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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 4784–4789
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Modulation of the propagation speed of mechanical waves in silicon quantum dots embedded in a silicon-nitride film

C. Torres-Torres, A. López-Suárez, R. Torres-Martínez, A. Rodriguez, J. A. Reyes-Esqueda, L. Castañeda, J. C. Alonso, and A. Oliver  »View Author Affiliations


Optics Express, Vol. 20, Issue 4, pp. 4784-4789 (2012)
http://dx.doi.org/10.1364/OE.20.004784


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Abstract

Using a vectorial picosecond self-diffraction method, we evaluate the modification of the speed of the sound in a silicon-nitride film containing silicon quantum dots prepared by remote plasma-enhanced chemical vapor deposition. Our non-contact technique is based on the stimulation of the electrostriction contribution to the nonlinearity of index exhibited by the sample in a multiwave mixing laser experiment. We identified the electronic birefringence using two of the incident beams to generate a self-diffraction signal, then, we modified the third order nonlinear response by means of the optical Kerr effect given by a phase-mismatched third beam which induced electrostriction. Our results indicated that the speed of the sound in a silicon-nitride film can be simultaneously tailored by an electronic nonlinear refractive index, and by an electrostriction effect, both resulting from silicon quantum dots doping.

© 2012 OSA

1. Introduction

2. Theory of picosecond vectorial self-diffraction enhanced by electrostriction

We consider two coherent pulses described as plane waves with the same frequency and different irradiances which interfere in a thin isotropic nonlinear medium. When a nonlinear refractive index is induced and an interference pattern with modulation of intensity or polarization results from this interaction, a self-diffraction response can be observed as the first order of diffraction travelling close to the neighborhood of the two incident beams. It has been demonstrated that comparing the self-diffraction effect originated by parallel and orthogonal polarization of the incident beams it is possible to measure the absorptive and refractive nonlinearities [15

15. C. Torres-Torres, A. V. Khomenko, L. Tamayo-Rivera, R. Rangel-Rojo, Y. Mao, and W. H. Watson, “Measurements of nonlinear optical refraction and absorption in an amino-triazole push-pull derivative by a vectorial self-diffraction method,” Opt. Commun. 281(12), 3369–3374 (2008). [CrossRef]

]. Since the electrostriction phenomenon takes some nanoseconds for its manifestation in the nonlinearity of refractive index [5

5. R. W. Boyd, Nonlinear Optics (Academic Press, 1992).

], a picosecond self-diffracted pulse originated by a picosecond two-wave mixing is short enough in time for allowing the observation of an electrostriction effect responsible of a nonlinear refractive index. However, by using a longer excitation, or by previously inducing a high intensity laser irradiation into the sample, before the grating of index is generated by the two-wave mixing, then it is possible to measure the contribution of the electrostrictive force to the self-diffraction signals. With the purpose of separately identify the modification of the refractive index by electrostriction and by electronic nonlinearity, in this work we proposed to provide an additional brief third optical beam and a delay in the two-wave mixing for the self-diffraction experimental setup. We use a description of the field in terms of circular polarization components as it has been previously reported [15

15. C. Torres-Torres, A. V. Khomenko, L. Tamayo-Rivera, R. Rangel-Rojo, Y. Mao, and W. H. Watson, “Measurements of nonlinear optical refraction and absorption in an amino-triazole push-pull derivative by a vectorial self-diffraction method,” Opt. Commun. 281(12), 3369–3374 (2008). [CrossRef]

]. The amplitudes of the transmitted and self-diffracted waves are described by
E1±(z)=[J0(Ψ±(1))E1±+iJ1(Ψ±(1))E2±]exp(iΨ±(0)α(I)z2),
(1)
E2±(z)=[J0(Ψ±(1))E2±iJ1(Ψ±(1))E1±]exp(iΨ±(0)α(I)z2),
(2)
E3±(z)=[iJ1(Ψ±(1))E1±J2(Ψ±(1))E2±]exp(iΨ±(0)α(I)z2),
(3)
E4±(z)=[iJ1(Ψ±(1))E2±J2(Ψ±(1))E1±]exp(iΨ±(0)α(I)z2),
(4)
where E (z) and E (z) are the complex amplitudes of the circular components of the transmitted waves beams; E3 ± (z) and E4 ± (z) are the amplitudes of the self-diffracted waves, E and E are the amplitudes of the incident waves, α(I) is the irradiance dependent absorption coefficient, I is the total irradiance of the incident beams, Jm±(1)) stands for the Bessel function of order m, z is the thickness of the nonlinear media, and

