Monocrystalline silicon nanometric cutting subsurface damage simulation analysis method

Abstract

This invention discloses a simulation analysis method for subsurface damage in single-crystal silicon nano-cutting. The method includes the following steps: establishing a molecular dynamics model for single-crystal silicon nano-cutting; characterizing the subsurface damage formation mechanism through atomic coordination number analysis, hydrostatic stress calculation, and temperature distribution monitoring; studying the influence of cutting crystal planes, cutting speed, tool rake angle, and relative tool sharpness on subsurface damage depth and surface roughness using single-factor analysis; designing orthogonal experiments and determining the influence of each machining parameter through range analysis and variance analysis; using grey relational analysis to transform the dual responses of subsurface damage depth and surface roughness into a single grey relational degree for parameter optimization; and establishing molecular dynamics models for nanoindentation and uniaxial stretching to study the influence of subsurface damage on the mechanical properties of the machined workpiece. This invention achieves accurate prediction of subsurface damage and multi-objective collaborative optimization of machining parameters during single-crystal silicon nano-cutting.

Description

Technical Field

[0001] This invention relates to the fields of nanofabrication and molecular dynamics simulation, and in particular to a method for predicting subsurface damage and optimizing processing parameters in single-crystal silicon nano-cutting based on molecular dynamics. Background Technology

[0002] Single-crystal silicon, as an important semiconductor and infrared optical material, directly affects device performance due to its processing precision. Nanomachining is a key technology for obtaining nanoscale surfaces, but subsurface damage (such as amorphous phase transformations and dislocations) is easily generated during processing, leading to a decline in the mechanical properties of the workpiece. Traditional experimental methods are difficult to directly observe the damage mechanism at the nanoscale, while molecular dynamics (MD) simulations can effectively reveal the removal behavior of atomic-level materials. However, existing studies mostly focus on single-factor analysis, failing to comprehensively consider the synergistic effects of cutting parameters (such as crystal planes, speed, and tool geometry) on subsurface damage and surface quality, and lacking quantitative assessment of the mechanical properties of the damaged layer. Therefore, it is necessary to develop a simulation method for multi-parameter synergistic optimization to achieve low-damage, high-precision processing control. Summary of the Invention

[0003] This invention provides a method for predicting subsurface damage and optimizing parameters in single-crystal silicon nano-cutting based on molecular dynamics. By establishing a multi-process coupled model of nano-cutting-indentation-stretching, the influence of cutting parameters on subsurface damage depth, surface roughness and mechanical properties is quantified, and orthogonal experiments and grey relational analysis are used for parameter optimization.

[0004] The technical solution adopted in this invention is a simulation analysis method for subsurface damage in single-crystal silicon nano-cutting, comprising the following steps:

[0005] A molecular dynamics model for nano-cutting of single-crystal silicon was established: the workpiece size was set to 16×10.5×8.68 nm³, the cutting tool was made of diamond with a rake angle of 15°, a clearance angle of 15°, and a tip radius of 1.5 nm; the Tersoff potential function was used to describe the Si-Si and Si-C atomic interactions; the boundary conditions were set to be free in the X / Y directions and periodic in the Z direction; the workpiece was divided into a fixed layer, an isothermal layer, and a Newtonian layer; the cutting speed was set to 400 m / s, the cutting depth to 1.2 nm, and the initial temperature to 298 K;

[0006] After the model was established, the subsurface damage formation mechanism was analyzed: the damage evolution was characterized by atomic coordination number, hydrostatic stress, temperature distribution and radial distribution function, and the transformation of the tool-workpiece contact area from diamond structure to amorphous phase under high pressure and high temperature was analyzed.

[0007] Single-factor analysis experiments were conducted to study the effects of cutting crystal planes, cutting speed, tool rake angle, and relative tool sharpness on subsurface damage depth and surface roughness.

[0008] Multi-parameter optimization and grey relational analysis were employed: an orthogonal experimental table was designed, and the multi-objectives of subsurface damage depth and surface roughness were transformed into single-objectives for optimization by combining grey relational degree, so as to obtain the optimal parameter combination.

[0009] Investigating the effect of subsurface damage depth on the mechanical properties of processed single-crystal silicon: The mechanical properties of the damaged layer were analyzed by nanoindentation and uniaxial tensile simulation.

[0010] Furthermore, in the analysis of the subsurface damage formation mechanism, the transition region between the diamond structure (coordination number 4) and the amorphous phase (coordination number 3 / 5) is identified by atomic coordination number.

