Critical behaviour of dark current and spontaneous polarization in ferroelectric SbSI

HAL Id: jpa-00209241

https://hal.archives-ouvertes.fr/jpa-00209241

Submitted on 1 Jan 1980

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished 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.

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 spon- taneous polarization in ferroelectric SbSI. Journal de Physique, 1980, 41 (3), pp.259-264.

�10.1051/jphys:01980004103025900�. �jpa-00209241�

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 Pierre-et-Marie-Curie, Tour 13, 4, place Jussieu, 75230 Paris Cedex 05, France

(Reçu ^{le 18} juillet 1979, accepté ^{le 12 novembre} 1979)

Résumé.

Le courant d’obscurité et la polarisation spontanée, ^{obtenus en mesurant le courant} pyroélectrique,

ont été utilisés pour faire l’étude de la transition ferro-paraélectrique ^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).

Abstract.

Dark current and spontaneous polarization, ^{obtained from} measurements of pyroelectric ^current,

have been used to study ^the ferro-paraelectric transition in SbSI crystals. The critical exponent ^{of the} spontaneous polarization ^{is found to} have the value predicted ^{from a mean field} theory (03B2

^{0.51 ±} 0.02).

Classification - Physics ^Abstracts

64.70 - 77.70

1. Introduction.

SbSI has been thoroughly investigated ^{for its} ferroelectric properties ^{and, as}

shown by the experimental ^{data, it} undergoes ^{a first}

order ferro-paraelectric transition of displacive ^nature

around 293 K [1 ^to 6]. SbSI exhibits photoconduc-

tive [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 0.02-0.03 eV [13, 14]. This transi- tion is also accompanied by ^a change ^{in the} coefficient of the temperature dependence ^{of the width of the}

forbidden band : (OEg’IOT) ^{9 x 10-4 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 0.2-0.3 eV [8,15,16]. Dielectric and static electronic

properties ^of single domain SbSI are quite well under- stood but’ data concerning non-equilibrium pheno-

mena are a matter of some controversy. In fact in a

first order ferro-paraelectric transition a metastable para ^or ferroelectric phase ^may both exist either below

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 incon-}

veniences reported ^above.

2. Experimental procedure.

Experimental ^results

were obtained _by using needle-shaped crystals, ^10-

15 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 ^c-axis 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

(*) ^{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 Scien-

tifique (C.N.R.S.).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01980004103025900

260

610 C electrometer under d.c. fields which varied over a range of 10 to 400 V cm-1. In the pyroelectric ^cur-

rent experiments ^the crystal ^{was first} polarized ^{with a}

d.c. field of about 400 V cm-1 while being ^cooled

down from 320 K to 190 K at nearly constant rates in the range 1-8 mK s - 1 ; ^{at 190 K} the electrodes were

short-circuited. The sample ^was then heated at constant rates (3 ^{to 8 mK} s-1) and in order to measure

the pyroelectric ^{current the} sample ^{was short-cir-}

cuited 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.

3 .1 TEM-

PERATURE DEPENDENCE OF DARK CURRENT PARALLEL TO c AxIS.

Dark 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 temperature _p T-c 2 x 10 K cm V _aE ^When

SbSI has a large resistivity ^{and E is} low, pyroelectric 7

Fig. ^1.

Dependence of the dark current (I) (logarithm scale)

on the inverse temperature ^{near the} critical temperature.

currents have a non negligible ^{effect on dark current}

values under non-equilibrium ^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 ^beha-

viour of currents which can be explained by ^a super-

position ^{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 tempera-

ture (Tc) ^{this rate was less than 0.5 mK s-1. The} sample ^{had been} previously ^cooled down, ^from

310 K at a decreasing ^{rate of 1 mK s-1 under a d.c.}

field of 370 V cm- 1 to avoid phase boundaries.

Experimental results for the temperature depen-

dence of dark current (I) ^{and its} temperature ^deriva- tive near the critical temperature ^{are shown in} figure ^2.

A method of sliding averages ^was used to calculate

Fig. ^2.

Temperature dependences ^{of the dark current} (I) (logarithm scale) ^{and of the} temperature derivative of dark current,

near the critical temperature, Tc

^{288.3 K.}

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 experimen-

tal 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} tempe-

rature where dIldT ^{has a} relative maximum as the critical temperature also called transition tempera-

ture. The value we have obtained for the critical tem-

perature (Tr

^288.3 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 cons-}

tant.

We have taken :

(correlation coefficient of linear regression

Et ^{and Et} (effective activation energies) ^{were deter-}

mined from data shown in figure ^1.

