The following article appeared in Journal of Applied Physics 106, 104910 (2009) and may be found under http://dx.doi.org/10.1063/1.3261734
On the role of surface plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond laser pulses Jörn Bonse1,a), Arkadi Rosenfeld2, and Jörg Krüger1 1
BAM Bundesanstalt für Materialforschung und –prüfung, Fachgruppe VI.4 Oberflächentechnologien, Unter
den Eichen 87, D-12205 Berlin, Germany 2
Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie (MBI), Max-Born-Straße 2a, D-12489
Berlin, Germany
ABSTRACT The formation of nearly wavelength-sized laser-induced periodic surface structures (LIPSS) on single-crystalline silicon upon irradiation with single or multiple femtosecond (fs) laser pulses (pulse duration τ = 130 fs, central wavelength λ = 800 nm) in air is studied experimentally and theoretically. In our theoretical approach, we model the LIPSS formation by combining the generally accepted first-principle theory of Sipe and co-workers with a Drude model in order to account for transient intra-pulse changes of the optical properties of the material due to the excitation of a dense electron-hole plasma. Our results are capable to explain quantitatively the spatial periods of the LIPSS being somewhat smaller than the laser wavelength, their orientation perpendicular to the laser beam polarization and their characteristic fluence dependence. Moreover, evidence is presented that surface plasmon polaritons play a dominant role during the initial stage of near-wavelength sized periodic surface structures in fs laser irradiated silicon and it is demonstrated that these LIPSS structures can be formed in silicon upon irradiation by single fs laser pulses.
PACS: 79.20.Ds, 71.36.+c, 68.47.Fg
a)
author to whom correspondence should be addressed; Electronic mail:
[email protected]
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I.
INTRODUCTION
Since the first experimental observation of laser-induced periodic surface structures (LIPSS, frequently called ripples) by Birnbaum,1 their investigation has developed into a scientific evergreen. During the past decade, this topic has gained remarkable attraction due to the rising availability of ultrashort (fs) laser pulses, where the formation of two distinct types of LIPSS has been observed upon irradiation with multiple linearly polarized fs laser pulses [socalled low spatial frequency LIPSS (LSFL) and high spatial frequency LIPSS (HSFL)].2,3,4,5,6,7,8,9 It is generally accepted that LSFL, having a spatial period close to the irradiation wavelength, are formed due to optical interference of the incident laser radiation with a surface-electromagnetic wave which is created during the irradiation.2,4,10 In contrast, the HSFL have spatial periods significant smaller than the irradiation wavelength and are solely observed for irradiation with ultrashort laser pulses (predominantly for below-band-gap excitation of transparent materials and hundreds to thousands of laser pulses per irradiation spot site). The nature of the HSFL is still quite controversially discussed in the literature3,4,5,6,8,11,12,13,14 and they are not within the scope of this work.
Ti:sapphire fs-laser pulse generated LSFL in silicon are typically observed after a few laser pulses at laser fluences slightly above the ablation threshold. For normal incident radiation, they usually have spatial periods ΛLSFL somewhat smaller than the laser wavelength (λ = 800 nm) and an orientation perpendicular to the polarization vector.2 So far, no satisfactory explanation has been presented why the experimentally observed fs-laser generated LSFL periods in silicon typically are 0.62 λ1×1022 cm-3 [Figs. 3(g) and 3(h)].
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For better comparison, we have quantitatively evaluated horizontal cross sections through the LSFL feature in the efficacy factor maps (κy = 0). From each cross-section (data not shown here), the maximal amplitude (see the right scale in Fig. 4) and the LSFL period corresponding to the position of the maximum via Λ peak = λ κ x ( LSFL ) have been evaluated as a function of the carrier density (see the black full circles in Fig. 4, left scale). In order to account for variations in the LSFL period, we have empirically chosen a 90%-of-maximumcriterion and have evaluated the corresponding minimum and maximum LSFL periods accordingly (see the triangles and the squares in Fig. 4, left scale).
Most strikingly, the LSFL periods show a minimum of ~720 nm around the critical carrier density Ne ~ Ncr = 4.275×1021 cm-3 with a variation of +30 nm and -70 nm. In contrast, the maximum amplitude of the LSFL peak is reached at somewhat higher carrier concentrations (Ne ~6×1021 cm-3). At carrier concentrations >1×1022 cm-3, the Sipe-Drude theory predicts LSFL period approaching the laser wavelength along with strongly decreasing peak amplitudes of the LSFL feature. The latter fact suggests that the LSFL should not be observed at very high excitation levels of the silicon. The carrier concentration range over which significantly reduced LSFL periods ΛLSFL (compared to λ) can be observed lies between ~2×1021 cm-3 …~1×1022 cm-3. For comparison with the experimental data shown in Fig. 1, we have estimated the carrier density in the CB as a function of the laser fluence using a model which considers solely linear and two-photon absorption in the material.17 The carrier density in NIR fs-laser-excited silicon is then given
(
)
by N e ≈ φ0 (1 − R ) α + βφ0 (1 − R ) 2 2πτ
( hν ) , with the linear absorption coefficient α =
1.1×103 cm-1 [Ref. 18], the surface reflectivity R(θ=0°)= 0.328,18 and the two-photon absorption coefficient β = 6.8 cm/GW.19 In the fluence range between the experimentally observed single pulse ablation threshold (0.52 J/cm2, see Ref.
