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Non-linear absorption of focused femtosecond laser pulses at 1.3 μm inside silicon: Independence on doping concentration
Applied Surface Science 278 (2013) 13–18
Contents lists available at SciVerse ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Non-linear absorption of focused femtosecond laser pulses at 1.3 m inside silicon: Independence on doping concentration S. Leyder a , D. Grojo a,∗ , P. Delaporte a , W. Marine b , M. Sentis a , O. Utéza a a b
Aix Marseille Université, CNRS, LP3 (Laboratoire Lasers, Plasmas et Procédés Photoniques) UMR 7341, 13288, Marseille, France Aix Marseille Université, CNRS, CINAM (Centre interdisciplinaire de Nanoscience de Marseille), UMR 7325, 13288, Marseille, France
a r t i c l e
i n f o
Article history: Available online 14 November 2012 Keywords: Femtosecond laser Silicon Non-linear absorption Multiphoton interaction 3D laser machining Spherical aberrations
a b s t r a c t We investigate experimentally local non-linear absorption when 1.3 m wavelength femtosecond pulses are tightly focused inside n-type doped silicon. We show that 130 fs pulses with only few nanojoule energy is enough to initiate free-carrier generation. Our results also demonstrate that the laser energy deposition is independent on the doping concentration for substrates with free-carrier densities up to 1018 cm−3 . For deep focusing experiments, the energy deposition can remain confined in micron-scale focal regions provided we perform the experiments with focused beam corrected for spherical aberration. The high degree of control observed in the experiments and the independence on doping are major assets for future 3D-micromachining technology developments based on this approach. © 2012 Elsevier B.V. All rights reserved.
1. Introduction During the last decades, many studies have been undertaken to understand the specificity of femtosecond laser interactions with silicon (Si). The ultrashort phase transformations in semiconductors using femtosecond laser pulses [1] have offered already many applications in microelectronics and photovoltaics [2,3]. However, since silicon is completely opaque up to a wavelength of 1 m, interactions by optical radiations in this range are limited to the surface. Then, microfabrication in semiconductors by femtosecond lasers remains today primarily a surface technology. One of the advantages of using infrared wavelength above 1 m is to make accessible the interior of silicon for laser-matter interactions. Then, direct femtosecond laser 3D-writing technologies similar to those developed for microfabrication inside optically transparent dielectrics [4–7] can be envisioned for semiconductors. As we show in this paper, by tightly focusing a very modest energy infrared femtosecond laser pulse inside silicon, it is possible to reach sufficient intensities in the focal volume to initiate local non-linear absorption. The involved processes include multiphoton absorption by valence electron and collision-assisted avalanche processes leading to free-carrier multiplication. The induced free-carrier generation can lead to optical breakdown and subsequent structural modifications of the materials. These effects were largely studied inside dielectrics [8–10] that have wide band gaps compared to
∗ Corresponding author. E-mail address: [email protected] (D. Grojo). 0169-4332/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2012.10.174
semiconductors and offer several applications like the fabrication of optical waveguides and integrated photonic devices [11,12], optical memory encoding [13] and the fabrication of microfluidic channel devices [14]. Despites some attempts of laser writing inside silicon by near infrared femtosecond absorption processes [15,16], the possibility to obtain these applications inside semiconductors are not clearly demonstrated at the moment. The difficulty relies on the ability to control a near-infrared femtosecond laser beam inside the material and to obtain an interaction sufficiently confined in the bulk while avoiding any surface effects or interactions. In this paper, we propose to concentrate on the investigation of non-linear absorption taking place when 1.3 m femtosecond pulses are tightly focused inside n-doped silicon. By transmission measurements, our aim is to show the degree of control and the nature of local energy deposition inside silicon. Whatever we consider experiments in dielectrics or semiconductors, the relative importance of multiphoton absorption and avalanche in free-carrier generation by intense femtosecond laser pulses is still today a matter of debate [17,18]. In mutiphoton interaction experiments in solids, the time-evolution of the injected freecarriers density n(t) associated with the pulse absorption is usually described by a simple rate equation: dn(t) = N I(t)N + ˛n(t)I(t) dt where ˛ is the avalanche ionization coefficient, N is the N-photon ionization coefficient and I(t) is the intensity of the laser pulse. At threshold intensities, we can assume that the band gap structure does not change significantly during the interaction thus ˛ and N are constants [19]. Besides, silicon is a semiconductor material that
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S. Leyder et al. / Applied Surface Science 278 (2013) 13–18
Table 1 Properties of the silicon samples used in the experiments. We indicate the dopant and type of silicon, the resistivity, the corresponding free-carrier density and the thickness of each substrate. All substrates are double side-polished and have the same orientation (1 0 0) ± 5%. Type of dopant n/Ph n/Ph n/Ph n/Ph n/Ph n/Ph
Resistivity ( cm) 50–150 10–14 2–6 0.5–0.8 0.02–0.021 0.003–0.006
Free-carrier density (cm−3 )
Thickness (m)
5(±2) × 1013 3.7(±0.7) × 1014 1(±3) × 1015 1(±1) × 1016 1.1(±0.1) × 1018 1(±1) × 1019
550(±10) 500(±10) 510(±10) 590(±10) 500(±10) 550(±10)
allows introducing an arbitrary initial concentration of free electrons by n-type doping. This is an important point for technical considerations but it allows also to change experimentally the initial importance of the second term (n(t = 0) = / 0) in the free-carrier density rate equation (see above). We propose the approach can be used to study the contribution of avalanche ionization seeded by free-carriers from doping on non-linear absorption. We test this concept on experiments by repeating the transmission measurements in samples with gradually increasing doping concentration up to 1018 cm−3 . Above this density, the substrates are completely opaque and transmission diagnostics become inoperative but we propose a double-pulse scheme that allows investigating higher densities by illuminating intrinsic silicon. Our results improve the understanding of non-linear laser energy deposition with nearinfrared femtosecond laser and reveal important processes that are involved in our context. This work represents a first step towards structural modifications inside semiconductors and future 3D laser micromachining applications.
