Face Turning of Single Crystal (111)Ge: Cutting Mechanics and Surface/Subsurface Characteristics

Infrared (IR)-transparent materials are used in the production of optical elements, with applications that can range from thermal sensors to imaging systems. One of the materials commonly used in such devices is single crystal Ge [1], for its transmittance in the spectral range from 2 µm up to 14 µm [2]. Bulk single crystals of Ge can be produced by the Czochralski method, with excellent crystal quality and accurate orientation. The single crystal can then be machined by single-point diamond turning, in which a stationary tool is fed across a rotating workpiece, to obtain a rotationally symmetric optical element that has the required tolerances for surface roughness and form accuracy. Turning is also commonly used to establish a planar surface perpendicular to the main spindle axis prior to more complex cutting geometries, such as flycutting [3,4].

Single crystal Ge is prone to undergo brittle fracture when machined. One of the important factors that determine the onset of fracture on the surface is the relationship between the crystallographic orientation of the specimen and the cutting direction of the tool. The anisotropic response to machining of single crystal Ge was first studied by Nakasuji et al. by performing on-axis turning experiments, and therefore cutting the surface with all possible in-plane cutting directions [5]. It was found that the surface condition was dependent on the relationship between the cutting direction and the lattice symmetry. Some cutting directions resulted in brittle fracture on the surface while others produced an apparent fracture-free surface. In our previous studies on the subsurface damage produced by single point diamond turning of single crystal Ge [4,6], ion channeling and Raman spectroscopy were employed and showed that there was an increase in lattice disorder in the near subsurface as the feedrate increased. There was also a change in the spatial distribution of the lattice disorder, which reached deeper below the surface for larger feedrates. In addition to surface and subsurface damage, diamond turning has been shown to introduce residual stresses into the machined surface with the magnitude and state of stress varying as a function of distance below the surface [3,7,8].

For machined components, characterization of the surface and subsurface damage is an important consideration because it affects both the optical and mechanical properties and therefore dictates the functional performance and lifetime of the optical elements [9–11]. Considering that surface roughness, lattice order below the surface, and machining-induced residual stresses all depend on the cutting parameters, it is important to assess the material condition after the new surface is generated. In this study, the combined effects of crystal anisotropy and feedrate were investigated by machining undoped single crystal specimens of (111)Ge using on-axis face turning with a single crystal diamond tool. The forces were measured during cutting. The machined surfaces were then characterized by several techniques. Nanoindentation was used to determine the elastic and plastic response of the surface, as well as to evaluate the fracture toughness of the material. Atomic force microscopy (AFM), scanning white light interferometry (SWLI), and Raman spectroscopy were used to characterize the surface topography and the crystalline quality of the lattice immediately below the surface. AFM and scanning electron microscopy (SEM) were also used to image the residual impressions left by the indenter.

An undoped single crystal (111)Ge wafer with a diameter of 25 mm and a thickness of 1 mm was obtained from Novotech, Inc (Action MA, USA). The as-received wafer was chemomechanically polished to an average surface roughness (Ra) of ∼2.2 nm. The wafer was mounted on a custom vacuum chuck and face turned on-axis using a Moore 350 Freeform Generator ultra-precision diamond machining center (see Fig. 1(a)) which had a linear and rotational resolution of 0.01 nm and 0.1 µ°, respectively. The cutting experiments were performed using a round nose single crystal diamond tool (see Fig. 1(b)) with a nose radius (R) of 1 mm and a rake angle of −25 deg. The spindle speed per revolution was adjusted for each band such that a cutting speed (V_c) of 4 m/s was obtained at the center of each band. Because of the relatively small change in radius within each band compared to the distance from the center of the spindle, the cutting speed for each band varied no more than ±6% from 4 m/s. The nominal depth of cut (t_c) was also held constant at 5 µm. The feedrate was varied (f = 0.5, 1, 2, 3, 5, 7, and 9 µm/rev) to create a total of seven concentric bands each with a width of ∼1 mm on the workpiece surface. Figure 1(c) shows the turned surfaces, where a shaded tri-lobed pattern corresponding to regions of increased surface roughness associated with brittle fracture is marked in red. As detailed in our previous study and those of others [4,5], in face turning of a (111)Ge single crystal, increased fracture is observed when cutting along the $[12¯1]$⁠, $[112¯]$⁠, or $[2¯11]$ in-plane orientations. Regions in between these lobes, centered along the $[21¯1¯]$⁠, $[1¯21¯]$⁠, or $[1¯1¯2]$ in-plane orientations, have a lower propensity for fracture and therefore exhibit a lower overall surface roughness. A model of single crystal Ge with those cutting directions highlighted is presented in Fig. 2. Experiments performed at the center of the lobes with increased fracture had the cutting direction belonging to the $<112¯>$ family, while experiments performed in between the lobes had the cutting direction belonging to the $<21¯1¯>$ family.

