# Multiphoton-initiated laser writing of semiconductors using nanosecond mid-infrared pulses

Pol Sopeña, Niladri Ganguly, Gabriel Spühler, Andrei Selivanau, David Grojo

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Pol Sopeña, Niladri Ganguly, Gabriel Spühler, Andrei Selivanau, David Grojo. Multiphoton-initiated laser writing of semiconductors using nanosecond mid-infrared pulses. Optics and Laser Technology, 2024, 179, pp.111419. 10.1016/j.optlastec.2024.111419. hal-04638380

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Submitted on 8 Jul 2024

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Full length article

# Multiphoton-initiated laser writing of semiconductors using nanosecond mid-infrared pulses

Pol Sopeña<sup>a, *</sup>, Niladri Ganguly<sup>a</sup>, Gabriel Spühler<sup>b</sup>, Andrei Selivanau<sup>b</sup>, David Grojo<sup>a</sup>

## ARTICLE INFO

**Keywords:**

- Laser processing
- Semiconductor
- Germanium
- Silicon
- Mid-infrared
- Nanosecond

## ABSTRACT

The advent of more powerful mid-infrared nanosecond laser sources allows using them as attractive tools in material laser processing. For semiconductor bulk processing, laser intensities must remain modest to avoid detrimental nonlinear propagation and pre-focal plasma screening effects. Accordingly, nanosecond pulses are usually appropriate to locally initiate energy deposition by multiphoton absorption and subsequent modification, hardly achievable with ultrashort pulses. Employing a 2.8-µm 2.5-ns laser source, we explore the possibility to modify silicon and other semiconductors. With interactions initiated by three-photon absorption, we modify and determine the surface and bulk modification thresholds of Si, GaAs, and InP. For Si, compared to previous studies at telecom wavelengths, we report on a reduction of the energy threshold for volume modification with processing depth, and repeatable rear-surface modifications. Compared to Si, we find for GaAs and InP important fluctuations in the modification responses, which we attribute to an absorption mechanism initially triggered by a greater presence of defects. We also study germanium, as this narrower bandgap semiconductor very interesting for mid-infrared electro-optical applications is transparent at the newly introduced wavelength. Despite the ability to modify the surface, the bulk of Ge remains inaccessible in this two-photon regime, mainly attributed to beam aberrations and nonlinearities. Nonetheless, we demonstrate the ability to process Si chips integrating Ge layers. All these results showcase the potential of mid-infrared wavelengths to offer new degrees of flexibility for 3D laser processing technologies turned to silicon photonics and microelectronics packaging.

## 1. Introduction

Compared to dielectrics, most common semiconductor materials, like silicon (Si), are opaque to the visible spectrum due to their narrow bandgap. Thus, laser sources from ultraviolet to near-infrared (NIR) are typically used to modify their surface [1,2]. In this spectral regime, femtosecond pulses, compared to nanosecond ones, have allowed performing extremely precise micrometric modifications thanks to the ignition of highly deterministic material responses and almost impossible thermal effects [3–5]. Capitalizing in this ultrashort regime and moving to wavelengths in the transparency window of semiconductors (i.e. 1.55 µm), three-dimensional (3D) writing applications are today envisioned. This relies on tightly focusing pulses so that high local intensities can be reached inside the materials to trigger confined multiphoton absorption and subsequent permanent modification. Nonetheless, the high refractive index and narrow bandgap in these situations respectively result in focusing limitations and strong

nonlinear energy delocalization and plasma effects inside the materials [6]. Consequently, the delivered intensities cannot exceed the modification threshold in most cases and so only non-invasive applications can be envisioned with ultrafast lasers [7].

In a quest to surpass this threshold, several studies have been carried out to reduce the apparent intensity causing detrimental nonlinear physical effects. These include hyperfocusing or temporal strategies with, for instance, the use of ultrafast train of pulses (burst mode) or longer pulses [6]. In the first approach, the proof-of-concept demonstration relied on interactions confined inside a silicon sphere, however, this approach remained limited as a practical implementation for equivalent solid-immersion focusing conditions would bring important technical complexities for large scale material processing [8]. Alternatively, with the temporal strategies, by relying on longer pulse durations in the pico- and nanosecond regime, the intensity and electron-plasma density can be decreased to significantly reduce strong absorption in the pre-focal volume and still induce sufficient multiphoton absorption

<footnote><sup>a</sup> Aix-Marseille Université, CNRS, LP3 UMR 7341, 163 Av. Luminy, 13009 Marseille, France</footnote>

<footnote><sup>b</sup> Glucoloop AG, Albisriederstrasse 203A, 8047 Zurich, Switzerland</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: pol.sopena-martinez@univ-amu.fr (P. Sopeña), david.grojo@univ-amu.fr (D. Grojo).</footnote>
to initiate local energy deposition for material bulk modification. With this approach, several practical demonstrations have been performed like waveguide inscription [9], the fabrication of Fresnel plates [6], or semiconductor laser welding [10].

