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Quantum interference in the Raman scattering from the silicon nanostructures
Physics Letters A 373 (2009) 2882–2886
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Quantum interference in the Raman scattering from the silicon nanostructures Rajesh Kumar ∗ , A.K. Shukla Department of Physics, Indian Institute of Technology Hauz Khas, New Delhi 110016, India
a r t i c l e
i n f o
Article history: Received 18 February 2009 Received in revised form 3 April 2009 Accepted 2 June 2009 Available online 6 June 2009 Communicated by R. Wu PACS: 78.67.Bf 78.55.-m 78.67.-n
a b s t r a c t We report here microscopic process involved in the photo-excited Fano interaction due to nonlinear process in the silicon nanostructures. Photo-excited Raman line-shapes are investigated to reveal the presence of nonlinear Fano interaction in the silicon nanostructures for three different sizes. The Fano interaction is found to be more prominent due to the phase matching between electronic and phonon Raman scatterings for smaller sized nanostructures. Phase matching is achieved by nonlinear process of two-wave mixing in the silicon nanostructures followed by the formation of electron–phonon bound state. © 2009 Elsevier B.V. All rights reserved.
Keywords: Raman spectroscopy Silicon nanostructures Phonon confinement effect
1. Introduction Understanding of microscopic level physical processes taking place in the silicon (Si) nanostructures (NSs) is essential for technological advancement of Si related industries. In crystalline Si (c-Si), the electron–phonon coupling in terms of interference between electronic transitions and optical phonons results in the asymmetric Raman line-shape. Observation of the Fano interference [1] is one of the well-studied properties in the heavily doped p-type [2,3] and n-type [4,5] Si. Doping for the interference has been reported to be greater than 1 × 1019 cm−3 in c-Si [6]. Oscillator strength of electronic Raman scattering is large enough to interfere with that of the phonon Raman scattering to show Fano type asymmetric Raman line-shape. Alternatively, Fano interaction involving the photo-excited electrons and the optical phonons can also be observed if an excitation laser power density of the order of 106 W/cm2 is used in the c-Si [7]. However, the presence of photo-excited Fano interaction in the Si NSs is proposed recently where detailed photo-excitation-dependent Raman studies are carried out on the Si NSs [8]. An increase in the asymmetry ratio of Raman line-shape is noticed as a function of low excitation laser power density in the range 0.22–1.76 kW/cm2 . Physical explanation of the photo-excited Fano interaction may be investigated by the quantum confinement effect on the Fano interaction.
*
Corresponding author. Tel.: +91 11 2659 6027. E-mail address: [email protected] (R. Kumar).
0375-9601/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2009.06.005
Quantum confinement of electronic Raman scattering due to low dimensionality will affect the photo-excited Fano interaction in the Si NSs. Nonlinear property of the Si NSs is utilized here to achieve the required phase matching condition by two-wave mixing. Aim of this Letter is to reveal nonlinear effect, which participates in the electronic Raman scattering in the quantum confined structures. Quantum interference between discrete optical phonon and photo-excited electronic transitions takes place in the Si NSs during Raman scattering. Fano interference between electronic and phonon Raman scatterings increases as the sizes of NSs are reduced. Study of quantum interference in the Si NSs will be helpful in understanding the nonlinear Fano processes in different quantum structures [9,10]. Present study provides the correlation of the microscopic level process taking place in the Si NSs with the observable macroscopic characterization tools. Asymmetric Raman line-shapes are also observed from the Si NSs [11,12] due to quantum confinement effect. Most authors have fitted the first-order experimental Raman band to an asymmetrical line-shape first proposed by Richter et al. [13] and then modified by Campbell et al. [14]. In this model, the asymmetry and red-shift in the Raman peak have been attributed to the confinement of phonons in the Si NSs. Effect of quantum confinement on electrons has also been discussed in terms of visible photoluminescence (PL) at room temperature [15,16]. At room temperature, visible PL is observed from the Si NSs due to modification in the electronic structures as a result of its low dimensionality. Modified electronic structure enhances electronic Raman scattering in low dimensions. Probability of interference between electronic Raman
R. Kumar, A.K. Shukla / Physics Letters A 373 (2009) 2882–2886
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scattering and discrete phonon Raman scattering increases with the decreasing size of the Si NSs. Study of quantum confinement effect on Fano interaction will reveal the electronic Raman scattering in the Si NSs as a function of their size. In this Letter, observation of the Fano interference in the Si NSs is explained by studying size-dependent Fano interaction. The Fano interaction between electronic Raman scattering and phonon Raman scattering is found to be more prominent in the smaller Si NSs. Higher quantum confinement of photo-excited electrons and phonons in smaller Si NSs are responsible for the photo-excited Fano interaction (i.e. quantum interference). Size-dependent Fano interaction is utilized here to extract the experimental electronic Raman scattering from the Si NSs for the first time. Two-wave mixing due to nonlinear effect is proposed here to explain the enhanced Fano effect in the Si NSs as compared to c-Si. 2. Experimental details Three samples (sample A, sample B and sample C) containing Si NSs are fabricated by the laser induced etching (LIE) method [17]. The LIE is done by immersing a Si wafer into HF acid and then focusing an argon-ion laser beam on it. The Si wafers were etched for different etching times to fabricate the Si NSs of different sizes for a given etching laser power density of 1.76 kW/cm2 . The etching times for sample A, sample B and sample C are 45 minutes, 60 minutes and 90 minutes, respectively. Other parameters (like laser power density, wavelength and concentration of HF) were not changed. Raman scattering was excited using photon energy of 2.41 eV of an argon ion laser at two different laser power densities of 0.2 and 1.0 kW/cm2 . Raman and PL spectra were recorded by employing a SPEX-1403 double monochromator with HAMAMATSU (R943-2) photomultiplier tube arrangement and an argon ion laser (COHERENT, INNOVA 90). 