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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 9 — Apr. 27, 2009
  • pp: 7368–7376
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Nonlinear optical properties of Phosphorous-doped Si nanocrystals embedded in phosphosilicate glass thin films

Kenji Imakita, Masahiko Ito, Minoru Fujii, and Shinji Hayashi  »View Author Affiliations


Optics Express, Vol. 17, Issue 9, pp. 7368-7376 (2009)
http://dx.doi.org/10.1364/OE.17.007368


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Abstract

Nonlinear optical properties of phosphorus (P) -doped silicon (Si) nanocrystals are studied by z-scan technique in femtosecond regime at around 1.6 eV. The nonlinear refractive index (n2) and nonlinear absorption coefficient (β) of Si-ncs are significantly enhanced by P-doping. The enhancement of n2 is accompanied by the increase of the linear absorption in the same energy region, suggesting that impurity-related energy states are responsible for the enhancement of the nonlinear optical response.

© 2009 Optical Society of America

1. Introduction

Silicon nanocrystal (Si-nc) is a topic of great interests in the field of optelectronics because of its high quantum efficiency of photoluminescence (PL) and relatively large nonlinear optical responses[1

1. L. T. Canham, “Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers”, Appl. Phys. Lett . 57, 1046–1048 (1990). [CrossRef]

, 2

2. S. Takeoka, M. Fujii, and S. Hayashi, “Size-dependent photoluminescence from surface-oxidized Si nanocrystals in a weak confinement regime”, Phys. Rev. B 62, 16820–16825 (2000). [CrossRef]

, 3

3. C. Delerue, M. Lannoo, G. Allan, and E. Martin, “Theoretical descriptions of porous silicon”, Thin Solid Films 255, 27–34 (1995). [CrossRef]

, 4

4. P. Bettotti, M. Cazzanelli, L. Dal Negro, B. Danese, Z. Gaburro, C. J. Oton, G. Vijaya Prakash, and L. Pavesi, “Silicon nanostructures for photonics”, J. Phys:Condens. Matter 14, 8253–8281 (2002). [CrossRef]

, 5

5. L. Pavesi, Z. Gaburro, L. Dal Negro, P. bettotti, G. Vijaya Prakash, M. Cazzaneli, and C. J. Oton, “Nanostructured silicon as a photonic material”, Opt. Lasers Eng. J. Opt. Soc. Am. B 39, 345–367 (2003). [CrossRef]

, 6

6. S. Moon, A. Lin, B. H. Kim, P. R. Watekar, and W.-T. Han, “Linear and nonlinear optical properties of the optical fiber doped with silicon nano-particles”, J. Non-Cryst. Solids 354, 602–606 (2008). [CrossRef]

]. The large nonlinear optical response has been reported in various forms of Si-ncs such as porous Si prepared by electrochemical etching[7

7. S. Lettieri and P. Maddalena, “Nonresonant Kerr effect in microporous silicon: Nonbulk dispersive behavior of below band gap of χ(3)”, J. Appl. Phys . 91, 5564–5570 (2002). [CrossRef]

, 8

8. Y. Kanemitsu, S. Okamoto, and A. Mito, “Third-order nonlinear optical susceptibility and photoluminescence in porous silicon”, Phys. Rev. B 52, 10752–10755 (1995). [CrossRef]

], Si-ncs doped SiOxNy deposited by plasma enhanced chemical vapor deposition (PECVD)[10

10. G. Vijaya Prakash, M. Cazzaneli, Z. Gaburro, L. Pavesi, F. Lacona, G. Franzo, and F. Priolo., “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition”, J. Appl. Phys . 91, 4607–4610 (2002). [CrossRef]

, 9

9. S. Hemandez, P. Pellegrino, A. Martinez, Y. lebour, B. Garrido, R. Spano, M. Cazzanelli, N. Daldosso, L. Pavesi, E. Jordana, and J. M. Fedeli, “Linear and nonlinear optical properties of Si nanocrystals in SiO2 deposited by plasma-enhanced chemical-vapor deposition”, J. Appl. Phys . 103, 064309 (2008). [CrossRef]

