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Cross relaxation mechanism among Tm3+ ions in Ge30Ga2As6S62 glass
Journal of Non-Crystalline Solids 316 (2003) 302–308 www.elsevier.com/locate/jnoncrysol
Cross relaxation mechanism among Tm3þ ions in Ge30Ga2As6S62 glass Yong Seop Han a, Jong Heo a
a,*
, Yong Beom Shin
b
Photonic Glasses Laboratory, Department of Materials Science and Engineering, Pohang University of Science and Technology, San 31, Hyoja-dong, Nam-gu, Pohang, Kyungbuk 790-784, South Korea b Telecommunication Basic Research Laboratory, Electronics and Telecommunications Research Institute, 161 Kajong-dong, Yusong-gu, Taejun 305-350, South Korea Received 11 September 2001; received in revised form 8 May 2002
Abstract Cross relaxation among Tm3þ ions in Ge30 Ga2 As6 S62 glass, where an ion excited to the 3 H4 level transfers part of its energy to a nearby ion in the ground state 3 H6 (3 H4 , 3 H6 ! 3 F4 , 3 F4 ), was investigated in the temperature range of 20– 300 K. The relative intensity ratio of the 1.48 lm emission to 1.84 lm increased with decreasing temperature. At the same time, the lifetime of the 3 H4 level increased. Analysis of decay curves of the 1.48 lm emission suggested that cross relaxation was assisted by phonons of 390 cm1 in frequency. These phonons are generated from the asymmetrical stretching vibration of GeS4 tetrahedra. Critical distance for cross relaxation decreased from 0.73 to 0.58 nm as the temperature decreased. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 42.70.Ce; 42.70.Hj; 42.60.Da
1. Introduction Glasses and crystals doped with Tm3þ have been investigated to develop lasers and fiber-optic amplifiers. Potential areas of application include amplifiers for 1.45–1.50 lm communication window, pumping lasers for GeO2 /SiO2 Raman amplifiers, and lasers for optical reading and sensing. Both pulsed and CW lasing operations at 0.82, 1.48, 1.9 and 2.3 lm in wavelength have been re-
*
Corresponding author. Tel.: +82-54 279 2147; fax: +82-54 279 5872. E-mail address: [email protected] (J. Heo).
ported using fluoride or silica glass fibers doped with Tm3þ [1–5]. Fluorescence centered at 1.48 lm originates from the 3 H4 ! 3 F4 transition in Tm3þ [2–6]. However, this transition suffers from cross relaxation among Tm3þ ions. During this energy transfer, an ion excited to the 3 H4 level transfers part of its energy to a nearby ion in the ground state 3 H6 . Consequently, both ions end up residing at the 3 F4 level (3 H4 , 3 H6 ! 3 F4 , 3 F4 ). This results in an increase of the 3 F4 level population and therefore, hampers the population inversion between the 3 H4 and 3 F4 levels. Several methods such as co-lasing with a 1.9 lm laser [2,4], upconversion pumping at 1064 nm [3,5], and co-doping with Tb3þ or Ho3þ
0022-3093/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 1 6 3 9 - 3
Y.S. Han et al. / Journal of Non-Crystalline Solids 316 (2003) 302–308
Fig. 1. Energy difference between 3 H6 ! 3 F4 absorption and 3 H4 ! 3 F4 emission in Tm3þ (0.2 mol%) doped Ge30 Ga2 As6 S62 glass.
ions [7–9] have been suggested to circumvent the difficulty. This paper reports the detailed analysis on the mechanism of cross relaxation phenomena in Tm3þ . There is little spectral overlap between emission from the 3 H4 ! 3 F4 transition and absorption of the 3 H6 ! 3 F4 transition (Fig. 1). In fact, the amount of energy being released by the emission is larger than that necessary for the absorption. It suggests that this cross relaxation releases additional energy, which is most probably converted to the lattice vibration [10]. Since lattice vibration depends on the temperature, it was possible to investigate the mechanism and rates of cross relaxation by carefully controlling the temperature between 20 and 300 K. When Tm3þ ions are doped into glasses with high phonon energy, they can experience several non-radiative transitions including multiphonon relaxation and cross relaxation. However, since sulfide glasses have low phonon energy of 350 cm1 [11,12], effect of multiphonon relaxation from the 3 H4 level can be minimized. Therefore, the cross relaxation phenomena (3 H4 , 3 H6 ! 3 F4 , 3 F4 ) can be investigated without being affected by other energy transfer phenomena.
