.
`(cid:14)
`Sensors and Actuators 82 2000 274–280
`
`www.elsevier.nlrlocatersna
`
`Fracture toughness of polysilicon MEMS devices
`H. Kahn a,), N. Tayebi b, R. Ballarini c, R.L. Mullen c, A.H. Heuer a
`a Department of Materials Science and Engineering, Case Western Reser˝e Uni˝ersity, 10900 Euclid A˝enue, Cle˝eland, OH 44106-7204, USA
`b Department of Mechanical and Aerospace Engineering, Case Western Reser˝e Uni˝ersity, 10900 Euclid A˝enue, Cle˝eland, OH 44106-7222, USA
`c Department of Ci˝il Engineering, Case Western Reser˝e Uni˝ersity, 10900 Euclid A˝enue, Cle˝eland, OH 44106-7201, USA
`
`Received 7 June 1999; received in revised form 9 November 1999; accepted 10 November 1999
`
`Abstract
`
`.
`(cid:14)
`Polysilicon fracture mechanics specimens have been fabricated using standard microelectro-mechanical systems MEMS processing
`techniques, with characteristic dimensions comparable to typical MEMS devices. These specimens are fully integrated with simultane-
`ously fabricated electrostatic actuators that are capable of providing sufficient force to ensure catastrophic crack propagation. Thus, the
`entire fracture experiment takes place on-chip, eliminating the difficulties associated with attaching the specimen to an external loading
`source. The specimens incorporate atomically sharp cracks created by indentation, and fracture is initiated using monotonic electrostatic
`(cid:14)
`.
`loading. The fracture toughness values are determined using finite element analysis FEA of the experimental data, and show a median
`value of 1.1 MPa m1r2. q 2000 Elsevier Science S.A. All rights reserved.
`
`Keywords: Microelectromechanical systems; Polysilicon; Fracture toughness; Surface micromachining
`
`1. Introduction
`
`.
`(cid:14)
`Numerous microelectro-mechanical systems MEMS
`devices have been developed which use polysilicon as the
`w x
`major structural material 1 . For applications where large
`movements are desirable, it is advantageous to design for
`deflections that correspond to a safe fraction of the polysil-
`icon strain limits. However, the relevant material proper-
`ties, such as fracture toughness, are not well characterized
`for polysilicon at these size scales, or for polysilicon which
`has been subjected to MEMS fabrication techniques.
`There have been a few recent reports on the fracture
`toughness of polysilicon MEMS test specimens which
`w x
`contained micromachined notches. Sharpe et al. 2 and
`w x
`Tsuchiya et al. 3 employed external piezoelectric load
`cells to fracture their notched specimens, and reported
`critical stress intensity factors, K , of 1.4 and 1.9 to 4.5
`Ic
`MPa m1r2, respectively. These are associated with finite
`(cid:14)
`.
`radius 1.0 and 0.23 mm, respectively notches and thus do
`not represent true fracture toughness. The present authors
`(cid:14)
`have previously reported J
`critical energy release rates
`c
`determined using the J-integral values of 16 to 62 Nrm
`.
`
`)
`
`Corresponding author. Tel.: q1-216-368-6499; fax: q1-216-368-
`3209.
`.
`(cid:14)
`E-mail address: hxk29@cwru.edu H. Kahn .
`
`w x
`for externally wedge-loaded specimens 4 and 63 "20
`w x
`Nrm for electrostatically loaded specimens 5 ; the nomi-
`nal fracture toughness of the latter specimens is 3.5 MPa
`1r2 w x
`6 , and all specimens included 1.0 mm radius notches.
`m
`Fractographic investigations of the electrostatically frac-
`tured polysilicon specimens can be used to determine the
`initial flaw size and indicate toughness values of 1 to 2
`1r2 w x
`MPa m
`5 . All of these values are higher than those
`1r2
`(cid:14)
`accepted for single crystal silicon K ;0.9 MPa m ; J
`Ic
`c
`w x.
`;4.8 Nrm 4 , as well as for the reported values for bulk
`x
`1r2. w
`(cid:14)
`polysilicon K 0.75 to 0.87 MPa m
`7,8 ; in those
`Ic
`latter tests, however, the polysilicon grain size was quite
`large, ;1 mm, and thus much larger than the flaw size,
`which is typically not the case for MEMS structures.
