- Email: [email protected]
Anisotropic distribution of residual strain around conical nanoindentation in silicon
Materials Letters 137 (2014) 389–392
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Anisotropic distribution of residual strain around conical nanoindentation in silicon X. Li a,b, Z. Li a, L.L. Ren b, S.T. Gao b, G.F. Xu a, X.F. Tao b,n a b
School of Materials Science and Engineering, Central South University, Changsha 410083, China Division of Nano Metrology and Materials Measurement, National Institute of Metrology, Beijing 100013, China
ar t ic l e i nf o
a b s t r a c t
Article history: Received 5 August 2014 Accepted 5 September 2014 Available online 16 September 2014
Residual strain around conical nanoindentations on silicon single crystals is mapped by electronic backscatter diffraction system and CrossCourt software. Both of the (001) and (111) planes display anisotropic strain features adjacent to nanoindentations in specific crystallographic orientations with strain resolutions of 3.5 10 4 and 3.3 10 4 for Si(001) and (111) surfaces, respectively. The anisotropic distributions of most strain components induced by isotropic load present central symmetry, which are related to the crystallographic orientation and slip system in silicon microstructures according to the Schmid law. The indentation deformation of single-crystal Si is a process of dislocation slip on specific plane in specific direction. & 2014 Elsevier B.V. All rights reserved.
Keywords: Residual strain Nanoindentation Silicon Surfaces Microstructure
1. Introduction Knowledge of local residual strain (ε) state in small regions of material is of crucial importance in determining the performance and service life of some silicon (Si)-based devices and structural engineering components [1]. Techniques that create and control the distribution of strains within complementary metal oxide semiconductor devices are being developed for improving device performance and for defect control [2]. In the field of optical excitation, residual strain in Si substrate changes the structure of photonic quantum-well and thus influence the output color and lifetime of visible light-emitting and laser diodes [3]. However, an overlarge strain can initiate dislocations in Si and subsequent plastic deformation, which usually lead to the effect of degradation [4]. The residual strain states of the devices are diverse and determined by their different manufacturing techniques and service environments. Therefore, the need to measure the distribution of residual strain is pervasive in many areas, particularly in the semiconductor industry [5]. Instrumented indentation has been widely employed in measuring mechanical properties of Si-based devices and evaluating the device reliability as a model of contact flaws [6]. At mediumto-large levels of indentation load, the plastic deformation of Si crystals is accomplished by phase transformation and dislocation slip [7]. The electron back scattered diffraction (EBSD) technique is a versatile tool that has shown powerful abilities in measuring residual strain/stress on the surface of crystalline materials with n
Corresponding author. Tel./fax: þ 86 10 64524908. E-mail address: [email protected] (X.F. Tao).
http://dx.doi.org/10.1016/j.matlet.2014.09.025 0167-577X/& 2014 Elsevier B.V. All rights reserved.
high resolution [8]. Earlier research revealed the stress distribution with sub-micron spatial resolution around a 30 μm 350 μm wedge indentation on Si single crystals using Raman microscopy and the EBSD technique [9]. The residual stress states of three Si single crystals in a 12.5 μm 12.5 μm filed induced by a 80 mN indenter load were mapped by confocal Raman, which clearly displayed anisotropic stress patterns with orientation specific symmetry [10]. However, the development of advanced micronano Si-based devices indicates that residual strain/stress distribution in Si materials needs to be studied at a smaller field and, where higher spatial and strain resolutions are required. In our previous work, strain distribution of indented single Si crystals in a 2.8 μm 2.8 μm field was two-dimensionally mapped by EBSD technique at high strain resolution [11]. However, the measured distribution of strain components did not exactly match the theoretical distribution and presented bad symmetry, which was suspected due to the anisotropic load of the applied pyramidal indenter. In this work, a conical indenter was employed to study anisotropic strain distribution around the nanoindentation of diamond cubic Si, where the symmetry of strain patterns induced by isotropic load was revealed. Moreover, the effect of crystallographic orientation on the anisotropic distribution of strain was discussed and the related mechanism was explained with the dislocation slip and Schmid law.
2. Materials and method The test Si single crystals were 200 μm thick 3 mm diameter, polished Si(001) and Si(111) crystallographic using ion milling.
