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Influence of matrix on third order optical nonlinearity for semiconductor nanocrystals embedded in glass thin films prepared by Rf-sputtering
Journal of Non-Crystalline Solids 351 (2005) 893–899 www.elsevier.com/locate/jnoncrysol
Influence of matrix on third order optical nonlinearity for semiconductor nanocrystals embedded in glass thin films prepared by Rf-sputtering Hiroyuki Nasu b
a,*
, Akimasa Tanaka a, Kenji Kamada b, Tadanori Hashimoto
a
a Department of Chemistry for Materials, Faculty of Engineering, Mie University, Kamihama 1515, Tsu 514-8507, Mie, Japan Photonics Research Institute, National Institute of Advanced Industrial Science and Technology, AIST Kansai, Midorigaoka 1-8-31, Ikeda, Osaka 563-8577, Japan
Received 1 July 2004; received in revised form 18 November 2004 Available online 24 March 2005
Abstract CdSe nanocrystals were successfully embedded in high index glass films by rf-sputtering technique. All films showed the shift of absorption edge to shorter wavelength compared with that of bulk CdSe, so-called, blue shift, and it was evident that there is a quantum confinement effect in the films. The amount of the blue shift depended on the kind of matrix glass as well as the size of embedded CdSe nanocrystals. The third-order optical nonlinearity evaluated by Z-scan technique also depended on the matrix glass. The larger nonlinearity was observed from the matrix glass with higher refractive index. In addition, it was found that the value of shift of absorption edge, or the quantum confinement effect was linearly related to the third-order nonlinearity for CdSe nanocrystals embedded in glass thin films. 2005 Elsevier B.V. All rights reserved.
1. Introduction Since Jain and Rind reported large third-order optical nonlinearity for commercially available CdSxSe1x nanocrystals embedded filter glasses [1], the semiconductor nanocrystals embedded glasses have been extensively studied. Among several ways to prepare semiconductor nanocrystals embedded glasses, such as conventional melt-quenching and sol-gel methods, rf-sputtering technique has advantages in embedding glasses with various kinds of semiconductor nanocrystals which are even volatile or reactive with atmosphere or matrix substances, and in preparing such composites in the form of films at low temperatures [2,3]. When the semiconductor
*
Corresponding author. Tel./fax: +81 59 231 9435. E-mail address: [email protected] (H. Nasu).
0022-3093/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.01.067
nanocrystals with the size below 10 nm are embedded in the dielectric materials, the quantum confinement effect begins to appear. Then, the oscillation strength between electrons and holes are drastically increased and the incident electromagnetic wave is concentrated to the particles in the transparent composite films. The optical third-order nonlinearity, thus, is significantly enhanced. Furthermore, because the quantum confinement effect restricts the spatial location of excited electrons and holes, relaxation takes place quickly as in ps order. There are two categories for the quantum confinement effect [4]. One is the exciton confinement effect which is for the semiconductors with small exciton Bohr radius (rB), compared to microcrystal radius (R) or R/ rB > 4, and the other is electron–hole independent confinement effect for the semiconductors with large exciton Bohr radius or R/rB < 2. For examples, CuCl and CuBr are the former case, and CdSe, GaAs and Si are the
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H. Nasu et al. / Journal of Non-Crystalline Solids 351 (2005) 893–899
latter case. As far, the study on the quantum confinement effect has been mainly concentrated to semiconductor nanocrystals exhibiting the exciton confinement effect, and there has been obtained much information on the glasses embedded with CuCl or CuBr nanocrystals. In specific, significant influence of the mean size of the nanocrystals has been reported by a group of Nagoya University [5] for the exciton confinement effect. On the other hand, with respect to the electron–hole independent confinement effect, there are only a few works on the influence of mean crystal size on the blue shift and/or third-order optical nonlinearity [6,7]. In addition, the present authors have found the significant influence of the matrix on the plots of the amount of the blue shift as a function of the reciprocal square of the mean microcrystal radius and pointed out the importance of the matrix in the quantum size confinement for the electron–hole independent confinement effect [8–10]. They also evaluated third-order optical nonlinear susceptibility jv(3)j of silica glass thin films doped with CdSe nanocrystals of different mean sizes by using Zscan method, and reported the first experimental evidence for the dependence of jv(3)j on reciprocal cubic of microcrystal size [11]. In the present work, third-order optical nonlinearity of the CdSe nanocrystals embedded high-index glass thin films was examined in order to clarify the influence of the matrix on jv(3)j.
