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Urbach’s rule of Bi4Ge3O12 doped with 3d and 4d ions
Optical Materials 34 (2011) 265–268
Contents lists available at SciVerse ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Urbach’s rule of Bi4Ge3O12 doped with 3d and 4d ions P. Petkova ⇑ Shumen University ‘‘Konstantin Preslavsky’’, 115 Universitetska street, 9712 Shumen, Bulgaria
a r t i c l e
i n f o
Article history: Received 11 May 2011 Received in revised form 9 August 2011 Accepted 18 August 2011 Available online 29 September 2011 Keywords: Eulitines 3d and 4d ions Urbach’s rule Excitons
a b s t r a c t In this work, the influence of 3d (Fe, Mn) and 4d (Ru) ions on the absorption coefficient of the doped Bi4Ge3O12 (BGO) in the spectral range 3.6–4.05 eV has been determined. The validity of Urbach’s rule is verified in an illuminated and an annealed state of the samples. The dependence between the incorporation of the different dopants and the values of their Urbach’s parameters is established. The creation and the destruction of the excitons, associated with the ionized donors, are explained. The Urbach’s energy of all samples is determined. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The effect of doping with 3d and 4d ions influences on the light – induced, optical and holographic properties of Bi4Ge3O12 single crystals. Therefore, holographic gratings are successfully recorded in Fe-doped BGO in the blue–green spectral range, and this situation repeats in Mn-doped BGO, but in the red spectral range [1]. Ruthenium is found to make eulitines sensitive in the red spectral range, and this dopant makes BGO a potential candidate for the thermoluminescence studies [2]. The doped eulitines appear strong photochromic and photorefractive effects [3]. The investigation of absorption of the doped BGO is very important in Urbach’s spectral region. The reason is due to several factors: a carrier impurity interaction, a carrier–phonon interaction, a structural disorder, etc. Each of these factors is discussed in this work at room temperature T = 300 K.
2. Experimental and results BGO single crystals, doped with Fe, Mn, Ru, Fe + Mn and Ru + Mn, are grown by Czochralski technique [1,3]. Some stoichiometric Bi2O3:GeO2 powders are mixed in a molar proportion 2:3. The purity of Bi2O3 and GeO2 is 99.999% in the mixture. The growth conditions have been established by the automatic diameter-weight control. The ruthenium is introduced into the melt in the form of RuO2 oxide. The iron is introduced to the melt solution during the crystal growth in the form of Fe2O3 oxide, and manganese is introduced there as MnO2 oxide. ⇑ Tel.: +359 54830495261; fax: +359 54830371. E-mail address: [email protected] 0925-3467/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2011.08.024
The concentration of doping elements is as follows: Mn – 5 1018 cm3, Fe – 3 1018 cm3, Ru – 6.1 1018 cm3 [3,4]. The doping concentration for double doped crystals is: Mn – 1 1018 cm3, Fe – 7 1018 cm3 (BGO:Mn + Fe); Mn – 1 1018 cm3, Ru – 3 1018 cm3 (BGO:Mn + Ru) [3,4]. It is well known that BGO possesses a complex crystal structure with an octahedron [Bi3O4]+ and a tetrahedron [GeO4]4 [5]. Each Bi3+ ion is coordinated by six oxygen ions and each Ge4+ ion is surrounded by four oxygen ions. Such a structure allows a number of charge trapping sites where the 3d ions are expected to enter in the cationic sites: Bi3+ site and/or Ge4+ site. EPR technique has been used to determine the location of Fe and Mn as well as their charge state in BGO. The manganese has been detected as Mn2+ in Bi site [6], and the iron ions have been detected as Fe3+ in the tetrahedral Ge4+ position [7]. The valence state of Ru in BGO crystals has not been known yet. The ruthenium could exist in three different valence states Ru3+/4+/5+ in similar cubic oxide crystals [8]. We can assume that Ru ions have the valence 4+. This ion is changing its valence to Ru3+ and Ru5+ in dependence on the existence of electrons or holes. It is assumed that Ru can replace Ge4+ ions in the tetrahedral position, as well as, it can occupy Bi3+ sites in the crystal lattice [4]. The experimental set up for the measurement of the absorption spectra consists of: a halogen lamp with a stabilized rectifier 3H-7, a monochromator SPM-2, a system of quartz lenses, a polarizer, a crystal holder with a sample and a detector Hamamatsu S2281-01. The samples are double polished plates with a thickness d < 1 mm. The absorption spectra are measured on two different initial states of the crystals: (1) after the thermal annealing at 450 °C in an oxygen atmosphere for 3 h (so called annealed state) and (2) after the preliminary illumination with the ultraviolet light coming from the mercury lamp (illuminated state).
