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Nano-confined and copper-defect in wide-bandgap semiconductors
Optics Communications 284 (2011) 5199–5202
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Nano-confined and copper-defect in wide-bandgap semiconductors M. Idrish Miah ⁎ Department of Physics, University of Chittagong, Chittagong, Chittagong, 4331, Bangladesh Queensland Micro- and Nanotechnology Centre, Griffith University, Nathan, Brisbane, QLD 4111, Australia
a r t i c l e
i n f o
Article history: Received 28 March 2011 Received in revised form 5 July 2011 Accepted 5 July 2011 Available online 28 July 2011 Keywords: Wide-bandgap semiconductor Nano-confined effect Second harmonic generation
a b s t r a c t Copper-doped cadmium iodide nanocrystals were synthesized and grown for an investigation of the optical nonlinear effects via the measurements of the second harmonic generation (SHG) and nonlinear transmittance (NLT). The second-order optical susceptibilities in dependences of the size of the nanocrystals as well as of their copper contents were calculated. The observed size dependence demonstrates the nanosized quantum-confined effect, where the quantum confinement dominates the material's electronic and optical properties, with a clear increase in the SHG with decreasing the thickness of the nanocrystals. A dramatic change of the second-order optical response with increasing copper content of the nanocrystals was also observed. Optical absorption of the nanocrystals studied using NLT technique shows a decrease of the two-photon absorption with increasing thickness of the nanocrystals. The obtained results are discussed in details by exploring the photo-induced electron-phonon anharmonic mechanism for noncentrosymmetry of the impure material processes involving quantization. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Multiphoton spectroscopy and second harmonic generation (SHG) are the two most important tools to investigate the higher-order optical nonlinear processes, particularly, in semiconductors [1,2]. Because the SHG (as one of the probes of the second-order optical nonlinear effects, particularly the surface effects of a material) is prevented by symmetry in a centrosymmetric material, one can expect SHG only in noncentrosymmetric materials. However, there is a possibility to enhance the SHG, e.g. by reducing the size of the crystals to the nanometer scale or by lowering the crystal temperature, or by the insertion of suitable impurities into the crystals with an appropriate amount [1]. The nanometer-sized crystals, or nanocrystals in short, take into account the nano-sized quantum-confined effect or nano-confined effect, or nano-effect (quantum confinement dominates the material's electronic and optical properties), where kspace bulk-like dispersion disappears and discrete excitonic-like nanolevels occur within the forbidden energy gap of the material processes [2]. Layered semiconductor cadmium iodide (CdI2) single crystals are indirect bandgap semiconductors having wide-bandgap (Eg ≃ 3.7 eV) 4 and space group C6v , with highly anisotropic chemical bonds. The band structure calculations of the CdI2 crystals have also shown a
large anisotropy [3–5] in the space charge density distribution causing high anisotropy in the corresponding optical spectra. The anisotropic behaviour of the CdI2 crystals favours the local noncentrosymmetry. Recent experimental works performed in undoped CdI2 single crystals using multiphoton spectroscopy have shown that CdI2 processes higher-order optical nonlinearities [6–10]. However, the first SHG investigation in copper-doped CdI2 crystals was reported by Kityk et al. [11]. In their investigation, they have studied magnetic field induced ferroelectricity and shown that the introduction of Cudoping in CdI2 makes the crystal noncentrosymmetric. Subsequent investigations for the systems were also available in the literature [12–15]. In this investigation, we study the size and copper-doping dependences of second-order optical nonlinear effects in Cu-doped CdI2 nanocrystals. An enhancement of SHG and optical absorption with decreasing thickness of the nanocrystals has been observed. The copper-doping density dependence has showed a fashionable character. 2. Experimental details Samples were taken from nanocrystals of Cu-doped CdI2 (i.e. CdI2– Cu), synthesized from the mixture of cadmium iodide and cuprous oxide (CuI), CdI2 þ CuI ≡ CdI2 Cu;
