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Electrical resistivity of vacuum-arc-deposited platinum thin films
Applied Surface Science 158 Ž2000. 217–222 www.elsevier.nlrlocaterapsusc
Electrical resistivity of vacuum-arc-deposited platinum thin films M. Avrekh ) , O.R. Monteiro, I.G. Brown Lawrence Berkeley National Laboratory, UniÕersity of California, Berkeley, CA 94720, USA Received 27 October 1999; accepted 22 December 1999
Abstract We report on our investigations of the electrical resistivity of very thin platinum films, with thickness in the range from 2.6 to 19 nm, formed using a filtered vacuum arc plasma deposition method. We find that the resistivity of these films can be well described by a grain-boundary scattering model, especially for thickness less than ; 5 nm. We also find that the grain size, and consequently the resistivity of the deposited film, is a function of the ion deposition energy, with measured grain size varying from ; 8 nm for ion deposition energy of 100 eV up to ; 11 nm at 2.2 keV. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Resistivity; Vacuum arc deposition; Platinum
1. Introduction The electrical resistance of metallic thin films increases over that given by the bulk resistivity of the film material as the film thickness decreases. This effect is due to electron scattering at the film surfaces and at grain boundaries within the metal film, and has been described by a number of authors w1–4x. Artunc and Ozturk w5x have reported on their measurements of the influence of grain boundary and surface scattering on the resistivity of thin copper films formed by thermal evaporation vacuum deposition and subsequently annealed; they show that grain boundary scattering is the dominant contribution to the excess resistivity compared to the bulk value. Maaroof and Evans w6x have reported on their measurements of the resistance of thin platinum and nickel films deposited by ion beam sputtering; they
)
Corresponding author.
observed an increased resistivity that could be described by grain boundary scattering for films thinner than about 5 nm. Van der Kraan et al. w7x have investigated quantum size effects and grain boundary scattering in polycrystalline cobalt disilicide films, and found an influence due to quantum effects for films of thickness below 10 nm. In the work described here, we measured the electrical resistivity of platinum thin films formed on glass substrates by a filtered vacuum arc deposition method, as a function of film thickness over a range extending from several tens of Angstroms to several hundred Angstroms. Films formed using ion deposition energies of 100 eV and 2.2 keV were explored. The films had a resistivity that depended both on the thickness of the film and on the ion deposition energy. Here we describe the energetic deposition process employed and the film characterization carried out. The results are compared to the predictions of a grain boundary scattering theory described by Mayadas and Shatzkes w3x.
0169-4332r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 0 0 . 0 0 0 2 1 - 0
218
M. AÕrekh et al.r Applied Surface Science 158 (2000) 217–222
2. Experimental Film formation by filtered vacuum arc Žalso called cathodic arc. plasma deposition is an established technique that has been well described in the literature w8,9x. The embodiment of the method that we have developed in our laboratory and used for a number of different film synthesis applications has been described in some detail elsewhere w10,11x. A simplified schematic of the set-up as used for the present work is shown in Fig. 1. A repetitively pulsed vacuum arc plasma gun w12x injects highly ionized metal plasma into a quarter torus magnetic duct macroparticle filter, with the substrate, on which the metal film is to be formed, positioned some distance from the duct exit. The substrate may be either grounded or pulse-biased so as to increase the ion deposition energy. If the substrate is not electrically conducting Že.g., glass, as here., then the metallic substrate holder is biased, and so long as the dielectric substrate is not too thick, then the effect of the bias is still felt by the arriving ions; also, by attaching the insulating substrate to the substrate holder with metallic screws, the bias can be applied directly to the growing film. In the present work, the plasma gun was fitted with a Pt cathode so as to produce Pt plasma in 5 ms pulses at a rate of 1 pulsers, and the substrate was located 14 cm from the duct exit. This configuration
Fig. 1. Simplified schematic of the plasma deposition set-up.
