In situ measurement of stresses in diamond-like carbon films

In situ measurement of stresses in diamond-like carbon films

Diamond and Related Materials 12 (2003) 2119–2127 In situ measurement of stresses in diamond-like carbon films Marie-Paule Delplancke-Ogletreea,1 , O...

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Diamond and Related Materials 12 (2003) 2119–2127

In situ measurement of stresses in diamond-like carbon films Marie-Paule Delplancke-Ogletreea,1 , Othon R. Monteirob,* a Universite Libre de Bruxelles, Brussels, Belgium Lawrence Berkeley National Laboratory, University of California, Mail Stop 53-004, One Cyclotron Road, Berkeley, CA 94720, USA

b

Received 20 February 2003; received in revised form 15 May 2003; accepted 5 June 2003

Abstract In situ determination of stresses in thin films can be used as an important tool to assist process development as well as to understand the thermodynamics of film formation. A simple technique for the measurement of stresses in growing films is described here. The technique consists of measuring the displacement of a laser beam reflected from the film surface. Displacement is induced by changes in the radius of the curvature of the substrate resulting from stresses in the film. The detector sensitivity at the used wavelength (635 nm) is approximately 12 mV mmy1 , for which our experimental set-up is equivalent to 4 mV mrady1. The actual data collected consist of the reflected beam displacement vs. time, and provides at any instant the value of the average stress. By knowing the deposition rate, time is directly correlated with film thickness, and the local stress can be determined. Examples of measurement of stresses in tetragonally bonded amorphous carbon films prepared by filtered cathodic arc are presented, as well as how this technique can be used to design the deposition process to virtually eliminate intrinsic stresses. 䊚 2003 Elsevier B.V. All rights reserved. Keywords: Diamond-like carbon; Position sensitive detector; Stresses

1. Introduction The magnitude of internal stresses in coatings has a significant impact in its physico-chemical properties and consequently in their ability to meet performance requirements. Phenomena affected by the level of stresses include its resistance to environmental attack, electromigration, phase stability, etc. However, presence of stresses in coatings is not necessarily a negative characteristic; some small compressive stress is usually beneficial for protective coatings. On the other hand, similar levels of stresses in membranes used in microelectro-mechanical systems would be unacceptable due to bending. Those two simple examples illustrate the importance of being able to measure and control the level of internal stresses in deposited films. *Corresponding author. Tel.: q1-510-486-6159; fax: q1-510-4864374. E-mail address: [email protected] (O.R. Monteiro). 1 Chercheur Qualifie´ of the National Fund for Scientific Research (French Community of Belgium).

Internal stresses are typically classified depending on its origin as thermal or intrinsic. Thermal stresses originate when there is a difference in thermal expansion coefficient between the film and the substrate, and the operating temperature of the coated piece is different from the deposition temperature. Intrinsic stresses on the other hand, have more ill-defined origins, which are typically associated with the growth process or postdeposition processing. In addition to the specific properties of the coating itself, adhesion between film and substrate is a critical property of the film–substrate system, and can also be greatly affected by the level of internal stresses. One material that has been plagued by the excessive level of intrinsic stresses is non-hydrogenated diamondlike carbon (DLC) w1–3x, in particular those with a high content of sp3 hybridization, commonly referred to as ta-C. An extensive review article on the methods of fabrication and properties of DLC has been recently published w4x. Until recently, for instance, only relatively thin DLC films could be prepared by filtered cathodic arc or laser ablation before delamination occurred. Ther-

0925-9635/03/$ - see front matter 䊚 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0925-9635(03)00240-1

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Fig. 1. Schematic representation of the stress measurement process. A micrometer is used to determine the shift of the reflected laser beam from the surface of the depositing film.

