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FIB-based technique for stress characterization on thin films for reliability purposes
Microelectronic Engineering 84 (2007) 1783–1787 www.elsevier.com/locate/mee
FIB-based technique for stress characterization on thin films for reliability purposes N. Sabate´
b
a,*
, D. Vogel b, J. Keller b, A. Gollhardt b, J. Marcos a, I. Gra`cia a, C. Cane´ a, B. Michel b
a Centro Nacional de Microelectro´nica, Campus UAB sn, 08193 Bellaterra-Barcelona, Spain Micro Materials Center Berlin, Fraunhofer Institute for Reliability and Microintegration (IZM), Gustav-Meyer Allee 25, 13355 Berlin, Germany
Available online 15 February 2007
Abstract This paper describes a novel approach of stress measurement based on the combined imaging–milling capabilities of a FIB equipment. This technique consists on the scaling down of two measurement techniques based on stress-relaxation, the slot and the hole-drilling methods. The main aspects of both approaches at a microscale are described and illustrated and some examples of their application to thin films are presented. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Residual stress; Hole-drilling method; Slot milling; Focused ion beam
1. Introduction The rapid development of MEMS and NEMS devices demands new concepts and approaches of reliability topics. Because of the major contribution of residual stresses to failure, its prediction and measurement are crucial to assess reliability of any structure during its lifetime. In this respect, simulation tools play an essential role in order to take into account reliability requirements during device design. Unfortunately, simulations are only as reliable as their input data, i.e., mechanical models, material properties, residual stress after manufacturing being one of the more complex factors to be predicted. During the last decade, a great deal of research effort has been directed towards residual stress determination. Methods like the curvature measurements at wafer level or the bulge based tests have become common ways to obtain stresses in thin films [1] whereas other approaches have focused on the onpurpose fabrication of micromachined structures with suitable geometries such as rings or cantilevers [2]. However, *
Corresponding author. E-mail address: [email protected] (N. Sabate´).
0167-9317/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2007.01.272
even if these methods have proved to provide acceptable measurements of the residual stress, dedicated structures must be fabricated and generally, no local measurement of the stress is available. In this respect, recent works based on the downscaling of stress-relaxation measurement techniques to a microscale have brought a new insight to this research field [3,4]. This method consists of the release of residual stresses by material removal and subsequent measurement of the induced displacements in the near surface region of the removed volume. In this paper, a general description of this approach and its stress measurement capabilities are presented. 2. Stress measurement based on the downscaling of the stress-relaxation methods The downscaling of the stress-release measurement methods is based on the combined milling–imaging capabilities provided by a focused ion beam (FIB) equipment. Thus, the ion beam replaces the traditional milling instruments (i.e., milling cutters, electro discharge machining, laser. . .) whereas scanning electron microscope (SEM) imaging combined with digital image correlation (DIC)
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techniques allows monitoring of the displacements originated by stress release. In the following section, measurement procedure is described in detail. 2.1. Measurement procedure description Measurement procedure starts with the recording of a first SEM image of the area to be analysed. Dimensions of the scanned area have to be set according to displacement measurement accuracy requirements. For highly accurate and stable SEM imaging, sample under inspection has to be electrically conductive since charging of the surface should be avoided. So, when the sample under test is insulating (as happens with ceramics or dielectric MEMs layers) it must be provided with an appropriate conductive coating. In order to avoid any mechanical impact on the structure under study, the coating layer thickness has to be kept to minimum. In this sense, platinum and gold flash coatings within the range of 10–20 nm thickness provide the required electron discharging without yielding any significant mechanical influence and deterioration during ion imaging. Once the first SEM image that will be taken as reference is captured, the ion beam is used to mill the feature that will locally release the residual stresses of the sample. As it will be explained later in this paper, the geometry of the removed material volume determines the direction of the released stresses. After milling, a second SEM image of the area around the milled zone is captured. DIC analysis between this SEM image and the image obtained before the milling process is performed by using a special crosscorrelation algorithm. This algorithm compares grey scale intensity patterns of a matrix of pixels of the two images and establishes where the reference matrix has to be shifted from the first to the second image to find the best matching