With the aim to further improve the localization of interaction, another strategy could rely on the use of longer wavelengths up to the mid-wavelength infrared (MWIR) domain of the spectrum. Notably, the mid-IR opens the possibility to modify even narrower bandgap semiconductors like germanium (Ge), very interesting for optics and sensing applications in the IR. In this spectral region, we could trigger multi-photon absorption beyond two-photon (2P) regimes and increase, in principle, the nonlinearity of energy deposition for a better localization, limiting the formation of a pre-focal plasma. In this direction, some works claim to have achieved below surface modification. For instance, waveguides in Si were produced with 150 fs at 2.4 µm, but the produced structures remained very shallow (90–130 µm) and this work line was not pursued [11]. Also, using 160 fs at 4.6 µm, single-shot micro-modifications at a depth of 125 µm were achieved in Si [12]. However, the authors confirm a nanosecond pedestal with a 10⁻² energy contrast which despite being below the modification threshold could act as a precursor [13,14]. In addition, in a picosecond regime at 2 µm, below-surface modifications were also produced with performances similar to those reported at 1.55 µm [15]. In view of the laser parameters employed in these studies, the question of the potential benefits of mid-IR wavelengths is not fully addressed. Complex nonlinear propagation and electronic plasma formation still occur in the studied case, but we can reasonably expect the balance between effects to change largely with the wavelength [16]. Therefore, there is clear interest to understand the specificities of this rather unexplored spectral range for laser processing applications, and even more so in the nanosecond regime due to a lack of intense sources.

In an ever-rising industrial and scientific demand to cover all wavelengths and pulse durations for laser sources, in the last years a new generation of more powerful mid-IR nanosecond laser sources has appeared allowing to target applications in material processing, range finding, LiDAR, IR optical communication, 3D scanning, or spectroscopy [17]. Taking benefit on this, and with the aim to extend laser processing to a wider range of semiconductors and applications, in this work we explore the use of a 2.5-ns 2.8-µm laser source for semiconductor laser processing. On one hand, we systematically investigate the surface and bulk effects of the main irradiation parameters, such as focusing conditions, pulse energy, and pulse number, on the semiconductors Si, gallium arsenide (GaAs), and indium phosphide (InP), relevant materials in optics and electronics applications. In this case, this wavelength should trigger three photon (3P) absorption instead of the 2P absorption attained by the typically employed 1.55 µm erbium-doped fiber laser [18], enhancing energy localization and, in turn, helping to develop applications such as IR photonics or stealth dicing [6]. On the other hand, this pulse duration and wavelength allow in principle envisioning to direct-write the bulk of Ge, transparent beyond 2 µm, thus not modifiable at 1.55 µm, and for which bulk processing has not been achieved yet. Therefore, following the same systematic approach, we also study the possibility of modifying both the surface and bulk of Ge, which will expand the laser processing technology to new materials, envisioning applications in the mid-IR like waveguide inscription for electro-optical devices, optical component design for night vision, or photodiodes in the mid-IR. In this regard, we determine the surface and volume modification thresholds for all materials and discuss the trends in view of the difference in material properties. Surprisingly, we observe a volume modification threshold that decreases with depth and the ability to produce rear surface modification routinely and reliably with the investigated laser conditions and materials. In the case of Ge, no modification below surface is achieved due to beam delocalization effects. However, we still demonstrate the possibility of modifying through it by focusing the beam inside a Si workpiece with a 2-µm thick Ge film deposited on top, which could not have been achieved with more

common 1.55-µm lasers. Moreover, after evaluating the Ge properties and response, one should expect to achieve bulk modification by enhanced optical engineering and/or moving to longer wavelengths. Altogether, in this work, we prove the feasibility of nanosecond mid-IR pulses for semiconductor laser processing, which expands this technology to new materials and applications still unattainable with most common laser sources.

## 2. Experimental Section

Irradiations were performed with a recently developed laser source from Glucoloop AG delivering 2.5 ns linearly polarized pulses with a central wavelength at 2.8 µm and average pulse energy of 17 µJ at a repetition rate of 800 Hz (root mean square (RMS) stability < 0.5%, peak to peak stability < 2%) and a Gaussian-like beam profile. Then, the clean mid-IR beam energy was precisely controlled by the combination of a half wave plate (Thorlabs WPLH05M) and a nanoparticle thin film linear polarizer (Thorlabs LPMIR100-MP). The pulse number was controlled by a mechanical shutter with a minimum aperture time of ~12 ms leading to 10 ± 1 pulses at 800 Hz. Finally, the beam was directed into a 0.56 numerical aperture (NA) aspheric lens (Thorlabs C036TME-D, f = 4.0 mm, AR coated 1.8 – 3 µm) that focused the beam on the sample mounted on xyz micrometric motorized stages. Moreover, the lens was placed on a motorized stage to have fine control of the focal position. Accounting for energy losses in the optical components and propagation in air, notably humidity, the maximum deliverable pulse energy at the focal point was ~6 µJ (in air). In the case of Ge bulk irradiation, we also tested a 0.85NA aspheric lens (Thorlabs C037TME-D, f = 1.87 mm, AR coated 1.8 – 3 µm). A scheme of the described experimental setup can be found in Fig. 1.