[0011] Furthermore, in the single-factor analysis experiment, the cutting crystal planes selected include (100), (110), and (111) crystal planes; the cutting speed range is 100–500 m / s; the tool rake angle range is -15° to 15°; and the relative tool sharpness range is 0.2–2.

[0012] Furthermore, in the multi-parameter optimization and grey relational analysis, the L25(56) orthogonal experimental table was used, and the variance analysis showed that the relative tool sharpness contributed 76.7% to the subsurface damage depth and 83.6% to the surface roughness.

[0013] Furthermore, the optimal parameter combination obtained from the multi-parameter optimization is: cutting crystal plane (100), cutting speed 200m / s, tool rake angle -5°, and relative tool sharpness 0.2.

[0014] Furthermore, in the investigation of the effect of subsurface damage depth on the mechanical properties of processed single-crystal silicon, the nanoindentation simulation results show that the residual compressive stress in the damaged layer increases the surface hardness with the increase of relative tool sharpness; the uniaxial tensile simulation results show that the damaged layer reduces the Young's modulus and tensile strength of the workpiece.

[0015] Furthermore, the method was verified through a nano-scratching experiment, with a normal load of 20-100 mN and a scratching speed of 30 μm / s.

[0016] Furthermore, the method is applicable to the simulation analysis of subsurface damage in similar hard and brittle materials such as single-crystal silicon carbide, with simulation results showing an error of less than 5% compared to experimental results.

[0017] Furthermore, the method employs atomic-scale simulation calculations using the molecular dynamics simulation software LAMMPS, and combines this with OVITO software for atomic structure visualization analysis.

[0018] Furthermore, the specific implementation steps of the method also include:

[0019] The system is relaxed by minimizing energy, and a Berendsen thermostat is used for temperature control in the NVE ensemble.

[0020] When simulating the nano-cutting process, the temperature of the isothermal layer is controlled under the NVT ensemble, and the atomic behavior of the Newtonian layer atoms is observed under the NVE ensemble during the cutting process.

[0021] A nanoindentation simulation model was established. A spherical diamond indenter was pressed into the processed surface at a speed of 200 m / s, and the load-displacement curve was recorded to calculate the surface hardness.

[0022] A uniaxial tensile simulation model was constructed, and a tensile speed of 100 m / s was applied to the machined workpiece. The stress-strain curve was monitored to obtain Young's modulus and tensile strength data.

[0023] Compared with the prior art, the present invention has the following advantages:

[0024] This invention, for the first time, couples the nano-cutting-indentation-stretching process to reveal the evolution law of the mechanical properties of the damaged layer. The established molecular dynamics model fully considers the discrete characteristics of material phase transitions and interatomic interactions at the nanoscale. Atomic coordination number analysis, hydrostatic stress field calculation, and temperature distribution monitoring are introduced into the simulation framework of the single-crystal silicon nano-cutting process, and an atomic-scale deformation model that can accurately describe the subsurface damage formation mechanism is derived. Through system simulation analysis, the influence of different cutting parameters (crystal orientation, cutting speed, tool geometry) on subsurface damage depth and surface roughness can be obtained. By comparing with the results of traditional continuum mechanics simulation and nano-scratching experimental data, the evolution behavior of machining damage can be predicted more accurately. This method has the advantage of atomic-scale observation and is more conducive to guiding the optimization of ultra-precision machining processes. A comparison of subsurface damage depth and surface roughness data analyzed using the simulation method of this invention and traditional methods shows that the prediction error of surface roughness by this method is reduced to 5.2%, while the error of the traditional method reaches 18.7%. The optimized process parameters, obtained through orthogonal experiments and grey relational analysis, reduce the subsurface damage depth by 69.9%, indicating that the multi-parameter collaborative optimization method proposed in this invention significantly improves the accuracy of machining quality prediction and the effect of process optimization. Furthermore, experiments verify that this method is applicable to similar hard and brittle materials such as silicon carbide, providing theoretical guidance for ultra-precision machining. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the molecular dynamics model for nano-cutting of single-crystal silicon.

[0026] Figure 2 It is the atomic structure distribution (coordination number analysis) of the subsurface damage layer.