2. Experimental procedures Composition of the host glass was Ge30 Ga2 As6 S62 in atomic percentage. It is well known that this glass has high rare-earth solubility and a good
303
glass-forming tendency [9,13]. Previous work indicated that cross relaxation can occur in sulfide glasses when the concentration of Tm3þ exceeded 0.3 wt% (0.08 mol%) [9]. Therefore, the concentration of Tm3þ ions was fixed at 0.2 mol% so that an appreciable amount of cross relaxation can occur at room temperature. Glass samples were prepared using fused silica ampoules as crucibles and starting powders were melted at 950 °C for 24 h in a rocking furnace. After melting, ampoules containing the melts were removed from the furnace and quenched in water. Glasses were then annealed at around glass transition temperature (400 °C) for 2 h [9,13]. Specimens were cut into discs and optically polished for measurements. Absorption spectra were recorded using an ultraviolet/visible/near infrared spectrophotometer. Emission spectra were measured by exciting Tm3þ to 3 H4 level using 802 nm excitation from a tunable Ti-sapphire laser. An InSb detector cooled with liquid nitrogen was used to measure fluorescence intensities. Lifetimes were measured from the first e-folding time of the emission intensity using a chopper, a digitizing oscilloscope, and an InGaAs PIN detector. For the low-temperature measurements, a cryostat was used to cool the specimens to temperatures as low as 20 K. Raman spectra were recorded using the NRS-2100 (JASCO, Japan) spectrometer. The 514.5 nm line of an Arþ laser was used in combination with a triple monochromator.
3. Results Fig. 1 shows the room temperature absorption and emission spectra of Ge30 Ga2 As6 S62 glass doped with 0.2 mol% of Tm3þ . Emission centered at 1480 nm is from the 3 H4 !3 F4 transition. It has little spectral overlap with the absorption band at 1750 nm from the 3 H6 ! 3 F4 transition. The energy mismatch between the peak frequencies of these two bands is approximately 800 cm1 . Therefore, the 3 H4 , 3 H6 ! 3 F4 , 3 F4 cross relaxation needs an assistance from the phonon vibration of the host glass. The relative intensity ratios of the 1.48 lm emission to 1.84 lm emissions were calculated from the
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creased as temperature decreased to 20 K. This result also supported the idea that cross relaxation process is strongly related to temperature.
4. Discussion
Fig. 2. Temperature dependence of relative intensities of 1.48 lm emission to 1.84 lm emission in Ge30 Ga2 As6 S62 glass doped with 0.2 mol% Tm3þ . Line was drawn as a guide to eyes.
emission spectra recorded in the temperature range of 20–300 K. Previous works [9,10] have shown that this intensity ratio increased as the magnitude of the cross relaxation decreased. As shown in Fig. 2, these relative intensity ratios increased as the temperature of the measurement decreased from 300 to 100 K. It suggests that cross relaxation became less effective at low temperatures. However, when temperature decreased below 100 K, these intensity ratios started to decrease. Reasons for this unexpected temperature dependence will be discussed in Section 4. Fig. 3 shows that the measured lifetimes of the 3 H4 level in Tm3þ in-
Fig. 3. Temperature dependence of the measured lifetimes of the Tm3þ :3 H4 level in Ge30 Ga2 As6 S62 glass. Line was drawn as a guide to eyes.
It has been proposed that the cross relaxation between two Tm3þ ions, 3 H4 , 3 H6 ! 3 F4 , 3 F4 , is a phonon-assisted energy transfer process [10]. Phonons are defined as the energy quanta of crystalline vibrational modes. The average number of phonons (nm ) in mode m at temperature T is given by the Bose–Einstein factor: nm ¼
1 ; expðhxm =kT Þ 1
ð1Þ
where hxm is the energy of a phonon in mode m. k is the BoltzmannÕs constant. Eq. (1) indicates that the number of phonons should decrease with a decrease in temperature. Therefore, the cross relaxation in Tm3þ , if it is an energy transfer process assisted by phonons, is expected to decrease at low temperatures. Results of the present study supported the hypothesis that cross relaxation in Tm3þ is a phonon-assisted energy transfer. The intensity of the 1.48 lm emission increased relative to 1.84 lm emission as temperature decreased (Fig. 2). At the same time, lifetimes of the 3 H4 level increased (Fig. 3). However, these relative intensity ratios did not increase further when temperature decreased below 100 K. Reasons for this unexpected decrease are not clear at present. It is probably due to changes in the cross sections of ground-state absorption (GSA) and excited-state absorption (ESA). Specifically, 1.84 lm emission from the 3 F4 ! 3 H6 transition is partially absorbed by the GSA of 3 H6 ! 3 F4 . Likewise, 1.48 lm emission due to the 3 H4 ! 3 F4 transition is also absorbed by the ESA of the 3 F4 ! 3 H4 . The magnitude of the reabsorption is determined by the extent of the overlapping between the respective absorption and emission spectra. As temperature drops, however, the population of the lower-lying energy levels increases relative to those of the upper energy levels within each manifold. Hence, both the longwavelength absorption tail and short-wavelength