2. Experimental details 2.1. Silicon substrates In the experiments, we illuminate commercial silicon substrates doped with Phosphorous atoms. Therefore, they are all associated with an initial free-electron density which is directly related to the doping concentration varying from 1013 to 1019 cm−3 in six different samples. All substrates are from the same provider (SILTRONIX). They are grown by the Czochralski process and have orientation (1 0 0) ± 5◦ . We report some details of all our silicon samples in Table 1. By using a tungsten (W) lamp and a NIR spectrometer (Ocean Optics, Model NIRQuest 512-2.5), the linear transmission (low intensity transmission) as a function of wavelength is measured for all samples in the near infrared region. Results are shown in Fig. 1. As expected, low-doped silicon substrates are fully transparent for wavelength above 1 m because in this spectral range the photon energy is below the band gap energy (Eg = 1.12 eV at 300 K). Losses on transmission measurements (T) are only due to multiple reflection (R) at air–Si interfaces (T = (1 − R)2 (1 + R2 + R4 · · ·) ∼ = 0.53 with R = 0.31 for silicon at 1.3 m). For wafers with doping concentrations above 1016 cm−3 , we note that the transmission decreases with the free-carrier density leading to opaque silicon for a doping concentration of 1019 cm−3 . We checked that the linear transmission change as a function of doping concentration can be easily fitted by using a simple Drude model [20] (not shown here). Accordingly, the absorption is due to Inverse-Bremsstrahlung (I-B) absorption that is a more efficient process when increasing the wavelength (observed in Fig. 1).
Fig. 1. Near-infrared (NIR) transmission spectra (left axis) of the substrates (see Table 1). The measurements are achieved by using a broad-band Tungsten lamp and a NIR spectrometer equipped with a cooled InGas array detector. Samples with doping concentrations above 1016 cm−3 exhibit a linear absorption component in the spectral range tested. For comparison, we show the spectrum measurement of the 1.3 m laser pulses used in the experiments (right axis).
2.2. Laser experiments In Fig. 1, we show the spectrum measurement of the femtosecond laser beam used in the experiment. The laser radiation is centered at 1.3 m with a 27 nm full width at half maximum (FWHM). The femtosecond pulses are obtained with a TitaniumSapphire laser (Spectra-Physics, Model Hurricane) emitting 1 mJ energy pulses at a fundamental wavelength of 800 nm and a repetition rate of 1 kHz. The pulse duration is measured at 100 fs with an autocorrelator system (APE, Model mini). Then the laser beam is directed to an OPA (optical parametric amplifier) system (Spectra Physics, Model 800CF) that is used to convert the wavelength to 1.3 m with pulse duration below 130 fs (as specified by the OPA supplier) and pulse energy above 10 J. At this wavelength, low intensity pulses are totally transmitted through silicon. Accordingly, we can confirm the measurement of Fig. 1 at 1.3 m by measuring the transmission of our unfocused laser beam through each substrate with an integrating sphere coupled to a germanium photodiode. These transmission results (circles in Fig. 1) are consistent with the previous measurements obtained with the tungsten lamp as the source of radiation (see Fig. 1). As we will show, we need to generate relatively high laser intensities inside silicon to initiate non-linear absorption. In these experiments, we use high numerical aperture reflective objective (Newport, gold coating, NA = 0.53) and NIR transmission objectives (Olympus, NA from 0.3 to 0.6) that allows to access high intensities interaction (I > 1012 W/cm2 ) with few nanojoules energy pulses. There are unique advantages to use tightly focused pulses. First, non-linear processes create free-carriers only in the high intensity focal volume that can be confined in a micrometric scale. The change of the numerical aperture allows us a control on geometrical properties of the focal volume mainly described with the waist w0 and the confocal parameter b = 2nSi w02 /0 . Second, the pulse power (P) can be maintained below the critical power for self-focusing while performing high intensity experiments. Here it is worth mentioning this aspect is critical when working in silicon. At 1.3 m, the non-linear refractive index of silicon (n2 ) has been measured in the femtosecond laser regime at n2 ∼ = 3 × 10−14 cm2 /W [21]. This value is associated with a critical power Pcr = (0.61)2 20 /8n0 n2 ∼ = 23 kW which is about 100 times more that for fused silica in which filamentation was widely reported [22,23]. We perform all this study with nanojoule energy pulses that is below or close to critical power for self-focusing. The
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Fig. 2. Experimental setup for non-linear transmission measurements. Femtosecond NIR laser pulses (∼1.3-m, 100 fs) from an optical parametric amplifier (OPA) are tightly focused inside the silicon samples by using microscope objectives (NA from 0.2 to 0.53). The sample and the focusing objective are on translation stages to move the focus in 3D space between laser shots. All transmitted light was collected by an integrating sphere. The signal (transmitted pulse energy) and reference (incoming pulse energy) are acquired independently for every laser shot by means of Germanium detectors and a computer-controlled procedure.
absence of self-focusing is also confirmed by the absence of selfphase modulation in the transmitted spectrum for all conditions tested in this work (not shown here). The experimental setup for transmission measurements with tightly focused femtosecond laser pulses is summarized in Fig. 2. The samples are mounted on XYZ motorized stages so that the focus of the laser beam can be positioned anywhere inside the silicon substrates. The stage velocity is adjusted in a way that each pulse interacts with a fresh region of the substrate during the experiments. Then all transmission measurements are based on single shot interactions. To perform the transmission measurements, we use integrating spheres equipped with amplified germanium photodiodes (Thorlabs, PDA50B) to monitor both the incoming light fluctuations and the transmitted laser light. This ensures that the transmitted beam is collected completely, even if there is scattering or defocusing by the plasma formed by ionization. A combination of a half-wave plate and a polarizer controls the intensity of incident light during the acquisition. By varying this parameter we measure the intensity threshold for non-linear absorption and the non-linear response for all our samples. This represents a result of importance to discuss the non-linear ionization physics in this regime since our beam interacts with substrate with strong doping level differences. It is also a major input for technological considerations since it shows how technological development based on this approach can apply in doped semiconductor materials.
