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Uncertainty compensation methods for quantitative hardness measurement of materials using atomic force microscope nanoindentation technique
Thin Solid Films 546 (2013) 448–452
Contents lists available at ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Uncertainty compensation methods for quantitative hardness measurement of materials using atomic force microscope nanoindentation technique Jungmin Lee ⁎, Chung Yi Kim, Minho Joo, Kyuho Park Materials and Components Laboratory, LG Electronics Advanced Research Institute, Seoul 137-724, Korea
a r t i c l e
i n f o
Available online 21 May 2013 Keywords: AFM nanoindentation Tip characterization Hardness measurement Uncertainty compensation
a b s t r a c t We suggest uncertainty compensation methods for the quantification of nanoscale indentation using atomic force microscopy (AFM). The main error factors in the force–distance curves originated from the difference between theoretical and real shape of AFM tip during nanoscale indentation measurements. For the uncertainty compensations of tip shapes and misalignment of loading axis, we applied the enhanced tip geometry function and Y-scanner moving to the AFM measurements. Three different materials such as Si wafer, glass, and Au film were characterized with these compensation methods. By applying compensation methods, our results show the decreased values from 167% to 39% below 100 nm indenting depth compared with the literature values. These compensation methods applied to thin films will show the advanced quantitative analysis of hardness measurements using nanoscale indenting AFM. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The nanoindentation method using atomic force microscopy (AFM) is well known for evaluating mechanical properties of thin films [1–3]. Before the development of AFM, there have been various studies for hardness measurement with load of indenter tip and deformed surface using indentation equipment. In the case of a thin film on substrate, however, it is not possible for quantitative hardness measurement because of a large tip radius and low sensitive control of force. In 1989, Burnham and Colton pioneered the use of AFMlike instruments as a nanoindenter to measure nanomechanical properties at surfaces with high sensitive control of force and piezoelectric scanner movement in the z direction [4]. In recent years, there have been various efforts to measure the quantitative hardness of thin films using AFM nanoindentation [5–12]. Unfortunately, as most of these reports have various uncertainties due to the lack of calibration of key components, the measured hardness values are non-uniform according to the indenting depth and far from the actual values. Therefore, it is essentially needed to compensate these errors resulting in the uncertainties. Among uncertainties, two factors are mainly considered as compensation parameters for quantitative hardness using AFM nanoindentation. One is that the theoretical tip geometry function representing the relationship between the projected contact area and the indenting depth is different with real tip geometry. A cube-corner tip is used for AFM nanoindentation. The projected contact area is generally
⁎ Corresponding author. E-mail address: [email protected] (J. Lee). 0040-6090/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tsf.2013.05.040
obtained by the calculation of theoretical tip geometry as a function of indenting depth, Ap ¼ 2:6hc
2
ð1Þ
where Ap is the projected contact area of tip and hc is the indenting depth. This theoretical function is available for only ideal cubecorner shape because the real shapes of tips are different from ideal model. Generally used cube-corner tips have tip radius, a few tens of nanometers, on the apex. This rounded shape of tip apex induces measurement errors according to the indenting depth below the depth of 100 nm [11,13]. The other is that the non-uniformity of perpendicular loading axis arises from cantilever deflection during indenting. This non-uniform loading axis to the sample makes the asymmetry shapes on the sample surface. A deformed surface shape is another error factor compared with a calculated projected contact area. In this paper, we suggest uncertainty compensation methods in AFM nanoindentation. The objective of this paper is to improve the quantitative hardness measurements of materials through applying the uncertainty compensation methods to AFM nanoindentation procedures. 2. Experimental details We carried out nanoindentation measurements using a XE-150 (ParkSystems Corp.) with cube-corner shaped diamond tip. The spring constant of the cantilever was determined by simulated value using the finite elements analysis in Fraderic and Sansoz's study [10].
J. Lee et al. / Thin Solid Films 546 (2013) 448–452
2.1. Uncertainty compensation methods To evaluate the real shape of tip, we performed three dimension (3D) tip characterization by scanning the tip on the standard sample. The standard sample TGT1 (NT-MDT Corp.) which has many spikes array with high aspect ratio formed on Si wafer surface was used. The period of spikes array is 3 μm. And the calculation of projected contact area was acquired from the 3D AFM image using python scientific analytical software tool. Si (100) wafer was used for verifying the compensation of loading axis misalignment through the piezoelectric scanner moving in y direction during indenting.
