- Email: [email protected]
On the Urbach rule in sulphur-implanted Cu6PS5I superionic conductors
ARTICLE IN PRESS Journal of Physics and Chemistry of Solids 71 (2010) 988–992
Contents lists available at ScienceDirect
Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
On the Urbach rule in sulphur-implanted Cu6PS5I superionic conductors I.P. Studenyak a,n, V.Yu. Izai a, V.O. Stefanovich a, V.V. Panko a, P. Ku´sˇ b, A. Plecenik b a b
Uzhhorod National University, 46 Pidhirna St., Uzhhorod 88000, Ukraine Comenius University, Mlynska dolina, 84248 Bratislava, Slovakia
a r t i c l e in f o
a b s t r a c t
Article history: Received 5 October 2009 Received in revised form 4 January 2010 Accepted 7 April 2010
Cu6PS5I superionic crystals, grown using chemical vapour transport, were implanted by sulphur ions. The ion implantation effect on the phase transitions is studied by temperature isoabsorption investigation of the optical absorption edge. For the implanted crystals the optical absorption edge shape is studied in the temperature range 77–320 K, the parameters of exciton–phonon interaction, resulting in the Urbach behaviour of the optical absorption edge, are determined, the temperature dependences of the optical pseudogap and Urbach energy are obtained. The implantation effect on the ordering–disordering processes in Cu6PS5I superionic conductors is studied. & 2010 Elsevier Ltd. All rights reserved.
Keywords: D. Phase transitions D. Optical properties
1. Introduction Cu6PS5I crystal with argyrodite structure is well known as a fast-ion conductor characterized by high ionic conductivity. It also exhibits ferroelastic and nonlinear optical properties [1–3]. The specific features of Cu6PS5I crystal structure and phase transitions (PT) have been studied in [1,4–6]. It has been shown that at room temperature Cu6PS5I crystal belongs to the cubic syngony (F4¯3m space group) [1]. With temperature decrease two PTs take place, one of which, at TII ¼(269 72) K, is a structural second-order PT (accompanied by the symmetry change F4¯3m-F4¯3c), while the second one, at TI ¼(14471) K, is simultaneously a superionic and ferroelastic first-order PT (accompanied by the symmetry change F4¯3c-Cc) [5,6]. At present, electrical, acoustic, calorimetric and some optical properties of Cu6PS5I compound have been studied quite extensively [2,3,5,7–9]. It should be noted that earlier studies of Cu6PS5I crystal absorption edge at high absorption levels have shown the existence of bound and free excitons at temperatures below the superionic phase transition; the excitons undergo considerable changes with the temperature increase [2]. At the transition to the superionic state not only the exciton structure is changed but also exponential parts appear at the long-wave absorption edge. At T4TI the temperature behaviour of the exponential parts of the Cu6PS5I crystal absorption edge is described by the empirical Urbach rule [10].
aðhn,TÞ ¼ a0 exp
n
sðhnE0 Þ kT
¼ a0 exp
hnE0 EU ðTÞ
Corresponding author. E-mail address: [email protected] (I.P. Studenyak).
0022-3697/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2010.04.007
where EU is the Urbach energy (a reciprocal of the absorption edge slope EU 1 ¼ Dðln aÞ=DðhnÞ), s is the absorption edge steepness parameter, a0 and E0 are the convergence point coordinates of the Urbach bundle, k is the Boltzmann constant, T is temperature, hn is photon energy. Incorporation of impurity atoms by ion implantation has already become a traditional and a highly efficient technique for modification of structure and variation of physical properties of solids. Studies of such type are important for obtaining information on the specific features of ion implantation-induced ordering and disordering and their effect on phase transitions, structural and optical properties of superionic conductors. They continue the series of studies regarding external effects on the physical properties of superionic conductors and possibilities of their applications (the effects of conditions of synthesis and growth, variation of chemical composition and electron irradiation were studied in Refs. [11,12]). The present study is aimed at the investigation of the influence of ion implantation on the PT temperatures, structural and optical properties, particularly on the Urbach absorption edge, as well as the main features of structural ordering–disordering processes in Cu6PS5I superionic conductors, which are the promising materials for the creation of the solid electrolyte energy sources, electrochemical and optical sensors.
2. Experimental ð1Þ Cu6PS5I single crystals were grown using the chemical vapour transport method [2]. For implantation the experimental set-up with magnetic separation and regulative accelerating voltage from 25 to 180 kV (9.6 10 6 Torr) was used. The angle
ARTICLE IN PRESS I.P. Studenyak et al. / Journal of Physics and Chemistry of Solids 71 (2010) 988–992
of incidence was 101 and the sulphur ion energy 149 keV. Implantation of Cu6PS5I crystals was performed using 32S + isotope, obtained from sulphur powder, heated above 400 1C, and delivered in the gaseous state to the ion source. The spectral dependence of the absorption coefficient a was studied in the temperature range 77–320 K. For the transmittance and reflectance measurements the samples were oriented at room temperature while being in the cubic phase. Linear absorption coefficient a as a function of transmittance, Ttr, and reflectance of the surface, R, was calculated using the well-known formula, which takes into account multiple internal reflections. 8 v" ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi9 #2 u > > = 2 1 <ð1RÞ2 u ð1RÞ ð2Þ a ¼ ln þt þ R2 > 2Ttr d > : 2Ttr ; where d denotes the plane-parallel sample thickness. The experimental setup and technique are described in Ref. [2]. The relative error in the determination of the absorption coefficient Da/a did not exceed 10% at 0.3 r adr3 [13]. Isoabsorption studies of optical absorption edge consisted in the determination of the energy position of the optical absorption edge Eag ðTÞ at fixed values of absorption coefficient a and temperature T.