mal annealing w5,6x and ion-bombardment w7–9x were later proposed to diminish stresses to levels compatible with thicker films. Since both of these processes can be used for controlling stresses during growth, process development can benefit from having an in situ tool that allows continuous monitoring of the stresses. This article reports on an inexpensive technique for the in situ determination of stress in growing films. The method is based on dynamic measurement of the radius of curvature of the substrate, and is similar to the one discussed by Honda et al. w10x for sputtered films. Here, we expand the treatment in Ref. w10x by determining both average and local stress. A later version of yet another similar technique was proposed by Fitz et al. w11x and corrects for effects of temperature gradients in the substrate. Fitz’s technique, however, requires complex shape substrates. In this article, we present and discuss our experimental technique, as well as demonstrate its usefulness to evaluate the dynamic evolution of the intrinsic stress in DLC produced by filtered cathodic arc. 2. Experimental technique A schematic representation of the stress measurement apparatus is shown in Fig. 1. A laser source (pen) with variable focus (Thorlabs, Inc.—available from: http:yy www.thorlabs.com) is focused onto the substrate surface. The laser spot size can be focussed to 75 mm, and the focal range varies from 50 mm to `. Variable focal length here is particularly advantageous to allow flexibility in substrate positioning inside the deposition chamber. The laser source and the detector are placed outside the process chamber. The position of the reflected laser beam is measured with a four-segment position sensitive detector (hereafter referred as PSD) (Pacific Silicon Sensor, Inc.—available from: http:yy www.pacific-sensor.com) with an active area of 50 mm2. The substrates used here were rectangular strips of (1 0 0) Si wafers with dimensions 20=5=0.5 mm3. The substrates were located 320 mm away from the detector surface, and clamped from one side onto a

water-cooled aluminum substrate holder. In order to improve the thermal contact with the substrate holder, a thin layer of conductive silver paste is painted between the substrate end and the holder. The photo currents (and voltages) produced in the four segments of the PSD are independently measured: UTR, UTL, UBR, UBL (top-right, top-left, bottom-right and bottom left, respectively). In our experimental setup (which also included a quartz window in the laser path going in and out of the deposition chamber), the highest detected voltage in the PSD was UTLqUBLq UTRqUBRs3.6 V. The detector is mounted on a high precision stage on an optical rail with a micrometer control with resolution of 1 mm, and the displacement of the beam is determined by the variation of signal from left to the right in the detector, i.e. (UTLqUBL)y (UTRqUBR). A displacement of 300 mm corresponds to a change in the voltage signal of (UTLqUBL)y(UTR qUBR ) from y50 to q50% the maximum. Therefore, detector response can be estimated to be 3.6 Vy3=10y4 ms12 mV mmy1, which for the experimental set-up here, correspond to approximately 4 mV mrady1. Thus, a noise level of 10 mV corresponds to a detection limit of the angular displacement of the laser beam of approximately 2.5 mrad. The actual sensitivity in terms of stress will depend on the physical characteristics of the substrate used, i.e. thinner substrates will bend more at smaller stresses. In the present study, the depositions were conducted on (0 0 1) silicon wafers with thickness approximately 500 mm, for which the bi-axial modulus is Yy(1yn)s181 GPa, and under these conditions stresses in the kPa range can be measured. In order to eliminate the effect of the laser intensity on the determination of the displacement of the reflected laser, we normalized the voltage difference by the total voltage B

Spot positionsfC D

ŽUTLqUBL.yŽUTRqUBR. E UTLqUBLqUTRqUBR

F G

(1)

Laser intensity may change over time due to changes of the properties of the film and some possible contamination of the quartz window, and this normalization eliminates such effects. In order to verify that there was no effect of unwanted temperature variation during deposition, the substrate curvature was monitored for 20 min after the end of each deposition experiment, and the changes observed were within the experimental accuracy of the measurement. Should there be distortions due to temperature variation, the procedure proposed in Ref. w11x can be used, although the complexity of the set-up increases. The DLC films used throughout this investigation were prepared by metal plasma immersion ion implan-

