**2.1. Heuristic equation and its correlation with the physical properties of the irradiated substrate**

Since the description of the different regimes observed in the ablation process was found to be a logistic function of the laser fluence, an ad hoc plasma detector was designed based on the works of Bredicce et al. [34] and M. Villagrán et al. [7]. This device, the working principles of which are detailed in reference [30], was used to detect the plasma during the machining. We found that for c-Si, the maximum value of the recorded signals was proportional to the amount of extracted material in each laser shot during the ablation regime according to references [7, 34]. **Figure 2** shows a plot of the induced electric signal maximum amplitude as a function of the incident fluence for c-Si and c-Si + SiO2(2400).

**Figure 2.** Amplitude of the electric signal versus laser fluence fitted by the logistic function of Eq. (1). (a) For c-Si and (b) for c-Si + SiO2(2400) along with the values of the fitting functions' parameters.

The results were fitted with the heuristic function described by the following Eq.(1) that relates its parameters to the physical properties of irradiated substrates [34]:

$$M\_J\left(\mathcal{Q}\right) = \left[\frac{A\_1\left(\mathcal{Q}\right) - A\_2\left(\mathcal{Q}\right)}{1 + \left(\frac{\mathcal{Q}}{\mathcal{Q}\_c}\right)^{S\_c}}\right] + A\_2\left(\mathcal{Q}\right) \tag{1}$$

where:

*MJ* (∅) is the amount of material removed per pulse which is proportional to the electric signal. Its units are [mass/(area)(time)], and it is a function of the laser fluence.

∅ is in the laser fluence in mJ/cm<sup>2</sup> .

*A*1 and *A*<sup>2</sup> represent the lower and higher plateau values related to the onset of the absorption and ablation regimes, respectively. Their units are [mass/(area)(time)].

*SC* is a dimensionless fitting parameter related to the surface roughness.

**∅***<sup>C</sup>* is the critical fluence. Its value indicates the onset of the true ablation process, that is, the fluence value from which on the material removal occurs mainly through ablation. For example, values of ∅*C* = 127 mJ/cm2 and ∅*C* = 139 mJ/cm2 were found for c-Si and c-Si + Si2O(2400), respectively (**Figure 2**).

Two plateaus were found for c-Si coated with thin films <1 μm. We postulated that these values indicated whether the laser radiation had reached the substrate or not. **Figures 3** and **4** show the results obtained for two different thicknesses of two kinds of films: c-Si + Si3N4(70) and c-Si + Si3N4(350), and, c-Si + SiO2(110) and c-Si + SiO2(220), respectively, along with the param‐ eters' values.

**Figure 2.** Amplitude of the electric signal versus laser fluence fitted by the logistic function of Eq. (1). (a) For c-Si and

The results were fitted with the heuristic function described by the following Eq.(1) that relates

( ) ( ) ( ) ( ) 1 2

é ù ê ú ê ú Æ- Æ Æ = ê ú + Æ ê ú æ ö Æ <sup>+</sup> ç ÷ ê ú ë û è ø Æ

*A A M A*

*C*

(∅) is the amount of material removed per pulse which is proportional to the electric signal.

*A*1 and *A*<sup>2</sup> represent the lower and higher plateau values related to the onset of the absorption

**∅***<sup>C</sup>* is the critical fluence. Its value indicates the onset of the true ablation process, that is, the fluence value from which on the material removal occurs mainly through ablation. For

1 *<sup>C</sup> J S*

Its units are [mass/(area)(time)], and it is a function of the laser fluence.

.

and ablation regimes, respectively. Their units are [mass/(area)(time)]. *SC* is a dimensionless fitting parameter related to the surface roughness.

2

(1)

(b) for c-Si + SiO2(2400) along with the values of the fitting functions' parameters.

where:

438 Radiation Effects in Materials

∅ is in the laser fluence in mJ/cm<sup>2</sup>

*MJ*

its parameters to the physical properties of irradiated substrates [34]:

**Figure 3.** Amplitude of the electric signal versus laser fluence fitted by the logistic function, Eq. (1) for Si3N4 thin films thicknesses deposited with the EPCVD technique on monocrystalline silicon: 70 and 350 nm. The parameters of the logistic function are shown too.

The fits show that the effect of the film is to change the surface roughness. This is evidenced by the value of the Sc parameter. The larger the value of this parameter, the lower is the roughness of the surface [7]. Thus, the film acts as a filter until the critical fluence, **∅** *<sup>C</sup>*, is reached. At that moment, the material is ejected from the surface through ablation and generates a nanostructure on the substrate.

**Figure 4.** Amplitude of the electric signal versus laser fluence fitted by the logistic function, of Eq. (1) for two silicon dioxide thin films thicknesses deposited with the EPCVD technique on monocrystalline silicon: 110 and 220 nm. The parameters of logistic function are shown too.