pattern [5,6]. In the case objects under investigation do not exhibit suitable image pattern for DIC treatment, the FIB tool can be used to generate appropriate patterns in the sample surface. Some commercial equipments are delivered with pattern generator capabilities, whereby pattern milling is carried out by copying arbitrarily structured bitmaps. This procedure can help to make visible some kind of patterns on surfaces commonly appearing without any structures in electron images. In this way, very smooth surfaces can be provided with patterns that are adequate for digital correlation of SEM images. An example of the transfer of one random pattern bitmap to a sample surface is shown in Fig. 1a and b. The increase of the sample surface roughness is visible in Fig. 1c, showing line profiles scanned after FIB pattern milling with an atomic force microscope. In DIC analysis, the result of the two-dimensional digital cross-correlation in the surroundings of a measuring point primarily gives the two components of the displacement vector. In this way, surface deformations around the milled trench originated by the local stress release are obtained. Fig. 2 shows the relative displacement of the meshes used in digital correlation analysis that takes place in the surrounding area when a hole is milled on a stressed material. Originally existing residual stresses can be computed from the measured displacement field by comparing them to a theoretical expression coming from mechanical analysis or to the results derived from finite element analysis (FEA). 2.2. Geometry of the milling stress-release features The most widely used stress-relaxation measurement techniques are the slot milling (also known as crack compliance) and the hole-drilling methods. Both of them are
Fig. 1. Patterning of a smooth surface with the focused ion beam. (a) Random pattern bitmap, (b) SEM image of the sample surface after patterning and (c) AFM line profiles of the sample surface before and after the patterning process.
N. Sabate´ et al. / Microelectronic Engineering 84 (2007) 1783–1787
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tion in the surrounding region, causing the local strains on the material surface to change correspondingly. Resulting deformation is then measured at sample surface around the milled slot and used to compute the residual stress that had originated them. Usually, slot milling allows to measure the stress component normal to the slot face. Incremental machining of the sample allows to find residual stress as a function of slot depth [7]. In particular, to determine the residual stress of a thin layer deposited on top of a thick substrate, a common situation in MEMS fabrication, one can fit the experimental displacement field to an analytical expression derived by linear elastic fracture mechanics [8]. The displacements generated when a surface slot is milled on a thin layer are normal to the slot plane and dependent on its depth a, the total film thickness h and the ratio of the Young’s modulus of the film to that of the substrate. The dependence can therefore be described analytically by plane strain two-dimensional analysis: Z r0 a a ux ðxÞ ¼ 0 f ; S; ES ; x da; ð1Þ h Ef 0 Fig. 2. Displacement of mesh nodes obtained after digital correlation of SEM images taken at the surrounding area of a milled hole.
considered semi-destructive methods, as they both require local material removal, but they differ in the geometry of the milled volume and the information obtained from stress-release. In the slot milling method, the introduction of a slot results in an immediate stress relaxation at the free surfaces of the milled feature that also changes the stress distribu-
where E0f accounts for its plane strain Young’s modulus E0f ¼ Ef =ð1 m2f Þ; mf for the Poisson ratio, and r0 for its residual stress and ES corresponds to substrate Young’s modulus. In the case of a single layer, ES is set equal to Ef and the effect of film thickness h is removed. This mathematical approximation assumes that the slot is infinitely long and narrow compared with its depth. In order to avoid a significant error coming from the idealization of the milled slot as a mathematical crack, displacements must be monitored at the central region; according to Kang and coworkers, a distance five times the milled depth from the
Fig. 3. Cross-section images of slots milled on a nickel layer at different depths (a) 500 nm and (b) 1100 nm. (c) and (d) show the contour map of the displacements generated by milling slots (a) and (b) respectively (data in nanometers).
