Young's modulus of pulsed-laser deposited V6O13 thin films

JOURNAL OF APPLIED PHYSICS 105, 113504 共2009兲

Young’s modulus of pulsed-laser deposited V6O13 thin films Armando Rúa,1 Félix E. Fernández,1,a兲 Rafmag Cabrera,2 and Nelson Sepúlveda2 1

Department of Physics, University of Puerto Rico, Mayagüez, Puerto Rico 00681, USA Department of Electrical and Computer Engineering, University of Puerto Rico, Mayagüez, Puerto Rico 00681, USA

2

共Received 2 March 2009; accepted 21 April 2009; published online 1 June 2009兲 The mixed valence vanadium oxide V6O13 is an interesting material which exhibits an insulator-to-metal or semiconductor-to-semiconductor transition at low temperatures. It is also a much studied cathode material for lithium-based thin film batteries. However, there is little information available about its mechanical properties. Young’s modulus of pulsed-laser deposited V6O13 thin films has been determined by measuring the fundamental resonant frequency of silicon dioxide microcantilevers coated with V6O13. Laser deflection techniques were used to measure the cantilevers’ resonant frequencies. The films were further characterized by x-ray diffraction, atomic force microscopy, and resistivity measurements. The value of Young’s modulus associated with the direction along the material’s 共001兲 planes was found to be approximately 100 GPa. The values obtained for films ranging from 90 to 200 nm were equal within experimental error. © 2009 American Institute of Physics. 关DOI: 10.1063/1.3137191兴 I. INTRODUCTION

Most vanadium oxides exhibit an insulator-to-metal transition, which makes them interesting materials from the point of view of both fundamental theory and potential device applications. In V6O13 crystals resistivity changes of at least four orders of magnitude along all crystal axes have been observed around 150 K,1 while for V6O13 thin films no sharp changes have been observed, but a semiconductorsemiconductor transition has been reported near 125 K.2 This mixed valence compound 共with two V+4 cations for every V+5 cation兲 has a monoclinic crystal structure at room temperature and a very similar structure, also monoclinic, for the low-temperature phase.3 Phase diagrams for the V–O binary system show a narrow stoichiometric stability range for this compound.4 Due to its high capacity for Li+ intercalation associated with the ability of the vanadium ion to change its valence state, V6O13 is a good cathode material for lithiumbased thin film batteries.5–7 Accordingly, most studies of V6O13 thin film properties have centered on electrochemical characterization, such as galvanostatic charge/discharge tests,8 but there is little information about other properties, and the authors are not aware of studies of its elastic properties. This letter reports the results for Young’s modulus of V6O13 thin films, which should be useful when designing microbatteries, microelectromechanical systems, or other devices with this material. II. SAMPLE PREPARATION AND CHARACTERIZATION

For this work, V6O13 thin films with three different thicknesses: 90 nm 共sample 1兲, 170 nm 共sample 2兲, and 200 nm 共sample 3兲 were deposited by pulsed-laser deposition 共PLD兲 on samples with a set of previously fabricated SiO2 microcantilevers of different lengths. The cantilevers were fabricated by patterning a 4.15 ␮m thick SiO2 layer deposited on a standard p-type Si wafer by using gigascale a兲

Electronic mail: [email protected].