⁎ Department of Physics, University of Chittagong, Chittagong-4331, Bangladesh. E-mail address: m.miah@griffith.edu.au. 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.07.004
ð1Þ
using standard Bridgman method. Structures were monitored using an X-ray diffractometer and the SEM (scanning electron microscopy)
M.I. Miah / Optics Communications 284 (2011) 5199–5202
and the homogeneity was controlled using a polarimeter. The nanocrystal sample thickness was controlled using a radio-frequency interferometer. The investigation was performed at 4.2 K by mounting the samples in a temperature-regulated cryostat. The SHG was measured using a method similar to that employed in Ref. [11]. We used a Nd:YAG laser, as a fundamental laser for the SHG, which generates picosecond pulses (average power 15 MW) with a repetition rate of 80 mHz. The output SHG (λ = 530 nm) and fundamental (λ = 1060 nm) signals were spectrally separated by a grating monochromator with a spectral resolution of ~5 nm mm − 1. Detection of the doubled-frequency (in the green spectral region) output SHG signal was performed by a photomultiplier (with time resolution about 0.5 ns), with an electronic boxcar integrator (EBI) for the registration of the output. During evaluation of the time-delayed nonlinear optical response, we measured the light intensities at the fundamental (ω) and doubled-frequencies (2ω) with time steps of ~ 50 fs using the EBI in the time-synchronized pump-probe conditions.
6 5
SHG (a. u.)
5200
4 3 2 1 0 0
100
200
300
400
PA (kW
500
600
700
800
mm-1)
Fig. 2. Dependence of the second harmonic generation on the pump power density for a 3.5-nm thick and 0.6% copper-doped nanocrystal. The insert shows a SEM image of the nanocrystals.
3. Results and discussion strong localized electron–phonon states due to the nanosize-confined effect.
3.1. SHG signals Figs. 1 and 2 shows the SHG signals as a function of pump power density (PA) for two different thicknesses of the nanocrystals. The inserts in Figs. 1 and 2 show the SEM images of the nanocrystals with thicknesses 0.8 and 3.5 nm. As can be seen, the SHG increases with decreasing the thickness (L) of the nanocrystals. The SHG dependence shows a beginning of slight preserve and is increased before reaching a value a little higher than background signal for the thick nanolayers. However, a significant enhancement in the SHG occurs for the nanocrystals with thickness lower than 3.5 nm. The maximum SHG signal as a function of the thickness of the nanocrystals is shown in Fig. 3. As seen, the maximum SHG is obtained for the thinnest nanocrystals. However, lowering the thickness of the nanocrystal from 8 nm shows another feature in which SHG has a weak secondary maximum near 600 kW mm − 1. The secondary maximum seems to be shifted slightly in the higher pump power density with decreasing thickness of the nanocrystals. The qualitative and quantitative changes that occurred for the thinner nanocrystals correspond to the manifestation of the quantum-confined excitonic levels perpendicularly to the layers. The relatively large relaxation time observed in the SHG pulses demonstrates the principal role of long-lived electron– phonon states in the observed effects, as explained within a model of photo-induced electron–phonon anharmonicity [11,15,16], where the relaxation time for the thin nanolayers should be larger than for the
3.2. Optical susceptibilities Nonlinear optical effects are generally described by the optical response of a material medium to an effective electric field E. In the dipole approximation, the polarization of the light field interacting with a medium under high intensity optical illumination can phenomenologically be expressed as [17] → → → → ð1Þ ð2 Þ ð3Þ P r ; t = χij Ej r ; t + χijk Ej Ek r ; t + χijkl Ej Ek El r ; t + :::::::; ð2Þ whereχij(1) is the susceptibility tensor of the first-order and rank 2. The term χij(1) is responsible for linear optical phenomena such as (2) (3) reflection and refraction of light. The terms χijk and χijkl are responsible for nonlinear optical phenomena and correspond to the second- and third-order optical effects respectively. Ek and El are electric field components of the electromagnetic wave. The generation of optically induced doubled frequency (2ω) second harmonic light is described by the second term in Eq. (2). The second harmonic polarization of the medium as a function of the frequency (ω) of the fundamental light is given by ð2Þ
Pi ð2ωÞ = χijk Ej ðωÞEk ðωÞ;
ð3Þ
8 8
6
4
SHGmax (a. u.)