], Si-ncs doped SiO2 prepared by cosputtering[11

11. K. Imakita, M. Ito, M. Fujii, S. Hayashi, and J. Appl. Phys. (to be published).

], laser ablated Si-ncs deposited on quartz substrate[12

12. S. Vijayalakshmi, A. Lan, Z. lqbal, and H. Grebel, “Nonlinear optical properties of laser ablated silicon nanostructures”, J. Appl. Phys . 92, 2490–2494 (2002). [CrossRef]

, 13

13. S. Vijayalakshmi, M. A. George, and H. Grebel, “Nonlinear optical properties of silicon nanoclusters”, Appl. Phys. Lett . 70, 708–710 (1997). [CrossRef]

], and so on. In these literatures, dependence of the nonlinear optical response on the size and volume fraction of Si-ncs has been studied in detail. Although the origin of the large nonlinear optical response is still not fully clarified, the quantum confinement effects are often believed to be responsible[9

9. S. Hemandez, P. Pellegrino, A. Martinez, Y. lebour, B. Garrido, R. Spano, M. Cazzanelli, N. Daldosso, L. Pavesi, E. Jordana, and J. M. Fedeli, “Linear and nonlinear optical properties of Si nanocrystals in SiO2 deposited by plasma-enhanced chemical-vapor deposition”, J. Appl. Phys . 103, 064309 (2008). [CrossRef]

, 11

11. K. Imakita, M. Ito, M. Fujii, S. Hayashi, and J. Appl. Phys. (to be published).

].

It has been demonstrated experimentally[15

15. M. Fujii, Y. Yamaguchi, Y. Takase, K. Ninomiya, and S. Hayashi, “Control of photoluminescence properties of Si nanocrystals by simultaneously doping n- and p-type impurities”, Appl. Phys. Lett . 85, 1158–1160 (2004). [CrossRef]

, 16

16. M. Fujii, Y. Yamaguchi, Y. Takase, K. Ninomiya, and S. Hayashi, “Photoluminescence from impurity codoped and compensated Si nanocrystals”, Appl. Phys. Lett . 87, 211919 (2005). [CrossRef]

, 17

17. A. Mimura, M. Fujii, S. Hayashi, D. Kovalev, and F. Koch, “Photoluminescence and free-electron absorption in heavily phosphorus-doped Si nanocrystals”, Phys. Rev. B 62, 12625–12627 (2000). [CrossRef]

, 18

18. B. J. Pawlak, T. Gregorkiewicz, C. A. J. Ammerlaan, W. Takkenberg, F. D. Tichelaar, and P. F. A. Alkemade, “Experimental investigation of band structure modification in silicon nanocrystals”, Phys. Rev. B 64, 115308 (2001). [CrossRef]

, 19

19. M. Fujii, A. Mimura, and S. Hayashi, “Hyperfine Structure of the Electron Spin Resonance of Phosphorus-Doped Si Nanocrystals”, Phys. Rev. Lett . 89, 206805 (2002). [CrossRef] [PubMed]

] and theoretically [20

20. G. Cantele, E. Degoli, E. Luppi, R. Magori, D. Ninno, G. Iadonisi, and S. Ossicini, “First-principles study of n - and p -doped silicon nanoclusters”, Phys. Rev. B 72, 113303 (2005). [CrossRef]

, 21

21. G. Allan, C. Delerue, M. Lannoo, and E. Martin, “Hydrogenic impurity levels, dielectric constant, and Coulomb charging effects in silicon crystallites”, Phys. Rev. B 52, 11982–11988 (1995). [CrossRef]

, 22

22. D. V. Melnikov and J. R. Chelikowsky, “Quantum Confinement in Phosphorus-Doped Silicon Nanocrystals”, Phys. Rev. Lett . 92, 046802 (2004). [CrossRef] [PubMed]

] that the electronic band structure, and the resultant optical and electrical transport properties of Si-ncs are significantly modified by impurity doping. Experimentally, PL properties of Si-ncs were found to be very sensitive to the impurity doping[15

15. M. Fujii, Y. Yamaguchi, Y. Takase, K. Ninomiya, and S. Hayashi, “Control of photoluminescence properties of Si nanocrystals by simultaneously doping n- and p-type impurities”, Appl. Phys. Lett . 85, 1158–1160 (2004). [CrossRef]