3. Results and discussions Figs. 1(a)–(c) show the SEM micrographs of sample A, sample B and sample C respectively. Figs. 1(a) and (b) show porous structures on the Si wafer. Pores in sample A and sample B are formed as a result of LIE in HF acid. Difference in pores in Fig. 1(a) and (b) is due to increased etching time. On the other hand, pillar type structures are formed in sample C in Fig. 1(c), where etching time is 90 min. Pores and pillar like structures are due to macro-surface morphology reconstructions during LIE at the wafer surface. Details about the surface morphology reconstruction is reported in our earlier work [17]. Figs. 2(a)–(c) show AFM images of the Si NSs formed in sample A, sample B and sample C respectively. The images shown in Fig. 2 are high-resolution images taken from the pore walls of the laser-etched samples. Fig. 2 shows the formation of the Si NSs having sizes in the range of a few nanometers. In Fig. 2, average Si NSs size of 10 nm, 7 nm and 5 nm are observed in sample A, sample B and sample C respectively. The Si NSs of smaller size are formed in the sample B as compared to the sample A due to increased etching time. Similarly, sample C contains further smaller Si NSs in comparison with sample B. These AFM images show the micro-surface morphology reconstruction taking place in the etched area as reported in our earlier work [17]. Higher quantum confinement is expected in sample B and sample C as compared to sample A. Possible quantum confinement effect in these Si NSs is investigated using room temperature PL spectroscopy. Figs. 3(a)–(c) show the room temperature PL spectra from sample A, sample B and sample C, respectively. Fig. 3(a) shows very low intensity visible PL, which suggests that weak quantum confinement is present in sample A. Broad PL spectra are observed from sample B and sample C. Sample C contains smaller Si NSs as compared to sample
Fig. 1. SEM micrographs showing surface morphologies of (a) sample A, (b) sample B and (c) sample C.
B due to larger etching time. As a result, the PL spectrum form sample C is blue-shifted as compared to sample B in Fig. 3. This type of size-dependent PL spectra further confirms the presence of quantum confinement of electrons [15,16] in our samples. Broad visible PL spectra in Fig. 3 reveal the presence of broad electronic states within which electronic transitions may take place for the electronic Raman scattering. The onset of PL around 1.6 eV suggests that the first available electronic transition has this much energy with a width of ∼ 800 meV (upto ∼ 2.4 eV). The width of available electronic states (800 meV) is higher that the typical phonon energy for Si (∼ 65 meV). Thus, there is a possibility of interference between the electronic and phonon Raman scatterings to yield Fano interaction [5]. Detailed investigation of Fano interaction is done using Raman scattering. Fig. 4(a) shows the Raman spectrum from sample A recorded using an excitation laser power density of 0.2 kW/cm2 . The Raman peak position is downshifted to 519 cm−1 as compared to the Raman active zone-center optic phonons at 520.5 cm−1 for c-Si. The Raman line-shape in Fig. 4(a) has asymmetry ratio of 1.93 and FWHM of 8 cm−1 due to weakly confined optical phonons in the Si NSs. The asymmetry ratio is defined here as Γl /Γh , where Γl and Γh are half widths on the low- and high-energy side of the maximum. Raman spectrum from the sample A recorded at 1.0 kW/cm2 is shown in Fig. 4(b). Raman line-shape in Fig. 4(b) has asymmetry ratio of 2.05 and FWHM of 9 cm−1 . Fig. 4(b) shows that asymmetry and FWHM in the Raman line-shape is increased by increasing laser power density. Changes in the Raman line-shape
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Fig. 3. Room temperature photoluminescence spectra from (a) sample A, (b) sample B and (c) sample C.
Fig. 2. High-resolution AFM images of silicon nanostructures in (a) sample A, (b) sample B and (c) sample C.
show reversible nature on decreasing the laser power density. This reversible nature reveals that the asymmetric Raman line-shape is not due to quantum confinement effect alone. It may be due to combined effect of quantum confinement and Fano interaction. Fano interaction takes place as a result of quantum interference between electronic Raman scattering involving photo-excited electrons within electronic states (seen in the PL spectrum) and usual discrete optic phonon scattering. When Raman scattering is excited with higher laser power density (1.0 kW/cm2 ), more number of photons are available for scattering. As a result, electronic Raman scattering will increase. Since the excitation laser power density is not high enough to produce any heating effect [18], anharmonic effect in the phonon Raman scattering can be neglected in Fig. 4(b). Thus, higher Raman intensity in Fig. 4(b) as compared to Fig. 4(a) is observed due to increase in the electronic Raman scattering for excitation laser power density of 1.0 kW/cm2 . Sample B contains smaller Si NSs as compared to that in sample A. Raman spectra of sample B are shown in Figs. 4(c) and (d) for the laser power densities of 0.2 and 1.0 kW/cm2 respectively. Raman spectrum in Fig. 4(c) has a peak at 518.5 cm−1 with asymmetry ratio of 2.41 and FWHM of 10 cm−1 whereas, Raman spectrum in Fig. 4(d) shows Raman mode at 518 cm−1 with asymmetry ratio of 2.75 and FWHM of 11 cm−1 . Similarly, Raman spectra from sample C recorded using excitation laser power density of 0.2 and 1.0 kW/cm2 are shown in Fig. 4(e) and (f), respectively. Raman spectra in Fig. 4(e) has a peak at 518 cm−1 with asymmetry ratio of 2.67 and FWHM of 12 cm−1 . Raman mode for excitation
Fig. 4. Raman spectra from sample A, sample B and sample C. The calculated Raman spectra are indicated by solid line curve and the experimental data are plotted as discrete points. Discrete points shown as solid squares and solid circles are recorded using excitation laser power density of 0.2 and 1.0 kW/cm2 respectively. Phonon confinement model has been used to fit the experimental data in (a), (c) and (e) whereas Eq. (1) is used to fit the data in (b), (d) and (f).
