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The origins of stress in thin nickel films
Thin Solid Films - Elsevier Sequoia S.A., Lausanne - Printed in Switzerland
71
THE ORIGINS OF STRESS IN THIN NICKEL FILMS*
F. A. DOLJACK** A N D R. W. HOFFMAN
Case Western Reserve University, Cleveland, Ohio 44106 (U.S.A.)
(Received May 15, 1972)
The intrinsic stress in thin, polycrystalline nickel films vapor-deposited onto polished silicon substrates was measured by viewing the substrate deflection using an optical interference method. Samples were stripped from their substrates, and since they were all approximately 2000 A thick, a 650 kV electron microscope was used to observe the microstructure directly. As a function of thickness, the instantaneous stress in the films was found to be constant except for the development of compressive stresses in the first 500-1000/~ of growth at the higher substrate temperatures. The magnitude of the observed tension decreased from 1.5 × 101° dyn/cm2 at 0 °C to 0.4 x 101° dyn/ cm 2 at 200 °C. The stress resulting from a constrained grain boundary relaxation was calculated from an average grain boundary potential and the experimental grain sizes. The fall-off of stress with increasing substrate temperature was well matched by the calculated values, and the calculated stress values agreed to within roughly 30 ~ of the measured values. It was concluded that the intrinsic stress was produced by this constrained grain boundary relaxation. The compressive stresses were suspected to be diffusion-induced stresses resulting from grain boundary diffusion of silicon into the nickel film.
INTRODUCTION
In addition to differential thermal expansion stress, the often large intrinsic stress has been responsible for mechanical failure of thin film devices. The origin of intrinsic stress in vacuum-deposited polycrystalline metal films has now been actively investigated for over 20 years, with little success in quantitative predictions. In this paper we present measurements of the stress in polycrystalline nickel films as a function of substrate temperature during deposition and compare these with values calculated from a grain boundary model for stress which was proposed earlier I and has recently been placed upon a detailed physical basis 2. + Paper presented at the International Conference on Thin Films, "Application of Thin Films ", Venice, Italy, May 15-19, 1972; Paper 2.3. "* Present address, Addressograph-Multigraph Corporation. Thin Solid Films, 12 (1972) 71-74
72
F.A.
DOLJACK, R. W . HOFF'MAN
EXPERIMENTAL
The intrinsic stress in an infinitesimal layer of film at any position through the thickness of the film (called the instantaneous stress) was found by differentiating the measured bending force per unit width v e r s u s thickness curves. The bending force was determined from the bending of a < 111 > oriented silicon wafer 0.015cm thick and 2.2cm in diameter. The changing interference fringe pattern produced between the substrate and an optical flat was photographically recorded. The substrate was rigidly clamped to a temperature controlled heat sink over a central, concentric circular area, leaving an annular portion free to bend. Any effects from differential thermal expansion and temperature gradients were thus negligible in this experiment. The depositions were made in a conventional diffusion pumped, liquid nitrogen trapped high vacuum system. All depositions were made at normal incidence at 30 A/sec in a vacuum of about 5 x 10-7 Torr. Microscopy samples were prepared by scratching the films to induce stress concentrations and by then peeling with pressure sensitive tape. RESULTS
The bending force per unit width as a function of thickness was measured in films made at - 4 2 °, 15°, 50°, 99 °, 150°, 195° and 225 °C. Differentiating these data showed that: (1) the instantaneous stress always approached a constant tension during the later stages of film growth and this value decreased with increasing substrate temperature, as shown in Fig. 1; and (2) a compressive component to the instantaneous stress became more significant with increasing substrate temperature. At the higher temperatures the total stress was compressive for film thicknesses less than 500-1000A and tensile for larger thicknesses. The high voltage electron micrographs revealed a dramatic increase in average grain size =E LU Z 1.5
I
'
'
I
'
'
'
I
/
MEASURED VALUES
--
CALCULATED FROM MEASURED GRAIN
t
0
'
o
x o~ 1.0 W
~ 0.5 W Z
o -~
i-
_._
Z I
,
,
,
0
,
I
,
,
,
,
I00
I
,
200
SUBSTRATE TEMPERATURE, T s ( o C )
Fig. 1. Comparison of calculated and measured values for the instantaneous tensile stress of nickel films over the temperature range - 5 0 ° to 250 °C.