Results of total transmission as function of laser pulse energy are shown in Fig. 3 for all samples. We observe the transmission curves start at a transmission level (Fig, 3, see circles) corresponding to the linear transmission measurements at 1.3 m (Fig. 1, see circles). This indicates losses observed with low energy pulses rely on reflection losses at air/Si and Si/air interfaces. Non-linear absorption is already observed with few nanojoule pulses that correspond to intensity in the order of magnitude of ∼1012 W/cm2 . It is two orders less than for the same femtosecond laser experiment performed inside fused silica (not shown here). This difference is closely linked to the multiphoton order of photoionization. Due to the small gap of silicon, photoionization relies on a 2-photon process at 1.3 m while it is typically a 10-photon process for fused silica experiments at the same wavelength. The associated intensity for ionization is obviously much lower in silicon than that measured in fused silica. We also note in Fig. 3 that the transmission drops monotonically from the low intensity transmission level with the initiation of two-photon ionization. The drop is particularly pronounced when we increase the energy up to few nanojoules. Repeating the measurement on substrates with doping concentration up to 1016 cm−3 , the results show that all substrates exhibit very similar non-linear responses. Interestingly, independently of the initial free electron introduced by doping, we observe identical energy threshold for nonlinear absorption but also similar transmission losses for the all range of energy tested (0.5–80 nJ). When the doping concentration reaches 1018 cm−3 the transmission curve is downshifted.
3. Results and discussions In the previous the part, we have shown that n-doped silicon are totally transparent to low intensity laser pulses up to doping concentration of 1016 cm−3 . Now, we perform the experiments in the high intensity regime to determine the non-linear absorption threshold and response of silicon in our context. In a first experiment, we use a reflective objective with strong numerical aperture of 0.53 giving a theoretical focal spot of 2 × w0 ∼ 1.3 m and a confocal parameter b ∼ 8 m inside silicon. Here we expect that the non-linear interaction occurs at least in this focal volume. We focus our attention at determining the minimum laser energy to initiate non-linear absorption. The approach must allow to estimate the intensity threshold for two-photon absorption at 1.3 m for all samples. For that, we focus the laser beam at a fixed depth (50 m) inside n-doped silicon sample of 500 m thickness and we change the laser pulse energy while measuring the substrate transmission.
Fig. 3. Comparison of non-linear absorption inside silicon for samples with different initial free-carrier densities. The transmission of pulses that are tightly focused 50 m below the surface is plotted as a function of pulse energy. The inserted graph shows the same result with normalized curves.
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Also it is of importance to determine if the shift relies only on the increase of linear absorption at this doping level as observed in the previous measurements. To compare all measurements, we normalize the transmission curves to the maximum transmission. The normalized measurements are shown in the inserted graph in Fig. 3. For all tested samples with doping concentration up to 1018 cm−3 , the intensity dependence of absorption at 1.3 m is strictly identical revealing the non-linear absorption physics remains the same for all these conditions. The initial free electron density (introduced by doping) does not influence the non-linear contribution of laser energy deposition. As a consequence, we can work independently inside silicon whatever the doping concentration up to 1018 cm−3 . One could predict that an initial free electron density above a given level yields an avalanche term in the density rate equation (see above) as the dominant free-carrier multiplication mechanism (over 2-photon ionization) from the beginning of the interaction [19]. This would be analogous to how pre-ionization can seed avalanche in dielectrics [24]. In this case, the absorption response is dependent on the initial free electron density. Obviously, this does not occur in the density range 1013 – 1018 cm−3 that can be tested by direct transmission diagnostics. Thus, our results indicate that 2-photon ionization remains likely the major seeding mechanism for the non-linear absorption. According to a multiphoton-based interaction, the laser energy deposition must remain confined in the focal volume (that is the region of highest intensity). To demonstrate this aspect, we also perform the measurements using a Z-scan method that consists in measuring the non-linear transmission of the samples while focusing the beam at different depths inside the substrate. While maintaining the laser pulse energy, the focus is translated through the sample by moving the Z stage and we acquire transmission values. Total transmission as a function of focusing position is shown in Fig. 4a for three samples of different doping concentrations and thicknesses. In this experiment, the laser pulse energy is fixed at 4 nJ. When the focal volume interacts in air (Z < 0 m and Z > 600 m), intensities arriving on the sample are not sufficient to initiate two-photon absorption. The measurement leads to 0.53 transmission revealing again that silicon is transparent at 1.3 m. Non-linear absorption takes place only when the laser focal volume is located in the substrate; it directly confirms a local laser energy deposition in the sample. The very sharp transition at the two interfaces of each sample reveals the confinement of the nonlinear interaction in the focal volume. The localization is so pronounced that the Z-scan measurement is sensitive to the difference of thickness t between the tested samples (t < 40 m). This demonstrates that we can deposit laser energy and we can generate free-carriers very similarly in all regions of about 500m thick silicon substrates with these focusing conditions. The length on which the absorption occurs (tabs ) corresponds to the thickness of the sample (tSi ) divided by the silicon refractive index (tabs ∼ tSi /nSi with nSi ∼ 3.5 at 1.3 m). Here it also worth noting that the measurement of Fig. 4a was performed for 3 samples of different doping concentration from 1013 cm−3 to 1016 cm−3 leading to the same absorption level. This result is consistent with the previous measurement where the initial free electron density does not influence the non-linear transmission response of silicon for doping concentration up to 1018 cm−3 (see Fig. 3). We can also notice that the transmission is constant in the bulk of silicon for the 3 samples of about 500 m thickness. It reveals that the geometrical property of the focal volume (and the peak intensity) is not strongly affected by the focusing depth and so the confinement of the interaction is relatively well conserved all over <600 m thick samples. In Fig. 4b, we repeat the same Z-scan experiment on one sample and we change the laser pulse energy. The energy dependence of the total transmission inside the sample is
Fig. 4. Z-scan transmission measurements of silicon samples with different doping concentrations and thicknesses. The transmission is plotted as a function of focus position along the optical axis. The experimental curve is obtained by translating the microscope objective along the optical axis while translating the sample (in the XY plane) so that fresh material is irradiated on each shot.
