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Rotational grinding of silicon wafers—sub-surface damage inspection
Materials Science and Engineering B107 (2004) 321–331
Rotational grinding of silicon wafers—sub-surface damage inspection Atte Haapalinna a,∗ , Saulius Nevas b , Dietmar Pähler c b
a Okmetic Oyj, P.O. Box 44, FIN-01301 Vantaa, Finland Metrology Research Institute, Helsinki University of Technology, FIN-02105 HUT Espoo, Finland c Fraunhofer Institut für Produktionstechnolgie IPT D-52074, Aachen, Germany
Received 1 October 2003; accepted 17 December 2003
Abstract Industrial practise in wafer manufacturing indicates that there is not one agreed method available to acquire a conclusive picture of the sub-surface damage, defined as structural inhomogeneities of the crystal lattice. Therefore, various methods have been studied and compared for measurement of the sub-surface damage introduced to single crystal silicon wafers during rotational grinding process. Several probing techniques were used to analyse a controlled set of ground silicon wafers. Optical methods were used to study the strain distribution, scattering-in depth and surface topography of the sample set. Acoustic and X-ray diffraction were used to directly observe variations in the Young’s modulus and the lattice constant, respectively. The techniques used ranged from point analysis to whole-wafer mapping and averaging. The study indicates that the various physical properties of the lattice damage arise from closely linked processes taking place during the grinding process. The correlations between the methods included in this study have been identified and quantified, and the relationships between the various observable quantities of sub-surface damage are discussed. © 2003 Elsevier B.V. All rights reserved. Keywords: Silicon wafer; metrology; sub-surface damage
1. Introduction Silicon wafers are the building blocks of the digital world. The search for higher performance and lower cost for integrated circuits requires an increasing level of sophistication from the whole silicon manufacturing chain. There is a constant need to improve both the processes used in the manufacturing of silicon wafers, and the properties of finished silicon wafers. Instead of improving the individual process steps, improvements can also be realised by introducing new, advanced manufacturing techniques, replacing some of the traditional parts of the process chain. The replacement of lapping by rotational grinding is one such proposed change. Grinding utilises the increasing wafer size and more stringent quality requirements in becoming an increasingly attractive solution versus lapping, both cost- and quality-wise. Various inspection methods have been used to characterise the surface condition and sub-surface damage in machined ∗ Corresponding author. Tel.: +358-40-528-5118; fax: +358-950-280300. E-mail address: [email protected] (A. Haapalinna).
0921-5107/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2003.12.008
silicon [1–4]. Other techniques, such as those reported for sub-surface analysis of materials such as Si3 N4 [5] and GaN [6] can also be applied to machined silicon. Process utilisation for most of the methods used is limited by the destructive nature and small sampling areas inherent to most of the techniques used. Novel inspection methods are required for successful optimisation of such advanced processes. In this paper, we discuss several methods which can be used to analyse the damage caused by rotational diamond-wheel grinding, aiming to link fast, whole-wafer mapping methods with the established point analysis. Most of the presented techniques can also be applied to lapped, sliced and sometimes even rough polished surfaces.
2. Sub-surface damage caused by mechanical manipulation of silicon For the purposes of this discussion, as-grown Czochralski silicon ingot is virtually defect-free. The slicing of wafers creates heavy mechanical damage on both sides of the wafer. In the traditional process the wafer is subsequently abrasively lapped, removing the slicing-induced damage, and
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problematic tool wear. The throughput issue can be improved by two-step grinding, and the tool wear can be solved with suitable materials and operating parameters.
3. Nature of the ground surface
Fig. 1. Sub-surface damage model by Hadamovsky [7].
at the same time, introducing a new, more uniform damage to the surfaces of the wafer. This is then removed in etching, which results in rough, but damage-free surfaces. Chemical–mechanical polishing (CMP) on one side results in the single-side polished (SSP) wafer, on which the electronic circuits are then integrated. The alternative process would replace lapping by grinding. By two-step grinding, in which the last step is carried out in the ductile mode, the damaged layer on the front surface will be very shallow. If it can be guaranteed that the damaged layer depth does not exceed a few microns, significant cost savings and performance improvements can be reached in the final CMP. The relative merits of all above mentioned techniques, and optimisation of the relevant process parameters requires accurate analysis of the sub-surface damage on the silicon surface. This requirement can only be met if both the severity and the distribution in depth, of the grinding-induced crystal damage, can be characterised. Several models have been presented for the damage distribution due in abraded crystalline silicon [7,8], such as the one depicted in Fig. 1. The damage-creation processes in slicing, lapping and grinding operations have obvious similarities. For example, multi-wire slicing can accurately be described as a variant of the abrasive lapping process. While the extent of the induced damage varies from process to process, the nature of the mechanically induced crystal damage is always quite similar. For the purposes of this discussion, grinding processes can be divided into two categories: ductile and non-ductile. As the name implies, ductile mode grinding removes material within plastic limits of the workpiece material. For brittle materials, such as monocrystalline silicon, this requires that several conditions are met. The primary requirement is that the applied cutting force must be low enough not to cause fractures in the material. This requires that the force must be applied to a very small volume, in order to separate this volume using low forces. Small removal volumes indicate low feed rates and small cutting elements, that is, small diamond sizes. These conditions imply low throughputs and
The surface structure of a rotation-ground wafer includes peaks and depressions, while depending on the process parameters; they still are in the same order of magnitude as the diamond size used in the grinding wheel. The damaged silicon layer can be described as polycrystalline, consisting of several, smaller, monocrystalline pieces packed very tightly. The packing density is, however, lower than that of the undamaged monocrystalline lattice. This causes compressive strain on the upper, ground, surface of the silicon wafer. If the lower surface is damage-free, the geometrical deformation of the wafer can be used to estimate the aggregate damage-induced on the upper surface of the wafer. The grooved texture is a property of rotation-ground wafers over a wide range of spatial frequencies, observed using various imaging techniques. Due to the nature of the rotational grinding process the direction of the cutting diamond is radial, and thus the wafer surface consists of scratches on top of other, longer wavelength grooves (Fig. 2). The periodical nature of the surface can be seen both in low-magnification interferometric images (Fig. 3) as well as in high-magnification SEM images (Fig. 4). The measured surface has been ground with a D6 wheel resulting in a smooth, fine ground surface. The tool index D6 indicates the average diamond size, in m, used in the tool as the fixed abrasive responsible for the material cutting. These grooved surfaces are caused by the directional nature of the processing. The fact that the forces induced to the material in rotational grinding are very directional is due to the geometry of the process. This combined with the anisotropic lattice of the silicon leads to a non-uniform
Fig. 2. The dynamics of rotational grinding. The grooves depicted on the wafer surface are due to the high rotational speeds used for the grinding wheel, which is an order of magnitude higher than the rotation speeds of the wafer.
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Fig. 5. Surface photovoltage signal, recorded for a fine ground 1 0 0-oriented wafer. The location of the notch is marked with a triangle, and the 1 1 0 glide plane directions are indicated with dotted lines.
measured with surface photo voltage (SPV) probe, as seen in Fig. 5. Fig. 3. White-light interferometer image of a ground wafer, ground with the D6 wheel (upper image) and a line scan extracted from the same image (lower image).
damage distribution in the wafer. Specifically, on a standard 1 0 0-oriented wafer the lattice is most prone for fractures and dislocations along the 1 1 0 glide planes. In rotational grinding the processing is aligned with these planes only for the 1 1 0 glide planes, which cross at the centre point. The damage distribution is not exactly aligned to these glide planes, because the wafer is rotated on the chuck. This phenomenon can be seen for example in etching of ground wafers in KOH, as these lines are the ones, which generate most hydrogen—indicating that the lattice is more strained along these axes. The same phenomenon is causing the patterns seen on surface recombination maps,
Fig. 4. Scanning electron microscope images of the same wafer, ground with the D6 wheel. The magnifications are 10,000× (left image) and 500× (right image). The most densely packed grooves found on the higher magnification image are some 150–200 nm apart, on the low magnification image the lines are around 1 m apart.
4. Measurement techniques employed in the study A total of seven different methods were included in our study. The specimens were prepared by grinding a controlled set of 200 mm silicon wafers. The grinding conditions were chosen in order to create a controlled variation in the damage introduced to the wafer set. The methods discussed in this chapter are briefly introduced and characterised in the following overview and discussed in detail thereafter. 1. Strain-induced deformation (bow), depicted in Fig. 6a Suitable measurement tools are readily available in the semiconductor industry, offering potential for large numbers of wafers to be measured. Measures the wafer strain due to the polycrystalline, topmost layer, created by the machining of the wafer. A whole-wafer averaging technique. 2. X-ray diffraction, depicted in Fig. 6b Chosen because X-ray diffraction is a well-established method to investigate lattice non-uniformities. A point analysis technique. 3. Surface roughness Suitable tools are readily available in the Semiconductor industry. Not a direct measure of damage but closely linked both to the grinding operation and the damage-creation processes through the surface feature size/diamond grid size dependence. Fast point analysis technique. 4. Spectral diffuse reflectance, depicted in Fig. 6c
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Novel method based on optical anisotropy introduced to silicon by the damage-induced straining. The measurand is the rotation of a linearly polarised laser beam. The rotation is proportional to the local straining integrated through the whole wafer. A whole-wafer mapping technique. 4.1. Geometrical deformation of the wafer under compressive strain
Fig. 6. Different principles used for measuring the SSD. (a) Bow: strain on the top layer of the wafer causes the wafer to deform in a measurable way. (b) X-ray diffraction: scattering angle of monoenergetic X-rays is defined by the lattice constant a. Lattice constant changes with strain, a , and the diffraction angle changes accordingly. In addition, polycrystalline top layer includes displaced crystal planes. Both of these effects result in widening of the diffraction angle θ, as defined by Bragg’s law. (c) Diffuse reflectance: the wafer is illuminated, and the refracted beam is partly scattered by lattice imperfections. Some of the scattered light exits the wafer and can be measured. (d) Surface acoustic waves: penetration of surface acoustic waves into the bulk of material depends on the frequency of the wave. Thus, the extent of the interaction with the lattice damage, concentrated in the top-layer, depends on the frequency.