390
X. Li et al. / Materials Letters 137 (2014) 389–392
The two crystallographic planes were indented using a conical indenter with a tip curvature radius of approximate 771 nm in a 103 clean room environment. During indentation experiments, the loading and unloading rates were 2 mN s 1. The load was linearly increased with time to the maximum value of 10 mN, kept for 2 s, and linearly decreased. A Nordlys Nano EBSD detector (1344 1024 pixels) assembled in a Zeiss Ultra 55 field-emission scanning electron microscope (FE-SEM) was employed to acquire the EBSD patterns of regions around indentations. The microscope worked at an acceleration voltage of 25 kV, a scanning step of 80 nm and a stage drift less than
12.5 nm/min. The obtained EBSD patterns were then analyzed using CrossCourt 3 software that has a strain resolution of 710 4 and a misorientation sensitivity of 70.0061 for residual strain calculation [12].
3. Results and discussion Figs. 1 and 2 present anisotropic distribution characteristics of positive and negative strain components around the indentations
Fig. 1. Residual strain mapped by EBSD of Si sample indented perpendicular to Si(001): (a) ε11; (b) ε22, the insets are corresponding load–displacement curve and SEM image; (c) ε33; (d) ε12; (e) ε13; and (f) ε23. Scan sizes: 6.8 μm 6.8 μm. The EBSD pattern of black spot is reference.
Fig. 2. Residual strain mapped by EBSD of Si sample indented perpendicular to Si(111): (a) ε11; (b) ε22, the insets are corresponding load–displacement curve and SEM image; (c) ε33; (d) ε12; (e) ε13; and (f) ε23. Scan sizes: 6.8 μm 6.8 μm. The EBSD pattern of black spot is reference.
X. Li et al. / Materials Letters 137 (2014) 389–392
on two crystallographic planes. The indentations are denoted by white circles from where EBSD data were deleted as the pattern quality is poor and the location is mismatching. For the indentation on Si(001) plane (Fig. 1), orientation data are represented with reference to a sample coordinate system consisting of X ¼[4̄ 50], Y¼ [5̄ 4̄ 0] and Z¼[001]. It is observed that strain component ε11 (crystal axes strain) is negative in the 7 [010] directions and positive in the 7[100] directions, whereas the distribution characteristics of ε22 is completely opposite compared with ε11. The component ε33 is large and positive in the [110] direction. Meanwhile, positive ε12 is detected along the 7[110] directions and ̄ directions. The anisotropic charnegative ε12 along the 7[110] acteristics of components ε13 and ε23 are not distinct, with negative and positive strain displayed in the [110] direction, respectively. Overall, three of the components present twofold strain patterns and the magnitude of strain significantly decreases with the increase of distance to the indentation center. For the indentation on Si(111) plane (Fig. 2), the sample coordinate system consists of X¼ [12̄1], Y¼[101̄ ] and Z¼[111]. Positive ε11 petals ̄ ̄2] directions and negative ε11 petal in the distribute in the 7[11 [12̄1] direction. The component ε22 is negative in the [101̄ ] and positive in the 7[011̄ ] directions. Meanwhile, negative and ̄ ̄2] positive ε33 values are respectively distributed along the 7[11 ̄ and 7[110] directions. Similarly, shear strain components also display anisotropic distribution characteristics. The distribution characteristic of ε12 is opposite compared with ε33. Moreover, negative and positive ε13 are respectively distributed along the 7 ̄ ̄ ] directions. Lastly, the component ε23 also [011̄ ] and 7[211 presents positive strain patterns in the 7[101̄ ] directions. The strain resolutions, obtained by calculating the minimum strain difference between two adjacent scanning points, are 3.5 10 4 and 3.3 10 4 for Si(001) and Si(111), respectively. Table 1 Schmid factor for two loading directions of diamond cubic Si. Slip plane
Burgers vector direction
Schmid factor for loading direction [001]
[111]
̄ 1) ̄ (11
[1̄01̄ ] ̄ ̄] [011 ̄ [110]
0.408 0.408 0
0.272 0.272 0
̄ (111)
̄ ̄] [011 [101̄ ] [110]
0.408 0.408 0
0.272 0 0.272
̄ (111)
[1̄01̄ ] [011̄ ] [110]
0.408 0.408 0
0.272 0 0.272
(111)