laser power density of 1.0 kW/cm2 for sample C is observed at 517 cm−1 with asymmetry ratio of 3 and FWHM of 14 cm−1 . It is observed that electronic Raman scattering increases with excitation laser power in Fig. 4. Comparison of Figs. 4(a) and (c) shows that Raman peak for sample B has more downshift and FWHM as compared to its counterpart in sample A because of higher quantum confinement in sample B in comparison to sample A. The same trend is seen in Raman spectra from sample C and sample B. One can also notice in Figs. 4(b), (d) and (f) that the increase in asymmetry ratio due to Fano interaction is maximum for smallest Si NSs (sample C), where quantum confinement effect dominates due to further smaller size of Si NSs. In Si NSs, the quantum confinement of electrons leads to discrete energy levels as characterized by PL spectra. Photo-excited electrons present in these electronic levels make transitions and participate in the electronic Raman scattering. At low laser power density, the electronic Raman scattering is negligible due to insufficient photo-excited electrons and this electronic Raman background cannot couple with usual optical phonon Raman line. As the laser power density is increased, electronic Raman component enhances and couples with the already asymmetric Raman phonon
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Table 1 Different fitting parameters used to fit the Raman line-shapes from sample A, sample B and sample C in Fig. 4. Sample
L 0 (nm)
L 1 (nm)
L 2 (nm)
σ (nm)
Sample A Sample B Sample C
6 5 3.5
4.5 3.5 3
7 .5 6 .5 6
1 1 1
line-shape from Si NSs to increase the asymmetry further as seen in Fig. 4. Therefore, Raman scattering from the Si NSs is seen as quantum interference in terms of asymmetric Fano–Raman lineshape. To quantitatively analyze this effect, experimental data in Fig. 4 are theoretically fitted with following Fano line-shape for the Si NSs:
1
L 2 I (ω) ∝
N (L) L1
0
2 2 2 (ε + q)2 2 exp −k L /4a d k dL , 1 + ε2
(1)
ω(k) where, ε = ω− Γ /2 . The ω(k) is the phonon dispersion relation of the optic phonons of c-Si. The q is Fano asymmetry parameter. The Γ , L and a are the line width, crystallite size and lattice constant, respectively. The term in curly bracket takes care of the Fano interaction and the exponential term takes into account the quantum confinement effect on the Fano interaction in the Si NSs of size L. The N ( L ) is a Gaussian function to take care of the NSs size distribution. The L 0 , L 1 and L 2 are the mean crystallite size, the minimum and the maximum confinement dimensions respectively. Fano effect is negligible (|1/q| ∼ 0) at low laser power density of 0.2 kW/cm2 due to insufficient number of photo-excited electrons. Therefore, the experimental Raman data shown as discrete squares in Figs. 4(a), (c) and (e) are fitted by considering only quantum confinement effect of optical phonons (Eq. (1) of Ref. [16]). The theoretically obtained value of mean crystallite size (L 0 ) is 6 nm for sample A, 5 nm for sample B and 3.5 nm for sample C. This implies that the quantum confinement effect is maximum in sample C and minimum in sample A. Other fitting parameters obtained for best fitting, corresponding to solid lines in Fig. 4, is listed in Table 1. These fitting parameters are used while fitting the experimental Raman data using Eq. (1) in Figs. 4(b), (d) and (f) shown by discrete circles. The experimental data in Figs. 4(b), (d) and (f) show a good fitting for the Fano asymmetry parameter |q| equal to 25 for the sample A, 16 for the sample B and 11 for sample C. It reveals highest photo-excited Fano interaction in the smallest size Si NSs (sample C) as compared to relatively larger size Si NSs (sample A and sample B). Size-dependent experimental electronic Raman spectra from sample A, sample B and sample C can be extracted from Fig. 4. Raman spectra in Figs. 4(a), (c) and (e) have no electronic contribution whereas Raman spectra in Figs. 4(b), (d) and (f) contains the contribution from electronic Raman scattering and phonon Raman scattering both. Raman spectra in Figs. 4(b), (d) and (f) have been normalized in such a way to make the Raman intensity at 600 cm−1 (where quantum interference is totally absent) as the base line. Thus, the electronic Raman spectra from Si NSs can be obtained by subtracting the spectra in Figs. 4(a), (c) and (e) from Figs. 4(b), (d) and (f), respectively. The experimentally extracted electronic Raman spectra from sample A, sample B and sample C are shown as discrete points in the Fig. 5. Fig. 5 also shows that the electronic Raman scattering is more enhanced in smaller Si NSs. The continuous lines in Fig. 5 are the theoretical fitting3 of the experimental data using Eq. (2):
√ I e (ω) =
(E
PL
h¯ ω
+ αh¯ ω − E exc )2
,
(2)
Fig. 5. Experimentally extracted electronic Raman spectra from (a) sample A, (b) sample B and (c) sample C.