another manifestation of the non-linear character of the interaction. The sharpness of the transition at the two interfaces is less pronounced when high intensity laser pulses are used due to the growth of the region in which the intensity dependent interaction takes place. Due to the high refractive index of silicon (nSi = 3.5 at 1.3 m wavelength), we predict that the focal volume gets affected by spherical aberration when performing deep focusing interactions. In Fig. 5a, we show the same Z-scan experiments performed on a 3 mm thick substrate (Si, orientation: 1 0 0, type: intrinsic, optical grade) while focusing the beam with a 0.45 NA NIR refractive objective (Olympus-LCPLN-20XIR). We observe that for the first 150 m of our Z-scan inside the material, the transmission remains quite constant confirming spherical aberrations do not affect the focal volume in this range. This result is consistent with the previous experiment made on <600 m silicon wafers with reflective conditions. However, we see with this thick sample that the absorption of the laser beam decreases as the focus position gets deeper inside the material. This response is very similar to that observed in dielectrics where it was attributed to spherical aberration [25]. Indeed, spherical aberration tends to progressively elongate the focal volume and the associated local peak intensity is lowered inside the material, explaining the decrease of non-linear absorption observed in the measurements. An advantage of performing the measurement with transmission objectives that are specially designed to work in the NIR domain for microelectronic device observation is that spherical aberration can be compensated by tuning a correction collar on the objective. The compensation holds for a single given thickness
S. Leyder et al. / Applied Surface Science 278 (2013) 13–18
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free-carrier densities because the substrates become opaque (see Fig. 1) making impossible any transmission diagnostics. However, 1018 cm−3 remains two orders of magnitude below the critical density and the opacity of the substrates relies on bulk absorption properties. Thus, to investigate higher densities by transmission, one way can be to populate the conduction band only inside the micron-size interaction region of intrinsic silicon substrates to maintain a relative transparency. While we have concentrated this paper on the interaction with doped samples, we will show in a future paper that this can be achieved by a double-pulse experiment, where a first pulse is focused inside intrinsic silicon and populates the conduction band in the focal region. The second pulse is focused at the same location and can experience strong nonlinear absorption triggered by the free-carriers injected by the first pulse. We have highlighted the independence on doping concentration of the non-linear laser energy deposition with Phosphorous-doped Silicon at levels up to 1018 cm−3 . This represents a signature of two-photon ionization as the main source triggering the multiplication of carriers and the subsequent absorption. It is also a result of major importance for technological considerations. The approach must allow future 3D laser modification applications inside semiconductors. Acknowledgments
Fig. 5. Transmission measured for the focusing of ∼18 nJ pulses inside 3 mm thick silicon at different depths with a NA = 0.45 lens with adjustable correction for spherical aberration. We compare the transmission with two correction collar adjustments corresponding to 0 mm (a) and 1.2 mm of silicon (b). The maximum of absorption is shifted with the adjustment.
of silicon but allows to directly confirm the role of aberration in our experiments. In Fig. 5b, we show the result of the same Z-scan measurement (similar to Fig. 5a) but for a focused beam corrected for the spherical aberration associated with propagation through 1.2mm thick silicon substrates. We obtain a minimum of transmission at a Z-position of d ≈ 350 m below the original position of the surface. This corresponds to a beam focus motion of d × nSi ≈ 1.2 mm. The accordance of this observation with the correction adjustment shows unambiguously that controlled focused interactions in bulk silicon require compensating for spherical aberrations. 3.1. Conclusion and perspectives We have shown that the presence of free-electrons introduced by doping does not influence the non-linear absorption of 1.3 m wavelength laser pulses inside silicon. The use of doped sample provides a way to perform a – model independent – study of avalanche inside silicon. Because seeded-avalanche by free carriers from doping was not observed, we can directly conclude avalanche is not efficiently triggered up to a 1018 cm−3 free electron density. We have estimated the two-photon absorption threshold to be on the order of 1012 W/cm2 . Our simple diagnostic shows (with Z-scan measurements) that the energy deposition remains confined in micron-scale regions. However, controlled illumination conditions with beams that are tightly (NA > 0.4) and deeply (>600 m) focused under the surface of silicon substrates require to work with focusing optics corrected for spherical aberration. Our method to investigate the role of avalanche relies on silicon doping but it is not applicable to investigate the effect of higher
This work was supported by the ANR (French Agency for National Research) “MultiPhoton e-Inject” project (grant 2010JCJC-913-01) and the DGE-FUI “MADISON” project. We would like to thank Thibault Derrien and Ilya Bogatyrev for fruitful discussions. References [1] S.K. Sundaram, E. Mazur, Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses, Nature Materials 4 (2002) 217–224. [2] C. Wu, C.H. Crouch, L. Zhao, J.E. Carey, R.J. Younkin, J.A. Levinson, E. Mazur, R.M. Farrel, P. Gothoskar, A. Karger, Near-unity below-band gap absorption by microstructured silicon, Applied Physics Letters 78 (2001) 1850–1852. [3] M.T. Winkler, D. Recht, M. Sher, A.J. Said, E. Mazur, M.J. Aziz, Insulator-tometal transition in sulfur-doped silicon, Physical Review Letters 106 (2011) 178701. [4] K.M. Davis, K. Miura, N. Sugimoto, K. Hirao, Writing waveguides in glass with a femtosecond laser, Optical Letters 21 (1996) 17291996. [5] R.R. Gattass, E. Mazur, Femtosecond laser micromachining in transparent materials, Nature Photonics 2 (2008) 219. [6] K. Miura, J.R. Qiu, H. Inouye, T. Mitsuyu, K. Hirao, Photowritten optical waveguides in various glasses with ultrashort pulse laser, Applied Physics Letters 71 (1997) 3329. [7] T. Barillot, D. Grojo, M. Gertsvorlf, S. Lei, D.M. Rayner, P.B. Corkum, High refractive-index modification of SiO2 created by femtosecond laser nanostructuring, Journal of Physics B 43 (2010) 125401. [8] D.M. Simanovskii, H.A. Schwettman, H. Lee, J. Welch, Midinfrared optical breakdown in transparent dielectrics, Physical Review Letters 91 (2003) 107601. [9] Ching-Hua, J.P. Longtin, Modeling optical breakdown in dielectrics during ultrafast laser processing, Applied Optics 40 (2001) 3124–3131. [10] C.B. Schaffer, A.O. Jamison, E. Mazur, Morphology of femtosecond laser-induced structural changes in bulk transparents material, Applied Physical Letters 84 (2004) 1441. [11] C.B. Schaffer, A. Brodeur, J.F. Garcia, E. Mazur, Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy, Optical Letters 26 (2001) 93–95. [12] D. Grojo, M. Gertsvorlf, H. Jean-Ruel, S. Lei, L. Ramunno, D.M. Rayner, P.B. Corkum, Self-controlled formation of micro-lenses by optical breakdown in wide band gap materials, Applied Physical Letters 93 (2008) 243118. [13] R. Taylor, C. Hnatovsky, E. Simova, Applications of femtosecond laser induced self-organized planar nanocracks inside fused silica glass, Laser and Photonics Reviews 2 (2008) 26–46. [14] Y. Bellouard, A. Said, M. Dugan, P. Bado, Fabrication of high-aspect ratio, microfluidic channels and tunnels using femtosecond laser pulses and chemical etching, Optics Express 12 (2004) 2120–2212. [15] H.A.H. Nejadmalayeri, P.R. Herman, J. Burghoff, M. Will, S. Nolte, A. Tunnermann, Inscription of optical waveguides in crystalline silicon by mid-infrared femtosecond laser pulses, Optics Letters 30 (2005) 964.