15) and the multi-pulse
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ablation threshold (~0.2 J/cm2, see Ref. 2) carrier densities between 1.4×1021 cm-3 and 6.7×1021 cm-3 are obtained. At the peak fluence value of 0.42 J/cm2 as used in Fig. 1, a carrier density of 4.6×1021 cm-3 is estimated which is close to the critical carrier density Ncr, indicating a remarkable agreement between experiments and the theory presented here.
Since the Sipe theory includes the possibility of the excitation of surface plasmon polaritons and the feature B becomes most pronounced in the η maps when the carrier concentration is large enough to change the sign of the dielectric permittivity ε% * (allowing the excitation of SPP), we propose here that the early stages of the LSFL formation in fs-pulse irradiated silicon is dominated by the excitation of SPP once the initially dielectric material turns into a metallic state upon the laser excitation. It should be noted here that SPP have already been proposed very early to be involved in the LIPSS formation, e.g., by Keilmann and Bai20 to explain periodic surface structures upon ns-CO2-laser pulse irradiation of quartz, later by many other authors,7,9,10 and – very recently – by Martsinovskii et al. specifically for IR-fslaser pulse irradiation of silicon.21
The SPP-hypothesis along with our numerical calculations is capable to explain the following important aspects of LSFL formation in fs-laser excited silicon under normal incident radiation: (a) LSFL lines are oriented predominantly perpendicular to the polarization vector (see Fig. 3). (b) LSFL exhibit spatial periods somewhat smaller than the laser wavelength, since the surface damage occurs at carrier concentrations close to the critical carrier density of SPP excitation where the LSFL peak in the efficacy factor η broadens (Figs. 3 and 4). The variation of the experimentally reported periods may be explained by the
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sensitivity of the LSFL periods at excitations levels close to the critical carrier density/ damage threshold. (c) LSFL are formed only in a relatively narrow fluence range where the laser-induced carrier concentration is of the order of 1021 - 1022 cm-3 (see Fig. 4). (d) In principle, it should be possible to observe LSFL already for single-pulse irradiation, provided that a SPP can be excited e.g., by a sufficiently rough surface or by surface defects.
However, since the Sipe-theory does not include the feedback phase, which is already proven to be important for the LIPSS formation, our theoretical results cannot directly be applied to multi-pulse experiments of LIPSS formation. According to our calculations the observation of LSFL should be possible already after a single laser pulse. Hence, we have analyzed in more detail the single-pulse generated ablation morphologies of fs-laser irradiated silicon surfaces and particularly the phenomena accompanying the “bubble formation” reported in Ref. 2.
Figure 5(a) shows a Nomarski optical micrograph of a (111) silicon wafer surface irradiated by a single Ti:sapphire 130-fs laser pulse at a peak fluence of φ0 = 4.63 J/cm2. Many laserinduced bubble formation features can be seen. Interestingly, only in the periphery of the ablation spot (where the local laser fluence has already dropped significantly from its peak value) some wave-like structures are surrounding the centers of the bubble formation sites. In this particular case, these bubbles are most likely formed by an increased local absorption of the laser pulse energy due to surface defects or contaminations which have been generated by other ablation experiments prior to single-pulse irradiation event (note the re-deposited material in the non-irradiated surface regions here). In order to characterize the periods of the wave-like structures, the micrograph shown in Fig. 5(a) has been subjected to a twodimensional Fourier transform (2D-FT) which is shown in Fig. 5(b). A sickle shaped feature 9
can be seen which corresponds to periods ranging between 680 and 795 nm, which excellently agrees with the values predicted by the theory (see Fig. 4). Moreover, the shape of the feature shown in Fig. 5(b) reasonably agrees with the LSFL feature shown in Fig. 3(e).