M.-P. Delplancke-Ogletree, O.R. Monteiro / Diamond and Related Materials 12 (2003) 2119–2127

tation and deposition (MePIIID). In this process, a plasma stream is produced by a pulsed cathodic arc plasma source w12x, and directed towards the substrate via a quarter torus macroparticle filter. The substrate is repetitively pulse-biased to negative voltages. During the periods that the bias voltage is off, plasma ions stream towards the substrate with relatively low energies (f20 eV), where they can condense or be implanted at very shallow depths. The native energy of this streaming plasma is a function of the ion species w13x. During the periods that the bias voltage is on, a high voltage sheath rapidly forms at the substrate–plasma boundary, and plasma ions are accelerated through the sheath and into the substrate. Therefore, during film growth there are alternating periods of high-energy ions and periods of low-energy ions or atoms. A full description of the deposition apparatus is given in Refs. w14,15x. Several DLC films were prepared under different conditions, and their stresses were monitored during growth. The arc conditions were the same, and the magnitude of the bias voltage applied to the substrate varied: y100, y2000 V and combination of both. In this article, we report on a chosen monolithic DLC film prepared with bias voltage of y100 V and on a multilayer formed by alternating the bias voltage applied to the substrate from y100 to y2000 V. The deposition of the multilayer starts with a bias voltage of y2000 V for 100 pulses. Then the bias voltage is decreased to y100 V for a predefined number of pulses (500). After that the bias voltage is alternated between high and low bias voltages, with the same number of pulses as the initial steps. Film density was estimated by a combination of atomic force microscopy and Rutherford backscattering spectroscopy. Concurrently with the stress measurements, DLC was deposited on witness coupons with well-defined masked regions. The total deposited C (atoms per cm2) was determined by Rutherford backscattering spectroscopy. The thickness of the films was measured by atomic force microscopy in contact mode on the step produced by the masked regions. The accuracy of the RBS data is of "5%. The density of the DLC films was then determined by dividing the total deposited C atoms per unit area by the film thickness. 3. Data analysis When the film and substrate are bonded, they are constrained to the same lateral dimension, and stresses develop to satisfy a force balance shown in Fig. 2. By assuming that the film thickness (hf) is much smaller than the substrate thickness (hS ), which is much smaller than the length of the substrate (L), hf
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Fig. 2. Balance of forces in a film–substrate system assuming no bending.

sfhfsysShS

(2)

or B

B Y E Yf E F´fhfsC S F´ShS, D 1ynf G D 1ynS G

C

(3)

where YS,f are the Young modulus for the substrate and film, respectively, and nS,f are the Poisson ratio. Since hf
NsMsy

YS h2S 1ynS 6hfR

(4)

Conventionally, compressive stresses are assigned a negative sign and tensile stresses a positive one. The measurement of sample curvature is carried out using an analysis similar to that presented by Suhir w17x. A schematic representation of the laser path for the incident and reflected beams is shown in Fig. 3, where all the relevant geometric parameters for the determination of the stress in the film are indicated. For small deflections, a bending plate can be described by a second order polynomial expression f(x) w17x: f(x)sax2qbxqc

(5)

which, by construction, can be simplified to f(x)sax2 Thus, the curvature is defined by

(6)

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Eqs. (11) and (12) yield d2 D2

y

1q

y1q as

(13)

d 2l D

and substituting Eq. (13) into Eq. (7), the radius of curvature is determined for a measured displacement d l Rs

d D

f 2

d 1q 2 D

y

y1q

Fig. 3. Geometric scheme of laser trajectory and substrate deflection.

d 2f 1 dx2 2a sB s 3y2 E R df (1q2ax)3y2 C1q F D dx G

(7)

and from the geometry of the arrangement shown in Fig. 3 df s2axstanw dx

(8)

and d D

(9)

Thus, the trigonometric identity 2tanw tan(2w)s 1ytan2w

(10)

y

1q

tanws

d2 D2

d D

df Z Z s2al dx Zxsl Z Z

hf

| s(z)dz

(15)