Y.S. Han et al. / Journal of Non-Crystalline Solids 316 (2003) 302–308
emission tail decrease in intensity [14]. It generally leads to a decrease in the magnitude of re-absorption. This effect is more pronounced for the 3 F4 ! 3 H6 emission (1.84 lm) than for the 3 H4 ! 3 F4 emission (1.48 lm) since the 3 H6 manifold experiences a broader splitting [15]. Therefore, at low temperatures, the amount of re-absorption of 1.84 lm emission decreases rapidly and as a result, the relative intensity ratios of I1:48 =I1:84 decrease. Rates of the cross relaxation were calculated from the measured and radiative lifetimes of the 3 H4 level. When the concentration of a dopant ion is high, the transition probability from a certain energy level other than the ground state can be expressed as follows [6]: 1 smeas
¼
1 srad
þ WMPR þ WET ;
ð2Þ
where smeas is the measured lifetime and srad is the radiative lifetime calculated from Judd–Ofelt analysis. WMPR and WET represent multiphonon relaxation and energy transfer rates, respectively. The energy gap between the 3 H4 and 3 H5 levels is approximately 4300 cm1 and the energy of the highest phonon in sulfide glasses is around 400 cm1 [10]. Therefore, multiphonon relaxation rates should be small and can be ignored in the present case. Then, energy transfer rates (i.e. cross relaxation rates) can be calculated from the following relationship: WET ¼
1 1 : smeas srad
ð3Þ
Fig. 4. Temperature dependence of cross relaxation rates (3 H4 , 3 H6 ! 3 F4 , 3 F4 ) in Ge30 Ga2 As6 S62 glass doped with Tm3þ ions. The solid line is the result of fitting from Eq. (4) by assuming 2-phonons of the 390 cm1 in energy.
where DE is the difference between the energies of the donor and acceptor levels. Raman spectrum of the Ge30 Ga2 As6 S62 glass in Fig. 5 showed two major bands at 338 and 232 cm1 . The band at 338 cm1 is mainly due to the symmetric stretching of GeS4 [17,18] and AsS3 pyramids [19]. The shoulders extending from 370 to 430 cm1 is related to several structural features including m3 -asymmetric stretching vibration mode of GeS4 tetrahedra (390 cm1 ) and S3 Ge–S–GeS3 vibrations (425 cm1 ) [17]. A broad band at 232 cm1 is associated with the formation of metal– metal bonds, such as As–As (231 cm1 ) and Ge– Ge (250 cm1 ) [18,20]. Numerical fitting of the
From the calculated lifetime of srad ¼ 230 ls [9] and the lifetimes measured at various temperatures, the effect of temperature on the energy transfer rates were calculated as shown in Fig. 4. When phonons of only one vibrational mode are involved in the phonon-assisted process, the temperature dependence of the energy transfer rate is expressed by [16] W ðT Þ ¼ W ð0Þð1 expð hx=kT ÞÞN :
ð4Þ
N represents the number of phonons participating in the energy transfer processes, and can be expressed as N ¼ DE= hx;
ð5Þ
305
Fig. 5. Raman spectrum of Ge30 Ga2 As6 S62 glass.
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measured energy transfer rates using Eq. (4) was most successful when one assumes that two phonons with an energy of 390 cm1 are involved in the energy transfer process (Fig. 4). Therefore, it was concluded that m3 -asymmetric stretching vibration mode of GeS4 tetrahedra is the major phonon contributing the 3 H4 , 3 H6 ! 3 F4 , 3 F4 cross relaxation process. Energy transfer processes are generally described in terms of three limiting cases; direct relaxation, fast diffusion, and diffusion-limited relaxation [21]. Fast diffusion is characterized by a simple exponential behavior in the fluorescence decay curve. However, decay curves in Fig. 6 did not show a simple exponential behavior. An overall de-excitation probability N ðtÞ of the donor fluorescence with time t is expressed as follows: N ðtÞ ¼ expfWo t PðtÞg;
ð6Þ
where Wo is a reciprocal of lifetime when no energy acceptor is present. PðtÞ is a magnitude of the departure from the intrinsic exponential behavior due to the energy transfer, and is proportional to t3=s , where s can be either 6, 8, or 10 depending upon the electric multipole character of the interaction [22]. The exponent can be revealed from a slope in the plot of lnf ln N ðtÞ Wo tg vs. lnðtÞ. The slopes were 0.71 and 0.75 at 20 and 280 K, respectively (Fig. 7). They correspond to the case where s ¼ 6 and suggest that a considerable
Fig. 7. Dependence of PðtÞ on lnðtÞ at (a) 20 K and (b) 280 K, respectively. Solid lines are the least-squares fit to the data.