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slot edge should be kept for an error under 5%. [9]. As an example, Fig. 3a and 3b show two different cross-sections after slot-milling of a nickel electroless layer. Fig. 3c and 3d show the corresponding displacements obtained after DIC analysis. As expected, greater displacements are to be seen at higher milled depths. A thorough description of slot-milling analysis with a FIB equipment can be found in recent works [4,10]. In the hole-drilling method, a hole is milled instead of a slot, causing a stress relaxation that allows to measure the in-plane components of the residual stress [11]. That is, unlike the slot-milling, generated displacements allow to discern rxx and ryy contributions of a biaxial stress. Analytical expression for the displacement field originated from the milling of a through hole of radius R0 on a sample with a biaxial residual stress can be computed from theory of elasticity by the superposition of solutions derived for uniaxial stress case [12]. General dependence is given by: rxx R0 ux;y ¼ f ; ; m; h ; ð2Þ E r where rxx accounts for the uniaxial stress intensity, E for the Young modulus and m the Poisson ratio of the film under investigation and r, h are the corresponding polar coordinates. In the case of a biaxial residual stress, a 90° rotated solution of the displacement field with a residual stress intensity of ryy must be superimposed on the solution given by (2). Under the presence of an homogeneous biaxial stress state, that is, rxx = ryy = r0, expressions for the dis-
placement field simplify considerably, leading to a circular symmetry of the displacement modulus juj ¼
r0 R20 ð1 þ mÞ: Er
ð3Þ
Fig. 4 shows the contour lines of the analytical displacement fields ux and uy corresponding to generic solutions of a homogeneous uniaxial and biaxial prestressed material. The higher displacements concentrate in the region near the hole and extend up to a certain distance. It can be seen that the nature of the residual stresses determines the shape of the displacement contour lines. Note in (3) that generated displacements are proportional to the square of the milled radius hole R0, so this parameter can be tuned to increase sensitivity in case of measurement of stiff films. Hole-milling approach has been successfully applied to a MEMS free standing structure consisting on a biaxially prestressed silicon nitride membrane. Fig. 5 shows the countour lines for ux and uy displacements corresponding to the stress release by hole-milling of one of the membrane structures. In most practical applications, the drilled hole is blind and the complex three-dimensional displacement field around them cannot be described with closed form solutions. However, the problem can be approached by extending the through-hole solution by means of empirical coefficients or by using finite element analysis. Fig. 6 shows an example of blind hole milling into a copper layer of a direct copper bonding (DCB) substrate. Similar ux and uy
Fig. 4. Contour lines of the analytical displacement fields ux and uy corresponding to generic solutions of a homogeneous uniaxial and biaxial prestressed material.
Fig. 5. ux and uy components of the experimental displacement field measured on a silicon nitride micromachined membrane (data in nanometers).
N. Sabate´ et al. / Microelectronic Engineering 84 (2007) 1783–1787
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Fig. 6. ux and uy displacement fields determined by DIC analysis of SEM images before and after hole milling with the ion beam on a DCB (copper on ceramics) layer. Diameter: 7.2 lm, hole depth: 6 lm.
displacement fields observed after milling revealed the homogeneity of the residual biaxial stress. When mapping in-depth stresses wants to be obtained, the different load cases can be analyzed sequentially assuming that the stress in the milling direction is constant at every milled step. Unlike slot milling, displacements generated by hole milling tend to saturate at increasing depths and generally, depths no greater than 3 or 4 times the hole diameter are exceeded. In this sense, Cheng et al. explicitly compared the in-depth sensitivity of slot milling to hole drilling and showed slot-milling to be significantly more sensitive [13]. 3. Conclusions In this paper the downscaling to a microscale of a wellestablished measurement technique based on stress release have been described. This novel approach takes advantage of the combined milling-imaging capabilities of a FIB equipment. The main aspects of the most widely used stress-relaxation measurement techniques, namely the slot and the hole-drilling methods have been described and some examples of their application by means of FIB analysis have been presented. Hole-drilling provides information about the in-plane stresses of a sample whereas when milling a slot, only the stresses perpendicular to the slot plane are determined. However, when in-depth stress mapping on a sample is desired, slot-milling generates bigger displacements with higher sensitivity. It has to be noted that regardless of the geometry of the milled volume, determination of residual stress with the present stress-release method requires the knowledge of elastic constants of the sample under test. Due to the direct dependency on these parameters, errors or uncertainties in the values of the elastic constants produce proportionally equivalent errors or uncertainties in the residual stresses. Therefore, mechanical properties have to be determined independently by other methods.