`The use of micromachined notches to create the stress
`concentrations necessary for
`fracture has two distinct
`shortcomings. Firstly, there simply is no singularity; there-
`fore K, the stress intensity, cannot be specified in the
`conventional manner, and the experimental results cannot
`be directly related to K . In fact, a study of the effect of
`Ic
`notch radius on the fracture of single crystal silicon along
`(cid:20)
`4
`the 111 plane reported nominal K values that varied
`Ic
`w x
`1r2
`for radii of 80 to 580 mm 9 .
`from 1.24 to 2.85 MPa m
`Secondly, the morphology of the etched surface, namely
`the smoothness of the sidewalls on the inside of the notch,
`will play an important role in the fracture behavior. There-
`
`0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved.
`(cid:14)
`.
`PII: S 0 9 2 4 - 4 2 4 7 9 9 0 0 3 6 6 - 0
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`H. Kahn et al.rSensors and Actuators 82 2000 274–280
`)
`(
`
`275
`
`fore, the measured fracture properties will display a depen-
`dence on the etching technique and will not be inherent
`materials properties.
`The present work involves micromachined fracture me-
`chanics specimens that were integrated with electrostatic
`actuators that contain either 1456 or 1658 pairs of interdig-
`itated comb fingers. The specimens include atomically
`sharp cracks created by indentation, which eliminates the
`complications involved with micromachined notches. To
`the present authors’ knowledge, this experiment is the first
`to report the fracture toughness of a MEMS material using
`(cid:14)
`an atomically sharp crack. Strictly speaking, as discussed
`below, the crack tip may not be ‘‘atomically’’ sharp, but
`.
`may be a few atomic spacings in radius. The integrated
`electrostatic actuator allows the entire experiment to take
`place on-chip without any external-loading source. An-
`other advantage is the possibility of resonating the actuator
`in order to achieve cyclic loading at very high frequencies
`(cid:14)
`.
`the resonance frequencies of the actuators are ;20 kHz ,
`in order to study fatigue behavior conveniently.
`
`2. Experiment
`
`2.1. De˝ice fabrication
`
`A completed device is shown in the scanning electron
`(cid:14)
`.
`micrograph SEM in Fig. 1a, with a magnified image of
`the fracture mechanics specimen in Fig. 1b, a higher
`magnification view of the initial crack in Fig. 1c, and a
`view of the specimen after fracture in Fig. 1d. The left side
`of the fracture mechanics specimen, as oriented in Fig. 1b,
`(cid:14)
`is fully released courtesy of the release holes visible in the
`.
`micrograph and is free to move, while the right side is
`anchored to the substrate. When a voltage is applied to the
`comb fingers of the actuator, it will pull the left side of the
`fracture mechanics specimen downward, creating a stress
`concentration at the crack tip. A sufficient voltage will
`cause enough displacement in the end of the specimen to
`establish a critical stress intensity, K , and catastrophic
`Ic
`propagation of the crack.
`
`.
`(cid:14)
`(cid:14) .
`(cid:14) .
`Fig. 1. SEM micrographs of a MEMS fracture device showing integrated actuator and fracture mechanics specimen, b magnified and rotated 908 view
`(cid:14)
`.
`(cid:14) .
`(cid:14) .
`of fracture mechanics specimen h indicates the beam depth , c magnified view of the specimen ligament showing the initial crack, d specimen
`(cid:14)
`.
`ligament following the fracture experiment y indicates the distance from the initial crack to the fixed end of the specimen .
`
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`H. Kahn et al.rSensors and Actuators 82 2000 274–280
`)
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`
`The devices were fabricated in a two-mask process,
`illustrated in Fig. 2 and summarized, as follows. The
`(cid:14)
`.
`release oxide 3.0 mm was thermally grown, the polysili-
`.
`(cid:14)
`con 3.5 mm was deposited by LPCVD at 5808C, fol-
`lowed by an anneal at 10008C for 1 h in nitrogen, and the
`(cid:14)
`.
