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silver interface of mirrors
Solar Energy Materials 9 (1983) 43-50 North-Holland
43
ANALYSIS O F A U G E R E L E C T R O N S P E C T R O S C O P Y D E P T H PROFILES OF THE COPPER/SILVER INTERFACE OF MIRRORS * Linda S. D A K E and John S. H A R T M A N Pacific Northwest Laboratory **, Richland, WA 99352, USA
Received 18 August 1982; in revised form 26 January 1983 Chemical depth profiling of commercial second surface silver/copper mirrors of the type proposed for solar energy applications has been performed using Auger electron spectroscopy. Instead of the sharp interface between the metal layers that might have been expected, there was a very broad asymmetrical transition region. Several possible explanations for this broad interface region are considered. A mathematical model was developed for one of the theories, and data generated using the theoretical model is compared with the experimental data.
1. Introduction
Second surface silver/copper mirrors, including those used for terrestrial solar applications, are manufactured using wet chemistry electroless deposition processes [1]. Mirror production begins with an abrasive scrub of the glass substrate, a thorough rinse, application of a tin sensitizer solution, and a final rinse. Silver and copper layers are then deposited sequentially using electroless processes to produce layers which are nominally 70 and 30 nm thick, respectively. During standard production, the copper layer is overcoated with a layer of paint approximately 0.025 m m thick. In this study, normal production-run commercial mirrors were examined by sputter depth profiling with Auger electron spectroscopy (AES). The paint layer was chemically removed prior to analysis. A typical AES depth profile is shown in fig. 1. Corrections were made for the different relative sputter rates for copper and silver (i.e. -- 2 : 3, respectively) [2]. The AES depth profile reveals a wide transition region between the copper and silver layers. Sputtering depths have been estimated from sputtering rates and elapsed times and are therefore approximate (est. + 10%). Nevertheless, the data indicates that the copper and silver layers coexist within an interface region on the order of several tens of nanometers deep. The width of the transition region indicated by these data is much greater than expected for two planar films (e.g., the SiO2/Si interface width is less than 2 nm) [3]. A similar broad interface region was also observed using X-ray photoelectron spectroscopy (XPS) [4]. * Work performed for the Basic Energy Sciences Division of the US Department of Energy under Contract DE-AC06-76RLO-1830. ** Operated by Battelle Memorial Institute. 0165-1633/83/0000-0000/$03.00 © 1983 North-Holland
44
L.S. Dake, J.S. ltartman / Depth profiles
of
copper~silver interface~
100
75 uJ I.g a. ¢D
50
,-.
~ll I//I 11]/~
O I.25
0
20
40
-
60
APPROXIMATE
80
COPPER
100
DEPTH (nm)
Fig. 1. Auger electron spectroscopy depth profile of copper/silver mirror.
This behavior was observed for a number of mirrors with the transition width numerically consistent to within 10%. Several factors might contribute to the observed breadth of the copper/silver interface region: 1) the sputtering process itself will broaden even sharp interfaces due to the knock-on process and sputter beam induced surface roughening; 2) diffusion between the copper and silver layers would result in mixing of the metals at the interface; and 3) silver film growth mechanisms could also affect the interface region. In particular, island growth of silver film could produce a pebbled surface, which would affect the appearance of the interface region. A more thorough consideration of each of the above factors follows. 1) Knock-on effects occur when the ions in the incident sputtering beam hit the sample surface atoms head on and imbed surface atoms into the sample rather than removing them from the sample [3, 5]. Thus, a depth profile will show some mixing of the silver and copper layers that is an artifact of the sputtering mechanism. Experiments done on SiOz/Si interfaces using a 3 keV argon ion beam for the sputter profiling (which was also used for these mirror profiles) have found interface widths due to knock-on effects of approximately 4.5 nm [3]. By using simple atomic mass and momentum considerations to explain the sputtering process, it is expected that 4.5 nm would be an upper limit for the interface width due to knock-on in the copper/silver system. This is roughly a factor of ten less than the observed interface width. Therefore, the knock-on process does not provide an adequate explanation of the experimental copper/silver interface width. Furthermore, recent studies show that interface broadening due to knockon increases with increasing energy of the sputtering ions [3,5]. Fig. 2 shows AES depth profiles measured during this study using sputter beam energies of 2, 3 and 5 keV. While the absolute sputtering rates varied considerably, analysis showed essentially the same interface width for all the beam energies as seen in fig. 3.