SHG (a. u.)
6
2
4
2
0 0
100
200
300
400
500
600
700
800
PA (kW mm-1) Fig. 1. Dependence of the second harmonic generation on the pump power density for a 0.8-nm thick and 0.6% copper-doped nanocrystal. The insert is a SEM image of the nanocrystals.
0 0
3
6
9
12
L (nm) Fig. 3. Size dependence of the second harmonic generation in nanocrystals.
M.I. Miah / Optics Communications 284 (2011) 5199–5202
ð2Þ 2 ω2 L2 χijk I2 ðω; t−Δt Þ sin LΔkðt Þ= 22 ; 3= 2 2 LΔkðt Þ=2 R nð2ωÞn2 ðωÞ π∈
3= 2
Ið2ω; t Þ =
2μ0
ð4Þ
0
60
56
α2 (cm GW-1)
(2) The third rank and second-order tensor χijk in Eq. (3) consists of 27 elements. However, as the electric field indices j and k can be interchanged for a single beam experiment, the number of independent elements is reduced to 18. After some traditional algebra, the following expression for the SHG intensity can be obtained:
5201
52
48
where L is the length of the nonlinear medium, R is the radius of the pumping beam which possesses a Gaussian-like form, μ0 and ∈0 are the static (low-frequency) values of the magnetic permeability and the electric permittivity respectively, n(ω) and n(2ω) are the refractive indexes for the pumping and the SHG doubled frequency, respectively, and Δk = k(2ω) − 2k(ω) is the phase matching wave vector factor defined by optically induced birefringence. For a (2) centrosymmetric material process, the tensor componentχijk is effectively zero because of the symmetry reason, and thus the SHG is forbidden in a centrosymmetric process. Fig. 4 shows the second-order tensor component, where the (2) susceptibilityχijk , evaluated from the SHG intensities using the relation given in Eq. (4), is plotted as a function of the thickness of the nanocrystals and copper content (CC). One can see that with decreasing thickness of the crystals (or increasing copper content up to 0.6%) the value of the tensor component for the SHG significantly increases. As shown earlier [11], the insertion of the copper impurities favours a stronger local photo-induced anharmonic electron–phonon interaction through the alignment of the local anharmonic dipole moments by the pumping light. As a particular role of the local electron–phonon anharmonicity is described by third-order-rank tensors in disordered systems [12], the SHG is very similar to that introduced for the third-order nonlinear optical susceptibility, which has been confirmed by observing the relatively large third-order susceptibility of undoped CdI2 single crystals [7–10]. The local disordering of the copper aggregators plays additional rule in the size effect of the nanocrystals. (2) For CC = 0.6%, the value of χijk achieves its maximum for any nanocrystals (Fig. 4). (2) Decrease of χijk with a further increase of CC might be caused by the aggregation of the copper impurities that is typical of such kinds of layered crystals [18]. The creation of the copper aggregators favours a reduction in the active electron–phonon centres, effectively contributing to the charge density noncentrosymmetry due to copperinduced local electron–phonon anharmonic interaction, as well as leads to the occurrence of metallic clusters [16], and consequently, suppresses the effect at higher CC through the limitation of the enhancement of the local hyperpolarizability for the copper aggrega-
44 0
3
6
9
12
L (nm) Fig. 5. Optical absorption as a function of the nanocrystal thickness.
tors as well as the corresponding nonlinear dielectric susceptibility. (2) However, χijk for a nanocrystal with high CC was found to be almost equal to that for the undoped crystals. Interestingly, the dependence (Fig. 4) shows a parabolic fashionable change of the second-order optical response with increasing copper content of the nanocrystals.
