In this study, we report first time the effect of laser pulse repetition frequency and pulse width of femtosecond laser radiation on silicon nanofibrous structure formation under ambient condition. Surface nanotexture analysis revealed the changes in fibrous structure density and size in respect of laser pulse width and repetition frequency. A phonon confinement model is used to explain the Raman spectra of processed specimens in order to understand the structure details of nanofibrous structure and hence to support the surface nanotexture analysis. The present investigation leads to a conclusion that nanofibrous structure is formed due to the aggregation of silicon nanoparticles and their size is estimated using the confinement model which is in the order of few nanometers.
© 2009 Optical Society of America
The development of zero and one-dimensional Si nanostructures has gained interest because of their imminent technological applications in areas such as optoelectronics , nanoelectronics , photovoltaic devices , memory devices  and sensors . All these applications are associated to the huge surface area of nanostructures and their very small size. Also the properties of nanostructures depend on their dimension and differ from their corresponding bulk. A proper understanding of the dependence of a given property on nanostructure dimensions can lead to modification of the structure for desired application. Investigations pertaining to nanostructure formation using ultra short laser processing of materials with background gas opened new possibilities in nanostructure synthesis [6–9]. Although several investigations have been reported about silicon nanostructure formation using femtosecond laser processing with kHz pulses with background gas , 10–12], studies relating to the nanostructure formation with MHz pulses in ambient condition are limited. In a previous study we reported first time the formation of nanofibrous structure in silicon and metallic targets by aggregation of nanoparticles using femtosecond laser ablation with MHz laser pulses under ambient condition . The similarity between the nanoparticles aggregation by laser vaporization controlled condensation technique  and femtosecond laser ablation indicates that the nanofibrous structure formation mechanism may well be related to nucleation and growth process of nanoparticles. It is also found that laser pulse frequency plays a critical role in the formation of nanofibrous structure. The critical time for nucleation of silicon nanoparticles corresponds to a frequency of 1.53 MHz, which agrees well with experimental observations where the silicon nanofibrous structure start to form at a threshold frequency of 2 MHz .
Nanostructures have been the subject of a number of experimental and theoretical investigations in an effort to understand their size dependent structural, electronic and optical properties [16, 17]. Raman spectroscopy has already been employed for the characterization of nanostructures on laser processed silicon surfaces [8, 18]. Generally the models explaining the optical properties of nanostructures assume the quantum confinement of electrons, holes and phonons . In addition the vibrational properties of nanostructures are sensitive not only to their dimensionality but also to the shape and growth-related parameters . This results a shift and broadening of Raman signal from the nanostructures. Changes in line broadening and peak position of the optical phonon mode in Raman spectra can be used to determine the dimension of nanostructures.
In this work we aim to study the effect of laser pulse width and frequency of femtosecond laser radiation on silicon nanofibrous structure formation by Scanning Electron Microscopy (SEM) and micro-Raman spectroscopy. Also a model based on confinement of phonons in nanoparticles is employed to explain the Raman spectra of laser processed specimens intend to clarify the nanofibrous structure details and to support nanotextural analysis.
The experimental setup used in the present study is similar to that reported in Ref. . The laser source is a diode-pumped Yb-doped fiber oscillator/amplifier system capable of producing variable pulse energies up to 10 mJ at a pulse frequency between 200 kHz and 25 MHz. The laser radiation is circularly polarized and its average power varies between 0-20W. Arrays of microvias were drilled on a specimen of boron doped blank silicon wafer with <100> crystal orientation using 428 fs laser pulses with frequencies 4, 8, 13 and 26 MHz. In another experiment the microvias were drilled in a different location of the specimen at a constant pulse frequency of 13 MHz with pulse widths 428, 714, 1428 and 3571 fs. In both set of experiments, the average laser power is kept constant. The specimens were then characterized using micro-Raman spectroscopy followed by SEM. Back scattering micro-Raman analysis was performed at room temperature using 532 nm line of Ar ion laser source. The amorphous 490 cm-1 peak is isolated from the crystalline 518 cm-1 peak by deconvolution prior to the Fourier decomposition.
