Subsurface nanoindentation deformation of Cu–Al multilayers mapped in 3D by focused ion beam microscopy

Authors


Dr B. J. Inkson, Department of Materials, Oxford University, Parks Road, Oxford OX1 3PH, U.K. Tel: +44 (0)1865 273759; fax: +44 (0)1865 273789; e-mail: beverley.inkson@materials.ox.ac.uk

Abstract

A new technique for the three-dimensional analysis of subsurface damage of nanocomposites is presented. Cu–Al multilayers, grown epitaxially on (0001)Al2O3 single crystals by ultra high vacuum molecular beam epitaxy, have been deformed by nanoindentation. Systematic slicing and imaging of the deformed region by focused ion beam microscopy enables a 3D data set of the damaged region to be collected. From this 3D data set, profiles of the deformed sub-surface interfaces can be extracted. This enables the deformation of the individual layers, substrate and overall film thickness to be determined around the damage site. These 3D deformation maps have exciting implications for the analysis of mechanical deformation of nanocomposites on a sub-micrometre scale.

1. Introduction

Nanostructured materials, such as bulk nanocomposites, multilayered thin film coatings, and nanoscale devices, are of increasing importance in industry. During use, such nanomaterials have to be resistant to deformation, which can be induced by thermal and stress cycling, or impact events. The nanoscale mixing of different phases and spatial confinement of defects, such as dislocations and cracks in multilayers, can significantly alter the mechanical properties of sub-micrometre systems compared to the bulk (Lehoczky, 1978; Siegel & Fougere, 1995; Griffin et al., 1995; Misra et al., 1998). To fully understand the mechanical behaviour of nanomaterials, it is necessary to characterize their response to mechanical tests such as nanoindentation with an understanding of their 3D microstructure at very high resolution. In particular with nanocomposites, mechanical behaviour is a complex function of the different phases present, how they are distributed, and of specimen shape.

Focused ion beams (FIB) are increasingly widely used for site-specific 2D sectioning and imaging of microstructures, for example, diagnosis of failure sites in electronic components (Kirk et al., 1987, 1989; Satoh et al., 1988; Nikawa, 1991). Unlike surface diagnostic techniques such as atomic force microscopy (AFM), by using a FIB as a sub-micrometre drill and milling into the surface, valuable information can be obtained on the subsurface evolution of microstructures. 2D FIB sectioning of nanoindentation sites has recently been used to investigate residual damage in 6 µm Ti–Al multilayers deformed by Knoop microindentation (Tsui et al., 1999a), and FIB drilling can also be used to extract TEM samples locally from indentation sites (Saka & Abe, 1997; Ando et al., 1999). Unless analysed samples are highly symmetric, the microstructures observed in 2D sectioning and single-slice TEM investigations of nanoindentation sites are not representative of most of the deformation zone. Because deformation sites are typically non-uniform in three dimensions, the microstructures need to be characterized in 3D to fully understand the deformation.

3D microstructural analysis has been successfully carried out by sequential 2D maps generated by layer-by-layer etching, ion sputtering or field-ion removal of material (Patkin & Morrison, 1982; Cerezo et al., 1988; Hutter et al., 1993). Field-ion based methods can give atomic resolution 3D analysis (Cerezo et al., 1988), but are only applicable to electrical conductors, samples with low residual stress and length scales <<100 nm. Current methods based on etching and sputtering (where the sputtered surface is perpendicular to the incident beam) typically rely on the assumption that material is removed from the crater at a constant rate (Patkin & Morrison, 1982; Hutter et al., 1993). The depth resolution degrades as material is removed as a result of roughening of surfaces due to preferential sputtering of boundaries and different phases, and redeposition of sputtered material onto the image plane (Ximen et al., 1990). Depth resolution can be improved by sputtering with a focused ion beam parallel to the imaged surface, generating highly planar cross-sectional surfaces (Satoh et al., 1988; Cheng et al., 1998; Sakamoto et al., 1998).

Cheng et al. (1998) have successfully used a dual FIB and SEM system, where the ion and electron beams are perpendicular, to obtain a set of parallel 2D electron-induced secondary electron images through an Al wire and SiO2 particle with 1 µm resolution (Cheng et al., 1998; Sakamoto et al., 1998). In this paper we present a new method for analysing sub-micrometre as-grown and deformed microstructures in 3D using a single FIB system to both sputter flat surfaces parallel to the Ga+ beam, and subsequently to image the surfaces using ion-induced secondary electrons (ISE). In our method each sputtered plane is imaged along two or more directions, and by cross-correlating reference markers in these images, the 2D images can be aligned in (x,y,z) space with better than 50 nm resolution (section 4). Once the sequential 2D images have been aligned, image analysis is used to extract 3D grain and phase boundary profiles.