L.S. Dake, J.S. Hartman / Depth profiles of copper/silver interfaces
45
7
6-
."
f
.J
,¢ z
t3 m "-" ~[
5
.Y
4
/ / ..... / ..................
a.ua O I-
3
~
,¢
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SPUTTER B E A M
.
ENERGIES
/
/
•.......... 2 keV
.... "'..........'""
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6
8
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10
12
14
16
18
20
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SPUTTER T I M E (minutes)
Fig. 2. Comparison of raw depth profile data of a copper/silver mirror sample obtained with various sputter beam energies. The boldface lines represent the copper profiles, while the regular lines represent the silver profiles.
This provides another indication that the knock-on process is not the dominant factor contributing to the width of the copper/silver transition region. Surface roughness can also contribute to the broadening of a depth profile interface. Sputter induced roughening can be caused by ion beam propagation of
F--%
I oo
80 70 -
~\
//
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SPUTTER SEAM ENERGIES
\ ~ 0 k-
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L 90
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Fig. 3. Comparison of interface widths obtained for a mirror sample using various sputter beam energies as determined from the data in fig. 2. The boldface lines represent the copper profiles, while the regular lines represent the silver profiles.
46
L.S. Dake. J.,$. tlartman / Depth profiles ,)~ copper/siher mtelT/ace.~
an initial surface roughness, by preferential sputtering, by statistical surface roughening, a n d by f o r m a t i o n of surface artifacts (cones, etc.) [5]. An e x p e r i m e n t was c o n d u c t e d to establish the c u m u l a t i v e effects of sputter b r o a d e n i n g on s i l v e r / c o p p e r interfaces. Thin metal films were d e p o s i t e d on bulk substrates. N o n - p l a n a r s u b s t r a t e surfaces (i.e., localized scratches and roughness) will also c o n t r i b u t e to the a p p a r e n t interface width seen in A E S d e p t h profile data. A silver film was sputter d e p o s i t e d o n t o a highly p o l i s h e d ( < 5 n m rms roughness) c o p p e r m i r r o r substrate. D e p t h profiles were r e c o r d e d using the same A E S p a r a m e t e r s used for the wet c h e m i s t r y m i r r o r profiles, a n d revealed an interface width less than 25% as large as the wet c h e m i s t r y m i r r o r interface. A c o p p e r film was sputter d e p o s i t e d o n t o a b u f f e d silver foil which was significantly rougher than the c o p p e r s u b s t r a t e (i.e., scratches were visible to the n a k e d eye). The d e p t h profile of this system showed an interface width 50% as large as the interface for the wet c h e m i s t r y mirrors. It is felt that the a p p a r e n t interface width of this s a m p l e has been increased by the s u b s t r a t e roughness. However, these two e x p e r i m e n t s d o p r o v i d e an u p p e r limit to the e x p e c t e d b e a m - i n d u c e d interface b r o a d e n i n g effects on s i l v e r / c o p p e r interfaces. T h e results are shown in fig. 4 a n d indicate that sputter i n d u c e d interface b r o a d e n i n g does not account for the interface widths m e a s u r e d for the wet chemistry mirrors. 2) D i f f u s i o n between the c o p p e r a n d silver layers could b r o a d e n the metal interface.
~WET CHEMISTRY MIRROR = "SPUI-I'ERED'Cu ON Ag FOIL ~ERED Ag ON Cu MIRROR
7 :
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.
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WET CHEMISTRY MIRROR
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........ Ag ON Cu MIRROR ROR
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1
0
0
1
2
3
4
5
6
7
SPUTTER TIME (minutes)
Fig. 4. Comparison of the interface width obtained for a wet chemistry mirror with the interface widths obtained for sputtered silver film on a polished copper mirror and sputtered copper film on silver foil. The boldface lines represent the copper profiles, while the regular lines represent the silver profiles. Interface widths for the different samples are shown above the curve.
