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Growth rate anisotropy and absorption studies on β-BaB2O4 single crystals grown by the top-seeded solution growth technique
Optical Materials 29 (2007) 801–805 www.elsevier.com/locate/optmat
Growth rate anisotropy and absorption studies on b-BaB2O4 single crystals grown by the top-seeded solution growth technique Rajeev Bhatt a, S. Ganesamoorthy
a,*
, Indranil Bhaumik a, A.K. Karnal a, V.K. Wadhawan
b
a
b
Crystal Growth Laboratory, Laser Materials Development and Devices Division, Raja Ramanna Centre for Advanced Technology, Indore 452 013, India Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India Received 5 January 2005; accepted 10 January 2006 Available online 10 February 2006
Abstract Beta barium borate (b-BaB2O4; BBO) single crystals have been grown from Na2O flux by the TSSG technique and the observed growth rate anisotropy is reported. The symmetrical conoscopic interference pattern on the c-cut plate confirmed strain-free and optical homogeneity of the crystals. The observed growth habits of as-grown crystals are explained using crystal growth theories. The relative growth rate along different crystallographic directions of BBO can be described by R[100] = R[010] > R[001]. The absorption measurements show a nearly 9 nm shift in fundamental absorption edges in X and Z cut samples. Band gap energies measured were 6.45 and 6.2 eV along the X and Z directions, respectively. The absorption spectra near the fundamental absorption edges (AE) follow Urbach’s rule. Ó 2006 Elsevier B.V. All rights reserved. PACS: 42.70.MP; 78.20.e; 81.10.Dn Keywords: Growth from solution; Single crystal; Top-seeded solution growth; Borate; Non-linear optical material
1. Introduction Low temperature phase b-BaB2O4 (BBO) is a technologically important non-linear optical (NLO) crystal, especially for deep UV applications because of its high NLO coefficient, high damage threshold and relatively low hygroscopic behaviour [1–6]. The growth of BBO crystals from the direct melt (Czochralski method) has been reported by employing a steep temperature gradient (200 °C/mm) at the crystal–melt interface [7,8]; however, obtaining large size crystals is still a challenging task. Hence it is preferable to grow them below the a–b transition temperature by employing the top-seeded solution growth technique (TSSG). Na2O is reported to be one of the best solvents in terms of quality and size of the grown
crystals [9]. However, incorporation of Na+ ions of the order of 100–300 ppm is also reported [10]. Unlike other borate family crystals, growth habits of BBO are quite different due to the difference in the growth conditions. For example, LBO and CLBO, require nearly a zero temperature gradient, BBO requires a high thermal gradient as well as slow pulling. Therefore, the TSSG growth of BBO can be described as a modified Czochralski growth, and hence as-grown crystals do not show any natural growth morphologies. In the present investigation, optical quality BBO crystals have been grown and their morphologies or habit shapes along different directions have been compared and analyzed. The as-grown crystals were characterized by optical absorption measurements. 2. Experimental
*
Corresponding author. Tel.: +91 731 2488657; fax: +91 731 2488650. E-mail address: [email protected] (S. Ganesamoorthy).
