The importance of wavelength for tight temperature control during μ-laser-assisted machining

The area of single point diamond turning of brittle materials like semiconductors and ceramics is significantly benefitted by incorporation of laser assistance. In a new developmental technology that is now recognized as micro-laser-assisted machining (μ-LAM), a laser is shone through a diamond tool to soften the high-pressure phase transformed ductile machining phases that in turn allows thermal softening and thereby enables a higher material removal rate during ductile mode machining. One of the lasers currently used in μ-LAM is the neodymium-doped yttrium aluminum garnet (Nd:YAG) laser operating at 100 W (continuous wave) at the wavelength of 1064 nm. Although this configuration has worked to the benefit of the technology, here we report futuristic developments that will significantly enhance temperature control by selecting a laser wavelength according to the material being machined, allowing tunable machining properties. The concept is illustrated with sample calculations for μ-LAM of silicon, and it appears to offer better target temperatures, thus enhancing the performance of the μ-LAM process.


Introduction
In pursuit of overcoming the challenges of machining difficult-to-machine materials, laser assistance during mechanical micromachining has been adopted worldwide. To date, seven major patents (in 1982 1 , 2006 2 , 2007 3 , 2011 4 , 2014 5,6 , 2017 7 and references therein) have been granted in the USA concerning the use of laser assistance during mechanical micromachining. While these patents fall in the category of thermally assisted machining (TAM), of particular interest is the patent on micro-laser-assisted machining (µ-LAM). 3 The concept of µ-LAM is quite unique in the sense that the laser beam is passed through the diamond tool itself (Figure 1). This approach exploits the fact that the diamond tool is transparent in the near infrared (IR) region of the spectrum, as are the atmospheric phases of the brittle materials (workpiece of silicon, tungsten carbide, etc.). However, it is established from the previously published literature on the topic that the amorphous phases generated in the cutting zone are not transparent to the laser. This allows precise and selective heating of the plastically deformed cutting zone, where ductile amorphous phases are generated by the virtue of high-pressure phase transformation. 8 When compared to other TAM processes, the µ-LAM approach avoids problems such as oxidation of the material, thermal damage, as well as other sorts of energy losses due to convection and radiation.
Consequently, the absorption of the IR by the high-pressure phases (exhibiting a metallic conductive nature) helps to achieve higher stock removal rates by an increase in the undeformed critical chip thickness. Reported values of the preferred parameters for laser power is in the range of 8 mW to 100 W (of which 40% is transmitted into the workpiece) and the preferred tip or edge radius of the tool is about 20 nm to 12 µm. Other advantages of µ-LAM are reduced surface roughness, which Mohammadi et al. (2015) found when turning silicon. More recently, the technique is being proposed to be capable of machining stainless steel almost at the traditional speeds of single point diamond turning (SPDT) process, thereby being more productive than techniques like ultrasonic elliptical vibration-assisted machining where the speed of cutting needs to be lowered significantly. 9 Neodymium-doped yttrium aluminum garnet (Nd:YAG) lasers (1064 nm) are often used in µ-LAM because of ease of installation as the laser can be taken to the source through a fiber optic cable. The selection of laser wavelength is critical because it determines the amount of heating that is caused in a given material, some materials absorbing more heat at a given wavelength and some less. It is also noteworthy that the absorptivity of the material changes as a function of material temperature, so the rate of heating changes continuously with time as the material being cut heats up primarily not only because of laser heating but also because of the cutting heat flux generated in the cutting zone due to plastic deformation of the material. Because of this, most materials display exponential heating so that heating is effectively limited within a given range to avoid extreme heating, which would result in melting of the material or combustion. This aspect, however, does not seems to be paid attention to in the experimental implementation of µ-LAM and in this article, we share our views on how this additional knowledge of laser-matter interaction may benefit this technology further.
It is to be noted that silicon like most other materials absorbs more heat at increased temperatures that can be explained by the relation of its electronic and optical properties. At wavelengths close to 294 nm, however, the absorptivity actually decreases as the temperature increases, thus limiting any attainable benefit by µ-LAM in this regime. 10 We postulate that there exists a specific threshold temperature beyond which no further heating takes place when exposed to laser. It is suggested that this concept could be used to set temperatures for materials cut by µ-LAM, by selecting lasers with most appropriate wavelengths so that the energy expenses incurred during laser heating are optimum.
In this article, this concept is illustrated with reference to silicon, which is a well-studied machinable material in ultraprecision machining. In our calculations, we also show that in addition to the heating time that the substrate should take, the depth at which the heating is taking place confirms that the heating penetrates deep enough into the substrate to make a significant contribution.