L.S. Dake, J.S. Hartman / Depth profiles of copper/silver interfaces
47
The existing diffusion and miscibility data for silver and copper does not predict the large amount of mixing observed experimentally [6,7]. However, that diffusion data has been compiled for bulk silver and copper samples and may not be valid for the thin film system under consideration here. Diffusion at grain boundaries where the bulk diffusion coefficients are not adequate may also be important. Thus, diffusion cannot be ruled out as an explanation for the observed interface width due to the lack of knowledge of diffusion processes in the silver/copper thin film system. 3) The concept of island growth of the silver film on the glass substrate can explain the observed copper/silver interface characteristics. This theory postulates that the small amounts of tin left on the glass by the sensitizing solution act as nucleation sites for the silver film growth [1,8,9]. The resulting silver layer consists of small islands of silver centered on the nucleation sites, rather than a smooth, continuous layer. The copper layer is then deposited on top of the silver and fills in any voids left between adjacent islands. Depending on the separation between the silver islands and the island radii, copper and silver could be detected together over considerable depths. If the islands are much smaller than the 5/~m electron beam used in the Auger profiling, the resultant silver/copper interface would not be sharply defined.
2. Computer analysis of simplified "island theory" After making several simplifying assumptions, the implications of the island growth theory were analyzed mathematically. A computer was then used to generate "depth profiles" based on the theoretical model. The calculated profiles were compared with the actual AES experimental data. It was assumed that the silver islands were hemispheres of uniform radius distributed in a regular array on the glass surface. Two array geometries were considered: "simple square" (SS) and "hexagonal close packed" (HCP). Various ratios of the hemisphere radius ( R ) and the nearest neighbor separation between the hemisphere centers (S) were considered for each model (SS and HCP). For R / S = 0.5, nearest neighbor hemispheres just touch at the glass surface, while for R / S > 0.5, the silver islands overlap. For R / S < 0.5, the silver islands are isolated, and considerable amounts of both silver and copper will be detected at the glass surface. Knock-on and diffusion effects were not taken into account. It was also assumed that 1) only copper and silver were present, 2) the copper filled in the voids between the silver islands, and 3) the copper formed a flat layer on top of the silver islands, rather than reproducing the silver film morphology.
3. Results and discussion For a given nucleation geometry (SS or HCP) and R / S value, the fractional amounts of silver and copper present were calculated and plotted as a function of depth into the film.
48
?, ,~'. Dak< ,1..~; tlap tm~**~ , Del)th proj)les 0/~ oppei'/ sllt:et mter/ace~
No absolute depths were assigned for the computer plots. The theoretical mirror was "profiled" from the top of the silver layer down to tile glass interface (i.e., 0 on the depth axis corresponds to the top of the silver hemispheres). The depth range of the profile plot corresponds to the radius of the hemispherical silver islands (R). Real mirrors were analyzed from the top of the copper layer to the glass layer (and deeper). To facilitate comparisons of the data, the experimental data has been replotted on the same scale as tile computer-generated data. The origin on the depth scale of the replotted experimental data corresponds to the point on the original AES profile where silver was first detected ( - - 2 0 nm on fig. 1). This point was chosen to represent the " t o p " of the silver layer. Curves obtained from R/S values greater than 0.5 give the best fit to the experimental data for both SS and HCP models. The best-fit SS data ( R/S = 0.66) is shown along with the experimental data in fig. 5. The most notable differences between the experimental and calculated data are seen at shallow depths and include the location of the crossover points.In order to get good fits, the theoretical curve must be displaced along the depth axis to tile right by about 3-5% as shown in fig. 4. In other words, the simple periodic hemisphere model does not accurately represent the top of the silver layer. In the computer model, the position that silver is first detected is at the top ol the uniform layer of silver hemispheres. The amount of silver present increases quite rapidly with depth. However, it is highly unlikely that the surface of the real silver layer is this regular. It is expected that the silver islands are probably not all the same height (since nucleation would not occur at the same time at all sensitized spots and individual island growth rates may differ). Diffusion of silver into the copper layer may also occur at least to some extent. So, small amounts of silver due to diffusion a n d / o r non-uniformities in the surface of the silver layer (due to both high spots and non-periodic arrays of silver islands) could be detected for a significant region above the more uniform film layer. This would contribute to a more gradual rise in the percent of silver detected after silver is first detected at the beginning of the experimental data. Once the surface irregularities have been bypassed, the amount of silver detected would begin to increase more rapidly with increasing depths, as is seen in both the experimental and theoretical data near the cross-over points. R/S values for the best-fit data for the SS and H C P arrays were 0.66 and 0.58, respectively. This corresponds to 99 and 100% silver coverage at the glass surface. This theoretical result is consistent with commercial mirrors since no copper is visibly detected at the metal/glass interface and absolute and spectral optical characteristics of the metal at the interface are consistent with pure silver. The nominal thickness of the silver layer on commercial mirrors (70 nm) is calculated from the measured weight of silver deposited per unit area by assuming a uniform planar silver layer [1]. Correcting for the non-planar surfaces resulting from the island growth model yields silver thicknesses of 92 and 94 nm for the SS and H C P configurations, respectively. These values correspond to the radii of the hemispheres. Calculations based upon these thickness values and the best-fit R/S values of 0.66 and 0.58 determined that the nearest neighbor separation between the silver islands was 140-160 nm.