Fig. 2a, the apex of spike contacts with the tip during the tip scanning on the TGT1. And after completing the scanning process, whole points of the tip below spike's height leaves a trace. A 2D AFM image of the tip as obtained by scanning the tip on the TGT1 is shown in Fig. 2b. From three line profiles in Fig. 2b, the half angle α of the equivalent cone and the tip radius R were 45.1° and 53 nm, respectively. Fig. 2c shows the projected contact area with indenting depth between the theoretical model and the compensated values of 3D tip characterization. The area function is represented by polynomial form according to, 4
2.2. Hardness measurement by using the compensation methods Si (100) wafer, Soda lime glass and Au film on were used as test samples for nanoindentation. Au films was deposited on Si (100) wafer by sputtering method. For the pre-experiments, we performed 5 × 5 matrix nanoindentation on the Si (100) surface. Fig. 1a shows the AFM image of non contact mode with a very sharp tip after nanoindentation. The matrix consists of the limit force of 5 steps by rows and 5 times repeats by columns. The line profile in Fig. 1b shows that how much the indenting depth according to the limit force at a look. Furthermore, after tip deconvolution to the AFM image, it can be a direct method for obtaining the projected contact area as the shape of deconvoluted image is same to the deformed shape. However, in this study, we did not the above direct methods but calculated the hardness by using the derived contact area function by 3D tip characterization. In the final hardness measurements, totally 30 times indenting with the recipe of limit force with 10 steps and 3 times repeat as 10 × 3 matrix nanoindentation, were performed per a sample. Consequently, the hardness values of samples were measured by applying the contact area function acquired from 3D tip characterization to the force-depth curves produced from indentation with the continuously compensated loading axis. 3. Results and discussion 3.1. 3D tip characterization The accurate 3D information of tip is obtainable by using the principle of tip dilation while AFM scanning a known sample. As shown in
449
3
2
A ¼ C0 h þ C1 h þ C2 h þ C3 h þ C4
ð2Þ
where C0…C4 are constants determined by curve fitting procedures. The beginning contact area below 10 nm indenting depth calculated from 3D tip characterization was found to be bigger than 10 times in comparison to the theoretical data. Fig. 2d shows the projected contact area ratio of experimental values Ae to theoretical values At. It is noted that the experimental values were over 10 times high in comparison with theoretical values within 10 nm indenting depth. This results show the determination of tip radius is very important to measure the hardness value in AFM nanoindentation. 3.2. Piezoelectric scanner moving in the y direction during indenting During nanoindenting, cantilever is deflected by non-uniform direction to loading axis. This non-uniform loading direction makes the asymmetric deformed sample surface showing the triangular pyramid shape. A systematic compensation during indentation is required for continuous perpendicular loading to sample. We modified the pieozoelectric scanner moving in the y direction with measurement software to acquire continuous perpendicular load to sample surface. The percentage of piezoelectric scanner movement to the y direction during indenting load was determined by calculating the displacement of tip sliding down from the deflection of cantilever in Fig. 3. The deflection angle of cantilever is calculated by following equation [14], θ¼
3z 180 ; 2L π
ð3Þ
Fig. 1. (a) 2 × 2 μ m AFM image of 5 × 5 nanoindentations on Si (100) wafer by scanning with non-contact tip. (b) Line profile of AFM image through the center of indenting shape.