amount of diffusion among Tm3þ ions occur. In the present case, when only one type of active ions is present, neighboring ions around the excited ions can act either as acceptors or as ions for energy migration. Hence, cross relaxation among Tm3þ ions can be described as a specific example of diffusion-limited relaxation. Therefore, the decay behavior is better described by the following equation derived by Yokota and Tanimoto [23]: ( 4 N ðtÞ ¼ exp Wo t p3=2 na C 1=2 t1=2 3 3=4 ) 1 þ 10:87x þ 15:50x2
; ð7Þ 1 þ 8:743x Fig. 6. Decay curves of 1.48 lm emission in Ge30 Ga2 As6 S62 glass doped with 0.2 mol% of Tm3þ .
where na is the concentration of acceptor ions, x ¼ DC 1=3 t2=3 . C is an interaction parameter and
Y.S. Han et al. / Journal of Non-Crystalline Solids 316 (2003) 302–308
307
phonon-assisted energy transfer process. As temperature decreased from room temperature to 100 K, the relative intensity ratios between the 1.48 and 1.84 lm emission increased together with an increase in the fluorescence lifetimes of the 3 H4 level. Fitting of the decay curves of the 1.48 lm emission with the theoretical expression was most successful when two phonons of the m3 -asymmetric stretching vibration mode of GeS4 tetrahedra (390 cm1 ) were assumed to control energy transfer. Critical distance for cross relaxation decreased from 0.73 to 0.58 nm with a decrease in temperature. Fig. 8. Temperature dependence of the calculated critical distances in Tm3þ -doped Ge30 Ga2 As6 S62 glass. Line was drawn as a guide to the eye.
D is a diffusion coefficient for the energy migration among donors. First, C values in a temperature interval of 20–300 K were obtained by fitting Eq. (7) to the measured decay curves of the 1.48 lm emission. Using these C values, the critical distance Ro , i.e. the distance at which the probability of energy transfer becomes equal to the intrinsic decay rate, was calculated at each temperature using the following relationship [23]: R6o ¼
C : Wo
ð8Þ
The critical distance does not indicate the actual distance between the ions, but expresses the extent to which the energy transfer can occur between them. An ion can easily transfer its energy to another ion located within the critical distance, but cannot transfer to another ion beyond the critical distance. Therefore, the longer the critical distance becomes, the more actively the energy transfer can occur. In Fig. 8, the critical distance decreased from 0.73 nm to as low as 0.58 nm as temperature decreased from 300 to 20 K. This again supported the results that the extent of cross relaxation among Tm3þ ions reduced as temperature decreased.
5. Conclusions
3
Cross relaxation among Tm3þ ions (3 H4 , 3 H6 ! F4 , 3 F4 ) in Ge30 Ga2 As6 S62 glass was identified as a
Acknowledgements This work was supported by a Korea Research Foundation Grant (KRF-2000-041-E00557).
References [1] R. Allen, L. Esterowitz, Appl. Phys. Lett. 55 (8) (1989) 721. [2] J.Y. Allain, M. Monerie, H. Poignant, Electron. Lett. 25 (24) (1989) 1660. [3] T. Komukai, T. Yamamoto, T. Sugawa, Y. Miyajima, Electron. Lett. 28 (9) (1992) 830. [4] R.M. Percival, D. Szebesta, S.T. Davey, Electron. Lett. 28 (20) (1992) 1866. [5] T. Komukai, T. Yamamoto, T. Sugawa, Y. Miyajima, IEEE J. Quant. Electron. 31 (11) (1995) 1880. [6] J. Sanz, R. Cases, R. Alcala, J. Non-Cryst. Solids 93 (1987) 377. [7] R.M. Percival, D. Szebesta, S.T. Davey, Electron. Lett. 29 (12) (1993) 1054. [8] T. Sakamoto, M. Shimizu, T. Kanamori, Y. Terunuma, Y. Ohishi, M. Yamada, S. Sudo, IEEE Photon. Tech. Lett. 7 (9) (1995) 983. [9] Y.B. Shin, J.H. Kim, Y.S. Kim, J. Heo, J. Appl. Phys. 88 (5) (2000) 2515. [10] Y.B. Shin, W.Y. Cho, J. Heo, J. Non-Cryst. Solids 208 (1996) 29. [11] Y.B. Shin, J. Heo, H.S. Kim, Chem. Phys. Lett. 317 (2000) 637. [12] A.R. Hilton, J. Non-Cryst. Solids 2 (1970) 28. [13] Y.G. Choi, K.H. Kim, B.J. Lee, Y.B. Shin, Y.S. Kim, J. Heo, J. Non-Cryst. Solids 278 (2000) 137. [14] M.T. Murtagh, G.H. Sigel Jr., J.C. Fajardo, B.C. Edwards, R.I. Epstein, J. Non-Cryst. Solids 256&257 (1999) 207. [15] B. Henderson, G.F. Imbusch, Optical Spectroscopy of Inorganic Solids, Oxford University, New York, 1989. [16] T. Miyakawa, D.L. Dexter, Phys. Rev. B 1 (1970) 2961.