results in a deposition rate of approximately 0.1 nmrpulse. The substrate was pulse-biased using negative-going pulses of width 2 ms and duty cycle 33% Ži.e., 2 ms pulse-on, 4 ms pulse-off. with amplitude that could be varied from zero up to y1 kV; the pulsed substrate biasing was applied only during the 5 ms plasma-on time. It is a characteristic feature of vacuum arc plasmas that the ions produced are, in general, multiply charged with a mean charge state of between 1 q and 3 q , depending on the particular cathode material employed w13x, and have an inherent streaming velocity of several centimeters per microsecond w14x. For Pt, the mean ion charge state is Q s 2.1 q , and the ion streaming velocity corresponds to an energy Eo ; 100 eV. Thus, we take the ion deposition energy for Pt, for the case of zero substrate bias, to be ; 100 eV. For a substrate biased at voltage yV bias , the ion deposition energy is given by Edep s QV bias q Eo , which for 1 kV bias in a Pt plasma is equal to 2.2 keV. Note that since the bias voltage is repetitively pulsed at 33% duty cycle, so also is the ion energy repetitively pulsed with the same duty cycle; thus, the high-energy Ž2.2 keV. deposition case is similar to an ion-beam-assisted deposition ŽIBAD. process. The vacuum system base pressure and the pressure during the deposition process were in the low 10 -4 Pa range Ž10 -6 Torr range.. The substrates were ordinary Pyrex glass microscope slides, of dimensions 2.5 = 7.5 cm2 and thickness 1 mm. Stripes of colloidal silver were painted onto the ends of the glass slides, to which thin strips of aluminum foil were glued so as to form electrodes or tabs by means of which the electrical resistance of the platinum film deposited between the electrodes could be measured in situ. For each deposition run, two such substrates were mounted on the aluminum substrate holder, allowing two sets of measurements to be obtained for each condition. The resistance of the deposited film was measured with an ohmmeter after every several dozen shots. To measure the resistance of the thinnest films, we used a similar setup with a picoammeter attached in series with a 40 V DC supply and calculated the resistance using Ohm’s law. The resistance measurements were converted to resistivity using the known film thickness, which was obtained from profilometry measurements for the thicker films and from Rutherford backscat-
M. AÕrekh et al.r Applied Surface Science 158 (2000) 217–222
tering spectrometry ŽRBS. measurements for the thinner films. The films were analyzed by RBS using 2 MeV Heq ions. The RBS-derived atomic line density Žatoms cmy2 . was converted to a thickness using the known bulk density of Pt Ž21.45 g cmy3 .. That the film density is given by the bulk solid density is a good assumption, since we know from prior work that one of the important features of our vacuum arc plasma deposition technique is that the films are formed void-free and non-columnar. This attractive feature of the method is a consequence of the deposition process being energetic w15,16x. Ions are deposited at an energy of Žhere, for Pt. ; 100 eV or 2.2 keV, as described above, leading to fully dense film formation as occurs also for other related IBAD methods. The grain size of the films was determined by X-ray diffraction ŽXRD. using the Scherrer equation w17x and incorporating a correction factor for instrumental line broadening. A Siemens D5000 spectrom˚ Cu a line was employed. ŽWe eter using the 1.54 A remark parenthetically that these measurements were made for only a selected few thicknesses. The resistance vs. thickness measurements were performed in situ within the vacuum chamber, allowing good resistance data collection but prohibiting convenient XRD measurement. We are thus unable to comment, in the present work, on the relationship between grain size and film thickness..
219
Mayadas and Shatzkes model, the normalized resistivity rexprr bulk is given by:
rexp
1 s
r bulk
fŽa.
,
Ž 1.
where 3 f Ž a . s 1 y a q 3 a 2 y 3 a 3ln Ž 1 q ay1 . , 2
Ž 2.
and
as
lŽ T . R DŽ1 y R.
,
Ž 3.
where lŽT . is the electron mean free path in the film material without grain boundaries at temperature T, equal to 20 nm at room temperature w20x, R is the electron reflection coefficient at grain boundaries, and D is the mean grain diameter of the film material. The electron reflection coefficient has been experimentally determined to be equal to 0.5–0.7 for platinum w21x. Fig. 2 shows the results of our film resistance measurements for Pt films deposited in the absence of any applied substrate bias, i.e., for ion deposition energy of 100 eV. The resistance was converted to resistivity using the film length and thickness, and normalized to the classical bulk resistivity of Pt
3. Results and discussion The effect of grain boundary scattering on the electrical resistance of thin films has been studied in great detail by a number of workers. Mayadas and Shatzkes w3x assume a theoretical model in which a series of potential barriers scatters electrons, with separation between the barriers described by a Gaussian distribution. Palasantzas w18x also takes into account surface roughness parameters. For our method of deposition, it has been shown w19x that the rms surface roughness is only a few monolayers, and therefore, we ignore the effect of surface roughness in our resistivity calculations. According to the
Fig. 2. Measured normalized resistivity rexp r r bulk as a function of film thickness, for ion deposition energy of 100 eV Žpoints and solid curve.. The theoretically predicted dependence is also plotted for comparison Ždashed curve..
