Laser Formation of Holes in Nonmetallic Substrates

The use of a pulse picosecond laser with a wavelength of 532 nm and frequency of 15 Hz in the formation of holes with diameters up to 0.1 mm in nonmetallic substrates (silicon, ceramics, etc.) was proposed. It was found by modeling in MathCAD and COMSOL Multiphysics that the half-angle value of the light cone aperture that depends on the focusing of laser radiation exerts a significant effect on the depth and diameter of holes in laser processing. The influence of the regimes of laser processing employing nanosecond and picosecond lasers with wavelengths of 1064 and 532 nm, respectively, on the conicity and time of formation of holes in silicon substrates was investigated. The preliminary heating of the substrate to 170–200°С reduces the time of formation of the holes by 20%.


INTRODUCTION
The motive tendency in microelectronics is a trend to produce more and more complicated and functional products in miniature volumes of substrates, boards, or cases. This can be reached due to the maximal miniaturization of components and shortening of interconnections, increasing of limiting working frequencies, parallelization of the information processing systems in a single device, transition from flat to 3D structures, etc. Integration of systems is accomplished using multichip modules, 3D integration systems, or vertical system integration (VSI) that is characterized by a high density of leads passing through holes in silicon crystals. The VSI technology involves the following stages: (1) formation of holes by the method of laser drilling or reactive ion etching, (2) filling of holes by a conductive material using metallization or chemical deposition, (3) wiring with superposition of plates (superposition and wiring), and (4) thinning of the plates to separate crystal assemblages (polishing or etching).
The method of formation of through holes possesses a range of advantages over the method of assembling of crystals on a plate. Among them can be noted a greater density of wiring, better functionality, superior characteristics (parallel leads, minimal length of connections, interconnections do not limit the speed of signal propagation), lower energy consumption, and end product cost [1]. However, it is extremely difficult at present and sometimes impossible to produce holes of the necessary diameter whose quality level is in compliance with the technological requirements using traditional drilling.
The laser processing of holes is one of the promising methods for manufacturing such holes. Under the action of a laser radiation pulse, the hole is formed due to the melting and evaporation of the material. The high quality of holes is ensured at drilling of evaporated nonmetals where a liquid phase is virtually absent when they are disintegrated under the action of laser radiation. The main method of increasing of the accuracy and quality of laser dimensional processing is a multipulse processing when holes in the material are formed as a result of a series of laser radiation pulses with a specified energy and duration that sequentially bring up the holes to the necessary dimensions.
Nowadays, one of the most important applications of laser technology is utilization of laser microcutting in technological processes of manufacturing of silicon and gallium arsenide substrates with coatings deposited on them, sapphire substrates with the thickness of 90 μm; millions of them are manufactured and used in powerful light-emitting diodes, aluminum nitride substrates used as radiators, and those of gallium nitride used in laser diodes [2].
Three kinds of lasers are most widely used for processing materials: solid-state yttrium aluminum garnet with neodymium (YAG:Nd) lasers, solid-state neodymium glass (glass:Nd) lasers, and molecular (gas) carbon-dioxide CO 2 lasers. Sold-state lasers possess the following advantages: high specific radiation power, high efficiency that amounts to 20% (with diode pumping), high energy (up to kJ/pulse), wide wavelength range, wide range of pulse durations (from 10 -2 to 10 -14 s), and the possibility of generating ultrashort pulses (down to 4 fs) [3].
The peculiarities of gas lasers are determined by the properties of the active medium whose density varies within a wide range; the pressure varies from 1.3 × 10 -6 to 10 5 Pa. The gas lasers allow one to obtain extremely narrow and stable generation lines. The low density of the active medium defines the small temperature variations of the refractive index. This makes it possible to obtain comparatively easy extremely low divergence of radiation close to the diffraction limit.
The redistribution of the liquid phase before the solidification moment plays an important role in the formation of holes when the melting material is processed by a single pulse. As a result, the hole shape can considerably differ from the shape that was defined at the pulse end moment by the ray geometry, kinetics of evaporation, and the hydrodynamics of ejection of the part of the liquid phase material.