, 16

16. M. Fujii, Y. Yamaguchi, Y. Takase, K. Ninomiya, and S. Hayashi, “Photoluminescence from impurity codoped and compensated Si nanocrystals”, Appl. Phys. Lett . 87, 211919 (2005). [CrossRef]

, 17

17. A. Mimura, M. Fujii, S. Hayashi, D. Kovalev, and F. Koch, “Photoluminescence and free-electron absorption in heavily phosphorus-doped Si nanocrystals”, Phys. Rev. B 62, 12625–12627 (2000). [CrossRef]

]. The doping of either n- or p-type impurities results in strong quenching of the PL, due to efficient Auger process between photo-excited electron-hole pairs and impurity-supplied carriers[17

17. A. Mimura, M. Fujii, S. Hayashi, D. Kovalev, and F. Koch, “Photoluminescence and free-electron absorption in heavily phosphorus-doped Si nanocrystals”, Phys. Rev. B 62, 12625–12627 (2000). [CrossRef]

]. The quenching can be suppressed by doping n- and p-type impurities simultaneously because of the compensation of carriers within Si-ncs. The PL of the codoped and compensated Si-ncs appears at very low energy; the PL peak reaches 0.9 eV in heavily-doped an compensated Si-ncs [15

15. M. Fujii, Y. Yamaguchi, Y. Takase, K. Ninomiya, and S. Hayashi, “Control of photoluminescence properties of Si nanocrystals by simultaneously doping n- and p-type impurities”, Appl. Phys. Lett . 85, 1158–1160 (2004). [CrossRef]

, 16

16. M. Fujii, Y. Yamaguchi, Y. Takase, K. Ninomiya, and S. Hayashi, “Photoluminescence from impurity codoped and compensated Si nanocrystals”, Appl. Phys. Lett . 87, 211919 (2005). [CrossRef]

]. These observed phenomena are successfully reproduced, at least qualitatively, by first principles calculations [20

20. G. Cantele, E. Degoli, E. Luppi, R. Magori, D. Ninno, G. Iadonisi, and S. Ossicini, “First-principles study of n - and p -doped silicon nanoclusters”, Phys. Rev. B 72, 113303 (2005). [CrossRef]

, 23

23. S. Ossicini, F. Iori, E. Degoli, E. Luppi, R. Magri, R. Poli, G. Cantele, F. Trani, and D. Ninno, “Understanding Doping In Silicon Nanostructures”, IEEE J. Sel. Top. Quantum Electron . 12, 1585–1591 (2006). [CrossRef]

].

In this paper, we study the effect of impurity doping on the nonlinear optical properties of Si-ncs by using the samples of phosphorus(P)-doped Si-ncs embedded in phosphosilicate glass (PSG) thin films.We show that P-doping further enhances the large nonlinear optical responses of Si-ncs and is thus an effective way to control the nonlinear optical properties of Si-ncs.

2. Experimental procedure

P-doped Si-ncs embedded in PSG thin films were prepared by a cosputtering method. Si, SiO2 and PSG were simultaneously sputter-deposited in Ar gas on a quartz substrate. Then the deposited films were annealed in a N2 gas (99.999 %) atmosphere for 30 min at 1150 ℃ to grow nanocrystals in the films. The size of Si-ncs was estimated by cross-sectional transmission electron microscopy (TEM) observations[24

24. M. Fujii, S. Hayashi, and K. Yamamoto, “Photoluminescence from B-doped Si nanocrystals”, J. Appl. Phys . 83, 7953–7956 (1998). [CrossRef]

]. The average diameter (D) was about 4.0 nm, and the standard deviation was about 1.0 nm. The concentration of excess Si (CexSi) and P2O5 (CP) were obtained by electron probe micro analysis (EPMA). CexSi was about 6.7 vol% and P2O5 was changed from 0 to 1.2 mol% . The linear refractive indices were estimated from the volume ratio of Si and SiO2 with the application of the Bruggeman effective medium theory [25

25. D. A. G. Bruggeman,“Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen”, Ann. Phys . 24, 636–679 (1935). [CrossRef]

] and was about 1.54 at 800 nm.