[011̄ ] [101̄ ] ̄ [110]
0.408 0.408 0
0 0 0
391
The symmetry is observed in most of the strain patterns induced by a conical indenter; however in that induced by the pyramidal indenter, symmetric characteristic is very weak [11]. For example, on Si(001), the strain pattern of ε22 induced by conical indenter presents symmetry with respect to the indentation center in the 7[100] and 7[010] directions while the same strain component induced by the conical indenter displays bad central symmetry in these directions, similar for the strain patterns of ε11 and ε12. Moreover, on Si(111), more strain components (ε22, ε33, ε12 and ε13) present central symmetry in specific crystallographic directions. Therefore, the symmetry of strain distribution in specific crystallographic orientations is well displayed at the condition of isotropic load. There are two possible deformation mechanisms occurring in the indentation deformation of Si materials: phase transformation and dislocation movement [13]. During indentation deformation, diamond cubic Si transforms to the β-tin phase, which can further transform to other high-pressure phases, an amorphous phase or a mixture of them [14,15]. There are no “pop-in/out” events in the load–displacement curves and no cracks in the SEM images (the insets of Figs. 1(b) and 2(b)) which suggests that the plastic deformation of the Si single crystal did not produce phase transformation and cracks around the indentation site. Dislocation movement and slip system are bound to the slip process in crystalline materials. In the diamond cubic Si, the dominant {111}〈110〉 slip systems have theoretical Burgers vectors of b¼(a/2) 〈110〉 and common dislocation line directions of 〈110〉 at 601 to the Burgers vectors, where a is the Si lattice constant. The conical indenter mainly activates two categories of dislocations: dislocations with b parallel and inclined to the indented surface. The former is largely suppressed at ambient temperature. The latter moves into the crystal on {111} planes and then converge or diverge under the indenter [12,16]. However, the converging dislocations tangle on the intersecting slip planes or split into the leading 301 partial dislocations that can form Lomer-Cottrell locks [17]. Therefore, the indentation deformation is accommodated by dislocations with b moving on {111} planes and diverging in the Si materials. In the diamond cubic Si single crystal, the Schmid factor is employed to evaluate the activation possibility of all twelve {111} 〈110〉 slip systems [18]. The larger the Schmid factor, the higher the possibility of slip, and vise versa. As listed in Table 1, eight slip systems are possible to be activated for the [001] loading direction and six for [111]. Fig. 3 represents the projection of the eight and six active slip systems onto the (001) and (111) indentation planes, respectively. The indicated crystallographic orientations in the schematic diagram are corresponding with the orientations in ̄ is a shared plane for an active slip Figs. 1 and 2. For example, (111) system, which has a dislocation line direction of [110] and two ̄ ̄ ]. It is noted that the perfect Burgers vectors of b ¼[101̄ ] and [011 measured distribution of strain components is not exactly in agreement with the theoretical distribution pattern even without
Fig. 3. Active slip planes projected onto indented planes (a) Si(001) and (b) Si(111). The slip planes are highlighted in gray. The active Burgers vectors are indicated by red arrows. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
392
X. Li et al. / Materials Letters 137 (2014) 389–392
the effect of anisotropic load. This is probably due to the high tilt angle of the sample (701) or some other deformation behaviors. In addition, the measured strain distribution can more or less be distorted by stage drift at the condition of high accelerating voltage and magnification. The effect of these factors on the strain distribution needs to be distinguished in the further work.
Acknowledgments This work was supported by the National Key Technology R&D Program with No. 2011BAK15B07.