Experimental set-up, offering potential for depthresolving studies due to fact that penetration depth of light varies with wavelength. The method is based on scattering of light from lattice imperfections. A technique averaging over a small area (100 mm2 , potentially up to hundreds of mm2 ). 5. Surface photo voltage and microwave photo conductive decay (PCD) The relevant tools are readily available in semiconductor industry and they potentially allow links to be established between sub-surface damage SSD and the electrical behaviour of the silicon material. The basis for measuring SSD with these methods lies in the dependence of the lifetime on the density of recombination centres, which created by non-homogenities in lattice, such as mechanical damage. A whole-wafer mapping technique. 6. Laser acoustic wave (LA-Wave), depicted in Fig. 6d Novel method based on dispersion of surface acoustic waves. Wavepackets are subjected to dispersion due to the frequency-dependent penetration depth of a surface acoustic wave and the location of the damage at the uppermost layer. A technique averaging over a small area (200–400 mm2 ). 7. Scanning infrared depolarization (SIRD)
The basic shape of a silicon wafer is defined by a parameter called bow. This is the deviation of the median surface of the wafer relative to the least-squares fitted plane, with the deviation measured at the centre, and the fitting done to the above mentioned median surface. We have measured this parameter using a commercial semiconductor tool, contactless capacitive gauge of the type Eichhorn + Hausmann MX203-8-49-B. The gage utilises 49 pairs of capacitive sensors to determine the local distance of the wafer surface from the sensor heads. These results are used in combination with calibration values, which include corrections to individual sensor heights. PC-software is used to calculate the local wafer thickness and local warpage of the wafer. These local values are then used to calculate global parameters, which describe the whole wafer, such as bow. The measured values of bow are influenced by the gravitation, which for compressively strained samples, such as ground wafers, pulls the centre of the wafer down, reducing the measured bow. In the gage used, however, the centre is supported, and thus the gravitational effect is not seen for wafers, which are only slightly curved. An example of such wafers would be the multi-wire sliced (MWS) sample wafers used in this study, which have very low natural, unstrained bow. For these wafers the unstrained bow values are essentially determined by the gage support pads. Therefore the change of bow due to machining in the grinding process is estimated assuming that the natural, unstrained bow is zero. This assumption is verified using another commercially used capacitive tool, ADE Ultrascan7200. The depth of the strain-inducing damage layer was investigated by successively etching very thin layers from differently ground wafers, and measuring the bow between each etching step. The measured bow results are affected by an offset in bow, mainly due to potentially uneven support pads and gravitation, and by a variation due to sensor deviations over time. This limitation prevents accurate bow measurements for the completely unstrained and very slightly strained wafers. The results of the bow-measurements are summarised in Figs. 7 and 8. Fig. 7 represents a result of a study, in which the various grinding machine parameters are evaluated based on the stress created on the processed surface of a 200 mm wafer with 1 0 0-orientation. The study indicates that measurement of strain-induced curvature in silicon wafers is a sufficiently sensitive method to distinguish not only between the differences in surface and sub-surface damage caused
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of the less damaged wafers, ground using optimum parameters, is clearly more concentrated on the thin upper layer than that of those with higher bow, and higher damage. Compared to staged etching experiments reported in [2], constant bow values, indicating total removal of the damage-induced strain, are reached after clearly smaller material removals. This can be caused by lower initial damage depths, differences in the sensitivity of the measurement methods used, or both. 4.2. X-ray diffraction
Fig. 7. Strain-induced bow for selected grinding parameters (vf : feed rate, ns : spindle rotation speed). The wheel used was a resinoid bonded D6 tool, with average diamond size of 6 m.
by different grinding wheels, but also the differences due to varying grinding parameters. The relaxation of the strain-induced bow is shown in Fig. 8, for 200 mm wafer ground with different grinding wheels. The etching was carried out using dilute KOH, the temperature of which was controlled to within ±1 ◦ C. The uniformity of the material removal from the front surface was improved using HF-strip to remove native oxides, and with careful pre-etch cleaning of the wafers. Nevertheless, there was some visible non-uniformity in the etched surface. Due to the dependence of the bow on the whole-wafer average of the stress, this influence on the results was limited. In order to measure the thickness of the removed layer, small parts of the ground wafer surface were impregnated, and thus made resistant to the etchants used. The height of the step-like structures created after etching such a surface, was used as the thickness of the removed layer. These heights were measured using white-light interferometry. The difference in the relaxation between the two wafers shown in Fig. 8 is significant. The strain-inducing damage
Fig. 8. The relaxation of strain-induced bow after successive etching steps. The triangles denote wafers with relatively heavy grinding-induced damage, and the boxes denote wafers with very small damage-induced strain, ground with optimum parameters.
The traditional method for investigating the integrity of the lattice structure in single crystal samples is to utilise Bragg diffraction of monoenergetic X-rays. The diffraction angles for the crystal planes in silicon are determined by the interatomic distances in the lattice, known as lattice constants. Using detection systems with high angular resolution and well monochromatic probe beams even small variations in the diffraction angle can be resolved, as for example in [2]. The typically Gaussian-shaped distribution of the diffraction angle around the theoretical value is called the rocking curve. The width of the rocking curve is defined by the bandwidth of the probe beam, the angular resolution of the detection system, the displacement of small pieces of crystal on the surface, and the variations of the lattice constant due to stresses in the damaged lattice. If the broadening of the rocking curve due to instrument parameters can be kept small enough, the width of the curve can be used to estimate the average strain in the lattice, and the extent to which the surface has been broken into physically displaced crystal pieces. The X-ray analysis was carried out by Fraunhofer Institute for Mechanics of Materials IWM, Freiburg, Germany, using the CrKα1 line radiation of the X-ray tube (5414 eV). The parameter studied was the full half-maximum (FWHM) width of the rocking curve. The crystal plane studied was the 3 1 1, and the penetration depth, above which some 63% of the information was gathered, was 7.3 m. The repeatability of the measurements was studied and the standard deviations for all of the measured rocking-curve widths were below 1%. In Figs. 9 and 10 the measured rocking-curve widths are compared against the surface roughness values measured for the same set of wafers. For the average roughness (roughness Ra ), shown in Fig. 9, a clear correlation with the rocking-curve width is found. This correlation can be approximated with an exponential function. The three different groups into which the datapoints fall into are due to the three tool types used. The tools used caused the material removal process to fall in following categories, in descending order of grinding induced lattice damage: pure brittle mode (D28 tool), mix of brittle and ductile (D15 tool) and pure ductile mode (mesh 3000 tool). For the peak-to-peak heights (roughness Rt ), shown in Fig. 10, the set of wafers is divided into two part, those wafers
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Fig. 9. Comparison between surface roughness Ra , measured with white-light interferometry, and the X-ray rocking-curve widths, for a set of wafers ground with various tools and various process parameters. The data ranges from ductile ground (diamonds) via partially brittle (triangles) to purely brittle wafers (open squares).
which have been ground in the ductile mode and those that include brittle fractures, and therefore also brittle break-outs from the surface. Wafers which have been ground in partially brittle mode, even those with relatively limited lattice damage, show clear break-outs from the surface, measured as peak-to-peak heights (roughness Rt ). These break-outs are several orders of magnitude higher than those for wafers ground in the purely ductile mode and the difference in the height of these break-outs is small when comparing wafers ground partially and purely in the brittle mode. Nevertheless, the positive correlation of peak-to-peak heights to rocking curves is still evident. 4.3. Roughness of the ground surface We have investigated the geometry of the wafer surface primarily by white-light interferometry. The instrument used
Fig. 10. Comparison between surface roughness Rt , measured with white-light interferometry, and the X-ray rocking-curve widths, for a set of wafers ground with various tools and various process parameters. The data ranges from ductile ground (diamonds) via partially brittle (triangles) to purely brittle wafers (open squares).
for interferometry is of the type Wyko RST and it is based around a CCD camera and a Mirau interferometer, using piezoelectric scanning. The PC-driven system allows measurements to be carried out both using phase-shifting interferometry (PSI) and vertical shifting interferometry (VSI), with PSI yielding higher precision and VSI complementing this on rough surfaces which have features outside the measurement range (160 nm) of the PSI mode. As the data acquisition procedures are completely different, these methods do not correlate very well with each other. For brittle mode grinding the VSI mode must be used, and the repeatability of the measurements slightly deteriorates. A coarse correlation can be found between the peak-to peak height Rt measured with high magnification on the one hand and with the strain-induced bow on the other hand. For brittle ground wafers the corresponding correlation for average roughness Ra is very weak. For brittle ground silicon the peak-to peak amplitude is mainly caused by fractured silicon sticking out from the surface. The reason for the existing correlation between bow and Rt is the fact that the roughness Rt increases with increasing chip thickness, which also causes the load on the single grain of the tool to increase, which is responsible for the increase in the bow-inducing strain. This is depicted in Fig. 11, for brittle, intermediate and mostly ductile ground wafers. For comparisons between wafers ground in purely ductile mode the VSI method no longer offers adequate resolution. For ductile ground wafers the PSI mode can, however, be used, and again a weak correlation can be found. Also for the ductile ground wafers the peak-to-peak roughness value Rt gives the best correlation to the strain-induced bow, but these wafers demonstrate a correlation also for the average roughness Ra . The relationship between the extent of the lattice damage and the surface roughness is obviously very complicated, but the existence of clear, even if not very strong correlation does support the
Fig. 11. Correlation of compressive strain-induced shape deformation of the wafer (bow) and the peak-to-peak roughness of the surface in silicon wafers ground under widely separated grinding conditions. The data ranges from ductile ground (open triangles) via partially ductile (black diamonds) to very rough ground wafers (open squares). R2 -value for the linear fit is 0.99.