The main processes that lead to the creation of holes in materials while using laser radiation are evaporation and melting of the substance. The hole's depth increases due to evaporation; its diameter increases due to melting of the walls and displacement of the liquid by excessive vapor pressure. When the laser radiation interacts with the surface of the material, a part of the radiation is absorbed and dissipated by the disintegration products. To obtain the through holes with the specified geometry and quality in nonmetal materials, the optimal parameters of the laser process should be defined: the power density, laser pulse repetition rate, laser beam diameter, and the pulse quantity.

MODELING OF THE LASER FORMATION
OF HOLES When a laser radiation beam impinges on the material's surface a part of radiation reflects from it, and a part penetrates the materials and is absorbed in it. The propagation of radiation in the substance is described by the Bouguer law: (1) where q(х) is the density of the radiation power in the substance at a distance х from its surface, q 0 is the density of the radiation power, R is the reflection index of the surface, α is the attenuation index of the radiation in the substance.
The laser micromachining of materials by laser radiation make certain demands on such parameters of the radiation source as the wavelength λ, angular divergence θ, and pulse duration τ p [4]. The active area defined by the minimal dimensions of the laser beam d in the lens focus is linked with the radiation wavelength by the relationship where f is the focal distance of the lens, D п is the diameter of unfocused laser beam, and M 2 is the beam propagation constant that characterizes the difference of the real laser beam from an ideal Gaussian beam with minimal diffraction divergence where w 0 is the Gaussian beam's radius-the radius in the point where the intensity diminishes to 1/e 2 or 0.135 from its value on the axis. Therefore, the shorter wavelength and smaller angular divergence values favor the possibility to focus the radiation and to provide the minimal possible dimensions of the active area. For longer pulses, the heat-affected area is equal to (4) where а is the thermal diffusivity that depends on the material's thermophysical properties.
The radiation energy Е falling to the surface S normal to the direction of radiation propagation is defined by the relationship (5) where Р is the radiation power, q is the radiation power density, and t is the duration of the radiation action.
During the formation of holes, the properties of the treated material substantially define the laser parameters that are needed to perform this operation. For the processing, pulse lasers are used that can work both in the regime of free-running lasing with the pulse duration of the order of 1 μs and in the regime of modulated Q-factor with the duration of several tens of nanoseconds. In both cases, the thermal action on the material and its melting and evaporation from the action area occur.
The model of kinetics of hole formation in nontransparent materials ( Fig. 1) is currently developed sufficiently thoroughly, and it provides the formulas [5] that defines the depth of the hole h and its radius where r 0 is the inlet radius of the hole, r 0 = D 0 /2; r is the outlet radius of the hole (D = 2r); is the averaged radiation energy of the pulse optical quantum generator (OQG), P is the laser's power; t is the duration of the action; Е i is the energy of a single pulse; γ is the half-angle of the light cone aperture: γ = θ/2; and L 0 is the specific evaporation energy of the material.
As a rule, the share of melt in the disintegration products diminishes in the multipulse regime of processing. This regime is used to manufacture high-precision or extremely deep holes. In essence, this is the regime of processing employing a series of short pulses with microsecond or nanosecond duration.
Analyzing Eqs. (6) and (7), one can demonstrate that, at the initial stage of the hole formation (h ! r 0 ), its depth increases linearly with time due to the material's evaporation over the area of the light spot, like in the one-dimensional model of quasi-stationary evaporation, though its diameter only slightly changes. Over the course of time, the hole growth rate in depth slows down. In the limiting case (t → ∝) its depth and radius increase proportionally to t 1/3 ; therefore, the hole's shape does not change. However, the values of h and D largely depend on tan γ that characterizes the light cone angle generated by the optical system. As a parameter specific for this process, one can use the conicity of the hole (8) Modeling of the diameter of holes at laser processing of silicon substrates employing a MathCAD software allowed us to obtain the dependences of the hole's outlet diameter versus the radiation energy of pulse OQG and the half-angle of the light cone aperture for various starting values of the diameter D 0 and initial data ( Table 1).
The expression that describes the dependence of energy for various values of the diameter of the radiation spot on the surface of the processed material is as follows (9) where d is the diameter of the spot of the focused radiation.