P. Petkova / Optical Materials 34 (2011) 265–268
3. Discussion One interesting point for discussion in the crystal spectroscopy is connected with the interactions of the excitations by the light absorption (excitons) with phonons of the crystal lattice. When the absorption coefficient at the band edge has an exponential shape at a certain temperature, it is the Urbach’s rule. It is shown that the fundamental absorption edge appears a temperature dependence in the Urbach’s rule region. The empirical Urbach’s rule is expressed by the following spectral dependence of a (E):
a ¼ a0 exp½rðEg hmÞ=kT;
ð1Þ
where a0 and Eg are constants; r is the parameter of the slope of the absorption edge. The parameter r is described by the equation:
rðTÞ ¼ r0 f½ð2kTÞ=ðhxÞth½ðhxÞ=ð2kTÞg:
ð2Þ
The localized exciton states manifest at the absorption edge of the eulitines because of the strong exciton–phonon interaction there (the phonons with the energy hxeff ¼ 0042 eV are most effective) [9]. The parameter r/kT consists information about the interaction between the excitons and LO phonons [10]. In the general case, r is the linear function of the impurity concentration. The value of r can increase or decrease depending on the direction of the shifting of the absorption maximum with the concentration [10]. The exciton–phonon interaction has a big value when r0 < 1 [10]. When the symmetry of the crystal field is lower, then r0 is smaller [10]. The formation of the exciton states is realized by trapping of the excitons of the local lattice deformations [11]. The exponential shape of the absorption edge is connected with the explanation that the electrons move themselves from the valence band to the free impurity states. This situation can be observed when the electrons of the valence band or these electrons of the impurity levels interact with the mono-energetic phonons [10]. Thus the exponential shape of the edge of the impurity bands can be explained by the effect of the phonons on the process of the absorption in the crystals. The electrons from the Valence band (VB) pass into the Conduction band (CB) after the illumination with the UV light (Fig. 1a). After that, the impurity levels in the Forbidden band (FB) act as electron traps. Thus, the electron, caught by the impurity level and its corresponding hole in VB, create together the exciton, associated with the
ionized donors Mn2+, Fe3+ or Ru4+. The captured electrons pass into CB after their interaction with the phonons and, in the end, they return into the VB. The excitons, associated with the ionized donors, destruct after the annealing (Fig. 1b). The Urbach’s rule region of BGO is compared with the same region of the illuminated and the annealed doped BGO on Figs. 2 and 3. It is seen that Fe3+ ions enlarge the Urbach’s rule region of the doped BGO in the illuminated and the annealed state (Fig. 2a). Mn2+ and Ru4+ ions shrink this region in the illuminated state and these ions enlarge Urbach’s rule region in the annealed state (Fig. 2b and c). Fe3+ ions have the bigger contribution in both states of BGO:Mn + Fe (Fig. 3a). This fact is confirmed in the work of Marinova et al., where the authors have been investigated the photochromic effect of these crystals [3]. The Urbach’s rule region shrinks in the case of the illuminated and the annealed BGO:Mn + Ru (Fig. 3b). The Urbach’s energy is connected with the carrier impurity interaction, the carrier–phonon interaction and the structural disorder [12]. That is why this energy is calculated by the formula:
Eu ¼ aðEÞ=ðda=dEÞ:
(a)
4.5
y = 3.1502x - 8.7585 R2 = 0.9976 BGO:Fe illuminated
4 3.5 3 2.5 2
y = 3.6092x - 10.576 R 2 = 0.9995 BGO:Fe annealed
1.5 1 0 3.5
3.6
3.7
3.8
3.9
4
4.1
E [eV]
(b)
3.5
y = 2.584x - 7.2348 R 2 = 0.9972 BGO:Mn illuminated
2.5
Conduction band
2
lnα
Impurity level
y = 4.3031x - 16.043 R2 = 0.9999 BGO
0.5
3
(a)
ð3Þ
The Eu is a constant for BGO in the spectral region 3.6–4 eV. The values of the Urbach’s energy of the illuminated and the annealed BGO:Fe are bigger than the Eu of the BGO (Fig. 4a). In comparison with the BGO, the Urbach’s energy has bigger values for BGO:Mn and BGO:Ru in illuminated state and this energy has smaller values for these crystals in annealed state (Fig. 4b and c). The Fe3+ ions
lnα
266
y = 6.5911x - 23.902 R2 = 0.9991 BGO:Mn annealed
1.5 1
y = 4.3031x - 16.043 R2 = 0.9999 BGO
0.5 0 3.5
3.6
3.7
3.8
3.9
4
4.1
E [eV]
Valence band
(c)
4 y = 3.7558x - 11.418 R 2 = 0.9974 BGO:Ru illuminated
3.5
Conduction band Phonon Impurity level
3 2.5
lnα
(b)
y = 4.3031x - 16.043 R 2 = 0.9999 BGO
2 y = 7.3534x - 26.594 R 2 = 0.9978 BGO:Ru annealed
1.5 1 0.5
Valence band
0 3.5
3.6
3.7
3.8
3.9
4
E [eV] Fig. 1. The model of exciton associated with the ionized donor in doped BGO: (a) after illumination; (b) after annealing.