220
M. AÕrekh et al.r Applied Surface Science 158 (2000) 217–222
Ž r bulk s 1.06 = 10 -5 V P cm.. The normalized resistivity rexprr bulk is plotted as a function of film thickness. In addition to the experimental data, the theoretical normalized resistivity based on the model w3x described by Eqs. 1–3 is also shown in Fig. 2. In calculating the theoretical curve, we have taken the average grain size to be proportional to the film thickness, with a proportionality constant equal to the ratio of the grain size for the thickest film divided by the thickness of the thickest film Ži.e., the film at the end of the deposition run.. The grain size of the thickest film was 8 nm, as determined by XRD. Since the deposition was done at low ion energy, we assume that the substrate remained near room temperature. At room temperature, which corresponds to 0.15 times the platinum melting temperature Ž2045 K., the mobility of Pt atoms at the surface is small, and grain growth in the lateral direction is slow. The agreement between experiment and theory for film thickness greater than about 7 nm is quite good, but the agreement for thickness below about 5 nm is not so good. This is not altogether unexpected. For very small grain sizes, the linear relationship between grain size and film thickness that we have assumed may not hold. Although this linear relationship has been used successfully for very low energy deposition, it may not be a good approximation for deposition energies that are significantly hyperthermal. Here, even in the absence of applied bias voltage, the Pt ions have a mean deposition energy of 100 eV, which is much greater than the surface binding energy for Pt and therefore should alter the growth pattern. Another effect, electron scattering by the Pt free surface and the glass–Pt interface, is expected to become important at low thickness, leading to increased resistivity. Finally, there is always the possibility of discontinuities Žislands. in the film at these very low thicknesses, even though AFM studies of films produced by filtered cathodic arc deposition have shown that films in a thickness ˚ are continuous with an range down to about 300 A ˚ w19x. rms roughness of only 1–2 A Similar data for films deposited at a substrate bias of 1 kV, corresponding to an ion deposition energy of 2.2 keV as described above, are shown in Fig. 3. The deposition rate for this case was significantly lower than for films deposited at zero bias Ži.e.,
Fig. 3. Measured normalized resistivity rexp r r bulk as a function of film thickness, for ion deposition energy of 2.2 keV Žpoints and solid curve.. Theoretically predicted dependencies are also plotted: curve A, assuming a grain size equal to the film thickness; curve B, assuming a linear grain growth with final grain size 11 nm for the thickest film.
; 100 eV ion deposition energy. due to sputter removal of previously deposited film material by newly incident energetic ions, i.e., a kind of ‘‘selfetching’’ of the film. For the same deposition time, the maximum film thickness obtained at 2.2 keV ion energy was 4.1 nm, compared to 19 nm for 100 eV deposition energy. The experimentally determined normalized resistivity for Pt films formed at 2.2 keV ion energy is shown in Fig. 3. We also plot two curves that have been calculated using the theoretical model described by Eqs. 1–3 with two different assumptions regarding the correlation between grain size and film thickness. Curve A was obtained assuming that the grain size d is equal to the film thickness t Ži.e, d s t .. Curve B assumes a linear grain growth with a final grain size of 11 nm as determined by XRD, similar to the assumption used for the calculated curve of Fig. 2 Ži.e., d s kt, where k s d finalrtfinal s 11 nmr4.1 nm s 2.7.. It is clear from Fig. 3 that the agreement between experiment and theory given by curve B is poor for small grain sizes Žless than 5 nm.. The agreement between experiment and theory is better for the case of curve A. We hypothesize that the assumption made for curve A is better than that made for curve B because of the thermal annealing that takes place simultaneously with the deposition for the case of the sample produced at 2.2 keV ion energy. For deposition at
M. AÕrekh et al.r Applied Surface Science 158 (2000) 217–222
221
to be ; 11 nm, 1.6 times greater than that for the 100 eV deposition Ž; 8 nm.. Larger grain size then leads to less grain boundary scattering and lower resistivity at low film thickness.