3. Results and discussion 3.1. Isoabsorption studies of Urbach absorption edge Temperature isoabsorption studies of the optical absorption edge enabled us to study the effect of ion implantation on the temperature of the superionic PT at T¼TI, which is simultaneously a ferroelastic one, as well as on the existence of superionic and ferroelastic states. At the temperature increase in the range 77–139 K the energy position of the optical absorption edge Eag remains almost unchanged; in the range of the first-order PT 139–150 K a step of Eag is observed ðdEag =dT 40Þ; at T4150 K a nonlinear decrease of Eag is observed, in the range of the secondorder PT a slight variation of the nonlinearity of the Eag ðTÞ slope is revealed (Fig. 1). In the range of the first-order superionic PT at T¼TI the temperature hysteresis is observed, the value of the PT temperature was determined in the heating mode. Ion implantation of Cu6PS5I crystals has shown (Fig. 1; Table 1) that introduction of defects by ion bombardment at the initial stage results in an essential increase of the temperature of the first-order
Fig. 1. Temperature dependences of Eag (a ¼ 250 cm 1) for the unimplanted (1) and implanted Cu6PS5I crystals for different fluences (ions/cm2): (2) 1 1013, (3) 1 1014, and (4) 2 1015.
989
superionic PT at T¼TI from 144 to 157 K (for the crystal implanted by the fluence of 1 1013 ions/cm2). At the subsequent increase of the amount of defects with the fluence increase up to 1 1014 ions/cm2 the PT temperature remains almost unchanged, and then decreases to 153 K for the fluence value of 2 1015 ions/cm2. Meanwhile, the PT temperature interval DTI shrinks from 11 to 4 K, which is evidence of the structural ordering of the crystal lattice due to the ionic implantation (Table 1). 3.2. Spectroscopic studies of Urbach absorption edge In Fig. 2 the spectral dependences of the absorption coefficient at 300 K are presented for unimplanted and implanted (at various fluence values) Cu6PS5I crystals. It is shown that the optical pseudogap Eg remains unchanged (2.08970.001 eV) with the fluence increase while the Urbach energy EU nonlinearly decreases (Fig. 2, inset). The latter is the evidence for structural ordering in Cu6PS5I crystal, which increases with increase in ion implantation. It should be noted that at ion implantation one can expect a certain amorphization of the crystal lattice; however, the studies performed have shown that, on the contrary, the fluence increase leads to a decrease of the EU value, characterizing the crystal structure disorder degree. Unimplanted crystals are characterized by a deviation from stoichiometry, namely the lack of sulphur. Implantation by sulphur ions results in an improvement of the crystal stoichiometry what is revealed as a decrease of EU what, in turn, indicates the crystal lattice structural ordering. The optical absorption edge temperature studies have shown the shape of the absorption edge of implanted Cu6PS5I crystals, similarly to the unimplanted one, to be exponential, following the Urbach rule. For example, Fig. 3 presents the spectral dependences of absorption coefficient at various temperatures for Cu6PS5I crystal implanted at the fluence of 1 1013 ions/cm2. Similar Urbach bundles are observed for all the implanted Cu6PS5I crystals. The coordinates of the Urbach bundle convergence point a0 and E0 for the implanted crystals at various fluence values are given in Table 1. For comparison, Table 1 contains corresponding parameters for the unimplanted Cu6PS5I crystal. It should be noted that in the range of the second-order structural PT at T¼ TII the coordinates of the Urbach bundle convergence point a0 and E0 remains unchanged, their values being listed in Table 1. The exponential shape of the absorption edge long-wavelength side is usually related to exciton (electron)–phonon interaction (EPI) [15]. In the whole investigated temperature interval, for the implanted Cu6PS5I crystals, like for the unimplanted one, the temperature dependences of the absorption edge steepness parameter s are described by the Mahr relation [15]: _op 2kT tanh ð3Þ sðTÞ ¼ s0 2kT _op An example of such dependence presented in the inset of Fig. 3. The s0 parameter is a constant, independent of temperature and related to the EPI constant g as s0 ¼2/3g, _op is the effective average phonon energy in a single-oscillator