`masking oxide 1.0 mm was deposited by LPCVD at
`(cid:14)
`.
`4508C Fig. 2a . The masking oxide was photolithographi-
`cally patterned and was dry etched using CHF rC F , and
`2 6
`3
`(cid:14)
`.
`the polysilicon was dry etched using Cl
`Fig. 2b . At this
`2
`.
`(cid:14)
`point a Vickers indent with a 200-g load was placed on
`the specimen, causing radial cracks to form at the indent
`(cid:14)
`.
`corners Fig. 2c ; an example is shown in Fig. 3. The
`(cid:14)
`.
`wafer was then annealed at 10008C for 30 min in air
`to
`relieve the residual stresses induced by indentation; other-
`wise, the portion of the specimen surrounding the indent
`often de-laminated from the substrate during further pro-
`cessing, as shown in Fig. 4. Presumably, the de-lamination
`is due to lateral cracks and high residual stresses induced
`by indentation. A lateral crack beneath the indent can be
`seen in the infrared microscope image in Fig. 5a;
`the
`(cid:14)
`.
`lateral crack remains after annealing Fig. 5b , but the
`reduced residual stresses do not provide sufficient driving
`force for the lateral crack to propagate. Following this
`anneal, a second photolithographic mask protected the
`majority of the device, allowing the indent and its related
`(cid:14)
`.
`damage to be etched away using Cl
`, while the radial
`2
`(cid:14)
`.
`cracks remained in the specimen Fig. 2d . The devices
`were then time-released in HF, followed by supercritical
`(cid:14)
`.
`(cid:14)
`CO drying Fig. 2e . This technique for forming sharp
`2
`
`Fig. 3. SEM micrograph of an indented specimen, before the second
`polysilicon etch.
`
`cracks in micromachined MEMS specimens was first pro-
`w
`x
`posed by Keller 10 ,
`though no fracture results were
`reported; it is commonly employed in studying bulk ce-
`.
`ramics. The residual stress of the released polysilicon was
`w x
`measured with an on-chip micro-strain gauge 5 to be
`12 "5 MPa. For sufficient conductivity for electrostatic
`actuation, the devices were sputter-coated with ;10 nm
`of palladium following release.
`A problem with performing photolithography on a sub-
`strate that contains cracks is that it is very difficult to
`remove any photoresist that enters the cracks. Therefore, in
`subsequent etching steps, some areas where the cracks had
`been will be unintentionally masked. In these devices, this
`causes debris to be present, which can be seen just above
`the initial crack in Fig. 1b, c and d. However, this extra
`material, which is polysilicon, is mostly unattached to the
`specimen and does not interfere with its movement. It is
`not believed to affect the experimental measurements.
`
`Fig. 2. Schematic drawings showing the fabrication sequence of the
`devices.
`
`Fig. 4. SEM micrograph of a specimen which was not annealed following
`indentation and suffered de-lamination.
`
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`H. Kahn et al.rSensors and Actuators 82 2000 274–280
`)
`(
`
`277
`
`(cid:14) .
`(cid:14) .
`Fig. 5. Infrared microscope images of indented specimens before the second polysilicon etch, a before annealing and b after annealing. Because of the
`poor contrast of the images, the specimens are artificially outlined in white, as a visual aid.
`
`2.2. Experimental procedure
`
`The initial crack lengths and positions for all of the
`fracture mechanics specimens were measured using an
`SEM before testing. The devices were tested using DC
`electrostatic actuation. The applied voltage was increased
`until the crack propagated catastrophically, at which point
`the voltage at fracture could be recorded directly from the
`power supply. A micrograph of a specimen after testing is
`shown in Fig. 1d. During the test, the displacement of the
`actuator was recorded. For half the experiments, the criti-
`cal actuator displacements were measured visually using
`an optical microscope with an accuracy of 0.3 mm. For the
`other half, the experiments were recorded on video tape
`using the same optical microscope, and the appropriate
`images were digitally captured and analyzed to determine
`the critical displacements with an accuracy of 0.15 mm.