0

and the instantaneous stress s(z) can be calculated by solving Eq. (15) for s(z) as a function of the experimentally determined parameters: NsM and hf. Differentiating Eq. (15), dNsM 1 sy 2 dhf hf

|

w

hf

s(z)dzq 0

s(z)sNsMZzqz (11)

Since tan wZxsls

1 hf

1 d hf dhf y

x|

hf

z

|

s(z)dz 0

(16)

~

and solving for s(z), we obtain

can be solved to yield; y1q

(14)

Oftentimes in thin films the stress is not uniform, and a stress dependence on film thickness is observed. This can be expected for instance in films that have a nonhomogeneous microstructure. The use of Stoney’s equation w16x to determine the stress in thin films assumes that the stress is uniform, which results in the average and the local stress being equal. When the stress field is not uniform, the stress calculated according to Eq. (4) is in fact the average stress over the thickness of the film. This is the reason why we wrote NsMinstead of s in Eq. (4). The average stress is defined as: NsMs

tan(2w)s

2Dl d

(12)

dNsM Z d Z s ŽtfNsMZtf. dt Zz dt Z Z

(17)

In the experimental procedure used here, the instantaneous film thickness is estimated by measuring the film thickness at the end of the deposition, and determining the deposition rate in nanometer per pulse, which is equivalent to nanometer per unit of time. As it will be discussed later in this article, a true monitoring of film thickness can minimize some uncertainties in the calculation of stresses.

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Fig. 4. Evolution of average intrinsic stress in the film during deposition of a monolithic DLC film, as calculated using Stoney’s equation.

Fig. 5. Absolute value of product stress=thickness for monolithic DLC film used to determine the localized stress.

4. Stress evolution in DLC films The apparatus and technique described in the former sections were used to continuously monitor the intrinsic stress in the DLC films during the deposition process. In the case of a DLC film prepared using a bias voltage of y100 V, the average stress is plotted in Fig. 4. Compressive stresses receive the conventional negative sign. According to Fig. 4, the average stress in very thin

films is compressive but with small magnitude, and increases as the film thickens. It eventually stabilizes approximately 12 GPa for films thicker than 8 nm. Stress of DLC films with thickness in the range of 50– 100 nm, and prepared under the same conditions has been reported in the range 10–12 GPa w6,18x. In order to determine the instantaneous stress, before Eq. (17) can be used, it is necessary to plot the absolute value of the product NsMhf vs. hf, as shown in Fig. 5.

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Fig. 6. Profile of carbon atoms sequentially deposited under two deposition conditions (y100 and y2000 V) obtained by Monte Carlo simulation (T-DYN). This profile indicates the depth of interaction between the incident ions and the film.

The instantaneous stress is low at the early stages of growth and increases with deposition to approximately 12 GPa. It is reasonable to expect that the instantaneous stress converges to the average stress in thick films, if the transient is limited to the early stages of deposition. It is relevant not to loose sight of the uncertainties involved in differentiating experimental data, but the accuracy of the calculation can improve with improving the data acquisition process. In general, during thin film deposition (using energetic processes or not), terminal levels of intrinsic stresses are achieved only after full coalescence of the film. Therefore, in a first analysis, one could conclude that the observed low instantaneous stress at the early stages of deposition here are also due to un-coalesced islands. However, the experimental evidence in DLC formation points towards a layer-type growth. For instance, transmission electron microscopy has shown that there is no evidence of any columnar growth in energetic deposition of carbon films w19x, and films as thin as 3 nm were tested for corrosion and show no indication of defects w20x. Thus, the low initial stress is tentatively linked to presence of a low density layer that has been observed by Siegal and co-workers w19x. It has been suggested previously w7–9x that stress reduction can be achieved by ion bombardment at high ion energies during the deposition of DLC. We have used the technique described in this article to verify this hypothesis. An experiment was then performed in which the bias voltage changed between y100 and y2000 V. Monolithic layers prepared with bias voltage of y100 V have typically high stress (10–12 GPa) w6x. The