2. Experimental procedure The commercially available magnetron rf-sputtering equipment (Hirano Koon, KS-1002) was used to prepare CdSe nanocrystals embedded glass films. In order to prepare the films, the composite target method was adopted, where the CdSe (99.99% purity) chips of 1 mm in diameter were placed on glass plates. Glasses used was SiO2 glass, 90TeO2 Æ 10TiO2 (mol%) and STIH53 (SiO2–TiO2–RO–R2O) glasses. SiO2 glass plate of 99.99% purity was obtained from Kojundo Kagaku and S-TIH53 (H-series) was donated from OHARA Co. Ltd. The 90TeO2 Æ 10TiO2 glass (T-series) was prepared by conventional melt-quenching technique after mixing TeO2 (99.9%) and TiO2 (99.9%). The substrates used were SiO2 glasses for optical measurements including Z-scan, offset Si single crystals for X-ray diffraction (XRD) measurements, and KBr pellet for transmission electron microscopy (TEM), respectively. The substrate temperature was 200 C. The sputtering gas used was high purity Ar, input power was kept at 75 W and the distance between targets and substrates was 40 mm. The sputtering time was usually 3 h, and for TEM observation it was 80–120 s. With respect to the influence on the film thickness between samples for optical measurements and TEM observation, it is not significant change since the mean diameters obtained from
XRD measurements and TEM observation measurements are quite similar to each other. The XRD measurement was performed to determine the crystal phase of CdSe. The X-ray source was Ni-filtered CuKa radiation generated at 40 kV and 100 mA. Measurement was carried out in step-scan mode in the range from 2h = 20 to 50, with the step interval of 0.05 and of 2 s. With respect to chemical state of CdSe nanocrystals embedded in glass thin films, X-ray photoelectron spectroscopy (XPS) measurement was carried out. The X-ray source used was MgKa radiation. The peaks measured were Cd 3d5/2 and Se 3d and C 1s. The C 1s peak (285 eV) was used as a reference for cancelling the surface charge effect. The mean size and size distribution of microcrystals were measured by TEM. The KBr pellet on which composite film was deposited was soaked into distilled water, and the separated film was put on the copper mesh. The acceleration voltage applied for TEM observation was 300 kV. The film thickness was measured by scanning electron microscopy (SEM). The typical thickness of the prepared films was about 1.5 lm. The bandgap energy of nanocrystals embedded in glass films was explored by NIR–Visible–UV spectrometer. For that purpose, we measured optical spectra from 190 nm to 1000 nm with a scan speed of 200 nm/ min. Z-scan measurements were carried out at AIST Kansai Center. The titanium: sapphire laser generating 116 fs pulses and 10 Hz repetition at 802 nm was used. The ultra high frequency of the initial laser pulse was mechanically chopped to 10 Hz. Real part of v(3) (Re v(3)) is estimated from the ratio of the incident power dependence of DTPV, which is the difference of top and bottom of the Z-scan spectra, of the sample to that of the reference SiO2 substrate glass. The Re v(3) is related to nonlinear refractive index (c) as [12], Re vð3Þ ¼ 2n20 e0 cc;
ð1Þ
where n0 is linear refractive index, e0 is dielectric constant of vacuum and c is the light velocity. Imaginary part of v(3)(Im v(3)) was calculated as follows. At first, q0 was estimated by fitting the experimental transmittance to the following equation, T ðz; S ¼ 1Þ 1 aLeff ¼ pffiffiffi pqðnÞ
Z
1
ln½1 þ qðnÞ expðx2 Þ dx;
ð2Þ
1
with qðnÞ ¼ q0 =ð1 þ n2 Þ;
ð3Þ
where n is the normalized location in z-axis with zR in Rayleigh range, a is linear absorption coefficient, Leff is effective path length, S = 1 stands for open aperture con-
H. Nasu et al. / Journal of Non-Crystalline Solids 351 (2005) 893–899
895
dition, and q0 is parameter. The q0 is related to two photon absorption coefficient (b), incident light intensity (I0) and effective path length (Leff) as q0 ¼ bI 0 Leff : Thus, Im v Im vð3Þ ¼
(3)
ð4Þ is related to b as
n20 e0 c2 b; x
ð5Þ
where x is angular frequency. The total optical thirdorder susceptibility (v(3)) is given, as follows [12] 2
2 1=2
jvð3Þ j ¼ fðRe vð3Þ Þ þ ðIm vð3Þ Þ g
:
ð6Þ
3. Results Fig. 1(a) and (b) show typical XPS spectra of Cd 3d5/2 and Se 3d of CdSe nanocrystals embedded in 90TeO2 Æ 10TiO2 glass matrix, respectively. Peaks are ascribable to Cd and Se in CdSe, respectively. Thus, it is considered that no serious oxidation, decomposition and reaction of CdSe have taken place during sputtering. Furthermore, the existence of CdSe crystal was found from XRD results. Typical TEM picture of the present films is shown in Fig. 2. The dispersed dark spots and crystal lattice images are seen in obscure glass matrix. The mean sizes and size distribution of nanocrystals are estimated from TEM pictures. Hereafter, the samples are called H for H-series and T for T-series which are followed by the mean particle size. Fig. 3 shows the size distribution of CdSe nanocrystals in H-series glass thin films H2.9, H3.7, H4.3, H4.8, H5.7 were prepared using the relative surface area ratio of chips of 3.7%, 4.9%, 6.2%, 7.4%,
Fig. 1. XPS spectra of (a) Cd 3d5/2 and (b) Se 3d for CdSe embedded in 90TeO2 Æ 10TiO2 glass.