`The critical voltage at fracture could be measured much
`more accurately than the displacements, and so the first
`attempt to determine the forces being applied to the speci-
`mens was to develop an accurate voltage versus force
`w
`x
`calibration for the actuators 11 . However, the actuator
`displacement versus voltage behavior did not correlate
`well from device to device. The most likely explanation is
`
`that varying amounts of debris can accumulate underneath
`(cid:14)
`.
`the actuators they are quite large , either during release or
`during subsequent handling in the non-clean room labora-
`tory environment. Therefore, the displacements of the ac-
`tuators,
`i.e.,
`the displacements of the free ends of the
`fracture mechanics specimens, were used in conjunction
`(cid:14)
`.
`with finite element analysis FEA of the structure, using
`w
`x
`the FRANC2D simulation program 12 , to determine the
`critical stress intensity. The crack was assumed to propa-
`gate catastrophically with no increase in the initial crack
`(cid:14)
`length, and the actual dimensions of the anchor including
`.
`the undercutting that occurred during release were in-
`cluded in the model. The error in the FEA calculations was
`determined to be on the order of a few percent by compari-
`son with handbook solutions.
`
`3. Results and discussion
`
`Three different fracture mechanics specimen designs
`were tested. They differed only in the depth of the beam
`(cid:14)
`.
`labeled h in Fig. 1b , which was 10, 15 or 20 mm. Due to
`the stochastic nature of the crack paths created by indenta-
`tion,
`the initial crack lengths varied a great deal. In
`
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`
`H. Kahn et al.rSensors and Actuators 82 2000 274–280
`)
`(
`
`Table 1
`Experimental fracture toughness, K , data for polysilicon fracture mechanics specimens
`Ic
`arh
`(cid:14)
`.
`%
`
`Distance from
`crack to fixed end
`(cid:14)
`.
`mm
`
`Critical
`displacement
`(cid:14)
`.
`mm
`
`Crack length
`(cid:14)
`.
`a mm
`
`Beam depth
`(cid:14)
`.
`h mm
`
`K
`Ic
`1r2
`(cid:14)
`MPa m
`
`.
`
`Experimental
`error in K Ic
`1r2
`(cid:14)
`.
`MPa m
`
`0.2
`0.44
`0.67
`0.82
`0.8
`0.87
`0.9
`0.94
`1.0
`1.1
`1.1
`1.1
`1.2
`1.5
`1.6
`1.7
`1.8
`1.9
`2.0
`2.2
`
`0.11
`0.04
`0.04
`0.07
`0.3
`0.22
`0.5
`0.23
`0.2
`0.10
`0.30
`0.27
`0.24
`0.16
`0.24
`0.17
`0.14
`0.48
`0.33
`0.45
`
`0.91
`4.9
`0.76
`1.3
`8.9
`15
`8.9
`11
`3.0
`2.9
`9.6
`1.9
`1.7
`7.6
`3.2
`5.7
`3.5
`7.6
`13
`10
`
`15
`10
`15
`15
`20
`20
`20
`20
`15
`15
`20
`15
`15
`20
`15
`15
`15
`20
`20
`20
`
`6
`49
`5
`9
`45
`75
`45
`55
`20
`19
`48
`13
`11
`38
`21
`38
`23
`38
`65
`50
`
`4.7
`2.7
`4.5
`3.0
`2.9
`0.9
`6.5
`1.8
`7.5
`2.7
`4.9
`0.0
`6.6
`5.3
`5.0
`2.2
`7.0
`4.5
`4.5
`4.1
`
`0.5
`1.85
`2.31
`1.5
`0.8
`1.2
`0.5
`1.2
`0.5
`1.54
`0.62
`1.54
`1.5
`1.38
`2.0
`1.54
`2.0
`1.2
`1.8
`1.50
`
`addition, the distance between the initial crack and the
`(cid:14)
`.
`fixed end of the specimen labeled y in Fig. 1c was also
`variable. However, both of these factors were taken into
`account in the FEA, as well as any perpendicular cracks
`that remained in other parts of the specimen, as seen in
`Figs. 1b and 3. The experimental results are listed in Table
`1, and the K values are plotted in Fig. 6, a Weibull plot
`Ic
`w
`x
`1r2
`13 . The Weibull scale parameter, K , is 1.4 MPa m ,
`Ic o(cid:14)
`and the Weibull modulus, m, is 1.9. The straight line fit
`.