Analysis
The relevant formulae for the calculations for heating of silicon are shown in this section. A material's surface temperature increase can be calculated according to the formula 11 : where T is the temperature (°C) of a material to be calculated at an initial temperature (T 0 ), α is the absorptivity (/m), q is the power density (W/m 2 ), t is the laser dwell time (s), R t is the reflectance, ρ is the density (kg/m 3 ), and C p is the specific heat capacity (J/kg K).
Absorptivity in turn is given by the formula: where α is the absorptivity (/m), n is the material's refractive index, k is the extinction coefficient, and λ is the wavelength of the light (m).
The refractive indices n and k are dependent on the temperature expressed by the formulae 10 : where T 0 is the base temperature (300 K), ΔT is change in temperature, and c n and c k represent the change in refractive index with temperature.
Green et al. 10 provided values of refractive index and extinction coefficient for silicon at various wavelengths, and the rate of change for the values (see Appendix 1). The refractive index and the value of extinction coefficient of silicon at a fixed temperature of 300 K (Figures 2(a) and 3(a)) and the coefficients for temperature dependence (Figures 2(b) and 3(b)) are presented. A significant difference in the value of refractive index and extinction coefficient, affecting the absorptivity, can be predicted at an elevated temperature. Taking this data, Figure 4 was obtained that shows that the absorptivity of silicon is indeed strongly dependent on the temperature. A change of sign in absorptivity of silicon was noted close to 0.29 to 0.31 µm for the calculations performed by assuming the silicon to be heated by 1110 K (which compares well to a melting temperature of 1140 K of silicon).    Formula 1 was then used to calculate the temperature absorbed incrementally by silicon (see Figure 5) assuming that the heating was done by a 1 W laser. It is evident that the heating to the target temperature of 1375 °C occurs within a timespan of about 14 ns and no further heating occurs thereafter as the absorptivity becomes negligible.
We next focus our attention on the depth of heating which is influential in deciding the depth of material being removed. The depth of absorption is the inverse of absorptivity and is given by the formula: where λ is the wavelength (m), n is the refractive index at that wavelength, and k is the extinction coefficient at that wavelength.
The equation reveals that for silicon, the depth of heating at 1375 °C is only about 200 nm. As the depth of heating is small, the following conductive heat transfer formulae were used: where Q is the heat transfer, k is the thermal conductivity, C P is the specific heat capacity, T HOT is the higher temperature, T COLD is the lower temperature, t is the time, d is the distance between the two points, and T is the temperature.
The parameters used to verify the heating of silicon are listed in Table 1.
Using the equations and Table 1 parameters, it can be shown that within 560 ns (which compares well with typical speed at which the laser moves during µ-LAM, considering the focal spot of the laser and its cutting speed), it is possible to heat a cube of 7 µm sides to the temperature of 1400 °C, indicating that the shallow depth of laser absorption may not be prohibitive.

Conclusions
This article sheds light on a possible improvement in the area of µ-LAM, which is an advancement to the SPDT process. As the analysis demonstrates, there seems to be potential for controlling temperature in µ-LAM by selection of the right laser wavelength according to the material's absorptivity. It seems that the temperature in actual experimentation must be significantly greater than those reported in prior experimental trials (1038 °C 14 ). It appears to be a way forward to achieve a consistent temperature in the cutting zone by more predictively using the laser parameters. It is difficult to predict the increased advantages that higher substrate temperature would provide, but Ravindra 14 identified from his studies that the optimal temperature is that closest (just below) the melting point achievable, so this technique may further facilitate that approach. It would be desirable to carry out experimental trials in which the effectiveness of the technique could be properly evaluated, although unfortunately there is not yet sufficient experimental information available, using even robust techniques like IR imaging or thermocouples to get the exact assessment of temperature in the cutting zone in µ-LAM.

Declaration of conflicting interests
The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding
This work was carried out in the Centre for Doctoral Training in Ultra-Precision, which is supported by the UKRI