PL spectra were measured by using a single grating monochromator and an InGaAs near-Infrared diode array. The spectral response of the detection system was calibrated with the aid of a reference spectrum of a standard tungsten lamp. For the measurement of the nonlinear optical properties, a z-scan method was used. Details of the z-scan method is found elsewhere[14

14. M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method”, Appl. Phys. B 70, 587–591 (2000). [CrossRef]

]. Briefly, in the z-scan method, the tight focusing gaussian beam is vertically irradiated onto a sample and the sample is moved along the direction of the beam propagation (z axis). The transmitted light intensity is recorded as a function of the distance from the focal point (z). When all of the transmitted light is detected (open aperture), the transmittance (Top(z)) is determined by the nonlinear absorption coefficient (β), and its dependence on z is

Top(z)=1+βI0L1+(z/z0)2,
(1)

where I 0, L, and z 0 are the peak intensity of the beam, sample thickness and the diffraction length of the beam, respectively. Note that Top doesn’t depend on the nonlinear refractive index (n 2) but only on β, thus open aperture measurement provides the information on β.

When a small aperture is placed in front of the detector to cut peripheral regions of the transmitted light (closed aperture), the transmittance (Tcl) depends both on n 2 and β. The information on n 2 is extracted by the division of Tcl by Top,

Tcl/Top(z)=1+4Δϕ((z/z0)2+9)((z/z0)2+1)
(2)

where ∆ϕ is the nonlinear phase change. n 2 is obtained from ∆ϕ as,

n2=λαΔϕ2πI0(1eαL),
(3)

where α and λ are the linear absorption coefficient and the wavelength of the beam, respectively.

For the gaussian beam, we used the mode-locked Ti:shaphire femtosecond laser with the pulse width of 70 fsec and the repetition frequency of 82 MHz. The photon energy was changed from 1.48 to 1.65 eV. The incident beam was focused on a sample by a lens with the focus length of 100 mm. The beam waist and diffraction length determined by a knife edge method were 18 μm and 1.1 mm, respectively. The peak intensity of the beam was typically 10 GW/cm2. No notable change of nonlinear optical properties was observed in the intensity range of 0.5-20 GW/cm2, suggesting that thermal effect was negligible in this measurement condition[10

10. G. Vijaya Prakash, M. Cazzaneli, Z. Gaburro, L. Pavesi, F. Lacona, G. Franzo, and F. Priolo., “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition”, J. Appl. Phys . 91, 4607–4610 (2002). [CrossRef]

, 9

9. S. Hemandez, P. Pellegrino, A. Martinez, Y. lebour, B. Garrido, R. Spano, M. Cazzanelli, N. Daldosso, L. Pavesi, E. Jordana, and J. M. Fedeli, “Linear and nonlinear optical properties of Si nanocrystals in SiO2 deposited by plasma-enhanced chemical-vapor deposition”, J. Appl. Phys . 103, 064309 (2008). [CrossRef]

]. The validity of the obtained data was checked by measuring a fused quartz plate as a reference.

3. Results and discussion

The inset of Fig. 1(a) shows the PL spectra of pure and P-doped Si-ncs. Both samples exhibit a broad PL band at around 1.3 eV. The PL is assigned to the recombination of electron-hole pairs within Si-ncs. This is evidenced by the temperature and the photon-energy dependence of the PL-lifetime[2

2. S. Takeoka, M. Fujii, and S. Hayashi, “Size-dependent photoluminescence from surface-oxidized Si nanocrystals in a weak confinement regime”, Phys. Rev. B 62, 16820–16825 (2000). [CrossRef]

], and also by the resonantly excited PL spectra[27

27. M. Fuji, D. Kovalev, J. Diener, F. Koch, S. Takkeoka, and S. Hayashi, “Breakdown of the k-conservation rule in Si1-xGex alloy nanocrystals: Resonant photoluminescence study”, J. Appl. Phys . 88, 5772–5776 (2000). [CrossRef]