2. Multilayer growth and deformation

The chosen materials system for this study was Cu–Al multilayers grown on Al2O3 substrates, which can be grown with well defined initial microstructures. Cu-based multilayers, thin films and wires are widely used in industry, e.g. for conductive interconnects and giant magnetoresistance (GMR) films, and Cu-based multilayered systems are known to exhibit enhanced mechanical properties (Lehoczky, 1978; Griffin et al., 1995; Misra et al., 1998).

2.1. Molecular beam epitaxial growth of Cu–Al multilayers

Cu–Al multilayers were grown on (0001) basal planes of Al2O3 single crystal substrates (10 × 10 × 0.5 mm3) using a M600 Metal UHV molecular beam epitaxy (MBE) System (DCA Instruments, Turku, Finland) with a base pressure below 10−8 Pa. The Al2O3 single crystals, optically polished on the (0001) surface, were sputter cleaned (Ar-ions with 200 eV) in the MBE chamber and annealed at 900 °C for 1 h. After annealing no surface contaminants could be detected by Auger electron spectroscopy. Cu and Al were evaporated from effusion cells, using a BN and an alumina crucible, respectively. The purity of the metals was 99.999%, the deposition rates varied between 0.01 and 0.05 nm s−1, and the growth temperature was 90 °C.

The multilayer growth was monitored by in-situ reflection high-energy electron diffraction (RHEED) investigations. The first Al and Cu layers grew with the following epitaxial orientation relationships: <110>Al,Cu// <1100>α-Al2O3 and {111}Al,Cu//(0001)α-Al2O3. The RHEED pattern of subsequent Cu and Al layers consisted of rings, indicating that these layers did not have epitaxial orientations with the layers underneath. Examination of the as-deposited films in cross-section by TEM confirmed the epitaxial orientation relationships detected by RHEED during growth, and that the films were fully dense with interfacial roughness < 10 nm. The Cu–Al films consisted of a layered structure α-Al2O3/150 nmAl/50 nmCu/110 nmAl/40 nmCu. Very occasional discontinuities in the layers were observed due to island growth of the Cu and non-coalescence of adjacent islands.

2.2. Nanoindentation

The Cu–Al multilayers deposited on Al2O3 substrates were deformed by depth-sensing nanoindentation, using a Nano Indenter XP (MTS Corp., Minnesota, U.S.A.) with a sharp diamond Berkovich tip at room temperature. For each sample, six indents were carried out in a row to maximum depth penetrations of 1000 nm below the original surface level. This was followed by six further rows, each of six indents, to maximum depths of 500, 200, 150, 100, 50 and 1000 nm (Fig. 1). The nanoindents were carried out at a constant strain rate and the lateral separation of the indent sites was at least 20 µm.

Figure 1.

Optical image of residual damage zones in a Cu–Al multilayer film resulting from nanoindents penetrating 500 nm and 1000 nm below the original surface height.

3. Two-dimensional cross-sectional microstructure evaluation by FIB

3.1. Method of 2D FIB sectioning

Using a FIB in three different operational modes, that is (i) localized deposition, (ii) drilling, and (iii) imaging, it is possible to section and image 2D cross-sections of microstructures through a given specimen surface (Kirk et al., 1987, 1989; Satoh et al., 1988; Nikawa, 1991). Here the microscope used was a FEI FIB 200TEM workstation with motorized stage. First a protective coating of Pt is deposited on the area of interest (Figs 2(a) and (b)), then a staircase trough is sputtered into the sample using 30 kV Ga+ ions incident perpendicular to the plane of the film (Figs 2(c) and (d)). Tilting the sample and imaging with ion-induced secondary electrons enables the thin film to be viewed in cross-section from the side (Figs 2(e) and (f)).

Figure 2.

Surface cross-sectioning by FIB. (a) Local deposition of protective Pt over region of interest. (b) Drilling of reference markers in sample surface. (c, d) Milling of staircase trough to expose surface cross-section. (e, f) 2D imaging of sample cross-section by tilting through angle θ° about the x-axis.

Throughout this paper we will define the specimen surface/milled-plane intersection to be the x-axis, the Ga+ beam axis to be the y-axis and the milled-plane normal to be the z-axis (i.e. the specimen surface is close to the xz plane and the plane of the milled face is the xy plane). Note that after a rotation of θ° about the x-axis in Fig. 2(e), distances along the y-axis in the milled plane are measured in projection to have lengths y′ = y sinθ, but directions parallel to the rotation x-axis are not foreshortened. The absolute dimensions along the x-axis were obtained from a calibrated FIB magnification scale, and FIB measurements of the undeformed film thickness were consistent with those obtained by cross-sectional TEM.