Ψ±(0)=4π2zn0λ[A(|E1±|2+|E2±|2)+(A+B)(|E1|2+|E2|2)],
(5)
Ψ±(1)=4π2zn0λ[AE1±E2±*+(A+B)E1E2*].
(6)

3. Experiment

3.1 Processing route of the samples

The silicon-nitride films were prepared using a remote plasma-enhanced chemical vapor deposition (RPECVD) system. The films were grown on quartz substrates using a working pressure of 300 mTorr, a substrate temperature of 300°C and a radio-frequency power of 200 W. The flow rates of H2, Ar, SiH2Cl2 and NH3 were 20, 150, 5 and 50 sccm (standard cubic centimeters per minute), respectively. During the deposition, Ar and NH3 gases were fed from the top of the chamber where the plasma is formed; meanwhile, the H2 and SiH2Cl2 gases were fed from the side and underneath the plasma by means of a dispersal ring located over the substrate holder. The silicon-nitride films were characterized by High-Resolution Transmission Electronic Microscopy (HRTEM).

3.2 Measurement of the different contributions to the nonlinear refractive index

3.3 Estimation of the speed of sound by electrostriction measurements

4. Results and discussion

Figure 2(a)
Fig. 2 (a) Typical HRTEM micrograph. (b) Statistical cumulative distribution of particle size. (c) Linear transmittance spectra.
shows the typical HRTEM micrograph of the resulting thin film samples, where several dark spots that correspond to the Si-QDs can be observed. A statistical analysis of the HRTEM micrographs in different zones of the samples was made in order to get the size distribution of the Si-QDs. The results of this analysis showed that the Si-QDs average size is 3.2 nm and the correspondent Boltzmann fit is shown in Fig. 2(b). The optical transmittance spectrum is presented in Fig. 2(c). One can clearly observe an absorbing edge towards the UV that starts approximately at 290 nm, this is associated with the band gap of the sample containing the Si-QDs embedded in silicon-nitride and deposited in the quartz substrate.

In order to perform the nonlinear optical measurements, initially the beam Ib was switched off in the experiments. Our measurement system was previously calibrated using carbon disulfide, CS2, with a thickness of D = 1 mm, as a nonlinear medium with a well-known third-order nonlinear susceptibility of |χ(3)| = 1.9 × 10−12 esu [5

5. R. W. Boyd, Nonlinear Optics (Academic Press, 1992).

]. In our case, the silicon-nitride sample has a thickness of D = 1.003 ± 0.12 μm. The polarized irradiances of the diffracted beams behind the sample were measured in two different cases of polarization of the incident beams; when the incident waves E1 and E2 had parallel and orthogonal linear polarizations. The axes of transmission of the analyzers A1-2 were aligned in order to detect, for each case, the parallel and the orthogonal components of the polarization of the waves. An error bar of ± 10% was estimated for the experimental irradiance data. By comparing numerical simulations of Eqs. (1-10) with the data obtained from the self-diffracted and transmitted irradiances in CS2 and that obtained from the silicon-nitride samples we obtained an optical linear absorption of α0 = 4.04 × 105 m−1, a saturated absorption with β = 7.7 × 10−9m/W, an electronic nonlinear refractive index of n2 = 1.8 × 10−16m2/W, and |χ1111(3)| = 4.6 × 10−10esu. Figure 3(a)
Fig. 3 (a) Vectorial self-diffraction results. (b) Modification of self-diffraction efficiency by the phase-mismatched beam. (c) Change in the speed of the induced mechanical waves vs. n2.
shows the experimental (marks) and numerical (continuous lines) self-diffraction efficiency η, as a function of the angle ϕ between planes of polarization of the incident waves with the best fitting of the numerical simulations. These results are consistent with the reported values obtained in a similar sample with a different self-diffraction method [17

17. A. López-Suárez, C. Torres-Torres, R. Rangel-Rojo, J. A. Reyes-Esqueda, G. Santana, J. C. Alonso, A. Ortiz, and A. Oliver, “Modification of the nonlinear optical absorption and optical Kerr response exhibited by nc-Si embedded in a silicon-nitride film,” Opt. Express 17(12), 10056–10068 (2009). [CrossRef] [PubMed]