0021-8979/2009/105共11兲/113504/4/$25.00

integration plasma-enhanced chemical vapor deposition and released by isotropic etching of the Si using xenon difluoride 共XeF2兲 gas. The SiO2 film thickness was measured using a spectrophotometer 共Leitz MV-SP兲, whereas a profilometer 共Tencor Alphastep兲 was used for the V6O13 thin films, employing steps created in the same samples. Four cantilevers with widths of 45 ␮m and lengths ranging from 200 to 500 ␮m in steps of 100 ␮m were tested in each sample. All cantilever lengths were measured with an optical micrometer and found to be within 0.3% of the design value. The V6O13 films were fabricated in an oxygen and argon atmosphere under a total pressure of 70 mTorr, measured with a diaphragm capacitance sensor, and with Ar and O2 gas flows independently adjusted to 10 and 15 SCCM 共SCCM denotes cubic centimeter per minute at STP兲, respectively, with mass flow controllers. Background pressure in the chamber was of order 10−6 torr. A rotating metallic vanadium target was ablated by a pulsed KrF excimer laser 共Lambda Physik Compex 110, wavelength ␭ = 248 nm, 20 ns pulse duration, 10 pulses/ s, 4 J / cm2 fluence兲. During deposition, substrate temperature was kept at 500 ° C by a resistive heater with proportional-integral-differential 共PID兲 feedback controller. The resulting films have the characteristic yellowish-green color of V6O13. After fabrication, observation of the released cantilevers with a microscope did not show noticeable cantilever deflection, indicating that residual stress was not substantial. Figure 1 shows a ␪-2␪ diffractometer scan 共Bruker-AXS D8 Discover, using Cu K␣ radiation兲 for a sample grown simultaneously on a substrate from the same SiO2 / Si wafer as the cantilever samples. All reflections correspond to the V6O13 phase and, typically, only those for 共00l兲 reflections and up to the eighth order or more are observed, evidencing that the films are very strongly oriented, with the a-b crystal plane parallel to the sample surface. This preferred orientation is commonly observed for V6O13 and is associated with the greater packing density for these planes. Therefore, values of Young’s modulus obtained in this work for the V6O13

105, 113504-1

© 2009 American Institute of Physics

Downloaded 24 Aug 2009 to 128.210.126.199. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp

113504-2

J. Appl. Phys. 105, 113504 共2009兲

Rúa et al.

FIG. 1. XRD scan for V6O13 thin film grown on SiO2 / Si wafer simultaneously with films deposited on microcantilever structures. High orders of 共00l兲 reflections observed reveal preferred orientation of the film.

films correspond to a direction parallel to these planes. The resistivity of a V6O13 film deposited with identical growth conditions as for the cantilever samples was measured in the 300– 20 K temperature range. A semiconductorsemiconductor transition was observed at 125 K, similar to that reported in Ref. 2. The topography of the same film was characterized by atomic force microscopy 共Park Scientific CP Autoprobe AFM兲. An image for a 3 ⫻ 3 ␮m2 scan is presented in Fig. 2, showing that the sample is well crystallized, with lateral crystallite sizes ranging from less than 100 nm to over 500 nm and no perceivable in-plane ordering, as could be expected for samples grown on amorphous SiO2. III. EXPERIMENTAL RESULTS AND DISCUSSION

The method used to determine Young’s modulus of the V6O13 thin films consists of piezoelectric actuation of the sample and laser deflection techniques for detection of the resulting cantilever resonant vibration, as described elsewhere.9 Measurements were performed in a vacuum chamber to avoid viscous damping by the atmosphere. A He–Ne laser beam entering through a glass window was focused on the surface of each cantilever in turn. Intensity modulation of the reflected signal due to cantilever vibration was analyzed with a network analyzer 共Agilent E4411T兲 as the driving frequency was scanned. Sharp amplitude maxima

FIG. 3. 共Color online兲 Cantilever fundamental resonant frequency vs squared inverse of cantilever length 共L兲 for uncoated cantilevers 共circles兲 and the same cantilevers coated with V6O13 共squares兲. Lines are linear fits to the experimental data points. Coating thickness was 200 nm for the case shown.

were found and recorded at the fundamental mechanical resonant frequency of each cantilever. This frequency depends on cantilever geometry and the density and elastic modulus of the material. Analytical expressions for resonant frequencies of coated and uncoated cantilevers with simple geometries are well known. For an uncoated cantilever with rectangular cross section, the fundamental resonant frequency 共f u兲 is approximately