model, describing the EPI [15]. It should be noted that for the implanted Cu6PS5I crystals, like for unimplanted one, the value s0 is greater than 1, which indicates a weak EPI [16]. The values of the effective phonon energy _op taking part in the formation of the absorption edge, and s0 parameter are given in Table 1. The dependences of the EPI parameter s0 and the effective average phonon energy _op on the ion fluence for the implanted Cu6PS5I crystals are presented in Fig. 4. It is shown that both s0 and _op first increase with fluence (by 17% and 52%, respectively), and then decrease while the fluence increases to 2 1015 ions/cm2. At the fluence of 2 1015 ions/cm2, the s0 parameter value is only by 10% greater
ARTICLE IN PRESS 990
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Table 1 Parameters of Urbach absorption edge, parameters of EPI and PT values for unimplanted and implanted Cu6PS5I crystals. Crystal
Unimplanted
Temperature interval Eg (300 K) (eV)
ToTII
EU (300 K) (meV) a0 (cm-1) E0 (eV)
s0 _op (meV) (EU)0 (meV) (EU)1 (meV) Eg (0) (eV)
1.18 25.7 298 10.8 21.9 2.166
Sg
5.06
yE (K)
TI (K) DTI (K)
Fluence 1 1013 ions/cm2 T4TII 2.0893
To TII
23.7
4.7 105 2.234
144 71 11
Fluence 1 1014 ions/cm2 T4TII 2.0883
To TII
21.7
1.1 106 2.240 1.16 22.1 257 9.6 19.1 2.170
1.32 29.8 346 11.2 22.8 2.161
4.98
5.30 157 71 6
Fluence 2 1015 ions/cm2 T4TII 2.0896
To TII
21.2
8.1 105 2.232 1.36 33.5 389 12.4 24.8 2.155
1.35 27.4 318 10.2 20.4 2.164
5.28
5.11 157.5 7 1 6
T4TII 2.0888 20.9 3.2 105 2.209
1.30 22.7 263 8.6 17.6 2.173
1.29 16.8 195 6.5 13.0 2.171
5.29
4.76
1.27 13.7 159 5.2 11.0 2.179 4.38 154 71 4
Eg (300 K) is the optical pseudogap at 300 K; EU (300 K) is the Urbach energy at 300 K; a0 and E0 are the convergence point coordinates of the Urbach bundle; s0 is a parameter, related to the EPI constant; _op is the effective average phonon energy in a single-oscillator model; yE is the Einstein temperature; (EU)0 and (EU)1 are constants, describing the EU (T) in Einstein model; Eg ð0Þ and Sg are the optical pseudogap at 0 K and a dimensionless constant, describing the Eg ðTÞ in Einstein model; TI is the superionic PT temperature; DTI is the superionic PT temperature interval.
Fig. 2. Spectral dependences of absorption coefficient at 300 K for the unimplanted (1) and implanted Cu6PS5I crystals for different fluences (ions/cm2): (2) 1 1013, (3) 1 1014, and (4) 2 1015. The inset shows the dependences of the optical pseudogap Eg (dark circles) and Urbach energy EU (open circles) on the fluence value for the implanted Cu6PS5I crystal.
Fig. 3. Spectral dependences of the Urbach absorption edge for Cu6PS5I crystal, implanted by the fluence of 1 1013 ions/cm2, at various temperatures: (1) 170, (2) 200, (3) 230, (4) 260, (5) 280, (6) 290, (7) 300, and (8) 320 K. The inset shows the temperature dependence of s steepness parameter.
than the one for the unimplanted crystal, while _op is only 62% of the similar value for the unimplanted crystal. It should be noted that in the range of the second-order structural PT at T¼TII the s0 and _op EPI parameters for the implanted crystals are changed, similarly to the unimplanted one (see Table 1). The temperature dependences of the optical pseudogap Eg and the Urbach energy EU, obtained from the temperature behaviour of the Urbach absorption edge for Cu6PS5I crystal, implanted by sulphur ion fluence of 1 1013 ions/cm2, are presented in Fig. 5. The temperature behaviour of Eg for the implanted Cu6PS5I crystal (Fig. 5) due to the EPI can be described in the Einstein model by a relation [17]: 1 ð4Þ Eg ðTÞ ¼ Eg ð0ÞSg kyE expðyE =TÞ1 where Eg ð0Þ and Sg are the optical pseudogap at 0 K and a dimensionless constant, respectively; yE is the Einstein temperature, corresponding to the average frequency of phonon excitations of a system of non-coupled oscillators. The performed calculations show that in the whole temperature range the
Fig. 4. Dependences of the EPI parameter s0 (dark circles) and the effective average phonon energy _op (open circles) on the ion fluence for the sulphurimplanted Cu6PS5I crystals.
ARTICLE IN PRESS I.P. Studenyak et al. / Journal of Physics and Chemistry of Solids 71 (2010) 988–992
991
Fig. 5. Temperature dependences of optical pseudogap Eg (1) and Urbach energy EU (2) for Cu6PS5I crystal, implanted by the fluence of 1 1013 ions/cm2: circles – experiment, curves – calculations.