Thin Solid Films, 12 (1972) 71-74
THE ORIGINS OF STRESS IN THIN NICKEL FILMS
73
from about 300 A to more than 1000 A for increasing substrate temperatures between - 4 2 ° and 225 °C. These grain sizes were measured by measuring grain images in both bright field and dark field micrographs. DISCUSSION
We identify the tensile component with the constraint introduced by the substrate as the film grows and the compression with impurity diffusion into the film. We will discuss origins of the stress in that order. In the grain boundary relaxation model the crystallites in a growing film are visualized as growing together from a stage where they are isolated, randomly oriented clumps. During the early stages of growth the observed bending force per unit width is governed by the changing surface tension of growing clumps that are constrained from expansion by their adhesion to the substrate. As the clumps grow together the interatomic forces exerted across the gap between two clump boundaries produce an elastic relaxation of the boundaries toward each other. This relaxation is also constrained by the adhesion of the clumps to the substrate. Physically, some of the change in energy of the free surface of a clump becoming a grain boundary goes into volume strain energy in the clump because of the constraint of the substrate. Vertical growth of the f i l l proceeds with the addition of layers of atoms to the tops of growing graias, and each layer suffers elastic strain in its plane by the relaxation produced at the grain boundary wall. In this way the stress in each layer is constant. Since the final grain sizes observed in this experiment are considerably bigger than the probable size of the clumps when they grow together, an annealing or recrystallization takes place among clumps to produce much larger grains. The atomic rearrangement during this process is three-dimensional and eliminates some of the strains produced by the former clump boundaries. As adhesion to the substrate is maintained during the development of the final grain sizes, the elastic strain left in the grain will be determined by the forces at the grain boundary wall of the final grain. At higher substrate temperatures the recrystallization is more complete, resulting in larger final grain sizes. Most importantly, the intrinsic stress is determined by the final state of the film. Only the parameters of final grain size, the surface free energy, the average grain boundary energy and the elastic constants are needed to calculate the intrinsic stress. The grain separation potential v(r) is constructed and the value for the grain boundary relaxation distance A is computed from this potential for each grain diameter d. The intrinsic stress is obtained by inserting the values of A and d in the expression {E/(1 -v)}A/d), where E and v are the usual elastic constants. For nickel A was about 0.8 A and increased slowly with grain size. The values calculated for the runs are superposed on the measured results plotted in Fig. 1. The calculated stresses reproduce the form of the measured stress versus substrate temperature curve satisfactorily, and numerical agreement is within roughly 30 9/0. We consider that the compression observed at smaller thicknesses results Thin Solid Films, 12 (1972) 71-74
74
F.A.
DOI.3ACK, R. W. HOFFMAN
from diffusion-controlled impurities in the nickel film. Low temperature diffusion of Co, Cu 3 and Au 4 into nickel films has been observed and the mechanism responsible was shown to be grain boundary diffusion4. Grain boundary diffusion has also apparently been responsible for the observed enhanced diffusion of silicon into aluminum films in integrated circuits s. In the case of Au into nickel the diffusion was observed to be markedly dependent on grain size. The possibility that significant amounts of silicon diffused into the growing nickel films at the higher substrate temperatures has been examined by an approximate calculation 2. It can thus be shown that grain boundary diffusion at 200 °C of silicon into nickel with grains 1000 A in size can produce compressive strains of a few tenths of 1 ~, which is about the size of the compressive strains observed in this experiment. Hence the diffusion of impurities is suggested as the cause of a temperature-dependent compression. ACKNOWLEDGEMENT
The authors wish to acknowledge the financial support of the U.S. Atomic Energy Commission. REFERENCES 1 2 3 4 5
J.D. Finegan and R. W. Hoffman, AEC Tech. Rept. No. 18, Case Institute of Technology, 1961. F . A . Doljack and R. W. Hoffman, to be published. G . O . Tronsdal and H. Sorum, Phys. Status Solidi, 4 (1964) 493. J.L. Richards and W. H. McCann, J. Vac. Sci. Technol., 6 (1969) 644. J.O. McCaldin and H. Sankur, Appl. Phys. Letters, 19 (1971) 524.