Fig. 2. The Urbach’s rule of doped Bi4Ge3O12 in illuminated state.
4.1
267
P. Petkova / Optical Materials 34 (2011) 265–268
(a)
4.5 4 3.5
y = 3.4736x - 9.9161 R2 = 0.9981 BGO:Mn+Fe illuminated
lnα
3 2.5 2
y = 4.3031x - 16.043 R2 = 0.9999 BGO
y = 4.2617x - 13.142 R2 = 0.9998 BGO:Mn+Fe annealed
1.5 1
0.4
Urbach's energy [eV]
(a)
0.5
BGO:Fe illuminated
0.35
BGO:Fe annealed
0.3 0.25 0.2
BGO
0.15 3.5
0 3.5
3.6
3.7
3.8
3.9
4
3.6
3.7
3.8
4.1
3.9
4
4.1
E [eV]
E [eV] 4 3.5
(b) y = 2.3121x - 5.6515 R 2 = 0.9978 BGO:Mn+Ru illuminated
3
lnα
2.5 y = 2.7779x - 7.7794 R2 = 0.9971 BGO:Mn+Ru annealed
2 1.5
y = 4.3031x - 16.043 R2 = 0.9999 BGO
0.5
Urbach's energy [eV]
(b)
1
BGO:Mn illuminated
0.4 0.3
BGO
0.2
BGO:Mn annealed
0.1 0 3.6
3.7
3.8
0.5 3.7
3.75
3.8
3.85
3.9
3.95
4
4
4.1
4.05
(c)
E [eV] Fig. 3. The Urbach’s rule of annealed doped Bi4Ge3O12 in annealed state.
have the predominant influence in the Eu for illuminated and annealed BGO:Mn + Fe (Fig. 5a). The values of Urbach’s energy for BGO:Mn + Ru are bigger in comparison with this constant energy for BGO (Fig. 5b). The ionic radius of Mn2+ is 0.67 in the low spin complexes and its ionic radius is 0.83 in the high spin complexes. Ru4+ ion has an ionic radius 0.62 and Bi3+ has an ionic radius 1.03. Thus the incorporation of the manganese and ruthenium in the bismuth sites leads to a shrinkage of the oxygen octahedrons in Urbach’s rule region. The ionic radius of Fe3+ is 0.635 and this radius of Ge4+ ion is 0.39. Therefore the substitution of the germanium ions with the iron ions leads to an enlargement of the oxygen tetrahedrons in the spectral region 3.6–4.05 eV. Our observation is that the octahedrons and tetrahedrons in the doped Bi4Ge3O12 are strong deformed because of the values of r0 (see Table 1). These two structures are the most deformed in BGO:Mn + Ru. This deformation decreases for the doped crystals in the following sequence: BGO:Mn + Fe, BGO:Mn, BGO:Fe and BGO:Ru. When the exciton–phonon interaction has to be determined, it is important to examine 1s exciton. In this case, we can calculate the exciton–phonon interaction constant g by the following formula g ¼ ð2=3Þr1 0 . The exciton–phonon coupling constant g is very big for BGO:Mn and it is the smallest for BGO:Ru in the illuminated state (Table 2). This constant has the biggest value for the illuminated BGO:Mn + Ru which means that Mn2+ impurity has a dominant influence in the double doped BGO. This predominant role is assigned to the impurity of Fe3+ in the case of the annealed BGO:Mn + Fe. The value of g is in the same range for Fe, Mn and Ru doped BGO in the annealed state. This value is bigger for the Table 1 The values of r and r0 for doped BGO samples in illuminated and annealed state. Sample Bi4Ge3O12:Fe Bi4Ge3O12:Mn Bi4Ge3O12:Ru Bi4Ge3O12:Mn + Fe Bi4Ge3O12:Mn + Ru
r
r
r0
r0
illuminated
annealed
illuminated
annealed
0.08 0.07 0.1 0.09 0.06
0.09 0.17 0.19 0.11 0.07
0.1 0.08 0.12 0.11 0.07
0.2 0.18 0.20 0.12 0.07
0.35
Urbach's energy [eV]
3.65
BGO:Ru illuminated
0.3
BGO
0.25 0.2 0.15 0.1
BGO:Ru annealed
0.05 0 3.65
3.7
3.75
3.8
3.85
3.9
3.95
4
4.05
E [eV] Fig. 4. The Urbach’s energy of single doped Bi4Ge3O12 in illuminated and annealed state.