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relation is not very strong, and it is interesting to note that the best correlation was reached with the roughness Ra , as opposed to the comparisons with the strain-induced bow. 4.4. Spectral diffuse reflectance
Fig. 12. The correlation between strain-induced bow values and peak-to peak surface roughness, calculated from surface profilometer images. The symbols denote average values for different subsets of wafers. In the processing of the wafers the tools (grinding wheels) and machine parameters were identical within the subsets, but varied between the subsets. The material removal mode for all the wafers included in this set was purely, or almost purely, ductile. R2 -value for the linear fit is 0.82.
assumption that in ductile mode grinding the extent of damage is heavily influenced by the amplitude of the vibrations. In addition to causing high peak forces applied to the material these vibrations also create a deeply corrugated surface, as depicted in Fig. 3. The roughness values of a surface image of the type used in this study are largely determined by the amplitude of such, relative to the image dimensions, low frequency roughness. This conclusion is supported by the fact that the frequencies calculated using the known machine parameters and the dimensions observed in images such as Fig. 3 are in the range which coincides with the separately analysed vibration modes of the grinding machine used in the study. The correlation depicted in Fig. 12 is thus due to the connection between the extent of the damage to the amplitude of the vibrations experienced by the grinding tool while in contact with the silicon material. Compared against surface acoustic wave dispersion measurements, the best correlation is reached for roughness parameter Ra . This correlation is presented in Fig. 13. The cor-
Fig. 13. Surface roughness average Ra calculated from white-light interferometry measurements plotted against Surface acoustic wave dispersion. R2 -value for the linear fit is 0.69.
The reference spectrometer of the Helsinki University of Technology (HUT) has been fitted with an accessory for measuring diffuse reflectance [9]. The automated measurement set-up consists of a thermal light source, a grating monochromator with reflective optics and a sample holding unit. The sample holding unit includes an integrating sphere and the actual sample and reference holding mechanics. This accessory was used to study the spectral behaviour of sample wafers. The measurement geometries were 0/d and 8/d, in which the sample was illuminated either at normal incidence or at the angle of incidence of 8◦ , and for which the specular component is excluded from the measurement by allowing it to exit the integrating sphere. The measurements were carried out using an opal glass reference sample, the reflectance factor of which has been determined separately. The wavelength range used was from 355 nm up to 565 or 790 nm. The complex refractive index [10] of silicon was used to calculate the corresponding penetration depths, which were from 13 nm to 2.5 or 12 m, respectively. The penetration depths above refer to the depth at which the intensity entering the wafer has been attenuated by one half. The measured diffuse reflectance shows scatter intensities rapidly decreasing with increasing wavelength. The measured diffusely reflected intensity can be expressed with the following formula Iscatter = I0 (Ssurface scatter (λ) +T 2 (λ)Ssubsurface scatter (λ))M(λ),
(1)
where I0 is the initial intensity striking the surface. Ssurface scatter (λ) is the coefficient for spectral scattering caused by the geometrical surface roughness, also known as haze. T(λ) is the spectral transmittance of the surface for a thickness corresponding to the penetration depth. Ssubsurface scatter (λ) is the coefficient for spectral scattering caused by the interaction between the light wave propagating inside the (top) layer of the wafer, and the damaged silicon lattice on top of the wafer. M(λ) is the relative spectral responsivity of the measurement system, which for the purposes of this discussion can be equated to unity. The scatter theory [11] can be used to calculate the spectral scatter H(λ) = Ssurface scatter (λ) from the surface with a known surface roughness Rq , using the equation H(λ) λ Rq = (2) 4π cos θ R(λ) where R(λ) denotes the spectral reflectance and θ is the angle of incidence. Solving Eq. (2) for spectral scatter H(λ) yields the simplified equation H(λ) = C0 R(λ)/λ2 , in which
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all factors not depending on wavelength have been combined into C0 . By normalising both the theoretical and measured data at one wavelength, the deviation of the spectral behaviour of the sample from the ideal can be studied. This deviation is caused partly by the scatter caused by sub-surface damage, the interacting proportion of which varies with the penetration depth. At the shortest wavelengths the measured scatter intensity is due to surface scatter only, as the penetration depth of light into silicon at this wavelength is negligible. Thus the normalisation is carried out at the shortest wavelength (355 nm) studied. Due to the penetration of the longer wavelengths and the resulting scattering from the sub-surface damage the scatter values measured are higher than those predicted by scatter theory and the short wavelength normalisation. Another spectral effect which must be taken into account before the spectral scatter data can be used to evaluate damage depth in the sample is the interaction between the probe beam and the studied damage. We propose a model, in which the spectral scattering coefficient of the lattice damage depends on the wavelength as 1/λ2 . The assumption is based on the following facts: The damaged layer depth for fine ground surfaces is known to be less than a few microns. This information is based on independent methods, such as iterative etching. It is definitely true if the damaged layer depth is defined as the depth in which the lattice damage is still substantial enough to influence such macroscopic phenomenon as propagation of light. Thus, for wavelengths that have penetration depth significantly higher than a few microns, the spectral behaviour cannot be due to different exposure to scattering damage. Spectral behaviour, at these longer wavelengths, not explained by the spectral surface scatter, is likely to be caused by the wavelength dependence of the probe beam–lattice damage interaction. The proposed dependence gives a good fit to long wavelength spectral behaviour of the scatter. The spectral behaviour of the interaction between surface roughness and the probe beam is of similar nature, scatter by inhomogenities much smaller than wavelength in dimension. Accordingly, it is reasonable to assume similar wavelength dependencies. One effect which could not be quantified in the experiments is the change in surface roughness Rq as the relevant spatial wavelengths differ for different wavelengths, as the power spectral density (PSD) of the surfaces measured is not uniform over the spatial wavelength range in question. Fig. 14 presents the results of a comparison measurement for two fine ground wafers, measured both at the edge and next to the centre. The measured intensity saturates at longer wavelengths when corrected for surface scatter and the wavelength dependence of the interaction between lattice damage and the probe beam. This indicates that the probe beam does not scatter below a layer, which is some 1 and 2.5–3 m thick for centre and edge measurements, respectively. This difference in damage depth correlates with the damage distributions measured over wafer area with scanning acoustic
Fig. 14. The spectral behaviour of measured scatter intensity, after corrections for surface scatter and spectral interaction coefficient of the type 1/2 . The dotted line, and the continuous black line, denote measurements carried out with samples taken from the edge of two fine ground sample wafers (a and b), over wavelength range of 355–790 nm. The grey continuous line, and the line marked with vertical bars, denote measurements carried out for samples taken from the same two wafers (a and b), right next to the centre of the wafers, over the wavelength range of 355–565 nm. The x-axis denotes the penetration depth calculated for the wavelengths used in the probe beams.
wave and scanning infrared depolarisation techniques, and the observed distribution of defects after iterative layer removal. The spectral diffuse spectral analysis indicates that the principle of spectral study does hold promise of an analysis, which would result in true depth distribution of the damage. 4.5. Surface photo voltage and microwave photo conductive decay The lifetime and diffusion length of minority carriers in semiconductors depends on the density of recombination centres. Such centres are, among others, transition metals and surface states, but in high-quality silicon the recombination due to the lattice defects contributes to the measured lifetimes and diffusion lengths. In [12] the photo conductive amplitude (PCA) was successfully used to analyse damaged layers in the immediate vicinity of the final polished wafer surface. The PCA is limited by the same physical processes as the signal strength of the microwave photo conductive decay and that of the surface photo voltage. A map of the signal strength of the SPV measurement carried out for a ground wafer is presented in Fig. 5, in which the distribution of the lattice damage is seen. The recombination of minority carriers in ground silicon wafers was studied using PCD and SPV scanners by Semilab Ltd., Budapest, Hungary. While the extent and depth of damage after grinding is several orders of magnitude more extensive than after CMP polishing, the same basic phenomenon of faster recombination in material with more recombination centres still holds. For the PCD measurements the upper surface was passivated chemically, and thus the signal amplitude (PCA) and PCD lifetimes were related to
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Fig. 15. The relationship between measured minority carrier lifetimes and strain-induced bow. The measurements inside the dotted circle were ground in the ductile mode, whereas those within the continuous circle have brittle ground surfaces.
the extent and nature of the sub-surface damage in the sample wafers. The correlation between strain and whole-wafer average of the carrier lifetime is presented in Fig. 15. It is notable that while the lifetimes recorded for various ductile ground wafers correlated with the compressive strain measurements (bow), the lifetimes of the rough ground wafers were fairly high, indicating a relative lack of recombination centres below the surface. The different form and distribution in-depth of the lattice damage for the two grinding modes are thus as important as the total amount of introduced strain in influencing the lifetime of the silicon material. For the SPV scanner the passivation was not necessary, as the measurement is not very much affected by surface recombination. A similar relationship as for PCD lifetimes was observed for SPV diffusion lengths for rough ground surfaces. As the measured lifetimes and diffusion lengths were very short in comparison to those observed for final polished wafers made from the same or from similar ingots the effect of metals can be assumed to be small. As a further verification to this assumption the Fe–B pair disassociation was verified not to be a significant factor in the PCD-lifetime of the ground wafers.