`2
`has a regression coefficient, R of 0.94. The Weibull
`distribution is commonly used to model fracture data and
`to predict failure statistics, but is not generally used for
`
`Fig. 6. Experimental fracture toughness, K , data for polysilicon fracture
`Ic
`mechanics specimens.
`
`fracture toughness, as K is assumed to be a material
`Ic
`parameter. Its use here is simply a convenient way to
`describe the statistics of our determination of K .Ic
`The median K for polysilicon from our work is 1.1
`Ic
`MPa m1r2. This value is lower than that determined by
`most notched polysilicon specimens reported previously
`w
`x
`1–5 , and is close to the values reported for single crystal
`silicon. The measured Weibull modulus is quite low, how-
`(cid:14)
`ever, which indicates a large deviation in the values. For
`good structural ceramics, the Weibull modulus is greater
`.
`than 10. As seen in Table 1,
`the K
`values do not
`Ic
`correlate with the initial crack length, beam depth or
`critical displacement. Following the experiments, the re-
`leased ends of the fracture mechanics specimens could be
`broken off, and the fracture surfaces examined. SEM
`(cid:14)
`micrographs of five different fracture surfaces
`in the
`.
`vicinity of the initial crack front are shown in Fig. 7a, b,
`c, d and e, which correspond to K values of 0.4, 1.0, 1.2,
`Ic
`1.6 and 2.2, respectively. The initial crack front can be
`seen quite clearly, probably due to some modest blunting
`of the crack tip from dislocation emission during the
`w
`x
`10008C anneal following indentation 14 . The morphology
`of all the fracture surfaces in Fig. 7 appear quite similar
`and do not reveal an obvious source of the differences in
`K .Ic
`One possible source for the large deviation in K Ic
`would be the effects of varying grain orientation near the
`crack tip. However, the grain size in these polysilicon
`(cid:14)
`.
`films is very small ;0.1 mm , and the precrack passes
`through many grains. In addition, the effect of orientation
`on K in silicon is not large for the low index planes,
`Ic
`
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`
`H. Kahn et al.rSensors and Actuators 82 2000 274–280
`)
`(
`
`279
`
`(cid:14) .
`(cid:14) .
`(cid:14) .
`(cid:14) .
`(cid:14) .
`Fig. 7. Cross-sectional SEM micrographs of fracture surfaces from specimens which exhibited K values of a 0.4, b 1.0, c 1.2, d 1.6 and e 2.2
`Ic
`MPa m1r2. The pre-crack is at the left of each micrograph.
`
`varying from 0.82 to 0.90 to 0.95 MPa m1r2 for fracture
`w x
`(cid:20)
`4 (cid:20)
`4
`(cid:20)
`4
`along 111 , 110 and 100 planes, respectively 7 , though
`the local K will be higher if the crack does not propagate
`IC
`through a gain along a low index cleavage plane.
`In addition, small variations were observed in the direc-
`tion of the crack path. Also, and perhaps the likeliest
`explanation, there may be variable effects of the 10008C
`annealing on the exact shape of the crack tip, depending on
`the specific grains in which the crack tip lies. In summary,
`there is significant variability in the fracture toughness
`data, which may be due to 2 combination of several
`factors.
`Another technique for creating sharp cracks is now
`being pursued. Following the first polysilicon etch, a suffi-
`(cid:14)
`.
`ciently large indent 1 kg load placed on the release oxide
`near the polysilicon specimen causes radial cracks, which
`
`propagate from the oxide up into the overlying polysilicon.
`In this way, sharp cracks can be formed in a simple
`one-mask process, and the 10008C anneal can be avoided.
`These specimens should eliminate the variability in our
`determination of K for this material, and provide a more
`Ic
`accurate value for the fracture toughness of polysilicon.
