Critical behaviour of dark current and spontaneous polarization in ferroelectric SbSI

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1 Critical behaviour of dark current and spontaneous polarization in ferroelectric SbSI R. Chaves, H. Amaral, S. Ziolkiewicz To cite this version: R. Chaves, H. Amaral, S. Ziolkiewicz. Critical behaviour of dark current and spontaneous polarization in ferroelectric SbSI. Journal de Physique, 1980, 41 (3), pp < /jphys: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1980 HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 Le Dark SbSI Experimental J. Physique 41 (1980) MARS 1980, E 259 Classification Physics Abstracts Critical behaviour of dark current and spontaneous polarization in ferroelectric SbSI (*) R. Chaves, H. Amaral Laboratório de Fisica, Universidade do Porto, Portugal and S. Ziolkiewicz Laboratoire d Ultrasons (**), Université PierreetMarieCurie, Tour 13, 4, place Jussieu, Paris Cedex 05, France (Reçu le 18 juillet 1979, accepté le 12 novembre 1979) 2014 Résumé. ont été utilisés pour faire l étude de la transition ferroparaélectrique du SbSI. La valeur obtenue pour l exposant critique de la polarisation spontanée est en accord avec la théorie du champ moyen (03B2 0,51 ± 0,02). courant d obscurité et la polarisation spontanée, obtenus en mesurant le courant pyroélectrique, 2014 Abstract. current and spontaneous polarization, obtained from measurements of pyroelectric current, have been used to study the ferroparaelectric transition in SbSI crystals. The critical exponent of the spontaneous polarization is found to have the value predicted from a mean field theory (03B ± 0.02). 1. Introduction. has been thoroughly investigated for its ferroelectric properties and, as shown by the experimental data, it undergoes a first order ferroparaelectric transition of displacive nature around 293 K [1 to 6]. SbSI exhibits photoconductive [7, 8, 9] and strong piezoelectric properties [10,11] and peculiar optoelectric effects [12]. During the phase transition of SbSI there is a jump of the intrinsic absorption edge of ev [13, 14]. This transition is also accompanied by a change in the coefficient of the temperature dependence of the width of the forbidden band : (OEg IOT) 9 x 104 ev K in the paraelectric region ; in the ferroelectric region [13, 14] and by a shift in the activation energy of the impurity levels amounting to ev [8,15,16]. Dielectric and static electronic properties of single domain SbSI are quite well understood but data concerning nonequilibrium phenomena are a matter of some controversy. In fact in a first order ferroparaelectric transition a metastable para or ferroelectric phase may both exist either below (*) This work has been supported by Laboratorio de Fisica da Universidade do Porto and Instituto Nacional de Investigariio Cientifica (I.N.I.C.). (**) Associated with the Centre National de la Recherche Scientifique (C.N.R.S.). or above critical temperature (Tc) in a temperature range typical of each material [17]. These metastable states are associated with a certain instability of the system and also with non reproducible results. As some data concerning transport phenomena are obtained from nonequilibrium conditions at very fast heating or cooling rates, contradictions may arise in results concerning these phenomena. In the following, we have studied the critical behaviour of dark current and spontaneous polarization near the critical point in ferroelectric SbSI, by using very low heating and cooling rates in order to avoid the inconveniences reported above. 2. Experimental procedure. results were obtained by using needleshaped crystals, mm in length and about 0.2 mm2 in cross section as determined by microscope measurements. The crystals were grown by vapour transport reaction from a mixture of Sb, S and I, and their electrical resistivity, at room temperature, was about Measurements of the dark current were carried out in the direction parallel to the polar caxis lying along the needle axis. Silver paste contacts were used. The temperature of the sample was varied, between 260 K and 320 K, almost linearly with time, using a heater winding. Dark current was measured with a Keithley Article published online by EDP Sciences and available at