3.2. Contrast formation in scanning ion microscopy

The contrast in the FIB ion-induced secondary electron images, that is the yield of secondary electrons from the interaction of the scanned ion beam (here Ga+) with the sample, depends on a number of factors. Generally, the intensity recorded at a particular point is proportional to the ion interaction volume (penetration depth and width), the local secondary electron generation rate (inelastic ion-electron scattering cross-section) and the probability of the secondary electrons reaching the detector (from the volume to the surface and from the surface to the detector). Major contrast mechanisms in the ISE images include (Prewett & Mair, 1991; Ishitani & Tsuboi, 1997):

1 Materials contrast, also called Z-contrast, refers to the dependence of ion penetration depth and electron emission probability on the pure material's properties (nuclear scattering cross-section for ions and electronic band structure of the crystal).

2 Orientation contrast (including ‘channelling contrast’) refers to the dependence of secondary electron yield on crystal orientation with respect to the incident ion beam (Levi-Setti et al., 1983). The channelling of incident ions along high-symmetry zone axes causes a drop in the secondary electron yield due to the deeper and narrower ion interaction volume. This mechanism allows polycrystalline grains and twins to be imaged (Levi-Setti et al., 1983; Nikawa, 1991).

3 Voltage contrast is observed in semiconductor devices under applied voltage (Kirk et al., 1987). It is caused by the linear induced change of work of emission with the applied voltage. Indirect voltage contrast is generated by charging of a material under the Ga+ ion beam. This causes oxide ceramics typically to appear dark, as the surface becomes positively charged (Kirk et al., 1987).

4 Topographic contrast refers to all edges, ridges and spikes on a surface appearing bright because of the intrinsic reduction in work of emission. For surfaces originally flat, topographic contrast will increase during imaging due to sputtering (and redeposition), particularly as a result of differential sputtering rates of different grain orientations and between different phases.

5 Surface chemistry and damage contrast: adsorbants, Ga+ implantation, amorphization, oxidation layers and other sources of contaminants will strongly affect the work of emission and thus the image contrast. This mechanism superimposes on (1) and (2).

6 Interface contrast is listed here separately, although it is strictly speaking a joint effect of mechanisms (1–5). Most notably, a metal–insulator interface will exhibit a Schottky-contact upon charging of the insulator. The curved bandstructure on the insulator side results in a bright line of contrast at the edge of the insulator, which may also have contributions from (4) if sputtering rates at the metal–insulator interface are unequal.

3.3. 2D FIB sectioning of nanoindented Cu–Al multilayers

2D FIB cross-sectioning was carried out on the < 350 nm thick Cu–Al films deformed by nanoindentation using a Berkovich tip. Figure 3 shows a cross-section through the site of an indent where the indenter penetrated 1000 nm below the original specimen surface height, imaged after a rotation of 45° about the x-axis lying horizontally in the image using secondary electrons. Images throughout this paper were taken with a single scan of a freshly milled surface using a 30 kV 100 pA Ga+ beam, with estimated beam diameter and penetration depth < 20 nm (Ishitani & Tsuboi, 1997; FEI FIB Magnum column).

Figure 3.

FIB cross-sectional image through the site of an indent which penetrated 1000 nm below the original Cu–Al multilayer surface, imaged after a rotation of 45° about the x-axis. Real distances y in the milled plane are imaged in projection as y′, where y = y′√2.

The individual Cu and Al metal layers can be clearly distinguished in Fig. 3, sandwiched between the protective Pt layer and the underlying Al2O3 substrate. The Cu layers appear the brightest in this orientation, emitting many more secondary electrons than the interleaving Al layers. Imaging freshly milled surfaces (with minimal topography) of both as-grown and deformed areas at different tilt angles (θ = 5°, 10°, 15°…) showed that the Cu always imaged brighter than the Al as a result of differential Z-contrast (section 3.2(1)). Some orientation contrast fluctuations (section 3.2(2)) between twins and grains within the individual Cu and Al layers could also be observed at different tilt angles (Fig. 4(c)) but this was a lesser contribution compared to the Z-contrast under these imaging conditions and did not affect identification of the individual Cu and Al layers. At all tilt angles the Al2O3 imaged darkly owing to positive charging resulting in voltage contrast (section 3.2(3)). The Al2O3 surface images bright because of the formation of a Schottky-barrier contact with the Al (section 3.2(6)).

Figure 4.

Magnifed FIB cross-sectional images through Cu–Al indents, with y-direction lengths corrected by √2. (a) 2D section close to the centre of a 530 nm deep indent. (b), (c) parallel sections through a 1000 nm deep indent, separated by z = 880 nm. Note how the severe flow of the Cu and Al creates complex ‘pile-up’ zones around the central residual indent zone.