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damaged silicon in the depth of the sample. Nevertheless, useful information can be gained from the distribution of the sub-surface damage by studying the dispersion of ultrasonic surface acoustic waves, generated by ultra-short laser pulses [13]. The dispersion of the surface acoustic waves is caused by the different intensity distributions in depth of various frequencies included in the laser-generated acoustic wave packet. Thus different effective elastic modules are experienced by different frequencies in the wave. A more through investigation of the physical principles is presented in [13]. A laser-acoustic measurement device LA-Wave by Fraunhofer Institute IWS, Dresden, Germany, was used to quantify to what extent the elastic modules of ground wafers are lowered during machining operation. As the measurement yields information on one propagation track from the laser impact point to the piezo-electric detector the method can also be used to study the spatial distribution of the damage on the wafer surface. Three locations were chosen on the 1 0 0-oriented wafers, one on the axis from the notch to the centre, one at 45◦ angle to the said axis, and one close to the edge. Fig. 16 reveals the relationship between the measured slope of the dispersion curve on the three measurement locations and the measured geometrical deformation (bow) on the same wafers. As the dispersion is a measure of the local amount of microcracks in the lattice, whereas the bow is caused by global stress, the correlation is not straightforward, and the measurement points follow the linear fit only approximately. One interesting result was the zero dispersion measured for a type of very fine ground wafer, for all three measurement points. The wafer was strained by the grinding-induced damage, as can be seen from the measured bow. There are two possible explanations to the observed result. 1. The surface acoustic wave-method, in the present form, is not sensitive enough to detect the amount of damage,
4.6. Surface acoustic waves The propagation of surface acoustic waves in a surface layer is determined by the elastic constant of the layer material, thickness of the layer and the density of the layer. For damaged surface layer of a single crystal sample, such as silicon wafer, the elastic module in the surface region is lowered by the microcracks which have been caused by the mechanical machining of the brittle material. Naturally, the damaged layer is not a layer with well-defined thickness and elastic module, but a region in which the elastic module gradually approaches that of un-
Fig. 16. The relationship between strain-induced bow and the dispersion of surface acoustic wave, for three acoustic wave measurement locations on each wafer. The locations are indicated on the insert in the upper left-hand corner. The general trend for the three separate measurement locations is denoted with the least-square fitted lines. Zero dispersion result is highlighted with a black bounding box.
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even though it was independently observed to be significant. 2. The surface acoustic wave is insensitive to damage concentrated to the very top layer, and the very fine ground wafer has the all the lattice damage concentrated in a very thin top layer of the wafer. In this case the signal from the surface acoustic waves would not be dominated by the inherently very heavily damaged thin top layer. The depth of damage, which is the most important parameter of the damage in a manufacturing process, could then be deduced by comparing surface acoustic wave results with some readily available quantity such as bow, X-ray diffraction or roughness. 4.7. Scanning infrared depolarisation The stresses induced in silicon material during processing gives rise to photoelastic effect, birefringence, in the otherwise optically isotropic media. This phenomenon is utilised in the scanning infrared depolarisation measurement [14]. The measurement principle is based on a linearly polarised laser beam, which is transmitted through the wafer. The local shear stress field-induced birefringence causes the polarisation plane of the laser beam to be rotated. A more detailed discussion of the measurement principle is presented in [14] and [15]. The damage introduced to the crystal lattice in mechanical machining of silicon wafers, such as grinding, causes such high stresses that the depolarisation effect is very strong and easily observed with the SIRD technique. A set of ground wafers was studied using the SIRD stress imager by TePla AG, Jena, Germany. The parameters chosen for a more thorough investigation were the average depolarisation D and the differential contrast, or differential of the depolarisation D. These quantities can be used to estimate the differential of the radial shear component σrϕ , defined in [15] as
Fig. 17. The depolarisation image of a 200 mm wafer after grinding with a D6 wheel. The depolarisation scale goes from 1100 units (1.100 kDU, dark centre area) to 6500 units (6.5 kDU, darkest lines on the edges), with average of 3870 units. The corresponding shear stresses range from 0.9 to 3.2 MPa.
(3)
Uniform stress in a non-uniform material gives rise to non-uniform straining. This is observed in 1 0 0-oriented wafer as isotropic straining of the lattice, for which the depolarisation signal varies as cos 4ω, where ω is the angle between the principal axis of the wafer (1 1 0 plane intersecting the centerpoint), and the vector drawn from the centre to the measured point. The magnitude of this signal corresponds to the differential in the elastic deformation of the wafer, along different crystal planes. This deformation differential is exactly proportional to the magnitude of the deformation, and thus to the strain. The correlation between the global deformation (Bow) and the angle-dependent stress differential (cos 4 fitted for differential contrast at 50 mm from centre) is presented in Fig. 18. The reason that the SIRD-analysis is sensitive to wafer straining, even as the analysis is aimed at resolving stress distributions, lies in the use of an optical stress constant Cσ averaged over crystal orientations. Thus different strain along different crystal planes yields different stresses, even if the original stress is, as it most probably is, uniforms.
in which Cσ is the mean optical stress constant of silicon for the 1.3 m wavelength used in the measurement. In Fig. 17 is depicted one SIRD measurement of a ground wafer. The average depolarisation measured was 3.87 units, and from the image it can be clearly seen that the radial shear stresses are the lowest at the middle and highest at the edges. This is caused by the radius dependent material removal rate, inherent to rotational grinding. The corresponding shear stress magnitudes calculated using the depolarisation values range from 0.9 to 3.2 MPa. The inverse number 700 seen opposite to the notch is caused by writing on the wafer, and the radial line pattern is the same as that seen visually on the surface. The figure also demonstrates the strong point of SIRD measurement as a true mapping analysis. These images can be used to locate and quantify localised problems, caused for example by misalignment of the grinding tools.
Fig. 18. The depolarisation contrast at half-radius, fitted for cos (4ω), compared against the global strain-induced bow measured for the same sample wafers. The continuous line denotes a sigmoidal fit to the data.
σrϕ =
D √ Cσ Dmean
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5. Discussion Several measurement methods based on a number of physical principles were used to evaluate the sub-surface damage in a controlled set of silicon wafers. Each method was evaluated against one or more other methods, and from the resulting correlations the following conclusions can be drawn. The type, extent and distribution of the sub-surface damage vary with different grinding conditions. Wafers ground in ductile mode are bound to have a different kind of damage distribution in depth than those ground partially or completely in brittle fracture mode. The existence of two types of sub-surface damage was demonstrated. This arises from the two modes, ductile and brittle, through which the material is removed and the lattice disturbed. For example, comparing surface roughness to X-ray measurements, or comparing strain-induced bow measurements to recombination lifetimes measured for the same wafers, the two types of damage give rise to different correlations. Most of the wafers used in this study were ground in the ductile mode. This is typically the type of surface found on a wafer after completing the grinding process, and thus the extent, and in particular the depth of damage on these wafers has direct influence in the subsequent processing of the wafer. The methods studied correlated with each other to an extent which suggests that when limiting the study to ductile ground surfaces the various aspects of the damage, such as the influence on Young’s modulus, induced shear stresses, global stressing, scattering of optical radiation and the geometrical roughness are linked to each other. These links most probably arise from the fact that forces required by the separation mechanism, dominant chip sizes and heat generation are closely interrelated. Thus surfaces for which these parameters of the grinding process have been successfully optimised are bound to exhibit low levels of lattice damage regardless of probing technique. Interesting possibilities are offered by the surface acoustic wave-method. In samples for which the assumption of insensitivity to the uppermost layer holds the measurable signal is closely linked to the commercially interesting depth of the damage. For process control and development the most important parameter undoubtedly is the maximum depth of damage, and the variation thereof. This depth is also currently impossible to measure directly using non-destructive methods. The indirect methods described in this paper can be used to gain insight into the relationship between machining parameters, total damage introduced to the lattice, and the
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distribution in depth. Iterative layer removal methods can be applied to most methods in order to more accurately correlate the damage distribution in depth with the results available with non-destructive methods. This study indicates that the results extracted using fast methods, typically already available for chip and wafer manufacturers, can be linked with the more thorough point evaluations, such as X-ray diffraction. The widely differing physical principles, on which the various methods described in this paper are based on, provide several independent methods for probing the sub-surface damage. A combination of methods can be used to gain more thorough understanding of the damage type and distribution in specific processes. The results, which link the physical aspects of the damage to each other, can be used to verify established grinding models. The refined models allow better understanding of the ductile mode cutting in brittle materials such as silicon. Understanding the creation and distribution of the damage allows the method best suited for practical measurement needs to be chosen.