450
J. Lee et al. / Thin Solid Films 546 (2013) 448–452
Fig. 2. 3D tip characterization. (a) TGT1 standard sample for tip characterization that has high aspect ratio spikes. (b) 2D image obtained by scanning the diamond tip over TGT1 and the line profiles of tip shape from 2D image with a half cone angle equal to 45.1° and 53 nm in tip radius. (c) Comparison of projected contact area between experimental and theoretical data. (d) The ratio of experimental Ae to theoretical data At of projected contact area according to the indenting depth.
where L is the length of the cantilever to actual position of tip, z is distance of cantilever deflection in the z direction and θ is deflection angle of cantilever. The deflection angle θ is 0.1° when the cantilever deflection z of 300 nm. In common hardness measurement for thin films using nanoindentation, as the angle of cantilever deflection is
smaller than 0.1°, the tip sliding distance d while the cantilever deflection z can be obtained by, d ¼ z tanðα Þ;
ð4Þ
where α is the inclination angle of the cantilever and the value is 12.5° in our system. We controlled y scanner movement using Eq. (4) to compensate asymmetric deformed sample surface. The controlled value of y scanner movement was 0.22 nm per 1.0 nm deflection. In Fig. 4a, Applying 60 μ N load to Si wafer without compensation, the maximum height of piled up Si deposits during indenting procedure is over 30 nm thick at the bottom side. Fig. 4b shows the almost equivalent amount of deposits in three sides of triangular pyramid after applying the y scanner movement. It means that the load of tip is perpendicular to sample surface. In the case of Si wafer, the projected contact area was found to 5.5% larger than the area acquired without scanner movement compensation as shown in Fig. 4a. 3.3. Hardness measurements by using the compensation methods
Fig. 3. Simplified representation of the tip sliding phenomenon under load.
We performed hardness measurements of (a) Si wafer, (b) Soda lime glass and (c) Au film on Si in Fig. 5. Nanoindentation was carried
J. Lee et al. / Thin Solid Films 546 (2013) 448–452
451
Fig. 4. (a) 0.3 × 0.3 μ m AFM image of nanoindentation in Si (100) wafer without the compensation of misalignment of loading axis. The deformed triangular pyramid shape is asymmetry. (b) 0.3 × 0.3 μ m AFM image of nanoindentation in Si (100) wafer with the compensation of misalignment of loading axis.
out with 10 × 3 matrix repetition in each sample. As the theoretical hardness data with a standard procedure has not consideration of the tip shape, the big error arises from the uncertainty of contact area in the beginning of indenting depth. While the theoretical hardness values are sharply increased below the indenting depth of 100 nm, the experimental data acquired by using the 3D tip characterization are almost constant above the indenting depth of 40 nm. It means that it is possible for evaluating the hardness in ultra thin films. The hardness values showing at the left side of graphs in Fig. 5, respectively, were obtained by exponential curve fitting. The hardness values by the uncertainty compensation methods were summarized in Table 1. This table shows that the measured hardness values are in good agreement with those reported in the literature for Si (100), Soda lime glass and Au films on Si wafers. Something to notice here, when the indenting depth of 100 nm in each material, the average error in real time hardness measurement with compensation methods is decreased from 167% to 39%. 4. Conclusions We present the uncertainty compensation methods for the quantitative measurement of hardness value using AFM nanoindentation.
Fig. 5. Comparison of hardness results between theoretical and experimental data in (a) Si (100) wafer, (b) soda lime glass, and (c) 200 nm thick Au films on Si wafer.
The main errors during indentation are AFM tip geometry and nonuniform loading direction to sample surface. We calculated real shape of tip apex by 3D tip characterization. For uniform direction of load, we considered y scanner movement compensation. Our experimental
452
J. Lee et al. / Thin Solid Films 546 (2013) 448–452
Table 1 Hardness values measured and reference data reported in the literature. Materials
Si (100) Soda lime Glass Au film on Si (100)
Measured Value
Reference
H (GPa)
H (GPa)
12.1 6.0 2.4
13.2–23.2 [15] 5.5 [16] 2.2–3.0 [17–19]
results show big different values within indenting depth of 40 nm compared with theoretical data. The average error in real time hardness measurement is decreased from 167% to 39% due to our compensation methods. In the case of ultra thin films, these compensation methods will make an important role of determining the quantitative value of hardness using AFM nanoindentation. References [1] A.L. Weisenhorn, M. Khorsandi, S. Kasas, V. Gotzos, H.-J. Butt, Nanotechnology 4 (1993) 106. [2] H.Y. Nie, M. Motomatsu, W. Mizutani, H. Tokumoto, Thin Solid Films 273 (1996) 143.