0925-3467/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2006.01.003
The composition used in the present study was 80 mol% BaB2O4 and 20 mol% Na2O [11]. The charge was synthe-
802
R. Bhatt et al. / Optical Materials 29 (2007) 801–805
sized from high purity BaCO3, Na2CO3 and B2O3 chemicals (99.9%). The chemicals were dried at 200 °C for 2 h in an oven before weighing, then filled into a polystyrene bottle and mixed on a ball miller for 5–10 h without balls. The mixed powder was then put into a platinum crucible (6 cm diameter and 5 cm height) and fired at the rate of 150 °C/h first to 350 °C for 5–8 h and then 725 °C for 15–20 h, followed by direct melting at 1050 °C. Borate melts or solutions are well known for their high viscosity and glass forming nature because of the existence of BO3 3 rings or –O–B–O– chains [5]. Therefore, high temperature gradient is required across the melt in order to grow good quality crystals. A high gradient two-zone furnace was designed and developed in-house to achieve the desired thermal profile. The maximum axial and radial temperature gradient achieved in this configuration was of the order of 10–12 °C/cm and 3–5 °C/cm. The melt was homogenized for 20–24 h at 20–30 °C above the saturation temperature. The saturation temperature was determined by repeated seeding, with an accuracy of ± 0.5 °C [12]. Crystals were grown along Z and X orientations. Rotation rates used were around 30–25 rpm during initial seeding, which was finally reduced to 4 rpm systematically. A gradually increasing cooling rate from 0.7 to 2.5 °C/day in steps of 0.01 °C/1–2 day was employed, whereas the pulling rate was optimised to 0.3–0.5 mm/ day. Some growth runs were performed without applying pulling of the crystal as well. Growth runs were performed in stable growth conditions under a closed system. The grown crystals were subjected to an X-ray diffraction study for the identification of phase and lattice parameter calculation. Transmission and absorption studies were performed on Z and X cut samples with unpolarised light at room temperature using a Shimadzu UV 3101PC spectrophotometer.
tures developed on the crystal boule were in agreement with that in the literature [13]. To ascertain the quality of the grown crystals, a conoscopic study was performed on a c-cut plate using an Olympus polarizing microscope in the transmission mode. The symmetrical fringe patterns shown in Fig. 2 reveal homogeneity and absence of strain in the crystal. Crystals grown under a uniform cooling rate of 0.04 °C/h and an axial temperature gradient of 12 °C/cm resulted in high quality transparent lens shape crystals with highly convex interface. But on application of pulling, there is a tendency of detachment of the growing crystal at the periphery. This limits the thickness in the grown crystal. Therefore, to increase the thickness the cooling rate was increased gradually in steps of 0.01 °C per 30–50 h, starting from 0.02 to 0.12 °C/h. The interface shape of the grown crystals was observed to be less convex in the latter case. Another crucial problem in the growth of thicker crystals is the occurrence of interface instability and solution entrapment into the crystal, resulting in the unwanted cellular growth at the bottom of the grown crystal (Fig. 3). However, growth along X and Y orientations is more prone to this instability and occurs only at the latter stage of the growth i.e., after a cooling of 25–35 °C. At this stage of growth, the solution viscosity increases so significantly that
3. Results and discussion Inclusion-free, highly transparent BBO single crystals have been grown along different orientations. Fig. 1 shows the photograph of a BBO crystal boule. The growth fea-
Fig. 2. Conoscopic pattern of a c-cut BBO crystal plate.
Fig. 1. The as-grown BBO crystal boule along the [0 0 1] direction.
Fig. 3. Crystal boule grown along the X direction, showing an elliptical cross-section and cellular growth.