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[17] G. Lucovsky, J.P. deNeufville, F.L. Galeener, Phys. Rev. B 9 (4) (1974) 1591. [18] G. Lucovsky, F.L. Galeener, R.C. Keezer, R.H. Geils, H.A. Six, Phy. Rev. B 10 (12) (1974) 5134. [19] B.G. Aitken, C.W. Ponader, J. Non-Cryst. Solids 256&257 (1999) 143.
[20] P.J.S. Ewen, A.E. Owen, J. Non-Cryst. Solids 35&36 (1980) 1191. [21] M.J. Weber, Phys. Rev. B 4 (9) (1971) 2932. [22] D.L. Dexter, J. Chem. Phys. 21 (1953) 836. [23] M. Yokota, O. Tanimoto, J. Phys. Soc. Jpn. 22 (1967) 779.
Cross relaxation mechanism among Tm3þ ions in Ge30Ga2As6S62 glass Yong Seop Han a, Jong Heo a
a,*
, Yong Beom Shin
b
Photonic Glasses Laboratory, Department of Materials Science and Engineering, Pohang University of Science and Technology, San 31, Hyoja-dong, Nam-gu, Pohang, Kyungbuk 790-784, South Korea b Telecommunication Basic Research Laboratory, Electronics and Telecommunications Research Institute, 161 Kajong-dong, Yusong-gu, Taejun 305-350, South Korea Received 11 September 2001; received in revised form 8 May 2002
Abstract Cross relaxation among Tm3þ ions in Ge30 Ga2 As6 S62 glass, where an ion excited to the 3 H4 level transfers part of its energy to a nearby ion in the ground state 3 H6 (3 H4 , 3 H6 ! 3 F4 , 3 F4 ), was investigated in the temperature range of 20– 300 K. The relative intensity ratio of the 1.48 lm emission to 1.84 lm increased with decreasing temperature. At the same time, the lifetime of the 3 H4 level increased. Analysis of decay curves of the 1.48 lm emission suggested that cross relaxation was assisted by phonons of 390 cm1 in frequency. These phonons are generated from the asymmetrical stretching vibration of GeS4 tetrahedra. Critical distance for cross relaxation decreased from 0.73 to 0.58 nm as the temperature decreased. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 42.70.Ce; 42.70.Hj; 42.60.Da
1. Introduction Glasses and crystals doped with Tm3þ have been investigated to develop lasers and fiber-optic amplifiers. Potential areas of application include amplifiers for 1.45–1.50 lm communication window, pumping lasers for GeO2 /SiO2 Raman amplifiers, and lasers for optical reading and sensing. Both pulsed and CW lasing operations at 0.82, 1.48, 1.9 and 2.3 lm in wavelength have been re-
*
Corresponding author. Tel.: +82-54 279 2147; fax: +82-54 279 5872. E-mail address: [email protected] (J. Heo).
ported using fluoride or silica glass fibers doped with Tm3þ [1–5]. Fluorescence centered at 1.48 lm originates from the 3 H4 ! 3 F4 transition in Tm3þ [2–6]. However, this transition suffers from cross relaxation among Tm3þ ions. During this energy transfer, an ion excited to the 3 H4 level transfers part of its energy to a nearby ion in the ground state 3 H6 . Consequently, both ions end up residing at the 3 F4 level (3 H4 , 3 H6 ! 3 F4 , 3 F4 ). This results in an increase of the 3 F4 level population and therefore, hampers the population inversion between the 3 H4 and 3 F4 levels. Several methods such as co-lasing with a 1.9 lm laser [2,4], upconversion pumping at 1064 nm [3,5], and co-doping with Tb3þ or Ho3þ
0022-3093/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 1 6 3 9 - 3
Y.S. Han et al. / Journal of Non-Crystalline Solids 316 (2003) 302–308
Fig. 1. Energy difference between 3 H6 ! 3 F4 absorption and 3 H4 ! 3 F4 emission in Tm3þ (0.2 mol%) doped Ge30 Ga2 As6 S62 glass.