]. In Figure 1(b), PL intensity at 1.3 eV and absorbance at 0.5 eV are plotted as a function of CP. In the lower CP region (below 0.4mol% ), no notable infrared absorption is observed, and PL intensity increases with increasing CP. Carriers are thus not supplied within Si-ncs. The increase of the PL intensity in the CP region is, as discussed in reference[28

28. M. Fujii, A. Mimura, and S. Hayashi, “Improvement in photoluminescence efficiency of SiO2 films containing Si nanocrystals by P doping: An electron spin resonance study”, J. Appl. Phys . 87, 1855–1857 (2000). [CrossRef]

], considered to be due to the termination of dangling bond defects at the surface of Si-ncs by electrons supplied by doping. In the higher CP region (above 0.6mol% ), the infrared absorption increases and PL intensity decreases with increasing CP. The PL quenching is accompanied by the shortening of the PL lifetime, and is considered to be nonradiative Auger recombination of photo-excited electron-hole pairs with the interaction with supplied carriers. It should be noted here that re-absorption by nearby clusters cannot explain the strong quenching because the samples are almost transparent in the energy range (optical transmittance > 80% ).

Fig. 1. (a)Absorption spectra of pure and P-doped Si-ncs (CP=0.8mol% ). The inset shows the PL spectra of the same samples. (b)P2O5 concentration (CP) dependence of PL intensity at 1.3 eV (Left axis) and absorbance at 0.5 eV (Right axis).

Figure 2 shows the results of z-scan measurements for (a) a closed aperture (Tcl), (b) an open aperture (Top), and (c) the ratio (Tcl/Top). Open squares and solid curves represent experimental data and fitted results, respectively. In Figs. 2(b) and 2(c), Eqs. (1) and (2), respectively, are used for the fittings. The solid curve in Fig. 2(a) is generated by using the parameters obtained by the fittings of Figs. 2(b) and 2(c). The agreement between the experimental data and the fitted curves is very good and the diffraction length estimated from the fitting coincides well with that measured by a knife edge method. In Fig. 2(c), all the z-scan spectra show valley to peak traces. This indicates that the sign of n 2 is positive for all the samples. We can see that the magnitude of the transmittance change depends on CP. It increases with increasing CP, suggesting that n 2 increases with increasing CP.

Figure 3 shows the results of the analysis of the z-scan spectra. For the pure Si-ncs sample, i.e. CP=0, the n 2 and β are ~ 1.7×10-13 cm2/W and ~ 1.0 cm/GW respectively. The observed n 2 is three orders of magnitudes larger than that of SiO2, and one order of magnitude than that of bulk-Si.

Fig. 2. z-scan measurements for (a) a closed aperture (Tcl), (b) an open aperture (Top) and (c) the ratio of the two results (Tcl/Top). The squares are experimental results and the solid curves are results of fittings. P2O5 concentration (CP) is changed from 0 to 1.2mol% .
Fig. 3. P2O5 concentration dependence of n 2 (left axis) and β (right axis).
Fig. 4. n 2 spectra of samples with different P2O5 concentration (CP). The inset shows the absorption spectra of the same samples.

Two different models have been proposed as the origin of the large n 2. The first one is a quantum confinement effect. This model has been proved by size-dependent n 2 enhancement[9

9. S. Hemandez, P. Pellegrino, A. Martinez, Y. lebour, B. Garrido, R. Spano, M. Cazzanelli, N. Daldosso, L. Pavesi, E. Jordana, and J. M. Fedeli, “Linear and nonlinear optical properties of Si nanocrystals in SiO2 deposited by plasma-enhanced chemical-vapor deposition”, J. Appl. Phys . 103, 064309 (2008). [CrossRef]

]. The other one is that the surface state of Si-ncs is responsible for the large n 2. Klimov et al studied the transient absorption spectra of Si-ncs prepared by ion-implantation, and found a Si/SiO2 interface state at around 1.6 eV, in addition to the size-dependent quantized states[32

32. V. I. Klimov, Ch. J. Schwarz, D. W. McBranch, and C. W. White, “Initial carrier relaxation dynamics in ionimplanted Si nanocrystals: Femtosecond transient absorption study”, Appl. Phys. Lett . 73, 2603–2605 (1998). [CrossRef]