R. Bhatt et al. / Optical Materials 29 (2007) 801–805
it disturbs the mass transport around the growing crystal. As a result, the diffusion boundary layer around the growing crystal is in non-equilibrium with respect to the actual equilibrium concentration. In other words, the equilibrium concentrations of the coexisting solution and crystal deviate from actual compositions, resulting in interface instability. 4. Growth rate anisotropy Different growth shapes (morphologies) have been observed experimentally in crystal boules grown along the X and Z directions. The Z oriented grown crystal developed a nearly circular cross-section, whereas crystals grown along other directions developed an oval cross-section (Fig. 3). The schematic of the observed morphology corresponding to different growth directions is shown in Fig. 4. Zhong et al. [14] have explained the crystal growth habits on the basis of orientation of structural units (B2O3)3 rings in the crystal. We are applying the growth rate theories to explain the observed results. According to crystal growth theories, the growth habits of the crystals are determined primarily by the anisotropy of the relative growth rates along different directions [15]. The Hartman–Perdoch theory [16] states that the relative growth rate of face (Rhkl) is determined by the magnitude of the attachment energy of att the growing face (h k l) as Rhkl Eatt hkl , where E hkl is the energy released per structural unit attached to the growing crystal surface at an appropriate crystallographic position from infinity. As per Donnay and Harker’s [17] assumption, the attachment energy is inversely proportional to the inter-planer spacing and is given by Rhkl Eatt hkl 1=d hkl . The growth rates along the crystallographic directions in a hexagonal system can be described by the relative growth of the corresponding principal planes (1 0 0), (0 1 0) and (0 0 1). The d-spacing of these planes can be given by pffiffiffi d 100 ¼ d 010 ¼ 3a=2; d 001 ¼ c;
803
energies and growth rates of the faces (1 0 0) and (0 1 0) are equal and greater than (0 0 1) faces. Therefore, the growth rate along crystallographic directions [1 0 0] and [0 1 0] is equal and greater than along the [0 0 1] direction, and can be described tentatively as R½100 ¼ R½010 > R½001. This explains the observed circular growth habits of the BBO crystals grown with Z-oriented ([0 0 1] direction) seeds. In fact, the actual morphology initially starts as hexagonal due to the presence of the threefold symmetry along the [0 0 1] direction and then finally turns to circular because of symmetric radial isotherms and modified Czochralski growth. Instead of Z[0 0 1]-oriented seeds, if the growth is started with an X[2 1 0]-oriented seed, oval shape morphology is observed. The observed oval habit shape is because of unequal growth rates along Y[0 1 0] and Z[0 0 1] directions as R[010] > R[001]. Since in our crystal growth experiments, all the growth parameters including the radial (3–5 °C/ cm) and axial (10–11 °C/cm) thermal gradients were kept the same, the observed growth habits are primarily due to anisotropy in growth rates. 4.1. Optical absorption studies Transmission measurements show more than 80% transmission for a 2 mm thick Z[0 0 1]-cut crystal plate. Fig. 5 shows the room temperature transmission spectra of the Z and X cut samples. The absorption coefficient (a in cm1) was calculated from the following equation using transmittance and absorbance data: 2
T ð1 RÞ ead ; where T is the transmittance, R is the reflectivity and d is the sample thickness. The inset of Fig. 5 shows the absorption plot of the BBO crystals orientated along the X and Z
where a and c are the lattice parameters. The lattice parameters obtained from single crystal X-ray diffraction mea˚ and c = 12.8094 A ˚. surements are given by a = 12.6378 A The corresponding d-spacing values are d100 = d010 = ˚ and d001 = 12.8094 A ˚ . Hence, the attachment 10.9446 A
Fig. 4. Typical growth morphologies or a cross-section of BBO crystal boules.
Fig. 5. Transmission spectra of the BBO crystal. The inset shows the absorption spectra of BBO crystals.