The dependence of the laser energy in the processing area versus the process duration and beam diameter is presented in Fig. 2. It shows that the energy falling to the treated material linearly depends on the radiation duration. When the diameter of the radiation area increases the energy increases exponentially, and it amounted to 1. Therefore, it is necessary to diminish the half-angle γ values to obtain a hole with smaller conicity. However, manufacturing of deep narrow holes is a substantially complicated problem that can be simplified in a limiting case when tan γ = 0.
At the initial stage of the hole formation process when h(t) < D(t) the hole depth h increases linearly with time, and the diameter D remains constant. The hole growth in depth then slows down; on the contrary, its diameter begins to increase dependent on the energy and the radiation spot (Fig. 5). At this stage of the hole formation, one should take into account the  Half-angle of the light cone aperture, γ 0-0.7 mrad motion of the melt and the relative arrangement of the material surface and focused radiation beam. However, a fundamental feature of the laser radiation action in a very fast pulse regime is that the heat generated in the material by the radiation has not enough time to leave the radiation area during the laser pulse. The laser pulse duration is shorter than the time of the thermal diffusion. At the high specific power in the radiation area, the process of laser ablation is accompanied by the evaporation of the material escaping the melting stage [6]. With these assumptions, the time needed to form a hole in the substrate amounts to (10) ( ) For the modeling, we adopted the following values: r 0 = 0.05 mm, γ = θ/2 = 0.2 mrad, h = 250 μm. We did not take into account the influence of the wavelength on the duration of the hole formation. It is shown in Fig. 6 that the time of the hole formation nonlinearly depends on the laser pulse energy.

EXPERIMENTAL
The choice of technological regimes for formation of holes employing laser beams is based on the account for the properties of the treated material-its absorption coefficient and reflectivity at the specified wavelength of laser radiation that define the process of energy absorption; specific heat conductivity and temperature conductivity, heat flux in the material, density, specific thermal capacity, latent heat and phase transition temperature, and energy intensity of the While choosing the regimes one should take into account the influence of the energy and temporal characteristics of the laser radiation [7]. For laser formation of holes in silicon substrates, laser installations manufactured by LOTIS TII company with wavelengths 1.06 μm and 532 nm, pulse duration within the range of 80-15 ns, and pulse repetition rate of 15 Hz were used. A solid-state yttrium aluminum garnet with neodymium laser LS-2151 (Nd:YAG) with active mode locking in МОРА-configuration, separate control of the pumping level of a monoblock driving generator and amplifier, autonomous cooling system with a water-air heat exchanger, thermal stabilization of electrooptical elements, mode locking and second harmonic crystal, built-in second harmonic (SH) generator, and photosensors of the driving generator, amplifier, and SH generator with energy indication in the control program screen was used [8].
The optical system formed the spatial characteristics of the beam as a processing tool. The focus distance amounted to 150 mm. For focusing of the optical radiation and centering of the optic system, a lowpower gas laser was used; its radiation was introduced in the optical system of the laser radiation formation using a semitransparent mirror.
For positioning of manufactured items, a coordinate table with two degrees of freedom and accuracy of ±0.01 mm was used. The laser and coordinate table were controlled by a computer. The laser was switched off using a control unit with a photosensor located under the substrate. The silicon substrate was placed on an annular support mounted on the coordinate table. The radiation power instability did not exceed 3.5%; at the radiation divergence of 0.4 mrad, the instability of the dimensions of radiation area on the substrate surface did not exceed 2%. During the exper-iments the beam diameter varied within a range of 0.1-0.2 mm (1 mm = 70 arbitrary scale divisions), and the rate of substrate motion was 7-10 mm/s. The quality of the through holes was evaluated using a microscope with magnification of 32×.
To control the power of laser radiation, a radiation power meter LabMax-Top (COHERENT company) with EnergyMax sensors was used that allowed us to control the radiation with wavelengths within 190 nm to 12 μm, power measurements from nanowatts to kilowatts, and energy from nanojoules to joules at the frequency of pulses up to 10 kHz.

RESULTS AND DISCUSSION
The process of laser formation of holes was investigated using a radiation spot diameter of dt rs = 0.1 mm, inlet hole diameters in the range within 0.1-0.12 mm, and the silicon substrate thickness of 250 μm. The power of a nanosecond laser LS-2145 with a wavelength of 1064 nm was in the range of 40-100 mW. The power of a picosecond laser LS-2151 with a wavelength of 532 nm varied within the range of 5.6-22 mW.