[3] M. Radmacher, M. Fritz, C.M. Kacher, J.P. Cleveland, P.K. Hansma, Biophys. J. 70 (1996) 556. [4] N.A. Burnham, R.J. Colton, J. Vac. Sci. Technol. A 7 (1989) 2906. [5] E.A. Hassan, W.F. Heinz, M.D. Antonik, N.P.D. D’Costa, S. Nageswaran, C.-A. Schoenenberger, J.H. Hoh, Biophys. J. 74 (1998) 1564. [6] E. Tomasetti, R. Legras, B. Nysten, Nanotechnology 9 (1998) 305. [7] B. Du, J. Zhang, Q. Zhang, Q. Yang, T. He, O. Tsui, Macromolecules 33 (2000) 7521. [8] M. Mareanukroh, R.K. Eby, R.J. Scavuzzo, G.R. Hamed, Rubber Chem. Technol. 73 (2000) 912. [9] Zhaohui Shan, Suresh K. Sitaraman, Thin Solid Films 437 (2003) 176. [10] Frederic Sansoz, Travis Gang, Ultramicroscopy 111 (2010) 11. [11] L. Calabri, N. Pugno, C. Menozzi, S. Valeri, J. Phys. Condens. Matter 20 (2008) 474208. [12] C.A. Clifford, M.P. Seah, Appl. Surf. Sci. 252 (2005) 1915. [13] W.C. Oliver, G.M. Parr, J. Mater. Res. 7 (1992) 1564. [14] K.E. Bisshopp, D.C. Druker, Q. Appl. Math. (1945) 272. [15] E.V. Anoikin, G.S. Ng, M.M. Yang, J.L. Chao, J. Elings, D. Brown, IEEE Trans. Magn. 34 (1998) 1717. [16] A. Chorfa, M.A. Madjoubi, M. Hamidouche, N. Bouras, J. Rubio, F. Rubio, CeramicsSilikáty 54 (3) (2010) 225. [17] E.T. Lilleodden, W.D. Nix, Acta Mater. 54 (2006) 1583. [18] Y.D. Yan, T. Sun, S. Dong, Wear 262 (2007) 477. [19] B. Kracke, B. Damaschke, Appl. Phys. Lett. 77 (2000) 361.
Contents lists available at ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Uncertainty compensation methods for quantitative hardness measurement of materials using atomic force microscope nanoindentation technique Jungmin Lee ⁎, Chung Yi Kim, Minho Joo, Kyuho Park Materials and Components Laboratory, LG Electronics Advanced Research Institute, Seoul 137-724, Korea
a r t i c l e
i n f o
Available online 21 May 2013 Keywords: AFM nanoindentation Tip characterization Hardness measurement Uncertainty compensation
a b s t r a c t We suggest uncertainty compensation methods for the quantification of nanoscale indentation using atomic force microscopy (AFM). The main error factors in the force–distance curves originated from the difference between theoretical and real shape of AFM tip during nanoscale indentation measurements. For the uncertainty compensations of tip shapes and misalignment of loading axis, we applied the enhanced tip geometry function and Y-scanner moving to the AFM measurements. Three different materials such as Si wafer, glass, and Au film were characterized with these compensation methods. By applying compensation methods, our results show the decreased values from 167% to 39% below 100 nm indenting depth compared with the literature values. These compensation methods applied to thin films will show the advanced quantitative analysis of hardness measurements using nanoscale indenting AFM. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The nanoindentation method using atomic force microscopy (AFM) is well known for evaluating mechanical properties of thin films [1–3]. Before the development of AFM, there have been various studies for hardness measurement with load of indenter tip and deformed surface using indentation equipment. In the case of a thin film on substrate, however, it is not possible for quantitative hardness measurement because of a large tip radius and low sensitive control of force. In 1989, Burnham and Colton pioneered the use of AFMlike instruments as a nanoindenter to measure nanomechanical properties at surfaces with high sensitive control of force and piezoelectric scanner movement in the z direction [4]. In recent years, there have been various efforts to measure the quantitative hardness of thin films using AFM nanoindentation [5–12]. Unfortunately, as most of these reports have various uncertainties due to the lack of calibration of key components, the measured hardness values are non-uniform according to the indenting depth and far from the actual values. Therefore, it is essentially needed to compensate these errors resulting in the uncertainties. Among uncertainties, two factors are mainly considered as compensation parameters for quantitative hardness using AFM nanoindentation. One is that the theoretical tip geometry function representing the relationship between the projected contact area and the indenting depth is different with real tip geometry. A cube-corner tip is used for AFM nanoindentation. The projected contact area is generally
⁎ Corresponding author. E-mail address: [email protected] (J. Lee). 0040-6090/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tsf.2013.05.040
obtained by the calculation of theoretical tip geometry as a function of indenting depth, Ap ¼ 2:6hc
2
ð1Þ