L.S. Dake, J.S. Hartman / Depth profiles of copper/silver interfaces
49
100 SILVER
75
t-Z
50 U 0 .<
25
COPPER 0
K 0.5
0
EXPERIMENTAL
I
I
(
)
I
0
I
0.5 THEORETICAL
FRACTIONAL
DEPTH
I I
(....... )
INTO
SILVER
LAYER
Comparison of experimental depth profile data and island growth model (simple square configuration; R / S = 0 . 6 6 ) for copper/silver mirrors. The solid lines represent the experimental data, while the dotted lines represent the theoretical data. 0 on the depth axis corresponds to the top of the silver layer. 1 on the depth axis corresponds to the glass surface. F i g . 5.
4. Conclusions Reasonable approximations to experimental AES depth profile data of commercial second surface silver/copper mirrors can be generated using a simple model based on island theory of film growth. The major differences between the theoretical and experimental data occur in a region near the surface of the silver layer. By taking the limitations of the simplified model into account, explanations for the differences can be formulated. On this basis, the island theory of silver growth is consistent with experimental AES depth profiles (but not necessarily at the expense of the other theories). Furthermore, R/S values obtained for the best-fit data were
50
L.S. Dake, J.S. Hartman "/ Depth profiles of copper/silver interJace~
0.66 a n d 0.58 for the SS a n d H C P arrays, respectively. The nearest neighbor separation between the silver islands was d e t e r m i n e d to be 140-160 n m for the best-fit model data a n d n o m i n a l film thickness values. P r o p o n e n t s of the island growth theory have calculated by i n d e p e n d e n t m e t h o d s that the separation of the silver islands is on the order of 100 n m [1,4,10] which is in qualitative agreement with the c o m p u t e r - g e n e r a t e d data reported here.
Acknowledgement The authors wish to t h a n k L.R. Pederson for his experimental characterization of the mirror samples a n d for m a n y helpful discussions.
References [1] M.A. Lind, C.Q. Buckwalter, J.L. Daniel, J.S. Hartman, M.T. Thomas and L.R. Pederson, Heliostat Mirror Survey and Analysis, PNL-3914 (1980). [2] H.H. Andersen and H.L. Bay, in: Topics in Applied Physics, vol. 47, ed. R.Behrisch (Springer-Verlag. New York, 1981)pp. 177, 182. [3] S.A, Schwarz and C.R. Helms, J. Vac. Sci. Tech. 16 (1979) 781. [4] L.R. Pederson and M.T. Thomas, Solar Energy Mater. 3 (1980) 151. [5] S. Hofmann, Surface Interface An. 2 (1980) 148. [6] J. Askill, Tracer Diffusion Data for Metals, Alloys and Simple Oxides (IFl Plenum. Ne~v York. 1970). [7] M. Hansen, Constitution of Binary Alloys (McGraw-Hill, New York, 1958). [8] W,A. Weyl, Colored Glasses (Dawsons of Pall Mall, London, 1959) p. 348. [9] C.H. de Minjer and P.F.J.v.d. Boom, J. Electrochem. Soc. 120 (1973) 1644. [10] J.L. Daniel and J.E. Coleman, Solar Energy Mater. 3 (1980) 135.