Thin Solid Films, 12 (1972) 71-74
71
THE ORIGINS OF STRESS IN THIN NICKEL FILMS*
F. A. DOLJACK** A N D R. W. HOFFMAN
Case Western Reserve University, Cleveland, Ohio 44106 (U.S.A.)
(Received May 15, 1972)
The intrinsic stress in thin, polycrystalline nickel films vapor-deposited onto polished silicon substrates was measured by viewing the substrate deflection using an optical interference method. Samples were stripped from their substrates, and since they were all approximately 2000 A thick, a 650 kV electron microscope was used to observe the microstructure directly. As a function of thickness, the instantaneous stress in the films was found to be constant except for the development of compressive stresses in the first 500-1000/~ of growth at the higher substrate temperatures. The magnitude of the observed tension decreased from 1.5 × 101° dyn/cm2 at 0 °C to 0.4 x 101° dyn/ cm 2 at 200 °C. The stress resulting from a constrained grain boundary relaxation was calculated from an average grain boundary potential and the experimental grain sizes. The fall-off of stress with increasing substrate temperature was well matched by the calculated values, and the calculated stress values agreed to within roughly 30 ~ of the measured values. It was concluded that the intrinsic stress was produced by this constrained grain boundary relaxation. The compressive stresses were suspected to be diffusion-induced stresses resulting from grain boundary diffusion of silicon into the nickel film.
INTRODUCTION
In addition to differential thermal expansion stress, the often large intrinsic stress has been responsible for mechanical failure of thin film devices. The origin of intrinsic stress in vacuum-deposited polycrystalline metal films has now been actively investigated for over 20 years, with little success in quantitative predictions. In this paper we present measurements of the stress in polycrystalline nickel films as a function of substrate temperature during deposition and compare these with values calculated from a grain boundary model for stress which was proposed earlier I and has recently been placed upon a detailed physical basis 2. + Paper presented at the International Conference on Thin Films, "Application of Thin Films ", Venice, Italy, May 15-19, 1972; Paper 2.3. "* Present address, Addressograph-Multigraph Corporation. Thin Solid Films, 12 (1972) 71-74
72
F.A.
DOLJACK, R. W . HOFF'MAN
EXPERIMENTAL
The intrinsic stress in an infinitesimal layer of film at any position through the thickness of the film (called the instantaneous stress) was found by differentiating the measured bending force per unit width v e r s u s thickness curves. The bending force was determined from the bending of a < 111 > oriented silicon wafer 0.015cm thick and 2.2cm in diameter. The changing interference fringe pattern produced between the substrate and an optical flat was photographically recorded. The substrate was rigidly clamped to a temperature controlled heat sink over a central, concentric circular area, leaving an annular portion free to bend. Any effects from differential thermal expansion and temperature gradients were thus negligible in this experiment. The depositions were made in a conventional diffusion pumped, liquid nitrogen trapped high vacuum system. All depositions were made at normal incidence at 30 A/sec in a vacuum of about 5 x 10-7 Torr. Microscopy samples were prepared by scratching the films to induce stress concentrations and by then peeling with pressure sensitive tape. RESULTS
The bending force per unit width as a function of thickness was measured in films made at - 4 2 °, 15°, 50°, 99 °, 150°, 195° and 225 °C. Differentiating these data showed that: (1) the instantaneous stress always approached a constant tension during the later stages of film growth and this value decreased with increasing substrate temperature, as shown in Fig. 1; and (2) a compressive component to the instantaneous stress became more significant with increasing substrate temperature. At the higher temperatures the total stress was compressive for film thicknesses less than 500-1000A and tensile for larger thicknesses. The high voltage electron micrographs revealed a dramatic increase in average grain size =E LU Z 1.5
I
'
'
I
'
'
'
I
/
MEASURED VALUES
--
CALCULATED FROM MEASURED GRAIN
t
0
'
o
x o~ 1.0 W
~ 0.5 W Z
o -~
i-
_._
Z I
,
,
,
0
,
I
,
,
,
,
I00
I
,
200
SUBSTRATE TEMPERATURE, T s ( o C )
Fig. 1. Comparison of calculated and measured values for the instantaneous tensile stress of nickel films over the temperature range - 5 0 ° to 250 °C.