]. Vijayalakshumi et al showed that the surface state was responsible for the n 2 enhancement at around 1.6 eV in these samples[33

33. S. Vijayalakshumi, H. Grebel, G. Yaglioglu, R. Pino, R. Dorsinville, and C. W. White, “Nonlinear optical response of Si nanostructures in a silica matrix”, J. Appl. Phys . 88, 6418–6422 (2000). [CrossRef]

, 34

34. S. Vijayalakshmi, H. Grebel, Z. lqbal, and C. W. White, “Artificial dielectrics: Nonlinear properties of Si nanoclusters formed by ion implantation in SiO2 glassy matrix”, J. Appl. Phys ., 84, 6502–6506 (1998). [CrossRef]

]. At present, no definite conclusion is obtained on the origin of the large n 2 and further intensive research is required to clarify the origin. However, since the investigation of pure Si-ncs is out of the scope of this work, we are going to focus on the effect of P-doping.

Fig. 5. n 2 is plotted as a function of linear refractive index. The dashed line is the prediction of the Miller’s rule. Circles, squares and triangles are the results of several kinds of typical glasses, P-doped Si-ncs embedded in PSG (P-doped Si-nc:PSG) and pure Si-ncs embedded in SiO2 (Si-nc:SiO2), respectively.

4. Conclusion

Acknowledgments

This work is supported by Asahi Glass Co. Ltd. and a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan. We would like to thank Dr. Tomoharu Hasegawa and Dr. Madoka Ono for their experimental supports and excellent discussions for this work.

References and links

1.

L. T. Canham, “Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers”, Appl. Phys. Lett . 57, 1046–1048 (1990). [CrossRef]

2.

S. Takeoka, M. Fujii, and S. Hayashi, “Size-dependent photoluminescence from surface-oxidized Si nanocrystals in a weak confinement regime”, Phys. Rev. B 62, 16820–16825 (2000). [CrossRef]

3.

C. Delerue, M. Lannoo, G. Allan, and E. Martin, “Theoretical descriptions of porous silicon”, Thin Solid Films 255, 27–34 (1995). [CrossRef]

4.

P. Bettotti, M. Cazzanelli, L. Dal Negro, B. Danese, Z. Gaburro, C. J. Oton, G. Vijaya Prakash, and L. Pavesi, “Silicon nanostructures for photonics”, J. Phys:Condens. Matter 14, 8253–8281 (2002). [CrossRef]

5.

L. Pavesi, Z. Gaburro, L. Dal Negro, P. bettotti, G. Vijaya Prakash, M. Cazzaneli, and C. J. Oton, “Nanostructured silicon as a photonic material”, Opt. Lasers Eng. J. Opt. Soc. Am. B 39, 345–367 (2003). [CrossRef]

6.

S. Moon, A. Lin, B. H. Kim, P. R. Watekar, and W.-T. Han, “Linear and nonlinear optical properties of the optical fiber doped with silicon nano-particles”, J. Non-Cryst. Solids 354, 602–606 (2008). [CrossRef]

7.

S. Lettieri and P. Maddalena, “Nonresonant Kerr effect in microporous silicon: Nonbulk dispersive behavior of below band gap of χ(3)”, J. Appl. Phys . 91, 5564–5570 (2002). [CrossRef]

8.

Y. Kanemitsu, S. Okamoto, and A. Mito, “Third-order nonlinear optical susceptibility and photoluminescence in porous silicon”, Phys. Rev. B 52, 10752–10755 (1995). [CrossRef]

9.

S. Hemandez, P. Pellegrino, A. Martinez, Y. lebour, B. Garrido, R. Spano, M. Cazzanelli, N. Daldosso, L. Pavesi, E. Jordana, and J. M. Fedeli, “Linear and nonlinear optical properties of Si nanocrystals in SiO2 deposited by plasma-enhanced chemical-vapor deposition”, J. Appl. Phys . 103, 064309 (2008). [CrossRef]

10.

G. Vijaya Prakash, M. Cazzaneli, Z. Gaburro, L. Pavesi, F. Lacona, G. Franzo, and F. Priolo., “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition”, J. Appl. Phys . 91, 4607–4610 (2002). [CrossRef]

11.