Fig. 6. Various Raman processes for nanostructures involving scattering from (a) phonon only, (b) electronic transition and (c) electron–phonon bound states.
is the energy of first available electronic transition conwhere, E PL tributing to the visible PL which is equal to 1.6 eV (onset of the electronic transition). The E exc is the excitation photon energy. α is a fitting parameter obtained by fitting the experimental electronic Raman data (discrete points) with Eq. (2). It gives a measure of electronic Raman scattering originating from the Si NSs for a given size distribution. In other words, α characterizes the structure of electronic states present beyond the PL onset energy. The best theoretical fitting in Fig. 4 is obtained with α equal to 12.4, 12.2 and 12 for sample A, sample B and sample C, respectively. Size-dependence of electronic Raman scattering and Fano interaction in the Si NSs can be understood as follows. In nanostructures, Raman scattering process can be intermediated by phonon or electron giving rise to pure phonon or pure electronic Raman spectra respectively. These two processes are schematically shown in Figs. 6(a) and (b), respectively. For Si NSs having sizes in the range 8 nm (weak quantum confinement), the phonon Raman scattering process results in an asymmetric Raman line-shape, which is red shifted as predicted by phonon confinement model [13,14]. On the other hand, the electronic Raman scattering involving the electronic transitions within the electronic states (as revealed in the PL spectra) is observed as a continuum background in the Raman spectrum without any characteristic peak. Our samples containing Si NSs are a nonlinear medium, i.e. a dielectric like medium, which has been reported in the Z-scan technique [19], optical fringe [20] and wave mixing [21,22]. As the size of NSs decreases, enhanced electronic gap of the Si NSs approaches the incident photon energy and probability of two-wave mixing increases by nonlinear process. This leads to phase matching by creation of electron–phonon bound state (interferon) as shown in Fig. 6(c). Interferon has been reported earlier by Balkanski et al. [3] for the c-Si. Concept of the interferon explains our experimental observations showing Fano
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interaction in the Si NSs. If δ is the phase angle between Raman active electronic and Raman active phonon wave-vectors, δ can be written empirically as: −1
|δ| = tan
E ex − E PL E ex
a result, strong electron–phonon interaction yields enhanced Fano interaction in the Raman scattering from the Si NSs. Acknowledgements
,
(3)
where, E ex is the excitation photon energy and E PL is the energy of PL peak corresponding to highest intensity. As the Si NSs size is decreased, the PL energy ( E PL ) approaches the excitation photon energy. Thus the phase matching condition satisfies for quantum interference, which results in the formation of bound state. This type of size-dependent behavior of Fano interaction in the Si NSs can be compared with the excitation wavelength-dependent Fano interaction [4] in c-Si. 4. Conclusions In conclusion, Fano interaction between discrete phonons and photo-excited electronic transitions is studied in the Si NSs as a function of NSs size and laser power density. More asymmetric, wider and red shifted Raman line-shapes are observed by increasing the excitation laser power density. This is due to the fact that more photo-excited electrons are generated at higher laser power density. These photo-excited electrons participate in the continuum of electronic Raman scattering and interacts with zone center optic phonons to yield Fano interaction. Experimental electronic Raman spectra can also be obtained from the photo-excitationdependent Raman spectra for samples containing different sized Si NSs. The nonlinear Fano interaction is more pronounced for smaller sized Si NSs for a given laser power density. Increased energy gap due to quantum confinement effect approaches more closer to the incident photon energy which enhances the electronic Raman scattering. This in turn satisfies the phase matching condition by nonlinear process of two-wave mixing in the Si NSs. As
Authors thank Prof. V.D. Vankar for useful discussions. Authors also acknowledge Dr. H.S. Mavi for valuable comments. Authors acknowledge the financial support from the Department of Science and Technology, Government of India, under the project “Optical Studies of Self-Assembled Quantum Dots of Semiconductors”. One of the authors (R.K.) acknowledges the financial support from Council of Scientific and Industrial Research (CSIR), India. Technical support from Mr. N.C. Nautiyal is also acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
U. Fano, Phys. Rev. 124 (1961) 1866. F. Cerdeira, M. Cardona, Phys. Rev. B 5 (1972) 1440. M. Balkanski, K.P. Jain, R. Beserman, M. Jouanne, Phys. Rev. B 12 (1975) 4328. M. Chandrasekhar, J.B. Renucci, M. Cardona, Phys. Rev. B 17 (1978) 1623. M. Jouanne, R. Beserman, I. Ipatova, A. Subashiev, Solid State Commun. 16 (1975) 1047. N.H. Nickel, P. Lengsfeld, I. Sieber, Phys. Rev. B 61 (2000) 15558. V. Magidson, R. Beserman, Phys. Rev. B 66 (2002) 195206. R. Kumar, H.S. Mavi, A.K. Shukla, V.D. Vankar, J. Appl. Phys. 101 (2007) 064315. M. Kroner, et al., Nature 451 (2008) 311. W. Zhang, A.O. Govorov, G.W. Bryant, Phys. Rev. Lett. 97 (2006) 146804. R. Wang, et al., Phys. Rev. B 61 (2000) 16827. M.J. Konstantinovic, et al., Phys. Rev. B 66 (2002) 161311. H. Richter, Z.P. Wang, L. Ley, Solid State Commun. 39 (1981) 625. I.H. Campbell, P.M. Fauchet, Solid State Commun. 58 (1986) 739. D.P. Yu, et al., Phys. Rev. B 59 (1999) 2498. H.S. Mavi, et al., Semicond. Sci. Technol. 21 (2006) 1627. R. Kumar, H.S. Mavi, A.K. Shukla, Micron 39 (2008) 287. R. Kumar, A.K. Shukla, B. Joshi, S.S. Islam, Jpn. J. Appl. Phys. 47 (2008) 8461. G. Vijayaprakash, et al., J. Appl. Phys. 91 (2002) 4607. S. Prusty, H.S. Mavi, A.K. Shukla, Phys. Rev. B 71 (2005) 113313. J.E. Sharping, et al., Opt. Express 14 (2006) 12388. L.A. Golovan, et al., Laser Phys. 11 (2001) 1292.