Examination of the cross-sections through the indent sites reveals that there is severe residual plastic deformation, where the microstructure of the film differs significantly from the as-deposited multilayered structure. Figure 4 shows at higher magnification a cross-section through the centre of a 530 nm indent (Fig. 4(a)) and two parallel xy cross-sections through a single 1000 nm indent (Figs 4(b) and (c)). It should be noted that the microstructures resolved in the 2D FIB profiles vary considerably depending on the cross-section position with respect to the geometrical centre of the indent. Major features in the severely deformed microstructure to note from the 2D cross-sections of the Berkovich indents in the Cu–Al multilayers on Al2O3 are:

(i) In the centre of the severe plastic deformation zone there are systematic reductions in the Al, Cu and total film thickness towards the geometrical centre of the indent, causing depression of the Cu–Al interfaces towards the substrate.

(ii) In the same central zone as (i), no residual plastic deformation of the Al2O3 was resolved where the indenter penetrated approximately 500 nm below the original specimen surface height (Fig. 4(a)). Underneath the 1000 nm indents, the Al2O3 is plastically deformed, with the Al–Al2O3 interface being locally depressed into the substrate (Figs 4(b) and (c)).

(iii) Around the central residual indent zone for the 500 nm and 1000 nm indents ‘pile-up’ zones exist where the total thickness of the metal film exceeds that of the as-grown film due to flow of the metal out from the centre of the indent.

(iv) In the pile-up zones, the Cu–Al interfaces and Cu-surface are highly rumpled/undulating, but the Al–Al2O3 interfaces remain undeformed. All of the four metal layers thicken in the pile-up zones, but not at an identical rate.

(v) Except at the very centre of the indent where individual layers cannot be resolved, all of the multilayer interfaces remain intact, indicating good adhesion, with no cracks or voids being resolved in the FIB images. In some cases the interface rotation away from the original xz plane is > 90°, producing interface ‘overhang’.

4. Three-dimensional mapping of subsurface microstructures

The microstructures observed in individual FIB cross-sections are 2D slices through a non-uniform 3D microstructure. In order to fully understand the structure of nanocomposites and how they respond to deformation, we need a method of mapping the microstructure in three dimensions.

4.1. 3D microstructure mapping by FIB

A 3D map of a microstructure can be determined from a set of sequential 2D maps through a structure which all have a known position with respect to each other (Patkin & Morrison, 1982; Hutter et al., 1993). The technique presented here uses a FIB to drill sequential 2D sections parallel to the ion beam (Satoh et al., 1988; Sakamoto et al., 1998). We then image the milled plane in-situ down two or more non-parallel directions to obtain structural data with known (x,y,z) co-ordinates. In detail, the 3D structure of nanocomposites are mapped using the following iterative procedure:

(i) Cross-sectional start-up: As for 2D, protective Pt is deposited locally on top of the site to be cross-sectioned and a deep staircase trough drilled into the film (Figs 2(a–d)). In addition, a set of positional reference markers are drilled into the xz plane of the specimen surface (Figs 2(a) and (b)) to enable subsequent alignment of multiple images in 3D space.

(ii) Iterative cross-sectioning loop:

(a) A rectangular box is drilled (by many parallel xy line scans stepped with incremental z) to produce the desired xy cross-section through the region of interest.

(b) The xz film plane is imaged along the y-axis (Ga+ beam axis) to determine the x and z co-ordinates of the milled plane (Fig. 2(d)).

(c) The specimen is rotated about the x-axis (common direction of the specimen surface and milled plane) by known angle θ° (Fig. 2(e)).

(d) The milled xy plane is imaged at angle θ° to give a 2D profile of the positions of the subsurface metal and substrate interfaces (Fig. 2(f)). If there is insufficient contrast to distinguish all the investigated phases and grains with a single tilt angle θ° and exposure, enhanced contrast can sometimes be achieved by re-imaging (implanting more Ga+), or tilting the sample and imaging again at further angles θi°, i = 1,2,3… Imaging at multiple tilt angles differentially alters the channelling contrast between different grains and is particularly useful for determining grain boundaries positions in single phase polycrystalline samples (Levi-Setti et al., 1983; Nikawa, 1991). It should be noted however, that each additional image taken with the ion beam not parallel to the xy plane increases the roughness of the surface (and hence 3D spatial error) due to non-uniform sputtering and redeposition effects.

(e) The specimen is rotated back to the xz plane and the sequence (a–e) repeated, drilling and imaging many parallel 2D xy cross-sections each separated by an incremental z position.