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Contents lists available at SciVerse ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Non-linear absorption of focused femtosecond laser pulses at 1.3 m inside silicon: Independence on doping concentration S. Leyder a , D. Grojo a,∗ , P. Delaporte a , W. Marine b , M. Sentis a , O. Utéza a a b
Aix Marseille Université, CNRS, LP3 (Laboratoire Lasers, Plasmas et Procédés Photoniques) UMR 7341, 13288, Marseille, France Aix Marseille Université, CNRS, CINAM (Centre interdisciplinaire de Nanoscience de Marseille), UMR 7325, 13288, Marseille, France
a r t i c l e
i n f o
Article history: Available online 14 November 2012 Keywords: Femtosecond laser Silicon Non-linear absorption Multiphoton interaction 3D laser machining Spherical aberrations
a b s t r a c t We investigate experimentally local non-linear absorption when 1.3 m wavelength femtosecond pulses are tightly focused inside n-type doped silicon. We show that 130 fs pulses with only few nanojoule energy is enough to initiate free-carrier generation. Our results also demonstrate that the laser energy deposition is independent on the doping concentration for substrates with free-carrier densities up to 1018 cm−3 . For deep focusing experiments, the energy deposition can remain confined in micron-scale focal regions provided we perform the experiments with focused beam corrected for spherical aberration. The high degree of control observed in the experiments and the independence on doping are major assets for future 3D-micromachining technology developments based on this approach. © 2012 Elsevier B.V. All rights reserved.
1. Introduction During the last decades, many studies have been undertaken to understand the specificity of femtosecond laser interactions with silicon (Si). The ultrashort phase transformations in semiconductors using femtosecond laser pulses [1] have offered already many applications in microelectronics and photovoltaics [2,3]. However, since silicon is completely opaque up to a wavelength of 1 m, interactions by optical radiations in this range are limited to the surface. Then, microfabrication in semiconductors by femtosecond lasers remains today primarily a surface technology. One of the advantages of using infrared wavelength above 1 m is to make accessible the interior of silicon for laser-matter interactions. Then, direct femtosecond laser 3D-writing technologies similar to those developed for microfabrication inside optically transparent dielectrics [4–7] can be envisioned for semiconductors. As we show in this paper, by tightly focusing a very modest energy infrared femtosecond laser pulse inside silicon, it is possible to reach sufficient intensities in the focal volume to initiate local non-linear absorption. The involved processes include multiphoton absorption by valence electron and collision-assisted avalanche processes leading to free-carrier multiplication. The induced free-carrier generation can lead to optical breakdown and subsequent structural modifications of the materials. These effects were largely studied inside dielectrics [8–10] that have wide band gaps compared to
∗ Corresponding author. E-mail address: [email protected] (D. Grojo). 0169-4332/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2012.10.174
semiconductors and offer several applications like the fabrication of optical waveguides and integrated photonic devices [11,12], optical memory encoding [13] and the fabrication of microfluidic channel devices [14]. Despites some attempts of laser writing inside silicon by near infrared femtosecond absorption processes [15,16], the possibility to obtain these applications inside semiconductors are not clearly demonstrated at the moment. The difficulty relies on the ability to control a near-infrared femtosecond laser beam inside the material and to obtain an interaction sufficiently confined in the bulk while avoiding any surface effects or interactions. In this paper, we propose to concentrate on the investigation of non-linear absorption taking place when 1.3 m femtosecond pulses are tightly focused inside n-doped silicon. By transmission measurements, our aim is to show the degree of control and the nature of local energy deposition inside silicon. Whatever we consider experiments in dielectrics or semiconductors, the relative importance of multiphoton absorption and avalanche in free-carrier generation by intense femtosecond laser pulses is still today a matter of debate [17,18]. In mutiphoton interaction experiments in solids, the time-evolution of the injected freecarriers density n(t) associated with the pulse absorption is usually described by a simple rate equation: dn(t) = N I(t)N + ˛n(t)I(t) dt where ˛ is the avalanche ionization coefficient, N is the N-photon ionization coefficient and I(t) is the intensity of the laser pulse. At threshold intensities, we can assume that the band gap structure does not change significantly during the interaction thus ˛ and N are constants [19]. Besides, silicon is a semiconductor material that
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Table 1 Properties of the silicon samples used in the experiments. We indicate the dopant and type of silicon, the resistivity, the corresponding free-carrier density and the thickness of each substrate. All substrates are double side-polished and have the same orientation (1 0 0) ± 5%. Type of dopant n/Ph n/Ph n/Ph n/Ph n/Ph n/Ph
Resistivity ( cm) 50–150 10–14 2–6 0.5–0.8 0.02–0.021 0.003–0.006
Free-carrier density (cm−3 )
Thickness (m)
5(±2) × 1013 3.7(±0.7) × 1014 1(±3) × 1015 1(±1) × 1016 1.1(±0.1) × 1018 1(±1) × 1019
550(±10) 500(±10) 510(±10) 590(±10) 500(±10) 550(±10)
allows introducing an arbitrary initial concentration of free electrons by n-type doping. This is an important point for technical considerations but it allows also to change experimentally the initial importance of the second term (n(t = 0) = / 0) in the free-carrier density rate equation (see above). We propose the approach can be used to study the contribution of avalanche ionization seeded by free-carriers from doping on non-linear absorption. We test this concept on experiments by repeating the transmission measurements in samples with gradually increasing doping concentration up to 1018 cm−3 . Above this density, the substrates are completely opaque and transmission diagnostics become inoperative but we propose a double-pulse scheme that allows investigating higher densities by illuminating intrinsic silicon. Our results improve the understanding of non-linear laser energy deposition with nearinfrared femtosecond laser and reveal important processes that are involved in our context. This work represents a first step towards structural modifications inside semiconductors and future 3D laser micromachining applications.
