Materials Chemtitry and Physics, 30 (1991) 121-126 121

Electrical transport properties of LuVO, single crystal

A. K. Pandit, R. S. Singh, B. M. Wanklyn” and R. A. Singh Department of Physics, Universiy of Gorakhpur, Gorakhpur 273009 (India)

(Received June 6, 1991; accepted July 15, 1991)

Abstract

A.c. and d.c. conductivities, thermoelectric power and the dielectric constant of the LuVO, single crystal in the temperature range 300-1000 K have been studied. LuVO, is found to be a n-type semiconductor with energy band gap 2.2 eV. It exhibits an extrinsic nature up to 650 K and an intrinsic nature above it. The thermoelectric power increases with temperature in the region 300-650 K whereas it decreases with temperature in the region 650-1000 K. The dielectric constant increases with temperature in the entire temperature range studied with a rapid increase starting at T- 675 K.

Introduction

In the present paper, an attempt has been made to explain the conduction mechanism in single crystal LuVO,. A great deal of interest has been directed in the last three decades to the study of rare-earth elements and their compounds, because of the fact that they show unique physical properties and promise potential technical applications [l-3]. LuVO, is an important rare earth vanadate with zircon type (ZrSiO,) crystal structure at room temperature. The tetragonal space group of LuVO, single crystal is Di”, (14Jamd) with four formula units in the unit cell [4]. The lattice arameters of the elementary cell are a =7.026 x and c= 6.231 A. Ismailzade et al. [S] have studied the low temperature dielectric properties of LuVO, and other rare earth vanadates. In all of the rare- earth vanadates, a piezoelectric effect was observed at 0 to 10 “C. Thus at close to room temperature, the space group symmetry of LuV04 and other vanadates is polar, Cit-141 md. This paper reports on measurements of the a.c. and d.c. conductivities, thermoelectric power and dielectric constant of lutetium vanadate in the temperature range 300- 1000 K.

Experimental

Single crystals of LuV04 were grown by the flux method at the Clarendon Laboratory, Dept. of

*Permanent address: Clarendon Laboratory, Dept. of Physics, University of Oxford, Oxford (UK).

Physics, University of Oxford, Oxford, UK. Details about the crystal growth and identification tech- niques are given elsewhere [6]. The single crystals of LuVO, have a brown colour and the crystal on which the measurements were carried out, has a dimension 5.4 mm x 2.0 mm x 2.0 mm. The d.c. conductivity and thermoelectric power have been measured with a digital multimeter type PM 2522/ 90, Philips, India, with an accuracy better than f0.25% and 0.20% for resistance and e.m.f. mea- surements respectively. The a.c. conductivity and dielectric constant have been determined using an autocomputing digital LCR-Q meter type 4910, Applied Electronic Ltd., Thane, India, at an in- ternal frequency of 1 kHz. For dielectric mea- surement, the crystal has been used as dielectric medium. For all the measurements perpendicular to the c-axis, the two probe method was employed. The temperatures are recorded with the help of chromel-alumel thermocouple wires attached to the platinum electrodes. The details regarding the sample holder assembly and measuring techniques are given elsewhere [7].

Results

The logarithms of the a.c. and d.c. conductivities

(log G.,. and log c~.~.) versus the inverse of absolute temperature (103/r) are plotted in Fig. 1. A marked kink occurs at T - 650 K. In the temperature range 300-650 K, the a.c. conductivity is slightly larger than the d.c. conductivity, but for the temperature

0254-0584/91/$3.50 0 1991 - Elsevier Sequoia, Lausanne

81 I t ! \

I

1.0 1.5 2.0 2.5 3.0 3.5

103/T (IT') -

Fig. 1. Variation of logarithms of a.c. and d.c. conductivities (log qC, and log CT~.=.) with inverse of absolute temperature (lO$T). 0: ax. conductivity, A: d.c. conductivity.

range 650-1000 K, the two conductivities become almost equal. Using the relation

a=a, exp(-WIkT) (1)

with k in units eV/K, the observed temperature dependence of ad.=. yields

a,,=6.84~ 10e4 ohm-’ cm-’ and W=O.24 eV for 300 K<T~650 K (2)

and

a,= 151.356 ohm-’ cm-’ and W=l.lO eV for 650 K<T<lOOO K (3)