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R. Bhatt et al. / Optical Materials 29 (2007) 801–805
directions. The shift in the UV absorption edge (AE) of the X and Z orientated samples can be clearly seen from these results. The AE was measured at 20 cm1 of the absorption coefficient. The measured values are 193 nm for the X cut and 201.8 nm for the Z cut samples. The corresponding band gap energies measured are 6.2 eV and 6.45 eV for the Z and X directions, respectively (Fig. 6). Freanch et al. [18] have reported the band gap of BBO crystals as 6.43 eV, using vacuum ultraviolet spectroscopy and valance band photoemission spectroscopy. Our results are well in agreement with it. From the band structure calculation, Cheng et al. [19] have reported the band gap energy of BBO to be 6.28 eV. A nearly 9 nm shift in the AE of Z and X cut BBO samples clearly reveals the anisotropy behaviour (structure property correlation) in the optical properties of BBO crystals. Li et al. [20] have described that the bottom of the conduction band of BBO is primarily composed of the Ba 6s orbital and they related the band gap of BBO to the transition from the valance orbital of the (B3O6)3 group to the Ba 6s orbital. The observed shift is expected because of the different orientations of basic structural unit (B3O6)3 anion rings in the crystal or different local bonding of structural units along these directions. Further, according to Wemple and Didomemenico [21], the refractive index (n) and band gap energy (Eg) of the materials can be predicated by following empirical relation: n2 1 þ c=Eg ; where c is a material dependent constant. For Z cut samples, the optical properties are governed by the ordinary refractive index for all polarization, whereas for X cut samples both ordinary and extraordinary refractive indices will contribute depending on polarization. The observed band gaps are in agreement with the above relation, since a lower band gap energy observed for the Z cut sample implies a higher ordinary refractive index of the material than an
extraordinary refractive index, which is true for negative uniaxial BBO crystals. Fig. 6 shows the plot of absorption coefficient (a) vs photon energy (hm). If we look at the absorption spectra near the fundamental AE of BBO in Fig. 6, it can be clearly seen that the absorption coefficient at the band edge is an exponential function of the photon energy. An exponentially increasing absorption edge (AE) is the characteristic of many ferroelectric crystals, known as Urbach–Martienssen’s rule [22] and given by the following empirical relation: a ¼ a0 exp½ðE E0 Þ=EU ; where E = hm is the photon energy, E0 is comparable to the band gap energy and EU is the temperature dependent inverse logarithmic slope of the absorption coefficient. Using the above equation, a plot of logarithms of a as a function of E can be approximated by a straight line below the fundamental AE. The inset of Fig. 6 shows the plot of ln a vs hm. The straight line fitting of the experimental data shows that the fundamental AE follow the Urbach rule, also called Urbach tail. Sumi et al. [23] have reported that the Urbach tail occurs due to the broadening of the exciton absorption band by the microfields existing in the lattice. 5. Conclusions Good quality BBO crystals have been grown using TSSG from a Na2O flux. Crystals grown with gradually increasing cooling rates with slow pulling are found to have a uniform diameter with a less convex interface. The interface instabilities have been observed as a main hindrance in increasing the crystal thickness. The growth rate habits were explained in terms of growth rate anisotropy. The qualitative analysis shows that the typical growth rate relationship can be described by R[100] = R[010] > R[001]. Room temperature absorption spectra show anisotropy in the fundamental absorption edges and follow the Urbach rule. References
Photon energy (eV)
Photon energy (eV) Fig. 6. Absorption spectra near the fundamental absorption edge of BBO crystals. The inset shows the plot of the logarithm of absorption coefficient vs incident photon energy.
[1] Y. Mori, Y.K. Yap, T. Kamimura, M. Yoshimura, T. Sasaki, Opt. Matt. 19 (2002) 1. [2] C.T. Chen, B. Wu, A.D. Jiang, S. You, Sci. Sinica. B 28 (1985) 235. [3] D. Eimerl, L. Davis, S. Velsko, J. Appl. Phys. 62 (1987) 1968. [4] K. Kato, IEEE J. Quantum. Electron. QE 22 (1986) 1013. [5] R.S. Figelson, R.J. Raymakers, R.K. Route, Prog. Cryst. Growth Ch. 20 (1990) 15. [6] A.D. Mighall, A. Perloff, S. Block, Acta. Crystal. 20 (1966) 819. [7] K. Itoh, F. Marumo, Y. Kuwano, J. Cryst. Growth 106 (1990) 728. [8] H. Kouta, Y. Kuwano, J. Cryst. Growth 166 (1996) 497. [9] A. Jiang, F. Chang, Q. Lin, Z. Chen, Y. Zheng, J. Cryst. Growth 79 (1980) 963. [10] S.C. Sabarwal, S. Sangeeta, J. Cryst. Growth 187 (1998) 253. [11] Q. Huang, J. Liang, Acta. Phys. Sinica. 30 (1981) 559. [12] Indranil Bhaunik, S. Ganesamoorthy, Rajeev Bhatt, A.K. Karnal, R. Sunder, V.K. Wadhawan, J. Cryst. Growth 243 (2002) 522. [13] B.G. Wang, Z.P. Lu, E.W. Shi, W.Z. Zhong, Cryst. Res. Technol. 33 (1998) 275. [14] W.Z. Zhong, H.C. Hong, Z.P. Lu, D.Y. Tang, Cryst. Res. Technol. 28 (1993) 867.