where Ap is the projected contact area of tip and hc is the indenting depth. This theoretical function is available for only ideal cubecorner shape because the real shapes of tips are different from ideal model. Generally used cube-corner tips have tip radius, a few tens of nanometers, on the apex. This rounded shape of tip apex induces measurement errors according to the indenting depth below the depth of 100 nm [11,13]. The other is that the non-uniformity of perpendicular loading axis arises from cantilever deflection during indenting. This non-uniform loading axis to the sample makes the asymmetry shapes on the sample surface. A deformed surface shape is another error factor compared with a calculated projected contact area. In this paper, we suggest uncertainty compensation methods in AFM nanoindentation. The objective of this paper is to improve the quantitative hardness measurements of materials through applying the uncertainty compensation methods to AFM nanoindentation procedures. 2. Experimental details We carried out nanoindentation measurements using a XE-150 (ParkSystems Corp.) with cube-corner shaped diamond tip. The spring constant of the cantilever was determined by simulated value using the finite elements analysis in Fraderic and Sansoz's study [10].
J. Lee et al. / Thin Solid Films 546 (2013) 448–452
2.1. Uncertainty compensation methods To evaluate the real shape of tip, we performed three dimension (3D) tip characterization by scanning the tip on the standard sample. The standard sample TGT1 (NT-MDT Corp.) which has many spikes array with high aspect ratio formed on Si wafer surface was used. The period of spikes array is 3 μm. And the calculation of projected contact area was acquired from the 3D AFM image using python scientific analytical software tool. Si (100) wafer was used for verifying the compensation of loading axis misalignment through the piezoelectric scanner moving in y direction during indenting.
Fig. 2a, the apex of spike contacts with the tip during the tip scanning on the TGT1. And after completing the scanning process, whole points of the tip below spike's height leaves a trace. A 2D AFM image of the tip as obtained by scanning the tip on the TGT1 is shown in Fig. 2b. From three line profiles in Fig. 2b, the half angle α of the equivalent cone and the tip radius R were 45.1° and 53 nm, respectively. Fig. 2c shows the projected contact area with indenting depth between the theoretical model and the compensated values of 3D tip characterization. The area function is represented by polynomial form according to, 4
2.2. Hardness measurement by using the compensation methods Si (100) wafer, Soda lime glass and Au film on were used as test samples for nanoindentation. Au films was deposited on Si (100) wafer by sputtering method. For the pre-experiments, we performed 5 × 5 matrix nanoindentation on the Si (100) surface. Fig. 1a shows the AFM image of non contact mode with a very sharp tip after nanoindentation. The matrix consists of the limit force of 5 steps by rows and 5 times repeats by columns. The line profile in Fig. 1b shows that how much the indenting depth according to the limit force at a look. Furthermore, after tip deconvolution to the AFM image, it can be a direct method for obtaining the projected contact area as the shape of deconvoluted image is same to the deformed shape. However, in this study, we did not the above direct methods but calculated the hardness by using the derived contact area function by 3D tip characterization. In the final hardness measurements, totally 30 times indenting with the recipe of limit force with 10 steps and 3 times repeat as 10 × 3 matrix nanoindentation, were performed per a sample. Consequently, the hardness values of samples were measured by applying the contact area function acquired from 3D tip characterization to the force-depth curves produced from indentation with the continuously compensated loading axis. 3. Results and discussion 3.1. 3D tip characterization The accurate 3D information of tip is obtainable by using the principle of tip dilation while AFM scanning a known sample. As shown in
449
3
2
A ¼ C0 h þ C1 h þ C2 h þ C3 h þ C4
ð2Þ