experimental values of Eg are well described by Eq. (4). The obtained Eg ð0Þ, Sg , and yE parameters for the unimplanted and implanted (with various fluences) crystals are given in Table 1, and the temperature dependence of the optical pseudogap Eg for Cu6PS5I crystal, implanted with the fluence of 1 1013 ions/cm2, calculated from Eq. (5), is shown in Fig. 5 as a solid line. It is well known that the Urbach energy EU in the Einstein model is described as [18] 1 ð5Þ ðEU Þ ¼ ðEU Þ0 þ ðEU Þ1 expðyE =TÞ1 where (EU)0 and (EU)1 are constants. The values of (EU)0 and (EU)1, obtained by fitting Eq. (5) to the experimental temperature dependences of EU, for the unimplanted and implanted (with various fluences) crystals are listed in Table 1. The temperature dependence of the Urbach energy EU for Cu6PS5I crystal, implanted with the fluence of 1 1013 ions/cm2, is shown in Fig. 5 as a dashed line. 3.3. Ordering–disordering processes in sulphur implanted Cu6PS5I superionic conductor In Ref. [14] it was shown that both temperature-related and structural disordering affect Urbach absorption edge shape, i.e. the Urbach energy EU is described by EU ¼ ðEU ÞT þðEU ÞX ¼ ðEU ÞT þ ðEU ÞX,stat þ ðEU ÞX,dyn
ð6Þ
where (EU)T and (EU)X are contributions of temperature-related and structural disordering to EU, respectively; (EU)X,stat and (EU)X,dyn are contributions of static structural disordering and dynamic structural disordering to (EU)X, respectively. The static structural disordering (EU)X,stat in Cu6PS5I crystal is caused by structural imperfectness due to the high concentration of disordered copper vacancies as well as the dynamic structural disordering (EU)X,dyn is related to the intense motion of mobile copper ions, participating in ion transfer, and is responsible for the ionic conductivity [9]. It should be noted that the first term in the right-hand side of Eq. (5) represents static structural disordering, and the second one – temperature-related types of disordering: temperature disordering due to thermal lattice vibrations and dynamic structural disordering due to the presence of mobile ions in superionic conductors. The contributions of static structural disordering and temperature-related types of disordering into the Urbach energy EU for the implanted Cu6PS5I crystals were evaluated. It is shown
Fig. 6. Dependence of the relative contribution of static structural disordering (EU)X,stat into the Urbach energy EU on the ion fluence for the sulphur-implanted Cu6PS5I crystals.
that the absolute contribution of static structural disordering at first increases with fluence by about 30% (at the fluence of 1 1013 ions/cm2), and then decreases, and at the fluence of 2 1015 ions/cm2 it is only 54% of the absolute contribution of static structural disordering for the unimplanted crystal (Table 1). It should be noted that relative contribution of structural disordering into Urbach energy (Fig. 6), which is 41% for the unimplanted crystal, grows to 57% (for the crystal, implanted with the fluence of 1 1013 ions/cm2) and drops down to 25% (for the crystal, implanted with the fluence of 2 1015 ions/cm2). The presented results are the evidence for the processes of ordering of Cu6PS5I superionic conductor crystal lattice under implantation by sulphur ions.
4. Conclusions Cu6PS5I single crystals, grown by chemical vapour transport, were implanted by different fluences of 149 keV 32S + ions. Influence of the sulphur ion implantation on the superionic PT temperature is studied. Optical absorption edge of both unimplanted and implanted Cu6PS5I crystals is of exponential shape, following the Urbach rule. The temperature behaviour of the Urbach absorption edge is determined by exciton–phonon interaction, which is weak in unimplanted Cu6PS5I crystals. Temperature dependences of optical pseudogap Eg and Urbach energy EU are obtained, being well described by curves, calculated in the framework of the Einstein model. The comparative analysis of the absorption edge parameters of sulphur-implanted Cu6PS5I crystals shows the ion implantation to result in: (i) the optical pseudogap Eg remaining unchanged and the Urbach energy EU decreasing; (ii) EPI increasing at fluences above 1 1013 ion/cm2 (evidenced by the decrease of s0) and effective phonon energy _op decreasing (Table 1); (iii) both absolute and relative contribution of static structural disordering to the Urbach energy decreasing for the fluences above 1 1013 ions/cm2.
Acknowledgments This work was supported by the Slovak Research and Development Agency under the Contract no. SK-UA-001407 and
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Ministry of Education and Science of Ukraine under the Contract no. M/35-2008. References [1] W.F. Kuhs, R. Nitsche, K. Scheunemann, Mater. Res. Bull. 11 (1976) 1115. [2] I.P. Studenyak, M. Kranjcˇec, Gy.Sh. Kovacs, V.V. Panko, D.I. Desnica, A.G. Slivka, P.P. Guranich, J. Phys. Chem. Solids 60 (1999) 1897. [3] R.B. Beeken, J.J. Garbe, N.R. Petersen, J. Phys. Chem. Solids 64 (2003) 1261. [4] T. Nilges, A. Pfitzner, Z. Kristallogr. 220 (2005) 281. [5] I.P. Studenyak, V.O. Stefanovich, M. Kranjcˇec, D.I. Desnica, Yu.M. Azhniuk, Gy.Sh. Kovacs, V.V. Panko, Solid State Ionics 95 (1997) 221. [6] A. Gagor, A. Pietraszko, D. Kaynts, J. Solid State Chem. 178 (2005) 3366. [7] S. Fiechter, E. Gmelin, Thermochim. Acta 85 (1985) 155. [8] V. Samulionis, J. Banys, Y. Vysochanskii, I. Studenyak, Ferroelectrics 336 (2006) 29.