References 4. Conclusions The present work employed nanoindenter and EBSD system to investigate the strain distribution around conical nanoindentation on single-crystal Si. It is measured that anisotropic strain patterns are present in specific crystallographic orientations with strain resolutions of 3.5 10 4 and 3.3 10 4 for Si(001) and Si(111), respectively. The anisotropic distributions of strain components induced by isotropic load display central symmetry are related to the crystallographic orientation and slip system of the Si crystals according to the Schmid law. Moreover, the strain distribution might be affected by some other factors except the load mode. It is concluded that the nanoindentation deformation of Si single crystal is a process of dislocation slip on a specific plane in a specific direction.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
Krondorfer RH, Kim YK. IEEE Trans Compon Packag Technol 2007;30:285–93. Chung J, Lian GD, Rabenberg L. Appl Phys Lett 2008;93:081909-1–3. Lee KS, Isnaeni, Yoo YS, Lee JH, Kim YC, Cho YH. J Appl Phys 2013;113:173512-1–5. Wu YQ, Huang H, Zou J, Dell JM. J Vac Sci Technol B 2009;27:1374–7. Chu M, Sun Y, Aghoram U, Thompson SE. Annu Rev Mater Res 2009;39: 203–29. Shi MR, Youssef K, Rozgonyi GA. Adv Eng Mater 2013;15:756–60. Jang J, Lance MJ, Wen SQ, Tsui TY, Pharr GM. Acta Mater 2005;53:1759–70. Wilkinson AJ, Randman D. Philos Mag 2010;90:1159–77. Vaudin MD, Gerbig YB, Stranick SJ, Cook RF. Appl Phys Lett 2008;93:193116-1–3. Gerbig YB, Stranick SJ, Cook RF. Scr Mater 2010;63:512–5. Li X, Li Z, Tao XF, Ren LL, Gao ST, Xu GF. Mater Lett 2014;132:285–9. Wilkinson AJ, Meaden G, Dingley DJ. Ultramicroscopy 2006;106:307–13. Vandeperre LJ, Giuliani F, Llloyd SJ, Clegg WJ. Acta Mater 2007;55:6307–15. Lin YH, Jian SR, Lai YS, Yang PF. Nanoscale Res Lett 2008;3:71–5. Jian SR, Chen GJ, Juang JY. Curr Opin Solid State Mater Sci 2010;14:69–74. Roberts SG, Warren PD, Hirsch PB. J Mater Res 1986;1:162–76. Elkajbaji M, Kirchner HO, Thibault-Desseaux J. Philos Mag A 1988;57:631–5. Nabarro FRN. Philos Mag 1966;14:861–6.
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Anisotropic distribution of residual strain around conical nanoindentation in silicon X. Li a,b, Z. Li a, L.L. Ren b, S.T. Gao b, G.F. Xu a, X.F. Tao b,n a b
School of Materials Science and Engineering, Central South University, Changsha 410083, China Division of Nano Metrology and Materials Measurement, National Institute of Metrology, Beijing 100013, China
ar t ic l e i nf o
a b s t r a c t
Article history: Received 5 August 2014 Accepted 5 September 2014 Available online 16 September 2014
Residual strain around conical nanoindentations on silicon single crystals is mapped by electronic backscatter diffraction system and CrossCourt software. Both of the (001) and (111) planes display anisotropic strain features adjacent to nanoindentations in specific crystallographic orientations with strain resolutions of 3.5 10 4 and 3.3 10 4 for Si(001) and (111) surfaces, respectively. The anisotropic distributions of most strain components induced by isotropic load present central symmetry, which are related to the crystallographic orientation and slip system in silicon microstructures according to the Schmid law. The indentation deformation of single-crystal Si is a process of dislocation slip on specific plane in specific direction. & 2014 Elsevier B.V. All rights reserved.
Keywords: Residual strain Nanoindentation Silicon Surfaces Microstructure
1. Introduction Knowledge of local residual strain (ε) state in small regions of material is of crucial importance in determining the performance and service life of some silicon (Si)-based devices and structural engineering components [1]. Techniques that create and control the distribution of strains within complementary metal oxide semiconductor devices are being developed for improving device performance and for defect control [2]. In the field of optical excitation, residual strain in Si substrate changes the structure of photonic quantum-well and thus influence the output color and lifetime of visible light-emitting and laser diodes [3]. However, an overlarge strain can initiate dislocations in Si and subsequent plastic deformation, which usually lead to the effect of degradation [4]. The residual strain states of the devices are diverse and determined by their different manufacturing techniques and service environments. Therefore, the need to measure the distribution of residual strain is pervasive in many areas, particularly in the semiconductor industry [5]. Instrumented indentation has been widely employed in measuring mechanical properties of Si-based devices and evaluating the device reliability as a model of contact flaws [6]. At mediumto-large levels of indentation load, the plastic deformation of Si crystals is accomplished by phase transformation and dislocation slip [7]. The electron back scattered diffraction (EBSD) technique is a versatile tool that has shown powerful abilities in measuring residual strain/stress on the surface of crystalline materials with n
Corresponding author. Tel./fax: þ 86 10 64524908. E-mail address: [email protected] (X.F. Tao).