3.3. Optical absorption The nonlinear transmittance technique gives directly the twophoton absorption (TPA) coefficient α2 of the sample medium by measuring the transmissivity. According to the basic theoretical consideration, the TPA induced decrease of transmissivity can be expressed [2] as I = I0 = ð1−α2 I0 LÞ;
ð5Þ
where I0 and I are incident and transmitted intensities respectively. In the derivation of Eq. (5) it is assumed that the linear absorption of the sample can be neglected and the beam has a nearly uniform transverse intensity distribution within the sample medium. From Eq. (5) one can see that the α2 value can be determined by measuring the transmitted intensity versus the incident intensity for a sample with a given L value. The calculated results are plotted in Fig. 5, where α2 is plotted as a function of L. As can be seen, the nanocrystal thickness dependence of α2 shows a decrease in its magnitude and hence the optical absorption with increasing L. The determination of α2 for thick CdI2 crystals at 80 K has been done in an earlier investigation [7]. The present result is in good agreement with that value and is consistence with that for other layered semiconductors [6].
0.7
χijk (pm/V)
χijk (pm/V)
0.7
0.6
0.6% 0.3% 0.05%
0.6
4. Conclusions
0.5 0.4 0
2
0.5
4
6
8
10
L (nm)
0.4 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
CC (%) Fig. 4. Second-order susceptibility as a function of the thickness of the nanocrystals and copper content (L = 0.8 nm).
Measurements of the SHG in copper-doped cadmium iodide nanocrystals were performed and the second-order optical susceptibilities in dependences of the size of the nanocrystals and of their copper contents were estimated. The observed size dependence demonstrated the nanosized quantum-confined effect with a clear increase in the SHG with decreasing the thickness of the nanocrystals. A fashionable parabolic change of the second-order optical response with increasing copper content of the nanocrystals was also observed. The optical absorption showed a decrease of the TPA coefficient with increasing thickness of the nanocrystals. The obtained results however highlight that CdI2–Cu nanocrystals are promising materials for applications in optoelectronic nanodevices and for the creation of the noncentrosymmetric processes.
5202
M.I. Miah / Optics Communications 284 (2011) 5199–5202
References [1] W.E. Born (Ed.), Ultrashort Processes in Condensed Matter, Plenum Press, New York, 1993. [2] H. Haug (Ed.), Optical Nonlinearities and Instabilities in Semiconductors, Academic press, New York, 1988. [3] J. Bordas, J. Robertson, A. Jakobsson, J. Phys. C 11 (1978) 2607. [4] J. Robertson, J. Phys. C 12 (1979) 4753. [5] Ya O. Dorgii, I.V. Kityk, Yu M. Aleksandrov, V.N. Kolobanov, V.N. Machov, V.V. Michailin, J. Appl. Spectrosc. 43 (1985) 1168. [6] I.M. Catalano, A. Cingolani, R. Ferrara, M. Lepore, Helv. Phys. Acta 58 (1985) 329. [7] M. Idrish Miah, Opt. Mater. 18 (2001) 231. [8] M. Idrish Miah, Opt. Mater. 25 (2004) 353. [9] M. Idrish Miah, Phys. Lett. A 374 (2009) 75.
[10] M. Idrish Miah, Mater. Chem. Phys. 119 (2010) 402. [11] I.V. Kityk, S.A. Pyroha, T. Mydlarz, J. Kasperczyk, M. Czerwinski, Ferroelectrics 205 (1998) 107. [12] V. Bondar, Mater. Sci. Eng. B 70 (2000) 258. [13] M. Idrish Miah, Higher-order optical nonlinearities in CdI2 and CdI2-Cu crystals, The First Conference on Advances in Optical Materials, Tucson, Arizona, USA, 2005 October 12–15. [14] D. Herest, F. Voolless, Opt. Lasers Eng. 41 (2004) 85. [15] M. Idrish Miah, J. Kasperczyk, Appl. Phys. Lett. 94 (2009) 053117. [16] S.A. Pyroha, S. Metry, I.D. Olekseyuk, I.V. Kityk, Funct. Mater. 7 (2000) 209. [17] C.C. Devis, Laser and electro-optics, fundamentals and engineering, Cambridge University Press, New York, 1985. [18] J.V. McCanny, R.H. Williams, R.B. Murray, P.C. Kemeny, J. Phys. C: Solid State Phys. 10 (1977) 4255.