Employing a custom transmission IR microscope (Mitutoyo M Plan Apo NIR 10.0X microscope objective and f = 200 mm tube lens) placed after the sample and coupled to a InSb camera for MWIR imaging (Zenics Onca-MWIR-InSb, 1.5–5.5 µm), we were able to detect the produced material modifications for all considered samples for our experiments. By a flip mirror placed just before the lens, the sample was through-illuminated by a halogen lamp (Thorlabs QTH10), which emits

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Schematic representation of the irradiation and visualization setup. For imaging the flip mirror is placed in the beam path and the focusing lens mounted on the turret is removed.</figcaption></figure>
between 400 and 2200 nm, in the transparency window of all the studied samples. When illuminating the sample and to allow visualization, the lens (mounted on a microscope turret) had to be removed to have full-field illumination. Therefore, this system allowed an xy in situ examination and positioning of the sample but not real time imaging when irradiating. Regarding the optical axis z, for fine positioning of the sample, we relied on a z-scan approach (discussed in the Surface modification Section) since the imaging setup depth of field did not guarantee fine focusing. By employing this microscope, we tried to image the focused beam in air. However, due to the limitations of this type of MWIR camera in terms of sensor sensitivity and the maximum delivered pulse energy, the beam profile could not be imaged.

We processed different semiconductor wafers including Si (intrinsic (100), 1-mm thick, 200–600 Ω·cm, Siltronix), GaAs (intrinsic (100), 600-µm thick, Neyco), InP (intrinsic (100), 375-µm thick, carrier concentration 0.3–2.0 × 10¹⁶ cm⁻³, Biotain Hong Kong Co.), and Ge (n-type (100), 500-µm thick, 5–40 Ω·cm, Neyco). Additionally, we prepared a sample composed of a 2-µm Ge film deposited on a Si wafer by thermal deposition (Edwards Auto 306).

Surface images of the processed samples were obtained by an optical microscope (Nikon Eclipse LV100ND) and ex situ images of the volume modifications in Si were acquired by a transmission microscope coupled to a NIR InGaAs sensor camera (Raptor Photonics Owl 1280, 0.6–1.7 µm). Finally, estimations of the refractive index variations of the modifications in Si were performed by an in-house phase microscope based on a Mach-Zender interferometer comprising a 1317-nm superluminescent diode (Thorlabs SLD1018S) as light source and the same InGaAs array sensor camera [19].

# 3. Results and discussion

## 3.1. Surface modification

In the direction towards the main objective of the work, evaluating the capacity of 2.8-µm nanosecond laser pulses for modifying the bulk of semiconductor materials, we first evaluated the surface material response to irradiation. Unlike in the volume, the main irradiation conditions such as focusing or total delivered fluence can be adequately controlled since there are no propagation nonlinearities expected in air before the target. Thus, in a first step, we determined the surface ablation threshold by focusing the beam with a 0.56 numerical aperture (NA) aspherical lens and changing the delivered energy on the samples. With the laser working at 100 Hz repetition rate and the mechanical shutter (opening time 12 ms), we first tried to produce single-shot irradiation. However, the maximum pulse energy (~3 µJ) was insufficient to result in modification on Si. Thus, we had to increase the repetition rate to 800 Hz (maximum pulse energy of ~6 µJ), which led to modification and resulted in 10 ± 1 pulses per spot. Despite working in multiple shot conditions, at this repetition rate, we should not expect multi-shot accumulation effects since the inter-pulse delay is much longer than the typical energy relaxation times [20]. In addition to the 10-pulse irradiations, we also irradiated with 100 and 800 pulses. To determine the best focal plane, we relied on a z-scan approach. For that, we varied both the pulse energy and the relative position of the lens with respect to the sample in 5-µm steps (in the order of the theoretical 2.8-µm Rayleigh distance, $z_R = \lambda/\pi NA^2$), to find the minimum energy and focus position at which we observed modification. We then considered that dataset as the best focal plane.

In Fig. 2a and b we display images of the performed ablation spots for varying energy and number of applied pulses in both Si and Ge, respectively. From a quick glance, we already observe some strong incubation effects in the case of Si that lead to an increasing ablation crater with the number of pulses, which is much less apparent for Ge and other semiconductors. Besides, we do not observe a decreasing minimum modification energy with the number of pulses, only an increase of visual contrast, which supports the assumption of modest incubation

<figure><img src="image_4.png" /><figcaption>Fig. 2. Optical microscopy images of ablated spots on the surface of (a) Si and (b) Ge performed at different pulse fluence/energy (top) and pulse number (left). Significant incubation is observed for Si but not for Ge. c) Measured area of the ablation spots performed on Si, GaAs, InP, and Ge at different pulse energies and 10 pulses. Lines correspond to a fit accounting for a thresholding of a Gaussian energy distribution (Table 1). All data points follow a linear trend. The inset corresponds to the evaluated modification energy threshold for each semiconductor bandgap.</figcaption></figure>

effects. Considering the spots performed with 10 pulses, in Fig. 2c, we plot the measured area of the ablated craters versus the delivered pulse energy for all the samples and we apply a linear fit (in log scale) analogous to Liu's analyses to all the datasets (Table 1) [21]. Needless to mention, threshold studies are typically performed by single shot, but this configuration was not possible in the current setup. First, we should stress that we can modify the surface of all the presented materials, including Ge, with the smallest spots exhibiting a ~3 µm diameter. Despite employing nanosecond pulses in their transparency windows, we can still rely on sufficient multiphoton ionization yield or other mechanisms to initiate surface absorption and overcome the modification threshold. Considering Fig. 2c, we observe that all points follow an increasing linear trend, indicating a situation equivalent to a material responding to Gaussian dose profiles. However, to verify this, we tried to image the beam with the MWIR camera, but the low sensitivity typical of these cameras alongside the low beam energy impeded us to characterize the beam size and compare with the fit parameters (Experimental Section).