43
ANALYSIS O F A U G E R E L E C T R O N S P E C T R O S C O P Y D E P T H PROFILES OF THE COPPER/SILVER INTERFACE OF MIRRORS * Linda S. D A K E and John S. H A R T M A N Pacific Northwest Laboratory **, Richland, WA 99352, USA
Received 18 August 1982; in revised form 26 January 1983 Chemical depth profiling of commercial second surface silver/copper mirrors of the type proposed for solar energy applications has been performed using Auger electron spectroscopy. Instead of the sharp interface between the metal layers that might have been expected, there was a very broad asymmetrical transition region. Several possible explanations for this broad interface region are considered. A mathematical model was developed for one of the theories, and data generated using the theoretical model is compared with the experimental data.
1. Introduction
Second surface silver/copper mirrors, including those used for terrestrial solar applications, are manufactured using wet chemistry electroless deposition processes [1]. Mirror production begins with an abrasive scrub of the glass substrate, a thorough rinse, application of a tin sensitizer solution, and a final rinse. Silver and copper layers are then deposited sequentially using electroless processes to produce layers which are nominally 70 and 30 nm thick, respectively. During standard production, the copper layer is overcoated with a layer of paint approximately 0.025 m m thick. In this study, normal production-run commercial mirrors were examined by sputter depth profiling with Auger electron spectroscopy (AES). The paint layer was chemically removed prior to analysis. A typical AES depth profile is shown in fig. 1. Corrections were made for the different relative sputter rates for copper and silver (i.e. -- 2 : 3, respectively) [2]. The AES depth profile reveals a wide transition region between the copper and silver layers. Sputtering depths have been estimated from sputtering rates and elapsed times and are therefore approximate (est. + 10%). Nevertheless, the data indicates that the copper and silver layers coexist within an interface region on the order of several tens of nanometers deep. The width of the transition region indicated by these data is much greater than expected for two planar films (e.g., the SiO2/Si interface width is less than 2 nm) [3]. A similar broad interface region was also observed using X-ray photoelectron spectroscopy (XPS) [4]. * Work performed for the Basic Energy Sciences Division of the US Department of Energy under Contract DE-AC06-76RLO-1830. ** Operated by Battelle Memorial Institute. 0165-1633/83/0000-0000/$03.00 © 1983 North-Holland
44
L.S. Dake, J.S. ltartman / Depth profiles
of
copper~silver interface~
100
75 uJ I.g a. ¢D
50
,-.
~ll I//I 11]/~
O I.25
0
20
40
-
60
APPROXIMATE
80
COPPER
100
DEPTH (nm)
Fig. 1. Auger electron spectroscopy depth profile of copper/silver mirror.
This behavior was observed for a number of mirrors with the transition width numerically consistent to within 10%. Several factors might contribute to the observed breadth of the copper/silver interface region: 1) the sputtering process itself will broaden even sharp interfaces due to the knock-on process and sputter beam induced surface roughening; 2) diffusion between the copper and silver layers would result in mixing of the metals at the interface; and 3) silver film growth mechanisms could also affect the interface region. In particular, island growth of silver film could produce a pebbled surface, which would affect the appearance of the interface region. A more thorough consideration of each of the above factors follows. 1) Knock-on effects occur when the ions in the incident sputtering beam hit the sample surface atoms head on and imbed surface atoms into the sample rather than removing them from the sample [3, 5]. Thus, a depth profile will show some mixing of the silver and copper layers that is an artifact of the sputtering mechanism. Experiments done on SiOz/Si interfaces using a 3 keV argon ion beam for the sputter profiling (which was also used for these mirror profiles) have found interface widths due to knock-on effects of approximately 4.5 nm [3]. By using simple atomic mass and momentum considerations to explain the sputtering process, it is expected that 4.5 nm would be an upper limit for the interface width due to knock-on in the copper/silver system. This is roughly a factor of ten less than the observed interface width. Therefore, the knock-on process does not provide an adequate explanation of the experimental copper/silver interface width. Furthermore, recent studies show that interface broadening due to knockon increases with increasing energy of the sputtering ions [3,5]. Fig. 2 shows AES depth profiles measured during this study using sputter beam energies of 2, 3 and 5 keV. While the absolute sputtering rates varied considerably, analysis showed essentially the same interface width for all the beam energies as seen in fig. 3.