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Nano-confined and copper-defect in wide-bandgap semiconductors M. Idrish Miah ⁎ Department of Physics, University of Chittagong, Chittagong, Chittagong, 4331, Bangladesh Queensland Micro- and Nanotechnology Centre, Griffith University, Nathan, Brisbane, QLD 4111, Australia
a r t i c l e
i n f o
Article history: Received 28 March 2011 Received in revised form 5 July 2011 Accepted 5 July 2011 Available online 28 July 2011 Keywords: Wide-bandgap semiconductor Nano-confined effect Second harmonic generation
a b s t r a c t Copper-doped cadmium iodide nanocrystals were synthesized and grown for an investigation of the optical nonlinear effects via the measurements of the second harmonic generation (SHG) and nonlinear transmittance (NLT). The second-order optical susceptibilities in dependences of the size of the nanocrystals as well as of their copper contents were calculated. The observed size dependence demonstrates the nanosized quantum-confined effect, where the quantum confinement dominates the material's electronic and optical properties, with a clear increase in the SHG with decreasing the thickness of the nanocrystals. A dramatic change of the second-order optical response with increasing copper content of the nanocrystals was also observed. Optical absorption of the nanocrystals studied using NLT technique shows a decrease of the two-photon absorption with increasing thickness of the nanocrystals. The obtained results are discussed in details by exploring the photo-induced electron-phonon anharmonic mechanism for noncentrosymmetry of the impure material processes involving quantization. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Multiphoton spectroscopy and second harmonic generation (SHG) are the two most important tools to investigate the higher-order optical nonlinear processes, particularly, in semiconductors [1,2]. Because the SHG (as one of the probes of the second-order optical nonlinear effects, particularly the surface effects of a material) is prevented by symmetry in a centrosymmetric material, one can expect SHG only in noncentrosymmetric materials. However, there is a possibility to enhance the SHG, e.g. by reducing the size of the crystals to the nanometer scale or by lowering the crystal temperature, or by the insertion of suitable impurities into the crystals with an appropriate amount [1]. The nanometer-sized crystals, or nanocrystals in short, take into account the nano-sized quantum-confined effect or nano-confined effect, or nano-effect (quantum confinement dominates the material's electronic and optical properties), where kspace bulk-like dispersion disappears and discrete excitonic-like nanolevels occur within the forbidden energy gap of the material processes [2]. Layered semiconductor cadmium iodide (CdI2) single crystals are indirect bandgap semiconductors having wide-bandgap (Eg ≃ 3.7 eV) 4 and space group C6v , with highly anisotropic chemical bonds. The band structure calculations of the CdI2 crystals have also shown a
large anisotropy [3–5] in the space charge density distribution causing high anisotropy in the corresponding optical spectra. The anisotropic behaviour of the CdI2 crystals favours the local noncentrosymmetry. Recent experimental works performed in undoped CdI2 single crystals using multiphoton spectroscopy have shown that CdI2 processes higher-order optical nonlinearities [6–10]. However, the first SHG investigation in copper-doped CdI2 crystals was reported by Kityk et al. [11]. In their investigation, they have studied magnetic field induced ferroelectricity and shown that the introduction of Cudoping in CdI2 makes the crystal noncentrosymmetric. Subsequent investigations for the systems were also available in the literature [12–15]. In this investigation, we study the size and copper-doping dependences of second-order optical nonlinear effects in Cu-doped CdI2 nanocrystals. An enhancement of SHG and optical absorption with decreasing thickness of the nanocrystals has been observed. The copper-doping density dependence has showed a fashionable character. 2. Experimental details Samples were taken from nanocrystals of Cu-doped CdI2 (i.e. CdI2– Cu), synthesized from the mixture of cadmium iodide and cuprous oxide (CuI), CdI2 þ CuI ≡ CdI2 Cu;
⁎ Department of Physics, University of Chittagong, Chittagong-4331, Bangladesh. E-mail address: m.miah@griffith.edu.au. 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.07.004