Stress-release techniques utilizing FIB systems bring new opportunities for material and component characterization in micro and nanotechnology. A focused ion beam instrument can be used in an effective manner to process test specimens and to measure surface deformations in the same equipment. One of the potential application areas of this technique is the measurement of residual stresses on sensors, MEMS structures and microelectronics components including a great variety of materials, not only after but also at a different fabrication stages. Moreover, due to its local nature, the method can be applied to analyze stresses in particular areas and, if required, to perform a stress mapping at a microscale. This would allow the detection of stress concentration points and therefore to avoid failure mechanism associated with them. References [1] M. Gad-el-Hak, The MEMS Handbook, CRC, BocaRaton, FL, 2002. [2] H. Guckel, T. Randazzo, D.W. Burns, Journal of Applied Physics 57 (5) (1985) 1671–1674. [3] K.J. Kang, N. Yao, M.Y. He, A.G. Evans, Thin Solid Films 443 (2003) 71–77. [4] N. Sabate, et al., Journal of Micromechanics and Microengineering 16(2) 254–259. [5] D. Vogel, A. Schubert, W. Faust, R. Dudek, B. Michel, Microelectronics and Reliability 36 (11/12) (1996) 1939–1942. [6] M.A. Sutton, W.J. Walters, W.H. Peters, W.F. Ranson, S.R. Neil, Image vision computing 1 (3) (1983) 133–139. [7] M.B. Prime, Applied Mechanics Reviews 52 (2) (1999) 75–96. [8] J.L. Beuth, Journal of Solids and Structures 29 (13) (1992) 1657– 1675. [9] K.J. Kang, S. Darzens, G.S. Choi, Journal of Engineering Materials and Technology (2004) 457–464. [10] N. Sabate et al., Nanotechnology 17 (2006) 1. [11] ASTM Standard E837. [12] S. Timoshenko, J.M. Goodier, Theory of Elasticity, McGraw-Hill, New York, 1951. [13] W. Cheng, I. Finnie, O. Vardar, Journal of Engineering Materials and Technology 113 (1991) 199.
FIB-based technique for stress characterization on thin films for reliability purposes N. Sabate´
b
a,*
, D. Vogel b, J. Keller b, A. Gollhardt b, J. Marcos a, I. Gra`cia a, C. Cane´ a, B. Michel b
a Centro Nacional de Microelectro´nica, Campus UAB sn, 08193 Bellaterra-Barcelona, Spain Micro Materials Center Berlin, Fraunhofer Institute for Reliability and Microintegration (IZM), Gustav-Meyer Allee 25, 13355 Berlin, Germany
Available online 15 February 2007
Abstract This paper describes a novel approach of stress measurement based on the combined imaging–milling capabilities of a FIB equipment. This technique consists on the scaling down of two measurement techniques based on stress-relaxation, the slot and the hole-drilling methods. The main aspects of both approaches at a microscale are described and illustrated and some examples of their application to thin films are presented. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Residual stress; Hole-drilling method; Slot milling; Focused ion beam
1. Introduction The rapid development of MEMS and NEMS devices demands new concepts and approaches of reliability topics. Because of the major contribution of residual stresses to failure, its prediction and measurement are crucial to assess reliability of any structure during its lifetime. In this respect, simulation tools play an essential role in order to take into account reliability requirements during device design. Unfortunately, simulations are only as reliable as their input data, i.e., mechanical models, material properties, residual stress after manufacturing being one of the more complex factors to be predicted. During the last decade, a great deal of research effort has been directed towards residual stress determination. Methods like the curvature measurements at wafer level or the bulge based tests have become common ways to obtain stresses in thin films [1] whereas other approaches have focused on the onpurpose fabrication of micromachined structures with suitable geometries such as rings or cantilevers [2]. However, *
Corresponding author. E-mail address: [email protected] (N. Sabate´).