[9] I.P. Studenyak, M. Kranjcˇec, M.V. Kurik, J. Phys. Chem. Solids 67 (2006) 807. [10] F. Urbach, Phys. Rev. 92 (1953) 1324. [11] I.P. Studenyak, M. Kranjcˇec, Gy.Sh. Kovacs, V.V. Panko, V.V. Mitrovcij, O.A. Mikajlo, Mater. Sci. Eng. B97 (2003) 34. [12] V.V. Panko, I.P. Studenyak, V.S. Dyordyai, Gy.S. Kovacs, A.N. Borets, Yu.V. Voroshilov, Neorg. Mater. 24 (1988) 120 in Russian. [13] F. Oswald, Optik 16 (1959) 527. [14] G.D. Cody, T. Tiedje, B. Abeles, B. Brooks, Y. Goldstein, Phys. Rev. Lett. 47 (1981) 1480. [15] M.V. Kurik, Phys. Status Solidi (a) 8 (1971) 9. [16] H. Sumi, A. Sumi, J. Phys. Soc. Japan 56 (1987) 2211. [17] M. Beaudoin, A.J.G. DeVries, S.R. Johnson, H. Laman, T. Tiedje, Appl. Phys. Lett. 70 (1997) 3540. [18] Z. Yang, K.P. Homewood, M.S. Finney, M.A. Harry, K.J. Reeson, J. Appl. Phys. 78 (1995) 1958.
Contents lists available at ScienceDirect
Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
On the Urbach rule in sulphur-implanted Cu6PS5I superionic conductors I.P. Studenyak a,n, V.Yu. Izai a, V.O. Stefanovich a, V.V. Panko a, P. Ku´sˇ b, A. Plecenik b a b
Uzhhorod National University, 46 Pidhirna St., Uzhhorod 88000, Ukraine Comenius University, Mlynska dolina, 84248 Bratislava, Slovakia
a r t i c l e in f o
a b s t r a c t
Article history: Received 5 October 2009 Received in revised form 4 January 2010 Accepted 7 April 2010
Cu6PS5I superionic crystals, grown using chemical vapour transport, were implanted by sulphur ions. The ion implantation effect on the phase transitions is studied by temperature isoabsorption investigation of the optical absorption edge. For the implanted crystals the optical absorption edge shape is studied in the temperature range 77–320 K, the parameters of exciton–phonon interaction, resulting in the Urbach behaviour of the optical absorption edge, are determined, the temperature dependences of the optical pseudogap and Urbach energy are obtained. The implantation effect on the ordering–disordering processes in Cu6PS5I superionic conductors is studied. & 2010 Elsevier Ltd. All rights reserved.
Keywords: D. Phase transitions D. Optical properties
1. Introduction Cu6PS5I crystal with argyrodite structure is well known as a fast-ion conductor characterized by high ionic conductivity. It also exhibits ferroelastic and nonlinear optical properties [1–3]. The specific features of Cu6PS5I crystal structure and phase transitions (PT) have been studied in [1,4–6]. It has been shown that at room temperature Cu6PS5I crystal belongs to the cubic syngony (F4¯3m space group) [1]. With temperature decrease two PTs take place, one of which, at TII ¼(269 72) K, is a structural second-order PT (accompanied by the symmetry change F4¯3m-F4¯3c), while the second one, at TI ¼(14471) K, is simultaneously a superionic and ferroelastic first-order PT (accompanied by the symmetry change F4¯3c-Cc) [5,6]. At present, electrical, acoustic, calorimetric and some optical properties of Cu6PS5I compound have been studied quite extensively [2,3,5,7–9]. It should be noted that earlier studies of Cu6PS5I crystal absorption edge at high absorption levels have shown the existence of bound and free excitons at temperatures below the superionic phase transition; the excitons undergo considerable changes with the temperature increase [2]. At the transition to the superionic state not only the exciton structure is changed but also exponential parts appear at the long-wave absorption edge. At T4TI the temperature behaviour of the exponential parts of the Cu6PS5I crystal absorption edge is described by the empirical Urbach rule [10].
aðhn,TÞ ¼ a0 exp
n
sðhnE0 Þ kT
¼ a0 exp
hnE0 EU ðTÞ
Corresponding author. E-mail address: [email protected] (I.P. Studenyak).
0022-3697/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2010.04.007
where EU is the Urbach energy (a reciprocal of the absorption edge slope EU 1 ¼ Dðln aÞ=DðhnÞ), s is the absorption edge steepness parameter, a0 and E0 are the convergence point coordinates of the Urbach bundle, k is the Boltzmann constant, T is temperature, hn is photon energy. Incorporation of impurity atoms by ion implantation has already become a traditional and a highly efficient technique for modification of structure and variation of physical properties of solids. Studies of such type are important for obtaining information on the specific features of ion implantation-induced ordering and disordering and their effect on phase transitions, structural and optical properties of superionic conductors. They continue the series of studies regarding external effects on the physical properties of superionic conductors and possibilities of their applications (the effects of conditions of synthesis and growth, variation of chemical composition and electron irradiation were studied in Refs. [11,12]). The present study is aimed at the investigation of the influence of ion implantation on the PT temperatures, structural and optical properties, particularly on the Urbach absorption edge, as well as the main features of structural ordering–disordering processes in Cu6PS5I superionic conductors, which are the promising materials for the creation of the solid electrolyte energy sources, electrochemical and optical sensors.