(a) Urbach's energy [eV]
3.6
0.33
BGO:Mn+Fe illuminated
0.31 0.29 0.27 0.25
BGO:Mn+Fe annealed
0.23
BGO
0.21 0.19 3.5
3.6
3.7
3.8
3.9
4
4.1
E [eV]
(b) Urbach's energy [eV]
0 3.55
3.9
E [eV]
0.7
BGO:Mn+Ru illuminated
0.6
BGO:Mn+Ru annealed
0.5 0.4 0.3
BGO
0.2 0.1 3.7
3.75
3.8
3.85
3.9
3.95
4
4.05
E [eV] Fig. 5. The Urbach’s energy of double doped Bi4Ge3O12 in illuminated and annealed state.
268
P. Petkova / Optical Materials 34 (2011) 265–268
Table 2 The values of g, ra and Wd for doped BGO samples at room temperature T = 300 K. Sample
g illuminated
Bi4Ge3O12:Fe Bi4Ge3O12:Mn Bi4Ge3O12:Ru Bi4Ge3O12:Mn + Fe Bi4Ge3O12:Mn + Ru
6.67 8.33 5.56 6.06 9.52
g annealed 3.33 3.7 3.33 5.56 9.52
ra (cm2) illuminated 19
17.56 10 21.32 1020 18.56 1020 7.18 1019 4.37 1019
annealed BGO:Mn + Fe and it is the biggest for BGO:Mn + Ru in the annealed state. Next step in the calculations is the determination of the crosssection of the impurity absorption [13]. It is very important to establish how the radiation is absorbed by the impurity ions in the crystals. The total cross-section ra of the impurity absorption is defined by the integration within the absorption band of the impurity ions (see the Eq. (3)).
ra ¼ ð1=NÞ
Z
aðkÞdk;
ð3Þ
where N is the number of the impurity ions in the unit volume, a is the impurity absorption coefficient typical of an energetic interval from E1 to E2. For the investigated crystals here E1 = 3.6 eV and E2 = 4.05 eV. The cross-section ra can vary significantly from one absorption band to another. The value of ra is smaller for the crystal BGO:Mn and BGO:Ru in the illuminated and the annealed state. It is bigger for BGO:Fe in these two states (Table 2). The values of ra for Fe3+, Mn2+ and Ru4+ ions confirm the fact that Bi octahedrons are shrinked and Ge tetrahedrons are enlarged. The broadening of the absorption edge is clearly observed demonstrating the dynamic disorder at the room temperature [14]. The formula Wd = kT/r describes this broadening. For Mn doped eulitine, Wd has the biggest value and its value is the smallest for BGO:Ru in the illuminated state (Table 2). The value of this parameter is in the middle in the case of the illuminated BGO:Fe. That is why the interaction between the excitons and LO phonons is the strongest for BGO:Ru in the illuminated state. This interaction is guided by Mn2+ for the illuminated BGO:Mn + Ru and it is guided by Fe3+ for the illuminated BGO:Mn + Fe. The broadening of the absorption edge is the biggest for BGO:Fe and it is the smallest for BGO:Ru when the crystals are annealed. The double doping leads to an increasing of this broadening in the case of the annealed samples.
ra (cm2) annealed 19
16.68 10 16.36 1020 17.17 1020 5.94 1019 3.41 1019
Wd (meV) illuminated
Wd (meV) annealed
324 370 259 288 432
288 152 136 235 370
4. Conclusions (1) The very small values of r0 give information that octahedrons and tetrahedrons in the crystal lattice of the doped eulitines are strong deformed. (2) The calculation of the cross-section ra is the proof that Fe3+ ions enlarge Ge tetrahedrons and Mn2+, Ru4+ shrink Bi octahedrons. (3) The interaction between the excitons and LO phonons is strongest for BGO:Ru in the illuminated state. (4) The exciton–phonon coupling constant g is the biggest for BGO:Mn in the illuminated and the annealed state.