ð1Þ
using standard Bridgman method. Structures were monitored using an X-ray diffractometer and the SEM (scanning electron microscopy)
M.I. Miah / Optics Communications 284 (2011) 5199–5202
and the homogeneity was controlled using a polarimeter. The nanocrystal sample thickness was controlled using a radio-frequency interferometer. The investigation was performed at 4.2 K by mounting the samples in a temperature-regulated cryostat. The SHG was measured using a method similar to that employed in Ref. [11]. We used a Nd:YAG laser, as a fundamental laser for the SHG, which generates picosecond pulses (average power 15 MW) with a repetition rate of 80 mHz. The output SHG (λ = 530 nm) and fundamental (λ = 1060 nm) signals were spectrally separated by a grating monochromator with a spectral resolution of ~5 nm mm − 1. Detection of the doubled-frequency (in the green spectral region) output SHG signal was performed by a photomultiplier (with time resolution about 0.5 ns), with an electronic boxcar integrator (EBI) for the registration of the output. During evaluation of the time-delayed nonlinear optical response, we measured the light intensities at the fundamental (ω) and doubled-frequencies (2ω) with time steps of ~ 50 fs using the EBI in the time-synchronized pump-probe conditions.
6 5
SHG (a. u.)
5200
4 3 2 1 0 0
100
200
300
400
PA (kW
500
600
700
800
mm-1)
Fig. 2. Dependence of the second harmonic generation on the pump power density for a 3.5-nm thick and 0.6% copper-doped nanocrystal. The insert shows a SEM image of the nanocrystals.
3. Results and discussion strong localized electron–phonon states due to the nanosize-confined effect.
3.1. SHG signals Figs. 1 and 2 shows the SHG signals as a function of pump power density (PA) for two different thicknesses of the nanocrystals. The inserts in Figs. 1 and 2 show the SEM images of the nanocrystals with thicknesses 0.8 and 3.5 nm. As can be seen, the SHG increases with decreasing the thickness (L) of the nanocrystals. The SHG dependence shows a beginning of slight preserve and is increased before reaching a value a little higher than background signal for the thick nanolayers. However, a significant enhancement in the SHG occurs for the nanocrystals with thickness lower than 3.5 nm. The maximum SHG signal as a function of the thickness of the nanocrystals is shown in Fig. 3. As seen, the maximum SHG is obtained for the thinnest nanocrystals. However, lowering the thickness of the nanocrystal from 8 nm shows another feature in which SHG has a weak secondary maximum near 600 kW mm − 1. The secondary maximum seems to be shifted slightly in the higher pump power density with decreasing thickness of the nanocrystals. The qualitative and quantitative changes that occurred for the thinner nanocrystals correspond to the manifestation of the quantum-confined excitonic levels perpendicularly to the layers. The relatively large relaxation time observed in the SHG pulses demonstrates the principal role of long-lived electron– phonon states in the observed effects, as explained within a model of photo-induced electron–phonon anharmonicity [11,15,16], where the relaxation time for the thin nanolayers should be larger than for the
3.2. Optical susceptibilities Nonlinear optical effects are generally described by the optical response of a material medium to an effective electric field E. In the dipole approximation, the polarization of the light field interacting with a medium under high intensity optical illumination can phenomenologically be expressed as [17] → → → → ð1Þ ð2 Þ ð3Þ P r ; t = χij Ej r ; t + χijk Ej Ek r ; t + χijkl Ej Ek El r ; t + :::::::; ð2Þ whereχij(1) is the susceptibility tensor of the first-order and rank 2. The term χij(1) is responsible for linear optical phenomena such as (2) (3) reflection and refraction of light. The terms χijk and χijkl are responsible for nonlinear optical phenomena and correspond to the second- and third-order optical effects respectively. Ek and El are electric field components of the electromagnetic wave. The generation of optically induced doubled frequency (2ω) second harmonic light is described by the second term in Eq. (2). The second harmonic polarization of the medium as a function of the frequency (ω) of the fundamental light is given by ð2Þ
Pi ð2ωÞ = χijk Ej ðωÞEk ðωÞ;
ð3Þ
8 8
6
4
SHGmax (a. u.)