[0027] Figure 3This is a comparison of damage depth and surface roughness under different cutting crystal planes. (a) is a morphology diagram of damage depth under different cutting crystal planes; (i) is for cutting crystal plane (100); (ii) is for cutting crystal plane (110); (iii) is for cutting crystal plane (111); (b) is a data comparison diagram of surface roughness under different cutting crystal planes.

[0028] Figure 4 These are orthogonal experimental range analysis plots. (a) is the main effect plot of each factor on subsurface damage depth. (b) is the main effect plot of each factor on subsurface roughness.

[0029] Figure 5 These are the mechanical property (hardness, tensile strength) curves of the machined workpiece under optimal parameters. (a) is a schematic diagram of load and indentation depth; (b) is a schematic diagram of stress and strain.

[0030] Figure 6 This is a flowchart of the method of the present invention. Detailed Implementation

[0031] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0032] This invention discloses a simulation analysis method for subsurface damage in single-crystal silicon nano-cutting. The method includes the following steps: establishing a molecular dynamics model for single-crystal silicon nano-cutting, including workpiece layered structure settings, boundary condition configuration, and potential function selection; characterizing the subsurface damage formation mechanism through atomic coordination number analysis, hydrostatic stress calculation, and temperature distribution monitoring; studying the influence of cutting crystal planes, cutting speed, tool rake angle, and relative tool sharpness on subsurface damage depth and surface roughness using single-factor analysis; designing a multi-factor, multi-level orthogonal experimental scheme, and determining the influence degree of each processing parameter through range analysis and variance analysis; using grey relational analysis to transform the dual responses of subsurface damage depth and surface roughness into a single grey relational degree for parameter optimization; and establishing molecular dynamics models for nanoindentation and uniaxial stretching to study the influence of subsurface damage on the mechanical properties of the processed workpiece. This invention achieves accurate prediction of subsurface damage and multi-objective collaborative optimization of processing parameters during single-crystal silicon nano-cutting.

[0033] The method described in this invention is implemented using molecular dynamics simulation software. The simulation platform uses LAMMPS (Large-scale Atomic / Molecular Massively ParallelSimulator) software developed by Sandia National Laboratories in the United States for atomic-scale simulation calculations, and is combined with OVITO (Open Visualization Tool) software for atomic structure visualization analysis.

[0034] The method described in this invention specifically includes the following steps:

[0035] Step 1: Establish a molecular dynamics model for single-crystal silicon nano-cutting. Divide the workpiece into three regions: a fixed layer, an isothermal layer, and a Newtonian layer. Set periodic boundary conditions and free boundary conditions, and use the Tersoff potential function to describe the interatomic interactions.

[0036] Step 2: Relax the system using the principle of energy minimization, and use a Berendsen thermostat to control the temperature under the NVE ensemble to bring the system to a stable state.

[0037] Step 3: Simulate the nano-cutting process. Control the temperature of the isothermal layer under the NVT ensemble, and observe the atomic behavior of Newtonian layer atoms during the cutting process under the NVE ensemble. Set the cutting speed to 100-500 m / s and the cutting depth to 0.2-2 nm.

[0038] Step 4: By analyzing atomic coordination number, calculating radial distribution function, and monitoring hydrostatic stress distribution, the subsurface damage formation mechanism is studied, and the amorphous phase transition region is identified.

[0039] Step 5: Single-factor analysis was used to study the effects of cutting crystal plane, cutting speed, tool rake angle and relative tool sharpness on subsurface damage depth and surface roughness.

[0040] Step 6: Design a multi-factor, multi-level orthogonal experimental scheme, and determine the degree and significance level of the influence of each processing parameter on subsurface damage through range analysis and variance analysis.

[0041] Step 7: Use grey relational analysis to transform the two responses, subsurface damage depth and surface roughness, into a single grey relational degree to achieve multi-objective parameter optimization.

[0042] Step 8: Establish a nanoindentation simulation model. Press the spherical diamond indenter into the processed surface at a speed of 200 m / s, record the load-displacement curve, and calculate the surface hardness.

[0043] Step 9: Construct a uniaxial tensile simulation model, apply a tensile speed of 100 m / s to the machined workpiece, monitor the stress-strain curve, and obtain Young's modulus and tensile strength data.

[0044] Example

[0045] A molecular dynamics model for nanocutting of single-crystal silicon was established: The workpiece size was 16 × 10.5 × 8.68 nm³, and the cutting tool was made of diamond (15° rake angle, 15° clearance angle, and 1.5 nm tip radius). The Tersoff potential function was used to describe the Si-Si and Si-C atomic interactions, and the boundary conditions were set to be free in the X / Y directions and periodic in the Z direction. The workpiece consisted of a fixed layer, an isothermal layer, and a Newtonian layer. The cutting speed was set to 400 m / s, the depth of cut to 1.2 nm, and the initial temperature to 298 K.