2. Experimental ð1Þ Cu6PS5I single crystals were grown using the chemical vapour transport method [2]. For implantation the experimental set-up with magnetic separation and regulative accelerating voltage from 25 to 180 kV (9.6 10 6 Torr) was used. The angle
ARTICLE IN PRESS I.P. Studenyak et al. / Journal of Physics and Chemistry of Solids 71 (2010) 988–992
of incidence was 101 and the sulphur ion energy 149 keV. Implantation of Cu6PS5I crystals was performed using 32S + isotope, obtained from sulphur powder, heated above 400 1C, and delivered in the gaseous state to the ion source. The spectral dependence of the absorption coefficient a was studied in the temperature range 77–320 K. For the transmittance and reflectance measurements the samples were oriented at room temperature while being in the cubic phase. Linear absorption coefficient a as a function of transmittance, Ttr, and reflectance of the surface, R, was calculated using the well-known formula, which takes into account multiple internal reflections. 8 v" ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi9 #2 u > > = 2 1 <ð1RÞ2 u ð1RÞ ð2Þ a ¼ ln þt þ R2 > 2Ttr d > : 2Ttr ; where d denotes the plane-parallel sample thickness. The experimental setup and technique are described in Ref. [2]. The relative error in the determination of the absorption coefficient Da/a did not exceed 10% at 0.3 r adr3 [13]. Isoabsorption studies of optical absorption edge consisted in the determination of the energy position of the optical absorption edge Eag ðTÞ at fixed values of absorption coefficient a and temperature T.
3. Results and discussion 3.1. Isoabsorption studies of Urbach absorption edge Temperature isoabsorption studies of the optical absorption edge enabled us to study the effect of ion implantation on the temperature of the superionic PT at T¼TI, which is simultaneously a ferroelastic one, as well as on the existence of superionic and ferroelastic states. At the temperature increase in the range 77–139 K the energy position of the optical absorption edge Eag remains almost unchanged; in the range of the first-order PT 139–150 K a step of Eag is observed ðdEag =dT 40Þ; at T4150 K a nonlinear decrease of Eag is observed, in the range of the secondorder PT a slight variation of the nonlinearity of the Eag ðTÞ slope is revealed (Fig. 1). In the range of the first-order superionic PT at T¼TI the temperature hysteresis is observed, the value of the PT temperature was determined in the heating mode. Ion implantation of Cu6PS5I crystals has shown (Fig. 1; Table 1) that introduction of defects by ion bombardment at the initial stage results in an essential increase of the temperature of the first-order
Fig. 1. Temperature dependences of Eag (a ¼ 250 cm 1) for the unimplanted (1) and implanted Cu6PS5I crystals for different fluences (ions/cm2): (2) 1 1013, (3) 1 1014, and (4) 2 1015.
989
superionic PT at T¼TI from 144 to 157 K (for the crystal implanted by the fluence of 1 1013 ions/cm2). At the subsequent increase of the amount of defects with the fluence increase up to 1 1014 ions/cm2 the PT temperature remains almost unchanged, and then decreases to 153 K for the fluence value of 2 1015 ions/cm2. Meanwhile, the PT temperature interval DTI shrinks from 11 to 4 K, which is evidence of the structural ordering of the crystal lattice due to the ionic implantation (Table 1). 3.2. Spectroscopic studies of Urbach absorption edge In Fig. 2 the spectral dependences of the absorption coefficient at 300 K are presented for unimplanted and implanted (at various fluence values) Cu6PS5I crystals. It is shown that the optical pseudogap Eg remains unchanged (2.08970.001 eV) with the fluence increase while the Urbach energy EU nonlinearly decreases (Fig. 2, inset). The latter is the evidence for structural ordering in Cu6PS5I crystal, which increases with increase in ion implantation. It should be noted that at ion implantation one can expect a certain amorphization of the crystal lattice; however, the studies performed have shown that, on the contrary, the fluence increase leads to a decrease of the EU value, characterizing the crystal structure disorder degree. Unimplanted crystals are characterized by a deviation from stoichiometry, namely the lack of sulphur. Implantation by sulphur ions results in an improvement of the crystal stoichiometry what is revealed as a decrease of EU what, in turn, indicates the crystal lattice structural ordering. The optical absorption edge temperature studies have shown the shape of the absorption edge of implanted Cu6PS5I crystals, similarly to the unimplanted one, to be exponential, following the Urbach rule. For example, Fig. 3 presents the spectral dependences of absorption coefficient at various temperatures for Cu6PS5I crystal implanted at the fluence of 1 1013 ions/cm2. Similar Urbach bundles are observed for all the implanted Cu6PS5I crystals. The coordinates of the Urbach bundle convergence point a0 and E0 for the implanted crystals at various fluence values are given