silver films as well (Fig. 1). Here also, one can see the increase in agglomeration rate as one goes to higher resistance films and the values of the agglomeration rate are much less than the value for a ! Mf~/['q film at room temperature. The initial tunnelling length at 125 K varies from 23 to 27.4 ]k for silver films and from 22.2 to 27.4/~ for copper films. The fact that the resistance spread is not very large results in dl values lying within a small interval. TABLE II MODIFIED A G G L O M E R A T I O N RATE D A T A FOR SILVER I S L A N D FILMS A T 1 2 5
Initial resistance (Mn/~)
K
AND ROOM TEMPERATURE
d I (]~)
d v (fk )
Agglomeration rate (,~ min ~)
At 125 K 10.0 21.0 60.0
23.03 25.35 27.41
23.11 25.46 27.57
0.0016 0.0020 0.0029
At room temperature 1.0
22.96
26.56
0.0655
One of the authors (M.S.) is thankful to the Council of Scientific and Industrial Research, Government of India, for a research fellowship. 1 2 3 4 5 6 7 8
F . P . Fehlner, J. Appl. Phys., 38 (1967) 2223. M. Nishiura and A. Kinbara, Thin Solid Films, 24 (1974) 79. J . G . Skofronick and W. B. Phillips, J. Appl. Phys., 38 (1967) 4791. M. Pattabi, M. S. Murali Sastry and V. Sivaramakrishnan, J. Appl. Phys., to be published. M. Pattabi, M. S. Murali Sastry, V. D a m o d a r a Das and V. Sivaramakrishnan, J. Mater. Sei., to be published. T. Andersson, J. Appl. Phys., 47 (1976) 1752. R . M . Hill, Proc. R. Soc. London, Ser. A, 309 (1969) 377. K. Kinosita, Thin Solid Films, 85 (1981) 223.
L61
LeRer Time variation of the interisland spacing at liquid nitrogen temperature for copper and silver island films MANJUNATHA PATTABI AND M. S. MURALI SASTRY Thin Film Laboratory, Department of Physics, Indian Institute of Technology, Madras 600036 (India) (Received January 20, 1988; accepted March 8, 1988)
Aging in island metal films has been explained by researchers as due to various causes 1-3. It is generally accepted that the mobility of islands followed by coalescence is responsible for the change in post-deposition resistance in such films and this has been supported by electron microscopy studies 3. In our earlier papers on the aging of copper 4 and silver 5 island films at near liquid nitrogen temperature, an agglomeration rate based on the functional dependence of the film resistance on time was defined to quantify the aging process. In this letter, we report on a new agglomeration rate with the evaluation of the tunnelling length (interisland spacing) and its time dependence by making use of Andersson's approach 6 with slight modifications. The data are taken for a few initial resistance films as an illustration from an earlier study which gives the experimental details 4' ~. The time variation of resistance of island metal films based on the quantum mechanical tunnelling model (after Hill 7) is given by R(t) - R°{d(0}2 exp{1.025(m*q~) / d(t)} exp
q~
(1)
where d(t) is the time-dependent interisland spacing, Ro is a constant, ~ois the mean tunnelling barrier for the tunnelling electron, m* is the effective mass of the tunnelling electron and 5E is the activation energy for charge carrier creation. If we assume that d(t) varies logarithmically with time, a good fit is obtained for the resistance vs. time data. In Andersson's case, he found an exponentially varying tunnelling length with time. Keeping this difference in mind, following Andersson 6, d(t) = dl + dsA In(t + 1)
(2)
where ds = dF-- dl
(3)
d~ is the interisland spacing immediately after stoppage of deposition and de the interisland spacing at the end of aging. The constant A is such that A In t = 1 for t = tmax where tmax is the interval of aging. This condition has to be satisfied as can be seen from eqns. (1)-(3). Substituting eqn. (2) in eqn. (1) and neglecting time-dependent changes in {d(t)} 2 and 0040-6090/88/$3.50
© ElsevierSequoia/Printedin The Netherlands
L62
LETTERS
exp(6E/kT) terms compared with the exp{ 1.025(m*~p)l/2d(t)} term, we obtain lnR(t) = l n R , + l n ( ~ )
A In t
(4)
where R~ is the initial resistance and R F is the final resistance at the end of aging for a period of time tm,x which is calculated by the method of least squares. The slope of the In R(t) vs. In t curves gives the agglomeration rate as defined in the earlier studies 4'5 and is equal to Aln(RF/RI). From eqns. (1) and (3), the change in the interisland spacing is evaluated to be ds = 1.54(1n R v - l n RI)
(5)
assuming m* = 0.4 and q~ = 1 eV. If RF and R~ are known, the change in the interisland spacing can be calculated. From eqn. (1) and for typical values of activation energies and interisland spacings, a reasonable approximation would be In Rv/ln R1 ~ dv/dl
(6)
From eqns. (5) and (6), dr and d~ can be calculated. The agglomeration rate may be now defined as (in hngstr6ms per minute) (dr- dO/tm,x. Figure 1 shows the variation of the tunnelling length with In t for some copper and silver films at 125 K and at room temperature. The change in tunnelling for the films at room temperature is considerably larger than for films at 125 K. In Fig, 2 the variation in normalized resistance with time is shown. Here also one can see that the change in resistance with time at room temperature is much more rapid than at 125 K. The linear dependence can be clearly seen from Fig. 1. The points in the figure cu
%
• Ro=I.3MD-/D • Ro=40MQ/D • Ro= 60Mr~/O
O Ro= 10MD-/D A RO= 21MD-/D I3 Ro= 60MP,/D
R=6~Mn/U
0 Ro= ~Mn/U
---------II
°.<
/
26.~
/
2Z,,.I
Z / ~-~
22.1
0
O
± 1.0
,O I 2.0
0 1 3.0
"
0
L.O
In t
Fig. 1. Variation in the interisland spacing with In t for some copper and silver island films at 125 K ( and 300 K ( - - ) .