K. Imakita, M. Ito, M. Fujii, S. Hayashi, and J. Appl. Phys. (to be published).

12.

S. Vijayalakshmi, A. Lan, Z. lqbal, and H. Grebel, “Nonlinear optical properties of laser ablated silicon nanostructures”, J. Appl. Phys . 92, 2490–2494 (2002). [CrossRef]

13.

S. Vijayalakshmi, M. A. George, and H. Grebel, “Nonlinear optical properties of silicon nanoclusters”, Appl. Phys. Lett . 70, 708–710 (1997). [CrossRef]

14.

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method”, Appl. Phys. B 70, 587–591 (2000). [CrossRef]

15.

M. Fujii, Y. Yamaguchi, Y. Takase, K. Ninomiya, and S. Hayashi, “Control of photoluminescence properties of Si nanocrystals by simultaneously doping n- and p-type impurities”, Appl. Phys. Lett . 85, 1158–1160 (2004). [CrossRef]

16.

M. Fujii, Y. Yamaguchi, Y. Takase, K. Ninomiya, and S. Hayashi, “Photoluminescence from impurity codoped and compensated Si nanocrystals”, Appl. Phys. Lett . 87, 211919 (2005). [CrossRef]

17.

A. Mimura, M. Fujii, S. Hayashi, D. Kovalev, and F. Koch, “Photoluminescence and free-electron absorption in heavily phosphorus-doped Si nanocrystals”, Phys. Rev. B 62, 12625–12627 (2000). [CrossRef]

18.

B. J. Pawlak, T. Gregorkiewicz, C. A. J. Ammerlaan, W. Takkenberg, F. D. Tichelaar, and P. F. A. Alkemade, “Experimental investigation of band structure modification in silicon nanocrystals”, Phys. Rev. B 64, 115308 (2001). [CrossRef]

19.

M. Fujii, A. Mimura, and S. Hayashi, “Hyperfine Structure of the Electron Spin Resonance of Phosphorus-Doped Si Nanocrystals”, Phys. Rev. Lett . 89, 206805 (2002). [CrossRef] [PubMed]

20.

G. Cantele, E. Degoli, E. Luppi, R. Magori, D. Ninno, G. Iadonisi, and S. Ossicini, “First-principles study of n - and p -doped silicon nanoclusters”, Phys. Rev. B 72, 113303 (2005). [CrossRef]

21.

G. Allan, C. Delerue, M. Lannoo, and E. Martin, “Hydrogenic impurity levels, dielectric constant, and Coulomb charging effects in silicon crystallites”, Phys. Rev. B 52, 11982–11988 (1995). [CrossRef]

22.

D. V. Melnikov and J. R. Chelikowsky, “Quantum Confinement in Phosphorus-Doped Silicon Nanocrystals”, Phys. Rev. Lett . 92, 046802 (2004). [CrossRef] [PubMed]

23.

S. Ossicini, F. Iori, E. Degoli, E. Luppi, R. Magri, R. Poli, G. Cantele, F. Trani, and D. Ninno, “Understanding Doping In Silicon Nanostructures”, IEEE J. Sel. Top. Quantum Electron . 12, 1585–1591 (2006). [CrossRef]

24.

M. Fujii, S. Hayashi, and K. Yamamoto, “Photoluminescence from B-doped Si nanocrystals”, J. Appl. Phys . 83, 7953–7956 (1998). [CrossRef]

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D. A. G. Bruggeman,“Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen”, Ann. Phys . 24, 636–679 (1935). [CrossRef]

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M. Fuji, D. Kovalev, J. Diener, F. Koch, S. Takkeoka, and S. Hayashi, “Breakdown of the k-conservation rule in Si1-xGex alloy nanocrystals: Resonant photoluminescence study”, J. Appl. Phys . 88, 5772–5776 (2000). [CrossRef]

28.

M. Fujii, A. Mimura, and S. Hayashi, “Improvement in photoluminescence efficiency of SiO2 films containing Si nanocrystals by P doping: An electron spin resonance study”, J. Appl. Phys . 87, 1855–1857 (2000). [CrossRef]

29.