Figure 6 shows a detail magnification on the left side of the irradiation spot previously shown in Fig. 5(a). The periodic surface structures surrounding the laser-induced bubble site are most visible within the ablation crater, where the surface topography exhibits a relief structure. Interestingly, the same periodic pattern also extents into the annular region of superficial laser-induced melting and subsequent amorphization (without material removal). Hence, we conclude that the periodic surface patterns are caused here by an optical interference effect between the incident fs laser beam and the surface near electromagnetic field generated by the SPP which was excited e.g. via coupling to a surface defect already during the fs laser pulse.22
The hypothesis that surface defect mediated excitation of SPP’s is essential also for the multipulse feedback phase in the LIPSS formation is directly supported by the image series shown in Fig. 1 of Ref. 23. In that figure it can be seen for 800 nm fs-laser pulse irradiation in SF6 environment, that such rather circular structures (as shown in Fig. 6 here) act as a seed and develop already after the second laser pulse into a LSFL pattern having predominantly parallel lines (as previously shown in Fig. 1 of this work).
IV. CONCLUSIONS The formation of low-spatial frequency LIPSS (LSFL) in single crystalline silicon upon irradiation with single and multiple NIR fs-laser pulses (τ = 130 fs, λ = 800 nm) in air was studied theoretically and experimentally elucidating the orientation of the ripple lines perpendicular to the beam polarization and that the LSFL periods can be reduced by up to
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some tens of percent compared to the laser wavelength. The LSFL origin lies in the defectinitiated generated excitation of surface plasmon polaritons which can interfere with the incident laser beam and then can lead to a modulated energy deposition into the material. This effect has been observed already after irradiation by a single laser pulse and is essential during the feedback phase of the LSFL formation. Moreover, our theoretical calculations reveal that LSFL are formed only in a relatively narrow fluence range where the laser-induced carrier concentration in the conduction band is of the order of 1021 - 1022 cm-3 - in good agreement with experimental observations.
ACKNOWLEDGMENTS
The authors would like to thank B. Strauss (BAM VI.4, Berlin, Germany) for taking the SEM images. This work was supported by the German Science Foundation (DFG) under grant no. KR 3638/1-1 and grant no. RO 2074/7-1.
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Capillary surface waves frozen in the residual melt layer can be ruled out here as a
mechanism for the formation of the surface relief structure: Fork et al. [Appl. Phys. Lett. 68, 2138 (1996)] have shown that capillary waves of Λcap~800 nm wavelength excited on a ~100 nm thick liquid layer have a propagation distance of less than 2 µm before they are damped – a value which is significantly smaller than the maximum radial extent of ~10 µm over which the surface relief pattern can be observed in Fig. 5. 23
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Figure Captions FIG. 1. (Color online) Nomarski optical micrograph (a) and detail magnification by scanning electron microscopy (b) of a (111) silicon wafer surface irradiated by five fs-laser pulses [φ0 = 0.42 J/cm2, N = 5] in air. The horizontal arrows marked with E in (a) indicate the direction of polarization of the fs-laser beam.
FIG. 2. (Color online) Geometry of the laser beam incidence to a rough surface, which has been used to model the formation of LIPSS.
FIG. 3. (Color online) Two-dimensional gray scale maps of the efficacy factor η for singlecrystalline silicon as a function of the normalized LIPSS wave vector (κx,κy = -5.0..5.0) for different excitation levels of the material [all for normal incident radiation (θ = 0°) at λ = 800 nm; the polarization E is indicated in (h)]. (a) Ne = 0 cm-3; n = 3.692, k = 0.065; (b) Ne = 1×1021 cm-3; n = 3.299, k = 0.170; (c) Ne = 2×1021 cm-3; n = 2.868, k = 0.382; (d) Ne = 4.275×1021 cm-3; n = 1.833, k = 1.262; (e) Ne = 6×1021 cm-3; n = 1.436, k = 2.254; (f) Ne = 7.5×1021 cm-3; n = 1.347, k = 2.999; (g) Ne = 2×1022 cm-3; n = 1.610, k = 6.668; (h) Ne = 5×1022 cm-3; n = 2.345, k = 11.429; ε% * = (n+ik)2; The values of η are encoded in a common linear gray scale with dark colors representing larger values. The symbols A and B label some characteristic features.
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FIG. 4. (Color online) LSFL period obtained from the B-feature position in the η-map (peak value and upper and lower limits as obtained from a 90%-criterion) and maximum value of the efficacy factor η for the LSFL feature as a function of the excitation level of the laserexcited silicon. Note the logarithmic carrier density scale.
FIG. 5. (Color online) Nomarski optical micrograph (a) of a (111) silicon wafer surface irradiated by a single fs laser pulse [φ0 = 4.63 J/cm2, N = 1] in air. In (b) the 2D-Fourier transform of (a) is shown indicating LIPSS with periods between 790 and 660 nm. The dashboxed region in (a) marks the region shown in Fig. 6. The horizontal arrows marked with E in (a) indicate the direction of polarization of the fs-laser beam.
FIG. 6. Detail magnification of the optical micrograph shown in Fig. 5(a).
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