4. Conclusion
Fig. 4. Measured resistivity rexp as a function of film thickness, for films deposited at ion energies of 100 eV and 2.2 keV. The bulk resistivity of Pt is shown by the dashed line.
high ion energy, there is a significant energy flux onto the growing film, which leads to an increase in temperature. During the early stages of deposition, when the film is still thin, the temperature of the film is low and very little grain growth due to annealing occurs. Towards the end of the deposition process, the total energy deposited into the film is high, and the film temperature is higher. Therefore, the rate of grain growth due to annealing at the end of the deposition is also higher. This difference in rates of grain growth between the early stages of deposition and the latter stages of deposition explains why the curve B assumption provides a bad fit, while curve A provides a reasonable fit. Finally, in Fig. 4, we show the same data as above for the two cases of high Ž2.2 keV. and low Ž100 eV. ion deposition energies, now plotted as unnormalized measured resistivity as a function of film thickness. One can see that the film resistivity is lower for the case of the more energetic deposition, and approaches the classical bulk resistivity value of 1.06 = 10y5 V P cm as the film thickness increases. Consistent with the description outlined above, we ascribe this as due to an elevated temperature of the growing film for the case of 2.2 keV ion deposition energy, in turn leading to a different grain growth regime. The higher ionratom surface mobility in this case leads to the formation of larger grains — the grain size for the 2.2 keV deposition was determined
We have investigated the electrical resistivity of thin platinum films in the thickness range 2.6–19 nm. The resistivity is dominated by grain boundary scattering for film thickness below ; 5 nm, and the measured values are in reasonable agreement with the theoretical model of Mayadas and Shatzkes. Films formed at higher ion deposition energy have larger grain size Ž11 nm at 2.2 keV. than those formed at lower ion deposition energy Ž8 nm at 100 eV., in turn leading to a resistivity at higher ion deposition energy that is lower than the low-energy deposition films because of reduced grain boundary scattering.
Acknowledgements This work was supported by the U.S. DOE, Office of Energy Research, under contract no. DEAC03-76SF00098.
References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x w11x
K. Fuchs, Proc. Cambridge Philos. Soc. 34 Ž1938. 100. E.H. Sondheimer, Adv. Phys. 1 Ž1952. 1. A.F. Mayadas, M. Shatzkes, Phys. Rev. B 1 Ž1970. 1382. P. Sheng, Philos. Mag. B 65 Ž1992. 357. N. Artunc, Z.Z. Ozturk, J. Phys.: Condens. Matter 5 Ž1993. 559. A.I. Maaroof, B.L. Evans, J. Appl. Phys. 76 Ž1994. 1047. R.G.P. van der Kraan, J.F. Jongste, H.M. Jaeger, G.C.A.M. Janssen, S. Radelaar, Phys. Rev. B 44 Ž1991. 13140. R.L. Boxman, P.J. Martin, .M. Sanders ŽEds.., Vacuum Arc Science and Technology, Noyes Data, New York, 1995. I.G. Brown, Cathodic arc deposition of films, in: Annu. Rev. Mater. Sci. Vol. 28 Annual Reviews, Palo Alto, CA, 1998. O.R. Monteiro, Z. Wang, I.G. Brown, J. Mater. Res. 12 Ž1997. 2401. M.-P. DelPlancke-Ogletree, O.R. Monteiro, J. Vac. Sci. Technol. A 15 Ž1997. 1943.
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w12x R.A. MacGill, M.R. Dickinson, A. Anders, O.R. Monteiro, I.G. Brown, Rev. Sci. Instrum. 69 Ž1998. 801. w13x I.G. Brown, Rev. Sci. Instrum. 65 Ž1994. 3061. w14x I.A. Krinberg, M.P. Lukovnikova, J. Phys. D: Appl. Phys. 29 Ž1996. 2901. w15x S. Machlin, Materials Science in Microelectronics — The Relationships Between Thin Film Processing and Structure, Gyro Press, New York, 1995. w16x M. Ohring, The Materials Science of Thin Films, Academic Press, San Diego, 1992.
w17x C. Barrett, T.B. Massalski, in: Structure of Metals, 3rd edn., Pergamon, New York, 1980, p. 155. w18x G. Palasantzas, Phys. Rev. B 58 Ž1998. 9685. w19x M.C. Salvadori, R.M. Galvao, O.R. Monteiro, I.G. Brown, Thin Solid Films 325 Ž1998. 19. w20x C. Kittel, Introduction to Solid State Physics, Wiley, New York, 1976. w21x G. Ramaswamy, A.K. Raychaudhuri, K. Das Gupta, G. Sambandamurthy, Appl. Phys. A 66 Ž1998. S435.