http://dx.doi.org/10.1016/j.matlet.2014.09.025 0167-577X/& 2014 Elsevier B.V. All rights reserved.
high resolution [8]. Earlier research revealed the stress distribution with sub-micron spatial resolution around a 30 μm 350 μm wedge indentation on Si single crystals using Raman microscopy and the EBSD technique [9]. The residual stress states of three Si single crystals in a 12.5 μm 12.5 μm filed induced by a 80 mN indenter load were mapped by confocal Raman, which clearly displayed anisotropic stress patterns with orientation specific symmetry [10]. However, the development of advanced micronano Si-based devices indicates that residual strain/stress distribution in Si materials needs to be studied at a smaller field and, where higher spatial and strain resolutions are required. In our previous work, strain distribution of indented single Si crystals in a 2.8 μm 2.8 μm field was two-dimensionally mapped by EBSD technique at high strain resolution [11]. However, the measured distribution of strain components did not exactly match the theoretical distribution and presented bad symmetry, which was suspected due to the anisotropic load of the applied pyramidal indenter. In this work, a conical indenter was employed to study anisotropic strain distribution around the nanoindentation of diamond cubic Si, where the symmetry of strain patterns induced by isotropic load was revealed. Moreover, the effect of crystallographic orientation on the anisotropic distribution of strain was discussed and the related mechanism was explained with the dislocation slip and Schmid law.
2. Materials and method The test Si single crystals were 200 μm thick 3 mm diameter, polished Si(001) and Si(111) crystallographic using ion milling.
390
X. Li et al. / Materials Letters 137 (2014) 389–392
The two crystallographic planes were indented using a conical indenter with a tip curvature radius of approximate 771 nm in a 103 clean room environment. During indentation experiments, the loading and unloading rates were 2 mN s 1. The load was linearly increased with time to the maximum value of 10 mN, kept for 2 s, and linearly decreased. A Nordlys Nano EBSD detector (1344 1024 pixels) assembled in a Zeiss Ultra 55 field-emission scanning electron microscope (FE-SEM) was employed to acquire the EBSD patterns of regions around indentations. The microscope worked at an acceleration voltage of 25 kV, a scanning step of 80 nm and a stage drift less than
12.5 nm/min. The obtained EBSD patterns were then analyzed using CrossCourt 3 software that has a strain resolution of 710 4 and a misorientation sensitivity of 70.0061 for residual strain calculation [12].
3. Results and discussion Figs. 1 and 2 present anisotropic distribution characteristics of positive and negative strain components around the indentations
Fig. 1. Residual strain mapped by EBSD of Si sample indented perpendicular to Si(001): (a) ε11; (b) ε22, the insets are corresponding load–displacement curve and SEM image; (c) ε33; (d) ε12; (e) ε13; and (f) ε23. Scan sizes: 6.8 μm 6.8 μm. The EBSD pattern of black spot is reference.
Fig. 2. Residual strain mapped by EBSD of Si sample indented perpendicular to Si(111): (a) ε11; (b) ε22, the insets are corresponding load–displacement curve and SEM image; (c) ε33; (d) ε12; (e) ε13; and (f) ε23. Scan sizes: 6.8 μm 6.8 μm. The EBSD pattern of black spot is reference.