Fig. 2. TEM picture of CdSe embedded glass. Arrow mark points out the crystal image of CdSe.
8.6%, respectively. Thus, it can be said that the increase of the relative surface area results in the increase of the mean particle size. From the figure, it is noted that the size distribution is narrow enough to evaluate the influence of particle size on third-order optical nonlinearity. On the other hand, the particle size distribution profiles of T-series are depicted in Fig. 4. T3.9, T4.4, T4.7, T5.1 correspond to the relative surface area ratio of 6.2%, 7.4%, 8.6%, 9.9%, respectively. As indicated in H-series, the particle size gradually increases with increasing the relative surface area. Further, the distribution profiles are also narrow enough to examine the influence of the crystal size. Fig. 5 shows the influence of particle size on the bandgap or absorption edge in H-series (a) and T-series (b). Because of the direct transition of CdSe, bandgap values are derived from (ahm)2 versus hm plots, where a is linear absorption coefficient and m is incident light frequency. In both figures, the band gap shifts to higher energy side (blue shift) with decreasing particle size. The existence of blue shift is evident, and it is confirmed that there is the quantum size confinement effect in the CdSe nanocrystals in this study. Tables 1 and 2 tabulate Z-scan results obtained from H-series and T-series, respectively. For the calculation, the proportional relationship between incident radiation and signal were examined in order to eliminate the influence of resonant effect near band edge. The dependence of Im v(3) on themean size in T-series and H-series looks different, but, from the intensity dependence measurements, it does not relate to the resonance effect since clear linear relationship was obtained. Since the data
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Fig. 3. Size distribution profiles of nanocrystal particles in H-series samples: (a) H2.9, (b) H3.7, (c) H4.3, (d) H4.8 and (e) H5.7.
Fig. 4. Size distribution profiles of nanocrystal particles in T-series samples: (a) T3.9, (b) T4.4, (c) T4.7 and (d) T5.1.
H. Nasu et al. / Journal of Non-Crystalline Solids 351 (2005) 893–899
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Table 2 Third-order nonlinearity of T-series Sample (3)
12
esu) Re v (10 Im v(3) (1012 esu) Normalized jv(3)j (1012 esu)
T0
T3.9
T4.3
T4.7
T5.1
0.0336
5.09 0.422 3.7
10.5 6.42 2.7
13.6 4.82 2.0
21.2 3.59 1.8
thy that all real parts of third-order optical nonlinearity of all the CdSe embedded glass films are negative. In order to eliminate the influence of the concentration of the particles, the whole values were normalized with respect to the concentration of CdSe, and called normalized jv(3)j [11]. In order to obtain the normalized jv(3)j, the observed value was divided by the molar concentration of CdSe = 1mol%, which was determined on the basis of XPS line intensity of Cd and/or Se as in the previous work [11]. The largest normalized jv(3)j was 3.7 · 1012 esu.
4. Discussion As mentioned above, the quantum size effect of semiconductor nanocrystals is divided into two categories. One is the exciton confinement effect and the other is the electron–hole independent confinement effect. For semiconductors with small exciton Bohr radius relative to particle size, such as CuCl or CuBr, the blue shift (DE) is expressed as follows, p2 h2 ; ð7Þ 2MR2 where M is the translational mass and M is me + mh (me: effective mass of electron, mh: effective mass of hole), and R is particle radius. On the other hand, for semiconductors with large exciton Bohr radius compared to the particle size, such as CdSe, CdTe, GaAs or Si, the blue shift is caused by the electron–hole independent confinement effect and expressed as, DE ¼
Fig. 5. Bandgap from (ahm)2 plot as a function of hm obtained from absorption spectra for (a) H-series and (b) T-series.
Table 1 Third-order nonlinearity of H-series Sample (3)
12
Re v (10 esu) Im v(3) (1012 esu) Normalized jv(3)j (1012 esu)
H0
H3.7
H4.3
H4.8
0.0287
12.8 3.03 3.4
12.0 2.14 1.8
12.9 2.34 1.2
shown is the raw data, the concentration of the particles may influence on the Im v(3) value. The error of the experiments is below 5%. The third-order nonlinearity increases with decreasing particle size, and it is notewor-
DE ¼
p2 h2 ; 2lR2
ð8Þ
where l is the reduced mass and 1/l = 1/me + 1/mh. The experimental data for CdSe embedded silica glass films significantly deviated from the theoretical curve given by Eq. (8) as seen in Fig. 6. Thus, we introduce Kayanumas model [13] in which the Coulomb interaction between electrons and holes is taken into consideration, DE ¼
p2 h2 e2 1:786 0:248Ry ; 2 eR 2lR
ð9Þ
where e is dielectric constant and Ry is the effective Rydberg energy. According to Haken [14], the dielectric
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Fig. 6. The amount of the blue shift as a function of inverse square of the nanocrystal radius.