L.S. Dake, J.S. Hartman / Depth profiles of copper/silver interfaces
45
7
6-
."
f
.J
,¢ z
t3 m "-" ~[
5
.Y
4
/ / ..... / ..................
a.ua O I-
3
~
,¢
2
SPUTTER B E A M
.
ENERGIES
/
/
•.......... 2 keV
.... "'..........'""
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------
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I,U
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6
8
I
I
I
I
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10
12
14
16
18
20
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24
SPUTTER T I M E (minutes)
Fig. 2. Comparison of raw depth profile data of a copper/silver mirror sample obtained with various sputter beam energies. The boldface lines represent the copper profiles, while the regular lines represent the silver profiles.
This provides another indication that the knock-on process is not the dominant factor contributing to the width of the copper/silver transition region. Surface roughness can also contribute to the broadening of a depth profile interface. Sputter induced roughening can be caused by ion beam propagation of
F--%
I oo
80 70 -
~\
//
/
SPUTTER SEAM ENERGIES
\ ~ 0 k-
50 -
30 -
-
2 keY 3 keV
l//~..'~"
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........
/~j~: ------
ii
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/;:I..;
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/...
0 0
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50
60
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80
L 90
100
DEPTH (nm)
Fig. 3. Comparison of interface widths obtained for a mirror sample using various sputter beam energies as determined from the data in fig. 2. The boldface lines represent the copper profiles, while the regular lines represent the silver profiles.
46
L.S. Dake. J.,$. tlartman / Depth profiles ,)~ copper/siher mtelT/ace.~
an initial surface roughness, by preferential sputtering, by statistical surface roughening, a n d by f o r m a t i o n of surface artifacts (cones, etc.) [5]. An e x p e r i m e n t was c o n d u c t e d to establish the c u m u l a t i v e effects of sputter b r o a d e n i n g on s i l v e r / c o p p e r interfaces. Thin metal films were d e p o s i t e d on bulk substrates. N o n - p l a n a r s u b s t r a t e surfaces (i.e., localized scratches and roughness) will also c o n t r i b u t e to the a p p a r e n t interface width seen in A E S d e p t h profile data. A silver film was sputter d e p o s i t e d o n t o a highly p o l i s h e d ( < 5 n m rms roughness) c o p p e r m i r r o r substrate. D e p t h profiles were r e c o r d e d using the same A E S p a r a m e t e r s used for the wet c h e m i s t r y m i r r o r profiles, a n d revealed an interface width less than 25% as large as the wet c h e m i s t r y m i r r o r interface. A c o p p e r film was sputter d e p o s i t e d o n t o a b u f f e d silver foil which was significantly rougher than the c o p p e r s u b s t r a t e (i.e., scratches were visible to the n a k e d eye). The d e p t h profile of this system showed an interface width 50% as large as the interface for the wet c h e m i s t r y mirrors. It is felt that the a p p a r e n t interface width of this s a m p l e has been increased by the s u b s t r a t e roughness. However, these two e x p e r i m e n t s d o p r o v i d e an u p p e r limit to the e x p e c t e d b e a m - i n d u c e d interface b r o a d e n i n g effects on s i l v e r / c o p p e r interfaces. T h e results are shown in fig. 4 a n d indicate that sputter i n d u c e d interface b r o a d e n i n g does not account for the interface widths m e a s u r e d for the wet chemistry mirrors. 2) D i f f u s i o n between the c o p p e r a n d silver layers could b r o a d e n the metal interface.
~WET CHEMISTRY MIRROR = "SPUI-I'ERED'Cu ON Ag FOIL ~ERED Ag ON Cu MIRROR
7 :
/
.
6
•
-i"
/
"
iI
iii
:
•
5 -
./ /
Z
(3 o 03
o
/
// /
4
WET CHEMISTRY MIRROR
/
........ Ag ON Cu MIRROR ROR
3
,¢
2
1
0
0
1
2
3
4
5
6
7
SPUTTER TIME (minutes)
Fig. 4. Comparison of the interface width obtained for a wet chemistry mirror with the interface widths obtained for sputtered silver film on a polished copper mirror and sputtered copper film on silver foil. The boldface lines represent the copper profiles, while the regular lines represent the silver profiles. Interface widths for the different samples are shown above the curve.