References [1] H. Tönshof, W. Schmieden, I. Inasaki, W. König, G. Spur, Ann. CIRP 39/2 (1990) 621. [2] C. Menz, Randzonenanalyse bearbeiteter Silizium-Oberflächen. VDI Verlag, Düsseldorf, 1997 (in German). [3] L.-Q. Chen, X. Zhang, T-Y. Zhang, H.Y. Lin, S. Lee, J. Mater. Res. 15 (2000) 1441. [4] Y. Li, S. Danyluk, Wear 200 (1996) 238. [5] H. Xu, S. Jahanmir, L. Ives, J. Mater. Res. 11 (1997) 1717. [6] T. Myers, B. VanMil, L. Holbert, C. Peng, C. Stinespring, J. Alam, J. Freitas, V. Dmitriev, A. Pechnikov, Y. Shapovalova, V. Ivantsov, J. Cryst. Growth 246 (2002) 244. [7] H.-F. Hadamovsky (Ed.), Werkstoffe der Halbleitertechnik. Leipzig: Deutscher Verlag für Grundstofftechnik, 1990 (in German). [8] P. Fisher, R.E.M. Vickers, Appl. Phys. Lett. 79 (2001) 3458. [9] S. Nevas, Facility for measurements of spectral diffuse reflectance. Master Thesis (M.Sc.), HUT, 2000. [10] G.E. Jellison Jr, Opt. Mater. 1 (1992) 41. [11] J.C. Stover, Optical Scattering: Measurement and Analysis, second ed., SPIE Press, 1995. [12] Y. Ogata, K. Kobayashi, H. Daio, J. Cryst. Growth 210 (2000) 36. [13] D. Schneider, B. Schultrich, P. Siemroth, M. Leonhardt, A. Franke, in: Proceedings of The Coatings 2001, 9–10 May 2001, Hannover, Germany. [14] H. Geiler, W. Kürner, O. Storbeck, MRS Proc. 591 (2000) 249–254. [15] H. Geiler, H. Karge, B. Krimbacher, in: Proceedings of the Electrochemical Society PV 2000-9, Toronto, Canada, Spring 2000, p. 347.
Rotational grinding of silicon wafers—sub-surface damage inspection Atte Haapalinna a,∗ , Saulius Nevas b , Dietmar Pähler c b
a Okmetic Oyj, P.O. Box 44, FIN-01301 Vantaa, Finland Metrology Research Institute, Helsinki University of Technology, FIN-02105 HUT Espoo, Finland c Fraunhofer Institut für Produktionstechnolgie IPT D-52074, Aachen, Germany
Received 1 October 2003; accepted 17 December 2003
Abstract Industrial practise in wafer manufacturing indicates that there is not one agreed method available to acquire a conclusive picture of the sub-surface damage, defined as structural inhomogeneities of the crystal lattice. Therefore, various methods have been studied and compared for measurement of the sub-surface damage introduced to single crystal silicon wafers during rotational grinding process. Several probing techniques were used to analyse a controlled set of ground silicon wafers. Optical methods were used to study the strain distribution, scattering-in depth and surface topography of the sample set. Acoustic and X-ray diffraction were used to directly observe variations in the Young’s modulus and the lattice constant, respectively. The techniques used ranged from point analysis to whole-wafer mapping and averaging. The study indicates that the various physical properties of the lattice damage arise from closely linked processes taking place during the grinding process. The correlations between the methods included in this study have been identified and quantified, and the relationships between the various observable quantities of sub-surface damage are discussed. © 2003 Elsevier B.V. All rights reserved. Keywords: Silicon wafer; metrology; sub-surface damage
1. Introduction Silicon wafers are the building blocks of the digital world. The search for higher performance and lower cost for integrated circuits requires an increasing level of sophistication from the whole silicon manufacturing chain. There is a constant need to improve both the processes used in the manufacturing of silicon wafers, and the properties of finished silicon wafers. Instead of improving the individual process steps, improvements can also be realised by introducing new, advanced manufacturing techniques, replacing some of the traditional parts of the process chain. The replacement of lapping by rotational grinding is one such proposed change. Grinding utilises the increasing wafer size and more stringent quality requirements in becoming an increasingly attractive solution versus lapping, both cost- and quality-wise. Various inspection methods have been used to characterise the surface condition and sub-surface damage in machined ∗ Corresponding author. Tel.: +358-40-528-5118; fax: +358-950-280300. E-mail address: [email protected] (A. Haapalinna).
0921-5107/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2003.12.008
silicon [1–4]. Other techniques, such as those reported for sub-surface analysis of materials such as Si3 N4 [5] and GaN [6] can also be applied to machined silicon. Process utilisation for most of the methods used is limited by the destructive nature and small sampling areas inherent to most of the techniques used. Novel inspection methods are required for successful optimisation of such advanced processes. In this paper, we discuss several methods which can be used to analyse the damage caused by rotational diamond-wheel grinding, aiming to link fast, whole-wafer mapping methods with the established point analysis. Most of the presented techniques can also be applied to lapped, sliced and sometimes even rough polished surfaces.
2. Sub-surface damage caused by mechanical manipulation of silicon For the purposes of this discussion, as-grown Czochralski silicon ingot is virtually defect-free. The slicing of wafers creates heavy mechanical damage on both sides of the wafer. In the traditional process the wafer is subsequently abrasively lapped, removing the slicing-induced damage, and
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problematic tool wear. The throughput issue can be improved by two-step grinding, and the tool wear can be solved with suitable materials and operating parameters.
3. Nature of the ground surface
Fig. 1. Sub-surface damage model by Hadamovsky [7].
at the same time, introducing a new, more uniform damage to the surfaces of the wafer. This is then removed in etching, which results in rough, but damage-free surfaces. Chemical–mechanical polishing (CMP) on one side results in the single-side polished (SSP) wafer, on which the electronic circuits are then integrated. The alternative process would replace lapping by grinding. By two-step grinding, in which the last step is carried out in the ductile mode, the damaged layer on the front surface will be very shallow. If it can be guaranteed that the damaged layer depth does not exceed a few microns, significant cost savings and performance improvements can be reached in the final CMP. The relative merits of all above mentioned techniques, and optimisation of the relevant process parameters requires accurate analysis of the sub-surface damage on the silicon surface. This requirement can only be met if both the severity and the distribution in depth, of the grinding-induced crystal damage, can be characterised. Several models have been presented for the damage distribution due in abraded crystalline silicon [7,8], such as the one depicted in Fig. 1. The damage-creation processes in slicing, lapping and grinding operations have obvious similarities. For example, multi-wire slicing can accurately be described as a variant of the abrasive lapping process. While the extent of the induced damage varies from process to process, the nature of the mechanically induced crystal damage is always quite similar. For the purposes of this discussion, grinding processes can be divided into two categories: ductile and non-ductile. As the name implies, ductile mode grinding removes material within plastic limits of the workpiece material. For brittle materials, such as monocrystalline silicon, this requires that several conditions are met. The primary requirement is that the applied cutting force must be low enough not to cause fractures in the material. This requires that the force must be applied to a very small volume, in order to separate this volume using low forces. Small removal volumes indicate low feed rates and small cutting elements, that is, small diamond sizes. These conditions imply low throughputs and
The surface structure of a rotation-ground wafer includes peaks and depressions, while depending on the process parameters; they still are in the same order of magnitude as the diamond size used in the grinding wheel. The damaged silicon layer can be described as polycrystalline, consisting of several, smaller, monocrystalline pieces packed very tightly. The packing density is, however, lower than that of the undamaged monocrystalline lattice. This causes compressive strain on the upper, ground, surface of the silicon wafer. If the lower surface is damage-free, the geometrical deformation of the wafer can be used to estimate the aggregate damage-induced on the upper surface of the wafer. The grooved texture is a property of rotation-ground wafers over a wide range of spatial frequencies, observed using various imaging techniques. Due to the nature of the rotational grinding process the direction of the cutting diamond is radial, and thus the wafer surface consists of scratches on top of other, longer wavelength grooves (Fig. 2). The periodical nature of the surface can be seen both in low-magnification interferometric images (Fig. 3) as well as in high-magnification SEM images (Fig. 4). The measured surface has been ground with a D6 wheel resulting in a smooth, fine ground surface. The tool index D6 indicates the average diamond size, in m, used in the tool as the fixed abrasive responsible for the material cutting. These grooved surfaces are caused by the directional nature of the processing. The fact that the forces induced to the material in rotational grinding are very directional is due to the geometry of the process. This combined with the anisotropic lattice of the silicon leads to a non-uniform
Fig. 2. The dynamics of rotational grinding. The grooves depicted on the wafer surface are due to the high rotational speeds used for the grinding wheel, which is an order of magnitude higher than the rotation speeds of the wafer.
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Fig. 5. Surface photovoltage signal, recorded for a fine ground 1 0 0-oriented wafer. The location of the notch is marked with a triangle, and the 1 1 0 glide plane directions are indicated with dotted lines.
measured with surface photo voltage (SPV) probe, as seen in Fig. 5. Fig. 3. White-light interferometer image of a ground wafer, ground with the D6 wheel (upper image) and a line scan extracted from the same image (lower image).
damage distribution in the wafer. Specifically, on a standard 1 0 0-oriented wafer the lattice is most prone for fractures and dislocations along the 1 1 0 glide planes. In rotational grinding the processing is aligned with these planes only for the 1 1 0 glide planes, which cross at the centre point. The damage distribution is not exactly aligned to these glide planes, because the wafer is rotated on the chuck. This phenomenon can be seen for example in etching of ground wafers in KOH, as these lines are the ones, which generate most hydrogen—indicating that the lattice is more strained along these axes. The same phenomenon is causing the patterns seen on surface recombination maps,
Fig. 4. Scanning electron microscope images of the same wafer, ground with the D6 wheel. The magnifications are 10,000× (left image) and 500× (right image). The most densely packed grooves found on the higher magnification image are some 150–200 nm apart, on the low magnification image the lines are around 1 m apart.