]. Once it was identified the electronic response of the samples, we stimulated the electrostriction contribution to the nonlinearity of index by means of Ib. This phase-mismatched third beam produced a heightening in the self-diffracted signal, and for that reason, a higher contrast in the birefringence grating at the center of the interference pattern generated for the incident beams could be expected. Comparing the results for the pure electronic response of n2 in our silicon-nitride samples, we measured an intensification of the self-diffraction efficiency of approximately 32% . The correspondent nonlinear refractive value given by the fitting of the experimental data are |χ1111(3)| = 1.822 × 10−16 esu and n2 = 2.2 × 10−20 m2/W, for the electrostriction effect. Using Eqs. (8) and (9) with no = 1.8, and ρo = 3180 Kg/m3 we estimated that the speed of the sound is υa = 3300 m/s. The third order nonlinear response given by electrostriction appears six orders of magnitude lower than the electronic response. As a comparative result, we measured the nonlinear refraction for a pure silicon-nitride film and then we find that υa = 7800 m/s. This last result is close to the acoustic speed measured for high frequencies in silicon-nitride from which, with a Young modulus (M) of 310GPa and with υa = (M/ρo)1/2, is equal to 9900 m/s [18

18. T. R. Albrecht, S. Akamine, T. E. Carver, and C. F. Quate, “Microfabrication of cantilever styli for atomic force microscopy,” J. Vac. Sci. Technol. A 8(4), 3386–3396 (1990). [CrossRef]

]. A time-resolved wave-mixing technique was performed in order to maximize the resulting nonlinear refractive index associated with electrostriction. The maximum studied delay between the two-beam interaction and the interaction originated by the beam Ib was about 2 ns; the best result was obtained for about 1.4 ns as it can be seen from Fig. 3(b). We calculate the change in the speed of sound in our sample by using Eqs. (8) and (9) and the numerical results based in experimental data are plotted as marks in Fig. 3(c) while the continuous line is a theoretical calculation; as it can be observed, a strong nonlinear modification on the speed of a mechanical wave can be achieved by an electrostrictive effect in a silicon-nitride film containing Si-QDs.

Low dimensional semiconductor structures have originated numerous scientific researches in order to propose platforms for implementing diverse optoelectronic circuits, nevertheless the development of nanomechanical configurations for controlling high-speed signals also seems to be in a promising progress [2

2. A. Cleland, Foundations of Nanomechanics: From Solid-State Theory to Device Applications (Springer, 2003).

]. The optical technique described in this works presents the advantage to be a non-contact and non-invasive method for estimating or modulating the speed of sound in transparent dielectric media; besides, mechanical parameters like the Young Modulus or the density can be derived by inducing an electrostriction effect. Moreover it seems that these effects of nonlinearity of index can potentially exhibit functional applications in photothermal processes where it is mandatory to control the density for manipulating the propagation of induced mechanical waves.

5. Conclusion

Acknowledgments

We kindly acknowledge the financial support from SIP-IPN, from COFAA-IPN, from DGAPA-PAPIIT-UNAM projects under contracts IN-100-510 and 108510, from ICyT-DF through grant PIUTE10-129; from CONACyT through grants 82708, 99224 and 80019, from the IF-BUAP, and from the SEP México through grant PROMEP/103.5/09/4194. The authors wish to acknowledge the technical assistance of J. G. Morales, K. Lopez and F. J. Jaimes.

References and links

1.

P. S. Waggoner, C. P. Tan, and H. G. Craighead, “Atomic layer deposited silicon dioxide films on nanomechanical silicon nitride resonators,” J. Appl. Phys. 107(11), 114505 (2010). [CrossRef]

2.

A. Cleland, Foundations of Nanomechanics: From Solid-State Theory to Device Applications (Springer, 2003).

3.

Y. R. Shen, “Electrostriction optical Kerr effect and self-focusing of laser beams,” Phys. Lett. 20(4), 378–380 (1966). [CrossRef]

4.

M. S. Chang, “Bragg electrostriction in optical waveguides,” Appl. Opt. 16(7), 1960–1965 (1977). [CrossRef] [PubMed]

5.

R. W. Boyd, Nonlinear Optics (Academic Press, 1992).

6.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys. 104(1), 014306 (2008). [CrossRef]

7.