For the measurement of the thermoelectric power (S), the formula used is

(4)

where AE is the therm0 e.m.f. produced across the crystal due to the temperature difference AT. The thermoelectric power of LuV04 was measured in the temperature range 300-1000 K, and AT was kept at approximately 20 K. A plot of S versus 103/T is shown in Fig. 2. Its negative value in the entire temperature range, shows that LuVO, is a

n-type semiconductor with electrons as majority charge carriers. The variation of S, in units V/K, with T according to the simple two band model is given by [8],

S=$T+K

where

(5)

w c-l r)=- - e (-1 c+l (6)

I (7)

c = &ph and a = m,/m,

Here m,, CL, and mh, p,., are effective masses and mobilities of electrons and holes respectively. The charge carrier mobility has been calculated from eqns. (2), (3) and (5) together with the value of a, given by

(amh)3’4(k + ph)

where T is the mean temperature of the respective range. The charge carrier mobility comes out, to be 2.43 x 10m3 and 16.43 cm2 v-l SC’ in the tem-

123

Fig. 2. Variation of thermoelectric power (S) with inverse of absolute temperature (103/T).

perature range 300-650 K and 650-1000 K, re- spectively.

The dielectric constant at various temperature has been estimated using the formula [9]

11.3t E’ZC_ A (9)

where E’ is the dielectric constant, C the capac- itance in picofarads, t the thickness of the crystal in centimeters and A is the area of the electrode in cm’. The plot of log E’ versus T is shown in the Fig. 3.

Discussion

In the low temperature region (300-650 K), the activation energy is 0.24 eV, which is too low to be the activation energy for intrinsic conduction. So it may be associated with some sort of impurities and defects. The charge carrier mobility in the low temperature region (T <650 K) has been estimated as 2.43X 10e3 cm2 V-’ s-l. The low value of the charge carrier mobility and the ac- tivation energy indicate that small polaron for- mation takes place in this compound below 650 K. The formation of small polarons seems to be quite probable due to the presence of a narrow 4f-band and due to the ionic nature of LuVO+ Small polarons conduct either via a hopping mech- anism or by a band mechanism. In the case of

2.L c

1.2 300 LOO 500 600 700 Boo 900 1mo

T(K)-+

of Fig. 3. Variation temperature (T).

dielectric constant (log E’) with absolute

the charge carriers decreases with increase in temperature but in the case of small polaron hopping conduction, the mobility increases ex- ponentially with temperature. In this compound, the charge carrier mobility increases with tem- perature as evidenced by the increase in the ther- moelectric power with temperature below 650 K. Therefore, the small polaron band conduction cannot take place in this compound in the tem- perature range 300-650 K. Hence the only pos-

small polaron band conduction, the mobility of sibility left is the conduction via the small polaron

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hopping mechanism. In hopping type conduction, small polarons move from one lattice site to another by a thermally activated hopping process [1] and mobility of the charge carriers increases with tem- perature according to the relation [lo]

w9

where p, is constant, E, is the activation energy for mobility and T is absolute temperature.

In the case of small polaron hopping conduction, the electrical conductivity (a) follows the relation Pl, 12’)

En aT’“=A(T) exp - - i 1 kT (11)

where A(T) is almost constant and En is the small pofaron hopping energy. Figure 4 shows the plot of log (aTIn) versus 103/T. The plot is a straight line and follows eqn. (11). The estimated value of EH, from the slope of the line is 0.26 eV. The small polaron hopping energy, 0.26 eV, is in rea- sonable agreement with the activation energy, 0.24 eV below 650 K, for LuVO,. Therefore, the electrical conduction in this solid below 650 K is due to the small polaron hopping mechanism and the activation energy is entirely due to the thermally increased mobility.

In the temperature region 650-1000 K, the ac- tivation energy has been estimated as 1.10 eV, which appears to be the activation energy for

intrinsic conduction and the change in the nature of the log o versus lO”/T at T-650 K is due to the change in the conduction mechanism i.e. tran- sition from extrinsic to intrinsic conduction. How- ever this change may also be due to a magnetic or phase transition which has not been reported around 650 K in this compound. The value of activation energy, 1.10 eV, and charge carrier mobility, 16.43 cm2 V-’ s-i, calculated in the temperature range 650-1000 K suggest the large polaron band conduction. In large polaron band conduction, the mobility of charge carriers de- creases with temperature. For this compound, the mobility of charge carriers decreases with tem- perature as evidenced by the decrease in ther- moelectric power with temperature above 650 K. Therefore, we infer that in the intrinsic region (T> 650 K), the electrical conduction in LuV04 is due to the large polaron band mechanism. The large polaron band conduction takes place via the normal band mechanism with enhanced mass of the charge carriers and the mobility of the charge carriers is expected to decrease with increase in temperature. In LuV04, the relevant bands for conduction are empty Lu3+:5d, V5+:4s and V5’:3d bands, partially filled Lu3 + :4f band and completely filled 02-:2p band. The electrons of the 4f band have atomic character even in rare-earth solids and form only very narrow and high correlated bands 113, 147. The value usually quoted for band width is 0.05 eV. Hence the pa~icipation of 4f electrons in conduction is not possible {15, 161.