where C0…C4 are constants determined by curve fitting procedures. The beginning contact area below 10 nm indenting depth calculated from 3D tip characterization was found to be bigger than 10 times in comparison to the theoretical data. Fig. 2d shows the projected contact area ratio of experimental values Ae to theoretical values At. It is noted that the experimental values were over 10 times high in comparison with theoretical values within 10 nm indenting depth. This results show the determination of tip radius is very important to measure the hardness value in AFM nanoindentation. 3.2. Piezoelectric scanner moving in the y direction during indenting During nanoindenting, cantilever is deflected by non-uniform direction to loading axis. This non-uniform loading direction makes the asymmetric deformed sample surface showing the triangular pyramid shape. A systematic compensation during indentation is required for continuous perpendicular loading to sample. We modified the pieozoelectric scanner moving in the y direction with measurement software to acquire continuous perpendicular load to sample surface. The percentage of piezoelectric scanner movement to the y direction during indenting load was determined by calculating the displacement of tip sliding down from the deflection of cantilever in Fig. 3. The deflection angle of cantilever is calculated by following equation [14], θ¼
3z 180 ; 2L π
ð3Þ
Fig. 1. (a) 2 × 2 μ m AFM image of 5 × 5 nanoindentations on Si (100) wafer by scanning with non-contact tip. (b) Line profile of AFM image through the center of indenting shape.
450
J. Lee et al. / Thin Solid Films 546 (2013) 448–452
Fig. 2. 3D tip characterization. (a) TGT1 standard sample for tip characterization that has high aspect ratio spikes. (b) 2D image obtained by scanning the diamond tip over TGT1 and the line profiles of tip shape from 2D image with a half cone angle equal to 45.1° and 53 nm in tip radius. (c) Comparison of projected contact area between experimental and theoretical data. (d) The ratio of experimental Ae to theoretical data At of projected contact area according to the indenting depth.
where L is the length of the cantilever to actual position of tip, z is distance of cantilever deflection in the z direction and θ is deflection angle of cantilever. The deflection angle θ is 0.1° when the cantilever deflection z of 300 nm. In common hardness measurement for thin films using nanoindentation, as the angle of cantilever deflection is
smaller than 0.1°, the tip sliding distance d while the cantilever deflection z can be obtained by, d ¼ z tanðα Þ;
ð4Þ
where α is the inclination angle of the cantilever and the value is 12.5° in our system. We controlled y scanner movement using Eq. (4) to compensate asymmetric deformed sample surface. The controlled value of y scanner movement was 0.22 nm per 1.0 nm deflection. In Fig. 4a, Applying 60 μ N load to Si wafer without compensation, the maximum height of piled up Si deposits during indenting procedure is over 30 nm thick at the bottom side. Fig. 4b shows the almost equivalent amount of deposits in three sides of triangular pyramid after applying the y scanner movement. It means that the load of tip is perpendicular to sample surface. In the case of Si wafer, the projected contact area was found to 5.5% larger than the area acquired without scanner movement compensation as shown in Fig. 4a. 3.3. Hardness measurements by using the compensation methods
Fig. 3. Simplified representation of the tip sliding phenomenon under load.
We performed hardness measurements of (a) Si wafer, (b) Soda lime glass and (c) Au film on Si in Fig. 5. Nanoindentation was carried
J. Lee et al. / Thin Solid Films 546 (2013) 448–452
451
Fig. 4. (a) 0.3 × 0.3 μ m AFM image of nanoindentation in Si (100) wafer without the compensation of misalignment of loading axis. The deformed triangular pyramid shape is asymmetry. (b) 0.3 × 0.3 μ m AFM image of nanoindentation in Si (100) wafer with the compensation of misalignment of loading axis.
out with 10 × 3 matrix repetition in each sample. As the theoretical hardness data with a standard procedure has not consideration of the tip shape, the big error arises from the uncertainty of contact area in the beginning of indenting depth. While the theoretical hardness values are sharply increased below the indenting depth of 100 nm, the experimental data acquired by using the 3D tip characterization are almost constant above the indenting depth of 40 nm. It means that it is possible for evaluating the hardness in ultra thin films. The hardness values showing at the left side of graphs in Fig. 5, respectively, were obtained by exponential curve fitting. The hardness values by the uncertainty compensation methods were summarized in Table 1. This table shows that the measured hardness values are in good agreement with those reported in the literature for Si (100), Soda lime glass and Au films on Si wafers. Something to notice here, when the indenting depth of 100 nm in each material, the average error in real time hardness measurement with compensation methods is decreased from 167% to 39%. 4. Conclusions We present the uncertainty compensation methods for the quantitative measurement of hardness value using AFM nanoindentation.