From the performed fits, we retrieve both the apparent irradiation spot size on the surface ($\omega_0$) and the energy threshold ($E_{th}$). Strictly speaking, by employing Liu's method, the extracted spot size corresponds to the laser beam size only in the case of strict thresholding response and should be obtained from single shot irradiations to avoid incubation effects. Nonetheless, observing the limited incubation effects for Ge (Fig. 2b) when increasing the pulse number (the beam waist for 100 and 800 pulses on Ge, was 6 and 7 µm, respectively), as well as for GaAs and InP, we can expect the single-pulse spot size to be
<caption>**Table 1**</caption>

Significant parameters of the processed semiconductors. The apparent irradiation waist ($\omega_0$) and energy threshold ($E_{th}$) are computed from the Liu's fits shown in Fig. 2c. Material bandgap (BG) and multiphoton order (N). Optical parameters at 2.8 µm: 2PA coefficient ($\beta$, $\alpha_2$), 3PA coefficient ($\gamma$, $\alpha_3$), refractive index ($n_0$), nonlinear refractive index ($n_2$). Material free carrier ($N_e$) and multiphoton absorption free carrier ($N_{eN}$) densities.

<table><thead><tr><th>Material</th><th>ω<sub>0</sub></th><th>E<sub>th</sub></th><th>BG</th><th>N</th><th>β, α<sub>2</sub></th><th>γ, α<sub>3</sub></th><th>n<sub>0</sub></th><th>n<sub>2</sub></th><th>N<sub>e</sub></th><th>N<sub>eN</sub></th></tr><tr><th></th><th>[µm]</th><th>[µJ]</th><th>[eV]</th><th></th><th>[cm/GW]</th><th>[cm<sup>3</sup>/GW<sup>2</sup>]</th><th></th><th>(×10<sup>-5</sup>) [cm<sup>2</sup>/GW]</th><th></th><th>[cm<sup>-3</sup>]</th></tr></thead><tbody><tr><td>Si</td><td>10.0</td><td>3.74</td><td>1.12</td><td>3</td><td>–</td><td>0.002 [22]</td><td>3.47</td><td>+2.5 [22]</td><td>2 × 10<sup>13</sup></td><td>1.7 × 10<sup>17</sup></td></tr><tr><td>GaAs</td><td>8.3</td><td>0.97</td><td>1.42</td><td>3</td><td>–</td><td>0.10 [23]</td><td>3.30</td><td>–10 [23]</td><td>–</td><td>1.5 × 10<sup>17</sup></td></tr><tr><td>InP</td><td>7.1</td><td>0.44</td><td>1.35</td><td>3</td><td>–</td><td>~0.10 [24]</td><td>3.11</td><td>~|10| [24]</td><td>0.3–2 × 10<sup>16</sup></td><td>1.4 × 10<sup>26</sup></td></tr><tr><td>Ge</td><td>7.5</td><td>0.46</td><td>0.67</td><td>2</td><td>~10–80 [25,26]</td><td>–</td><td>4.00</td><td>–9 [26]</td><td>4 × 10<sup>13</sup></td><td>5.0 × 10<sup>19</sup></td></tr></tbody></table>

approximately evaluated from the fits for these materials. Therefore, from our measurements (Table 1), we can assume it is in the order of 7 µm in radius. As already stated, despite using the same focusing conditions, the apparent value for Si is larger than for the other materials but it does not reveal an experiment performed with different laser beam size and it is attributed to more incubation effects related to progressive defect accumulations from resolidification and re-ablation shot after shot (Fig. 2a) [27,28]. Additionally, knowing the lens characteristics, we calculate a minimum beam waist for a diffraction limited spot at 1.5 µm ($\omega_0 = \lambda/\pi NA$), which is surely significantly underestimated due to a difference in design wavelength for the lens, imperfect beam quality, incomplete filling of the lens, and potential aberrations. Finally, from the obtained $\omega_0$, we can estimate the fluence threshold for the different materials, finding values around 0.5–1 J/cm$^2$, which is comparable to those routinely found in semiconductors [27,29,30]. However, one should be careful not to make detailed absolute comparisons of fluence threshold values given the limitations of our measurements made under multi-pulse conditions.