`
`4. Conclusions
`
`The fracture behavior of micromachined polysilicon has
`been investigated using on-chip MEMS electrostatic actua-
`tors integrated with fracture mechanics specimens. Speci-
`mens with cracks produced by indentation and subse-
`quently annealed at 10008C showed a median fracture
`toughness, K , of 1.1 MPa m1r2, although significant
`Ic
`variability was experienced in its determination. K has
`IC
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`H. Kahn et al.rSensors and Actuators 82 2000 274–280
`)
`(
`
`now been determined with the one-mask process men-
`tioned in Section 3. The average value is 1.2qry 0.2
`MPa m1r2, and the data show less scatter.
`
`Acknowledgements
`
`This work was supported by the National Science Foun-
`dation under Grant MSS94-16752, by DARPA under Grant
`DABT63-95-C0070, by ARO-MURI, and by the Glennan
`Microsystems Initiative.
`
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`Biographies
`
`Harold Kahn received the BS degree in metallurgical engineering from
`Lafayette College, Easton, PA, in 1985, and the PhD degree in electronic
`materials from the Massachusetts Institute of Technology, Department of
`Materials Science and Engineering, Cambridge, MA,
`in 1992. He is
`currently a Senior Research Associate in the Department of Materials
`Science and Engineering, Case Western Reserve University, Cleveland,
`OH, working on wafer-level mechanical testing of surface-micromac-
`hined materials and shape-memory actuated microfluidic devices.
`
`Noureddine Tayebi was born in Algiers, Algeria, in 1977. He received
`(cid:14)
`.
`the Ingeniorat d’Etat BS degree with honors from Ecole Nationale
`Polytechnique d’Alger in 1998. During the same year he joined the
`Department of Mechanical and Aerospace Engineering at Case Western
`Reserve University, where he currently is pursuing his Graduate Studies
`toward obtaining the MS degree. His graduate work involves the design
`and development of fracture devices for static and fatigue measurements
`of surface micromachined films as well as a probabilistic analysis of the
`fracture mechanics behavior of micro-polycrystalline films.
`
`Roberto Ballarini received the BE degree in civil engineering from City
`College of New York in 1980, the MS degree in civil engineering from
`Northwestern University in 1981, and the PhD degree in civil engineering
`from Northwestern University in 1985. He is Professor of Civil Engineer-
`ing at Case Western Reserve University, with secondary appointments in
`Mechanical and Aerospace Engineering and in Materials Science and
`Engineering. He is interested in developing and applying theoretical and
`experimental techniques to characterize the response of materials and
`structures to mechanical, thermal and environmental loads. He is particu-
`larly interested in characterizing fracture and fatigue of materials and
`structures. Dr. Ballarini has been a visiting Professor at Politecnico di
`Torino, Universita di Pisa, and University of Minnesota.
`
`Robert L. Mullen received the BS degree in structural engineering in
`1976 and the MS degree in structural mechanics in 1977, both from the
`University of Illinois at Chicago, and the PhD degree in applied mechan-
`ics from Northwestern University in 1981. He is Professor of Civil
`Engineering at Case Western Reserve University with a secondary ap-
`pointment
`in Mechanical and Aerospace Engineering, and has been
`Chairman of the Civil Engineering Department since 1999. He is inter-
`ested in numerical analyses and finite element methods, particularly as
`applied to microdevices.
`
`Arthur H. Heuer received the BS degree in chemistry from the City
`College of New York in 1956 and the PhD degree in applied science and
`the DS degree in physical ceramics, both from the University of Leeds, in
`1966 and 1977, respectively. He joined the Department of Materials
`Science and Engineering, Case Western Reserve University, Cleveland,
`OH, in 1967 as an Assistant Professor and is currently the Kyocera
`Professor of Ceramics. He is world renowned for his research accom-
`plishments on phase transformations in ceramics and intermetallics, trans-
`mission electron microscopy of defects in materials, high-resolution
`electron microscopy studies of interfaces in advanced structural compos-
`ites, dislocations in ceramics, biomimetic processing of ceramics, MEMS,
`and rapid prototyping of engineering materials. He served as Editor of the
`Journal of the American Ceramic Society from 1988 to 1990. Dr. Heuer
`was elected to the National Academy of Engineering in 1990 and was
`made an external Member of the Max-Planck Institute for Materials
`Science, Stuttgart, Germany, in 1991.
`
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