R. Bhatt et al. / Optical Materials 29 (2007) 801–805 [15] P. Bennema, in: D.T.J. Hurle (Ed.), Handbook on Crystal Growth, North-Holland, Amsterdam, 1993, p. 477. [16] P. Hartman, W.G. Perdok, Acta. Crystallogr. 8 (1955) 49. [17] J.D.H. Donnay, D. Harker, Am. Mineral. 22 (1937) 446. [18] R.H. French, J.W. Ling, F.S. Ohuchi, C.T. Chen, Phys. Rev. B 44 (1991) 8496.
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[19] W.-D. Cheng, J.-S. Huang, J.-X. Lu, Phys. Rev. B 57 (1998) 1527. [20] J. Li, C.G. Duan, Z.Q. Gu, D.S. Wang, Phys. Rev. B 57 (1998) 6925. [21] S. Wempal, D. Didomenico, J. Appl. Phys. 40 (1969) 735. [22] M.V. Kurik, Phys. Stat. Sol. (a) 8 (1971) 9. [23] H. Sumi, Y. Toyozawa, J. Phys. Soc. Jpn. 31 (1971) 342.
Growth rate anisotropy and absorption studies on b-BaB2O4 single crystals grown by the top-seeded solution growth technique Rajeev Bhatt a, S. Ganesamoorthy
a,*
, Indranil Bhaumik a, A.K. Karnal a, V.K. Wadhawan
b
a
b
Crystal Growth Laboratory, Laser Materials Development and Devices Division, Raja Ramanna Centre for Advanced Technology, Indore 452 013, India Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India Received 5 January 2005; accepted 10 January 2006 Available online 10 February 2006
Abstract Beta barium borate (b-BaB2O4; BBO) single crystals have been grown from Na2O flux by the TSSG technique and the observed growth rate anisotropy is reported. The symmetrical conoscopic interference pattern on the c-cut plate confirmed strain-free and optical homogeneity of the crystals. The observed growth habits of as-grown crystals are explained using crystal growth theories. The relative growth rate along different crystallographic directions of BBO can be described by R[100] = R[010] > R[001]. The absorption measurements show a nearly 9 nm shift in fundamental absorption edges in X and Z cut samples. Band gap energies measured were 6.45 and 6.2 eV along the X and Z directions, respectively. The absorption spectra near the fundamental absorption edges (AE) follow Urbach’s rule. Ó 2006 Elsevier B.V. All rights reserved. PACS: 42.70.MP; 78.20.e; 81.10.Dn Keywords: Growth from solution; Single crystal; Top-seeded solution growth; Borate; Non-linear optical material
1. Introduction Low temperature phase b-BaB2O4 (BBO) is a technologically important non-linear optical (NLO) crystal, especially for deep UV applications because of its high NLO coefficient, high damage threshold and relatively low hygroscopic behaviour [1–6]. The growth of BBO crystals from the direct melt (Czochralski method) has been reported by employing a steep temperature gradient (200 °C/mm) at the crystal–melt interface [7,8]; however, obtaining large size crystals is still a challenging task. Hence it is preferable to grow them below the a–b transition temperature by employing the top-seeded solution growth technique (TSSG). Na2O is reported to be one of the best solvents in terms of quality and size of the grown
crystals [9]. However, incorporation of Na+ ions of the order of 100–300 ppm is also reported [10]. Unlike other borate family crystals, growth habits of BBO are quite different due to the difference in the growth conditions. For example, LBO and CLBO, require nearly a zero temperature gradient, BBO requires a high thermal gradient as well as slow pulling. Therefore, the TSSG growth of BBO can be described as a modified Czochralski growth, and hence as-grown crystals do not show any natural growth morphologies. In the present investigation, optical quality BBO crystals have been grown and their morphologies or habit shapes along different directions have been compared and analyzed. The as-grown crystals were characterized by optical absorption measurements. 2. Experimental
*
Corresponding author. Tel.: +91 731 2488657; fax: +91 731 2488650. E-mail address: [email protected] (S. Ganesamoorthy).