[0046] After establishing the model, the subsurface damage formation mechanism was analyzed: Damage evolution was characterized by atomic coordination number, hydrostatic stress, temperature distribution, and radial distribution function (RDF). The formula for calculating hydrostatic stress in nano-cutting is as follows:

[0047]

[0048] in These are the principal stresses in the X, Y, and Z directions, respectively. In molecular dynamics, atomic temperature is generally calculated from its kinetic energy; the conversion formula between temperature and kinetic energy is:

[0049]

[0050] Where N is the number of atoms in the Newtonian layer, and 3 indicates that the model is a three-dimensional model. The Boltzmann constant is represented by ; This represents the kinetic energy of the i-th atom.

[0051] The results show that the high pressure (>13 GPa) and high temperature (>750 K) in the tool-workpiece contact area cause the single crystal silicon to transform from a diamond structure (coordination number 4) to an amorphous phase (coordination number 3 / 5), forming a subsurface damage layer.

[0052] The influence of cutting parameters was analyzed through experiments: First, a single-factor analysis was conducted to study the effects of cutting crystal planes ((100), (110), (111)), cutting speed (100–500 m / s), tool rake angle (-15°–15°), and relative tool sharpness (RTS=h / r, 0.2–2) on subsurface damage depth and surface roughness. Experiments showed that cutting damage was minimal along the (100) crystal plane; damage was low at speeds of 200–300 m / s; a positive rake angle tool could reduce damage; and increasing RTS exacerbated damage and surface roughness. The universality of the findings was verified through nano-scratching experiments and single-crystal silicon carbide simulations, with an error of <5%.

[0053] Further research was conducted on the changes in subsurface damage depth and surface roughness of single-crystal silicon nano-cutting under the combined influence of multiple factors. Multi-parameter optimization and grey relational analysis were employed: an L25(56) orthogonal experimental table was designed, and the multi-objective (damage depth, roughness) was transformed into single-objective optimization by combining grey relational analysis. Analysis of variance showed that RTS contributed 76.7% to damage depth and 83.6% to roughness. The optimal parameter combination was obtained: cutting crystal plane (100), speed 200 m / s, rake angle -5°, RTS=0.2, which improved the grey relational analysis by 69.9%.

[0054] The influence of subsurface damage depth on the mechanical properties of processed monocrystalline silicon was investigated. The mechanical properties of the damaged layer were analyzed through nanoindentation and uniaxial tensile simulations. Indentation results showed that the residual compressive stress in the damaged layer increased the surface hardness with increasing RTS (up to 38.5 GPa). Tensile results showed that the damaged layer reduced the Young's modulus and tensile strength of the workpiece; under optimized parameters, the mechanical properties were close to those of intact monocrystalline silicon (Young's modulus 93.32 GPa, tensile strength 21.23 GPa).

[0055] The simulation results were verified through nano-scraping experiments. A Keysight G200 nano-scraping instrument was used, with a normal load of 20-100 mN and a scratching speed of 30 μm / s. Surface roughness and friction coefficient were measured. The experiment found that the optimal parameters resulted in a surface roughness of 0.1289 nm and a subsurface damage depth of 1.0884 nm, representing reductions of 21.2% and 37.5%, respectively, compared to the unoptimized parameters. The optimized grey relational degree, achieved through orthogonal experiments, reached 0.873, a 69.9% improvement over the unoptimized result. This demonstrates that the multi-parameter collaborative optimization method proposed in this invention significantly improves the accuracy of machining quality prediction and the effectiveness of process optimization.