A picosecond laser with a wavelength of 532 nm allows one to reduce the processing time if compared with a nanosecond laser. When radiation of a picosecond laser that creates a radiation power density of q = 10 11 W/cm 2 is used, the concentration of free electrons on the surface of the material substrate reaches N 1 0 22 cm -3 . Under the action of radiation in the processing area the electrons acquire the energy and transfer to various levels of the conduction band; then the acquired energy transforms into the thermal energy.
The influence of the laser wavelength on the duration of laser formation of holes in silicon and ceramics was investigated using picosecond lasers with wave-  (Fig. 7). It was stated that, at the same duration t = 3 s for hole formation, one should spend the energy of 100 mJ using laser radiation with a wavelength of 1064 nm, but it should be a factor of ten lesser (approximately 10 mJ) using a laser with wavelength of 532 nm. At the same radiation energy, a laser with a wavelength of 532 nm reduces the duration of formation of a hole by approximately a factor of two. Application of a picosecond laser with a wavelength of 532 nm is more efficient since this not only reduces the processing time but also improves the quality of the hole formed in the silicon substrate; furthermore, the area of thermal action decreases by 30-40% (Fig. 8).
The parameters of formation of holes using a nanosecond laser in silicon substrates with a thickness of 250 μm are presented in Table 2. Note that, at the wavelength of 532 nm, the quality of the holes improves when the radiation power increases up to 100 mW. The conicity of the holes at a power of 40 mW amounted to 0.168, then it decreased by 25% at the power of 100 mW. At the wavelength of 1064 nm when the power increased from 40 to 100 mW, the conicity increased by approximately a factor of three.
Formation of holes using a LS-2151 picosecond laser in comparison with a nanosecond laser provides the possibility to make holes with minimal conicity at lower radiation energy (Table 3).
Heat transfer into the substrate material plays an important role in laser processing. A decisive factor that defines the heat transfer rate and structure of the material is the initial material temperature. Therefore, to improve the quality and efficiency of laser processing, one should take into account the influence of the initial temperature of the substrate on the duration of laser formation of holes. To investigate the influence of heating on the process of laser formation of holes, we proposed a preliminary heating of nonmetallic substrates to a specified temperature. It is supposed that, at the optimal duration for the specified substrate thickness, the area of the hole that is formed in the nonmetallic substrate with a higher initial temperature will reach greater values than for unheated holes. The following conditions were investigated: (1) the temperature of IR heater 700-750°C; (2) the rate of the substrate heating 3-5°C/s;  The results are presented in Table 4. Note that the processing time of the holes with preliminary heating reduced; the hole area of 0.55 mm 2 was reached within 40-45 s on the heated substrate and within 50 s without heating.
However, one should also investigate the influence of the preliminary heating of the geometry of holes, that is, their conicity, for optimization of the process. The appropriate choice of the processing regimes allows us to transition from manufacturing of rough holes to the formation of clean-cut holes with the accuracy of dimensions up to the 7-grade quality class.

CONCLUSIONS
It was proposed to use a pulse picosecond laser with wavelength 532 nm and repetition frequency 15 Hz to form holes with diameters up to 0.1 mm in nonmetallic surfaces: silicon, ceramics, etc. This allowed us to reduce the duration of processing by a factor of two and decrease the area of thermal action by 30-40% in comparison with a nanosecond laser.
The dependences of the conicity of the holes versus the energy and the diameter of the laser radiation spot were obtained using the modeling of parameters of laser formation of holes in silicon substrates employing MathCAD and COMSOL Multiphysics. It was stated that the value of the angle γ that depends on the focusing of laser radiation significantly influences the depth and diameter of the holes at laser processing in silicon substrates. When the radius of laser radiation decreases, the heating temperature in the processing area increases due to the higher concentration of radiation energy.
The method of laser formation of holes in nonmetallic substrates using an IR heater for preliminary heating of nonmetallic substrates up to 170-200°С was developed; this reduces the duration of hole formation by 20%.