SHG (a. u.)
6
2
4
2
0 0
100
200
300
400
500
600
700
800
PA (kW mm-1) Fig. 1. Dependence of the second harmonic generation on the pump power density for a 0.8-nm thick and 0.6% copper-doped nanocrystal. The insert is a SEM image of the nanocrystals.
0 0
3
6
9
12
L (nm) Fig. 3. Size dependence of the second harmonic generation in nanocrystals.
M.I. Miah / Optics Communications 284 (2011) 5199–5202
ð2Þ 2 ω2 L2 χijk I2 ðω; t−Δt Þ sin LΔkðt Þ= 22 ; 3= 2 2 LΔkðt Þ=2 R nð2ωÞn2 ðωÞ π∈
3= 2
Ið2ω; t Þ =
2μ0
ð4Þ
0
60
56
α2 (cm GW-1)
(2) The third rank and second-order tensor χijk in Eq. (3) consists of 27 elements. However, as the electric field indices j and k can be interchanged for a single beam experiment, the number of independent elements is reduced to 18. After some traditional algebra, the following expression for the SHG intensity can be obtained:
5201
52
48
where L is the length of the nonlinear medium, R is the radius of the pumping beam which possesses a Gaussian-like form, μ0 and ∈0 are the static (low-frequency) values of the magnetic permeability and the electric permittivity respectively, n(ω) and n(2ω) are the refractive indexes for the pumping and the SHG doubled frequency, respectively, and Δk = k(2ω) − 2k(ω) is the phase matching wave vector factor defined by optically induced birefringence. For a (2) centrosymmetric material process, the tensor componentχijk is effectively zero because of the symmetry reason, and thus the SHG is forbidden in a centrosymmetric process. Fig. 4 shows the second-order tensor component, where the (2) susceptibilityχijk , evaluated from the SHG intensities using the relation given in Eq. (4), is plotted as a function of the thickness of the nanocrystals and copper content (CC). One can see that with decreasing thickness of the crystals (or increasing copper content up to 0.6%) the value of the tensor component for the SHG significantly increases. As shown earlier [11], the insertion of the copper impurities favours a stronger local photo-induced anharmonic electron–phonon interaction through the alignment of the local anharmonic dipole moments by the pumping light. As a particular role of the local electron–phonon anharmonicity is described by third-order-rank tensors in disordered systems [12], the SHG is very similar to that introduced for the third-order nonlinear optical susceptibility, which has been confirmed by observing the relatively large third-order susceptibility of undoped CdI2 single crystals [7–10]. The local disordering of the copper aggregators plays additional rule in the size effect of the nanocrystals. (2) For CC = 0.6%, the value of χijk achieves its maximum for any nanocrystals (Fig. 4). (2) Decrease of χijk with a further increase of CC might be caused by the aggregation of the copper impurities that is typical of such kinds of layered crystals [18]. The creation of the copper aggregators favours a reduction in the active electron–phonon centres, effectively contributing to the charge density noncentrosymmetry due to copperinduced local electron–phonon anharmonic interaction, as well as leads to the occurrence of metallic clusters [16], and consequently, suppresses the effect at higher CC through the limitation of the enhancement of the local hyperpolarizability for the copper aggrega-
44 0
3
6
9
12
L (nm) Fig. 5. Optical absorption as a function of the nanocrystal thickness.
tors as well as the corresponding nonlinear dielectric susceptibility. (2) However, χijk for a nanocrystal with high CC was found to be almost equal to that for the undoped crystals. Interestingly, the dependence (Fig. 4) shows a parabolic fashionable change of the second-order optical response with increasing copper content of the nanocrystals.