0167-9317/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2007.01.272
even if these methods have proved to provide acceptable measurements of the residual stress, dedicated structures must be fabricated and generally, no local measurement of the stress is available. In this respect, recent works based on the downscaling of stress-relaxation measurement techniques to a microscale have brought a new insight to this research field [3,4]. This method consists of the release of residual stresses by material removal and subsequent measurement of the induced displacements in the near surface region of the removed volume. In this paper, a general description of this approach and its stress measurement capabilities are presented. 2. Stress measurement based on the downscaling of the stress-relaxation methods The downscaling of the stress-release measurement methods is based on the combined milling–imaging capabilities provided by a focused ion beam (FIB) equipment. Thus, the ion beam replaces the traditional milling instruments (i.e., milling cutters, electro discharge machining, laser. . .) whereas scanning electron microscope (SEM) imaging combined with digital image correlation (DIC)
1784
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techniques allows monitoring of the displacements originated by stress release. In the following section, measurement procedure is described in detail. 2.1. Measurement procedure description Measurement procedure starts with the recording of a first SEM image of the area to be analysed. Dimensions of the scanned area have to be set according to displacement measurement accuracy requirements. For highly accurate and stable SEM imaging, sample under inspection has to be electrically conductive since charging of the surface should be avoided. So, when the sample under test is insulating (as happens with ceramics or dielectric MEMs layers) it must be provided with an appropriate conductive coating. In order to avoid any mechanical impact on the structure under study, the coating layer thickness has to be kept to minimum. In this sense, platinum and gold flash coatings within the range of 10–20 nm thickness provide the required electron discharging without yielding any significant mechanical influence and deterioration during ion imaging. Once the first SEM image that will be taken as reference is captured, the ion beam is used to mill the feature that will locally release the residual stresses of the sample. As it will be explained later in this paper, the geometry of the removed material volume determines the direction of the released stresses. After milling, a second SEM image of the area around the milled zone is captured. DIC analysis between this SEM image and the image obtained before the milling process is performed by using a special crosscorrelation algorithm. This algorithm compares grey scale intensity patterns of a matrix of pixels of the two images and establishes where the reference matrix has to be shifted from the first to the second image to find the best matching
pattern [5,6]. In the case objects under investigation do not exhibit suitable image pattern for DIC treatment, the FIB tool can be used to generate appropriate patterns in the sample surface. Some commercial equipments are delivered with pattern generator capabilities, whereby pattern milling is carried out by copying arbitrarily structured bitmaps. This procedure can help to make visible some kind of patterns on surfaces commonly appearing without any structures in electron images. In this way, very smooth surfaces can be provided with patterns that are adequate for digital correlation of SEM images. An example of the transfer of one random pattern bitmap to a sample surface is shown in Fig. 1a and b. The increase of the sample surface roughness is visible in Fig. 1c, showing line profiles scanned after FIB pattern milling with an atomic force microscope. In DIC analysis, the result of the two-dimensional digital cross-correlation in the surroundings of a measuring point primarily gives the two components of the displacement vector. In this way, surface deformations around the milled trench originated by the local stress release are obtained. Fig. 2 shows the relative displacement of the meshes used in digital correlation analysis that takes place in the surrounding area when a hole is milled on a stressed material. Originally existing residual stresses can be computed from the measured displacement field by comparing them to a theoretical expression coming from mechanical analysis or to the results derived from finite element analysis (FEA). 2.2. Geometry of the milling stress-release features The most widely used stress-relaxation measurement techniques are the slot milling (also known as crack compliance) and the hole-drilling methods. Both of them are
Fig. 1. Patterning of a smooth surface with the focused ion beam. (a) Random pattern bitmap, (b) SEM image of the sample surface after patterning and (c) AFM line profiles of the sample surface before and after the patterning process.