constant e in Eq. (9) depends on the particle size, and can be expressed by the following equation, 1 1 1 1 ¼ eðr Þ e1 e1 e0 expðr =q1 Þ þ expðr =q2 Þ 1 ; ð10Þ 2 where r* is the mean distance between the electron and hole, and r* = 0.69932R. The q1 and q2 are the polaron radii of electron and hole, respectively, and calculated to be 3.38 and 1.03 nm, respectively. The effective dielectric constant affecting the quantum size confinement effect is presumed to be that of matrix, and Haken potential is used for the analysis by introducing the polaron effect. For bulk CdSe (R = 1), e(r*) = e0 from Eq. (10) and should be 9.56. On the other hand, e(r*) = e1 when r* = 0. In this case there are two possibilities for e1 as those of CdSe and matrix glass. Fig. 6 shows the plot of theoretical lines of Eqs. (8) and (10) using e1 of matrix glass. One can see good agreement of experimental data with theoretical curves using Eq. (10). S-series in this figure corresponds to CdSe embedded in SiO2 glass matrix. Therefore, it is said that the matrix has significant influence of the quantum confinement effect. Fig. 7 shows the normalized jv(3)j as a function of the inverse cubic of the microcrystal radius. In each system, the jv(3)j depends on the microcrystal size, and increases as the decrease of mean microcrystal radius according to the r3 law as pointed out for S-series [11]. In addition, one can notice that there is the influence of matrix glass species on the third-order optical nonlinearity. The higher refractive index, in other words, higher dielectric constant is found to yield larger jv(3)j. In this discussion, data on S-series are not plotted in this and the following figures. This is because some jv(3)j data of S-series depend on the intensity of the incident radiation, or significant resonant effect is encountered.
Fig. 7. Third-order optical nonlinearity as a function of the inverse cubic of the nanocrystal radius.
So far, it has been believed that DEg or confinement effect is related to large jv(3)j. For the exciton confinement effect as in the case of CuCl or CuBr, it has been reported that there is a maximum in the relationship between the third-order nonlinearity and DEg [5], and the appearance such a maximum was interpreted in terms of the chapnge of oscillation strength of excitons with particle size. The argument on the jv(3)j versus DEg relation for the electron–hole independent confinement has still remained qualitative. In order to explore the relationship quantitatively the jv(3)j of the CdSe nanocrystals embedded in glass films is plotted against DEg in Fig. 8. We, now, notice linear relation for the electron–hole independent confinement effect in this figure. Furthermore, it should be noted that the jv(3)j versus DEg relation is no longer. dependent of the glass matrix species. Thus,
Fig. 8. The relationship between third-order nonlinearity and the amount of the blue shift.
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it is pointed out that deep quantum well built up in small particles surrounded by the matrix of high dielectric constant gives rise to strong interaction between electron and hole, and result in the large third-order optical nonlinearity for CdSe nanocrystals embedded in glass thin films.
Acknowledgement
5. Conclusion
References
The influence of the matrix glass on the third-order optical nonlinearity of CdSe nanocrystals was explored. CdSe nanocrystals were successfully embedded in the various kinds of glasses. The mean microcrystal size was controllable by the relative surface area ratio of CdSe chips, and the increase of the ratio increased the mean particle size. Blue shift in absorption edge was observed for whole present films, and it was evident for the occurrence of the quantum size confinement effect. The deviation of the amount of blue shift from the theoretical curve was interpreted by considering the Coulomb interaction between electrons and holes and the influence of the dielectric constant of matrix. The third-order optical nonlinearity depended on the dielectric constant of matrix glass as well as mean particle size, and linear relationship between third-order nonlinearity, and the blue shift was experimentally evidenced for the electron–hole independent confinement system.
[1] R.K. Jain, R.C. Lind, J. Opt. Soc. Am. 73 (1983) 647. [2] K. Tsunetomo, H. Nasu, H. Kitayama, A. Kawabuchi, Y. Osaka, K. Takiyama, Jpn. J. Appl. Phys. 28 (1989) 1928. [3] R. Hayashi, M. Yamamoto, K. Tsunetomo, K. Kohno, Y. Osaka, H. Nasu, Jpn. J. Appl. Phys. 29 (1990) 756. [4] Al.L. Efros, A.L. Efros, Sov. Phys. JETP 16 (1981) 772. [5] A. Nakamura, New Glass 14 (1999) 3. [6] S. Nomura, T. Kobayashi, Solid State Commun. 78 (1991) 677. [7] T. Tokisaki, H. Akiyama, T. Takaya, A. Nakamura, J. Cryst. Growth 117 (1992) 603. [8] H. Nasu, J. Matsuoka, K. Kamiya, J. Non-Cryst. Solids 178 (1994) 148, Vol II. [9] H. Nasu, T. Iwano, T. Hashimoto, K. Kamiya, J. Mater. Sci. 35 (2000) 3097. [10] H. Nasu, H. Iwatani, T. Iwano, T. Hashimoto, K. Kamiya, Jpn. J. Appl. Phys. 42 (2003) 270. [11] H. Nasu, A. Tanaka, K. Kamada, Y. Yamamoto, Y. Matsuzaki, T. Hashimoto, J. Ceram. Soc. Jpn. 110 (2002) 921. [12] M. Sheik-Bahae, A.A. Said, T. Wei, T.J. Hagan, E.W. VanStryl, IEEE J. Quantum Electron. 26 (1990) 760. [13] Y. Kayanuma, Phys. Rev. B 38 (1988) 9797. [14] H. Haken, Nuovo Cimento 10 (1956) 1230.