冋

fu =

1/2

共1兲

,

where L, t1, ␳1, and E1 are, respectively, the length, thickness, density, and Young’s modulus of the material,10 while for a coated cantilever the fundamental 共f c兲 is11 fc =

冉

3.52 E1 2 ␲ L 2 t 1␳ 1 + t 2␳ 2

冊冉 1/2

At32 t31 At2t1共t2 + t1兲2 + + 12 12 4共At2 + t1兲

冊

1/2

, 共2兲

where t2 and ␳2 are the thickness and density of the coating, and A = E2 / E1 is the ratio of Young’s moduli of the two materials 共A = EV6O13 / ESiO2 in this case兲. Validity of this expression is not limited to the case t2 Ⰶ t1. Squaring the expressions for the frequencies and dividing them, it is directly found that f 2c f 2u

FIG. 2. 共Color online兲 AFM image for V6O13 film surface. The area scanned is 3 ⫻ 3 ␮m2.

冉冊册

1.016 E1t21 2␲L2 ␳1

=

12 t21

冉

␳1 t 1␳ 1 + t 2␳ 2

冊冉

冊

At32 t31 At2t1共t1 + t2兲2 . + + 12 12 4共At2 + t1兲

共3兲

Since there can be substantial differences between the mechanical properties of SiO2 thin films deposited by different methods—and sometimes even different runs—the uncoated cantilevers were tested first in order to obtain SiO2 Young’s modulus for each sample. The fundamental resonant frequency of the four cantilevers in each of the three samples were measured and plotted against 1 / L2. Figure 3 shows the experimental data 共circles兲 and a linear fit for sample 3. Measurement errors associated with the frequency and inverse squared lengths are smaller than the data markers in this plot. While the cantilever lengths are known to ⫾0.3%, as mentioned before, underetching effects may result in effective lengths somewhat different from measured values. From the


113504-3

J. Appl. Phys. 105, 113504 共2009兲

Rúa et al.

FIG. 4. 共Color online兲 Normalized cantilever vibration amplitude measured as a function of frequency, showing fundamental resonant peaks for the same 300 ␮m long SiO2 cantilever before 共left curve兲 and after 共right curve兲 it was coated with a 200 nm thick V6O13 film. Note the scale change after the break in the frequency scale.

graph, this effect appears to be negligible for this sample, but because the value of the cantilever length is raised to the fourth power when computing the bare cantilever modulus, even small deviations can cause non-negligible error in the calculated E1 values. Density and thickness of the cantilever material can be assumed to be the same for all cantilevers in one sample, since they are very close in the substrate. However, uncertainties in these values are not negligible and strongly affect the error associated with the final E1 result. The instrumental accuracy of the spectrophotometer thickness measurements is ⫾3% and densities for SiO2 films depend strongly on deposition conditions. In order to improve the accuracy of the cantilever parameter data, SiO2 / Si samples with thinner SiO2 films but produced in the same manner were tested with a multiple-wavelength ellipsometer 共J. A. Woolam M-44兲. Ellipsometric data were fitted using a three-parameter Cauchy relation for the refractive index of the films and with thicknesses consistent with those measured with the spectrophotometer. Based on these models, a SiO2 film density of 2160 kg/ m3 ⫾ 5% was estimated. This was the value assumed in all subsequent calculations. Taking into account the errors for density, thickness, and lengths, the averaged value obtained for Young’s modulus of the cantilever material for all samples was 44⫾ 4 GPa. In each of the samples, the greatest deviation was found for the shortest cantilever 共L = 200 ␮m兲, with a calculated E1 value which was always noticeably lower than those for the other cantilevers. This may be due in part to the larger effect of the cantilever underetching. After the V6O13 coatings were deposited in the manner described before on the same microcantilever samples, these were again tested to find the new resonance frequencies. The second plot in Fig. 3 共squares兲 shows again the first mode resonant frequency versus 1 / L2 for the same four cantilevers as before, but now after these were coated. Hence, the 1 / L2 dependency described by Eq. 共2兲 is also well satisfied. Figure 4 shows the resonant peaks for the same 300 ␮m long SiO2 cantilever before and after the V6O13 coating 共200 nm thick兲. Even though the mass of the coated cantilever is greater than before, its resonant frequency is increased because the effective rigidity has increased, revealing that Young’s modulus of the coating is substantially higher than that of the bare can-