0925-3467/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2006.01.003
The composition used in the present study was 80 mol% BaB2O4 and 20 mol% Na2O [11]. The charge was synthe-
802
R. Bhatt et al. / Optical Materials 29 (2007) 801–805
sized from high purity BaCO3, Na2CO3 and B2O3 chemicals (99.9%). The chemicals were dried at 200 °C for 2 h in an oven before weighing, then filled into a polystyrene bottle and mixed on a ball miller for 5–10 h without balls. The mixed powder was then put into a platinum crucible (6 cm diameter and 5 cm height) and fired at the rate of 150 °C/h first to 350 °C for 5–8 h and then 725 °C for 15–20 h, followed by direct melting at 1050 °C. Borate melts or solutions are well known for their high viscosity and glass forming nature because of the existence of BO3 3 rings or –O–B–O– chains [5]. Therefore, high temperature gradient is required across the melt in order to grow good quality crystals. A high gradient two-zone furnace was designed and developed in-house to achieve the desired thermal profile. The maximum axial and radial temperature gradient achieved in this configuration was of the order of 10–12 °C/cm and 3–5 °C/cm. The melt was homogenized for 20–24 h at 20–30 °C above the saturation temperature. The saturation temperature was determined by repeated seeding, with an accuracy of ± 0.5 °C [12]. Crystals were grown along Z and X orientations. Rotation rates used were around 30–25 rpm during initial seeding, which was finally reduced to 4 rpm systematically. A gradually increasing cooling rate from 0.7 to 2.5 °C/day in steps of 0.01 °C/1–2 day was employed, whereas the pulling rate was optimised to 0.3–0.5 mm/ day. Some growth runs were performed without applying pulling of the crystal as well. Growth runs were performed in stable growth conditions under a closed system. The grown crystals were subjected to an X-ray diffraction study for the identification of phase and lattice parameter calculation. Transmission and absorption studies were performed on Z and X cut samples with unpolarised light at room temperature using a Shimadzu UV 3101PC spectrophotometer.
tures developed on the crystal boule were in agreement with that in the literature [13]. To ascertain the quality of the grown crystals, a conoscopic study was performed on a c-cut plate using an Olympus polarizing microscope in the transmission mode. The symmetrical fringe patterns shown in Fig. 2 reveal homogeneity and absence of strain in the crystal. Crystals grown under a uniform cooling rate of 0.04 °C/h and an axial temperature gradient of 12 °C/cm resulted in high quality transparent lens shape crystals with highly convex interface. But on application of pulling, there is a tendency of detachment of the growing crystal at the periphery. This limits the thickness in the grown crystal. Therefore, to increase the thickness the cooling rate was increased gradually in steps of 0.01 °C per 30–50 h, starting from 0.02 to 0.12 °C/h. The interface shape of the grown crystals was observed to be less convex in the latter case. Another crucial problem in the growth of thicker crystals is the occurrence of interface instability and solution entrapment into the crystal, resulting in the unwanted cellular growth at the bottom of the grown crystal (Fig. 3). However, growth along X and Y orientations is more prone to this instability and occurs only at the latter stage of the growth i.e., after a cooling of 25–35 °C. At this stage of growth, the solution viscosity increases so significantly that
3. Results and discussion Inclusion-free, highly transparent BBO single crystals have been grown along different orientations. Fig. 1 shows the photograph of a BBO crystal boule. The growth fea-
Fig. 2. Conoscopic pattern of a c-cut BBO crystal plate.