Despite this uncertainty, since we always used identical focusing conditions, we can still reasonably make relative comparisons of the modification energy thresholds (Table 1) between the materials. We find a substantial difference between the different materials that could be initially attributed to the different bandgap, which is the minimum energy required to excite an electron. In the inset of Fig. 2c, we represent $E_{th}$ in terms of the bandgap. We observe a random distribution in which Si clearly stands out from the other semiconductors instead of an increasing trend. To account for this behavior, we should consider the multiphoton absorption order corresponding to the employed laser wavelength (2.8 µm, 0.44 eV). In this regard, as already anticipated, we obtain three photon absorption (3PA) in Si, GaAs and InP, whereas it relies on two photon absorption (2PA) for Ge. The different multiphoton absorption order makes it hard to compare all the multiphoton absorption coefficients ($\beta$ and $\gamma$, for 2PA and 3PA respectively), which indicate the absorption efficiency. Nonetheless, we can still compare those at 3P, observing that $\gamma$ for Si is two orders of magnitude smaller than the ones for GaAs and InP, which could explain a higher modification threshold for Si. Another important consideration is that $E_{th}$ for Si is probably underestimated by incubation effects, as we only find modification above 4.4 µJ and never below this value. Therefore, the exact values for this material should be considered with discretion.

Aside from multiphoton absorption, there could be other mechanisms like material defects that contribute to absorption. In this regard, we roughly estimate the multiphoton free carrier densities by $N_{eN} = \sigma_N N^* t_p$ (Table 1) where $\sigma_N = \alpha_N / N_{e\gamma}$ is the multiphoton cross section, and N the multiphoton order, I the peak intensity (considering a 7 µm beam waist and $E_{th}$), $t_p$ the pulse duration, $\alpha_N$ the multiphoton absorption coefficient, and $E_\gamma$ the photon energy. Comparing the obtained values to the expected initial free carrier concentrations ($N_e$) of the materials (Table 1), we observe that for Si and Ge, the free carrier multiphoton excitation is four orders of magnitude higher. Thus, absorption is primarily triggered by multiphoton absorption. However, in the case of InP, the carrier density $N_e$ is similar to the multiphoton one $N_{eN}$, indicating that material defects are at least partially responsible for initial absorption before a high concentration of multiphoton carriers

has been excited. For GaAs we have no purity characteristics specified by the supplier, but we might expect similar values given the same bi-element nature of the group III-V semiconductors. Taking a closer look at the plot in Fig. 2, we can observe a slightly larger dispersion for GaAs and InP, as well as some missing craters, which might be related to a less deterministic absorption relying on defects. It is interesting to note that pure InP and GaAs have free carrier densities around $10^6-10^7$ cm$^{-3}$. Therefore, despite employing advanced manufacturing processes, a large number of defects are still unavoidable. All in all, regardless of the material absorption mechanism, we always achieve surface modification with this laser source, which is the main purpose of the work.

## 3.2. Volume inscription

After the surface study proving multiphoton absorption, we moved into the bulk. Being Si the most employed semiconductor from both commercial and scientific point of view, we decided to perform the initial tests in this material. We focused the beam at approximately 500 µm below the surface and we varied both the pulse energy and pulse number obtaining the modifications observed in Fig. 3. From these bright field infrared transmission images, we can already confirm that below-surface modification based on 3PA processes can be performed in Si with nanosecond pulses at 2.8-µm wavelength. In this case, the minimum writing energy for all pulse numbers is between 4.4–4.8 µJ, indicating that, as mentioned, modest incubation (if any) affects this estimate, which is related to the source low repetition rate [31]. Interestingly, the obtained value is similar to the one found for surface $E_{th}$ surface = 4.4 µJ (see Table 1), which should be larger and around 6.3 µJ if we assume a similar material response (surface and bulk) and simply account for the surface reflection for the bulk interaction (~30%). This already may put into evidence some kind of beam propagation distortions concentrating light in Si that might appear due to lens aberrations and/or nonlinearities. Considering the modifications morphology, by increasing the pulse energy at a fixed pulse number, we do not observe a significant variation in size. However, by changing the number of applied pulses at a fixed energy, we obtain the smallest modifications with 10 pulses (10 µm wide, 75 µm long) and these grow with the total number of applied pulses (15 µm wide, 150 µm long for 800 pulses).

After modifying at a fixed depth, we decided to scan the laser beam along the whole Si wafer thickness (1 mm) at different pulse energies employing 800 pulses to have the maximum contrast when imaging. In Fig. 4 we display both optical reflection and IR transmission images of a processed sample in which we first irradiated the front surface (Fig. 4a) and we repeat the procedure while gradually displacing the beam focus inside the sample in steps of 100 µm (Fig. 4b) until reaching the rear surface (Fig. 4c).