References [1] P. Petkova, V. Marinova, I. Iliev, T. Dimov, S.H. Lin, K.Y. Hsu, Proc. SPIE 6252 (2006). 62520O-1–62520O-4. [2] N. Uzunov, H. Hristov, N. Arhangelova, I. Penev, V. Marinova, M. Bello, G. Moschini, Comptes Rendus De L’Academie Bulgare Des Sciences 64 (2011). [3] V. Marinova, D. Petrova, S.H. Lin, K.Y. Hsu, Opt. Commun. 281 (2008) 37–43. [4] V. Marinova, S.H. Lin, K.Y. Hsu, J. Appl. Phys. 98 (2005). 113527-1–113527-5. [5] A.A. Kaminskii, D. Schultze, B. Hermoneit, S.E. Sarkisov, L. Li, J. Bohm, P. Reiche, R. Ehlert, A.A. Mayer, V.A. Lomonov, V.A. Balashov, Phys. Status Solidi (a) 33 (1976) 737. [6] D. Bravo, L. Arizmendi, M. Aguilar, F.J. Lopez, J. Phys. Condens. Mater. 2 (1990) 10123. [7] A. Martin, D. Bravo, E. Dieguez, F.J. Lopez, Phys. Rev. B 54 (1996) 12915. [8] L. Kovacs, E. Moya, K. Polgar, F.J. Lopez, C. Zaldo, Appl. Phys. A 52 (1991) 307. [9] B.V. Shulgin, T.I. Polupanova, A.V. Kruzhalov, V.M. Skorikov, Bismuth Orthogermanate Vneshtorgizdat, Sverdlovsk, 1992 (in Russian). [10] M.V. Kurik, Phys. Status Solidi (a) 8 (1971) 9–45. [11] H. Sumi, Y. Toypzawa, Urbach, J. Phys. Soc. Japan 31 (2) (1971) 342–357. [12] Sk. Faruque Ahmed, Myoung-Woon Moon, Kwang-Ryeol Lee, Thin Solid Films 517 (2009) 4035–4038. [13] Jai Singh (Ed.), Optical Properties of Condensed Matter and Applications, John Wiley & Sons, 2006. [14] V.P. Kunets, N.R. Kulish, Vas.P. Kunets, M.P. Lisitsa, Semiconductor Physics, Quantum Electron Optoelectron 5 (1) (2002) 9–15.
Contents lists available at SciVerse ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Urbach’s rule of Bi4Ge3O12 doped with 3d and 4d ions P. Petkova ⇑ Shumen University ‘‘Konstantin Preslavsky’’, 115 Universitetska street, 9712 Shumen, Bulgaria
a r t i c l e
i n f o
Article history: Received 11 May 2011 Received in revised form 9 August 2011 Accepted 18 August 2011 Available online 29 September 2011 Keywords: Eulitines 3d and 4d ions Urbach’s rule Excitons
a b s t r a c t In this work, the influence of 3d (Fe, Mn) and 4d (Ru) ions on the absorption coefficient of the doped Bi4Ge3O12 (BGO) in the spectral range 3.6–4.05 eV has been determined. The validity of Urbach’s rule is verified in an illuminated and an annealed state of the samples. The dependence between the incorporation of the different dopants and the values of their Urbach’s parameters is established. The creation and the destruction of the excitons, associated with the ionized donors, are explained. The Urbach’s energy of all samples is determined. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The effect of doping with 3d and 4d ions influences on the light – induced, optical and holographic properties of Bi4Ge3O12 single crystals. Therefore, holographic gratings are successfully recorded in Fe-doped BGO in the blue–green spectral range, and this situation repeats in Mn-doped BGO, but in the red spectral range [1]. Ruthenium is found to make eulitines sensitive in the red spectral range, and this dopant makes BGO a potential candidate for the thermoluminescence studies [2]. The doped eulitines appear strong photochromic and photorefractive effects [3]. The investigation of absorption of the doped BGO is very important in Urbach’s spectral region. The reason is due to several factors: a carrier impurity interaction, a carrier–phonon interaction, a structural disorder, etc. Each of these factors is discussed in this work at room temperature T = 300 K.
2. Experimental and results BGO single crystals, doped with Fe, Mn, Ru, Fe + Mn and Ru + Mn, are grown by Czochralski technique [1,3]. Some stoichiometric Bi2O3:GeO2 powders are mixed in a molar proportion 2:3. The purity of Bi2O3 and GeO2 is 99.999% in the mixture. The growth conditions have been established by the automatic diameter-weight control. The ruthenium is introduced into the melt in the form of RuO2 oxide. The iron is introduced to the melt solution during the crystal growth in the form of Fe2O3 oxide, and manganese is introduced there as MnO2 oxide. ⇑ Tel.: +359 54830495261; fax: +359 54830371. E-mail address: [email protected] 0925-3467/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2011.08.024
The concentration of doping elements is as follows: Mn – 5 1018 cm3, Fe – 3 1018 cm3, Ru – 6.1 1018 cm3 [3,4]. The doping concentration for double doped crystals is: Mn – 1 1018 cm3, Fe – 7 1018 cm3 (BGO:Mn + Fe); Mn – 1 1018 cm3, Ru – 3 1018 cm3 (BGO:Mn + Ru) [3,4]. It is well known that BGO possesses a complex crystal structure with an octahedron [Bi3O4]+ and a tetrahedron [GeO4]4 [5]. Each Bi3+ ion is coordinated by six oxygen ions and each Ge4+ ion is surrounded by four oxygen ions. Such a structure allows a number of charge trapping sites where the 3d ions are expected to enter in the cationic sites: Bi3+ site and/or Ge4+ site. EPR technique has been used to determine the location of Fe and Mn as well as their charge state in BGO. The manganese has been detected as Mn2+ in Bi site [6], and the iron ions have been detected as Fe3+ in the tetrahedral Ge4+ position [7]. The valence state of Ru in BGO crystals has not been known yet. The ruthenium could exist in three different valence states Ru3+/4+/5+ in similar cubic oxide crystals [8]. We can assume that Ru ions have the valence 4+. This ion is changing its valence to Ru3+ and Ru5+ in dependence on the existence of electrons or holes. It is assumed that Ru can replace Ge4+ ions in the tetrahedral position, as well as, it can occupy Bi3+ sites in the crystal lattice [4]. The experimental set up for the measurement of the absorption spectra consists of: a halogen lamp with a stabilized rectifier 3H-7, a monochromator SPM-2, a system of quartz lenses, a polarizer, a crystal holder with a sample and a detector Hamamatsu S2281-01. The samples are double polished plates with a thickness d < 1 mm. The absorption spectra are measured on two different initial states of the crystals: (1) after the thermal annealing at 450 °C in an oxygen atmosphere for 3 h (so called annealed state) and (2) after the preliminary illumination with the ultraviolet light coming from the mercury lamp (illuminated state).