3. Results and discussion
The SEM micrograph in Fig. 1 shows areas adjacent to the microvias of specimen processed with frequencies 4, 8, 13 and 26 MHz and a pulse width of 428 fs. This frequency range is well above the threshold frequency for nanoparticle formation . Nanofibrous structure with a certain degree of porosity is observed for all the frequencies with no evidence of molten droplets. When compared to nanofibrous structure density observed with specimens processed at 4 MHz (Fig. 1a), a significant increase in density is observed for 8 MHz (Fig. 1b). Since laser power and spot size were kept constant in our experiments, pulse energy reduces with the increase of pulse repetition rate and results a reduction in nanoparticle size. For repetition rates above the nanoparticles formation threshold, ablation from successive laser pulses happens before the ablated nanoparticles on the specimen due to previous pulse cools down. Consequently nanoparticles ejected by successive laser pulses prefer to agglomerate with particles ablated from the previous laser pulse, which are still at very high temperature and results an increase of nanofibrous structure density. Further increase in frequency can increase the number of nanoparticles which are agglomerating to the nanofibrous structure. SEM micrographs of specimens processed with a frequency of 13 MHz and 26 MHz show an increase in fibrous structure size and surface porosity (Fig. 1c & d). As the repetition rate increases from 13 MHz to 26 MHz the energy per pulse decreases. The fibrous structure formation stabilizes for repetition rates between 4 MHz to 26 MHz . The pulse separation time is about 39 ns for 26 MHz repetition rate. The vapor is supplied continuously by the successive laser pulses to the expanding plume and leads to coalescence of several nuclei and increase the size of the particle.
SEM micrographs of the areas of specimen processed with a frequency of 13 MHz and 428, 714, 1428 and 3571 fs laser pulses are presented in Fig. 2. It is observed that the nanofibrous structure size increases with pulse width. However this increase is not due to the increase in number of nanoparticles which are agglomerating to form the structure but this is mainly due to an increase in the individual nanoparticles size (Fig.2). This is because the interaction time increases with pulse width. Thus as explained earlier the size of the nucleus formed increases due to coalescence of many nucleuses and as a consequence the size of the individual nanoparticle increases.
For laser processing parameters used in the present study nanofibrous structure size is observed to vary between 50 to 70 nm. In order to evaluate further the nanofibrous structural details in both cases, micro-Raman scattering experiments are performed on the same areas where the SEM micrographs has been taken.
Raman spectroscopy is a sensitive probe to local atomic arrangements and vibrations (phonons) in solids . This technique has been used to characterize nanostructures that provide information about the nature of crystalline structure, disorder and amorphization. In the lattice of single crystal, both optic and acoustic phonons can propagate as a wave and exhibit dispersion depending on their wavelength or equivalently their wave vector in the Brillouin zone. In nanostructured materials when a grain boundary is encountered the phonon propagation is interrupted. The phonon of an isolated grain can get reflected from the boundaries and remain confined within the grain. For nanoparticles and quantum dots the phonon confinement is 3 dimensional and the wave propagation is restricted in all three directions. Raman spectroscopy technique sample the optic phonons close to the Brillouin zone center (q = 0) and is a consequence of the periodicity of the crystal lattice. In the case of nanoparticles this crystal periodicity is interrupted, (q = 0) selection rule is relaxed and phonons away from the Brillouin zone center also contribute to the phonon line shape. Similar to the optical phonons, the acoustic phonons also get confined within the nanoparticles. In the elastic continuum limit, the confinement of long-wavelength acoustic phonons leads to the emergence of discrete modes of particle which depend on the elastic properties through the longitudinal and transverse sound velocities.