(iii) 3D data reconstruction: The parallel xz and xy images from the multiple 2D cross-sections are aligned in 3D space using cross-correlation of the positions of the reference markers in each image. From the aligned images the x, y and z co-ordinates of subsurface features in the milled cross-sections can be determined, and analysis of this 3D data set using interpolation techniques can then be used to extract the position of phase and grain boundaries in 3D space.

4.2. 3D mapping of indented Cu–Al multilayers

The method of 3D FIB mapping detailed in section 4.1 was used to investigate the plastic deformation resulting from indenting a Cu–Al multilayer coating approximately 530 nm below the original surface height (150% of film thickness) with a pyramidal Berkovich tip (Fig. 1). Figure 5 shows the raw data load–displacement load–unload curve obtained for the indent chosen to be analysed in 3D. Fifteen parallel 2D FIB images were taken through the indent, each with known relative (x,y,z) position determined from cross-correlation and alignment of multiple images containing drilled reference markers. A single image of each milled surface taken at θ° = 45 was sufficient in this case to locate the individual Cu, Al and Al2O3 phases (section 3.3). Drilling and imaging were carried out using a 30 kV 100 pA Ga+ beam, and the z-separation of images was in the range 0.26–0.66 µm (the spacing does not have to be regular). The xy dimensions of the milled plane were larger than the investigated deformation zone to avoid spurious edge sputtering effects. The 2D images were aligned in a 3D x,y,z box (schematic in Fig. 6), and the images stretched along the y-axis by √2 to compensate for the 45° imaging angle. Errors incurred due to inaccuracy of the motorized tilt drive, causing deviation away from the chosen tilt axis and angle, have been neglected in this initial study.

Figure 5.

Load–displacement curve for the nanoindent in a Cu–Al multilayer analysed by 3D FIB mapping (raw data).

Figure 6.

Schematic of alignment of 2D FIB images through a nanoindent site in 3D space according to determined (x,y,z) co-ordinates.

Once the data are aligned in 3D, it is possible to section the data set in any direction, for example, xz sections through the data set at different y-heights relative to the original height of the film surface. Maps formed by interpolation of the intensity between the individual cross-sections tended to suffer from contrast variations between different original images. Therefore to characterize in more detail the deformation of the individual layers, three line profiles corresponding to the positions of the maximum intensity from the Cu layers and Al–Al2O3 interface were extracted from each of the 2D images. The Cu layers (originally 40–50 nm thick) gave such narrow intensity peaks (approximately 6 pixels) that it was only possible to determine the maximum in intensity corresponding to the centre of the Cu layer rather than determining the positions of the individual Al–Cu interfaces. In the residual indent zone automatic determination of three line profiles failed close to the centre of the indent site because the contrast from the two Cu layers and Al–Al2O3 interface merges in the 2D FIB images due to severe thinning of the metal multilayer. In this regime the line profiles were manually set all to be equal, although it may be the case that distinct continuous Cu and Al layers still exist at high resolution.

The 15 individual line profiles for each of the two Cu layers and the Al–Al2O3 interface were aligned in 3D, and bilinear interpolation between the line profiles was then used to generate three surface maps. Figure 7 shows the 3D surface map generated from the 3D FIB sectioning for the surface Cu layer. This map corresponds to the location of the centre of the outer 40 nm Cu layer. It is thus distinct from, but closely related to, an AFM map of the same indent, which would measure the profile of the outer surface contamination (e.g. Cu oxide) above this Cu layer.

Figure 7.

3D colour/contour map of the deformation of the outermost Cu layer around the site of a 530 nm nanoindent with Berkovich tip. The y height of the Cu layer deviates with height range: ymax bsl00051 ymin = 600 nm.

The 3D profile of the Cu-layer in Fig. 7 clearly shows the severe plastic deformation induced around the nanoindentation site. Immediately identifiable is the nearly three-fold symmetry of the residual deformation induced by the pyramidal shape of the Berkovich indenter. Around the central trough at the geometrical centre of the indent are three zones where the outer Cu layer is significantly raised up from its original plane. The peak height to minimum depth of the profile is measured to be 600 ± 70 nm (for errors see section 4.4), which is larger than the maximum depth of the original indent (measured from the undeformed multilayer surface), which was 530 nm (Fig. 5). The pile-up zones are orientated adjacent to where the three flat faces of the pyramidal indenter intersected with the specimen, and give rise to the circular contrast around the indent sites in the optical images (Fig. 1). The asymmetry in the shape of the three pile-up zones in Fig. 7 is thought to stem predominantly from errors arising from insufficient sectioning density across the lower pile-up zone (see section 4.4(v)), which masks in this case the measurement of any real effect arising from specimen anisotropy or indenter/surface misalignment.