X. Li et al. / Materials Letters 137 (2014) 389–392
on two crystallographic planes. The indentations are denoted by white circles from where EBSD data were deleted as the pattern quality is poor and the location is mismatching. For the indentation on Si(001) plane (Fig. 1), orientation data are represented with reference to a sample coordinate system consisting of X ¼[4̄ 50], Y¼ [5̄ 4̄ 0] and Z¼[001]. It is observed that strain component ε11 (crystal axes strain) is negative in the 7 [010] directions and positive in the 7[100] directions, whereas the distribution characteristics of ε22 is completely opposite compared with ε11. The component ε33 is large and positive in the [110] direction. Meanwhile, positive ε12 is detected along the 7[110] directions and ̄ directions. The anisotropic charnegative ε12 along the 7[110] acteristics of components ε13 and ε23 are not distinct, with negative and positive strain displayed in the [110] direction, respectively. Overall, three of the components present twofold strain patterns and the magnitude of strain significantly decreases with the increase of distance to the indentation center. For the indentation on Si(111) plane (Fig. 2), the sample coordinate system consists of X¼ [12̄1], Y¼[101̄ ] and Z¼[111]. Positive ε11 petals ̄ ̄2] directions and negative ε11 petal in the distribute in the 7[11 [12̄1] direction. The component ε22 is negative in the [101̄ ] and positive in the 7[011̄ ] directions. Meanwhile, negative and ̄ ̄2] positive ε33 values are respectively distributed along the 7[11 ̄ and 7[110] directions. Similarly, shear strain components also display anisotropic distribution characteristics. The distribution characteristic of ε12 is opposite compared with ε33. Moreover, negative and positive ε13 are respectively distributed along the 7 ̄ ̄ ] directions. Lastly, the component ε23 also [011̄ ] and 7[211 presents positive strain patterns in the 7[101̄ ] directions. The strain resolutions, obtained by calculating the minimum strain difference between two adjacent scanning points, are 3.5 10 4 and 3.3 10 4 for Si(001) and Si(111), respectively. Table 1 Schmid factor for two loading directions of diamond cubic Si. Slip plane
Burgers vector direction
Schmid factor for loading direction [001]
[111]
̄ 1) ̄ (11
[1̄01̄ ] ̄ ̄] [011 ̄ [110]
0.408 0.408 0
0.272 0.272 0
̄ (111)
̄ ̄] [011 [101̄ ] [110]
0.408 0.408 0
0.272 0 0.272
̄ (111)
[1̄01̄ ] [011̄ ] [110]
0.408 0.408 0
0.272 0 0.272
(111)
[011̄ ] [101̄ ] ̄ [110]
0.408 0.408 0
0 0 0
391
The symmetry is observed in most of the strain patterns induced by a conical indenter; however in that induced by the pyramidal indenter, symmetric characteristic is very weak [11]. For example, on Si(001), the strain pattern of ε22 induced by conical indenter presents symmetry with respect to the indentation center in the 7[100] and 7[010] directions while the same strain component induced by the conical indenter displays bad central symmetry in these directions, similar for the strain patterns of ε11 and ε12. Moreover, on Si(111), more strain components (ε22, ε33, ε12 and ε13) present central symmetry in specific crystallographic directions. Therefore, the symmetry of strain distribution in specific crystallographic orientations is well displayed at the condition of isotropic load. There are two possible deformation mechanisms occurring in the indentation deformation of Si materials: phase transformation and dislocation movement [13]. During indentation deformation, diamond cubic Si transforms to the β-tin phase, which can further transform to other high-pressure phases, an amorphous phase or a mixture of them [14,15]. There are no “pop-in/out” events in the load–displacement curves and no cracks in the SEM images (the insets of Figs. 1(b) and 2(b)) which suggests that the plastic deformation of the Si single crystal did not produce phase transformation and cracks around the indentation site. Dislocation movement and slip system are bound to the slip process in crystalline materials. In the diamond cubic Si, the dominant {111}〈110〉 slip systems have theoretical Burgers vectors of b¼(a/2) 〈110〉 and common dislocation line directions of 〈110〉 at 601 to the Burgers vectors, where a is the Si lattice constant. The conical indenter mainly activates two categories of dislocations: dislocations with