P. Petkova / Optical Materials 34 (2011) 265–268
3. Discussion One interesting point for discussion in the crystal spectroscopy is connected with the interactions of the excitations by the light absorption (excitons) with phonons of the crystal lattice. When the absorption coefficient at the band edge has an exponential shape at a certain temperature, it is the Urbach’s rule. It is shown that the fundamental absorption edge appears a temperature dependence in the Urbach’s rule region. The empirical Urbach’s rule is expressed by the following spectral dependence of a (E):
a ¼ a0 exp½rðEg hmÞ=kT;
ð1Þ
where a0 and Eg are constants; r is the parameter of the slope of the absorption edge. The parameter r is described by the equation:
rðTÞ ¼ r0 f½ð2kTÞ=ðhxÞth½ðhxÞ=ð2kTÞg:
ð2Þ
The localized exciton states manifest at the absorption edge of the eulitines because of the strong exciton–phonon interaction there (the phonons with the energy hxeff ¼ 0042 eV are most effective) [9]. The parameter r/kT consists information about the interaction between the excitons and LO phonons [10]. In the general case, r is the linear function of the impurity concentration. The value of r can increase or decrease depending on the direction of the shifting of the absorption maximum with the concentration [10]. The exciton–phonon interaction has a big value when r0 < 1 [10]. When the symmetry of the crystal field is lower, then r0 is smaller [10]. The formation of the exciton states is realized by trapping of the excitons of the local lattice deformations [11]. The exponential shape of the absorption edge is connected with the explanation that the electrons move themselves from the valence band to the free impurity states. This situation can be observed when the electrons of the valence band or these electrons of the impurity levels interact with the mono-energetic phonons [10]. Thus the exponential shape of the edge of the impurity bands can be explained by the effect of the phonons on the process of the absorption in the crystals. The electrons from the Valence band (VB) pass into the Conduction band (CB) after the illumination with the UV light (Fig. 1a). After that, the impurity levels in the Forbidden band (FB) act as electron traps. Thus, the electron, caught by the impurity level and its corresponding hole in VB, create together the exciton, associated with the
ionized donors Mn2+, Fe3+ or Ru4+. The captured electrons pass into CB after their interaction with the phonons and, in the end, they return into the VB. The excitons, associated with the ionized donors, destruct after the annealing (Fig. 1b). The Urbach’s rule region of BGO is compared with the same region of the illuminated and the annealed doped BGO on Figs. 2 and 3. It is seen that Fe3+ ions enlarge the Urbach’s rule region of the doped BGO in the illuminated and the annealed state (Fig. 2a). Mn2+ and Ru4+ ions shrink this region in the illuminated state and these ions enlarge Urbach’s rule region in the annealed state (Fig. 2b and c). Fe3+ ions have the bigger contribution in both states of BGO:Mn + Fe (Fig. 3a). This fact is confirmed in the work of Marinova et al., where the authors have been investigated the photochromic effect of these crystals [3]. The Urbach’s rule region shrinks in the case of the illuminated and the annealed BGO:Mn + Ru (Fig. 3b). The Urbach’s energy is connected with the carrier impurity interaction, the carrier–phonon interaction and the structural disorder [12]. That is why this energy is calculated by the formula:
Eu ¼ aðEÞ=ðda=dEÞ:
(a)
4.5
y = 3.1502x - 8.7585 R2 = 0.9976 BGO:Fe illuminated
4 3.5 3 2.5 2
y = 3.6092x - 10.576 R 2 = 0.9995 BGO:Fe annealed
1.5 1 0 3.5
3.6
3.7
3.8
3.9
4
4.1
E [eV]
(b)
3.5
y = 2.584x - 7.2348 R 2 = 0.9972 BGO:Mn illuminated
2.5
Conduction band
2
lnα
Impurity level
y = 4.3031x - 16.043 R2 = 0.9999 BGO
0.5
3
(a)
ð3Þ
The Eu is a constant for BGO in the spectral region 3.6–4 eV. The values of the Urbach’s energy of the illuminated and the annealed BGO:Fe are bigger than the Eu of the BGO (Fig. 4a). In comparison with the BGO, the Urbach’s energy has bigger values for BGO:Mn and BGO:Ru in illuminated state and this energy has smaller values for these crystals in annealed state (Fig. 4b and c). The Fe3+ ions
lnα
266
y = 6.5911x - 23.902 R2 = 0.9991 BGO:Mn annealed
1.5 1
y = 4.3031x - 16.043 R2 = 0.9999 BGO
0.5 0 3.5
3.6
3.7
3.8
3.9
4
4.1
E [eV]
Valence band
(c)
4 y = 3.7558x - 11.418 R 2 = 0.9974 BGO:Ru illuminated
3.5
Conduction band Phonon Impurity level
3 2.5
lnα
(b)
y = 4.3031x - 16.043 R 2 = 0.9999 BGO
2 y = 7.3534x - 26.594 R 2 = 0.9978 BGO:Ru annealed
1.5 1 0.5
Valence band
0 3.5
3.6
3.7
3.8
3.9
4
E [eV] Fig. 1. The model of exciton associated with the ionized donor in doped BGO: (a) after illumination; (b) after annealing.