Figure 8 shows the 3D FIB profile generated for the position of the internal Cu layer originally 150–200 nm below the film surface. These are unique sub-surface data which cannot be extracted from AFM studies. The plastic deformation of this internal Cu layer is also clearly defined by the three-fold symmetry of the Berkovich indenter and its associated strain field, despite not being constrained by direct contact with the indenter as was the outer Cu layer (Fig. 7). Three pile-up zones occur where the Cu is pushed up above its original height by material flow underneath emanating from the centre of the indentation. The peak height to minimum depth of the internal Cu profile is measured to be 400 ± 70 nm. The ripples in the pile-up surface observed in the 2D sections are visible, although their positions and shapes are not well resolved with only 15 sections.

Figure 8.

3D map of the deformed internal Cu layer under the Cu layer in Fig. 7. y height range: ymax bsl00051 ymin = 400 nm.

The 3D maps of the deformed Cu layers contrast distinctly with the 3D map of the internal Al–Al2O3 interface (Fig. 9). The peak height to minimum depth of the interface map is measured to be 120 ± 70 nm. The y-height variations in this map are due both to errors in the data extraction method as for the other maps (see section 4.4), and also there exists a small systematic decrease of 50 nm in y-height along the x-axis for all of the 2-D profiles across the mapped area. This systematic change is due to a real tilt of the substrate surface by about 4° as a result of the specimen mounting, and is present in the Cu maps as well (Figs 7 and 8).

Figure 9.

3D map of the Al–Al2O3 interface under Figs 7 and 8. y height range: ymax bsl00051 ymin = 120 nm.

For the nominally 530 nm deep indent, which should penetrate 180 nm below the original 350 nm thick multilayer film, the Al–Al2O3 interface showed no identifiable residual plastic deformation in the 2D slice closest to the centre of the indent site (Fig. 4(a)), although sections through 1000 nm deep indents clearly show residual depression of the Al2O3 surface (Figs 4(b) and (c)). This indicates that the Al2O3 substrate undergoes some elastic recovery as the indenter is removed, which is visible in the unload segment of the load-displacement curve in Fig. 5 (superimposed with the elastic recovery of the Cu–Al coating). The discrepancy in the apparent final displacement of the surface from the initial surface height of approximately 450 nm in Fig. 5, and the maximum residual indent depth of the order of the coating thickness (350 ± 50 nm) measured by FIB sectioning, can be attributed to a number of factors including (i) the error in the zero position of the raw data load–displacement curve (i.e. the true indent depth is not 530 nm), (ii) the load–displacement curve is uncorrected for thermal drift or machine constants, and (iii) any residual plastic deformation of the Al2O3 under the analysed indent was masked by current errors in the method (in particular insufficient 2D sectioning density misses the geometrical centre of the indent and so underestimates the maximum residual indent depth).

4.3. Determination of material flow

Once extracted, 3D maps of individual subsurface layers and interfacial positions can be used to calculate further deformation maps, although errors accumulate. In particular, the relative positions of two 3D interfaces can be used to calculate volumes of grains, and maps of individual layer and total film thickness. For microstructures that are well characterized in their initial state, such as the metal multilayers in this study which have initial constant thickness, the changes in individual layer thickness around a deformation site can be used to analyse material flow.

The difference between the position of an outer surface and an internal coating/substrate interface measures the total thickness of the coating. Figure 10 shows the map calculated from the difference between the position of the surface Cu layer and the Al–Al2O3 interface. This is effectively the local thickness of the Cu–Al multilayer coating around the site of the 530 nm deep indent, neglecting here the difference between the centre and outer surface of the originally 40 nm thick Cu layer which could not be differentiated in the original analysis (section 4.2).

Figure 10.

Map of total Cu–Al multilayer film thickness around the site of the 530 nm deep nanoindent: ymax bsl00051 ymin = 600 nm.

Compared to the original deposited 350 nm Cu–Al multilayer coating thickness, significant material flow out from the centre of the indent to three pile-up zones causes a maximum thickness of 600 ± 70 nm (170% of original). The volume of material up-lifted above the original multilayer thickness is calculated to be 0.9 µm3, and the missing volume of the residual indent zone at the indent centre is calculated to be 1.2 µm3. A comparison of these two measurements is an indication of excess/deficient volume resulting from residual elastic/plastic deformation and/or material removal during the deformation testing. In this study the pile-up/residual indent volume difference could be entirely due to errors in the measurement.

It should be noted that in this special case, the zones where the coating's surface (outer Cu layer) is displaced above its original position correspond to the ‘material pile-up’ zones of the total film thickness because the Al2O3 substrate had no resolvable residual plastic deformation. In a general case, where the substrate is also deformed, the total film thickness cannot be deduced from just a surface measurement.