4. Measurement techniques employed in the study A total of seven different methods were included in our study. The specimens were prepared by grinding a controlled set of 200 mm silicon wafers. The grinding conditions were chosen in order to create a controlled variation in the damage introduced to the wafer set. The methods discussed in this chapter are briefly introduced and characterised in the following overview and discussed in detail thereafter. 1. Strain-induced deformation (bow), depicted in Fig. 6a Suitable measurement tools are readily available in the semiconductor industry, offering potential for large numbers of wafers to be measured. Measures the wafer strain due to the polycrystalline, topmost layer, created by the machining of the wafer. A whole-wafer averaging technique. 2. X-ray diffraction, depicted in Fig. 6b Chosen because X-ray diffraction is a well-established method to investigate lattice non-uniformities. A point analysis technique. 3. Surface roughness Suitable tools are readily available in the Semiconductor industry. Not a direct measure of damage but closely linked both to the grinding operation and the damage-creation processes through the surface feature size/diamond grid size dependence. Fast point analysis technique. 4. Spectral diffuse reflectance, depicted in Fig. 6c
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Novel method based on optical anisotropy introduced to silicon by the damage-induced straining. The measurand is the rotation of a linearly polarised laser beam. The rotation is proportional to the local straining integrated through the whole wafer. A whole-wafer mapping technique. 4.1. Geometrical deformation of the wafer under compressive strain
Fig. 6. Different principles used for measuring the SSD. (a) Bow: strain on the top layer of the wafer causes the wafer to deform in a measurable way. (b) X-ray diffraction: scattering angle of monoenergetic X-rays is defined by the lattice constant a. Lattice constant changes with strain, a , and the diffraction angle changes accordingly. In addition, polycrystalline top layer includes displaced crystal planes. Both of these effects result in widening of the diffraction angle θ, as defined by Bragg’s law. (c) Diffuse reflectance: the wafer is illuminated, and the refracted beam is partly scattered by lattice imperfections. Some of the scattered light exits the wafer and can be measured. (d) Surface acoustic waves: penetration of surface acoustic waves into the bulk of material depends on the frequency of the wave. Thus, the extent of the interaction with the lattice damage, concentrated in the top-layer, depends on the frequency.
Experimental set-up, offering potential for depthresolving studies due to fact that penetration depth of light varies with wavelength. The method is based on scattering of light from lattice imperfections. A technique averaging over a small area (100 mm2 , potentially up to hundreds of mm2 ). 5. Surface photo voltage and microwave photo conductive decay (PCD) The relevant tools are readily available in semiconductor industry and they potentially allow links to be established between sub-surface damage SSD and the electrical behaviour of the silicon material. The basis for measuring SSD with these methods lies in the dependence of the lifetime on the density of recombination centres, which created by non-homogenities in lattice, such as mechanical damage. A whole-wafer mapping technique. 6. Laser acoustic wave (LA-Wave), depicted in Fig. 6d Novel method based on dispersion of surface acoustic waves. Wavepackets are subjected to dispersion due to the frequency-dependent penetration depth of a surface acoustic wave and the location of the damage at the uppermost layer. A technique averaging over a small area (200–400 mm2 ). 7. Scanning infrared depolarization (SIRD)
The basic shape of a silicon wafer is defined by a parameter called bow. This is the deviation of the median surface of the wafer relative to the least-squares fitted plane, with the deviation measured at the centre, and the fitting done to the above mentioned median surface. We have measured this parameter using a commercial semiconductor tool, contactless capacitive gauge of the type Eichhorn + Hausmann MX203-8-49-B. The gage utilises 49 pairs of capacitive sensors to determine the local distance of the wafer surface from the sensor heads. These results are used in combination with calibration values, which include corrections to individual sensor heights. PC-software is used to calculate the local wafer thickness and local warpage of the wafer. These local values are then used to calculate global parameters, which describe the whole wafer, such as bow. The measured values of bow are influenced by the gravitation, which for compressively strained samples, such as ground wafers, pulls the centre of the wafer down, reducing the measured bow. In the gage used, however, the centre is supported, and thus the gravitational effect is not seen for wafers, which are only slightly curved. An example of such wafers would be the multi-wire sliced (MWS) sample wafers used in this study, which have very low natural, unstrained bow. For these wafers the unstrained bow values are essentially determined by the gage support pads. Therefore the change of bow due to machining in the grinding process is estimated assuming that the natural, unstrained bow is zero. This assumption is verified using another commercially used capacitive tool, ADE Ultrascan7200. The depth of the strain-inducing damage layer was investigated by successively etching very thin layers from differently ground wafers, and measuring the bow between each etching step. The measured bow results are affected by an offset in bow, mainly due to potentially uneven support pads and gravitation, and by a variation due to sensor deviations over time. This limitation prevents accurate bow measurements for the completely unstrained and very slightly strained wafers. The results of the bow-measurements are summarised in Figs. 7 and 8. Fig. 7 represents a result of a study, in which the various grinding machine parameters are evaluated based on the stress created on the processed surface of a 200 mm wafer with 1 0 0-orientation. The study indicates that measurement of strain-induced curvature in silicon wafers is a sufficiently sensitive method to distinguish not only between the differences in surface and sub-surface damage caused
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of the less damaged wafers, ground using optimum parameters, is clearly more concentrated on the thin upper layer than that of those with higher bow, and higher damage. Compared to staged etching experiments reported in [2], constant bow values, indicating total removal of the damage-induced strain, are reached after clearly smaller material removals. This can be caused by lower initial damage depths, differences in the sensitivity of the measurement methods used, or both. 4.2. X-ray diffraction
Fig. 7. Strain-induced bow for selected grinding parameters (vf : feed rate, ns : spindle rotation speed). The wheel used was a resinoid bonded D6 tool, with average diamond size of 6 m.
by different grinding wheels, but also the differences due to varying grinding parameters. The relaxation of the strain-induced bow is shown in Fig. 8, for 200 mm wafer ground with different grinding wheels. The etching was carried out using dilute KOH, the temperature of which was controlled to within ±1 ◦ C. The uniformity of the material removal from the front surface was improved using HF-strip to remove native oxides, and with careful pre-etch cleaning of the wafers. Nevertheless, there was some visible non-uniformity in the etched surface. Due to the dependence of the bow on the whole-wafer average of the stress, this influence on the results was limited. In order to measure the thickness of the removed layer, small parts of the ground wafer surface were impregnated, and thus made resistant to the etchants used. The height of the step-like structures created after etching such a surface, was used as the thickness of the removed layer. These heights were measured using white-light interferometry. The difference in the relaxation between the two wafers shown in Fig. 8 is significant. The strain-inducing damage
Fig. 8. The relaxation of strain-induced bow after successive etching steps. The triangles denote wafers with relatively heavy grinding-induced damage, and the boxes denote wafers with very small damage-induced strain, ground with optimum parameters.
The traditional method for investigating the integrity of the lattice structure in single crystal samples is to utilise Bragg diffraction of monoenergetic X-rays. The diffraction angles for the crystal planes in silicon are determined by the interatomic distances in the lattice, known as lattice constants. Using detection systems with high angular resolution and well monochromatic probe beams even small variations in the diffraction angle can be resolved, as for example in [2]. The typically Gaussian-shaped distribution of the diffraction angle around the theoretical value is called the rocking curve. The width of the rocking curve is defined by the bandwidth of the probe beam, the angular resolution of the detection system, the displacement of small pieces of crystal on the surface, and the variations of the lattice constant due to stresses in the damaged lattice. If the broadening of the rocking curve due to instrument parameters can be kept small enough, the width of the curve can be used to estimate the average strain in the lattice, and the extent to which the surface has been broken into physically displaced crystal pieces. The X-ray analysis was carried out by Fraunhofer Institute for Mechanics of Materials IWM, Freiburg, Germany, using the CrKα1 line radiation of the X-ray tube (5414 eV). The parameter studied was the full half-maximum (FWHM) width of the rocking curve. The crystal plane studied was the 3 1 1, and the penetration depth, above which some 63% of the information was gathered, was 7.3 m. The repeatability of the measurements was studied and the standard deviations for all of the measured rocking-curve widths were below 1%. In Figs. 9 and 10 the measured rocking-curve widths are compared against the surface roughness values measured for the same set of wafers. For the average roughness (roughness Ra ), shown in Fig. 9, a clear correlation with the rocking-curve width is found. This correlation can be approximated with an exponential function. The three different groups into which the datapoints fall into are due to the three tool types used. The tools used caused the material removal process to fall in following categories, in descending order of grinding induced lattice damage: pure brittle mode (D28 tool), mix of brittle and ductile (D15 tool) and pure ductile mode (mesh 3000 tool). For the peak-to-peak heights (roughness Rt ), shown in Fig. 10, the set of wafers is divided into two part, those wafers
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Fig. 9. Comparison between surface roughness Ra , measured with white-light interferometry, and the X-ray rocking-curve widths, for a set of wafers ground with various tools and various process parameters. The data ranges from ductile ground (diamonds) via partially brittle (triangles) to purely brittle wafers (open squares).
which have been ground in the ductile mode and those that include brittle fractures, and therefore also brittle break-outs from the surface. Wafers which have been ground in partially brittle mode, even those with relatively limited lattice damage, show clear break-outs from the surface, measured as peak-to-peak heights (roughness Rt ). These break-outs are several orders of magnitude higher than those for wafers ground in the purely ductile mode and the difference in the height of these break-outs is small when comparing wafers ground partially and purely in the brittle mode. Nevertheless, the positive correlation of peak-to-peak heights to rocking curves is still evident. 4.3. Roughness of the ground surface We have investigated the geometry of the wafer surface primarily by white-light interferometry. The instrument used
Fig. 10. Comparison between surface roughness Rt , measured with white-light interferometry, and the X-ray rocking-curve widths, for a set of wafers ground with various tools and various process parameters. The data ranges from ductile ground (diamonds) via partially brittle (triangles) to purely brittle wafers (open squares).