N. Sabate´ et al. / Microelectronic Engineering 84 (2007) 1783–1787
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tion in the surrounding region, causing the local strains on the material surface to change correspondingly. Resulting deformation is then measured at sample surface around the milled slot and used to compute the residual stress that had originated them. Usually, slot milling allows to measure the stress component normal to the slot face. Incremental machining of the sample allows to find residual stress as a function of slot depth [7]. In particular, to determine the residual stress of a thin layer deposited on top of a thick substrate, a common situation in MEMS fabrication, one can fit the experimental displacement field to an analytical expression derived by linear elastic fracture mechanics [8]. The displacements generated when a surface slot is milled on a thin layer are normal to the slot plane and dependent on its depth a, the total film thickness h and the ratio of the Young’s modulus of the film to that of the substrate. The dependence can therefore be described analytically by plane strain two-dimensional analysis: Z r0 a a ux ðxÞ ¼ 0 f ; S; ES ; x da; ð1Þ h Ef 0 Fig. 2. Displacement of mesh nodes obtained after digital correlation of SEM images taken at the surrounding area of a milled hole.
considered semi-destructive methods, as they both require local material removal, but they differ in the geometry of the milled volume and the information obtained from stress-release. In the slot milling method, the introduction of a slot results in an immediate stress relaxation at the free surfaces of the milled feature that also changes the stress distribu-
where E0f accounts for its plane strain Young’s modulus E0f ¼ Ef =ð1 m2f Þ; mf for the Poisson ratio, and r0 for its residual stress and ES corresponds to substrate Young’s modulus. In the case of a single layer, ES is set equal to Ef and the effect of film thickness h is removed. This mathematical approximation assumes that the slot is infinitely long and narrow compared with its depth. In order to avoid a significant error coming from the idealization of the milled slot as a mathematical crack, displacements must be monitored at the central region; according to Kang and coworkers, a distance five times the milled depth from the
Fig. 3. Cross-section images of slots milled on a nickel layer at different depths (a) 500 nm and (b) 1100 nm. (c) and (d) show the contour map of the displacements generated by milling slots (a) and (b) respectively (data in nanometers).
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slot edge should be kept for an error under 5%. [9]. As an example, Fig. 3a and 3b show two different cross-sections after slot-milling of a nickel electroless layer. Fig. 3c and 3d show the corresponding displacements obtained after DIC analysis. As expected, greater displacements are to be seen at higher milled depths. A thorough description of slot-milling analysis with a FIB equipment can be found in recent works [4,10]. In the hole-drilling method, a hole is milled instead of a slot, causing a stress relaxation that allows to measure the in-plane components of the residual stress [11]. That is, unlike the slot-milling, generated displacements allow to discern rxx and ryy contributions of a biaxial stress. Analytical expression for the displacement field originated from the milling of a through hole of radius R0 on a sample with a biaxial residual stress can be computed from theory of elasticity by the superposition of solutions derived for uniaxial stress case [12]. General dependence is given by: rxx R0 ux;y ¼ f ; ; m; h ; ð2Þ E r where rxx accounts for the uniaxial stress intensity, E for the Young modulus and m the Poisson ratio of the film under investigation and r, h are the corresponding polar coordinates. In the case of a biaxial residual stress, a 90° rotated solution of the displacement field with a residual stress intensity of ryy must be superimposed on the solution given by (2). Under the presence of an homogeneous biaxial stress state, that is, rxx = ryy = r0, expressions for the dis-
placement field simplify considerably, leading to a circular symmetry of the displacement modulus juj ¼
r0 R20 ð1 þ mÞ: Er
ð3Þ
Fig. 4 shows the contour lines of the analytical displacement fields ux and uy corresponding to generic solutions of a homogeneous uniaxial and biaxial prestressed material. The higher displacements concentrate in the region near the hole and extend up to a certain distance. It can be seen that the nature of the residual stresses determines the shape of the displacement contour lines. Note in (3) that generated displacements are proportional to the square of the milled radius hole R0, so this parameter can be tuned to increase sensitivity in case of measurement of stiff films. Hole-milling approach has been successfully applied to a MEMS free standing structure consisting on a biaxially prestressed silicon nitride membrane. Fig. 5 shows the countour lines for ux and uy displacements corresponding to the stress release by hole-milling of one of the membrane structures. In most practical applications, the drilled hole is blind and the complex three-dimensional displacement field around them cannot be described with closed form solutions. However, the problem can be approached by extending the through-hole solution by means of empirical coefficients or by using finite element analysis. Fig. 6 shows an example of blind hole milling into a copper layer of a direct copper bonding (DCB) substrate. Similar ux and uy
Fig. 4. Contour lines of the analytical displacement fields ux and uy corresponding to generic solutions of a homogeneous uniaxial and biaxial prestressed material.