Considering the variation in thickness of the individual layers in the coating, Fig. 11 shows the relative separation of the adjacent Cu layers (numerically close to the thickness of the upper Al layer as Al thickness >>Cu thickness), and the separation of the lower Cu layer and the Al–Al2O3 interface (numerically close to the thickness of the lower Al layer). Both these maps show three pile-up zones, and the sum of the two maps gives the film thickness in Fig. 10. It should be noted that the morphology and maxima/minima of the pile-up/residual indent zones in the FIB maps of individual layers are not identical to one another, because each layer undergoes different deformation in the non-uniform strain field under the Berkovich indenter. Thus, because of their different spatial location, the sum of the maxima from Figs 11(a) and (b) is greater than the maximum of the total film thickness (Fig. 10).

Figure 11.

Maps of interfacial separation around the 530 nm nanoindent site. (a) Separation of the surface and subsurface Cu layers: ymax bsl00051 ymin = 380 nm (b) Separation of subsurface Cu and Al–Al2O3 interface: ymax bsl00051 ymin = 340 nm.

4.4. Estimation of uncertainties

The 3D FIB maps and quantitative measurements given in section 4.2 and 4.3 are subject to specific error bars classified into five groups as follows:

(i) The basic precision of measurements from individual FIB images, especially the determination of positions of intensity maxima, depends on the FIB instrumental resolution and on the magnification used (here 50 K). In combination with the peak search algorithm used during image processing, we estimate this positional error here to be Δy = ± 22 pixels ≡ ± 20 nm. This error can be reduced by using a higher magnification; however, in this study part of the field of view of the complete indent zone would then have been sacrificed.

(ii) A second important but systematic error arises from the interpretation of the origin of the image contrast in the secondary electron image, for example the direct attribution of lines of maximum intensities to a materials feature such as an interface. This error is very complex and will be subject of a forthcoming paper. The contrast in the FIB images, taken with secondary electrons induced by the incident Ga+ ions, can be altered by many factors (section 3.2, Levi-Setti et al., 1983; Prewett & Mair, 1991; Ishitani & Tsuboi, 1997), and imaging conditions are therefore a tradeoff between voltage, beam current, image exposure and noise. In this study we used a 30 kV 100 pA beam current for both milling and imaging as a compromise between reasonable milling rate, minimal Ga+ implantation and sputtering, and sufficient resolution for imaging sub-50 nm Cu layers. SEM imaging, which would eradicate any sputtering during imaging, could be carried out in dual FIB/SEM systems. We assume here that the image intensity maxima due to Cu correspond to the centres of Cu layers for reasons of symmetry. The bright line at the Al/Al2O3 interface might be displaced by as much as 50 nm. All error (ii), however, disappears for all measurements of relative distances within a given map and between equivalent maps due to its systematic nature.

(iii) The 3D FIB imaging method relies on a reliable determination of relative (x,y,z) coordinates of sequential 2D images (section 4.2), which at present is affected by alignment and other technical errors. These errors are expected to be largely reducible by additional experimental and image processing effort. We have neglected at present the angular errors arising from (a) the milled planes not being truly parallel to the axis of the incident Ga+ beam due the finite beam profile (Ximen et al., 1990), and (b) the motorized stage tilt inaccuracy, i.e. errors in the stage x/y/z purities and angular tilt purity through θ° about the x-axis. The effects of unwanted redeposition and stage drift during drilling (x,y,z) boxes were minimized by drilling many sequential x-y sections parallel to the incident Ga+ beam with incremental z, rather than xz sections with incremental y. The effects of stage drift in x, y and z between imaging sequential 2D sections was compensated for by cross-correlating the images using the drilled reference markers. We estimate all class (iii) errors here to sum up to Δx = Δy = Δz = ± 30 nm.

(iv) Error propagation affects derived data, such as the determination of differences between positions. Within one 2D slice twice the basic error (i) but no systematic error (ii) is achieved, Δy = ± 2 × 20 nm = ± 40 nm. For height differences derived from separate slices (worst case), such as the maximum variation in y-position of a metal layer around an indent (section 4.2) or maximum variation in film thickness (section 4.3), errors up to Δy =±30 nm ± 2 × 20nm = ± 70 nm accumulate. Errors in the other directions of Δx = Δz = ± 30 nm remain unchanged.