ions [7–9] have been suggested to circumvent the difficulty. This paper reports the detailed analysis on the mechanism of cross relaxation phenomena in Tm3þ . There is little spectral overlap between emission from the 3 H4 ! 3 F4 transition and absorption of the 3 H6 ! 3 F4 transition (Fig. 1). In fact, the amount of energy being released by the emission is larger than that necessary for the absorption. It suggests that this cross relaxation releases additional energy, which is most probably converted to the lattice vibration [10]. Since lattice vibration depends on the temperature, it was possible to investigate the mechanism and rates of cross relaxation by carefully controlling the temperature between 20 and 300 K. When Tm3þ ions are doped into glasses with high phonon energy, they can experience several non-radiative transitions including multiphonon relaxation and cross relaxation. However, since sulfide glasses have low phonon energy of 350 cm1 [11,12], effect of multiphonon relaxation from the 3 H4 level can be minimized. Therefore, the cross relaxation phenomena (3 H4 , 3 H6 ! 3 F4 , 3 F4 ) can be investigated without being affected by other energy transfer phenomena.
2. Experimental procedures Composition of the host glass was Ge30 Ga2 As6 S62 in atomic percentage. It is well known that this glass has high rare-earth solubility and a good
303
glass-forming tendency [9,13]. Previous work indicated that cross relaxation can occur in sulfide glasses when the concentration of Tm3þ exceeded 0.3 wt% (0.08 mol%) [9]. Therefore, the concentration of Tm3þ ions was fixed at 0.2 mol% so that an appreciable amount of cross relaxation can occur at room temperature. Glass samples were prepared using fused silica ampoules as crucibles and starting powders were melted at 950 °C for 24 h in a rocking furnace. After melting, ampoules containing the melts were removed from the furnace and quenched in water. Glasses were then annealed at around glass transition temperature (400 °C) for 2 h [9,13]. Specimens were cut into discs and optically polished for measurements. Absorption spectra were recorded using an ultraviolet/visible/near infrared spectrophotometer. Emission spectra were measured by exciting Tm3þ to 3 H4 level using 802 nm excitation from a tunable Ti-sapphire laser. An InSb detector cooled with liquid nitrogen was used to measure fluorescence intensities. Lifetimes were measured from the first e-folding time of the emission intensity using a chopper, a digitizing oscilloscope, and an InGaAs PIN detector. For the low-temperature measurements, a cryostat was used to cool the specimens to temperatures as low as 20 K. Raman spectra were recorded using the NRS-2100 (JASCO, Japan) spectrometer. The 514.5 nm line of an Arþ laser was used in combination with a triple monochromator.
3. Results Fig. 1 shows the room temperature absorption and emission spectra of Ge30 Ga2 As6 S62 glass doped with 0.2 mol% of Tm3þ . Emission centered at 1480 nm is from the 3 H4 !3 F4 transition. It has little spectral overlap with the absorption band at 1750 nm from the 3 H6 ! 3 F4 transition. The energy mismatch between the peak frequencies of these two bands is approximately 800 cm1 . Therefore, the 3 H4 , 3 H6 ! 3 F4 , 3 F4 cross relaxation needs an assistance from the phonon vibration of the host glass. The relative intensity ratios of the 1.48 lm emission to 1.84 lm emissions were calculated from the
304
Y.S. Han et al. / Journal of Non-Crystalline Solids 316 (2003) 302–308
creased as temperature decreased to 20 K. This result also supported the idea that cross relaxation process is strongly related to temperature.
4. Discussion
Fig. 2. Temperature dependence of relative intensities of 1.48 lm emission to 1.84 lm emission in Ge30 Ga2 As6 S62 glass doped with 0.2 mol% Tm3þ . Line was drawn as a guide to eyes.
emission spectra recorded in the temperature range of 20–300 K. Previous works [9,10] have shown that this intensity ratio increased as the magnitude of the cross relaxation decreased. As shown in Fig. 2, these relative intensity ratios increased as the temperature of the measurement decreased from 300 to 100 K. It suggests that cross relaxation became less effective at low temperatures. However, when temperature decreased below 100 K, these intensity ratios started to decrease. Reasons for this unexpected temperature dependence will be discussed in Section 4. Fig. 3 shows that the measured lifetimes of the 3 H4 level in Tm3þ in-
Fig. 3. Temperature dependence of the measured lifetimes of the Tm3þ :3 H4 level in Ge30 Ga2 As6 S62 glass. Line was drawn as a guide to eyes.