LETTERS
L63
Cu
Ag
• P~= 3 M ~ #
o % ° IoM~/o
• Ro= 40M~/o • RO= 60Mi]/o 4) Ro= 61MCl/O(300K)
ZS Ro= 21M£~/o [] Ro= 60MD./o 0 Ro= }MCI/o
(30OK) 28.C
0 16.C
0
o
5
0
0
5
0 o
4C
2.
$ # ¢
1.E "•@
•
•
•
g
•
).0 'ol3C~n Ci~O C~ 20
~ a 0
40 t ime (mini
60
Fig. 2. Variation in normalized resistance with time for copper and silver island films at 125 and 300 K. are d e t e r m i n e d from the e x p e r i m e n t a l d a t a , using the expression d(t) = dv -- 1.54{In Rv -- In R(t)}
T a b l e ! gives the m o d i f i e d a g g l o m e r a t i o n rates for c o p p e r island films at 125 K a n d for a film at r o o m t e m p e r a t u r e for c o m p a r i s o n . I n t e r i s l a n d spacings at the b e g i n n i n g (dl) a n d after 20 m i n (dr) are also given. F o r c o m p a r i s o n tma~ was cut o f f a t 20 m i n for all the films. It can be seen that, as one goes to higher initial resistance films (thinner films), the a g g l o m e r a t i o n rate is higher. As the thickness increases, the island size d i s t r i b u t i o n b e c o m e s c o a r s e a n d the density of larger, less m o b i l e islands increases s. Less m o b i l e islands coalesce m o r e slowly a n d hence the slow rate of TABLE I MODIFIED A G G L O M E R A T I O N RATE D A T A FOR C O P P E R ISLAND FILMS AT
Initial resistance
d I (A)
d F (A)
(Mfl/D)
125 K A N D ROOM T E M P E R A T U R E Agglomeration rate
(A min - l)
At 125 K 1.3 40.0 60.0
22.24 26.25 27.38
22.41 26.48 27.68
0.0085 0.0116 0.0146
At room temperature 61.0
27.54
28.57
0.0515
L64
LETTERS
change of interisland spacing with time (agglomeration rate) is expected for low resistance films, as is observed. Also, since the mobility of islands is a thermally activated process, one would expect a slower rate of change of interisland spacing with time at lower temperatures. As can be seen from Table I, and Fig. 1 for almost same initial resistance films, the change in interisland spacing with time is larger at r o o m temperature than at 125 K. This shows the applicability of the thermally activated mobility coalescence model in explaining the post-deposition resistance increase in island copper films. Table II gives the modified agglomeration rate data for silver films at 125 K. In this case, tmax was 55 min for all the films. In the case of silver films, there was an initial fall in resistance for a m a x i m u m period of 5 min followed by an increase in resistance with time. The instant of resistance increase was taken as t = 0 for the calculations. The same functional dependence of d(t) on time was found for silver films as well (Fig. 1). Here also, one can see the increase in agglomeration rate as one goes to higher resistance films and the values of the agglomeration rate are much less than the value for a ! Mf~/['q film at room temperature. The initial tunnelling length at 125 K varies from 23 to 27.4 ]k for silver films and from 22.2 to 27.4/~ for copper films. The fact that the resistance spread is not very large results in dl values lying within a small interval. TABLE II MODIFIED A G G L O M E R A T I O N RATE D A T A FOR SILVER I S L A N D FILMS A T 1 2 5
Initial resistance (Mn/~)
K
AND ROOM TEMPERATURE
d I (]~)
d v (fk )
Agglomeration rate (,~ min ~)
At 125 K 10.0 21.0 60.0
23.03 25.35 27.41
23.11 25.46 27.57
0.0016 0.0020 0.0029
At room temperature 1.0
22.96
26.56
0.0655
One of the authors (M.S.) is thankful to the Council of Scientific and Industrial Research, Government of India, for a research fellowship. 1 2 3 4 5 6 7 8
F . P . Fehlner, J. Appl. Phys., 38 (1967) 2223. M. Nishiura and A. Kinbara, Thin Solid Films, 24 (1974) 79. J . G . Skofronick and W. B. Phillips, J. Appl. Phys., 38 (1967) 4791. M. Pattabi, M. S. Murali Sastry and V. Sivaramakrishnan, J. Appl. Phys., to be published. M. Pattabi, M. S. Murali Sastry, V. D a m o d a r a Das and V. Sivaramakrishnan, J. Mater. Sei., to be published. T. Andersson, J. Appl. Phys., 47 (1976) 1752. R . M . Hill, Proc. R. Soc. London, Ser. A, 309 (1969) 377. K. Kinosita, Thin Solid Films, 85 (1981) 223.