(v) The accuracy of the 3D reconstruction depends on choosing an incremental spacing between sequential 2D cross-sections sufficiently small to locate all changes in the microstructure being examined. The chosen bilinear interpolation between neighbouring 2D cross-sections will underestimate the true maxima and overestimate the true minima of the surfaces. In particular, in regions where the surface height is changing rapidly in a direction perpendicular to the milled planes (here the z-axis), the spacing between parallel 2D images should be as small as possible. In this initial study on a Cu-Al indent 15 line profiles were used to generate each 3D surface map, separated by 0.26–0.66 µm. As is apparent in Fig. 7, sectioning of the lower pile-up zone should have been done at smaller z-increments in order to determine the correct pile-up profile (which appears different from the other two pile-up zones), and a higher density of 2D cross-sections would have been necessary to accurately map the ripples in all three pile-up zones.

With further work on the technique, errors in classes (i)–(v) can all be reduced. The future limit of FIB microscopy as a 3D mapping technique will, however, be dominated by error (i), and can probably be pushed to ± 15 nm.

5. Conclusions

The tolerance of nanostructured materials to mechanical deformation is an increasingly important factor in the design of a wide range of devices such as wear-resistant coatings, structural nanocomposites, and microelectromechanical systems devices. Here we have presented an exciting new method using FIB, which can be used to map sub-micrometre as-grown and deformed microstructures in 3D with spatial resolution << 100 nm. FIB is used to systematically slice and image a specific area of a sample. Collection of many sequential 2D images at indexed locations enables a 3D data set of a microstructure to be built up. From this data set, the 3D positions of individual interfaces, such as grain and phase boundaries, and cracks can be extracted. The 3D FIB mapping method may be applied to both single phase polycrystalline materials and nanocomposites, provided that sufficient ISE contrast can be obtained from the features to be analysed (see section 3.2).

Because the site of 3D FIB analysis can be chosen with a spatial resolution < 50 nm (depending on FIB beam profile), the technique can be used to analyse specific deformation sites such as nanoindentation tests, scratch tests and fracture surfaces. This means that the analysed 3D microstructures can be directly related to the mechanical data extracted from the deformation tests, which will be of enormous benefit in the understanding of mechanical properties at the nanoscale.

We have carried out the first 3D quantification of the localized residual deformation of metal multilayers around a nanoindentation event. We have applied the method to the Cu–Al multilayer–Al2O3 substrate system, which is an example of a soft sub-micrometre nanocomposite coating on a hard substrate (Tsui et al., 1999a). Indent sites have been examined in the regime where a Berkovich indenter has penetrated below the original position of the coating/substrate interface. The 3D morphology of individual deformed metal layers and substrate surface resulting from the local non-uniform strain generated during the indent cycle (loading and unloading) have been mapped. Analysis of the relative separation of interfaces and layers is used to evaluate the total film thickness around the indent, and map material flow within the initially uniform layered structure.

For the Cu–Al system, the extreme difference in the mechanical properties of the Al-Cu multilayer compared to the Al2O3, results in the soft ductile metal layers undergoing extreme plastic deformation and material flow around the indent sites (Figs 4, 7 and 8), whereas in this study we only resolved residual plastic deformation of the Al2O3 substrate at the centre of the 1000 nm indent sites (Figs 4 and 9). It is observed that the surface pile-up and residual indent zones, which can be observed by surface optical and AFM techniques (Fig. 1), are the net result of complex deformation patterns of individual subsurface layers and the substrate, each with their own distinct pile-up and residual indent zones (section 4.3). Owing to the different flow patterns of metal within the individual Cu and Al layers the relative thickness and shape of the layers completely change, with substantial ‘rippling’ of the layers occurring in the pile-up zones on a scale < 100 nm, which will locally alter the mechanical properties (Lehoczky, 1978). Despite plastic deformation so extreme as to even produce interface ‘overhang’ (Fig. 4), the Cu–Al interfaces prove to have good adhesion, with no voids or cracks being detected where the individual layers could be resolved. Delamination of the multilayer films from the Al2O3 substrate was not observed.

The technique of 3D FIB mapping has obviously still to be optimized and a number of errors exist. Five basic classes of error have been identified, arising from (i) the instrumental resolution of the 2D FIB images, (ii) the physical contrast interpretation, (iii) determination of the 3D co-ordinates, (iv) data processing, and (v) sectioning density (section 4.4). In general, the scale of microstructural features suitable to be examined by the 3D FIB mapping technique lies approximately in the range 30 nm−30 µm, with the limits being determined by desired resolution, microscope parameters and time. Despite some intrinsic limitations, the 3D FIB sectioning method is very powerful in its applications for the site-specific 3D nanoscale analysis of inhomogeneous materials.

Acknowledgements

This work was supported by a British Council/DAAD ARC grant, Project 1100, with additional funding from The Royal Society and the EPSRC. Dr Oliver Kraft and Professor Eduard Arzt of the MPI in Stuttgart are gratefully thanked for the use of their Nano Indenter XP system.

Ancillary