The force exerted by the tool was recorded during the cutting experiments by mounting the tool on top of a Kistler 9256C1 miniature dynamometer comprised of a fluid-proof piezoelectric. The range and resolution of the dynamometer were ±250 N and 0.002 N, respectively. The unloaded natural frequency of the dynamometer (∼5 kHz) was reduced by nearly 40% (∼3 kHz) upon loading it with the tool assembly. Thus, inverse filtering was applied to extend the usable frequency range beyond the reduced natural limit. A Kistler type 5010 dual mode charge amplifier was then used to convert the charge output to voltage.

Surface topography of the turned surfaces along the $<112¯>$ and $<21¯1¯>$ cutting directions was characterized using a commercial atomic force microscope. The AFM scans were collected using tapping mode. Quantitative values of areal surface roughness (Sa) were also obtained using a Zygo Newview 5000 scanning white light interferometer.

Near-surface lattice disorder along the $<112¯>$ and $<21¯1¯>$ cutting directions was studied by Raman spectroscopy using a confocal microscope in a backscattering configuration. Light with a wavelength of 532 nm was directed at an incident angle normal to the surface through a 100x/0.9NA objective. The same objective was used to collect the scattered light in reflection. The collected light was then focused onto a 50 µm diameter optical fiber which acted as a confocal pinhole. A 0.3 m monochromator with an 1800 groove/mm grating was subsequently used to disperse the light. Finally, a thermoelectrically cooled charge coupled device (CCD) camera was used to detect the light. The excitation spot was scanned over the area of interest using a piezoelectrically driven stage. Each collected spectrum was fitted to a Lorentzian curve using the microscope software to quantify the spatial variations in the Raman response. Spatial maps of the Raman peak intensity, spectral center, and width were then created based on the curve fitting results. Histograms of the spectral center and peak width were subsequently generated using the obtained spatial maps. To avoid anomalous features in the spectra (e.g., cosmic rays), the highest and lowest 1% of the histogram population were omitted in the calculation of the average and standard deviation. The laser power was optimized to minimize heating of the specimen while producing a peak intensity of the spectra to allow for Lorentzian curve fitting.

Mechanical response of the turned surfaces was studied by nanoindentation experiments performed with a Hysitron Triboindenter in load controlled mode. The specimen was left inside the instrument chamber overnight to allow for thermal equilibration. Furthermore, the instrument's drift rate was monitored over a 5 s interval in the beginning of each indentation and results were excluded when the drift was higher than 0.1 nm/s. The system was calibrated by calculating the area function of the indenter and the instrument's frame compliance by performing indentations in fused silica and tungsten reference specimens using the procedure of Oliver and Pharr [13] and of ISO 14577 [14]. A diamond Berkovich indenter was used to measure elastic modulus and hardness of the turned surfaces along both the $<112¯>$ and $<21¯1¯>$ cutting directions. In addition, a diamond cube corner indenter was used to study the effects of feedrate on indentation fracture toughness of the turned surfaces along the $<112¯>$ cutting direction. For both the Berkovich and cube corner indentations, the load applied to the indenter was increased over a 30 s interval to the selected maximum force followed by a 60 s hold to minimize any time-dependent plastic deformation. Then, the load was decreased to 10% of the maximum applied force over a 10 s interval followed by another 60 s hold to evaluate and compensate for the remaining thermal drift. Finally, the indenter was fully unloaded over a 2 s interval. The AFM was used to examine the areas around selected Berkovich indentations to characterize the deformation mechanisms. The indentations made with the cube corner indenter were studied by a Hitachi S-4800 field emission scanning electron microscope to measure the length of the radial cracks formed as a result of indentation. The obtained crack lengths were then used to evaluate the indentation fracture toughness of the turned surfaces.