Authors are grateful for the financial support from Nano Glass Technology Project of New Glass Forum. Authors are also grateful for the assistance to summarize data by Mr M. Kimura, Mie Univesity.
Influence of matrix on third order optical nonlinearity for semiconductor nanocrystals embedded in glass thin films prepared by Rf-sputtering Hiroyuki Nasu b
a,*
, Akimasa Tanaka a, Kenji Kamada b, Tadanori Hashimoto
a
a Department of Chemistry for Materials, Faculty of Engineering, Mie University, Kamihama 1515, Tsu 514-8507, Mie, Japan Photonics Research Institute, National Institute of Advanced Industrial Science and Technology, AIST Kansai, Midorigaoka 1-8-31, Ikeda, Osaka 563-8577, Japan
Received 1 July 2004; received in revised form 18 November 2004 Available online 24 March 2005
Abstract CdSe nanocrystals were successfully embedded in high index glass films by rf-sputtering technique. All films showed the shift of absorption edge to shorter wavelength compared with that of bulk CdSe, so-called, blue shift, and it was evident that there is a quantum confinement effect in the films. The amount of the blue shift depended on the kind of matrix glass as well as the size of embedded CdSe nanocrystals. The third-order optical nonlinearity evaluated by Z-scan technique also depended on the matrix glass. The larger nonlinearity was observed from the matrix glass with higher refractive index. In addition, it was found that the value of shift of absorption edge, or the quantum confinement effect was linearly related to the third-order nonlinearity for CdSe nanocrystals embedded in glass thin films. 2005 Elsevier B.V. All rights reserved.
1. Introduction Since Jain and Rind reported large third-order optical nonlinearity for commercially available CdSxSe1x nanocrystals embedded filter glasses [1], the semiconductor nanocrystals embedded glasses have been extensively studied. Among several ways to prepare semiconductor nanocrystals embedded glasses, such as conventional melt-quenching and sol-gel methods, rf-sputtering technique has advantages in embedding glasses with various kinds of semiconductor nanocrystals which are even volatile or reactive with atmosphere or matrix substances, and in preparing such composites in the form of films at low temperatures [2,3]. When the semiconductor
*
Corresponding author. Tel./fax: +81 59 231 9435. E-mail address: [email protected] (H. Nasu).
0022-3093/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.01.067
nanocrystals with the size below 10 nm are embedded in the dielectric materials, the quantum confinement effect begins to appear. Then, the oscillation strength between electrons and holes are drastically increased and the incident electromagnetic wave is concentrated to the particles in the transparent composite films. The optical third-order nonlinearity, thus, is significantly enhanced. Furthermore, because the quantum confinement effect restricts the spatial location of excited electrons and holes, relaxation takes place quickly as in ps order. There are two categories for the quantum confinement effect [4]. One is the exciton confinement effect which is for the semiconductors with small exciton Bohr radius (rB), compared to microcrystal radius (R) or R/ rB > 4, and the other is electron–hole independent confinement effect for the semiconductors with large exciton Bohr radius or R/rB < 2. For examples, CuCl and CuBr are the former case, and CdSe, GaAs and Si are the
894
H. Nasu et al. / Journal of Non-Crystalline Solids 351 (2005) 893–899
latter case. As far, the study on the quantum confinement effect has been mainly concentrated to semiconductor nanocrystals exhibiting the exciton confinement effect, and there has been obtained much information on the glasses embedded with CuCl or CuBr nanocrystals. In specific, significant influence of the mean size of the nanocrystals has been reported by a group of Nagoya University [5] for the exciton confinement effect. On the other hand, with respect to the electron–hole independent confinement effect, there are only a few works on the influence of mean crystal size on the blue shift and/or third-order optical nonlinearity [6,7]. In addition, the present authors have found the significant influence of the matrix on the plots of the amount of the blue shift as a function of the reciprocal square of the mean microcrystal radius and pointed out the importance of the matrix in the quantum size confinement for the electron–hole independent confinement effect [8–10]. They also evaluated third-order optical nonlinear susceptibility jv(3)j of silica glass thin films doped with CdSe nanocrystals of different mean sizes by using Zscan method, and reported the first experimental evidence for the dependence of jv(3)j on reciprocal cubic of microcrystal size [11]. In the present work, third-order optical nonlinearity of the CdSe nanocrystals embedded high-index glass thin films was examined in order to clarify the influence of the matrix on jv(3)j.