It has been proposed that the cross relaxation between two Tm3þ ions, 3 H4 , 3 H6 ! 3 F4 , 3 F4 , is a phonon-assisted energy transfer process [10]. Phonons are defined as the energy quanta of crystalline vibrational modes. The average number of phonons (nm ) in mode m at temperature T is given by the Bose–Einstein factor: nm ¼
1 ; expðhxm =kT Þ 1
ð1Þ
where hxm is the energy of a phonon in mode m. k is the BoltzmannÕs constant. Eq. (1) indicates that the number of phonons should decrease with a decrease in temperature. Therefore, the cross relaxation in Tm3þ , if it is an energy transfer process assisted by phonons, is expected to decrease at low temperatures. Results of the present study supported the hypothesis that cross relaxation in Tm3þ is a phonon-assisted energy transfer. The intensity of the 1.48 lm emission increased relative to 1.84 lm emission as temperature decreased (Fig. 2). At the same time, lifetimes of the 3 H4 level increased (Fig. 3). However, these relative intensity ratios did not increase further when temperature decreased below 100 K. Reasons for this unexpected decrease are not clear at present. It is probably due to changes in the cross sections of ground-state absorption (GSA) and excited-state absorption (ESA). Specifically, 1.84 lm emission from the 3 F4 ! 3 H6 transition is partially absorbed by the GSA of 3 H6 ! 3 F4 . Likewise, 1.48 lm emission due to the 3 H4 ! 3 F4 transition is also absorbed by the ESA of the 3 F4 ! 3 H4 . The magnitude of the reabsorption is determined by the extent of the overlapping between the respective absorption and emission spectra. As temperature drops, however, the population of the lower-lying energy levels increases relative to those of the upper energy levels within each manifold. Hence, both the longwavelength absorption tail and short-wavelength
Y.S. Han et al. / Journal of Non-Crystalline Solids 316 (2003) 302–308
emission tail decrease in intensity [14]. It generally leads to a decrease in the magnitude of re-absorption. This effect is more pronounced for the 3 F4 ! 3 H6 emission (1.84 lm) than for the 3 H4 ! 3 F4 emission (1.48 lm) since the 3 H6 manifold experiences a broader splitting [15]. Therefore, at low temperatures, the amount of re-absorption of 1.84 lm emission decreases rapidly and as a result, the relative intensity ratios of I1:48 =I1:84 decrease. Rates of the cross relaxation were calculated from the measured and radiative lifetimes of the 3 H4 level. When the concentration of a dopant ion is high, the transition probability from a certain energy level other than the ground state can be expressed as follows [6]: 1 smeas
¼
1 srad
þ WMPR þ WET ;
ð2Þ
where smeas is the measured lifetime and srad is the radiative lifetime calculated from Judd–Ofelt analysis. WMPR and WET represent multiphonon relaxation and energy transfer rates, respectively. The energy gap between the 3 H4 and 3 H5 levels is approximately 4300 cm1 and the energy of the highest phonon in sulfide glasses is around 400 cm1 [10]. Therefore, multiphonon relaxation rates should be small and can be ignored in the present case. Then, energy transfer rates (i.e. cross relaxation rates) can be calculated from the following relationship: WET ¼
1 1 : smeas srad
ð3Þ
Fig. 4. Temperature dependence of cross relaxation rates (3 H4 , 3 H6 ! 3 F4 , 3 F4 ) in Ge30 Ga2 As6 S62 glass doped with Tm3þ ions. The solid line is the result of fitting from Eq. (4) by assuming 2-phonons of the 390 cm1 in energy.
where DE is the difference between the energies of the donor and acceptor levels. Raman spectrum of the Ge30 Ga2 As6 S62 glass in Fig. 5 showed two major bands at 338 and 232 cm1 . The band at 338 cm1 is mainly due to the symmetric stretching of GeS4 [17,18] and AsS3 pyramids [19]. The shoulders extending from 370 to 430 cm1 is related to several structural features including m3 -asymmetric stretching vibration mode of GeS4 tetrahedra (390 cm1 ) and S3 Ge–S–GeS3 vibrations (425 cm1 ) [17]. A broad band at 232 cm1 is associated with the formation of metal– metal bonds, such as As–As (231 cm1 ) and Ge– Ge (250 cm1 ) [18,20]. Numerical fitting of the
From the calculated lifetime of srad ¼ 230 ls [9] and the lifetimes measured at various temperatures, the effect of temperature on the energy transfer rates were calculated as shown in Fig. 4. When phonons of only one vibrational mode are involved in the phonon-assisted process, the temperature dependence of the energy transfer rate is expressed by [16] W ðT Þ ¼ W ð0Þð1 expð hx=kT ÞÞN :
ð4Þ
N represents the number of phonons participating in the energy transfer processes, and can be expressed as N ¼ DE= hx;
ð5Þ
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Fig. 5. Raman spectrum of Ge30 Ga2 As6 S62 glass.