Thin Solid Films, 12 (1972) 71-74
THE ORIGINS OF STRESS IN THIN NICKEL FILMS
73
from about 300 A to more than 1000 A for increasing substrate temperatures between - 4 2 ° and 225 °C. These grain sizes were measured by measuring grain images in both bright field and dark field micrographs. DISCUSSION
We identify the tensile component with the constraint introduced by the substrate as the film grows and the compression with impurity diffusion into the film. We will discuss origins of the stress in that order. In the grain boundary relaxation model the crystallites in a growing film are visualized as growing together from a stage where they are isolated, randomly oriented clumps. During the early stages of growth the observed bending force per unit width is governed by the changing surface tension of growing clumps that are constrained from expansion by their adhesion to the substrate. As the clumps grow together the interatomic forces exerted across the gap between two clump boundaries produce an elastic relaxation of the boundaries toward each other. This relaxation is also constrained by the adhesion of the clumps to the substrate. Physically, some of the change in energy of the free surface of a clump becoming a grain boundary goes into volume strain energy in the clump because of the constraint of the substrate. Vertical growth of the f i l l proceeds with the addition of layers of atoms to the tops of growing graias, and each layer suffers elastic strain in its plane by the relaxation produced at the grain boundary wall. In this way the stress in each layer is constant. Since the final grain sizes observed in this experiment are considerably bigger than the probable size of the clumps when they grow together, an annealing or recrystallization takes place among clumps to produce much larger grains. The atomic rearrangement during this process is three-dimensional and eliminates some of the strains produced by the former clump boundaries. As adhesion to the substrate is maintained during the development of the final grain sizes, the elastic strain left in the grain will be determined by the forces at the grain boundary wall of the final grain. At higher substrate temperatures the recrystallization is more complete, resulting in larger final grain sizes. Most importantly, the intrinsic stress is determined by the final state of the film. Only the parameters of final grain size, the surface free energy, the average grain boundary energy and the elastic constants are needed to calculate the intrinsic stress. The grain separation potential v(r) is constructed and the value for the grain boundary relaxation distance A is computed from this potential for each grain diameter d. The intrinsic stress is obtained by inserting the values of A and d in the expression {E/(1 -v)}A/d), where E and v are the usual elastic constants. For nickel A was about 0.8 A and increased slowly with grain size. The values calculated for the runs are superposed on the measured results plotted in Fig. 1. The calculated stresses reproduce the form of the measured stress versus substrate temperature curve satisfactorily, and numerical agreement is within roughly 30 9/0. We consider that the compression observed at smaller thicknesses results Thin Solid Films, 12 (1972) 71-74
74
F.A.
DOI.3ACK, R. W. HOFFMAN
from diffusion-controlled impurities in the nickel film. Low temperature diffusion of Co, Cu 3 and Au 4 into nickel films has been observed and the mechanism responsible was shown to be grain boundary diffusion4. Grain boundary diffusion has also apparently been responsible for the observed enhanced diffusion of silicon into aluminum films in integrated circuits s. In the case of Au into nickel the diffusion was observed to be markedly dependent on grain size. The possibility that significant amounts of silicon diffused into the growing nickel films at the higher substrate temperatures has been examined by an approximate calculation 2. It can thus be shown that grain boundary diffusion at 200 °C of silicon into nickel with grains 1000 A in size can produce compressive strains of a few tenths of 1 ~, which is about the size of the compressive strains observed in this experiment. Hence the diffusion of impurities is suggested as the cause of a temperature-dependent compression. ACKNOWLEDGEMENT
The authors wish to acknowledge the financial support of the U.S. Atomic Energy Commission. REFERENCES 1 2 3 4 5
J.D. Finegan and R. W. Hoffman, AEC Tech. Rept. No. 18, Case Institute of Technology, 1961. F . A . Doljack and R. W. Hoffman, to be published. G . O . Tronsdal and H. Sorum, Phys. Status Solidi, 4 (1964) 493. J.L. Richards and W. H. McCann, J. Vac. Sci. Technol., 6 (1969) 644. J.O. McCaldin and H. Sankur, Appl. Phys. Letters, 19 (1971) 524.
Thin Solid Films, 12 (1972) 71-74