deposition here was carried out for a large number of pulses (500) with bias voltage of y100 V, followed by y2000 V for a short number of pulses (50 in one case and 100 in another). A Monte Carlo simulation software, T-DYN w21,22x, was used to calculate the profile of the C atoms in the multilayer produced in this experiment, and the results are shown in Fig. 6. The atomic fraction of the C atoms produced in each phase of the deposition is plotted in Fig. 6, and shows that the tail of the C concentration produced at y2 kV bias voltage penetrates through the entire y100 V layer, and thus can alter the properties of the entire layer. On the contrary, the 100 V Cq ions cause very little modification on the immediately preceding layer. The average stress during deposition of the multilayer described in the previous paragraph is shown in Fig. 7. It is readily seen that after each high-energy step, the average stress in the film is brought to (approximately) zero. Attempts have been made in the past to reduce intrinsic stresses in DLC films by producing mutilayers consisting of alternating layers of sp3-rich (‘hard’) and sp3-not-so-rich (‘soft’) carbon layers w2x. The multilayers in that case consisted of fully developed individual layers: one with high density and the other one with low density. In that case, the final stress would be some average of the properties of the individual layers. Here, on the contrary, the high-energy step is too short duration to form a discrete ‘soft’ DLC film. Film density was used here as a parameter to indicate the degree of change in sp3 content w23x in DLC as a consequence of the high-energy bombardment. The DLC density of the films produced at y100 and y2000 V

M.-P. Delplancke-Ogletree, O.R. Monteiro / Diamond and Related Materials 12 (2003) 2119–2127

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Fig. 7. Evolution of average intrinsic stress in a DLC multilayer during deposition, in which we alternate long periods of deposition with low bias voltages, with short periods of deposition with high bias voltages.

were 2.81 and 2.47 g cmy3, respectively. The density of a stress relaxed film was 2.79 g cmy3. This reduction in density is small (in fact it is within the uncertainty of the measurement), and should not account for large changes in sp3 content and therefore in film properties. Increasing the number of high voltage pulses between the low voltage pulses led to greater density reduction.

In the deposition process used here, stress relaxation in the multilayer is accomplished layer by layer. Since the measured stress is the average stress, the increase in the measured stress of the entire film after the addition of the nth-layer is entirely due to the stress in that layer. The instantaneous stress is estimated from the graph in Fig. 8, as the slope of each segment, according to Eq.

Fig. 8. Absolute value of product stress=thickness for multilayer DLC film used to determine the localized stress.

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(17). The slope for the first four sections (four inclined segments in Fig. 8) is 10.5"1.0 GPa. This value agrees well with the values calculated for the stress in the monolithic films. The last two segments in Fig. 8 on the other hand have larger slopes (up to 20 GPa). This value is too high, and does not agree with the data presented in Figs. 4 and 5, which supports a stabilization of the stress after some initial transient period. Variation of substrate temperature has been ruled out as a source of error because no displacement of the laser beam was observed after the deposition was stopped. One possible source of errors is the estimation of the film thickness, as previously mentioned. The actual measurables in this experiment are the deflection of the laser beam and the final thickness of the film. The stress is calculated from Eqs. (4) and (17), which have the radius of curvature and the film thickness as variables. Calculation of the radius of curvature of the film substrate system involves only geometric considerations (Eq. (14)), and therefore is independent of the physics of the deposition. On the other hand, errors on the estimation of thickness can affect the curve in Fig. 8. These errors are expected to worsen towards the end of the deposition, when the cathode is heavily worn. In order to improve the accuracy of the method described here, it is important to implement an in situ measurement of the film thickness. The assumption (implicitly made here) that the total amount of Cq ions deposited in each arc pulse is constant through the entire deposition and independent of the bias voltage is not fully correct. Some long-term decrease in ion flux due to cathode consumption may occur. Moreover, selfsputtering rates of the carbon film will differ for different bias voltages. Thus, an upgrade for the system will require real thickness monitoring. 5. Summary and conclusions We have presented a technique for in situ determination of stress, and applied it to investigate the stress evolution during the deposition of DLC films prepared by filtered cathodic arc deposition. The deflection of a laser beam reflected from the surface of the growing film of known thickness is measured, and the average stresses are calculated by using Stoney’s equation. An expression for the local stress as a function of the average stress and the geometry of the system is deduced. For many practical applications, local stress, rather than average stress, is the important parameter that affects the thermodynamics of the system. We provide examples of application of this technique for the growth of a monolithic DLC film and a multilayer, and discuss possible causes for errors. The stress evolution during deposition of the monolithic film is characterized by an initial stage where the stress increas-

