Size-dependent Fano Interaction in the Laser-etched Silicon Nanostructures
- Rajesh Kumar^{1},
- AK Shukla^{1}Email author,
- HS Mavi^{1} and
- VD Vankar^{1}
Received: 13 November 2007
Accepted: 14 February 2008
Published: 4 March 2008
Abstract
Photo-excitation and size-dependent Raman scattering studies on the silicon (Si) nanostructures (NSs) prepared by laser-induced etching are presented here. Asymmetric and red-shifted Raman line-shapes are observed due to photo-excited Fano interaction in the quantum confined nanoparticles. The Fano interaction is observed between photo-excited electronic transitions and discrete phonons in Si NSs. Photo-excited Fano studies on different Si NSs show that the Fano interaction is high for smaller size of Si NSs. Higher Fano interaction for smaller Si NSs is attributed to the enhanced interference between photo-excited electronic Raman scattering and phonon Raman scattering.
Keywords
Fano interference Silicon nanostructures Raman spectraIntroduction
Raman scattering from the silicon (Si) nanostructures (NSs) has been extensively studied in recent years [1–4]. Observed Raman line-shapes from the Si NSs are asymmetrically broadened and red-shifted from its counterpart for the bulk Si. Most authors have fitted the first-order experimental Raman band to an asymmetrical line-shape first proposed by Richter et al. [5] and then modified by Campbell et al. [6]. In this model, the asymmetry and red-shift in the Raman peak have been attributed to the confinement of phonons in the Si NSs. Many others [3, 4] have explained the asymmetry and downshift in the Raman line-shape in terms of a combined effect of quantum confinement and laser heating. Magidson and Beserman [7] have observed the Fano interference [8, 9] between photo-excited electrons and discrete phonons in bulk Si when Raman spectra were recorded using laser power density of 10^{6} W/cm^{2}. However, the presence of photo-excited Fano interaction in Si NSs was proposed very recently where detailed photo-excitation-dependent Raman studies were carried out on the Si NSs [10]. An increase in the asymmetry ratio of Raman line-shape was noticed as a result of increasing excitation laser power density in the range 0.22–1.76 kW/cm^{2}. Effect of the quantum confinement on Fano resonance is not studied yet and needs further studies to elucidate the behavior of Fano interaction as a function of Si NSs size and laser power density.
The purpose of this paper is to study the Fano interaction in the Si NSs as a function of the NSs size and laser power density. The Si NSs of two different sizes are fabricated by laser-induced etching (LIE) method [11] by etching using two different etching times for same laser power. Surface morphology is studied by atomic force microscopy (AFM) to see the formation of quantum confined Si NSs. Raman spectra are recorded using two different laser power densities of 0.2 and 0.88 kW/cm^{2} for both the samples. Raman spectra recorded using 0.2 kW/cm^{2} are fitted using phenomenological phonon confinement model [5, 6] to calculate the most probable Si NSs size. Using these NSs sizes, Raman spectra recorded using 0.88 kW/cm^{2} are fitted using Fano-Raman line-shape [10] to find the Fano asymmetry parameter to see the effect of Si NSs size on the Fano interaction. Higher Fano interaction is seen for smaller Si NSs as compared to large Si NSs.
Experimental Details
Two samples (samples A and B) containing Si NSs are fabricated by the LIE method [11]. The LIE is done by immersing a Si wafer (resistivity of 3–5 Ω cm) into 48% HF acid and then focusing a 500 mW argon-ion laser beam (E _{ex} = 2.41 eV) to a circular spot of 120-μm on the wafer. The etching time is 45 min for the sample A and 60 min for the sample B keeping other parameters (like laser power density, wavelength, and concentration of HF) the same. Raman scattering was excited using photon energy ∼2.54 eV of the argon-ion laser at two different laser power densities of 0.2 and 0.88 kW/cm^{2}. The reason for choosing low laser power density is to avoid heating of the sample during Raman recording. Raman spectra were recorded by employing an SPEX-1403 doublemonochromator with HAMAMATSU (R943-2) photomultiplier tube arrangement and an argon ion laser (COHERENT, INNOVA 90).