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Quantum interference in the Raman scattering from the silicon nanostructures Rajesh Kumar ∗ , A.K. Shukla Department of Physics, Indian Institute of Technology Hauz Khas, New Delhi 110016, India
a r t i c l e
i n f o
Article history: Received 18 February 2009 Received in revised form 3 April 2009 Accepted 2 June 2009 Available online 6 June 2009 Communicated by R. Wu PACS: 78.67.Bf 78.55.-m 78.67.-n
a b s t r a c t We report here microscopic process involved in the photo-excited Fano interaction due to nonlinear process in the silicon nanostructures. Photo-excited Raman line-shapes are investigated to reveal the presence of nonlinear Fano interaction in the silicon nanostructures for three different sizes. The Fano interaction is found to be more prominent due to the phase matching between electronic and phonon Raman scatterings for smaller sized nanostructures. Phase matching is achieved by nonlinear process of two-wave mixing in the silicon nanostructures followed by the formation of electron–phonon bound state. © 2009 Elsevier B.V. All rights reserved.
Keywords: Raman spectroscopy Silicon nanostructures Phonon confinement effect
1. Introduction Understanding of microscopic level physical processes taking place in the silicon (Si) nanostructures (NSs) is essential for technological advancement of Si related industries. In crystalline Si (c-Si), the electron–phonon coupling in terms of interference between electronic transitions and optical phonons results in the asymmetric Raman line-shape. Observation of the Fano interference [1] is one of the well-studied properties in the heavily doped p-type [2,3] and n-type [4,5] Si. Doping for the interference has been reported to be greater than 1 × 1019 cm−3 in c-Si [6]. Oscillator strength of electronic Raman scattering is large enough to interfere with that of the phonon Raman scattering to show Fano type asymmetric Raman line-shape. Alternatively, Fano interaction involving the photo-excited electrons and the optical phonons can also be observed if an excitation laser power density of the order of 106 W/cm2 is used in the c-Si [7]. However, the presence of photo-excited Fano interaction in the Si NSs is proposed recently where detailed photo-excitation-dependent Raman studies are carried out on the Si NSs [8]. An increase in the asymmetry ratio of Raman line-shape is noticed as a function of low excitation laser power density in the range 0.22–1.76 kW/cm2 . Physical explanation of the photo-excited Fano interaction may be investigated by the quantum confinement effect on the Fano interaction.
*
Corresponding author. Tel.: +91 11 2659 6027. E-mail address: [email protected] (R. Kumar).
0375-9601/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2009.06.005
Quantum confinement of electronic Raman scattering due to low dimensionality will affect the photo-excited Fano interaction in the Si NSs. Nonlinear property of the Si NSs is utilized here to achieve the required phase matching condition by two-wave mixing. Aim of this Letter is to reveal nonlinear effect, which participates in the electronic Raman scattering in the quantum confined structures. Quantum interference between discrete optical phonon and photo-excited electronic transitions takes place in the Si NSs during Raman scattering. Fano interference between electronic and phonon Raman scatterings increases as the sizes of NSs are reduced. Study of quantum interference in the Si NSs will be helpful in understanding the nonlinear Fano processes in different quantum structures [9,10]. Present study provides the correlation of the microscopic level process taking place in the Si NSs with the observable macroscopic characterization tools. Asymmetric Raman line-shapes are also observed from the Si NSs [11,12] due to quantum confinement effect. Most authors have fitted the first-order experimental Raman band to an asymmetrical line-shape first proposed by Richter et al. [13] and then modified by Campbell et al. [14]. In this model, the asymmetry and red-shift in the Raman peak have been attributed to the confinement of phonons in the Si NSs. Effect of quantum confinement on electrons has also been discussed in terms of visible photoluminescence (PL) at room temperature [15,16]. At room temperature, visible PL is observed from the Si NSs due to modification in the electronic structures as a result of its low dimensionality. Modified electronic structure enhances electronic Raman scattering in low dimensions. Probability of interference between electronic Raman
R. Kumar, A.K. Shukla / Physics Letters A 373 (2009) 2882–2886