The main point to highlight is the ability to process at different planes through all the Si sample. Additionally, a surprising observation is rear-surface modification, which has been somehow challenging in previous experiments due to high energy depletion in the bulk, unstable modification, and other interface effects which are only partially understood [31–33]. For this analysis, we also performed a fine 5-µm z-scan around the rear surface to find the best focusing plane. If we consider the points in Fig. 4c, and we plot them alongside those on the
<figure><img src="image_5.png" /><figcaption>Fig. 3. IR transmission images of volume modifications produced at 500 µm below the surface of Si at increasing number of (a) 10, (b) 100, and (c) 800 pulses. For each number of pulses, the energy (top) increases from right to left. The top image corresponds to a high-angle image whereas the bottom one is the corresponding lateral view. The red arrow represents the beam propagation direction. The produced modifications slightly increase with the pulse energy and number. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. (a) Optical visible microscopy and (b) ir transmission (focused on the front surface) images of 800-pulse modifications produced on si at different depth (left) and pulse energy (top). (c) Rear surface optical image of the same sample. As we gradually move into the volume the minimum modification energy decreases (even below $E_{th \ surface}$). We also modified the rear surface. (d) Volume modification threshold ($E_{th \ volume}$) within Si, GaAs, InP, and Si with a 2-µm thick Ge film (Si + Ge). The energy is normalized to $E_{th \ surface}$. For energy normalization of Si + Ge, we consider $E_{th \ surface}$ of Ge for the surface and Si for the volume. The dotted vertical lines represent the rear surface of the processed wafers. In all cases except for Ge, below- and rear-surface modifications were achieved.</figcaption></figure>

front surface (Fig. 2c), we can immediately observe smaller spots of around 5 µm, which is related to a large bulk structure growing inwards from the rear surface that reduces lateral growth on the surface when applying multiple shots (Fig. 3). Considering now the minimum modification energy, we find similar values to that on the front surface, which should be again higher on the rear if we simply considered each interface reflection and nonlinear beam absorption through the material. Thus, this indicates propagation distortions that enhance energy localization and decrease the apparent modification threshold, as well as a possible beneficial contribution from the rear-surface reflected signal. Remarkably, this observation is completely the opposite of what has been previously reported with 2-µm 7-ns pulses, where the rear-surface threshold (~17 J/cm²) was considerably higher than that of the front surface (~2.9 J/cm²) [34].

Surprisingly, the bulk minimum modification energy varies as a function of the depth. To clearly observe this effect, in Fig. 4d we plot the minimum modification energy $E_{th \ volume}$ (normalized to $E_{th \ surface}$) as a function of the focusing depth for Si. In the first instance, if we modify

just below the surface at 100 µm, $E_{th \ volume}$ is slightly higher than $E_{th \ surface}$. Nonetheless, as we move deeper, $E_{th \ volume}$ gradually decreases and even becomes smaller than $E_{th \ surface}$ when beyond a ~600 µm depth. This trend can be attributed to beam aberrations related to the lens, since we are slightly off the design wavelength (2.5 µm), which is also supported by a modification threshold drop at the vicinity of the rear surface. However, despite our efforts to image the beam profile, this aspect could not be verified in this work (technical limitations described before). In view of the positive nonlinear refractive index of Si (Table 1), one could also be prompted to think that this phenomenon is enhanced by self-focusing as the beam propagates deeper through the material and accumulates more nonlinear distortions. However, by a simple calculation of the critical power ($P_{cr}$) before beam collapse, we find $P_{cr} = 130$ kW, which is larger than the applied beam power (2.4 kW). Thus, if any, nonlinear self-focusing effects are expected to remain modest and so to barely contribute to energy re-localization compared to beam aberrations.

Once we considered the bulk modification in Si, we performed the
same experiment in GaAs, InP, and Ge. On the one hand, we can also modify the volume of GaAs and InP (Fig. 4d), with average minimum modification energies around 1.5–3 times higher than the surface threshold. This higher threshold is more reasonable if we account for interface losses, which can be also enhanced by a higher concentration of defects and a certain degree of nonlinear delocalization (Table 1). Nonetheless, we do not observe a clear trend with depth but random behavior. On the one hand, in Ge, despite being transparent to the laser wavelength, we could not observe any below-surface modification. We even employed a 0.85NA aspheric lens to increase the delivered intensity but all attempts to achieve internal structuring of this material simply failed. Despite this lens featured a higher NA and shorter focal length, it also exhibited more aberrations due to a design wavelength around 9.5 µm, which do not guarantee an improvement respect to the original focusing conditions. This puts into evidence that despite working with long nanosecond pulses that reach lower intensities than ultrashort ones, the narrow bandgap, high 2PA coefficient, and negative nonlinear refractive index of Ge (Table 1) result in an interplay which prevents sufficient energy delivery at the focus to achieve permanent modifications in the studied cases. In fact, for GaAs, InP, and Ge, the critical power for self-focusing is inferior to the one in Si, estimated at $P_{cr} \sim 35$ kW. It is still higher than the applied beam power but could account for increased nonlinear effects. However, we anticipate minimal contributions compared to beam aberration problems. For the specific case of Ge, by moving to longer wavelengths around 4 µm, where the absorption mechanism is governed by 3P, we could expect a decrease of the nonlinear absorption yield, as well as the nonlinear refractive index [26]. This, together with optical engineering considerations for better focusing conditions and increased intensity delivery, holds potential for a solution with less propagation nonlinearities and more localized absorption and should be considered for future work.