As shown in Fig. 4(b), the relative increase of F_v compared to F_a resulted in the rotation of the resultant force angle (δ) from 56 deg at f = 0.5 µm/rev to 31 deg at f = 9 µm/rev. This indicates a transition from indentation-dominant to cutting-dominant behavior at higher feedrates and is consistent with our previous observations from round-nosed flycutting of (111)Ge over a range of feedrates [4].

Figure 5 shows 50 × 50 µm² AFM scans of surfaces turned along the $<112¯>$ and $<21¯1¯>$ cutting directions. In general, surfaces machined with f < 3 µm/rev show limited amount of fracture as demonstrated by the lack of pits. At f = 3 µm/rev, surface pits began to appear, visualized as ellipsoids with dark rims and bright centers. The emergence of surface pits was accompanied by ∼4 nm and ∼300 nm jumps in the average surface roughness (Ra) and average maximum roughness height (R_max), respectively. The number, area, and depth of the pits monotonically increased at larger feedrates. Surfaces turned along the $<21¯1¯>$ cutting directions that had evidence of surface fracture show fewer number of pits with larger areal sizes compared to the surfaces created along the $<112¯>$ cutting directions. To provide a quantitative comparison between the surface roughness values along the $<112¯>$ and $<21¯1¯>$ cutting directions, variations in surface roughness were also studied by SWLI over a 408 × 408 µm² area. For each family of cutting directions, three separate areas were scanned at each feedrate to obtain the average Sa values and corresponding standard deviations reported in Fig. 6. Increasing the feedrate led to an initial decrease in Sa for f <3 µm/rev, followed by an increase at higher feedrates. This is consistent with the AFM observations that only showed evidence of brittle surface fracture at f ≥ 3 µm/rev. After the onset of brittle surface fracture, the average Sa of the surfaces turned along the $<21¯1¯>$ cutting directions are consistently lower than those along the $<112¯>$ cutting directions. This agrees with the observed force oscillations during each revolution (shown in the inset of Fig. 3) suggesting a higher propensity for brittle fracture along the $<112¯>$ cutting directions.

The subsurface damage of the turned surfaces was investigated by Raman spectroscopy. Spatial mapping of the Raman response was performed on 25 × 25 µm² areas with 676 individual spectra being collected from each scanned area. A typical Raman spectrum of the surface turned with f = 0.5 µm/rev along the $<112¯>$ cutting direction is shown in Fig. 7. The spectrum shows only one peak centered at ∼300.6 cm⁻¹ which has been attributed to the triply degenerate crystalline Ge mode. The Ge Raman peak was fit with a Lorentzian peak shape, and histograms of the results were used to determine the peak width (FWHM) and peak center. The FWHM of the Raman peak has been correlated with the crystalline quality of semiconductors (Ge, Si, and GaAs) where lattice disorder decreases the phonon lifetime and thus results in peak broadening. Therefore, variations in the FWHM can be used to qualitatively distinguish between regions of different crystal quality [15–19]. Figure 8(a) shows the average and standard deviation of the FWHM for the turned surfaces along both families of cutting directions. Increasing the feedrate results in an overall increase in the FWHM of the Raman mode from 6.7 ± 0.3 cm⁻¹ to 10.3 ± 1.5 cm⁻¹, indicating an increase in lattice disorder below the surface. Furthermore, Fig. 8(a) shows larger standard deviations of the FWHM at f ≥ 3 µm/rev as evidenced by the larger error bars. This shows that the FWHM varies more over the set of points collected on the surface, therefore suggesting an increase in the spatial variations of the subsurface damage. The damage is also seen to be higher for the surfaces cut along the $<112¯>$ cutting directions further supporting the in-plane anisotropy of brittle fracture in (111)Ge.