b parallel and inclined to the indented surface. The former is largely suppressed at ambient temperature. The latter moves into the crystal on {111} planes and then converge or diverge under the indenter [12,16]. However, the converging dislocations tangle on the intersecting slip planes or split into the leading 301 partial dislocations that can form Lomer-Cottrell locks [17]. Therefore, the indentation deformation is accommodated by dislocations with b moving on {111} planes and diverging in the Si materials. In the diamond cubic Si single crystal, the Schmid factor is employed to evaluate the activation possibility of all twelve {111} 〈110〉 slip systems [18]. The larger the Schmid factor, the higher the possibility of slip, and vise versa. As listed in Table 1, eight slip systems are possible to be activated for the [001] loading direction and six for [111]. Fig. 3 represents the projection of the eight and six active slip systems onto the (001) and (111) indentation planes, respectively. The indicated crystallographic orientations in the schematic diagram are corresponding with the orientations in ̄ is a shared plane for an active slip Figs. 1 and 2. For example, (111) system, which has a dislocation line direction of [110] and two ̄ ̄ ]. It is noted that the perfect Burgers vectors of b ¼[101̄ ] and [011 measured distribution of strain components is not exactly in agreement with the theoretical distribution pattern even without
Fig. 3. Active slip planes projected onto indented planes (a) Si(001) and (b) Si(111). The slip planes are highlighted in gray. The active Burgers vectors are indicated by red arrows. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
392
X. Li et al. / Materials Letters 137 (2014) 389–392
the effect of anisotropic load. This is probably due to the high tilt angle of the sample (701) or some other deformation behaviors. In addition, the measured strain distribution can more or less be distorted by stage drift at the condition of high accelerating voltage and magnification. The effect of these factors on the strain distribution needs to be distinguished in the further work.
Acknowledgments This work was supported by the National Key Technology R&D Program with No. 2011BAK15B07.
References 4. Conclusions The present work employed nanoindenter and EBSD system to investigate the strain distribution around conical nanoindentation on single-crystal Si. It is measured that anisotropic strain patterns are present in specific crystallographic orientations with strain resolutions of 3.5 10 4 and 3.3 10 4 for Si(001) and Si(111), respectively. The anisotropic distributions of strain components induced by isotropic load display central symmetry are related to the crystallographic orientation and slip system of the Si crystals according to the Schmid law. Moreover, the strain distribution might be affected by some other factors except the load mode. It is concluded that the nanoindentation deformation of Si single crystal is a process of dislocation slip on a specific plane in a specific direction.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
Krondorfer RH, Kim YK. IEEE Trans Compon Packag Technol 2007;30:285–93. Chung J, Lian GD, Rabenberg L. Appl Phys Lett 2008;93:081909-1–3. Lee KS, Isnaeni, Yoo YS, Lee JH, Kim YC, Cho YH. J Appl Phys 2013;113:173512-1–5. Wu YQ, Huang H, Zou J, Dell JM. J Vac Sci Technol B 2009;27:1374–7. Chu M, Sun Y, Aghoram U, Thompson SE. Annu Rev Mater Res 2009;39: 203–29. Shi MR, Youssef K, Rozgonyi GA. Adv Eng Mater 2013;15:756–60. Jang J, Lance MJ, Wen SQ, Tsui TY, Pharr GM. Acta Mater 2005;53:1759–70. Wilkinson AJ, Randman D. Philos Mag 2010;90:1159–77. Vaudin MD, Gerbig YB, Stranick SJ, Cook RF. Appl Phys Lett 2008;93:193116-1–3. Gerbig YB, Stranick SJ, Cook RF. Scr Mater 2010;63:512–5. Li X, Li Z, Tao XF, Ren LL, Gao ST, Xu GF. Mater Lett 2014;132:285–9. Wilkinson AJ, Meaden G, Dingley DJ. Ultramicroscopy 2006;106:307–13. Vandeperre LJ, Giuliani F, Llloyd SJ, Clegg WJ. Acta Mater 2007;55:6307–15. Lin YH, Jian SR, Lai YS, Yang PF. Nanoscale Res Lett 2008;3:71–5. Jian SR, Chen GJ, Juang JY. Curr Opin Solid State Mater Sci 2010;14:69–74. Roberts SG, Warren PD, Hirsch PB. J Mater Res 1986;1:162–76. Elkajbaji M, Kirchner HO, Thibault-Desseaux J. Philos Mag A 1988;57:631–5. Nabarro FRN. Philos Mag 1966;14:861–6.