Electrical resistivity of vacuum-arc-deposited platinum thin films M. Avrekh ) , O.R. Monteiro, I.G. Brown Lawrence Berkeley National Laboratory, UniÕersity of California, Berkeley, CA 94720, USA Received 27 October 1999; accepted 22 December 1999
Abstract We report on our investigations of the electrical resistivity of very thin platinum films, with thickness in the range from 2.6 to 19 nm, formed using a filtered vacuum arc plasma deposition method. We find that the resistivity of these films can be well described by a grain-boundary scattering model, especially for thickness less than ; 5 nm. We also find that the grain size, and consequently the resistivity of the deposited film, is a function of the ion deposition energy, with measured grain size varying from ; 8 nm for ion deposition energy of 100 eV up to ; 11 nm at 2.2 keV. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Resistivity; Vacuum arc deposition; Platinum
1. Introduction The electrical resistance of metallic thin films increases over that given by the bulk resistivity of the film material as the film thickness decreases. This effect is due to electron scattering at the film surfaces and at grain boundaries within the metal film, and has been described by a number of authors w1–4x. Artunc and Ozturk w5x have reported on their measurements of the influence of grain boundary and surface scattering on the resistivity of thin copper films formed by thermal evaporation vacuum deposition and subsequently annealed; they show that grain boundary scattering is the dominant contribution to the excess resistivity compared to the bulk value. Maaroof and Evans w6x have reported on their measurements of the resistance of thin platinum and nickel films deposited by ion beam sputtering; they
)
Corresponding author.
observed an increased resistivity that could be described by grain boundary scattering for films thinner than about 5 nm. Van der Kraan et al. w7x have investigated quantum size effects and grain boundary scattering in polycrystalline cobalt disilicide films, and found an influence due to quantum effects for films of thickness below 10 nm. In the work described here, we measured the electrical resistivity of platinum thin films formed on glass substrates by a filtered vacuum arc deposition method, as a function of film thickness over a range extending from several tens of Angstroms to several hundred Angstroms. Films formed using ion deposition energies of 100 eV and 2.2 keV were explored. The films had a resistivity that depended both on the thickness of the film and on the ion deposition energy. Here we describe the energetic deposition process employed and the film characterization carried out. The results are compared to the predictions of a grain boundary scattering theory described by Mayadas and Shatzkes w3x.
0169-4332r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 0 0 . 0 0 0 2 1 - 0
218
M. AÕrekh et al.r Applied Surface Science 158 (2000) 217–222
2. Experimental Film formation by filtered vacuum arc Žalso called cathodic arc. plasma deposition is an established technique that has been well described in the literature w8,9x. The embodiment of the method that we have developed in our laboratory and used for a number of different film synthesis applications has been described in some detail elsewhere w10,11x. A simplified schematic of the set-up as used for the present work is shown in Fig. 1. A repetitively pulsed vacuum arc plasma gun w12x injects highly ionized metal plasma into a quarter torus magnetic duct macroparticle filter, with the substrate, on which the metal film is to be formed, positioned some distance from the duct exit. The substrate may be either grounded or pulse-biased so as to increase the ion deposition energy. If the substrate is not electrically conducting Že.g., glass, as here., then the metallic substrate holder is biased, and so long as the dielectric substrate is not too thick, then the effect of the bias is still felt by the arriving ions; also, by attaching the insulating substrate to the substrate holder with metallic screws, the bias can be applied directly to the growing film. In the present work, the plasma gun was fitted with a Pt cathode so as to produce Pt plasma in 5 ms pulses at a rate of 1 pulsers, and the substrate was located 14 cm from the duct exit. This configuration
Fig. 1. Simplified schematic of the plasma deposition set-up.