2. Experimental details 2.1. Silicon substrates In the experiments, we illuminate commercial silicon substrates doped with Phosphorous atoms. Therefore, they are all associated with an initial free-electron density which is directly related to the doping concentration varying from 1013 to 1019 cm−3 in six different samples. All substrates are from the same provider (SILTRONIX). They are grown by the Czochralski process and have orientation (1 0 0) ± 5◦ . We report some details of all our silicon samples in Table 1. By using a tungsten (W) lamp and a NIR spectrometer (Ocean Optics, Model NIRQuest 512-2.5), the linear transmission (low intensity transmission) as a function of wavelength is measured for all samples in the near infrared region. Results are shown in Fig. 1. As expected, low-doped silicon substrates are fully transparent for wavelength above 1 m because in this spectral range the photon energy is below the band gap energy (Eg = 1.12 eV at 300 K). Losses on transmission measurements (T) are only due to multiple reflection (R) at air–Si interfaces (T = (1 − R)2 (1 + R2 + R4 · · ·) ∼ = 0.53 with R = 0.31 for silicon at 1.3 m). For wafers with doping concentrations above 1016 cm−3 , we note that the transmission decreases with the free-carrier density leading to opaque silicon for a doping concentration of 1019 cm−3 . We checked that the linear transmission change as a function of doping concentration can be easily fitted by using a simple Drude model [20] (not shown here). Accordingly, the absorption is due to Inverse-Bremsstrahlung (I-B) absorption that is a more efficient process when increasing the wavelength (observed in Fig. 1).
Fig. 1. Near-infrared (NIR) transmission spectra (left axis) of the substrates (see Table 1). The measurements are achieved by using a broad-band Tungsten lamp and a NIR spectrometer equipped with a cooled InGas array detector. Samples with doping concentrations above 1016 cm−3 exhibit a linear absorption component in the spectral range tested. For comparison, we show the spectrum measurement of the 1.3 m laser pulses used in the experiments (right axis).
2.2. Laser experiments In Fig. 1, we show the spectrum measurement of the femtosecond laser beam used in the experiment. The laser radiation is centered at 1.3 m with a 27 nm full width at half maximum (FWHM). The femtosecond pulses are obtained with a TitaniumSapphire laser (Spectra-Physics, Model Hurricane) emitting 1 mJ energy pulses at a fundamental wavelength of 800 nm and a repetition rate of 1 kHz. The pulse duration is measured at 100 fs with an autocorrelator system (APE, Model mini). Then the laser beam is directed to an OPA (optical parametric amplifier) system (Spectra Physics, Model 800CF) that is used to convert the wavelength to 1.3 m with pulse duration below 130 fs (as specified by the OPA supplier) and pulse energy above 10 J. At this wavelength, low intensity pulses are totally transmitted through silicon. Accordingly, we can confirm the measurement of Fig. 1 at 1.3 m by measuring the transmission of our unfocused laser beam through each substrate with an integrating sphere coupled to a germanium photodiode. These transmission results (circles in Fig. 1) are consistent with the previous measurements obtained with the tungsten lamp as the source of radiation (see Fig. 1). As we will show, we need to generate relatively high laser intensities inside silicon to initiate non-linear absorption. In these experiments, we use high numerical aperture reflective objective (Newport, gold coating, NA = 0.53) and NIR transmission objectives (Olympus, NA from 0.3 to 0.6) that allows to access high intensities interaction (I > 1012 W/cm2 ) with few nanojoules energy pulses. There are unique advantages to use tightly focused pulses. First, non-linear processes create free-carriers only in the high intensity focal volume that can be confined in a micrometric scale. The change of the numerical aperture allows us a control on geometrical properties of the focal volume mainly described with the waist w0 and the confocal parameter b = 2nSi w02 /0 . Second, the pulse power (P) can be maintained below the critical power for self-focusing while performing high intensity experiments. Here it is worth mentioning this aspect is critical when working in silicon. At 1.3 m, the non-linear refractive index of silicon (n2 ) has been measured in the femtosecond laser regime at n2 ∼ = 3 × 10−14 cm2 /W [21]. This value is associated with a critical power Pcr = (0.61)2 20 /8n0 n2 ∼ = 23 kW which is about 100 times more that for fused silica in which filamentation was widely reported [22,23]. We perform all this study with nanojoule energy pulses that is below or close to critical power for self-focusing. The
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Fig. 2. Experimental setup for non-linear transmission measurements. Femtosecond NIR laser pulses (∼1.3-m, 100 fs) from an optical parametric amplifier (OPA) are tightly focused inside the silicon samples by using microscope objectives (NA from 0.2 to 0.53). The sample and the focusing objective are on translation stages to move the focus in 3D space between laser shots. All transmitted light was collected by an integrating sphere. The signal (transmitted pulse energy) and reference (incoming pulse energy) are acquired independently for every laser shot by means of Germanium detectors and a computer-controlled procedure.