Interestingly micro-Raman spectra of regions around the laser drilled microvias of the specimens show two sharp peaks as well as a broad band (Fig. 3). At 4 MHz with 428 fs pulses, the sharp Raman peaks are centered at 518 cm-1 and 491 cm-1 while the broad band at 283 cm-1 (Fig. 3a). As frequency increases, the 518 cm-1 peak remain at same position while 491 cm-1 peak is shifted to lower wave number side and appears at 490 and 488.6 cm-1 respectively for 8 and 13 MHz. Nevertheless for 26 MHz this peak is shifted back to 490 cm-1. In Fig. 3b spectra of the specimen areas processed at a constant frequency of 13 MHz with pulse widths 428, 714, 1428 and 3571 fs are presented. As in first case, with increasing pulse width the peak at 518 cm-1 continues at the same position while the other sharp peak appears at 488.6, 488.1, 492.2 and 498 cm-1. Moreover the two sharp peaks are shifted by an amount of ~2 cm-1 and ~30 cm-1 respectively from the peak at 520 cm-1 that corresponds to bulk silicon. In all the processed regions a broad band centered at 283 cm-1 is observed. The peaks at ~490 cm-1 and 283 cm-1 are in excellent agreement with the predicted transverse optic (TO) and the 2-fold transverse acoustic (TA) modes of silicon nanoparticles [20, 21].
For bulk silicon 520 cm-1 peak arises from first-order Raman scattering of transverse optical (TO) phonon modes which are degenerated at the Γ-point (phonon wave vector q = 0 near the center of the Brillouin zone). The 518 cm-1 sharp peak can be attributed to substrate silicon and the 2 cm-1 shift when compared to crystalline silicon peak at 520 cm-1, is possibly due to the strain induced by laser radiation. Therefore it is difficult to retain the crystal structure, and the sharp peak at 520 cm-1 . The stress in the irradiated silicon surface can be likely due to changes in the material resulting from crystalline variations of the resolidified material . For a uniaxial stress, there is a linear relation between the internal stress (σ) and the Raman peak shift. ∆ω (cm-1) = -2 × 10-9 σ (Pa) . A positive value of the shift indicates compressive stress, and a negative value of the shift indicates tensile stress. A shift of -2 cm-would correspond to a tensile stress of 1 GPa.
The size of the nanostructures can be determined by the phonon confinement model which was introduced to describe Raman scattering from optical phonons in nanostructures . One dimensional confinement occurs in thin films and a 2-d confinement occurs in nanowires . The 3-d confinement occurs in quantum dots and nanoparticles. As the dimensionality of phonon confinement reduces, the magnitude of the Raman peak shift reduced considerably [16, 23]. A 2-d confinement may not be appropriate for the observed Raman peak shift (~30 cm-1). Therefore in the present analysis we have considered a 3-d confinement. Further in a previous study it was shown that the formation of nanofibrous structure is due to nanoparticles agglomeration . Gaussian confinement function has been extensively used as weight factor of the phonon wave function and is given by [16, 23, 24]:
where L is the correlation length related with the size of the nanoparticles. The square of the Fourier coefficient which gives the scattering probability of phonons with wave vector q and is given by:
The Raman spectrum I(ω) due to this confined optical phonon is given by:
where a0 is lattice constant (0.543 nm) of silicon and Γ2 Raman line width of bulk silicon (4.5 cm-1). The phonon dispersion relation ω(q) is given by:
where ω0 is the zone-center optical phonon frequency and q0=2π/a0.
Having fixed the Raman line shift, when the Fourier coefficient (Eqn. 2) is inserted in the integral formula (Eq. 3), the nanoparticle size L can be calculated. The size calculated with respect to laser pulse repetition frequency and pulse width using the phonon confinement model is presented in Fig. 4 and corroborates the previous discussion of nanofibrous structure formation.
In conclusion, this study reports first time the study of silicon nanofibrous structure generated using femtosecond laser radiation in air at atmospheric pressure. SEM analysis of nanofibrous structure shows that laser pulse width and frequency has a significant effect on fibrous structure size and density. Further Micro-Raman peaks of the processed specimens are explained using the phonon confinement model and leads to the conclusion that the nanofibrous structure is a consequence of agglomeration of silicon nanoparticles. The change in nanoparticle size calculated as a function of laser pulse repetition frequency and pulse width using the confinement model agree well with the surface nanotexture analysis.
This research is funded by Natural Science and Engineering Research Council of Canada.
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