results in a deposition rate of approximately 0.1 nmrpulse. The substrate was pulse-biased using negative-going pulses of width 2 ms and duty cycle 33% Ži.e., 2 ms pulse-on, 4 ms pulse-off. with amplitude that could be varied from zero up to y1 kV; the pulsed substrate biasing was applied only during the 5 ms plasma-on time. It is a characteristic feature of vacuum arc plasmas that the ions produced are, in general, multiply charged with a mean charge state of between 1 q and 3 q , depending on the particular cathode material employed w13x, and have an inherent streaming velocity of several centimeters per microsecond w14x. For Pt, the mean ion charge state is Q s 2.1 q , and the ion streaming velocity corresponds to an energy Eo ; 100 eV. Thus, we take the ion deposition energy for Pt, for the case of zero substrate bias, to be ; 100 eV. For a substrate biased at voltage yV bias , the ion deposition energy is given by Edep s QV bias q Eo , which for 1 kV bias in a Pt plasma is equal to 2.2 keV. Note that since the bias voltage is repetitively pulsed at 33% duty cycle, so also is the ion energy repetitively pulsed with the same duty cycle; thus, the high-energy Ž2.2 keV. deposition case is similar to an ion-beam-assisted deposition ŽIBAD. process. The vacuum system base pressure and the pressure during the deposition process were in the low 10 -4 Pa range Ž10 -6 Torr range.. The substrates were ordinary Pyrex glass microscope slides, of dimensions 2.5 = 7.5 cm2 and thickness 1 mm. Stripes of colloidal silver were painted onto the ends of the glass slides, to which thin strips of aluminum foil were glued so as to form electrodes or tabs by means of which the electrical resistance of the platinum film deposited between the electrodes could be measured in situ. For each deposition run, two such substrates were mounted on the aluminum substrate holder, allowing two sets of measurements to be obtained for each condition. The resistance of the deposited film was measured with an ohmmeter after every several dozen shots. To measure the resistance of the thinnest films, we used a similar setup with a picoammeter attached in series with a 40 V DC supply and calculated the resistance using Ohm’s law. The resistance measurements were converted to resistivity using the known film thickness, which was obtained from profilometry measurements for the thicker films and from Rutherford backscat-
M. AÕrekh et al.r Applied Surface Science 158 (2000) 217–222
tering spectrometry ŽRBS. measurements for the thinner films. The films were analyzed by RBS using 2 MeV Heq ions. The RBS-derived atomic line density Žatoms cmy2 . was converted to a thickness using the known bulk density of Pt Ž21.45 g cmy3 .. That the film density is given by the bulk solid density is a good assumption, since we know from prior work that one of the important features of our vacuum arc plasma deposition technique is that the films are formed void-free and non-columnar. This attractive feature of the method is a consequence of the deposition process being energetic w15,16x. Ions are deposited at an energy of Žhere, for Pt. ; 100 eV or 2.2 keV, as described above, leading to fully dense film formation as occurs also for other related IBAD methods. The grain size of the films was determined by X-ray diffraction ŽXRD. using the Scherrer equation w17x and incorporating a correction factor for instrumental line broadening. A Siemens D5000 spectrom˚ Cu a line was employed. ŽWe eter using the 1.54 A remark parenthetically that these measurements were made for only a selected few thicknesses. The resistance vs. thickness measurements were performed in situ within the vacuum chamber, allowing good resistance data collection but prohibiting convenient XRD measurement. We are thus unable to comment, in the present work, on the relationship between grain size and film thickness..
219
Mayadas and Shatzkes model, the normalized resistivity rexprr bulk is given by:
rexp
1 s
r bulk
fŽa.
,
Ž 1.
where 3 f Ž a . s 1 y a q 3 a 2 y 3 a 3ln Ž 1 q ay1 . , 2
Ž 2.
and
as
lŽ T . R DŽ1 y R.
,
Ž 3.
where lŽT . is the electron mean free path in the film material without grain boundaries at temperature T, equal to 20 nm at room temperature w20x, R is the electron reflection coefficient at grain boundaries, and D is the mean grain diameter of the film material. The electron reflection coefficient has been experimentally determined to be equal to 0.5–0.7 for platinum w21x. Fig. 2 shows the results of our film resistance measurements for Pt films deposited in the absence of any applied substrate bias, i.e., for ion deposition energy of 100 eV. The resistance was converted to resistivity using the film length and thickness, and normalized to the classical bulk resistivity of Pt
3. Results and discussion The effect of grain boundary scattering on the electrical resistance of thin films has been studied in great detail by a number of workers. Mayadas and Shatzkes w3x assume a theoretical model in which a series of potential barriers scatters electrons, with separation between the barriers described by a Gaussian distribution. Palasantzas w18x also takes into account surface roughness parameters. For our method of deposition, it has been shown w19x that the rms surface roughness is only a few monolayers, and therefore, we ignore the effect of surface roughness in our resistivity calculations. According to the
Fig. 2. Measured normalized resistivity rexp r r bulk as a function of film thickness, for ion deposition energy of 100 eV Žpoints and solid curve.. The theoretically predicted dependence is also plotted for comparison Ždashed curve..