Fig. 1. The as-grown BBO crystal boule along the [0 0 1] direction.
Fig. 3. Crystal boule grown along the X direction, showing an elliptical cross-section and cellular growth.
R. Bhatt et al. / Optical Materials 29 (2007) 801–805
it disturbs the mass transport around the growing crystal. As a result, the diffusion boundary layer around the growing crystal is in non-equilibrium with respect to the actual equilibrium concentration. In other words, the equilibrium concentrations of the coexisting solution and crystal deviate from actual compositions, resulting in interface instability. 4. Growth rate anisotropy Different growth shapes (morphologies) have been observed experimentally in crystal boules grown along the X and Z directions. The Z oriented grown crystal developed a nearly circular cross-section, whereas crystals grown along other directions developed an oval cross-section (Fig. 3). The schematic of the observed morphology corresponding to different growth directions is shown in Fig. 4. Zhong et al. [14] have explained the crystal growth habits on the basis of orientation of structural units (B2O3)3 rings in the crystal. We are applying the growth rate theories to explain the observed results. According to crystal growth theories, the growth habits of the crystals are determined primarily by the anisotropy of the relative growth rates along different directions [15]. The Hartman–Perdoch theory [16] states that the relative growth rate of face (Rhkl) is determined by the magnitude of the attachment energy of att the growing face (h k l) as Rhkl Eatt hkl , where E hkl is the energy released per structural unit attached to the growing crystal surface at an appropriate crystallographic position from infinity. As per Donnay and Harker’s [17] assumption, the attachment energy is inversely proportional to the inter-planer spacing and is given by Rhkl Eatt hkl 1=d hkl . The growth rates along the crystallographic directions in a hexagonal system can be described by the relative growth of the corresponding principal planes (1 0 0), (0 1 0) and (0 0 1). The d-spacing of these planes can be given by pffiffiffi d 100 ¼ d 010 ¼ 3a=2; d 001 ¼ c;
803
energies and growth rates of the faces (1 0 0) and (0 1 0) are equal and greater than (0 0 1) faces. Therefore, the growth rate along crystallographic directions [1 0 0] and [0 1 0] is equal and greater than along the [0 0 1] direction, and can be described tentatively as R½100 ¼ R½010 > R½001. This explains the observed circular growth habits of the BBO crystals grown with Z-oriented ([0 0 1] direction) seeds. In fact, the actual morphology initially starts as hexagonal due to the presence of the threefold symmetry along the [0 0 1] direction and then finally turns to circular because of symmetric radial isotherms and modified Czochralski growth. Instead of Z[0 0 1]-oriented seeds, if the growth is started with an X[2 1 0]-oriented seed, oval shape morphology is observed. The observed oval habit shape is because of unequal growth rates along Y[0 1 0] and Z[0 0 1] directions as R[010] > R[001]. Since in our crystal growth experiments, all the growth parameters including the radial (3–5 °C/ cm) and axial (10–11 °C/cm) thermal gradients were kept the same, the observed growth habits are primarily due to anisotropy in growth rates. 4.1. Optical absorption studies Transmission measurements show more than 80% transmission for a 2 mm thick Z[0 0 1]-cut crystal plate. Fig. 5 shows the room temperature transmission spectra of the Z and X cut samples. The absorption coefficient (a in cm1) was calculated from the following equation using transmittance and absorbance data: 2
T ð1 RÞ ead ; where T is the transmittance, R is the reflectivity and d is the sample thickness. The inset of Fig. 5 shows the absorption plot of the BBO crystals orientated along the X and Z
where a and c are the lattice parameters. The lattice parameters obtained from single crystal X-ray diffraction mea˚ and c = 12.8094 A ˚. surements are given by a = 12.6378 A The corresponding d-spacing values are d100 = d010 = ˚ and d001 = 12.8094 A ˚ . Hence, the attachment 10.9446 A
Fig. 4. Typical growth morphologies or a cross-section of BBO crystal boules.