2. Experimental procedure The commercially available magnetron rf-sputtering equipment (Hirano Koon, KS-1002) was used to prepare CdSe nanocrystals embedded glass films. In order to prepare the films, the composite target method was adopted, where the CdSe (99.99% purity) chips of 1 mm in diameter were placed on glass plates. Glasses used was SiO2 glass, 90TeO2 Æ 10TiO2 (mol%) and STIH53 (SiO2–TiO2–RO–R2O) glasses. SiO2 glass plate of 99.99% purity was obtained from Kojundo Kagaku and S-TIH53 (H-series) was donated from OHARA Co. Ltd. The 90TeO2 Æ 10TiO2 glass (T-series) was prepared by conventional melt-quenching technique after mixing TeO2 (99.9%) and TiO2 (99.9%). The substrates used were SiO2 glasses for optical measurements including Z-scan, offset Si single crystals for X-ray diffraction (XRD) measurements, and KBr pellet for transmission electron microscopy (TEM), respectively. The substrate temperature was 200 C. The sputtering gas used was high purity Ar, input power was kept at 75 W and the distance between targets and substrates was 40 mm. The sputtering time was usually 3 h, and for TEM observation it was 80–120 s. With respect to the influence on the film thickness between samples for optical measurements and TEM observation, it is not significant change since the mean diameters obtained from
XRD measurements and TEM observation measurements are quite similar to each other. The XRD measurement was performed to determine the crystal phase of CdSe. The X-ray source was Ni-filtered CuKa radiation generated at 40 kV and 100 mA. Measurement was carried out in step-scan mode in the range from 2h = 20 to 50, with the step interval of 0.05 and of 2 s. With respect to chemical state of CdSe nanocrystals embedded in glass thin films, X-ray photoelectron spectroscopy (XPS) measurement was carried out. The X-ray source used was MgKa radiation. The peaks measured were Cd 3d5/2 and Se 3d and C 1s. The C 1s peak (285 eV) was used as a reference for cancelling the surface charge effect. The mean size and size distribution of microcrystals were measured by TEM. The KBr pellet on which composite film was deposited was soaked into distilled water, and the separated film was put on the copper mesh. The acceleration voltage applied for TEM observation was 300 kV. The film thickness was measured by scanning electron microscopy (SEM). The typical thickness of the prepared films was about 1.5 lm. The bandgap energy of nanocrystals embedded in glass films was explored by NIR–Visible–UV spectrometer. For that purpose, we measured optical spectra from 190 nm to 1000 nm with a scan speed of 200 nm/ min. Z-scan measurements were carried out at AIST Kansai Center. The titanium: sapphire laser generating 116 fs pulses and 10 Hz repetition at 802 nm was used. The ultra high frequency of the initial laser pulse was mechanically chopped to 10 Hz. Real part of v(3) (Re v(3)) is estimated from the ratio of the incident power dependence of DTPV, which is the difference of top and bottom of the Z-scan spectra, of the sample to that of the reference SiO2 substrate glass. The Re v(3) is related to nonlinear refractive index (c) as [12], Re vð3Þ ¼ 2n20 e0 cc;
ð1Þ
where n0 is linear refractive index, e0 is dielectric constant of vacuum and c is the light velocity. Imaginary part of v(3)(Im v(3)) was calculated as follows. At first, q0 was estimated by fitting the experimental transmittance to the following equation, T ðz; S ¼ 1Þ 1 aLeff ¼ pffiffiffi pqðnÞ
Z
1
ln½1 þ qðnÞ expðx2 Þ dx;
ð2Þ
1
with qðnÞ ¼ q0 =ð1 þ n2 Þ;
ð3Þ
where n is the normalized location in z-axis with zR in Rayleigh range, a is linear absorption coefficient, Leff is effective path length, S = 1 stands for open aperture con-
H. Nasu et al. / Journal of Non-Crystalline Solids 351 (2005) 893–899
895
dition, and q0 is parameter. The q0 is related to two photon absorption coefficient (b), incident light intensity (I0) and effective path length (Leff) as q0 ¼ bI 0 Leff : Thus, Im v Im vð3Þ ¼
(3)
ð4Þ is related to b as
n20 e0 c2 b; x
ð5Þ
where x is angular frequency. The total optical thirdorder susceptibility (v(3)) is given, as follows [12] 2
2 1=2
jvð3Þ j ¼ fðRe vð3Þ Þ þ ðIm vð3Þ Þ g
:
ð6Þ
3. Results Fig. 1(a) and (b) show typical XPS spectra of Cd 3d5/2 and Se 3d of CdSe nanocrystals embedded in 90TeO2 Æ 10TiO2 glass matrix, respectively. Peaks are ascribable to Cd and Se in CdSe, respectively. Thus, it is considered that no serious oxidation, decomposition and reaction of CdSe have taken place during sputtering. Furthermore, the existence of CdSe crystal was found from XRD results. Typical TEM picture of the present films is shown in Fig. 2. The dispersed dark spots and crystal lattice images are seen in obscure glass matrix. The mean sizes and size distribution of nanocrystals are estimated from TEM pictures. Hereafter, the samples are called H for H-series and T for T-series which are followed by the mean particle size. Fig. 3 shows the size distribution of CdSe nanocrystals in H-series glass thin films H2.9, H3.7, H4.3, H4.8, H5.7 were prepared using the relative surface area ratio of chips of 3.7%, 4.9%, 6.2%, 7.4%,
Fig. 1. XPS spectra of (a) Cd 3d5/2 and (b) Se 3d for CdSe embedded in 90TeO2 Æ 10TiO2 glass.