Fig. 2. The Urbach’s rule of doped Bi4Ge3O12 in illuminated state.
4.1
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P. Petkova / Optical Materials 34 (2011) 265–268
(a)
4.5 4 3.5
y = 3.4736x - 9.9161 R2 = 0.9981 BGO:Mn+Fe illuminated
lnα
3 2.5 2
y = 4.3031x - 16.043 R2 = 0.9999 BGO
y = 4.2617x - 13.142 R2 = 0.9998 BGO:Mn+Fe annealed
1.5 1
0.4
Urbach's energy [eV]
(a)
0.5
BGO:Fe illuminated
0.35
BGO:Fe annealed
0.3 0.25 0.2
BGO
0.15 3.5
0 3.5
3.6
3.7
3.8
3.9
4
3.6
3.7
3.8
4.1
3.9
4
4.1
E [eV]
E [eV] 4 3.5
(b) y = 2.3121x - 5.6515 R 2 = 0.9978 BGO:Mn+Ru illuminated
3
lnα
2.5 y = 2.7779x - 7.7794 R2 = 0.9971 BGO:Mn+Ru annealed
2 1.5
y = 4.3031x - 16.043 R2 = 0.9999 BGO
0.5
Urbach's energy [eV]
(b)
1
BGO:Mn illuminated
0.4 0.3
BGO
0.2
BGO:Mn annealed
0.1 0 3.6
3.7
3.8
0.5 3.7
3.75
3.8
3.85
3.9
3.95
4
4
4.1
4.05
(c)
E [eV] Fig. 3. The Urbach’s rule of annealed doped Bi4Ge3O12 in annealed state.
have the predominant influence in the Eu for illuminated and annealed BGO:Mn + Fe (Fig. 5a). The values of Urbach’s energy for BGO:Mn + Ru are bigger in comparison with this constant energy for BGO (Fig. 5b). The ionic radius of Mn2+ is 0.67 in the low spin complexes and its ionic radius is 0.83 in the high spin complexes. Ru4+ ion has an ionic radius 0.62 and Bi3+ has an ionic radius 1.03. Thus the incorporation of the manganese and ruthenium in the bismuth sites leads to a shrinkage of the oxygen octahedrons in Urbach’s rule region. The ionic radius of Fe3+ is 0.635 and this radius of Ge4+ ion is 0.39. Therefore the substitution of the germanium ions with the iron ions leads to an enlargement of the oxygen tetrahedrons in the spectral region 3.6–4.05 eV. Our observation is that the octahedrons and tetrahedrons in the doped Bi4Ge3O12 are strong deformed because of the values of r0 (see Table 1). These two structures are the most deformed in BGO:Mn + Ru. This deformation decreases for the doped crystals in the following sequence: BGO:Mn + Fe, BGO:Mn, BGO:Fe and BGO:Ru. When the exciton–phonon interaction has to be determined, it is important to examine 1s exciton. In this case, we can calculate the exciton–phonon interaction constant g by the following formula g ¼ ð2=3Þr1 0 . The exciton–phonon coupling constant g is very big for BGO:Mn and it is the smallest for BGO:Ru in the illuminated state (Table 2). This constant has the biggest value for the illuminated BGO:Mn + Ru which means that Mn2+ impurity has a dominant influence in the double doped BGO. This predominant role is assigned to the impurity of Fe3+ in the case of the annealed BGO:Mn + Fe. The value of g is in the same range for Fe, Mn and Ru doped BGO in the annealed state. This value is bigger for the Table 1 The values of r and r0 for doped BGO samples in illuminated and annealed state. Sample Bi4Ge3O12:Fe Bi4Ge3O12:Mn Bi4Ge3O12:Ru Bi4Ge3O12:Mn + Fe Bi4Ge3O12:Mn + Ru
r
r
r0
r0
illuminated
annealed
illuminated
annealed
0.08 0.07 0.1 0.09 0.06
0.09 0.17 0.19 0.11 0.07
0.1 0.08 0.12 0.11 0.07
0.2 0.18 0.20 0.12 0.07
0.35
Urbach's energy [eV]
3.65
BGO:Ru illuminated
0.3
BGO
0.25 0.2 0.15 0.1
BGO:Ru annealed
0.05 0 3.65
3.7
3.75
3.8
3.85
3.9
3.95
4
4.05
E [eV] Fig. 4. The Urbach’s energy of single doped Bi4Ge3O12 in illuminated and annealed state.