in Table 1. For comparison, Table 1 contains corresponding parameters for the unimplanted Cu6PS5I crystal. It should be noted that in the range of the second-order structural PT at T¼ TII the coordinates of the Urbach bundle convergence point a0 and E0 remains unchanged, their values being listed in Table 1. The exponential shape of the absorption edge long-wavelength side is usually related to exciton (electron)–phonon interaction (EPI) [15]. In the whole investigated temperature interval, for the implanted Cu6PS5I crystals, like for the unimplanted one, the temperature dependences of the absorption edge steepness parameter s are described by the Mahr relation [15]: _op 2kT tanh ð3Þ sðTÞ ¼ s0 2kT _op An example of such dependence presented in the inset of Fig. 3. The s0 parameter is a constant, independent of temperature and related to the EPI constant g as s0 ¼2/3g, _op is the effective average phonon energy in a single-oscillator model, describing the EPI [15]. It should be noted that for the implanted Cu6PS5I crystals, like for unimplanted one, the value s0 is greater than 1, which indicates a weak EPI [16]. The values of the effective phonon energy _op taking part in the formation of the absorption edge, and s0 parameter are given in Table 1. The dependences of the EPI parameter s0 and the effective average phonon energy _op on the ion fluence for the implanted Cu6PS5I crystals are presented in Fig. 4. It is shown that both s0 and _op first increase with fluence (by 17% and 52%, respectively), and then decrease while the fluence increases to 2 1015 ions/cm2. At the fluence of 2 1015 ions/cm2, the s0 parameter value is only by 10% greater
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Table 1 Parameters of Urbach absorption edge, parameters of EPI and PT values for unimplanted and implanted Cu6PS5I crystals. Crystal
Unimplanted
Temperature interval Eg (300 K) (eV)
ToTII
EU (300 K) (meV) a0 (cm-1) E0 (eV)
s0 _op (meV) (EU)0 (meV) (EU)1 (meV) Eg (0) (eV)
1.18 25.7 298 10.8 21.9 2.166
Sg
5.06
yE (K)
TI (K) DTI (K)
Fluence 1 1013 ions/cm2 T4TII 2.0893
To TII
23.7
4.7 105 2.234
144 71 11
Fluence 1 1014 ions/cm2 T4TII 2.0883
To TII
21.7
1.1 106 2.240 1.16 22.1 257 9.6 19.1 2.170
1.32 29.8 346 11.2 22.8 2.161
4.98
5.30 157 71 6
Fluence 2 1015 ions/cm2 T4TII 2.0896
To TII
21.2
8.1 105 2.232 1.36 33.5 389 12.4 24.8 2.155
1.35 27.4 318 10.2 20.4 2.164
5.28
5.11 157.5 7 1 6
T4TII 2.0888 20.9 3.2 105 2.209
1.30 22.7 263 8.6 17.6 2.173
1.29 16.8 195 6.5 13.0 2.171
5.29
4.76
1.27 13.7 159 5.2 11.0 2.179 4.38 154 71 4
Eg (300 K) is the optical pseudogap at 300 K; EU (300 K) is the Urbach energy at 300 K; a0 and E0 are the convergence point coordinates of the Urbach bundle; s0 is a parameter, related to the EPI constant; _op is the effective average phonon energy in a single-oscillator model; yE is the Einstein temperature; (EU)0 and (EU)1 are constants, describing the EU (T) in Einstein model; Eg ð0Þ and Sg are the optical pseudogap at 0 K and a dimensionless constant, describing the Eg ðTÞ in Einstein model; TI is the superionic PT temperature; DTI is the superionic PT temperature interval.
Fig. 2. Spectral dependences of absorption coefficient at 300 K for the unimplanted (1) and implanted Cu6PS5I crystals for different fluences (ions/cm2): (2) 1 1013, (3) 1 1014, and (4) 2 1015. The inset shows the dependences of the optical pseudogap Eg (dark circles) and Urbach energy EU (open circles) on the fluence value for the implanted Cu6PS5I crystal.
Fig. 3. Spectral dependences of the Urbach absorption edge for Cu6PS5I crystal, implanted by the fluence of 1 1013 ions/cm2, at various temperatures: (1) 170, (2) 200, (3) 230, (4) 260, (5) 280, (6) 290, (7) 300, and (8) 320 K. The inset shows the temperature dependence of s steepness parameter.
than the one for the unimplanted crystal, while _op is only 62% of the similar value for the unimplanted crystal. It should be noted that in the range of the second-order structural PT at T¼TII the s0 and _op EPI parameters for the implanted crystals are changed, similarly to the unimplanted one (see Table 1). The temperature dependences of the optical pseudogap Eg and the Urbach energy EU, obtained from the temperature behaviour of the Urbach absorption edge for Cu6PS5I crystal, implanted by sulphur ion fluence of 1 1013 ions/cm2, are presented in Fig. 5. The temperature behaviour of Eg for the implanted Cu6PS5I crystal (Fig. 5) due to the EPI can be described in the Einstein model by a relation [17]: 1 ð4Þ Eg ðTÞ ¼ Eg ð0ÞSg kyE expðyE =TÞ1 where Eg ð0Þ and Sg are the optical pseudogap at 0 K and a dimensionless constant, respectively; yE is the Einstein temperature, corresponding to the average frequency of phonon excitations of a system of non-coupled oscillators. The performed calculations show that in the whole temperature range the
Fig. 4. Dependences of the EPI parameter s0 (dark circles) and the effective average phonon energy _op (open circles) on the ion fluence for the sulphurimplanted Cu6PS5I crystals.