Fig. 2. TEM picture of CdSe embedded glass. Arrow mark points out the crystal image of CdSe.
8.6%, respectively. Thus, it can be said that the increase of the relative surface area results in the increase of the mean particle size. From the figure, it is noted that the size distribution is narrow enough to evaluate the influence of particle size on third-order optical nonlinearity. On the other hand, the particle size distribution profiles of T-series are depicted in Fig. 4. T3.9, T4.4, T4.7, T5.1 correspond to the relative surface area ratio of 6.2%, 7.4%, 8.6%, 9.9%, respectively. As indicated in H-series, the particle size gradually increases with increasing the relative surface area. Further, the distribution profiles are also narrow enough to examine the influence of the crystal size. Fig. 5 shows the influence of particle size on the bandgap or absorption edge in H-series (a) and T-series (b). Because of the direct transition of CdSe, bandgap values are derived from (ahm)2 versus hm plots, where a is linear absorption coefficient and m is incident light frequency. In both figures, the band gap shifts to higher energy side (blue shift) with decreasing particle size. The existence of blue shift is evident, and it is confirmed that there is the quantum size confinement effect in the CdSe nanocrystals in this study. Tables 1 and 2 tabulate Z-scan results obtained from H-series and T-series, respectively. For the calculation, the proportional relationship between incident radiation and signal were examined in order to eliminate the influence of resonant effect near band edge. The dependence of Im v(3) on themean size in T-series and H-series looks different, but, from the intensity dependence measurements, it does not relate to the resonance effect since clear linear relationship was obtained. Since the data
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Fig. 3. Size distribution profiles of nanocrystal particles in H-series samples: (a) H2.9, (b) H3.7, (c) H4.3, (d) H4.8 and (e) H5.7.
Fig. 4. Size distribution profiles of nanocrystal particles in T-series samples: (a) T3.9, (b) T4.4, (c) T4.7 and (d) T5.1.
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Table 2 Third-order nonlinearity of T-series Sample (3)
12
esu) Re v (10 Im v(3) (1012 esu) Normalized jv(3)j (1012 esu)
T0
T3.9
T4.3
T4.7
T5.1
0.0336
5.09 0.422 3.7
10.5 6.42 2.7
13.6 4.82 2.0
21.2 3.59 1.8
thy that all real parts of third-order optical nonlinearity of all the CdSe embedded glass films are negative. In order to eliminate the influence of the concentration of the particles, the whole values were normalized with respect to the concentration of CdSe, and called normalized jv(3)j [11]. In order to obtain the normalized jv(3)j, the observed value was divided by the molar concentration of CdSe = 1mol%, which was determined on the basis of XPS line intensity of Cd and/or Se as in the previous work [11]. The largest normalized jv(3)j was 3.7 · 1012 esu.
4. Discussion As mentioned above, the quantum size effect of semiconductor nanocrystals is divided into two categories. One is the exciton confinement effect and the other is the electron–hole independent confinement effect. For semiconductors with small exciton Bohr radius relative to particle size, such as CuCl or CuBr, the blue shift (DE) is expressed as follows, p2 h2 ; ð7Þ 2MR2 where M is the translational mass and M is me + mh (me: effective mass of electron, mh: effective mass of hole), and R is particle radius. On the other hand, for semiconductors with large exciton Bohr radius compared to the particle size, such as CdSe, CdTe, GaAs or Si, the blue shift is caused by the electron–hole independent confinement effect and expressed as, DE ¼
Fig. 5. Bandgap from (ahm)2 plot as a function of hm obtained from absorption spectra for (a) H-series and (b) T-series.