Meanwhile, there are already clear and immediate benefits which can be demonstrated with the use of mid-IR wavelengths. Working at a wavelength in the transparency window of very narrow bandgap materials like Ge, we can show that it is possible to process Si chips through layers opaque for the common 1.55 µm used in previous works. Following the same approach as before, we irradiated the bulk of a Si workpiece which had a 2-µm thick Ge film deposited on top. The obtained minimum modification energies at different depths are displayed in Fig. 4d. The surface threshold value was normalized to the $E_{th}$ surface of Ge, whereas the volume ones were normalized to that of Si. Indeed, we can modify the volume of Si through Ge, finding a similar response as for only Si but with higher measured thresholds, which is consistent with the energy losses due to the added interfaces and layer reflection. Among the specific observations made in this configuration, we can note the absence of modification for beams focused just below the surface. The reason is most likely that the required energy for modification was above the maximum available energy. We also observe a slightly higher surface modification threshold (Ge film) than that of bulk Ge, which might be an effect of the underlying contribution of bulk Si given its lower multiphoton absorption efficiency. It is important to stress out the importance of this demonstration and compare it with a laser at $\lambda = 1.55$ µm (the typical wavelength employed for Si laser processing). At 1.55 µm Ge is opaque but it still transmits up to 25% through a 2-µm thick film. Accounting for these beam losses, the required pulse energies to induce volume modification would be above the limit of current 1.55-µm commercial lasers with compactness similar to the tested technology in this work [10]. This identifies a clear benefit for mid-IR laser sources.

### 3.3. Modification probability

After observing an erratic volume modification threshold behavior for GaAs and InP, as well as a wider dispersion for these materials in the surface modification plot (Fig. 2c), we decided to investigate both the surface and volume modification probability. If we first consider surface modification, we performed matrices of > 10 spots around the threshold

at a fixed focal plane (as observed in the inset of Fig. 5a), and we then computed the modification probability for each energy value. In Fig. 5a we plot the measured surface modification probability values around the modification threshold with 800 pulses per spot, showing a sharp threshold transition for Si whereas this transition is slower for GaAs and InP ($E > 1.3E_{th}$ to consider 100% modification probability).

Moving to the volume, we focused the beam 200 µm below the surface (center of InP, the thinnest studied wafer) and repeated the experiment for all samples (Fig. 5b). We observe the same behavior as before for the different semiconductors but a wider threshold uncertainty for GaAs and InP ($E > 1.5E_{th}$ to reach 100% modification probability). For both surface and volume, the threshold uncertainty could be related to the different nature of the semiconductors. In Si we observed that the defect density is much lower than the multiphoton free carrier ionization (Table 1). Thus, absorption is primarily triggered by multiphoton absorption and not defects, resulting in a clear threshold transition. On the contrary, in InP the defects density is similar to the expected multiphoton ionization yield (Table 1). Therefore, when employing low energies close to the threshold, defects can become the main trigger for absorption, which will occasionally result in modification depending on the local defect concentration. As we increase the energy above threshold, the number of multiphoton-induced free carriers gradually increases, resulting in a more deterministic absorption mechanism that finally results in a 100% modification probability when absorption is mainly triggered by multiphoton. The threshold uncertainty width difference between surface and volume threshold can be attributed to the irradiated volume. On the surface, we can roughly assume that only half of the focal volume interacts with the material, which results in a reduced defect absorption probability compared to the volume. Besides, in the volume, light is propagating through the material which increases the probability of defect absorption and thus results in a more arbitrary absorption. Although we focus this analysis on InP, the same reasoning should be expected for GaAs since it is also a III-V group semiconductor. This phenomenon has already been observed in other works such as for instance when using 1.55-µm 900-fs pulses to modify the rear surface of Si or when employing 1.55-µm ultrashort THz bursts to modify the bulk of GaAs, where a 100% modification probability was never reached [31,35]. However, unlike that study, we can achieve reliable modification in all materials by increasing the pulse energy above threshold ($>1.5E_{th}$). Alternatively, one could be tempted to think that this behavior is a consequence of pulse-to-pulse energy stability. However, the employed laser source is very stable ($\Delta E_{RMS} < 0.5\%$) with fluctuations clearly below the observed uncertainty around the threshold and confirmed by the quite deterministic response of Si.

### 3.4. Proof-of-concept

One of the strong observations of the current study is the capability of modifying the front, bulk, and rear of Si, GaAs, and InP. This opens the possibility to create 3D digital complex structures just by precisely scanning the laser beam. A simple proof-of-concept was conceived by inscribing the logos of Glucoloop, the company developing the laser technology used in this work (Fig. 6a), and the one of LP3 laboratory (Fig. 6b) in both the surface and volume of Si. Writing was performed by laterally overlapping spots separated by 15 µm and consisting in 400 pulses at the highest available energy (~6 µJ, $E > 1.5E_{th}$ volume) to obtain the best visual contrast. Both patterns are split, so that one part is written on the surface and the other in the bulk. This way, by optical microscopy, we only see a 'C' or a '3', whereas by IR transmission imaging, we can see the whole patterns as the complementing part of the pattern is inscribed in the volume. This proves the capability to digitally structure the surface or to write embedded structures in different planes with great accuracy.