The average and standard deviation of the Raman peak center were measured for surfaces turned with different feedrates along both families of cutting directions. Increasing the feedrate was seen to result in a shift of the peak center to higher wavenumbers, indicating a more compressive residual stress [8]. Residual stress is generated below the surface whenever inhomogeneous deformation occurs [20]. When cutting-induced thermal effects are negligible, the residual stress below the surface is typically compressive [21]. Previous reports of the effects of applied hydrostatic pressure on the position of the Ge Raman mode allow for the residual stress to be estimated using σ = 260(300.6 − ω), where σ is the stress in MPa and ω is the measured center of the crystalline Ge Raman mode (the stress-free center is 300.6 cm⁻¹) [22,23]. The values of residual stress estimated from the shifts in Raman mode peak position are shown in Fig. 8(b). In general, increasing the feedrate resulted in higher magnitudes of compressive residual stress and larger standard deviations along both the $<112¯>$ and $<21¯1¯>$ cutting directions. Prior to the onset of brittle surface fracture (f < 3 µm/rev), the magnitude of the compressive residual stress along the $<21¯1¯>$ cutting directions was found to be larger than that along the $<112¯>$ cutting directions. It is speculated that the material machined along the $<112¯>$ cutting directions relieved some of the compressive stress generated by the tool through fracture. Fracturing allows the lattice to reorganize and liberate some of the stress while maintaining the crystallinity. For f ≥ 3, there was no clear difference in residual stress when comparing the two machining direction families, likely due to the pronounced fracture below the surface.

A Berkovich indenter was used to perform nanoindentation experiments on the turned surfaces in order to characterize their mechanical response. Figure 9 shows representative curves of the applied indentation force (P) plotted against penetration depth (h) for the surfaces turned with the lowest (0.5 µm/rev) and highest (9 µm/rev) feedrates along both families of cutting directions. Each curve shows loading, hold at a maximum force (P_max) of 10 mN, and unloading. Multiple small pop-ins can also be observed in the loading portion of the curves. Indentation pop-ins of single crystal Ge have been attributed to a variety of instability mechanisms including phase transformation from a diamond cubic to a denser metallic phase (β-Sn) during loading [24], discontinuous crack extension and chipping [25], and deformation via slip/defect propagation [24,26]. To identify the mechanism contributing to the pop-ins observed in the present study, a series of Berkovich indentations were performed on the surface turned with f = 1 µm/rev along the $<112¯>$ cutting directions. These indentations were performed over a range of maximum forces (P_max = 1, 2, 3, 4, 5, 6, 8, or 10 mN) and the residual impressions were studied by AFM. Figures 10 and 11 show the force versus penetration depth curves and the corresponding post-indentation AFM images obtained at P_max of 5 mN and 6 mN. For the maximum applied force of 5 mN, the loading portion of the force versus penetration depth curves is seen to be smooth and no cracks are observed in the corresponding AFM images. Similar observations were made when indentations were performed at P_max < 5 mN. Increasing the maximum applied force to 6 mN, however, results in formation of pop-ins in the force versus penetration depth curve. Furthermore, radial cracks are found to emanate from the corners of the corresponding residual impressions. It is thus concluded that the pop-ins observed in the force versus penetration depth curves of Berkovich indentations are resultant from the formation or extension of radial cracks.