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scattering and discrete phonon Raman scattering increases with the decreasing size of the Si NSs. Study of quantum confinement effect on Fano interaction will reveal the electronic Raman scattering in the Si NSs as a function of their size. In this Letter, observation of the Fano interference in the Si NSs is explained by studying size-dependent Fano interaction. The Fano interaction between electronic Raman scattering and phonon Raman scattering is found to be more prominent in the smaller Si NSs. Higher quantum confinement of photo-excited electrons and phonons in smaller Si NSs are responsible for the photo-excited Fano interaction (i.e. quantum interference). Size-dependent Fano interaction is utilized here to extract the experimental electronic Raman scattering from the Si NSs for the first time. Two-wave mixing due to nonlinear effect is proposed here to explain the enhanced Fano effect in the Si NSs as compared to c-Si. 2. Experimental details Three samples (sample A, sample B and sample C) containing Si NSs are fabricated by the laser induced etching (LIE) method [17]. The LIE is done by immersing a Si wafer into HF acid and then focusing an argon-ion laser beam on it. The Si wafers were etched for different etching times to fabricate the Si NSs of different sizes for a given etching laser power density of 1.76 kW/cm2 . The etching times for sample A, sample B and sample C are 45 minutes, 60 minutes and 90 minutes, respectively. Other parameters (like laser power density, wavelength and concentration of HF) were not changed. Raman scattering was excited using photon energy of 2.41 eV of an argon ion laser at two different laser power densities of 0.2 and 1.0 kW/cm2 . Raman and PL spectra were recorded by employing a SPEX-1403 double monochromator with HAMAMATSU (R943-2) photomultiplier tube arrangement and an argon ion laser (COHERENT, INNOVA 90). 3. Results and discussions Figs. 1(a)–(c) show the SEM micrographs of sample A, sample B and sample C respectively. Figs. 1(a) and (b) show porous structures on the Si wafer. Pores in sample A and sample B are formed as a result of LIE in HF acid. Difference in pores in Fig. 1(a) and (b) is due to increased etching time. On the other hand, pillar type structures are formed in sample C in Fig. 1(c), where etching time is 90 min. Pores and pillar like structures are due to macro-surface morphology reconstructions during LIE at the wafer surface. Details about the surface morphology reconstruction is reported in our earlier work [17]. Figs. 2(a)–(c) show AFM images of the Si NSs formed in sample A, sample B and sample C respectively. The images shown in Fig. 2 are high-resolution images taken from the pore walls of the laser-etched samples. Fig. 2 shows the formation of the Si NSs having sizes in the range of a few nanometers. In Fig. 2, average Si NSs size of 10 nm, 7 nm and 5 nm are observed in sample A, sample B and sample C respectively. The Si NSs of smaller size are formed in the sample B as compared to the sample A due to increased etching time. Similarly, sample C contains further smaller Si NSs in comparison with sample B. These AFM images show the micro-surface morphology reconstruction taking place in the etched area as reported in our earlier work [17]. Higher quantum confinement is expected in sample B and sample C as compared to sample A. Possible quantum confinement effect in these Si NSs is investigated using room temperature PL spectroscopy. Figs. 3(a)–(c) show the room temperature PL spectra from sample A, sample B and sample C, respectively. Fig. 3(a) shows very low intensity visible PL, which suggests that weak quantum confinement is present in sample A. Broad PL spectra are observed from sample B and sample C. Sample C contains smaller Si NSs as compared to sample
Fig. 1. SEM micrographs showing surface morphologies of (a) sample A, (b) sample B and (c) sample C.
B due to larger etching time. As a result, the PL spectrum form sample C is blue-shifted as compared to sample B in Fig. 3. This type of size-dependent PL spectra further confirms the presence of quantum confinement of electrons [15,16] in our samples. Broad visible PL spectra in Fig. 3 reveal the presence of broad electronic states within which electronic transitions may take place for the electronic Raman scattering. The onset of PL around 1.6 eV suggests that the first available electronic transition has this much energy with a width of ∼ 800 meV (upto ∼ 2.4 eV). The width of available electronic states (800 meV) is higher that the typical phonon energy for Si (∼ 65 meV). Thus, there is a possibility of interference between the electronic and phonon Raman scatterings to yield Fano interaction [5]. Detailed investigation of Fano interaction is done using Raman scattering. Fig. 4(a) shows the Raman spectrum from sample A recorded using an excitation laser power density of 0.2 kW/cm2 . The Raman peak position is downshifted to 519 cm−1 as compared to the Raman active zone-center optic phonons at 520.5 cm−1 for c-Si. The Raman line-shape in Fig. 4(a) has asymmetry ratio of 1.93 and FWHM of 8 cm−1 due to weakly confined optical phonons in the Si NSs. The asymmetry ratio is defined here as Γl /Γh , where Γl and Γh are half widths on the low- and high-energy side of the maximum. Raman spectrum from the sample A recorded at 1.0 kW/cm2 is shown in Fig. 4(b). Raman line-shape in Fig. 4(b) has asymmetry ratio of 2.05 and FWHM of 9 cm−1 . Fig. 4(b) shows that asymmetry and FWHM in the Raman line-shape is increased by increasing laser power density. Changes in the Raman line-shape
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Fig. 3. Room temperature photoluminescence spectra from (a) sample A, (b) sample B and (c) sample C.