Finally, we relied on phase microscopy to determine the nature of the produced modifications in the bulk. In Fig. 6c we can see the IR-transmission and the corresponding retrieved phase images of
<figure><img src="image_7.png" /><figcaption>Fig. 5. (A) Surface and (b) volume modification occurrence probability for Si, GaAs, and InP around $E_{th}$ by microscopy observation of a set of > 10 separated irradiation spots at each energy value and employing 800 pulses per spot. Inset images exemplify typical spot dispersions. Solid lines correspond to error function fits. For both surface and volume, we observe a sharp $E_{th}$ transition for Si, whereas there is a large uncertainty for GaAs and InP.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. Logos of (a) the Glucoloop laser company, and (b) LP3 laboratory laser-written by individual spots on the surface and volume of Si with 400 pulses at 6 µJ. The schematic representation displays the different focusing depths with corresponding optical and IR transmission images. The complete logos are only visible through IR transmission imaging. (c) IR-transmission image and corresponding phase image of modifications produced at different energies (top) with 400 pulses and 500 µm below the surface of Si. We observe a positive phase variation indicating a positive refractive index change.</figcaption></figure>

modifications produced in Si between 5–6 µJ, with 400 pulses at 500-µm depth. By measuring the phase contrast ($Δφ$) at different points we estimate a positive refractive index variation $Δn = λΔφ/2πD$ of (1.6 ± 0.4) × 10⁻², where λ is the measuring wavelength and D is the modification width. The positive sign of $Δn$ indicates that after melting and resolidification of the irradiated region, it exhibits a higher density. This potentially corresponds to stressed crystalline state and/or the formation of lattice defects that can lead to a response corresponding to partial polycrystalline and amorphous phases [36]. We make this comment as a total amorphization is expected to exhibit even higher positive refractive index variation (>10⁻¹) [37]. However, no void cavities or dislocations can be inferred from this measurement, as they would result in a negative index variation. Taking advantage of the high positive refractive index variation of 0.45% with respect to the surrounding material, this could be employed to fabricate light-guiding structures like waveguides or diffracting elements [38]. Despite we only performed this proof-of-concept in Si, if we set ourselves in conditions comfortably above threshold ($E > 1.5E_{th}$), similar results could be obtained for both

GaAs and InP. This demonstrates an advance in versatility using mid-IR nanosecond laser pulses to modify the surface and bulk of different semiconductors. The observed significant structural changes open the door to target manufacturing applications in sensing and photonic devices in the IR like waveguides, diffractive optical elements, permanent memories, or even laser welding, stealth dicing, and microfluidic device writing [39].

## 4. Conclusion

Motivated by light detection and ranging applications, the appearance of more intense mid-IR nanosecond laser sources has opened the possibility to use them in material laser processing applications. By employing a 2.8-µm 2.5-ns laser source, we investigated the possibility to process the surface and bulk of relatively narrow bandgap semiconductors like Ge as well as most common ones like Si, GaAs, and InP. Unlike typically used 1.55 µm Er-doped fiber laser relying on two photon absorption, we successfully modified the surface, bulk, and rear surface
of Si, GaAs, InP induced by three photon absorption mechanisms. In the case of Si, we observe a defined volume modification threshold that decreases with the focusing depth and precise rear-surface modification. On the contrary, in GaAs and InP we observe a considerable threshold uncertainty around the modification threshold that becomes deterministic at energies above 1.5E<sub>th</sub>. We attribute this lack of determinism to an intrinsic material defect density similar to that of the multiphoton-induced free carriers. This results in an absorption initially triggered by defects at low energies and so depending on material inhomogeneities that gradually becomes more deterministic for energies surpassing the threshold.

In the case of Ge, energy deposition relies on the two-photon absorption regime allowing to successfully ablate the surface. Nonetheless, in the considered spectral domain, Ge exhibits a very high two photon absorption coefficient and negative nonlinear refractive index that, alongside enhanced aberrations by the high refractive index, result in beam delocalization and propagation distortions impeding bulk inscription. However, we expect this to be feasible by optical engineering for improved focusing conditions and/or moving to even longer wavelengths. Still, by irradiating the bulk of Si through a 2-µm thick Ge film deposited on it, we were able to modify below the surface and already put into evidence important advantages of using 2.8 µm and other mid-IR wavelengths instead of typically shorter ones. For instance, we evidence conditions leading to superior rear surface processing performance. With a special interest of laser processing for semiconductor-based optics and photonics, we estimated a positive refractive index variation of (1.6 ± 0.4) × 10<sup>-2</sup> with internal structuring of Si. This must allow to create functional 3D waveguides not only in Si but also other semiconductors and open new perspectives for new emerging technologies for microelectronics packaging applications including semiconductor laser bonding and dicing.

## CRediT authorship contribution statement

**Pol Sopeña:** Conceptualization, Methodology, Investigation, Funding acquisition, Writing – original draft, Writing – review & editing.
**Niladri Ganguly:** Investigation, Writing – review & editing.
**Gabriel Spühler:** Methodology, Writing – review & editing.
**Andrei Selivanau:** Methodology, Writing – review & editing.
**David Grojo:** Conceptualization, Investigation, Funding acquisition, Supervision, Writing – review & editing.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

Data will be made available on request.

## Acknowledgements

This work was conducted using LaMP facilities at LP3. The project received funding from the French National Research Agency (ANR-22-CE92-0057-0, KiSS project) and the European Union's Horizon 2020 research and innovation program under grant agreements No. 101034324 (MSCA-COFUND) and No. 724480 (ERC).

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