220
M. AÕrekh et al.r Applied Surface Science 158 (2000) 217–222
Ž r bulk s 1.06 = 10 -5 V P cm.. The normalized resistivity rexprr bulk is plotted as a function of film thickness. In addition to the experimental data, the theoretical normalized resistivity based on the model w3x described by Eqs. 1–3 is also shown in Fig. 2. In calculating the theoretical curve, we have taken the average grain size to be proportional to the film thickness, with a proportionality constant equal to the ratio of the grain size for the thickest film divided by the thickness of the thickest film Ži.e., the film at the end of the deposition run.. The grain size of the thickest film was 8 nm, as determined by XRD. Since the deposition was done at low ion energy, we assume that the substrate remained near room temperature. At room temperature, which corresponds to 0.15 times the platinum melting temperature Ž2045 K., the mobility of Pt atoms at the surface is small, and grain growth in the lateral direction is slow. The agreement between experiment and theory for film thickness greater than about 7 nm is quite good, but the agreement for thickness below about 5 nm is not so good. This is not altogether unexpected. For very small grain sizes, the linear relationship between grain size and film thickness that we have assumed may not hold. Although this linear relationship has been used successfully for very low energy deposition, it may not be a good approximation for deposition energies that are significantly hyperthermal. Here, even in the absence of applied bias voltage, the Pt ions have a mean deposition energy of 100 eV, which is much greater than the surface binding energy for Pt and therefore should alter the growth pattern. Another effect, electron scattering by the Pt free surface and the glass–Pt interface, is expected to become important at low thickness, leading to increased resistivity. Finally, there is always the possibility of discontinuities Žislands. in the film at these very low thicknesses, even though AFM studies of films produced by filtered cathodic arc deposition have shown that films in a thickness ˚ are continuous with an range down to about 300 A ˚ w19x. rms roughness of only 1–2 A Similar data for films deposited at a substrate bias of 1 kV, corresponding to an ion deposition energy of 2.2 keV as described above, are shown in Fig. 3. The deposition rate for this case was significantly lower than for films deposited at zero bias Ži.e.,
Fig. 3. Measured normalized resistivity rexp r r bulk as a function of film thickness, for ion deposition energy of 2.2 keV Žpoints and solid curve.. Theoretically predicted dependencies are also plotted: curve A, assuming a grain size equal to the film thickness; curve B, assuming a linear grain growth with final grain size 11 nm for the thickest film.
; 100 eV ion deposition energy. due to sputter removal of previously deposited film material by newly incident energetic ions, i.e., a kind of ‘‘selfetching’’ of the film. For the same deposition time, the maximum film thickness obtained at 2.2 keV ion energy was 4.1 nm, compared to 19 nm for 100 eV deposition energy. The experimentally determined normalized resistivity for Pt films formed at 2.2 keV ion energy is shown in Fig. 3. We also plot two curves that have been calculated using the theoretical model described by Eqs. 1–3 with two different assumptions regarding the correlation between grain size and film thickness. Curve A was obtained assuming that the grain size d is equal to the film thickness t Ži.e, d s t .. Curve B assumes a linear grain growth with a final grain size of 11 nm as determined by XRD, similar to the assumption used for the calculated curve of Fig. 2 Ži.e., d s kt, where k s d finalrtfinal s 11 nmr4.1 nm s 2.7.. It is clear from Fig. 3 that the agreement between experiment and theory given by curve B is poor for small grain sizes Žless than 5 nm.. The agreement between experiment and theory is better for the case of curve A. We hypothesize that the assumption made for curve A is better than that made for curve B because of the thermal annealing that takes place simultaneously with the deposition for the case of the sample produced at 2.2 keV ion energy. For deposition at
M. AÕrekh et al.r Applied Surface Science 158 (2000) 217–222
221
to be ; 11 nm, 1.6 times greater than that for the 100 eV deposition Ž; 8 nm.. Larger grain size then leads to less grain boundary scattering and lower resistivity at low film thickness.