Assuming ^{that the} changes ⁱⁿ mobility and effective

mass of free carriers in the phase transition are rela-

tively small, ^the anomalous variation in the dark current at the critical region ^can only be associated with the free carrier concentration. Using ^this assump- tion 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 for- bidden 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

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 assump- tion made above, concerning E(T).

Fig. ^3.

^Schematic 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

^0.998 8) ^and

E *

0.81 eV (R

^0.999 0). ^Critical temperature also varies with the heating ^or cooling ^{rates and in this} experiment ^{we found 284.7 K.}

3.2 PYROELECTRIC CURRENT AND TEMPERATURE DEPENDENCE OF SPONTANEOUS POLARIZATION. -

Experimental ^{results of} pyroelectric ^{current measu-}

rement at uniform heating ^{rate of 8 mK s-1 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 pyro- electric 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}

262

Fig. ^4.

Pyroelectric ^current (Ip) ^{for SbSI.}

ferroelectric materials; ^for SbSI, dTc/dE ^is approxi- mately ^{2-3 x 10- 3 K cm} y-l, ^{and for an} applied

field of 400 V cm-1 a variation of the order of 1-2 K

in Tc ^is expected [15].

The carrier concentration, and thus the dark cur-

rent, changes ^{due to} the gap variation with the tempe-

rature 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} pola-

rization. If the change ⁱⁿ temperature ^{occurs in a}

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 ^cm-2 and these results

are in fair agreement ^{with the values} reported by

Fatuzzo et al. [21] and Imai et al. [22].

Fig. ^5.

Temperature 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 ferro-}

electric 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} tempera-

ture 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} para-

meter varies as (To - T)1/2 ^{in the low} temperature

phase; To ^{is a} value which can be expressed ^{in terms}

Fig. ^6.

Temperature 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}

Pr

^B l’è 11/2 ^{with s}

(To - T)ITO. ^{We have}

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 transi- tion (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} inhomoge-

neities in the sample. ^This diagram immediately gives

the temperature T’o ^{for which} Ps ^{= 0. We find}

0

A log-log plot ^of P. as ^a function of To - ^T (Figs. ⁷

and 8) gives ^{the value of 0.51} ± 0.02 for ^the polari-

zation 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) X-ray ^line (proportional ^to Ps ) they obtain ^{= 0.28.}

Soft-mode behaviour of SbSI was studied by improved

reflection techniques and Raman scattering expe- riments [25 ^to 28]. According ^to Harbeke et al. [28]

the soft-mode frequency ^{follows a law} Q. - (Tr - T ) n3

ju iu lu

Fig. ^7.

Logarithm ^of spontaneous polarization plotted against logarithm E

I To - T to > ^To 11 ^{T with} To

^{286 K.}

Fig. ^8.

Logarithm ^of spontaneous polarization plotted against logarithm E

T, T To > T with To

^{286 K.}

To

for T Tr. ^{We wish to} point ^{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 soft-mode}

frequency is related to the temperature dependence

264

of the dielectric constant so(T) ^as Q., - EO(T)- ^1/2.

Therefore this means that the soft-mode 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.

These results obtained on sponta-

neous 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 ferro- electric which satisfies the Landau theory.

Acknowledgements.

The 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) ^2341.

[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) ^5759.

[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) ^1886.

[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) ^1510.

[15] PIKKA, ^{T. A. and} FRIDKIN, V. M., Sov. Phys. Solid State 10

(1969) ^2668.

[16] SASAKI, Y., Japan. ^J. Appl. Phys. ³ (1964) ^558.

[17] BLINC, ^{R. and} ZEKS, B., Soft ^{modes in} ferroelectrics ^{and anti-} ferroelectrics (North-Holland publishing Company,

Amsterdam) ^1974.

[18] GRIGAS, ^V. P., GRIGAS, ^{I. P.} and BELYATSKAS, ^R. P., ^Sov.

Phys. ^{Solid State 9} (1967) ^1203.

[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) 1893.

[21] FATUZZO, E., HARBEKE, G., MERZ, ^W. J., NITSCHE, R., ROETSCHI, H. and RUPPEL, W., Phys. ^{Rev. 127} (1962)

2036.

[22] IMAI, K., KAWADA, S., IDA, M., ^J. Phys. ^Soc. Japan ²¹ (1966)

1855.

[23] GINSBURG, ^V. L., ^Sov. Phys. Solid State 2 (1961) ^1824.

[24] STEIGMEIER, E. F. and HARBEKE, G., ^J. Physique Colloq. ³³ (1972) ^C2-55.

[25] PETZELT, J., Phys. Status Solidi 36 (1969) ^321.

[26] SUGAWARA, ^F. and NAKAMURA, T., ^J. Phys. Chem. Solids 33

(1972) ^1665.

[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) ^1765.

[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.