for interferometry is of the type Wyko RST and it is based around a CCD camera and a Mirau interferometer, using piezoelectric scanning. The PC-driven system allows measurements to be carried out both using phase-shifting interferometry (PSI) and vertical shifting interferometry (VSI), with PSI yielding higher precision and VSI complementing this on rough surfaces which have features outside the measurement range (160 nm) of the PSI mode. As the data acquisition procedures are completely different, these methods do not correlate very well with each other. For brittle mode grinding the VSI mode must be used, and the repeatability of the measurements slightly deteriorates. A coarse correlation can be found between the peak-to peak height Rt measured with high magnification on the one hand and with the strain-induced bow on the other hand. For brittle ground wafers the corresponding correlation for average roughness Ra is very weak. For brittle ground silicon the peak-to peak amplitude is mainly caused by fractured silicon sticking out from the surface. The reason for the existing correlation between bow and Rt is the fact that the roughness Rt increases with increasing chip thickness, which also causes the load on the single grain of the tool to increase, which is responsible for the increase in the bow-inducing strain. This is depicted in Fig. 11, for brittle, intermediate and mostly ductile ground wafers. For comparisons between wafers ground in purely ductile mode the VSI method no longer offers adequate resolution. For ductile ground wafers the PSI mode can, however, be used, and again a weak correlation can be found. Also for the ductile ground wafers the peak-to-peak roughness value Rt gives the best correlation to the strain-induced bow, but these wafers demonstrate a correlation also for the average roughness Ra . The relationship between the extent of the lattice damage and the surface roughness is obviously very complicated, but the existence of clear, even if not very strong correlation does support the
Fig. 11. Correlation of compressive strain-induced shape deformation of the wafer (bow) and the peak-to-peak roughness of the surface in silicon wafers ground under widely separated grinding conditions. The data ranges from ductile ground (open triangles) via partially ductile (black diamonds) to very rough ground wafers (open squares). R2 -value for the linear fit is 0.99.
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relation is not very strong, and it is interesting to note that the best correlation was reached with the roughness Ra , as opposed to the comparisons with the strain-induced bow. 4.4. Spectral diffuse reflectance
Fig. 12. The correlation between strain-induced bow values and peak-to peak surface roughness, calculated from surface profilometer images. The symbols denote average values for different subsets of wafers. In the processing of the wafers the tools (grinding wheels) and machine parameters were identical within the subsets, but varied between the subsets. The material removal mode for all the wafers included in this set was purely, or almost purely, ductile. R2 -value for the linear fit is 0.82.
assumption that in ductile mode grinding the extent of damage is heavily influenced by the amplitude of the vibrations. In addition to causing high peak forces applied to the material these vibrations also create a deeply corrugated surface, as depicted in Fig. 3. The roughness values of a surface image of the type used in this study are largely determined by the amplitude of such, relative to the image dimensions, low frequency roughness. This conclusion is supported by the fact that the frequencies calculated using the known machine parameters and the dimensions observed in images such as Fig. 3 are in the range which coincides with the separately analysed vibration modes of the grinding machine used in the study. The correlation depicted in Fig. 12 is thus due to the connection between the extent of the damage to the amplitude of the vibrations experienced by the grinding tool while in contact with the silicon material. Compared against surface acoustic wave dispersion measurements, the best correlation is reached for roughness parameter Ra . This correlation is presented in Fig. 13. The cor-
Fig. 13. Surface roughness average Ra calculated from white-light interferometry measurements plotted against Surface acoustic wave dispersion. R2 -value for the linear fit is 0.69.
The reference spectrometer of the Helsinki University of Technology (HUT) has been fitted with an accessory for measuring diffuse reflectance [9]. The automated measurement set-up consists of a thermal light source, a grating monochromator with reflective optics and a sample holding unit. The sample holding unit includes an integrating sphere and the actual sample and reference holding mechanics. This accessory was used to study the spectral behaviour of sample wafers. The measurement geometries were 0/d and 8/d, in which the sample was illuminated either at normal incidence or at the angle of incidence of 8◦ , and for which the specular component is excluded from the measurement by allowing it to exit the integrating sphere. The measurements were carried out using an opal glass reference sample, the reflectance factor of which has been determined separately. The wavelength range used was from 355 nm up to 565 or 790 nm. The complex refractive index [10] of silicon was used to calculate the corresponding penetration depths, which were from 13 nm to 2.5 or 12 m, respectively. The penetration depths above refer to the depth at which the intensity entering the wafer has been attenuated by one half. The measured diffuse reflectance shows scatter intensities rapidly decreasing with increasing wavelength. The measured diffusely reflected intensity can be expressed with the following formula Iscatter = I0 (Ssurface scatter (λ) +T 2 (λ)Ssubsurface scatter (λ))M(λ),
(1)
where I0 is the initial intensity striking the surface. Ssurface scatter (λ) is the coefficient for spectral scattering caused by the geometrical surface roughness, also known as haze. T(λ) is the spectral transmittance of the surface for a thickness corresponding to the penetration depth. Ssubsurface scatter (λ) is the coefficient for spectral scattering caused by the interaction between the light wave propagating inside the (top) layer of the wafer, and the damaged silicon lattice on top of the wafer. M(λ) is the relative spectral responsivity of the measurement system, which for the purposes of this discussion can be equated to unity. The scatter theory [11] can be used to calculate the spectral scatter H(λ) = Ssurface scatter (λ) from the surface with a known surface roughness Rq , using the equation H(λ) λ Rq = (2) 4π cos θ R(λ) where R(λ) denotes the spectral reflectance and θ is the angle of incidence. Solving Eq. (2) for spectral scatter H(λ) yields the simplified equation H(λ) = C0 R(λ)/λ2 , in which
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all factors not depending on wavelength have been combined into C0 . By normalising both the theoretical and measured data at one wavelength, the deviation of the spectral behaviour of the sample from the ideal can be studied. This deviation is caused partly by the scatter caused by sub-surface damage, the interacting proportion of which varies with the penetration depth. At the shortest wavelengths the measured scatter intensity is due to surface scatter only, as the penetration depth of light into silicon at this wavelength is negligible. Thus the normalisation is carried out at the shortest wavelength (355 nm) studied. Due to the penetration of the longer wavelengths and the resulting scattering from the sub-surface damage the scatter values measured are higher than those predicted by scatter theory and the short wavelength normalisation. Another spectral effect which must be taken into account before the spectral scatter data can be used to evaluate damage depth in the sample is the interaction between the probe beam and the studied damage. We propose a model, in which the spectral scattering coefficient of the lattice damage depends on the wavelength as 1/λ2 . The assumption is based on the following facts: The damaged layer depth for fine ground surfaces is known to be less than a few microns. This information is based on independent methods, such as iterative etching. It is definitely true if the damaged layer depth is defined as the depth in which the lattice damage is still substantial enough to influence such macroscopic phenomenon as propagation of light. Thus, for wavelengths that have penetration depth significantly higher than a few microns, the spectral behaviour cannot be due to different exposure to scattering damage. Spectral behaviour, at these longer wavelengths, not explained by the spectral surface scatter, is likely to be caused by the wavelength dependence of the probe beam–lattice damage interaction. The proposed dependence gives a good fit to long wavelength spectral behaviour of the scatter. The spectral behaviour of the interaction between surface roughness and the probe beam is of similar nature, scatter by inhomogenities much smaller than wavelength in dimension. Accordingly, it is reasonable to assume similar wavelength dependencies. One effect which could not be quantified in the experiments is the change in surface roughness Rq as the relevant spatial wavelengths differ for different wavelengths, as the power spectral density (PSD) of the surfaces measured is not uniform over the spatial wavelength range in question. Fig. 14 presents the results of a comparison measurement for two fine ground wafers, measured both at the edge and next to the centre. The measured intensity saturates at longer wavelengths when corrected for surface scatter and the wavelength dependence of the interaction between lattice damage and the probe beam. This indicates that the probe beam does not scatter below a layer, which is some 1 and 2.5–3 m thick for centre and edge measurements, respectively. This difference in damage depth correlates with the damage distributions measured over wafer area with scanning acoustic
Fig. 14. The spectral behaviour of measured scatter intensity, after corrections for surface scatter and spectral interaction coefficient of the type 1/2 . The dotted line, and the continuous black line, denote measurements carried out with samples taken from the edge of two fine ground sample wafers (a and b), over wavelength range of 355–790 nm. The grey continuous line, and the line marked with vertical bars, denote measurements carried out for samples taken from the same two wafers (a and b), right next to the centre of the wafers, over the wavelength range of 355–565 nm. The x-axis denotes the penetration depth calculated for the wavelengths used in the probe beams.
wave and scanning infrared depolarisation techniques, and the observed distribution of defects after iterative layer removal. The spectral diffuse spectral analysis indicates that the principle of spectral study does hold promise of an analysis, which would result in true depth distribution of the damage. 4.5. Surface photo voltage and microwave photo conductive decay The lifetime and diffusion length of minority carriers in semiconductors depends on the density of recombination centres. Such centres are, among others, transition metals and surface states, but in high-quality silicon the recombination due to the lattice defects contributes to the measured lifetimes and diffusion lengths. In [12] the photo conductive amplitude (PCA) was successfully used to analyse damaged layers in the immediate vicinity of the final polished wafer surface. The PCA is limited by the same physical processes as the signal strength of the microwave photo conductive decay and that of the surface photo voltage. A map of the signal strength of the SPV measurement carried out for a ground wafer is presented in Fig. 5, in which the distribution of the lattice damage is seen. The recombination of minority carriers in ground silicon wafers was studied using PCD and SPV scanners by Semilab Ltd., Budapest, Hungary. While the extent and depth of damage after grinding is several orders of magnitude more extensive than after CMP polishing, the same basic phenomenon of faster recombination in material with more recombination centres still holds. For the PCD measurements the upper surface was passivated chemically, and thus the signal amplitude (PCA) and PCD lifetimes were related to
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Fig. 15. The relationship between measured minority carrier lifetimes and strain-induced bow. The measurements inside the dotted circle were ground in the ductile mode, whereas those within the continuous circle have brittle ground surfaces.
the extent and nature of the sub-surface damage in the sample wafers. The correlation between strain and whole-wafer average of the carrier lifetime is presented in Fig. 15. It is notable that while the lifetimes recorded for various ductile ground wafers correlated with the compressive strain measurements (bow), the lifetimes of the rough ground wafers were fairly high, indicating a relative lack of recombination centres below the surface. The different form and distribution in-depth of the lattice damage for the two grinding modes are thus as important as the total amount of introduced strain in influencing the lifetime of the silicon material. For the SPV scanner the passivation was not necessary, as the measurement is not very much affected by surface recombination. A similar relationship as for PCD lifetimes was observed for SPV diffusion lengths for rough ground surfaces. As the measured lifetimes and diffusion lengths were very short in comparison to those observed for final polished wafers made from the same or from similar ingots the effect of metals can be assumed to be small. As a further verification to this assumption the Fe–B pair disassociation was verified not to be a significant factor in the PCD-lifetime of the ground wafers.