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V. Sa-yakanit and H. R. Glyde, “Impurity-band density of states in heavily doped semiconductors: A variational calculation”, Phys. Rev. B 22, 6222–6232 (1980). [CrossRef]

31.

E. L. de Oliveira, E. L. Albuquerque, J. S. de Sousa, and G. A. Farias, “Radiative transitions in P- and B-doped silicon nanocrystals”, Appl. Phys. Lett . 94, 103114 (2009). [CrossRef]

32.

V. I. Klimov, Ch. J. Schwarz, D. W. McBranch, and C. W. White, “Initial carrier relaxation dynamics in ionimplanted Si nanocrystals: Femtosecond transient absorption study”, Appl. Phys. Lett . 73, 2603–2605 (1998). [CrossRef]

33.

S. Vijayalakshumi, H. Grebel, G. Yaglioglu, R. Pino, R. Dorsinville, and C. W. White, “Nonlinear optical response of Si nanostructures in a silica matrix”, J. Appl. Phys . 88, 6418–6422 (2000). [CrossRef]

34.

S. Vijayalakshmi, H. Grebel, Z. lqbal, and C. W. White, “Artificial dielectrics: Nonlinear properties of Si nanoclusters formed by ion implantation in SiO2 glassy matrix”, J. Appl. Phys ., 84, 6502–6506 (1998). [CrossRef]

35.

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals”, Appl. Phys. Lett . 5, 17 (1964). [CrossRef]

36.

C. C. Wang, “Empirical Relation between the Linear and the Third-Order Nonlinear Optical Susceptibilities”, Phys. Rev. B 2, 2045–2048 (1970). [CrossRef]

37.

S. Kim, T. Yoko, and S. Sakka, “Linear and nonlinear optical properties of TeO2 glass”, J. Am. Ceram. Soc . 76, 2486–2490 (2005). [CrossRef]

38.

N. Sugimoto, H. Kanbara, S. Fujiwara, K. Tanaka, Y. Shimizugawa, and K. Hirao, “Third-order optical nonlinearities and their ultrafast response in Bi2O3-B2O3-SiO2 glasses”, J. Opt. Soc. Am. B 16, 1904–1908 (1999). [CrossRef]

39.

G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Spalter, R. E. Slusher, S.-W. Cheong, J. S. Sanghera, and I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses”, Opt. Lett . 25, 254–256 (2000). [CrossRef]

40.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses”, Appl. Phys. Lett . 54, 1293 (1989). [CrossRef]

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter

ToC Category:
Nonlinear Optics

History
Original Manuscript: March 9, 2009
Revised Manuscript: April 10, 2009
Manuscript Accepted: April 13, 2009
Published: April 20, 2009

Citation
Kenji Imakita, Masahiko Ito, Minoru Fujii, and Shinji Hayashi, "Nonlinear optical properties of Phosphorous-doped Si nanocrystals embedded in phosphosilicate glass thin films," Opt. Express 17, 7368-7376 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7368


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  32. V. I. Klimov, Ch. J. Schwarz, and D. W. McBranch, and C. W. White, "Initial carrier relaxation dynamics in ionimplanted Si nanocrystals: Femtosecond transient absorption study," Appl. Phys. Lett. 73, 2603-2605 (1998). [CrossRef]
  33. S. Vijayalakshumi, H. Grebel, G. Yaglioglu, R. Pino, R. Dorsinville, and C. W. White, "Nonlinear optical response of Si nanostructures in a silica matrix," J. Appl. Phys. 88, 6418-6422 (2000). [CrossRef]
  34. S. Vijayalakshmi, H. Grebel, Z. lqbal, and C. W. White, "Artificial dielectrics: Nonlinear properties of Si nanoclusters formed by ion implantation in SiO2 glassy matrix," J. Appl. Phys. 84, 6502-6506 (1998). [CrossRef]
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  36. C. C. Wang, "Empirical Relation between the Linear and the Third-Order Nonlinear Optical Susceptibilities," Phys. Rev. B 2, 2045-2048 (1970). [CrossRef]
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