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Fig. 5. Temperature dependences of optical pseudogap Eg (1) and Urbach energy EU (2) for Cu6PS5I crystal, implanted by the fluence of 1 1013 ions/cm2: circles – experiment, curves – calculations.
experimental values of Eg are well described by Eq. (4). The obtained Eg ð0Þ, Sg , and yE parameters for the unimplanted and implanted (with various fluences) crystals are given in Table 1, and the temperature dependence of the optical pseudogap Eg for Cu6PS5I crystal, implanted with the fluence of 1 1013 ions/cm2, calculated from Eq. (5), is shown in Fig. 5 as a solid line. It is well known that the Urbach energy EU in the Einstein model is described as [18] 1 ð5Þ ðEU Þ ¼ ðEU Þ0 þ ðEU Þ1 expðyE =TÞ1 where (EU)0 and (EU)1 are constants. The values of (EU)0 and (EU)1, obtained by fitting Eq. (5) to the experimental temperature dependences of EU, for the unimplanted and implanted (with various fluences) crystals are listed in Table 1. The temperature dependence of the Urbach energy EU for Cu6PS5I crystal, implanted with the fluence of 1 1013 ions/cm2, is shown in Fig. 5 as a dashed line. 3.3. Ordering–disordering processes in sulphur implanted Cu6PS5I superionic conductor In Ref. [14] it was shown that both temperature-related and structural disordering affect Urbach absorption edge shape, i.e. the Urbach energy EU is described by EU ¼ ðEU ÞT þðEU ÞX ¼ ðEU ÞT þ ðEU ÞX,stat þ ðEU ÞX,dyn
ð6Þ
where (EU)T and (EU)X are contributions of temperature-related and structural disordering to EU, respectively; (EU)X,stat and (EU)X,dyn are contributions of static structural disordering and dynamic structural disordering to (EU)X, respectively. The static structural disordering (EU)X,stat in Cu6PS5I crystal is caused by structural imperfectness due to the high concentration of disordered copper vacancies as well as the dynamic structural disordering (EU)X,dyn is related to the intense motion of mobile copper ions, participating in ion transfer, and is responsible for the ionic conductivity [9]. It should be noted that the first term in the right-hand side of Eq. (5) represents static structural disordering, and the second one – temperature-related types of disordering: temperature disordering due to thermal lattice vibrations and dynamic structural disordering due to the presence of mobile ions in superionic conductors. The contributions of static structural disordering and temperature-related types of disordering into the Urbach energy EU for the implanted Cu6PS5I crystals were evaluated. It is shown
Fig. 6. Dependence of the relative contribution of static structural disordering (EU)X,stat into the Urbach energy EU on the ion fluence for the sulphur-implanted Cu6PS5I crystals.
that the absolute contribution of static structural disordering at first increases with fluence by about 30% (at the fluence of 1 1013 ions/cm2), and then decreases, and at the fluence of 2 1015 ions/cm2 it is only 54% of the absolute contribution of static structural disordering for the unimplanted crystal (Table 1). It should be noted that relative contribution of structural disordering into Urbach energy (Fig. 6), which is 41% for the unimplanted crystal, grows to 57% (for the crystal, implanted with the fluence of 1 1013 ions/cm2) and drops down to 25% (for the crystal, implanted with the fluence of 2 1015 ions/cm2). The presented results are the evidence for the processes of ordering of Cu6PS5I superionic conductor crystal lattice under implantation by sulphur ions.
4. Conclusions Cu6PS5I single crystals, grown by chemical vapour transport, were implanted by different fluences of 149 keV 32S + ions. Influence of the sulphur ion implantation on the superionic PT temperature is studied. Optical absorption edge of both unimplanted and implanted Cu6PS5I crystals is of exponential shape, following the Urbach rule. The temperature behaviour of the Urbach absorption edge is determined by exciton–phonon interaction, which is weak in unimplanted Cu6PS5I crystals. Temperature dependences of optical pseudogap Eg and Urbach energy EU are obtained, being well described by curves, calculated in the framework of the Einstein model. The comparative analysis of the absorption edge parameters of sulphur-implanted Cu6PS5I crystals shows the ion implantation to result in: (i) the optical pseudogap Eg remaining unchanged and the Urbach energy EU decreasing; (ii) EPI increasing at fluences above 1 1013 ion/cm2 (evidenced by the decrease of s0) and effective phonon energy _op decreasing (Table 1); (iii) both absolute and relative contribution of static structural disordering to the Urbach energy decreasing for the fluences above 1 1013 ions/cm2.
Acknowledgments This work was supported by the Slovak Research and Development Agency under the Contract no. SK-UA-001407 and
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