Table 1 Third-order nonlinearity of H-series Sample (3)
12
Re v (10 esu) Im v(3) (1012 esu) Normalized jv(3)j (1012 esu)
H0
H3.7
H4.3
H4.8
0.0287
12.8 3.03 3.4
12.0 2.14 1.8
12.9 2.34 1.2
shown is the raw data, the concentration of the particles may influence on the Im v(3) value. The error of the experiments is below 5%. The third-order nonlinearity increases with decreasing particle size, and it is notewor-
DE ¼
p2 h2 ; 2lR2
ð8Þ
where l is the reduced mass and 1/l = 1/me + 1/mh. The experimental data for CdSe embedded silica glass films significantly deviated from the theoretical curve given by Eq. (8) as seen in Fig. 6. Thus, we introduce Kayanumas model [13] in which the Coulomb interaction between electrons and holes is taken into consideration, DE ¼
p2 h2 e2 1:786 0:248Ry ; 2 eR 2lR
ð9Þ
where e is dielectric constant and Ry is the effective Rydberg energy. According to Haken [14], the dielectric
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Fig. 6. The amount of the blue shift as a function of inverse square of the nanocrystal radius.
constant e in Eq. (9) depends on the particle size, and can be expressed by the following equation, 1 1 1 1 ¼ eðr Þ e1 e1 e0 expðr =q1 Þ þ expðr =q2 Þ 1 ; ð10Þ 2 where r* is the mean distance between the electron and hole, and r* = 0.69932R. The q1 and q2 are the polaron radii of electron and hole, respectively, and calculated to be 3.38 and 1.03 nm, respectively. The effective dielectric constant affecting the quantum size confinement effect is presumed to be that of matrix, and Haken potential is used for the analysis by introducing the polaron effect. For bulk CdSe (R = 1), e(r*) = e0 from Eq. (10) and should be 9.56. On the other hand, e(r*) = e1 when r* = 0. In this case there are two possibilities for e1 as those of CdSe and matrix glass. Fig. 6 shows the plot of theoretical lines of Eqs. (8) and (10) using e1 of matrix glass. One can see good agreement of experimental data with theoretical curves using Eq. (10). S-series in this figure corresponds to CdSe embedded in SiO2 glass matrix. Therefore, it is said that the matrix has significant influence of the quantum confinement effect. Fig. 7 shows the normalized jv(3)j as a function of the inverse cubic of the microcrystal radius. In each system, the jv(3)j depends on the microcrystal size, and increases as the decrease of mean microcrystal radius according to the r3 law as pointed out for S-series [11]. In addition, one can notice that there is the influence of matrix glass species on the third-order optical nonlinearity. The higher refractive index, in other words, higher dielectric constant is found to yield larger jv(3)j. In this discussion, data on S-series are not plotted in this and the following figures. This is because some jv(3)j data of S-series depend on the intensity of the incident radiation, or significant resonant effect is encountered.
Fig. 7. Third-order optical nonlinearity as a function of the inverse cubic of the nanocrystal radius.
So far, it has been believed that DEg or confinement effect is related to large jv(3)j. For the exciton confinement effect as in the case of CuCl or CuBr, it has been reported that there is a maximum in the relationship between the third-order nonlinearity and DEg [5], and the appearance such a maximum was interpreted in terms of the chapnge of oscillation strength of excitons with particle size. The argument on the jv(3)j versus DEg relation for the electron–hole independent confinement has still remained qualitative. In order to explore the relationship quantitatively the jv(3)j of the CdSe nanocrystals embedded in glass films is plotted against DEg in Fig. 8. We, now, notice linear relation for the electron–hole independent confinement effect in this figure. Furthermore, it should be noted that the jv(3)j versus DEg relation is no longer. dependent of the glass matrix species. Thus,
Fig. 8. The relationship between third-order nonlinearity and the amount of the blue shift.
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it is pointed out that deep quantum well built up in small particles surrounded by the matrix of high dielectric constant gives rise to strong interaction between electron and hole, and result in the large third-order optical nonlinearity for CdSe nanocrystals embedded in glass thin films.
Acknowledgement
5. Conclusion
References
The influence of the matrix glass on the third-order optical nonlinearity of CdSe nanocrystals was explored. CdSe nanocrystals were successfully embedded in the various kinds of glasses. The mean microcrystal size was controllable by the relative surface area ratio of CdSe chips, and the increase of the ratio increased the mean particle size. Blue shift in absorption edge was observed for whole present films, and it was evident for the occurrence of the quantum size confinement effect. The deviation of the amount of blue shift from the theoretical curve was interpreted by considering the Coulomb interaction between electrons and holes and the influence of the dielectric constant of matrix. The third-order optical nonlinearity depended on the dielectric constant of matrix glass as well as mean particle size, and linear relationship between third-order nonlinearity, and the blue shift was experimentally evidenced for the electron–hole independent confinement system.
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Authors are grateful for the financial support from Nano Glass Technology Project of New Glass Forum. Authors are also grateful for the assistance to summarize data by Mr M. Kimura, Mie Univesity.