Fig. 5. Transmission spectra of the BBO crystal. The inset shows the absorption spectra of BBO crystals.
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R. Bhatt et al. / Optical Materials 29 (2007) 801–805
directions. The shift in the UV absorption edge (AE) of the X and Z orientated samples can be clearly seen from these results. The AE was measured at 20 cm1 of the absorption coefficient. The measured values are 193 nm for the X cut and 201.8 nm for the Z cut samples. The corresponding band gap energies measured are 6.2 eV and 6.45 eV for the Z and X directions, respectively (Fig. 6). Freanch et al. [18] have reported the band gap of BBO crystals as 6.43 eV, using vacuum ultraviolet spectroscopy and valance band photoemission spectroscopy. Our results are well in agreement with it. From the band structure calculation, Cheng et al. [19] have reported the band gap energy of BBO to be 6.28 eV. A nearly 9 nm shift in the AE of Z and X cut BBO samples clearly reveals the anisotropy behaviour (structure property correlation) in the optical properties of BBO crystals. Li et al. [20] have described that the bottom of the conduction band of BBO is primarily composed of the Ba 6s orbital and they related the band gap of BBO to the transition from the valance orbital of the (B3O6)3 group to the Ba 6s orbital. The observed shift is expected because of the different orientations of basic structural unit (B3O6)3 anion rings in the crystal or different local bonding of structural units along these directions. Further, according to Wemple and Didomemenico [21], the refractive index (n) and band gap energy (Eg) of the materials can be predicated by following empirical relation: n2 1 þ c=Eg ; where c is a material dependent constant. For Z cut samples, the optical properties are governed by the ordinary refractive index for all polarization, whereas for X cut samples both ordinary and extraordinary refractive indices will contribute depending on polarization. The observed band gaps are in agreement with the above relation, since a lower band gap energy observed for the Z cut sample implies a higher ordinary refractive index of the material than an
extraordinary refractive index, which is true for negative uniaxial BBO crystals. Fig. 6 shows the plot of absorption coefficient (a) vs photon energy (hm). If we look at the absorption spectra near the fundamental AE of BBO in Fig. 6, it can be clearly seen that the absorption coefficient at the band edge is an exponential function of the photon energy. An exponentially increasing absorption edge (AE) is the characteristic of many ferroelectric crystals, known as Urbach–Martienssen’s rule [22] and given by the following empirical relation: a ¼ a0 exp½ðE E0 Þ=EU ; where E = hm is the photon energy, E0 is comparable to the band gap energy and EU is the temperature dependent inverse logarithmic slope of the absorption coefficient. Using the above equation, a plot of logarithms of a as a function of E can be approximated by a straight line below the fundamental AE. The inset of Fig. 6 shows the plot of ln a vs hm. The straight line fitting of the experimental data shows that the fundamental AE follow the Urbach rule, also called Urbach tail. Sumi et al. [23] have reported that the Urbach tail occurs due to the broadening of the exciton absorption band by the microfields existing in the lattice. 5. Conclusions Good quality BBO crystals have been grown using TSSG from a Na2O flux. Crystals grown with gradually increasing cooling rates with slow pulling are found to have a uniform diameter with a less convex interface. The interface instabilities have been observed as a main hindrance in increasing the crystal thickness. The growth rate habits were explained in terms of growth rate anisotropy. The qualitative analysis shows that the typical growth rate relationship can be described by R[100] = R[010] > R[001]. Room temperature absorption spectra show anisotropy in the fundamental absorption edges and follow the Urbach rule. References
Photon energy (eV)
Photon energy (eV) Fig. 6. Absorption spectra near the fundamental absorption edge of BBO crystals. The inset shows the plot of the logarithm of absorption coefficient vs incident photon energy.
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