#### **2.2. Nanostructuring and nanoparticles manufacturing or generation**

#### *2.2.1. Nanostructuring on monocrystalline silicon (c-Si)*

Nanostructuring on c-Si was observed during the manufacture of prototypes of nanopores and micro-cavities used as molecules' detectors, drug-delivery control, 2D microstructures, replication matrices, etc. in biological applications. These devices were manufactured using the following techniques in the specified order: (1) laser ablation micromachining (one laser shot cavities), (2) selective chemical attack, and (3) ultrasound cleaning (sonication) [35, 36]. The c-Si nanostructuring was observed after the ns laser pulse impacts on the c-Si + Si3N4(370) sample. The cavity formed and its nanostructured base can be observed in the SEM (scanning electron microscope) micrographies shown in **Figure 5**. c-Si nanostructuring has been reported in the literature only with sub-picosecond laser pulses [36–38]. The nanostructures produced in the irradiated zones reduce the reflection of the silicon surface. This effect would be of great interest in the manufacture of silicon photovoltaic cells.

**Figure 5.** c-Si + Si3N4(370) nanostructuring obtained with a ns laser pulse (Nd:YAG, 8 ns, 532 nm). (a) Complete cavity. (b) Magnification of the cavity base.

Nanostructuring was also observed in the machining of a micro-chromatographic column in a c-Si + Si3N4(50) commercial wafer [30]. The roughness of the grooves, inherent to the c-Si laser interaction—was found to be very useful to increase the sample concentration. The microcolumn was manufactured as a sequence of straight lines. Part of this micro-chromatographic column and the roughness of the walls of the grooves is shown in **Figure 6**. The larger channels' depth was 50 μm. Devices used for separating substances require roughnesses similar to those of the sample's channels [39].

**Figure 4.** Amplitude of the electric signal versus laser fluence fitted by the logistic function, of Eq. (1) for two silicon dioxide thin films thicknesses deposited with the EPCVD technique on monocrystalline silicon: 110 and 220 nm. The

Nanostructuring on c-Si was observed during the manufacture of prototypes of nanopores and micro-cavities used as molecules' detectors, drug-delivery control, 2D microstructures, replication matrices, etc. in biological applications. These devices were manufactured using the following techniques in the specified order: (1) laser ablation micromachining (one laser shot cavities), (2) selective chemical attack, and (3) ultrasound cleaning (sonication) [35, 36]. The c-Si nanostructuring was observed after the ns laser pulse impacts on the c-Si + Si3N4(370) sample. The cavity formed and its nanostructured base can be observed in the SEM (scanning electron microscope) micrographies shown in **Figure 5**. c-Si nanostructuring has been reported in the literature only with sub-picosecond laser pulses [36–38]. The nanostructures produced in the irradiated zones reduce the reflection of the silicon surface. This effect would be of great

**2.2. Nanostructuring and nanoparticles manufacturing or generation**

parameters of logistic function are shown too.

440 Radiation Effects in Materials

*2.2.1. Nanostructuring on monocrystalline silicon (c-Si)*

interest in the manufacture of silicon photovoltaic cells.

**Figure 6.** SEM micrographies of (a) the c-Si sample surface after machining. (b) Magnification of part of the machined channels to show the deeper channels. In order to observe the roughness of the channel's wall, the sample's surface was placed forming an angle of 20° with electron beam.

Finally, microstructures and nanostructures were obtained on the walls of cylindrical and conical cavities. For this purpose, the machining station was used with either both percussion and trepanning drilling modes.

In the percussion drilling mode, the laser pulse always impacts in the same sample's area removing material until the desired depth is reached. Grooves of several microns width are obtained as can be seen in **Figure 7a**.

In the trepanning technique, a rotating movement is generated by applying sine wave voltages to the piezoelectric motors with coordinate phases associated to the XY axis of the positioning system. This circular nanometric movement produces a sand-down effect which decreases the drilled cavity walls' roughness. The misalignments of the laser beam focusing system as well as the beam's inhomogeneities are averaged and holes with controlled walls' shapes and roughness can be drilled. As a result, well-controlled circular holes with sub-micrometric structures on the wall can be drilled.

The SEM micrographies of **Figure 7** show cavities drilled on a sample of c-Si + Si2O(300) with different number of laser pulses of 110 mJ/cm2 . A drilling performed with 2400 pulses with the percussion method can be seen in **Figure 7a**. The grooves on the walls and the debris can be also observed. The debris tower several microns over the silicon surface. A cavity drilled by trepanning with 200 pulses is presented in **Figure 7b**. Marks left by single pulses can be also seen on the sides. In this case, the field of view of electronic microscope allows observing the cavity bottom. Micrography (**Figure 7c**) corresponds to a cavity drilled by trepanning with 2000 laser pulses, the bottom of which can no longer be seen due to its depth. The walls of the cavities of **Figure 7b,c**, show the typical smoothness of the trepanning mode.

**Figure 7.** SEM micrographies of (a) c-Si wafer drilled by percussion with 2400 pulses. The sample was inclined 45° to observe the cavity's walls were grooves of ~10 μm are seen. (b, c) Micrographies of cavities drilled by trepanning with 200 and 2000 pulses, respectively. The effect of increasing the laser pulse number for a fixed sample-lens distance and a laser fluence of 110 mJ/cm2 can be compared. A sine wave voltage of 10 V and 3 Hz was applied to the piezoelectric motors.

### *2.2.2. Nanostructuring in metals*

The micromachining experiments in metals were performed with the machining station of **Figure 1**. Nanostructuring on the surface of the devices machined on metallic substrates was observed by electronic microscopy [30]. In this section, the most relevant results obtained are presented.