M. Klopfer and R. K. Jain, “Plasmonic quantum dots for nonlinear optical applications,” Opt. Mater. Express 1(7), 1353–1366 (2011). [CrossRef]

8.

G. Burlak, “Four-wave acousto-electromagnetic interactions in crystals with a nonlinear electrostriction,” Physica D 166(3-4), 197–207 (2002). [CrossRef]

9.

G. Coppola, L. Sirleto, I. Rendina, and M. Iodice, “Advance in thermo-optical switches: Principles, materials, design, and device structure,” Opt. Eng. 50(7), 071112 (2011). [CrossRef]

10.

M. Ito, K. Imakita, M. Fujii, and S. Hayashi, “Nonlinear optical properties of silicon nanoclusters/nanocrystals doped SiO2 films: Annealing temperature dependence,” J. Appl. Phys. 108(6), 063512 (2010). [CrossRef]

11.

G.-R. Lin, C.-W. Lian, C.-L. Wu, and Y.-H. Lin, “Gain analysis of optically-pumped Si nanocrystal waveguide amplifiers on silicon substrate,” Opt. Express 18(9), 9213–9219 (2010). [CrossRef] [PubMed]

12.

A. Martínez, J. Blasco, P. Sanchis, J. V. Galán, J. García-Rupérez, E. Jordana, P. Gautier, Y. Lebour, S. Hernández, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Martí, “Ultrafast all-optical switching in a silicon-nanocrystal-based silicon slot waveguide at telecom wavelengths,” Nano Lett. 10(4), 1506–1511 (2010). [CrossRef] [PubMed]

13.

D. Timmerman, J. Valenta, K. Dohnalová, W. D. A. M. de Boer, and T. Gregorkiewicz, “Step-like enhancement of luminescence quantum yield of silicon nanocrystals,” Nat. Nanotechnol. 6(11), 710–713 (2011). [CrossRef] [PubMed]

14.

Y. Zhu, F. Zhang, J. Yang, H. Zheng, and F. Yang, “Stability of mechanical properties for submicrometer single-crystal silicon cantilever under cyclic load,” Microelectromech. Syst. 20, 178–183 (2011).

15.

C. Torres-Torres, A. V. Khomenko, L. Tamayo-Rivera, R. Rangel-Rojo, Y. Mao, and W. H. Watson, “Measurements of nonlinear optical refraction and absorption in an amino-triazole push-pull derivative by a vectorial self-diffraction method,” Opt. Commun. 281(12), 3369–3374 (2008). [CrossRef]

16.

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, 1996).

17.

A. López-Suárez, C. Torres-Torres, R. Rangel-Rojo, J. A. Reyes-Esqueda, G. Santana, J. C. Alonso, A. Ortiz, and A. Oliver, “Modification of the nonlinear optical absorption and optical Kerr response exhibited by nc-Si embedded in a silicon-nitride film,” Opt. Express 17(12), 10056–10068 (2009). [CrossRef] [PubMed]

18.

T. R. Albrecht, S. Akamine, T. E. Carver, and C. F. Quate, “Microfabrication of cantilever styli for atomic force microscopy,” J. Vac. Sci. Technol. A 8(4), 3386–3396 (1990). [CrossRef]

19.

A. Othonos, E. Lioudakis, and A. G. Nassiopoulou, “Surface-related states in oxidized silicon nanocrystals enhance carrier relaxation and inhibit Auger recombination,” Nanoscale Res. Lett. 3(9), 315–320 (2008). [CrossRef]

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(190.3270) Nonlinear optics : Kerr effect
(190.4223) Nonlinear optics : Nonlinear wave mixing
(160.4236) Materials : Nanomaterials

ToC Category:
Nonlinear Optics

History
Original Manuscript: December 6, 2011
Revised Manuscript: December 31, 2011
Manuscript Accepted: January 5, 2012
Published: February 10, 2012

Citation
C. Torres-Torres, A. López-Suárez, R. Torres-Martínez, A. Rodriguez, J. A. Reyes-Esqueda, L. Castañeda, J. C. Alonso, and A. Oliver, "Modulation of the propagation speed of mechanical waves in silicon quantum dots embedded in a silicon-nitride film," Opt. Express 20, 4784-4789 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4784