4. Conclusion
Fig. 4. Measured resistivity rexp as a function of film thickness, for films deposited at ion energies of 100 eV and 2.2 keV. The bulk resistivity of Pt is shown by the dashed line.
high ion energy, there is a significant energy flux onto the growing film, which leads to an increase in temperature. During the early stages of deposition, when the film is still thin, the temperature of the film is low and very little grain growth due to annealing occurs. Towards the end of the deposition process, the total energy deposited into the film is high, and the film temperature is higher. Therefore, the rate of grain growth due to annealing at the end of the deposition is also higher. This difference in rates of grain growth between the early stages of deposition and the latter stages of deposition explains why the curve B assumption provides a bad fit, while curve A provides a reasonable fit. Finally, in Fig. 4, we show the same data as above for the two cases of high Ž2.2 keV. and low Ž100 eV. ion deposition energies, now plotted as unnormalized measured resistivity as a function of film thickness. One can see that the film resistivity is lower for the case of the more energetic deposition, and approaches the classical bulk resistivity value of 1.06 = 10y5 V P cm as the film thickness increases. Consistent with the description outlined above, we ascribe this as due to an elevated temperature of the growing film for the case of 2.2 keV ion deposition energy, in turn leading to a different grain growth regime. The higher ionratom surface mobility in this case leads to the formation of larger grains — the grain size for the 2.2 keV deposition was determined
We have investigated the electrical resistivity of thin platinum films in the thickness range 2.6–19 nm. The resistivity is dominated by grain boundary scattering for film thickness below ; 5 nm, and the measured values are in reasonable agreement with the theoretical model of Mayadas and Shatzkes. Films formed at higher ion deposition energy have larger grain size Ž11 nm at 2.2 keV. than those formed at lower ion deposition energy Ž8 nm at 100 eV., in turn leading to a resistivity at higher ion deposition energy that is lower than the low-energy deposition films because of reduced grain boundary scattering.
Acknowledgements This work was supported by the U.S. DOE, Office of Energy Research, under contract no. DEAC03-76SF00098.
References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x w11x
K. Fuchs, Proc. Cambridge Philos. Soc. 34 Ž1938. 100. E.H. Sondheimer, Adv. Phys. 1 Ž1952. 1. A.F. Mayadas, M. Shatzkes, Phys. Rev. B 1 Ž1970. 1382. P. Sheng, Philos. Mag. B 65 Ž1992. 357. N. Artunc, Z.Z. Ozturk, J. Phys.: Condens. Matter 5 Ž1993. 559. A.I. Maaroof, B.L. Evans, J. Appl. Phys. 76 Ž1994. 1047. R.G.P. van der Kraan, J.F. Jongste, H.M. Jaeger, G.C.A.M. Janssen, S. Radelaar, Phys. Rev. B 44 Ž1991. 13140. R.L. Boxman, P.J. Martin, .M. Sanders ŽEds.., Vacuum Arc Science and Technology, Noyes Data, New York, 1995. I.G. Brown, Cathodic arc deposition of films, in: Annu. Rev. Mater. Sci. Vol. 28 Annual Reviews, Palo Alto, CA, 1998. O.R. Monteiro, Z. Wang, I.G. Brown, J. Mater. Res. 12 Ž1997. 2401. M.-P. DelPlancke-Ogletree, O.R. Monteiro, J. Vac. Sci. Technol. A 15 Ž1997. 1943.
222
M. AÕrekh et al.r Applied Surface Science 158 (2000) 217–222
w12x R.A. MacGill, M.R. Dickinson, A. Anders, O.R. Monteiro, I.G. Brown, Rev. Sci. Instrum. 69 Ž1998. 801. w13x I.G. Brown, Rev. Sci. Instrum. 65 Ž1994. 3061. w14x I.A. Krinberg, M.P. Lukovnikova, J. Phys. D: Appl. Phys. 29 Ž1996. 2901. w15x S. Machlin, Materials Science in Microelectronics — The Relationships Between Thin Film Processing and Structure, Gyro Press, New York, 1995. w16x M. Ohring, The Materials Science of Thin Films, Academic Press, San Diego, 1992.
w17x C. Barrett, T.B. Massalski, in: Structure of Metals, 3rd edn., Pergamon, New York, 1980, p. 155. w18x G. Palasantzas, Phys. Rev. B 58 Ž1998. 9685. w19x M.C. Salvadori, R.M. Galvao, O.R. Monteiro, I.G. Brown, Thin Solid Films 325 Ž1998. 19. w20x C. Kittel, Introduction to Solid State Physics, Wiley, New York, 1976. w21x G. Ramaswamy, A.K. Raychaudhuri, K. Das Gupta, G. Sambandamurthy, Appl. Phys. A 66 Ž1998. S435.