3 Dependence Dark 3 Temperature C electrometer under d.c. fields which varied over a range of 10 to 400 V cm1. In the pyroelectric current experiments the crystal was first polarized with a d.c. field of about 400 V cm1 while being cooled down from 320 K to 190 K at nearly constant rates in the range 18 mk s 1 ; at 190 K the electrodes were shortcircuited. The sample was then heated at constant rates (3 to 8 mk s1) and in order to measure the pyroelectric current the sample was shortcircuited with a resistance (RS) which is two to four orders of magnitude less than the sample resistance, so leakage current through the crystal could be neglected compared to pyroelectric current. The potential difference across RS, arising from the pyroelectric current originated at the crystal, was detected with the above mentioned electrometer. 3. Experimental results and discussion..1 TEM PERATURE DEPENDENCE OF DARK CURRENT PARALLEL TO c AxIS. current measured along the c axis of SbSI increased linearly with an applied electrical field (E ) (from 10 V cm to 400 V cm ) and it was found that the value of the electrical field in this range has a small effect on the value of the critical p temperature Tc 2 x 10 K cm V When ae 7 SbSI has a large resistivity and E is low, pyroelectric currents have a non negligible effect on dark current values under nonequilibrium thermal conditions, even at very low heating or cooling rates (quasistatic method). For heating rates of the order of 40 mk s we observed in the critical region an irregular behaviour of currents which can be explained by a superposition of a dark current and a pyroelectric current. Grigas et al. [18] observed a similar behaviour in large resistivity SbSI crystals, without giving any explanation. In order to minimize the pyroelectric current effects on dark currents, we have chosen a high value of E (370 V cm ) and very low heating rates. Dark current (I ) versus the inverse temperature (T) curve shown in figure 1 indicates a difference in temperature dependence above and below the critical region. These results were obtained at a constant increasing temperature rate of approximately 1 mk s far from the transition, while near the critical temperature (Tc) this rate was less than 0.5 mk s1. The sample had been previously cooled down, from 310 K at a decreasing rate of 1 mk s1 under a d.c. field of 370 V cm 1 to avoid phase boundaries. Experimental results for the temperature dependence of dark current (I) and its temperature derivative near the critical temperature are shown in figure 2. A method of sliding averages was used to calculate Fig. 1. of the dark current (I) (logarithm scale) on the inverse temperature near the critical temperature. Fig. 2. dependences of the dark current (I) (logarithm scale) and of the temperature derivative of dark current, near the critical temperature, Tc K.

4 . Schematic 261 the first derivative of I(T). The method consists of fitting a polynomial to a set of adjacent experimental points and calculating the derivative of the fitted curve. By sliding the polynomial along the experimental curve and choosing new sets of points, derivatives at each experimental point can be determined [19]. It has been a common practice to take the temperature where dildt has a relative maximum as the critical temperature also called transition temperature. The value we have obtained for the critical temperature (Tr K) is slightly below the values usually reported in literature. Grigas et al. [18] and Agrawal and Perry [20] also found Tc 288 K for SbSI. As we can see from figure 1, dark currents I+ above Tc and I_ below Tc obey the relations : where A + are constant and k is the Boltzmann constant. We have taken : (correlation coefficient of linear regression from our data : We can also evaluate [ a+ a I from the relation exp( a + a Ilk) A + /A _ leading to a value of 10.4 x 10 4 ev K 1. This value agrees fairly well with the result just reported above. The values obtained for AE, and a+ a [ are approximately one half of the shift of the gap of SbSI at Tc and of (aeg /at) (oeg+ /at) respectively. This suggests that the impurity level moves away similarly from the valence and the conduction bands, i.e. the conduction band raises relatively to the impurity level and the valence band lowers relatively to the impurity level as the temperature decreases. A schematic representation of the position of the impurity level relative to the bands, in both phases, is shown in figure 3. The good agreement between transport and optical data seems to justify the assumption made above, concerning E(T). Et and Et (effective activation energies) were determined from data shown in figure 1. Assuming that the changes in mobility and effective mass of free carriers in the phase transition are relatively small, the anomalous variation in the dark current at the critical region can only be associated with the free carrier concentration. Using this assumption and assuming an impurity level of activation energy E, we have I(T) A exp( E/kT ). Taking into account optical data [13, 14] it seems plausible to assume that the activation energies of impurity levels vary with the temperature, in ferro and paraelectric phases accompanying a width variation of the forbidden band with temperature. Let us suppose that : where Eo +, Ea are the activation energies of the impurity levels for T Tc in the paraelectric phase and ferroelectric phase, respectively; and a+, a are constant. Accordingly : and The shift of activation energy (flee) at the critical temperature is given by Fig. 3. representation of the position of the impurity level relative to the bands in the paraelectric phase (a) and the ferroelectric phase (b). The value of Et changed when we used a much faster heating rate (> 10 mk s ). For the same sample we found E* 0.59 ev (R ) and E * 0.81 ev (R ). Critical temperature also varies with the heating or cooling rates and in this experiment we found K. 3.2 PYROELECTRIC CURRENT AND TEMPERATURE DEPENDENCE OF SPONTANEOUS POLARIZATION. Experimental results of pyroelectric current measurement at uniform heating rate of 8 mk s1 in SbSI are shown in figure 4. As the temperature rises the current passes through a sharp maximum near Tc (282.9 K) and then gradually approches zero. The maximum of temperature dependence of the pyroelectric current and the dark current do not coincide. Without pretending to give a full explanation of this fact we would like to make some remarks. An applied d.c. electric field raises the critical temperature of a

5 Pyroelectric Temperature 262 time interval bt, the current in the external circuit is equal to With a constant increasing temperature rate, the spontaneous polarization is given by : Using this result the temperature dependence of the spontaneous polarization of SbSI as deduced from figure 4 can be seen in figure 5. The spontaneous polarization at 245 K is 15 03BCC cm2 and these results are in fair agreement with the values reported by Fatuzzo et al. [21] and Imai et al. [22]. Fig. 4. current (Ip) for SbSI. ferroelectric materials; for SbSI, dtc/de is approximately 23 x 10 3 K cm yl, and for an applied field of 400 V cm1 a variation of the order of 12 K in Tc is expected [15]. The carrier concentration, and thus the dark current, changes due to the gap variation with the temperature and also the temperature variation itself So the temperatures corresponding to the maxima of the temperature dependence of dark current and the temperature dependence of the gap width are different. The temperature of the maximum of gap width should be very similar to the temperature of the maximum of pyroelectric current. This analysis seems to qualitatively justify the shift of Tc towards higher temperature in dark current measurements. As is well known, the pyroelectric current is related to the change in the spontaneous polarization (Pg) An increase of5tin the temperature of the ferroelectric SbSI corresponds to a decrease of 6P. in its polarization. If the change in temperature occurs in a Fig. 5. dependence of spontaneous polarization (PS) for SbSI as deduced from the pyroelectric current. The Landau theory to describe second order phase transition is valid when the fluctuations of the order parameter are not too strong, i.e. for temperature not to close to the critical temperature Tc which coincides with the Curie temperature To. Ginzburg [23] has given a criterion which allows an estimation to be made of the width of the temperature range around To where this theory is not valid. In ferroelectric materials, because of the long range of the dipolar interaction, the region where the Landau theory does not apply is very narrow, typically of the order of 10 or 10 wheres I (To T)ITO I. For a first order transition, the change of phase occurs at a temperature Tc which is not To. The critical temperature Tc is higher than the temperature To (stability limit of the paraelectric phase), and lower than the stability limit of the ferroelectric phase temperature To [17]. The Landau theory predicts that the order parameter varies as (To T)1/2 in the low temperature phase; To is a value which can be expressed in terms

6 Temperature Logarithm Logarithm 263 Fig. 6. dependence of spontaneous polarization (Ps)2 for SbSI as deduced from. the pyroelectric current. of To and the Landau expansion coefficients of the free energy in powers of the order parameter, To > Tc [17]. For SbSI the order parameter is the electric polarization PS ; then we expect to have T)ITO. We have Pr B l è 11/2 with s (To checked this result by plotting the points of figure 5 in a diagram where the square of P. is represented versus T, on figure 6. Experimental points lie well c along a straight line, except far from the transition (T 260 K) where the points are below the line, as usual. For T T, there is a discontinuity with c some rounding probably due to weak inhomogeneities in the sample. This diagram immediately gives the temperature T o for which Ps 0. We find 0 Fig. 7. ju iu lu logarithm E To of spontaneous polarization plotted against I To 11 T to > T with To 286 K. A loglog plot of P. as a function of To T (Figs. 7 and 8) gives the value of 0.51 ± 0.02 for the polarization critical exponent p. Steigmeir and Harbeke [24] have analysed their results as a function of Be I (Tc T)jTc I. From their spontaneous polarization measurements they find fl 0.36 and from the Bragg intensity of the (082) Xray line (proportional to Ps ) they obtain Softmode behaviour of SbSI was studied by improved reflection techniques and Raman scattering experiments [25 to 28]. According to Harbeke et al. [28] the softmode frequency follows a law Q. (Tr T ) n3 Fig. 8. logarithm E of spontaneous polarization plotted against T, T To > T with To To for T Tr. We wish to point 286 K. out that these results which give for the exponent fl values different from 1/2 were all obtained through analysis with (T,, T)P of (To T)fl. On the other hand Ishikawa et al. [29] have shown that Go 1 varies linearly with temperature, i.e. the dielectric constant so of SbSI follows a Curie law. Moreover Agrawal and Perry [20] estimated that the temperature dependence of the softmode frequency is related to the temperature dependence

7 These The 264 of the dielectric constant so(t) as Q., EO(T) 1/2. Therefore this means that the softmode frequency exponent should be 1/2 in accordance with the mean field theory and our results. A new analysis of the results contained in [24] and [30] taking into account the first order character of this transition would be interesting. 4. Conclusion. results obtained on spontaneous polarization critical exponent (f3 1/2) are in accordance with the prediction of the molecular field theory. This agreement is given through an analysis which assumes the form Ps B s lfl with Previous results [24 and 30] which desagree with ours (and with the mean field theory) were obtained with the assumption P. Be J E III with Ge I (Tc T)ITC I which does not seem to be justified for a first order phase transition. We conclude that SbSI is a ferroelectric which satisfies the Landau theory. Acknowledgements. authors wish to express their gratitude to Pr. M. Balkanski for his kind interest and valuable suggestions and to Pr. M. K. Teng for helpful discussions. They also thank their Colleagues of the Physics Department for providing some equipment. Facilities from the Service Culturel, Scientifique et de Cooperation Technique de I Ambassade de France au Portugal are gratefully acknowledged. References [1] TENG, M. K., BALKANSKI, M., MASSOT, M. and ZIOLKIE WICZ, M. K., Phys. Status Solidi (b) 62 (1974) 173. [2] KIKUCHI, A., OKA, Y. and SAWAGUCHI, E., J. Phys. Soc. Japan 23 (1967) 337 and references therein. [3] FURMAN, E., BRAFMAN, O. and MAKOVSKY, J., Phys. Rev. B 8 (1973) [4] TAKAMA, T. and MITSUI, T., J. Phys. Soc. Japan 23 (1967) 331. [5] MORI, T., TAMURA, H. and SAWAGUCHI, E., J. Phys. Soc. Japan 20 (1965) 281. [6] NAKO, K. and BALKANSKI, M., Phys. Rev. B 8 (1973) [7] NITSCHE, R. and MERZ, W. J., J. Phys. Chem. Solids 13 (1960) 154. [8] Nosov, V. N. and FRIDKIN, V. M., Sov. Phys. Solid State 8 (1966) 113. [9] SASAKI, Y., Japan. J. Appl. Phys. 4 (1965) 228. [10] BERLINCOURT, D., JAFFE, H., MERZ, W. J. and NITSCHE, R., Appl. Phys. Lett. 4 (1964) 61. [11] HAMANO, K., NAKAMURA, T., ISHIBASHI, Y. and DOYANE, T., J. Phys. Soc. Japan 20 (1965) [12] HARBEKE, G., J. Phys. Chem. Solids 24 (1963) 957. [13] FRIDKIN, F. M., GERZANICH, E. I., GROSHIK, I. I. and LYAKHO VITSKAYA, V. A., JETP Lett. 4 (1966) 139. [14] FRIDKIN, V. M., GULYAMOV, K., LYAKHOVITSKAYA, V. A., Nosov, V. N., TIKHOMIROVA, N. A., Sov. Phys. Solid State 8 (1966) [15] PIKKA, T. A. and FRIDKIN, V. M., Sov. Phys. Solid State 10 (1969) [16] SASAKI, Y., Japan. J. Appl. Phys. 3 (1964) 558. [17] BLINC, R. and ZEKS, B., Soft modes in ferroelectrics and antiferroelectrics (NorthHolland publishing Company, Amsterdam) [18] GRIGAS, V. P., GRIGAS, I. P. and BELYATSKAS, R. P., Sov. Phys. Solid State 9 (1967) [19] ZUMSTEG, F. C. and PARKS, R. D., Phys. Rev. Lett. 24 (1970) 520. [20] AGRAWAL, D. K. and PERRY, C. H., Phys. Rev. B 4 (1971) [21] FATUZZO, E., HARBEKE, G., MERZ, W. J., NITSCHE, R., ROETSCHI, H. and RUPPEL, W., Phys. Rev. 127 (1962) [22] IMAI, K., KAWADA, S., IDA, M., J. Phys. Soc. Japan 21 (1966) [23] GINSBURG, V. L., Sov. Phys. Solid State 2 (1961) [24] STEIGMEIER, E. F. and HARBEKE, G., J. Physique Colloq. 33 (1972) C255. [25] PETZELT, J., Phys. Status Solidi 36 (1969) 321. [26] SUGAWARA, F. and NAKAMURA, T., J. Phys. Chem. Solids 33 (1972) [27] PERRY, C. H. and AGRAWAL, D. K., Solid State Commun. 8 (1970) 225. [28] HARBEKE, G., STEIGMEIER, E. F. and WEHNER, R. K., Solid State Commun. 8 (1970) [29] ISHIKAWA, K., SHIKATA, Y. and TOYODA, K., Phys. Status Solidi (a) 25 (1974) K187. [30] TENG, M. K., BALKANSKI, M. and MASSOT, M., Phys. Rev. B 5 (1972) 1031.