Study on nanometric cutting of germanium by molecular dynamics simulation
© Lai et al.; licensee Springer. 2013
Received: 29 October 2012
Accepted: 20 December 2012
Published: 5 January 2013
Three-dimensional molecular dynamics simulations are conducted to study the nanometric cutting of germanium. The phenomena of extrusion, ploughing, and stagnation region are observed from the material flow. The uncut thickness which is defined as the depth from bottom of the tool to the stagnation region is in proportion to the undeformed chip thickness on the scale of our simulation and is almost independent of the machined crystal plane. The cutting resistance on (111) face is greater than that on (010) face due to anisotropy of germanium. During nanometric cutting, both phase transformation from diamond cubic structure to β-Sn phase and direct amorphization of germanium occur. The machined surface presents amorphous structure.
Monocrystalline germanium is widely used in the fields of semiconductors, infrared optics, high-frequency electronics, and so on. Single-point diamond turning is usually adopted to achieve high surface finish and intricate features. However, it is hard to obtain perfect optical quality and complex surfaces for monocrystalline germanium because of its brittle nature. Therefore, understanding the mechanism of nanometric cutting and machined surface characteristics is of great significance in manufacturing high quality germanium components.
Since 1990s, Shimada et al. have conducted a series of investigations on the mechanism of nanometric cutting of single crystals by molecular dynamics (MD) simulation. They found dislocations generated during nanometric cutting of aluminum and copper [1, 2]. The single crystal silicon was removed in ductile mode when the depth of cut decreased to nanoscale, and amorphous silicon on machined surface was observed after nanometric cutting [3, 4]. Komanduri et al. studied the effect of crystal orientation on the nature of cutting deformation for copper and aluminum by molecular dynamics simulation [5–7]. They concluded that the phase transformation from a diamond cubic to β-Sn structure appeared in the case of nanometric cutting on silicon. Fang et al. proposed the extrusion model for cutting materials at nanometric scale, indicating that the conventional cutting theory could no longer explain the mechanism of nanoscale cutting [8–11]. The process of nanocutting was affected by the tool-edge radius, and monocrystalline crystal silicon transformed into polycrystal and amorphous structure during and after nanocutting.
Previous investigations indicate that the deformation mechanism of single crystal copper and aluminum during nanometric cutting is mainly the formation and extension of dislocations. However, silicon is removed in ductile mode; phase transformation and amorphization are the main deformations during nanometric cutting, observed by molecular dynamics simulation. At present, study on the nanometric cutting of germanium by molecular dynamics simulation has rarely been reported. In this paper, large-scale three-dimensional MD simulations are conducted to study the nanometric cutting of germanium. Attentions are focused on the material flow, cutting force and energy, crystal orientation effect, and surface-subsurface deformation.
MD simulation method
In this paper, the tool is modeled as the shape of a real cutter, which was firstly conducted by Zhang et al. , as shown in the Figure 1. The tool-edge radius is 10 nm, and the undeformed chip thickness is set as 1 to 3 nm in order to get large negative rake angle, which agrees with the condition of the real nanocutting.
Model condition and simulation parameters
a = 5.657 Å
Potential for germanium
Potential of C-Ge
De = 0.125778 eV, α = 2.58219 Å−1, 0 r0 = 2.2324 Å
45 × 27 × 12 nm
Tool clearance angle
on (010) surface
on (111) surface
Depth of cut
1, 2, 3 nm
Results and discussion
Model of nanometric cutting
The uncut thickness in different combinations of depth of cut and lattice plane
Cutting depth (nm)
Uncut thickness (nm)
on (010) surface
on (111) surface
Cutting force and energy
Average cutting force and frictional coefficient with different undeformed chip thickness
Cutting depth (nm)
Tangential force (nN)
Normal force (nN)
on (010) surface
on (111) surface
on (010) surface
on (111) surface
on (010) surface
on (111) surface
Figure 9c shows the variation in specific energy with the change of depth of cut. The specific energy decreases with an increase in undeformed chip thickness, which can be explained by the size effect . This phenomenon depends on several factors such as material strengthening, extrusion and ploughing due to finite edge radius, material separation effects, and so on.