(a) Urbach's energy [eV]
3.6
0.33
BGO:Mn+Fe illuminated
0.31 0.29 0.27 0.25
BGO:Mn+Fe annealed
0.23
BGO
0.21 0.19 3.5
3.6
3.7
3.8
3.9
4
4.1
E [eV]
(b) Urbach's energy [eV]
0 3.55
3.9
E [eV]
0.7
BGO:Mn+Ru illuminated
0.6
BGO:Mn+Ru annealed
0.5 0.4 0.3
BGO
0.2 0.1 3.7
3.75
3.8
3.85
3.9
3.95
4
4.05
E [eV] Fig. 5. The Urbach’s energy of double doped Bi4Ge3O12 in illuminated and annealed state.
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P. Petkova / Optical Materials 34 (2011) 265–268
Table 2 The values of g, ra and Wd for doped BGO samples at room temperature T = 300 K. Sample
g illuminated
Bi4Ge3O12:Fe Bi4Ge3O12:Mn Bi4Ge3O12:Ru Bi4Ge3O12:Mn + Fe Bi4Ge3O12:Mn + Ru
6.67 8.33 5.56 6.06 9.52
g annealed 3.33 3.7 3.33 5.56 9.52
ra (cm2) illuminated 19
17.56 10 21.32 1020 18.56 1020 7.18 1019 4.37 1019
annealed BGO:Mn + Fe and it is the biggest for BGO:Mn + Ru in the annealed state. Next step in the calculations is the determination of the crosssection of the impurity absorption [13]. It is very important to establish how the radiation is absorbed by the impurity ions in the crystals. The total cross-section ra of the impurity absorption is defined by the integration within the absorption band of the impurity ions (see the Eq. (3)).
ra ¼ ð1=NÞ
Z
aðkÞdk;
ð3Þ
where N is the number of the impurity ions in the unit volume, a is the impurity absorption coefficient typical of an energetic interval from E1 to E2. For the investigated crystals here E1 = 3.6 eV and E2 = 4.05 eV. The cross-section ra can vary significantly from one absorption band to another. The value of ra is smaller for the crystal BGO:Mn and BGO:Ru in the illuminated and the annealed state. It is bigger for BGO:Fe in these two states (Table 2). The values of ra for Fe3+, Mn2+ and Ru4+ ions confirm the fact that Bi octahedrons are shrinked and Ge tetrahedrons are enlarged. The broadening of the absorption edge is clearly observed demonstrating the dynamic disorder at the room temperature [14]. The formula Wd = kT/r describes this broadening. For Mn doped eulitine, Wd has the biggest value and its value is the smallest for BGO:Ru in the illuminated state (Table 2). The value of this parameter is in the middle in the case of the illuminated BGO:Fe. That is why the interaction between the excitons and LO phonons is the strongest for BGO:Ru in the illuminated state. This interaction is guided by Mn2+ for the illuminated BGO:Mn + Ru and it is guided by Fe3+ for the illuminated BGO:Mn + Fe. The broadening of the absorption edge is the biggest for BGO:Fe and it is the smallest for BGO:Ru when the crystals are annealed. The double doping leads to an increasing of this broadening in the case of the annealed samples.
ra (cm2) annealed 19
16.68 10 16.36 1020 17.17 1020 5.94 1019 3.41 1019
Wd (meV) illuminated
Wd (meV) annealed
324 370 259 288 432
288 152 136 235 370
4. Conclusions (1) The very small values of r0 give information that octahedrons and tetrahedrons in the crystal lattice of the doped eulitines are strong deformed. (2) The calculation of the cross-section ra is the proof that Fe3+ ions enlarge Ge tetrahedrons and Mn2+, Ru4+ shrink Bi octahedrons. (3) The interaction between the excitons and LO phonons is strongest for BGO:Ru in the illuminated state. (4) The exciton–phonon coupling constant g is the biggest for BGO:Mn in the illuminated and the annealed state.
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