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measured energy transfer rates using Eq. (4) was most successful when one assumes that two phonons with an energy of 390 cm1 are involved in the energy transfer process (Fig. 4). Therefore, it was concluded that m3 -asymmetric stretching vibration mode of GeS4 tetrahedra is the major phonon contributing the 3 H4 , 3 H6 ! 3 F4 , 3 F4 cross relaxation process. Energy transfer processes are generally described in terms of three limiting cases; direct relaxation, fast diffusion, and diffusion-limited relaxation [21]. Fast diffusion is characterized by a simple exponential behavior in the fluorescence decay curve. However, decay curves in Fig. 6 did not show a simple exponential behavior. An overall de-excitation probability N ðtÞ of the donor fluorescence with time t is expressed as follows: N ðtÞ ¼ expfWo t PðtÞg;
ð6Þ
where Wo is a reciprocal of lifetime when no energy acceptor is present. PðtÞ is a magnitude of the departure from the intrinsic exponential behavior due to the energy transfer, and is proportional to t3=s , where s can be either 6, 8, or 10 depending upon the electric multipole character of the interaction [22]. The exponent can be revealed from a slope in the plot of lnf ln N ðtÞ Wo tg vs. lnðtÞ. The slopes were 0.71 and 0.75 at 20 and 280 K, respectively (Fig. 7). They correspond to the case where s ¼ 6 and suggest that a considerable
Fig. 7. Dependence of PðtÞ on lnðtÞ at (a) 20 K and (b) 280 K, respectively. Solid lines are the least-squares fit to the data.
amount of diffusion among Tm3þ ions occur. In the present case, when only one type of active ions is present, neighboring ions around the excited ions can act either as acceptors or as ions for energy migration. Hence, cross relaxation among Tm3þ ions can be described as a specific example of diffusion-limited relaxation. Therefore, the decay behavior is better described by the following equation derived by Yokota and Tanimoto [23]: ( 4 N ðtÞ ¼ exp Wo t p3=2 na C 1=2 t1=2 3 3=4 ) 1 þ 10:87x þ 15:50x2
; ð7Þ 1 þ 8:743x Fig. 6. Decay curves of 1.48 lm emission in Ge30 Ga2 As6 S62 glass doped with 0.2 mol% of Tm3þ .
where na is the concentration of acceptor ions, x ¼ DC 1=3 t2=3 . C is an interaction parameter and
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phonon-assisted energy transfer process. As temperature decreased from room temperature to 100 K, the relative intensity ratios between the 1.48 and 1.84 lm emission increased together with an increase in the fluorescence lifetimes of the 3 H4 level. Fitting of the decay curves of the 1.48 lm emission with the theoretical expression was most successful when two phonons of the m3 -asymmetric stretching vibration mode of GeS4 tetrahedra (390 cm1 ) were assumed to control energy transfer. Critical distance for cross relaxation decreased from 0.73 to 0.58 nm with a decrease in temperature. Fig. 8. Temperature dependence of the calculated critical distances in Tm3þ -doped Ge30 Ga2 As6 S62 glass. Line was drawn as a guide to the eye.
D is a diffusion coefficient for the energy migration among donors. First, C values in a temperature interval of 20–300 K were obtained by fitting Eq. (7) to the measured decay curves of the 1.48 lm emission. Using these C values, the critical distance Ro , i.e. the distance at which the probability of energy transfer becomes equal to the intrinsic decay rate, was calculated at each temperature using the following relationship [23]: R6o ¼
C : Wo
ð8Þ
The critical distance does not indicate the actual distance between the ions, but expresses the extent to which the energy transfer can occur between them. An ion can easily transfer its energy to another ion located within the critical distance, but cannot transfer to another ion beyond the critical distance. Therefore, the longer the critical distance becomes, the more actively the energy transfer can occur. In Fig. 8, the critical distance decreased from 0.73 nm to as low as 0.58 nm as temperature decreased from 300 to 20 K. This again supported the results that the extent of cross relaxation among Tm3þ ions reduced as temperature decreased.
5. Conclusions
3
Cross relaxation among Tm3þ ions (3 H4 , 3 H6 ! F4 , 3 F4 ) in Ge30 Ga2 As6 S62 glass was identified as a
Acknowledgements This work was supported by a Korea Research Foundation Grant (KRF-2000-041-E00557).
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