Fig. 2. High-resolution AFM images of silicon nanostructures in (a) sample A, (b) sample B and (c) sample C.
show reversible nature on decreasing the laser power density. This reversible nature reveals that the asymmetric Raman line-shape is not due to quantum confinement effect alone. It may be due to combined effect of quantum confinement and Fano interaction. Fano interaction takes place as a result of quantum interference between electronic Raman scattering involving photo-excited electrons within electronic states (seen in the PL spectrum) and usual discrete optic phonon scattering. When Raman scattering is excited with higher laser power density (1.0 kW/cm2 ), more number of photons are available for scattering. As a result, electronic Raman scattering will increase. Since the excitation laser power density is not high enough to produce any heating effect [18], anharmonic effect in the phonon Raman scattering can be neglected in Fig. 4(b). Thus, higher Raman intensity in Fig. 4(b) as compared to Fig. 4(a) is observed due to increase in the electronic Raman scattering for excitation laser power density of 1.0 kW/cm2 . Sample B contains smaller Si NSs as compared to that in sample A. Raman spectra of sample B are shown in Figs. 4(c) and (d) for the laser power densities of 0.2 and 1.0 kW/cm2 respectively. Raman spectrum in Fig. 4(c) has a peak at 518.5 cm−1 with asymmetry ratio of 2.41 and FWHM of 10 cm−1 whereas, Raman spectrum in Fig. 4(d) shows Raman mode at 518 cm−1 with asymmetry ratio of 2.75 and FWHM of 11 cm−1 . Similarly, Raman spectra from sample C recorded using excitation laser power density of 0.2 and 1.0 kW/cm2 are shown in Fig. 4(e) and (f), respectively. Raman spectra in Fig. 4(e) has a peak at 518 cm−1 with asymmetry ratio of 2.67 and FWHM of 12 cm−1 . Raman mode for excitation
Fig. 4. Raman spectra from sample A, sample B and sample C. The calculated Raman spectra are indicated by solid line curve and the experimental data are plotted as discrete points. Discrete points shown as solid squares and solid circles are recorded using excitation laser power density of 0.2 and 1.0 kW/cm2 respectively. Phonon confinement model has been used to fit the experimental data in (a), (c) and (e) whereas Eq. (1) is used to fit the data in (b), (d) and (f).
laser power density of 1.0 kW/cm2 for sample C is observed at 517 cm−1 with asymmetry ratio of 3 and FWHM of 14 cm−1 . It is observed that electronic Raman scattering increases with excitation laser power in Fig. 4. Comparison of Figs. 4(a) and (c) shows that Raman peak for sample B has more downshift and FWHM as compared to its counterpart in sample A because of higher quantum confinement in sample B in comparison to sample A. The same trend is seen in Raman spectra from sample C and sample B. One can also notice in Figs. 4(b), (d) and (f) that the increase in asymmetry ratio due to Fano interaction is maximum for smallest Si NSs (sample C), where quantum confinement effect dominates due to further smaller size of Si NSs. In Si NSs, the quantum confinement of electrons leads to discrete energy levels as characterized by PL spectra. Photo-excited electrons present in these electronic levels make transitions and participate in the electronic Raman scattering. At low laser power density, the electronic Raman scattering is negligible due to insufficient photo-excited electrons and this electronic Raman background cannot couple with usual optical phonon Raman line. As the laser power density is increased, electronic Raman component enhances and couples with the already asymmetric Raman phonon
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Table 1 Different fitting parameters used to fit the Raman line-shapes from sample A, sample B and sample C in Fig. 4. Sample
L 0 (nm)
L 1 (nm)
L 2 (nm)
σ (nm)
Sample A Sample B Sample C
6 5 3.5
4.5 3.5 3
7 .5 6 .5 6
1 1 1
line-shape from Si NSs to increase the asymmetry further as seen in Fig. 4. Therefore, Raman scattering from the Si NSs is seen as quantum interference in terms of asymmetric Fano–Raman lineshape. To quantitatively analyze this effect, experimental data in Fig. 4 are theoretically fitted with following Fano line-shape for the Si NSs:
1
L 2 I (ω) ∝
N (L) L1
0
2 2 2 (ε + q)2 2 exp −k L /4a d k dL , 1 + ε2
(1)
ω(k) where, ε = ω− Γ /2 . The ω(k) is the phonon dispersion relation of the optic phonons of c-Si. The q is Fano asymmetry parameter. The Γ , L and a are the line width, crystallite size and lattice constant, respectively. The term in curly bracket takes care of the Fano interaction and the exponential term takes into account the quantum confinement effect on the Fano interaction in the Si NSs of size L. The N ( L ) is a Gaussian function to take care of the NSs size distribution. The L 0 , L 1 and L 2 are the mean crystallite size, the minimum and the maximum confinement dimensions respectively. Fano effect is negligible (|1/q| ∼ 0) at low laser power density of 0.2 kW/cm2 due to insufficient number of photo-excited electrons. Therefore, the experimental Raman data shown as discrete squares in Figs. 4(a), (c) and (e) are fitted by considering only quantum confinement effect of optical phonons (Eq. (1) of Ref. [16]). The theoretically obtained value of mean crystallite size (L 0 ) is 6 nm for sample A, 5 nm for sample B and 3.5 nm for sample C. This implies that the quantum confinement effect is maximum in sample C and minimum in sample A. Other fitting parameters obtained for best fitting, corresponding to solid lines in Fig. 4, is listed in Table 1. These fitting parameters are used while fitting the experimental Raman data using Eq. (1) in Figs. 4(b), (d) and (f) shown by discrete circles. The experimental data in Figs. 4(b), (d) and (f) show a good fitting for the Fano asymmetry parameter |q| equal to 25 for the sample A, 16 for the sample B and 11 for sample C. It reveals highest photo-excited Fano interaction in the smallest size Si NSs (sample C) as compared to relatively larger size Si NSs (sample A and sample B). Size-dependent experimental electronic Raman spectra from sample A, sample B and sample C can be extracted from Fig. 4. Raman spectra in Figs. 4(a), (c) and (e) have no electronic contribution whereas Raman spectra in Figs. 4(b), (d) and (f) contains the contribution from electronic Raman scattering and phonon Raman scattering both. Raman spectra in Figs. 4(b), (d) and (f) have been normalized in such a way to make the Raman intensity at 600 cm−1 (where quantum interference is totally absent) as the base line. Thus, the electronic Raman spectra from Si NSs can be obtained by subtracting the spectra in Figs. 4(a), (c) and (e) from Figs. 4(b), (d) and (f), respectively. The experimentally extracted electronic Raman spectra from sample A, sample B and sample C are shown as discrete points in the Fig. 5. Fig. 5 also shows that the electronic Raman scattering is more enhanced in smaller Si NSs. The continuous lines in Fig. 5 are the theoretical fitting3 of the experimental data using Eq. (2):
√ I e (ω) =
(E
PL
h¯ ω
+ αh¯ ω − E exc )2
,
(2)
Fig. 5. Experimentally extracted electronic Raman spectra from (a) sample A, (b) sample B and (c) sample C.