Fig. 5. Comparison of hardness results between theoretical and experimental data in (a) Si (100) wafer, (b) soda lime glass, and (c) 200 nm thick Au films on Si wafer.
The main errors during indentation are AFM tip geometry and nonuniform loading direction to sample surface. We calculated real shape of tip apex by 3D tip characterization. For uniform direction of load, we considered y scanner movement compensation. Our experimental
452
J. Lee et al. / Thin Solid Films 546 (2013) 448–452
Table 1 Hardness values measured and reference data reported in the literature. Materials
Si (100) Soda lime Glass Au film on Si (100)
Measured Value
Reference
H (GPa)
H (GPa)
12.1 6.0 2.4
13.2–23.2 [15] 5.5 [16] 2.2–3.0 [17–19]
results show big different values within indenting depth of 40 nm compared with theoretical data. The average error in real time hardness measurement is decreased from 167% to 39% due to our compensation methods. In the case of ultra thin films, these compensation methods will make an important role of determining the quantitative value of hardness using AFM nanoindentation. References [1] A.L. Weisenhorn, M. Khorsandi, S. Kasas, V. Gotzos, H.-J. Butt, Nanotechnology 4 (1993) 106. [2] H.Y. Nie, M. Motomatsu, W. Mizutani, H. Tokumoto, Thin Solid Films 273 (1996) 143.
[3] M. Radmacher, M. Fritz, C.M. Kacher, J.P. Cleveland, P.K. Hansma, Biophys. J. 70 (1996) 556. [4] N.A. Burnham, R.J. Colton, J. Vac. Sci. Technol. A 7 (1989) 2906. [5] E.A. Hassan, W.F. Heinz, M.D. Antonik, N.P.D. D’Costa, S. Nageswaran, C.-A. Schoenenberger, J.H. Hoh, Biophys. J. 74 (1998) 1564. [6] E. Tomasetti, R. Legras, B. Nysten, Nanotechnology 9 (1998) 305. [7] B. Du, J. Zhang, Q. Zhang, Q. Yang, T. He, O. Tsui, Macromolecules 33 (2000) 7521. [8] M. Mareanukroh, R.K. Eby, R.J. Scavuzzo, G.R. Hamed, Rubber Chem. Technol. 73 (2000) 912. [9] Zhaohui Shan, Suresh K. Sitaraman, Thin Solid Films 437 (2003) 176. [10] Frederic Sansoz, Travis Gang, Ultramicroscopy 111 (2010) 11. [11] L. Calabri, N. Pugno, C. Menozzi, S. Valeri, J. Phys. Condens. Matter 20 (2008) 474208. [12] C.A. Clifford, M.P. Seah, Appl. Surf. Sci. 252 (2005) 1915. [13] W.C. Oliver, G.M. Parr, J. Mater. Res. 7 (1992) 1564. [14] K.E. Bisshopp, D.C. Druker, Q. Appl. Math. (1945) 272. [15] E.V. Anoikin, G.S. Ng, M.M. Yang, J.L. Chao, J. Elings, D. Brown, IEEE Trans. Magn. 34 (1998) 1717. [16] A. Chorfa, M.A. Madjoubi, M. Hamidouche, N. Bouras, J. Rubio, F. Rubio, CeramicsSilikáty 54 (3) (2010) 225. [17] E.T. Lilleodden, W.D. Nix, Acta Mater. 54 (2006) 1583. [18] Y.D. Yan, T. Sun, S. Dong, Wear 262 (2007) 477. [19] B. Kracke, B. Damaschke, Appl. Phys. Lett. 77 (2000) 361.