Results and Discussions
Laser power density-dependent Raman spectra from smaller Si NSs in sample B are shown in Fig. 2c, d. Figure 2c, d is the Raman spectra from sample B when recorded using excitation laser power densities of 0.2 and 0.88 kW/cm^{2}, respectively. Raman spectrum in Fig. 2c has peak at 518 cm^{−1}with asymmetry ratio of 2.9 and FWHM of 13.5 cm^{−1}. Higher asymmetry ratio and phonon softening in Fig. 2c as compared to Fig. 2a is due to higher quantum confinement effect from Si NSs in sample B than in sample A. The Raman spectrum peaked at 517 cm^{−1}with asymmetry ratio of 3.7 and FWHM of 16.5 cm^{−1}is observed in Fig. 2d due to photo-excited Fano interaction in sample B.
Different fitting parameters used to fit the Raman line-shapes from samples A and sample B in the Fig. 2
Sample | L _{0}(nm) | L _{1}(nm) | L _{2}(nm) | σ(nm) |
---|---|---|---|---|
Sample A | 4.5 | 3.5 | 5 | 1 |
Sample B | 3 | 2.5 | 4 | 1 |
Experimental Raman data in Fig. 2b, d shown as discrete triangles are fitted with Fano-Raman line-shape of Eq. 1 with the appropriate L _{0} L _{1}, and L _{2} values obtained earlier for samples A and B as given in Table 1. In order to fit the experimental Raman data in Fig. 2b, d, ‘q’ is used as the fitting parameter. The experimental data in Fig. 2b, d show a good fitting for the Fano asymmetry parameter |q| equal to 16 and 10 for the samples A and B, respectively. It reveals higher photo-excited Fano interaction in the smaller size NSs (sample B) as compared to larger size NSs (sample A). While fitting Raman data, the value of ‘q’ was kept constant for a given L _{0}, where the distribution of size is very narrow (σ = 1 nm). The smaller sizes present in the sample B are much smaller in size as compared to the Bohr’s exciton radius of 5 nm for Si [16]. Thus, the confinement effect will be more in sample B in comparison with sample A. Quantum confinement of electrons lead to discrete energy levels. Photo-excited electrons interact with incident photon by electronic Raman scattering. This is possible when photo-excited electrons make transitions between discrete levels. Electronic Raman scattering may interfere with usual optical phonon scattering when optical phonon energy lies in the region ΔE = E _{1} − E _{2}(where, E _{1} and E _{2} are energy of discrete electronic levels). Probability of interference increases in the smaller size NSs where discrete electronic levels are separated by optical phonon energy. Such type of Fano interaction cannot be seen in bulk Si or larger sized NSs. Fano interaction can be seen in the bulk Si when doping is above 10^{19} cm^{−3} [17]. Therefore, size-dependent Fano interaction in Si NSs is due to quantum confinement of electrons and phonons in laser-etched Si.
Conclusions
In summary, the Raman line-shapes from the Si NSs are investigated as a function of Si NSs size and excitation laser power density. The Raman line-shape becomes more asymmetric, wider, and shifts to lower wavenumber when the Raman spectra are recorded with higher laser power density. This behavior is attributed to the Fano interference between discrete phonons and photo-excited electronic transitions. Fano interaction is more pronounced for smaller size NSs at same laser power density. In other words, smaller size NSs will start showing photo-excited Fano interaction at lower excitation laser power density than for larger size NSs. Higher quantum confinement of photo-excited electrons and phonons in smaller Si NSs is responsible for observation of size-dependent photo-excited Fano interaction in laser-etched Si NSs.
Declarations
Acknowledgments
Authors acknowledge the financial support from the Department of Science and Technology, Goverment of India under the project “Optical studies of self-assembled quantum dots of semiconductors”. One of the authors (R. Kumar) acknowledges the financial support from Council of Scientific and Industrial Research (CSIR), India. Technical support from Mr. N.C. Nautiyal is also acknowledged.
Authors’ Affiliations
References
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