es with thickness, and eventually levels off at a value similar to previously reported. The initial transient phase is tentatively here correlated to the presence of a low density phase at the DLC-silicon interface. In situ determination of stress during the multilayer deposition provides some insight on the overall film properties. It was possible to relax stresses on a layer by layer process, so that the final average stress is determined solely by the stress in the last (un-relaxed) DLC layer. Stress relaxation was accomplished without significantly changing the properties of the film. This process totally removes the constrain on film thickness imposed by the high level of intrinsic stresses typically associated to DLC films. Fully relaxed DLC can indeed be prepared by terminating the process with a highenergy phase. Acknowledgments We would like to express their gratitude for the assistance of Robert A. MacGill and Joe Wallig. We also would like to thank the helpful discussions with Frank Ogletree, Andre Anders and Marcela M.M. Bilek. This work was supported by US Department of Energy, under contract No. DE-AC03-76SF00098. References w1x D.R. McKenzie, D. Muller, B.A. Pailthorpe, Phys. Rev. Lett. 67 (6) (1991) 773–776. w2x S. Anders, D.L. Callahan, G.M. Pharr, T.Y. Tsui, C. Singh Bhatia, Surf. Coat. Technol. 94y95 (1997) 189–194. w3x Y. Lifshitz, Diamond Relat. Mater. 8 (1999) 1659–1676. w4x Robertson, J. Mater. Sci. Eng. R 37 (2002) 129–281. w5x T.A. Friedmann, J.P. Sullivan, J.A. Knapp, et al., Appl. Phys. Lett. 71 (26) (1997) 3820–3822. w6x O.R. Monteiro, J.W. Ager III, D.H. Lee, R. Yu Lo, K.C. Walter, M.J. Nastasi, J. Appl. Phys. 88 (5) (2000) 2395–2399. w7x R.N. Tarrant, C.S. Montross, D.R. McKenzie, Surf. Coat. Technol. 136 (2001) 188–191. w8x M.M.M. Bilek, D.R. McKenzie, R.N. Tarrant, S.H.M. Lim, D.G. McCulloch, Surf. Coat. Technol. 156 (2002) 136–142. w9x M.M.M. Bilek, R.N. Tarrant, D.R. McKenzie, S.H.N Lim, D.G. McCulloch, Proceedings of the XXth International Symposium on Discharges and Electrical Insulation in Vacuum, 95–102 (2002), Ed. IEEE. w10x N. Honda, F. Shoji, S. Kidoguchi, Y. Hamada, M. Nagata, K. Oura, Sensors Actuators A 62 (1997) 663–667. w11x C. Fitz, W. Fukarek, A. Kolitsch, W. Moller, Surf. Coat. Technol. 128–129 (2000) 474–478. w12x R.A. MacGill, M.R. Dickinson, A. Anders, O.R. Monteiro, I.G. Brown, Rev. Sci. Instrum. 69 (1998) 801–803. w13x I.G. Brown, Annu. Rev. Mater. Sci. 28 (1998) 243–269. w14x O.R. Monteiro, W. Zhi, I.G. Brown, J. Mater. Res. 12 (1997) 2401–2410. w15x A. Anders, S. Anders, I.G. Brown, M.R. Dickinson, R.A. MacGill, J. Vac. Sci. Technol. B 12 (2) (1994) 815–820. w16x G. Stoney, Proc. R. Soc. Lond. A 82 (1909) 172–176.

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