L.S. Dake, J.S. Hartman / Depth profiles of copper/silver interfaces
47
The existing diffusion and miscibility data for silver and copper does not predict the large amount of mixing observed experimentally [6,7]. However, that diffusion data has been compiled for bulk silver and copper samples and may not be valid for the thin film system under consideration here. Diffusion at grain boundaries where the bulk diffusion coefficients are not adequate may also be important. Thus, diffusion cannot be ruled out as an explanation for the observed interface width due to the lack of knowledge of diffusion processes in the silver/copper thin film system. 3) The concept of island growth of the silver film on the glass substrate can explain the observed copper/silver interface characteristics. This theory postulates that the small amounts of tin left on the glass by the sensitizing solution act as nucleation sites for the silver film growth [1,8,9]. The resulting silver layer consists of small islands of silver centered on the nucleation sites, rather than a smooth, continuous layer. The copper layer is then deposited on top of the silver and fills in any voids left between adjacent islands. Depending on the separation between the silver islands and the island radii, copper and silver could be detected together over considerable depths. If the islands are much smaller than the 5/~m electron beam used in the Auger profiling, the resultant silver/copper interface would not be sharply defined.
2. Computer analysis of simplified "island theory" After making several simplifying assumptions, the implications of the island growth theory were analyzed mathematically. A computer was then used to generate "depth profiles" based on the theoretical model. The calculated profiles were compared with the actual AES experimental data. It was assumed that the silver islands were hemispheres of uniform radius distributed in a regular array on the glass surface. Two array geometries were considered: "simple square" (SS) and "hexagonal close packed" (HCP). Various ratios of the hemisphere radius ( R ) and the nearest neighbor separation between the hemisphere centers (S) were considered for each model (SS and HCP). For R / S = 0.5, nearest neighbor hemispheres just touch at the glass surface, while for R / S > 0.5, the silver islands overlap. For R / S < 0.5, the silver islands are isolated, and considerable amounts of both silver and copper will be detected at the glass surface. Knock-on and diffusion effects were not taken into account. It was also assumed that 1) only copper and silver were present, 2) the copper filled in the voids between the silver islands, and 3) the copper formed a flat layer on top of the silver islands, rather than reproducing the silver film morphology.
3. Results and discussion For a given nucleation geometry (SS or HCP) and R / S value, the fractional amounts of silver and copper present were calculated and plotted as a function of depth into the film.
48
?, ,~'. Dak< ,1..~; tlap tm~**~ , Del)th proj)les 0/~ oppei'/ sllt:et mter/ace~
No absolute depths were assigned for the computer plots. The theoretical mirror was "profiled" from the top of the silver layer down to tile glass interface (i.e., 0 on the depth axis corresponds to the top of the silver hemispheres). The depth range of the profile plot corresponds to the radius of the hemispherical silver islands (R). Real mirrors were analyzed from the top of the copper layer to the glass layer (and deeper). To facilitate comparisons of the data, the experimental data has been replotted on the same scale as tile computer-generated data. The origin on the depth scale of the replotted experimental data corresponds to the point on the original AES profile where silver was first detected ( - - 2 0 nm on fig. 1). This point was chosen to represent the " t o p " of the silver layer. Curves obtained from R/S values greater than 0.5 give the best fit to the experimental data for both SS and HCP models. The best-fit SS data ( R/S = 0.66) is shown along with the experimental data in fig. 5. The most notable differences between the experimental and calculated data are seen at shallow depths and include the location of the crossover points.In order to get good fits, the theoretical curve must be displaced along the depth axis to tile right by about 3-5% as shown in fig. 4. In other words, the simple periodic hemisphere model does not accurately represent the top of the silver layer. In the computer model, the position that silver is first detected is at the top ol the uniform layer of silver hemispheres. The amount of silver present increases quite rapidly with depth. However, it is highly unlikely that the surface of the real silver layer is this regular. It is expected that the silver islands are probably not all the same height (since nucleation would not occur at the same time at all sensitized spots and individual island growth rates may differ). Diffusion of silver into the copper layer may also occur at least to some extent. So, small amounts of silver due to diffusion a n d / o r non-uniformities in the surface of the silver layer (due to both high spots and non-periodic arrays of silver islands) could be detected for a significant region above the more uniform film layer. This would contribute to a more gradual rise in the percent of silver detected after silver is first detected at the beginning of the experimental data. Once the surface irregularities have been bypassed, the amount of silver detected would begin to increase more rapidly with increasing depths, as is seen in both the experimental and theoretical data near the cross-over points. R/S values for the best-fit data for the SS and H C P arrays were 0.66 and 0.58, respectively. This corresponds to 99 and 100% silver coverage at the glass surface. This theoretical result is consistent with commercial mirrors since no copper is visibly detected at the metal/glass interface and absolute and spectral optical characteristics of the metal at the interface are consistent with pure silver. The nominal thickness of the silver layer on commercial mirrors (70 nm) is calculated from the measured weight of silver deposited per unit area by assuming a uniform planar silver layer [1]. Correcting for the non-planar surfaces resulting from the island growth model yields silver thicknesses of 92 and 94 nm for the SS and H C P configurations, respectively. These values correspond to the radii of the hemispheres. Calculations based upon these thickness values and the best-fit R/S values of 0.66 and 0.58 determined that the nearest neighbor separation between the silver islands was 140-160 nm.