Fig. 6. Various Raman processes for nanostructures involving scattering from (a) phonon only, (b) electronic transition and (c) electron–phonon bound states.
is the energy of first available electronic transition conwhere, E PL tributing to the visible PL which is equal to 1.6 eV (onset of the electronic transition). The E exc is the excitation photon energy. α is a fitting parameter obtained by fitting the experimental electronic Raman data (discrete points) with Eq. (2). It gives a measure of electronic Raman scattering originating from the Si NSs for a given size distribution. In other words, α characterizes the structure of electronic states present beyond the PL onset energy. The best theoretical fitting in Fig. 4 is obtained with α equal to 12.4, 12.2 and 12 for sample A, sample B and sample C, respectively. Size-dependence of electronic Raman scattering and Fano interaction in the Si NSs can be understood as follows. In nanostructures, Raman scattering process can be intermediated by phonon or electron giving rise to pure phonon or pure electronic Raman spectra respectively. These two processes are schematically shown in Figs. 6(a) and (b), respectively. For Si NSs having sizes in the range 8 nm (weak quantum confinement), the phonon Raman scattering process results in an asymmetric Raman line-shape, which is red shifted as predicted by phonon confinement model [13,14]. On the other hand, the electronic Raman scattering involving the electronic transitions within the electronic states (as revealed in the PL spectra) is observed as a continuum background in the Raman spectrum without any characteristic peak. Our samples containing Si NSs are a nonlinear medium, i.e. a dielectric like medium, which has been reported in the Z-scan technique [19], optical fringe [20] and wave mixing [21,22]. As the size of NSs decreases, enhanced electronic gap of the Si NSs approaches the incident photon energy and probability of two-wave mixing increases by nonlinear process. This leads to phase matching by creation of electron–phonon bound state (interferon) as shown in Fig. 6(c). Interferon has been reported earlier by Balkanski et al. [3] for the c-Si. Concept of the interferon explains our experimental observations showing Fano
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interaction in the Si NSs. If δ is the phase angle between Raman active electronic and Raman active phonon wave-vectors, δ can be written empirically as: −1
|δ| = tan
E ex − E PL E ex
a result, strong electron–phonon interaction yields enhanced Fano interaction in the Raman scattering from the Si NSs. Acknowledgements
,
(3)
where, E ex is the excitation photon energy and E PL is the energy of PL peak corresponding to highest intensity. As the Si NSs size is decreased, the PL energy ( E PL ) approaches the excitation photon energy. Thus the phase matching condition satisfies for quantum interference, which results in the formation of bound state. This type of size-dependent behavior of Fano interaction in the Si NSs can be compared with the excitation wavelength-dependent Fano interaction [4] in c-Si. 4. Conclusions In conclusion, Fano interaction between discrete phonons and photo-excited electronic transitions is studied in the Si NSs as a function of NSs size and laser power density. More asymmetric, wider and red shifted Raman line-shapes are observed by increasing the excitation laser power density. This is due to the fact that more photo-excited electrons are generated at higher laser power density. These photo-excited electrons participate in the continuum of electronic Raman scattering and interacts with zone center optic phonons to yield Fano interaction. Experimental electronic Raman spectra can also be obtained from the photo-excitationdependent Raman spectra for samples containing different sized Si NSs. The nonlinear Fano interaction is more pronounced for smaller sized Si NSs for a given laser power density. Increased energy gap due to quantum confinement effect approaches more closer to the incident photon energy which enhances the electronic Raman scattering. This in turn satisfies the phase matching condition by nonlinear process of two-wave mixing in the Si NSs. As
Authors thank Prof. V.D. Vankar for useful discussions. Authors also acknowledge Dr. H.S. Mavi for valuable comments. Authors acknowledge the financial support from the Department of Science and Technology, Government of India, under the project “Optical Studies of Self-Assembled Quantum Dots of Semiconductors”. One of the authors (R.K.) acknowledges the financial support from Council of Scientific and Industrial Research (CSIR), India. Technical support from Mr. N.C. Nautiyal is also acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
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