Claims

1. A method for simulating and analyzing subsurface damage in single-crystal silicon nano-cutting, characterized in that, Includes the following steps: A molecular dynamics model for nano-cutting of single-crystal silicon was established: the workpiece size was set to 16×10.5×8.68 nm³, the cutting tool was made of diamond with a rake angle of 15°, a clearance angle of 15°, and a tip radius of 1.5 nm; the Tersoff potential function was used to describe the Si-Si and Si-C atomic interactions; the boundary conditions were set to be free in the X / Y directions and periodic in the Z direction; the workpiece was divided into a fixed layer, an isothermal layer, and a Newtonian layer; the cutting speed was set to 400 m / s, the cutting depth to 1.2 nm, and the initial temperature to 298 K; After the model was established, the subsurface damage formation mechanism was analyzed: the damage evolution was characterized by atomic coordination number, hydrostatic stress, temperature distribution and radial distribution function, and the transformation of the tool-workpiece contact area from diamond structure to amorphous phase under high pressure and high temperature was analyzed. Single-factor analysis experiments were conducted to study the effects of cutting crystal planes, cutting speed, tool rake angle, and relative tool sharpness on subsurface damage depth and surface roughness. Multi-parameter optimization and grey relational analysis were employed: an orthogonal experimental table was designed, and the multi-objectives of subsurface damage depth and surface roughness were transformed into single-objectives for optimization by combining grey relational degree, so as to obtain the optimal parameter combination. Investigating the effect of subsurface damage depth on the mechanical properties of processed single-crystal silicon: The mechanical properties of the damaged layer were analyzed by nanoindentation and uniaxial tensile simulation.

2. The method for simulating and analyzing subsurface damage in single-crystal silicon nano-cutting according to claim 1, characterized in that, In the analysis of the subsurface damage formation mechanism, the transition region between the diamond structure (coordination number 4) and the amorphous phase (coordination number 3 / 5) is identified by atomic coordination number.

3. The method for simulating and analyzing subsurface damage in single-crystal silicon nano-cutting according to claim 1, characterized in that, In the single-factor analysis experiment, the cutting crystal planes selected included (100), (110), and (111) crystal planes; the cutting speed range was 100–500 m / s; the tool rake angle range was -15° to 15°; and the relative tool sharpness range was 0.2–2.

4. The method for simulating and analyzing subsurface damage in single-crystal silicon nano-cutting according to claim 1, characterized in that, In the multi-parameter optimization and grey relational analysis, the L25(56) orthogonal experimental table was used, and the variance analysis showed that the relative tool sharpness contributed 76.7% to the subsurface damage depth and 83.6% to the surface roughness.

5. The method for simulating and analyzing subsurface damage in single-crystal silicon nano-cutting according to claim 1, characterized in that, The optimal parameter combination obtained from the multi-parameter optimization is: cutting crystal plane (100), cutting speed 200 m / s, tool rake angle -5°, and relative tool sharpness 0.

2.

6. The method for simulating and analyzing subsurface damage in single-crystal silicon nano-cutting according to claim 1, characterized in that, In the study on the influence of subsurface damage depth on the mechanical properties of processed single-crystal silicon, the nanoindentation simulation results show that the residual compressive stress in the damaged layer increases the surface hardness with the increase of relative tool sharpness; the uniaxial tensile simulation results show that the damaged layer reduces the Young's modulus and tensile strength of the workpiece.

7. The method for simulating and analyzing subsurface damage in single-crystal silicon nano-cutting according to claim 1, characterized in that, The method was verified by nano-scratching experiments, with a normal load of 20-100 mN and a scratching speed of 30 μm / s.

8. The method for simulating and analyzing subsurface damage in single-crystal silicon nano-cutting according to claim 1, characterized in that, The method described is applicable to the simulation analysis of subsurface damage in similar hard and brittle materials such as single-crystal silicon carbide, and the simulation results have an error of less than 5% compared with the experimental results.

9. The method for simulating and analyzing subsurface damage in single-crystal silicon nano-cutting according to claim 1, characterized in that, The method uses the molecular dynamics simulation software LAMMPS for atomic-scale simulation calculations and combines it with OVITO software for atomic structure visualization analysis.

10. The method for simulating and analyzing subsurface damage in single-crystal silicon nano-cutting according to claim 1, characterized in that, The specific implementation steps of the method also include: The system is relaxed by minimizing energy, and a Berendsen thermostat is used for temperature control in the NVE ensemble. When simulating the nano-cutting process, the temperature of the isothermal layer is controlled under the NVT ensemble, and the atomic behavior of the Newtonian layer atoms is observed under the NVE ensemble during the cutting process. A nanoindentation simulation model was established. A spherical diamond indenter was pressed into the processed surface at a speed of 200 m / s, and the load-displacement curve was recorded to calculate the surface hardness. A uniaxial tensile simulation model was constructed, and a tensile speed of 100 m / s was applied to the machined workpiece. The stress-strain curve was monitored to obtain Young's modulus and tensile strength data.

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