tilever material itself. The breadth of the resonance peak is also noticeably increased for the coated cantilever 共note the change in horizontal scale in Fig. 4兲 due to the larger energy losses in that case. Using both measured frequencies for each cantilever, Eq. 共3兲 was solved to determine the value of the ratio A. In this analysis the bulk value of 3910 kg/ m3 was assumed for the V6O13 films, which can be considered an upper limit. Once the value of A is obtained, inserting the average value of E1 determined for the same sample before coating yields Young’s modulus of the V6O13 film material. For each of the three samples, the averages of the four results for V6O13 Young’s modulus are 95⫾ 12, 95⫾ 8, and 110⫾ 9 GPa, for the 90, 170, and 200 nm thick films, respectively. The larger relative error for the first sample is due to the larger effect of film thickness error.

IV. CONCLUSIONS

The elastic modulus for V6O13 thin films with different thicknesses was measured by a vibrating cantilever technique. The films were deposited by PLD onto SiO2 glass microcantilevers and had strong preferred orientation, with the 共001兲 planes parallel to the sample surface. While the thickest film yielded the largest value for the modulus, the results were equal within experimental error and average to 100⫾ 10 GPa. Although the density of the V6O13 films is expected to be lower than its bulk crystal value, the effect on the resulting modulus is relatively small, with a 10% reduction in density lowering the calculated modulus by less than 4 GPa for all samples. In future work it should be of interest to extend these measurements to thicker films and to compare the results with those which could be obtained with other techniques, such as nanoindentation. In addition, similar studies of lithiated phases of this material 共LixV6O13兲 would provide insight about how its elastic properties are affected during charge-discharge cycles.

ACKNOWLEDGMENTS

Microcantilever fabrication for this work was performed at the Cornell NanoScale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation 共Grant No. ECS0335765兲. N.S. was supported by the NNIN Laboratory Experience for Faculty Program. 1

K. Kawashima, Y. Ueda, K. Kosuge, and S. Kachi, J. Cryst. Growth 26, 321 共1974兲. 2 M. B. Sahana and S. A. Shivashankar, J. Mater. Res. 19, 2859 共2004兲. 3 International Centre for Diffraction Data, Powder Diffraction File 75– 1140. 4 H. Katzke, P. Tolédano, and W. Depmeier, Phys. Rev. B 68, 024109 共2003兲. 5 D. F. Shriver and G. C. Farrington, Chem. Eng. News 20, 43 共1985兲. 6 T. Schmitt, A. Augustsson, J. Nordgren, L.-C. Duda, J. Höwing, T. Gustafsson, U. Schwingenschlögl, and V. Eyert, Appl. Phys. Lett. 86, 064101 共2005兲. 7 M. Menetrier, A. Levasseur, and C. Delmas, Mater. Sci. Eng., B 3, 103


113504-4

共1989兲. Y. J. Park, K. S. Ryu, N.-G. Park, Y.-S. Hong, and S. H. Chang, J. Electrochem. Soc. 149, A597 共2002兲. 9 N. Sepúlveda, A. Rúa, R. Cabrera, and F. Fernández, Appl. Phys. Lett. 92, 8

J. Appl. Phys. 105, 113504 共2009兲

Rúa et al.

191913 共2008兲. W. C. Young, Roark’s Formulas for Stress and Strain 共McGraw-Hill, New York, 1989兲, p. 117. 11 Q. M. Wang and L. E. Cross, J. Appl. Phys. 83, 5358 共1998兲.

10