absence of self-focusing is also confirmed by the absence of selfphase modulation in the transmitted spectrum for all conditions tested in this work (not shown here). The experimental setup for transmission measurements with tightly focused femtosecond laser pulses is summarized in Fig. 2. The samples are mounted on XYZ motorized stages so that the focus of the laser beam can be positioned anywhere inside the silicon substrates. The stage velocity is adjusted in a way that each pulse interacts with a fresh region of the substrate during the experiments. Then all transmission measurements are based on single shot interactions. To perform the transmission measurements, we use integrating spheres equipped with amplified germanium photodiodes (Thorlabs, PDA50B) to monitor both the incoming light fluctuations and the transmitted laser light. This ensures that the transmitted beam is collected completely, even if there is scattering or defocusing by the plasma formed by ionization. A combination of a half-wave plate and a polarizer controls the intensity of incident light during the acquisition. By varying this parameter we measure the intensity threshold for non-linear absorption and the non-linear response for all our samples. This represents a result of importance to discuss the non-linear ionization physics in this regime since our beam interacts with substrate with strong doping level differences. It is also a major input for technological considerations since it shows how technological development based on this approach can apply in doped semiconductor materials.
Results of total transmission as function of laser pulse energy are shown in Fig. 3 for all samples. We observe the transmission curves start at a transmission level (Fig, 3, see circles) corresponding to the linear transmission measurements at 1.3 m (Fig. 1, see circles). This indicates losses observed with low energy pulses rely on reflection losses at air/Si and Si/air interfaces. Non-linear absorption is already observed with few nanojoule pulses that correspond to intensity in the order of magnitude of ∼1012 W/cm2 . It is two orders less than for the same femtosecond laser experiment performed inside fused silica (not shown here). This difference is closely linked to the multiphoton order of photoionization. Due to the small gap of silicon, photoionization relies on a 2-photon process at 1.3 m while it is typically a 10-photon process for fused silica experiments at the same wavelength. The associated intensity for ionization is obviously much lower in silicon than that measured in fused silica. We also note in Fig. 3 that the transmission drops monotonically from the low intensity transmission level with the initiation of two-photon ionization. The drop is particularly pronounced when we increase the energy up to few nanojoules. Repeating the measurement on substrates with doping concentration up to 1016 cm−3 , the results show that all substrates exhibit very similar non-linear responses. Interestingly, independently of the initial free electron introduced by doping, we observe identical energy threshold for nonlinear absorption but also similar transmission losses for the all range of energy tested (0.5–80 nJ). When the doping concentration reaches 1018 cm−3 the transmission curve is downshifted.
3. Results and discussions In the previous the part, we have shown that n-doped silicon are totally transparent to low intensity laser pulses up to doping concentration of 1016 cm−3 . Now, we perform the experiments in the high intensity regime to determine the non-linear absorption threshold and response of silicon in our context. In a first experiment, we use a reflective objective with strong numerical aperture of 0.53 giving a theoretical focal spot of 2 × w0 ∼ 1.3 m and a confocal parameter b ∼ 8 m inside silicon. Here we expect that the non-linear interaction occurs at least in this focal volume. We focus our attention at determining the minimum laser energy to initiate non-linear absorption. The approach must allow to estimate the intensity threshold for two-photon absorption at 1.3 m for all samples. For that, we focus the laser beam at a fixed depth (50 m) inside n-doped silicon sample of 500 m thickness and we change the laser pulse energy while measuring the substrate transmission.
Fig. 3. Comparison of non-linear absorption inside silicon for samples with different initial free-carrier densities. The transmission of pulses that are tightly focused 50 m below the surface is plotted as a function of pulse energy. The inserted graph shows the same result with normalized curves.
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Also it is of importance to determine if the shift relies only on the increase of linear absorption at this doping level as observed in the previous measurements. To compare all measurements, we normalize the transmission curves to the maximum transmission. The normalized measurements are shown in the inserted graph in Fig. 3. For all tested samples with doping concentration up to 1018 cm−3 , the intensity dependence of absorption at 1.3 m is strictly identical revealing the non-linear absorption physics remains the same for all these conditions. The initial free electron density (introduced by doping) does not influence the non-linear contribution of laser energy deposition. As a consequence, we can work independently inside silicon whatever the doping concentration up to 1018 cm−3 . One could predict that an initial free electron density above a given level yields an avalanche term in the density rate equation (see above) as the dominant free-carrier multiplication mechanism (over 2-photon ionization) from the beginning of the interaction [19]. This would be analogous to how pre-ionization can seed avalanche in dielectrics [24]. In this case, the absorption response is dependent on the initial free electron density. Obviously, this does not occur in the density range 1013 – 1018 cm−3 that can be tested by direct transmission diagnostics. Thus, our results indicate that 2-photon ionization remains likely the major seeding mechanism for the non-linear absorption. According to a multiphoton-based interaction, the laser energy deposition must remain confined in the focal volume (that is the region of highest intensity). To demonstrate this aspect, we also perform the measurements using a Z-scan method that consists in measuring the non-linear transmission of the samples while focusing the beam at different depths inside the substrate. While maintaining the laser pulse energy, the focus is translated through the sample by moving the Z stage and we acquire transmission values. Total transmission as a function of focusing position is shown in Fig. 4a for three samples of different doping concentrations and thicknesses. In this experiment, the laser pulse energy is fixed at 4 nJ. When the focal volume interacts in air (Z < 0 m and Z > 600 m), intensities arriving on the sample are not sufficient to initiate two-photon absorption. The measurement leads to 0.53 transmission revealing again that silicon is transparent at 1.3 m. Non-linear absorption takes place only when the laser focal volume is located in the substrate; it directly confirms a local laser energy deposition in the sample. The very sharp transition