Surface and subsurface deformation
Germanium and silicon belong to the group IV elements, of which the single crystals are important technological materials with a wide range of applications in semiconductor field, and their natures are similar in many aspects. With an increase in pressure, both experimental and theoretical investigations show that phase transformation in germanium from its diamond cubic structure to the metallic β-Sn structure would take place under pure hydrostatic pressure of about 10 GPa . On slow pressure release, a simple tetragonal phase with 12 atoms per unit cell (ST12) [19, 20] forms, while a metastable body-centered cubic structure with eight atoms per unit cell (denoted BC8)  forms on fast pressure release. Previous investigations show that the phase transformation from diamond cubic phase to the β-Sn phase of silicon occurs during nanometric cutting, and the amorphous silicon is observed after machining.
Figure 12a,b show the crystal structure of surface and subsurface for germanium during and after nanocutting, respectively. When the tool cuts on the surface to get the maximum stress, the distorted diamond cubic structure and other structures with fivefold or sixfold coordinated atoms are observed in the subsurface region shown in black rectangle, and they all transform back to the diamond cubic structure with coordination number of 4 after stress release. In the case of deformed region above it, the high-pressure disordered structures form amorphous germanium instead of recovering back to the diamond cubic structure after nanometric cutting. Whether the phase transformation or amorphization would take place depends on the pressure. For example, the threshold pressure inducing the phase transformation from diamond cubic structure to Ge-II and to ST12-Ge on pressure release is about 12 GPa . Therefore, the pressure of the two regions shown in the Figure 12a,b during the cutting process is calculated, as displayed in Figure 12c. The maximum pressure in subsurface region (black rectangle) is about 4 GPa, which is less than the threshold pressure of phase transformation from diamond cubic structure to β-Sn phase. However, the maximum pressure produced during machining in machined surface region (above the black rectangle) is about 11 GPa, more than the critical pressure of phase transformation from diamond cubic structure to β-Sn phase, but less than 12GPa, which means that the phase transformation from β-Sn structure to ST12-Ge on pressure release would not happen. As a result, the amorphization of germanium occurs after pressure release.
The material flow of nanometric cutting on monocrystalline germanium is the same with that on cooper and silicon, which has extrusion and ploughing. The stagnation region is also observed.
On the same crystal plane, the uncut thickness is in proportion to the depth of cut on the scale of our simulation. However, with the same undeformed chip thickness, the uncut thickness is almost the same on different machining crystal plane.
The cutting force and frictional coefficient increase with an increase in the undeformed chip thickness, while the specific energy decreases because of the size effect. With the same undeformed chip thickness, the cutting resistance of machining on (111) surface is greater than that on (010) surface.
Monocrystalline germanium undergoes phase transformation from diamond cubic structure to β-Sn phase, and direct amorphization with the pressure derives from the cutting of tool. The surface presents amorphous structure after machining, while some parts of subsurface recover back to distorted diamond cubic structure.
ML is a Ph.D. student in the Centre of Micro/nano Manufacturing Technology (MNMT) at Tianjin University, studying in the mechanism of ultra-precision machining. XZ is an associate professor in MNMT at Tianjin University. His research interests include ultra-precision machining and metrology, freeform optics manufacture and applications. FF is a professor in MNMT, working in the areas of optical freeform manufacturing, micro/nano machining, ultra-precision machining and metrology. He is the editor-in-chief of the International Journal of Nanomanufacturing, the president of the International Society for Nanomanufacturing, and a fellow of the International Academy for Production Engineering. YW is a professor of Physics at Nankai University. Current research interests include surfaced enhanced Raman spectra, light scattering of nanoparticles and first principles calculation of materials. MF is working at Nankai University as a technician with the research objective in investigating the electronic, magnetic, and thermodynamic properties of materials using first-principles calculation, potential model, and Monte Carlo simulation. WT is studying as a masters student in optics at Nankai University.
The authors appreciate the supports of the National Natural Science Foundation of China (grant no. 90923038), the National Basic Research Program of China (973 Program, grant no. 2011CB706703), and the ‘111’ Project by the State Administration of Foreign Experts Affairs and the Ministry of Education of China (grant no. B07014).
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