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References

  1. P. S. Waggoner, C. P. Tan, and H. G. Craighead, “Atomic layer deposited silicon dioxide films on nanomechanical silicon nitride resonators,” J. Appl. Phys.107(11), 114505 (2010). [CrossRef]
  2. A. Cleland, Foundations of Nanomechanics: From Solid-State Theory to Device Applications (Springer, 2003).
  3. Y. R. Shen, “Electrostriction optical Kerr effect and self-focusing of laser beams,” Phys. Lett.20(4), 378–380 (1966). [CrossRef]
  4. M. S. Chang, “Bragg electrostriction in optical waveguides,” Appl. Opt.16(7), 1960–1965 (1977). [CrossRef] [PubMed]
  5. R. W. Boyd, Nonlinear Optics (Academic Press, 1992).
  6. C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys.104(1), 014306 (2008). [CrossRef]
  7. M. Klopfer and R. K. Jain, “Plasmonic quantum dots for nonlinear optical applications,” Opt. Mater. Express1(7), 1353–1366 (2011). [CrossRef]
  8. G. Burlak, “Four-wave acousto-electromagnetic interactions in crystals with a nonlinear electrostriction,” Physica D166(3-4), 197–207 (2002). [CrossRef]
  9. G. Coppola, L. Sirleto, I. Rendina, and M. Iodice, “Advance in thermo-optical switches: Principles, materials, design, and device structure,” Opt. Eng.50(7), 071112 (2011). [CrossRef]
  10. M. Ito, K. Imakita, M. Fujii, and S. Hayashi, “Nonlinear optical properties of silicon nanoclusters/nanocrystals doped SiO2 films: Annealing temperature dependence,” J. Appl. Phys.108(6), 063512 (2010). [CrossRef]
  11. G.-R. Lin, C.-W. Lian, C.-L. Wu, and Y.-H. Lin, “Gain analysis of optically-pumped Si nanocrystal waveguide amplifiers on silicon substrate,” Opt. Express18(9), 9213–9219 (2010). [CrossRef] [PubMed]
  12. A. Martínez, J. Blasco, P. Sanchis, J. V. Galán, J. García-Rupérez, E. Jordana, P. Gautier, Y. Lebour, S. Hernández, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Martí, “Ultrafast all-optical switching in a silicon-nanocrystal-based silicon slot waveguide at telecom wavelengths,” Nano Lett.10(4), 1506–1511 (2010). [CrossRef] [PubMed]
  13. D. Timmerman, J. Valenta, K. Dohnalová, W. D. A. M. de Boer, and T. Gregorkiewicz, “Step-like enhancement of luminescence quantum yield of silicon nanocrystals,” Nat. Nanotechnol.6(11), 710–713 (2011). [CrossRef] [PubMed]
  14. Y. Zhu, F. Zhang, J. Yang, H. Zheng, and F. Yang, “Stability of mechanical properties for submicrometer single-crystal silicon cantilever under cyclic load,” Microelectromech. Syst.20, 178–183 (2011).
  15. C. Torres-Torres, A. V. Khomenko, L. Tamayo-Rivera, R. Rangel-Rojo, Y. Mao, and W. H. Watson, “Measurements of nonlinear optical refraction and absorption in an amino-triazole push-pull derivative by a vectorial self-diffraction method,” Opt. Commun.281(12), 3369–3374 (2008). [CrossRef]
  16. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, 1996).
  17. A. López-Suárez, C. Torres-Torres, R. Rangel-Rojo, J. A. Reyes-Esqueda, G. Santana, J. C. Alonso, A. Ortiz, and A. Oliver, “Modification of the nonlinear optical absorption and optical Kerr response exhibited by nc-Si embedded in a silicon-nitride film,” Opt. Express17(12), 10056–10068 (2009). [CrossRef] [PubMed]
  18. T. R. Albrecht, S. Akamine, T. E. Carver, and C. F. Quate, “Microfabrication of cantilever styli for atomic force microscopy,” J. Vac. Sci. Technol. A8(4), 3386–3396 (1990). [CrossRef]
  19. A. Othonos, E. Lioudakis, and A. G. Nassiopoulou, “Surface-related states in oxidized silicon nanocrystals enhance carrier relaxation and inhibit Auger recombination,” Nanoscale Res. Lett.3(9), 315–320 (2008). [CrossRef]

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