at the two interfaces of each sample reveals the confinement of the nonlinear interaction in the focal volume. The localization is so pronounced that the Z-scan measurement is sensitive to the difference of thickness t between the tested samples (t < 40 m). This demonstrates that we can deposit laser energy and we can generate free-carriers very similarly in all regions of about 500m thick silicon substrates with these focusing conditions. The length on which the absorption occurs (tabs ) corresponds to the thickness of the sample (tSi ) divided by the silicon refractive index (tabs ∼ tSi /nSi with nSi ∼ 3.5 at 1.3 m). Here it also worth noting that the measurement of Fig. 4a was performed for 3 samples of different doping concentration from 1013 cm−3 to 1016 cm−3 leading to the same absorption level. This result is consistent with the previous measurement where the initial free electron density does not influence the non-linear transmission response of silicon for doping concentration up to 1018 cm−3 (see Fig. 3). We can also notice that the transmission is constant in the bulk of silicon for the 3 samples of about 500 m thickness. It reveals that the geometrical property of the focal volume (and the peak intensity) is not strongly affected by the focusing depth and so the confinement of the interaction is relatively well conserved all over <600 m thick samples. In Fig. 4b, we repeat the same Z-scan experiment on one sample and we change the laser pulse energy. The energy dependence of the total transmission inside the sample is
Fig. 4. Z-scan transmission measurements of silicon samples with different doping concentrations and thicknesses. The transmission is plotted as a function of focus position along the optical axis. The experimental curve is obtained by translating the microscope objective along the optical axis while translating the sample (in the XY plane) so that fresh material is irradiated on each shot.
another manifestation of the non-linear character of the interaction. The sharpness of the transition at the two interfaces is less pronounced when high intensity laser pulses are used due to the growth of the region in which the intensity dependent interaction takes place. Due to the high refractive index of silicon (nSi = 3.5 at 1.3 m wavelength), we predict that the focal volume gets affected by spherical aberration when performing deep focusing interactions. In Fig. 5a, we show the same Z-scan experiments performed on a 3 mm thick substrate (Si, orientation: 1 0 0, type: intrinsic, optical grade) while focusing the beam with a 0.45 NA NIR refractive objective (Olympus-LCPLN-20XIR). We observe that for the first 150 m of our Z-scan inside the material, the transmission remains quite constant confirming spherical aberrations do not affect the focal volume in this range. This result is consistent with the previous experiment made on <600 m silicon wafers with reflective conditions. However, we see with this thick sample that the absorption of the laser beam decreases as the focus position gets deeper inside the material. This response is very similar to that observed in dielectrics where it was attributed to spherical aberration [25]. Indeed, spherical aberration tends to progressively elongate the focal volume and the associated local peak intensity is lowered inside the material, explaining the decrease of non-linear absorption observed in the measurements. An advantage of performing the measurement with transmission objectives that are specially designed to work in the NIR domain for microelectronic device observation is that spherical aberration can be compensated by tuning a correction collar on the objective. The compensation holds for a single given thickness
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free-carrier densities because the substrates become opaque (see Fig. 1) making impossible any transmission diagnostics. However, 1018 cm−3 remains two orders of magnitude below the critical density and the opacity of the substrates relies on bulk absorption properties. Thus, to investigate higher densities by transmission, one way can be to populate the conduction band only inside the micron-size interaction region of intrinsic silicon substrates to maintain a relative transparency. While we have concentrated this paper on the interaction with doped samples, we will show in a future paper that this can be achieved by a double-pulse experiment, where a first pulse is focused inside intrinsic silicon and populates the conduction band in the focal region. The second pulse is focused at the same location and can experience strong nonlinear absorption triggered by the free-carriers injected by the first pulse. We have highlighted the independence on doping concentration of the non-linear laser energy deposition with Phosphorous-doped Silicon at levels up to 1018 cm−3 . This represents a signature of two-photon ionization as the main source triggering the multiplication of carriers and the subsequent absorption. It is also a result of major importance for technological considerations. The approach must allow future 3D laser modification applications inside semiconductors. Acknowledgments
Fig. 5. Transmission measured for the focusing of ∼18 nJ pulses inside 3 mm thick silicon at different depths with a NA = 0.45 lens with adjustable correction for spherical aberration. We compare the transmission with two correction collar adjustments corresponding to 0 mm (a) and 1.2 mm of silicon (b). The maximum of absorption is shifted with the adjustment.
of silicon but allows to directly confirm the role of aberration in our experiments. In Fig. 5b, we show the result of the same Z-scan measurement (similar to Fig. 5a) but for a focused beam corrected for the spherical aberration associated with propagation through 1.2mm thick silicon substrates. We obtain a minimum of transmission at a Z-position of d ≈ 350 m below the original position of the surface. This corresponds to a beam focus motion of d × nSi ≈ 1.2 mm. The accordance of this observation with the correction adjustment shows unambiguously that controlled focused interactions in bulk silicon require compensating for spherical aberrations. 3.1. Conclusion and perspectives We have shown that the presence of free-electrons introduced by doping does not influence the non-linear absorption of 1.3 m wavelength laser pulses inside silicon. The use of doped sample provides a way to perform a – model independent – study of avalanche inside silicon. Because seeded-avalanche by free carriers from doping was not observed, we can directly conclude avalanche is not efficiently triggered up to a 1018 cm−3 free electron density. We have estimated the two-photon absorption threshold to be on the order of 1012 W/cm2 . Our simple diagnostic shows (with Z-scan measurements) that the energy deposition remains confined in micron-scale regions. However, controlled illumination conditions with beams that are tightly (NA > 0.4) and deeply (>600 m) focused under the surface of silicon substrates require to work with focusing optics corrected for spherical aberration. Our method to investigate the role of avalanche relies on silicon doping but it is not applicable to investigate the effect of higher
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