Fig. 5. ux and uy components of the experimental displacement field measured on a silicon nitride micromachined membrane (data in nanometers).
N. Sabate´ et al. / Microelectronic Engineering 84 (2007) 1783–1787
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Fig. 6. ux and uy displacement fields determined by DIC analysis of SEM images before and after hole milling with the ion beam on a DCB (copper on ceramics) layer. Diameter: 7.2 lm, hole depth: 6 lm.
displacement fields observed after milling revealed the homogeneity of the residual biaxial stress. When mapping in-depth stresses wants to be obtained, the different load cases can be analyzed sequentially assuming that the stress in the milling direction is constant at every milled step. Unlike slot milling, displacements generated by hole milling tend to saturate at increasing depths and generally, depths no greater than 3 or 4 times the hole diameter are exceeded. In this sense, Cheng et al. explicitly compared the in-depth sensitivity of slot milling to hole drilling and showed slot-milling to be significantly more sensitive [13]. 3. Conclusions In this paper the downscaling to a microscale of a wellestablished measurement technique based on stress release have been described. This novel approach takes advantage of the combined milling-imaging capabilities of a FIB equipment. The main aspects of the most widely used stress-relaxation measurement techniques, namely the slot and the hole-drilling methods have been described and some examples of their application by means of FIB analysis have been presented. Hole-drilling provides information about the in-plane stresses of a sample whereas when milling a slot, only the stresses perpendicular to the slot plane are determined. However, when in-depth stress mapping on a sample is desired, slot-milling generates bigger displacements with higher sensitivity. It has to be noted that regardless of the geometry of the milled volume, determination of residual stress with the present stress-release method requires the knowledge of elastic constants of the sample under test. Due to the direct dependency on these parameters, errors or uncertainties in the values of the elastic constants produce proportionally equivalent errors or uncertainties in the residual stresses. Therefore, mechanical properties have to be determined independently by other methods.
Stress-release techniques utilizing FIB systems bring new opportunities for material and component characterization in micro and nanotechnology. A focused ion beam instrument can be used in an effective manner to process test specimens and to measure surface deformations in the same equipment. One of the potential application areas of this technique is the measurement of residual stresses on sensors, MEMS structures and microelectronics components including a great variety of materials, not only after but also at a different fabrication stages. Moreover, due to its local nature, the method can be applied to analyze stresses in particular areas and, if required, to perform a stress mapping at a microscale. This would allow the detection of stress concentration points and therefore to avoid failure mechanism associated with them. References [1] M. Gad-el-Hak, The MEMS Handbook, CRC, BocaRaton, FL, 2002. [2] H. Guckel, T. Randazzo, D.W. Burns, Journal of Applied Physics 57 (5) (1985) 1671–1674. [3] K.J. Kang, N. Yao, M.Y. He, A.G. Evans, Thin Solid Films 443 (2003) 71–77. [4] N. Sabate, et al., Journal of Micromechanics and Microengineering 16(2) 254–259. [5] D. Vogel, A. Schubert, W. Faust, R. Dudek, B. Michel, Microelectronics and Reliability 36 (11/12) (1996) 1939–1942. [6] M.A. Sutton, W.J. Walters, W.H. Peters, W.F. Ranson, S.R. Neil, Image vision computing 1 (3) (1983) 133–139. [7] M.B. Prime, Applied Mechanics Reviews 52 (2) (1999) 75–96. [8] J.L. Beuth, Journal of Solids and Structures 29 (13) (1992) 1657– 1675. [9] K.J. Kang, S. Darzens, G.S. Choi, Journal of Engineering Materials and Technology (2004) 457–464. [10] N. Sabate et al., Nanotechnology 17 (2006) 1. [11] ASTM Standard E837. [12] S. Timoshenko, J.M. Goodier, Theory of Elasticity, McGraw-Hill, New York, 1951. [13] W. Cheng, I. Finnie, O. Vardar, Journal of Engineering Materials and Technology 113 (1991) 199.