L.S. Dake, J.S. Hartman / Depth profiles of copper/silver interfaces
49
100 SILVER
75
t-Z
50 U 0 .<
25
COPPER 0
K 0.5
0
EXPERIMENTAL
I
I
(
)
I
0
I
0.5 THEORETICAL
FRACTIONAL
DEPTH
I I
(....... )
INTO
SILVER
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Comparison of experimental depth profile data and island growth model (simple square configuration; R / S = 0 . 6 6 ) for copper/silver mirrors. The solid lines represent the experimental data, while the dotted lines represent the theoretical data. 0 on the depth axis corresponds to the top of the silver layer. 1 on the depth axis corresponds to the glass surface. F i g . 5.
4. Conclusions Reasonable approximations to experimental AES depth profile data of commercial second surface silver/copper mirrors can be generated using a simple model based on island theory of film growth. The major differences between the theoretical and experimental data occur in a region near the surface of the silver layer. By taking the limitations of the simplified model into account, explanations for the differences can be formulated. On this basis, the island theory of silver growth is consistent with experimental AES depth profiles (but not necessarily at the expense of the other theories). Furthermore, R/S values obtained for the best-fit data were
50
L.S. Dake, J.S. Hartman "/ Depth profiles of copper/silver interJace~
0.66 a n d 0.58 for the SS a n d H C P arrays, respectively. The nearest neighbor separation between the silver islands was d e t e r m i n e d to be 140-160 n m for the best-fit model data a n d n o m i n a l film thickness values. P r o p o n e n t s of the island growth theory have calculated by i n d e p e n d e n t m e t h o d s that the separation of the silver islands is on the order of 100 n m [1,4,10] which is in qualitative agreement with the c o m p u t e r - g e n e r a t e d data reported here.
Acknowledgement The authors wish to t h a n k L.R. Pederson for his experimental characterization of the mirror samples a n d for m a n y helpful discussions.
References [1] M.A. Lind, C.Q. Buckwalter, J.L. Daniel, J.S. Hartman, M.T. Thomas and L.R. Pederson, Heliostat Mirror Survey and Analysis, PNL-3914 (1980). [2] H.H. Andersen and H.L. Bay, in: Topics in Applied Physics, vol. 47, ed. R.Behrisch (Springer-Verlag. New York, 1981)pp. 177, 182. [3] S.A, Schwarz and C.R. Helms, J. Vac. Sci. Tech. 16 (1979) 781. [4] L.R. Pederson and M.T. Thomas, Solar Energy Mater. 3 (1980) 151. [5] S. Hofmann, Surface Interface An. 2 (1980) 148. [6] J. Askill, Tracer Diffusion Data for Metals, Alloys and Simple Oxides (IFl Plenum. Ne~v York. 1970). [7] M. Hansen, Constitution of Binary Alloys (McGraw-Hill, New York, 1958). [8] W,A. Weyl, Colored Glasses (Dawsons of Pall Mall, London, 1959) p. 348. [9] C.H. de Minjer and P.F.J.v.d. Boom, J. Electrochem. Soc. 120 (1973) 1644. [10] J.L. Daniel and J.E. Coleman, Solar Energy Mater. 3 (1980) 135.