2 I t

1.S 2.0 2.5

103/l (ii’)-

Fig. 4. Variation of log (UT’“) with id/r.

The 5d band in rare-earth solids is regarded as the conduction band [14]. Thus it seems likely that electrons in the 5d band, caused by the thermal excitation of electrons from 4f or 5p bands and holes left thereby are responsible for the electrical conduction above T - 650 K. So, the only appro- priate bands for high mobility electrical conduction are the Lu3+:5d empty band and the O*-:2p filled band. The 2p band is expected to be an ordinary band (about 4 eV wide) and the large polaron theory of conduction should be applied in this band. The 5d band is in comparison a narrow band, and the mobility of charge carriers in the 5d band is thus expected to be low in comparison to the mobility of charge carriers in the O*-:2p band. Thus intrinsic conductivity should be dom- inated by large polarons. The electron or hole current domination will depend upon the effective mass of the charge carriers in the empty band Lu3+:5d and the filled band O*-:2p [17, 181. However, both these holes and electrons are ex- pected to interact with the lattice and this may lead to the formation of large polarons as discussed by several authors [ll, 19, 201. The electrical conduction of a large polaron is of band type and the expression for the conductivity is

IT= a, exp( - E,/2kT) (12)

where E, is the energy band gap of the solid and a, is a constant. In the temperature range 650- 1000 K, the log g versus 103/T plot is a straight line and conduction is probably band type due to large polarons. The estimated band gap for LuVO, single crystal is 2.2 eV.

Below 650 K, a.c. conductivity is slightly higher than d.c. conductivity, which predicts that the conductivity in the temperature range 300-650 K is ionic as well as electronic. Higher value of aa.,. also indicates that some imperfections are present in the compound due to which dielectric loss occurs. Beyond 650 K, the two conductivities (a,.,, and oh.,.) coincide. Coincidence of the a.c. and d.c. conductivities at higher temperature shows that the material is predominantly an electronic semi- conductor.

The change at T- 650 K in the thermoelectric power versus 103R plot is associated with the change in the conduction mechanism from extrinsic to intrinsic. The increase in thermoelectric power with temperature up to 650 K is due to the small polaron hopping mechanism because in this mech- anism, the mobility of the charge carriers increases with temperature. The decrease in thermoelectric power with temperature in the range 650-1000 K confirms our conclusion of large polaron band

125

conduction in LuVO, above 650 K. In the large polaron band conduction, the number of the charge carriers increases exponentially with the temper- ature and the mobility of the charge carriers decreases with temperature. Due to these factors, thermoelectric power decreases with temperature in the region 650-1000 K.

The slow increase in E’ up to 675 K is due to the ionic nature of the compound. In ionic solids the dielectric constant increases slowly at low temperatures [21-231. This happens because the lattice expands and the polarizability of the ion is affected by changes in the temperature and the available volume. The ionic and electronic polar- izations will also be considerable because these polarizations always exist at low frequencies [24]. Moreover, the dielectric loss due to defects will also contribute below 650 K, because the compound has extrinsic nature up to this temperature.

The rapid increase in E’ above 675 K is due to the large polaron formation [25]. These large polarons increase the polarizability of the ions to a greater extent, thereby resulting in a large in- crease in E’. The exponential increase in the number of the charge carriers in the intrinsic region (above 650 K) produces high space charge polarization which will contribute considerably to the dielectric constant.

Conclusion

Lutetium vanadate is a n-type semiconductor with energy band gap 2.2 eV. Below 650 K, it exhibits extrinsic nature and the conduction is hopping type due to small polarons. Above 650 K, the compound exhibits intrinsic nature and the conduction is band type due to large polarons.

Acknowledgement

The authors are thankful to the University Grants Commission (UGC), New Dehli, India, for providing financial support.

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