The length of radial cracks can be used to evaluate indentation fracture toughness. Although cracks were observed in post-indentation AFM images of Berkovich impressions, precise measurement of the crack lengths was challenging because most cracks were smaller than 400 nm. To accentuate the cracks, another set of nanoindentation experiments was performed using a diamond cube corner indenter. Even though the cube corner and Berkovich indenters both have a tetrahedron geometry, the cube corner indenter is more acute than the Berkovich (centerline-to-face angle of 35.3 deg versus 65.3 deg). Thus, at a given applied force the cube corner indenter displaces a larger volume of material compared to the Berkovich indenter (≥3 times). Subsequently, the applied stresses beneath the cube corner indenter are also greater in magnitude [38] and larger cracks could be generated. Using a cube corner indenter could also result in a phase transformation in Ge from diamond cubic to metallic (β-Sn) phase because the formation and propagation of quasi-plasticity mechanisms cannot occur fast enough to prevent the pressure under the indenter from exceeding the phase transformation threshold [39]. Upon unloading, different metastable phases may form (depending on the unloading rate and temperature), which will eventually transform back to the stable diamond cubic phase [25,40]. Figure 13 shows typical curves of the applied force plotted against penetration depth for the surfaces turned with the lowest (0.5 µm/rev) and highest (9 µm/rev) feedrates along the $<112¯>$ cutting directions using a cube corner indenter. Compared to the Berkovich indentations performed at P_max = 10 mN (see Figs. 9(a) and 9(b)), the cube corner indenter resulted in larger maximum penetration depths during contact and larger permanent indentation depths after unloading. The cube corner indenter also produced larger pop-ins in the loading curves. During unloading the Berkovich indenter produced curves with the expected behavior of elastic recovery, while the cube corner indenter produced an elbow (marked by arrows). The elbow has been observed during indentation of single crystal Ge in cases where the β-Sn phase transforms to an amorphous phase upon unloading [24].

Figure 14 shows SEM images of the residual impressions of the cube corner indentations. An SEM image of the residual impression of a Berkovich indentation on the surface turned with a feedrate of 0.5 µm/rev is also shown for comparison. At all feedrates, material appeared to be extruded out of the contact area between the indenter and the surface. Similar observations have been reported during nanoindentation of single crystal diamond cubic Ge using a cube corner indenter, where the extruded material was attributed to the formation of a softer ductile phase (e.g., β-Sn) beneath the diamond indenter [25]. In contrast to the cube corner impressions, the impression of the Berkovich indentation exhibited no extruded material. These observations along with the observation of an elbow during unloading suggest that during indentation with a cube corner indenter, deformation is dominated by a phase transformation of Ge from a diamond cubic to a β-Sn phase [39], which upon unloading transforms to an amorphous phase [24].

Increasing the feedrate (or a subsequent increase in maximum chip thickness) during the on-axis diamond turning of single crystal (111)Ge using a round nose tool resulted in a shift from indentation-dominant to cutting-dominant behavior. Characterization of the surface and subsurface damage demonstrated that at sufficiently low feedrates, brittle surface fracture is prevented. Compressive residual stress was found to be present at all feedrates and its magnitude significantly increased at higher feedrates. The $<112¯>$ in-plane directions of (111)Ge showed a higher propensity for brittle fracture resulting in a higher surface roughness and a lower subsurface crystal quality, especially after transitioning to the brittle-dominated cutting domain.

Evaluation of the mechanical response of the turned surfaces using nanoindentation demonstrated that quasi-plastic deformation of (111)Ge can be accommodated through activation of various quasi-plasticity mechanisms including defect propagation, crack formation and extension, and phase transformation. The dominant quasi-plasticity mechanisms were found to be dictated by the geometry of the indenter which in turn affected the state of stress experienced by the material. Increasing the feedrate resulted in an increase in elastic modulus of the turned surfaces, plausibly due to the pinning of dislocations on machining-induced crystalline defects. Hardness, in contrast, was found to be insensitive to the feedrate and in-plane crystallographic orientations over a maximum indentation depth of 230–250 nm. The near-surface compressive residual stress suppressed the propagation of radial cracks and resulted in higher indentation fracture toughness values after the onset of brittle fracture.

This research was partially supported by the NSF I/UCRC Center for Freeform Optics (IIP-1338877 and IIP-1338898), NSF grants 1437225, 1437232, 2210365, and 2210394 and grants from the II-VI Foundation. The help of Mr. Matthew Luebbe with performing cube corner nanoindentation experiments and evaluation of indentation fracture toughness is gratefully acknowledged.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.