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damaged silicon in the depth of the sample. Nevertheless, useful information can be gained from the distribution of the sub-surface damage by studying the dispersion of ultrasonic surface acoustic waves, generated by ultra-short laser pulses [13]. The dispersion of the surface acoustic waves is caused by the different intensity distributions in depth of various frequencies included in the laser-generated acoustic wave packet. Thus different effective elastic modules are experienced by different frequencies in the wave. A more through investigation of the physical principles is presented in [13]. A laser-acoustic measurement device LA-Wave by Fraunhofer Institute IWS, Dresden, Germany, was used to quantify to what extent the elastic modules of ground wafers are lowered during machining operation. As the measurement yields information on one propagation track from the laser impact point to the piezo-electric detector the method can also be used to study the spatial distribution of the damage on the wafer surface. Three locations were chosen on the 1 0 0-oriented wafers, one on the axis from the notch to the centre, one at 45◦ angle to the said axis, and one close to the edge. Fig. 16 reveals the relationship between the measured slope of the dispersion curve on the three measurement locations and the measured geometrical deformation (bow) on the same wafers. As the dispersion is a measure of the local amount of microcracks in the lattice, whereas the bow is caused by global stress, the correlation is not straightforward, and the measurement points follow the linear fit only approximately. One interesting result was the zero dispersion measured for a type of very fine ground wafer, for all three measurement points. The wafer was strained by the grinding-induced damage, as can be seen from the measured bow. There are two possible explanations to the observed result. 1. The surface acoustic wave-method, in the present form, is not sensitive enough to detect the amount of damage,
4.6. Surface acoustic waves The propagation of surface acoustic waves in a surface layer is determined by the elastic constant of the layer material, thickness of the layer and the density of the layer. For damaged surface layer of a single crystal sample, such as silicon wafer, the elastic module in the surface region is lowered by the microcracks which have been caused by the mechanical machining of the brittle material. Naturally, the damaged layer is not a layer with well-defined thickness and elastic module, but a region in which the elastic module gradually approaches that of un-
Fig. 16. The relationship between strain-induced bow and the dispersion of surface acoustic wave, for three acoustic wave measurement locations on each wafer. The locations are indicated on the insert in the upper left-hand corner. The general trend for the three separate measurement locations is denoted with the least-square fitted lines. Zero dispersion result is highlighted with a black bounding box.
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even though it was independently observed to be significant. 2. The surface acoustic wave is insensitive to damage concentrated to the very top layer, and the very fine ground wafer has the all the lattice damage concentrated in a very thin top layer of the wafer. In this case the signal from the surface acoustic waves would not be dominated by the inherently very heavily damaged thin top layer. The depth of damage, which is the most important parameter of the damage in a manufacturing process, could then be deduced by comparing surface acoustic wave results with some readily available quantity such as bow, X-ray diffraction or roughness. 4.7. Scanning infrared depolarisation The stresses induced in silicon material during processing gives rise to photoelastic effect, birefringence, in the otherwise optically isotropic media. This phenomenon is utilised in the scanning infrared depolarisation measurement [14]. The measurement principle is based on a linearly polarised laser beam, which is transmitted through the wafer. The local shear stress field-induced birefringence causes the polarisation plane of the laser beam to be rotated. A more detailed discussion of the measurement principle is presented in [14] and [15]. The damage introduced to the crystal lattice in mechanical machining of silicon wafers, such as grinding, causes such high stresses that the depolarisation effect is very strong and easily observed with the SIRD technique. A set of ground wafers was studied using the SIRD stress imager by TePla AG, Jena, Germany. The parameters chosen for a more thorough investigation were the average depolarisation D and the differential contrast, or differential of the depolarisation D. These quantities can be used to estimate the differential of the radial shear component σrϕ , defined in [15] as
Fig. 17. The depolarisation image of a 200 mm wafer after grinding with a D6 wheel. The depolarisation scale goes from 1100 units (1.100 kDU, dark centre area) to 6500 units (6.5 kDU, darkest lines on the edges), with average of 3870 units. The corresponding shear stresses range from 0.9 to 3.2 MPa.
(3)
Uniform stress in a non-uniform material gives rise to non-uniform straining. This is observed in 1 0 0-oriented wafer as isotropic straining of the lattice, for which the depolarisation signal varies as cos 4ω, where ω is the angle between the principal axis of the wafer (1 1 0 plane intersecting the centerpoint), and the vector drawn from the centre to the measured point. The magnitude of this signal corresponds to the differential in the elastic deformation of the wafer, along different crystal planes. This deformation differential is exactly proportional to the magnitude of the deformation, and thus to the strain. The correlation between the global deformation (Bow) and the angle-dependent stress differential (cos 4 fitted for differential contrast at 50 mm from centre) is presented in Fig. 18. The reason that the SIRD-analysis is sensitive to wafer straining, even as the analysis is aimed at resolving stress distributions, lies in the use of an optical stress constant Cσ averaged over crystal orientations. Thus different strain along different crystal planes yields different stresses, even if the original stress is, as it most probably is, uniforms.
in which Cσ is the mean optical stress constant of silicon for the 1.3 m wavelength used in the measurement. In Fig. 17 is depicted one SIRD measurement of a ground wafer. The average depolarisation measured was 3.87 units, and from the image it can be clearly seen that the radial shear stresses are the lowest at the middle and highest at the edges. This is caused by the radius dependent material removal rate, inherent to rotational grinding. The corresponding shear stress magnitudes calculated using the depolarisation values range from 0.9 to 3.2 MPa. The inverse number 700 seen opposite to the notch is caused by writing on the wafer, and the radial line pattern is the same as that seen visually on the surface. The figure also demonstrates the strong point of SIRD measurement as a true mapping analysis. These images can be used to locate and quantify localised problems, caused for example by misalignment of the grinding tools.
Fig. 18. The depolarisation contrast at half-radius, fitted for cos (4ω), compared against the global strain-induced bow measured for the same sample wafers. The continuous line denotes a sigmoidal fit to the data.
σrϕ =
D √ Cσ Dmean
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5. Discussion Several measurement methods based on a number of physical principles were used to evaluate the sub-surface damage in a controlled set of silicon wafers. Each method was evaluated against one or more other methods, and from the resulting correlations the following conclusions can be drawn. The type, extent and distribution of the sub-surface damage vary with different grinding conditions. Wafers ground in ductile mode are bound to have a different kind of damage distribution in depth than those ground partially or completely in brittle fracture mode. The existence of two types of sub-surface damage was demonstrated. This arises from the two modes, ductile and brittle, through which the material is removed and the lattice disturbed. For example, comparing surface roughness to X-ray measurements, or comparing strain-induced bow measurements to recombination lifetimes measured for the same wafers, the two types of damage give rise to different correlations. Most of the wafers used in this study were ground in the ductile mode. This is typically the type of surface found on a wafer after completing the grinding process, and thus the extent, and in particular the depth of damage on these wafers has direct influence in the subsequent processing of the wafer. The methods studied correlated with each other to an extent which suggests that when limiting the study to ductile ground surfaces the various aspects of the damage, such as the influence on Young’s modulus, induced shear stresses, global stressing, scattering of optical radiation and the geometrical roughness are linked to each other. These links most probably arise from the fact that forces required by the separation mechanism, dominant chip sizes and heat generation are closely interrelated. Thus surfaces for which these parameters of the grinding process have been successfully optimised are bound to exhibit low levels of lattice damage regardless of probing technique. Interesting possibilities are offered by the surface acoustic wave-method. In samples for which the assumption of insensitivity to the uppermost layer holds the measurable signal is closely linked to the commercially interesting depth of the damage. For process control and development the most important parameter undoubtedly is the maximum depth of damage, and the variation thereof. This depth is also currently impossible to measure directly using non-destructive methods. The indirect methods described in this paper can be used to gain insight into the relationship between machining parameters, total damage introduced to the lattice, and the
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distribution in depth. Iterative layer removal methods can be applied to most methods in order to more accurately correlate the damage distribution in depth with the results available with non-destructive methods. This study indicates that the results extracted using fast methods, typically already available for chip and wafer manufacturers, can be linked with the more thorough point evaluations, such as X-ray diffraction. The widely differing physical principles, on which the various methods described in this paper are based on, provide several independent methods for probing the sub-surface damage. A combination of methods can be used to gain more thorough understanding of the damage type and distribution in specific processes. The results, which link the physical aspects of the damage to each other, can be used to verify established grinding models. The refined models allow better understanding of the ductile mode cutting in brittle materials such as silicon. Understanding the creation and distribution of the damage allows the method best suited for practical measurement needs to be chosen.
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