3.3. Optical absorption The nonlinear transmittance technique gives directly the twophoton absorption (TPA) coefficient α2 of the sample medium by measuring the transmissivity. According to the basic theoretical consideration, the TPA induced decrease of transmissivity can be expressed [2] as I = I0 = ð1−α2 I0 LÞ;
ð5Þ
where I0 and I are incident and transmitted intensities respectively. In the derivation of Eq. (5) it is assumed that the linear absorption of the sample can be neglected and the beam has a nearly uniform transverse intensity distribution within the sample medium. From Eq. (5) one can see that the α2 value can be determined by measuring the transmitted intensity versus the incident intensity for a sample with a given L value. The calculated results are plotted in Fig. 5, where α2 is plotted as a function of L. As can be seen, the nanocrystal thickness dependence of α2 shows a decrease in its magnitude and hence the optical absorption with increasing L. The determination of α2 for thick CdI2 crystals at 80 K has been done in an earlier investigation [7]. The present result is in good agreement with that value and is consistence with that for other layered semiconductors [6].
0.7
χijk (pm/V)
χijk (pm/V)
0.7
0.6
0.6% 0.3% 0.05%
0.6
4. Conclusions
0.5 0.4 0
2
0.5
4
6
8
10
L (nm)
0.4 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
CC (%) Fig. 4. Second-order susceptibility as a function of the thickness of the nanocrystals and copper content (L = 0.8 nm).
Measurements of the SHG in copper-doped cadmium iodide nanocrystals were performed and the second-order optical susceptibilities in dependences of the size of the nanocrystals and of their copper contents were estimated. The observed size dependence demonstrated the nanosized quantum-confined effect with a clear increase in the SHG with decreasing the thickness of the nanocrystals. A fashionable parabolic change of the second-order optical response with increasing copper content of the nanocrystals was also observed. The optical absorption showed a decrease of the TPA coefficient with increasing thickness of the nanocrystals. The obtained results however highlight that CdI2–Cu nanocrystals are promising materials for applications in optoelectronic nanodevices and for the creation of the noncentrosymmetric processes.
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References [1] W.E. Born (Ed.), Ultrashort Processes in Condensed Matter, Plenum Press, New York, 1993. [2] H. Haug (Ed.), Optical Nonlinearities and Instabilities in Semiconductors, Academic press, New York, 1988. [3] J. Bordas, J. Robertson, A. Jakobsson, J. Phys. C 11 (1978) 2607. [4] J. Robertson, J. Phys. C 12 (1979) 4753. [5] Ya O. Dorgii, I.V. Kityk, Yu M. Aleksandrov, V.N. Kolobanov, V.N. Machov, V.V. Michailin, J. Appl. Spectrosc. 43 (1985) 1168. [6] I.M. Catalano, A. Cingolani, R. Ferrara, M. Lepore, Helv. Phys. Acta 58 (1985) 329. [7] M. Idrish Miah, Opt. Mater. 18 (2001) 231. [8] M. Idrish Miah, Opt. Mater. 25 (2004) 353. [9] M. Idrish Miah, Phys. Lett. A 374 (2009) 75.
[10] M. Idrish Miah, Mater. Chem. Phys. 119 (2010) 402. [11] I.V. Kityk, S.A. Pyroha, T. Mydlarz, J. Kasperczyk, M. Czerwinski, Ferroelectrics 205 (1998) 107. [12] V. Bondar, Mater. Sci. Eng. B 70 (2000) 258. [13] M. Idrish Miah, Higher-order optical nonlinearities in CdI2 and CdI2-Cu crystals, The First Conference on Advances in Optical Materials, Tucson, Arizona, USA, 2005 October 12–15. [14] D. Herest, F. Voolless, Opt. Lasers Eng. 41 (2004) 85. [15] M. Idrish Miah, J. Kasperczyk, Appl. Phys. Lett. 94 (2009) 053117. [16] S.A. Pyroha, S. Metry, I.D. Olekseyuk, I.V. Kityk, Funct. Mater. 7 (2000) 209. [17] C.C. Devis, Laser and electro-optics, fundamentals and engineering, Cambridge University Press, New York, 1985. [18] J.V. McCanny, R.H. Williams, R.B. Murray, P.C. Kemeny, J. Phys. C: Solid State Phys. 10 (1977) 4255.