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Materials Research

Print version ISSN 1516-1439On-line version ISSN 1980-5373

Mat. Res. vol.6 no.4 São Carlos Oct./Dec. 2003 



Characterization of Bi4Ge3O12 single crystal by impedance spectroscopy



Zélia Soares MacedoI, *; André Luiz MartinezII; Antonio Carlos HernandesII, *

IDepartamento de Física, Universidade Federal de Sergipe C.P. 353, 49100-000 São Cristovão - SE, Brazil
IIInstituto de Física de São Carlos, Universidade de São Paulo C.P. 369, 13560-970 São Carlos - SP, Brazil




Bi4Ge3O12 (bismuth germanate — BGO) single crystals were produced by the Czochralski technique and their electrical and dielectric properties were investigated by impedance spectroscopy. The isothermal ac measurements were performed for temperatures from room temperature up to 750 °C, but only the data taken above 500 °C presented a complete semicircle in the complex impedance diagrams. Experimental data were fitted to a parallel RC equivalent circuit, and the electrical conductivity was obtained from the resistivity values. Conductivity values from 5.4 × 109 to 4.3 × 10-7 S/cm were found in the temperature range of 500 to 750 °C. This electrical conductivity is thermally activated, following the Arrhenius law with an apparent activation energy of (1.41 ± 0.04) eV. The dielectric properties of BGO single crystal were also studied for the same temperature interval. Permittivity values of 20 ± 2 for frequencies higher than 103 Hz and a low-frequency dispersion were observed. Both electric and dielectric behavior of BGO are typical of systems in which the conduction mechanism dominates the dielectric response.

Keywords: bismuth germanate, impedance spectroscopy



1. Introduction

Bismuth germanate (Bi4Ge3O12 — BGO), which has a cubic crystalline structure known as eulitine, has been demanded a great deal of interest due to its electro-optic, electro-mechanical and scintillator properties1-3. In particular, the use of BGO single crystals in electromagnetic measurements presents many advantages, since it possesses small temperature-dependence of electro-optic effect, high electrical resistivity, no optical activity, no natural birefringence and no pyroelectric effects2,4. The use of bismuth germanate as optical fiber sensor for simultaneous measurement of current and voltage was considered recently5 and it was successfully tested for ac currents from 0.05 to 10 A and voltages from 1 to 235 V.

The literature presents several papers about the BGO crystal structure, scintillation, refractive index, absorption and luminescence over varied wavelengths and conditions. Dielectric permittivity of Bi4Ge3O12 was reported by Link et al.6 only at 103 Hz, in the temperature range from 6 to 325 K, and to our knowledge there is no report on the conductive behaviour of this crystal. The aim of this paper is to present data about the electrical and dielectric parameters of BGO single crystals determined by ac measurements for frequencies between 102 and 106 Hz, in the temperature interval of 500 to 700 °C. This knowledge would provide a better understanding of the defect structure of this material and it would be an advance in the optimization of their properties.


2. Experimental

BGO single crystals were grown by the Czochralski technique from high temperature stoichiometric compositions, using high purity cylindrical platinum crucibles of 50 cm3 in volume. BGO seeds oriented along the [0 0 1] direction were held in a pure platinum seed holder and used to initiate the crystal growth. The runs were carried out in room atmosphere and the growing temperature was 1120 °C. The pulling and rotation rates were 0.2 mm/h and 14 rpm, respectively. Transparent single crystals without inclusions were produced with typical sizes of 10 mm in radius and 20 mm in height.

For the impedance spectroscopy measurements, the crystal was cut in slices of 4 × 4 × 1 mm3 and polished with alumina powder. The samples were cleaned with acetone in ultrasonic bath for 15 min and dried at 100 °C. Electric contact was made by applying Pt paste on the (110) faces of the samples and firing it at 700 °C for 30 min. The measurements were made in the frequency range from 100 Hz to 1 MHz, with an applied potential of 500 mV, using a Solartron 1260 Impedance Analyzer controlled by a personal computer. Isothermal ac measurements were taken from room temperature up to 750 °C. The measured values of impedance Z* = Z' + iZ'' were analyzed using the software Zview7, adopting equivalent circuits to simulate the immitance spectra and complex diagrams.


3. Results and Discussion

3.1. Electrical Characterization

Figure 1 shows the complex impedance diagrams for measurements acquired at 600, 650, 700 and 750 °C. These complex plots form semicircular arcs, and each experimental point corresponds to a frequency value. The semicircle diameter expresses the electrical resistivity of the sample at the specified temperature and the maximum value corresponds to the relaxation frequency w = 1/RC. As the impedance measurements performed for BGO below 500 °C did not present a complete semicircle, they were not considered in this study. The diagrams show only the contribution in the high frequency region. No other relaxation mechanism, such as the electrode effect and ionic species diffusion, was identified for the analyzed frequency range8.



The equivalent circuit adopted to simulate the experimental data consisted in a simple parallel RC. The fitting is exemplified in Fig. 2, which shows the experimental data taken at 750 °C, as well as the simulated curve and the equivalent circuit employed. Good agreement between the experimental and theoretical curves was observed. The electrical properties of Bi4Ge3O12 crystal can thus be associated with a simple RC equivalent circuit.



The existence of a single relaxation mechanism was corroborated by the plots of the imaginary and real parts of Z* as functions of the frequency, as seen in Fig. 3. In these plots, shown for T = 750 °C, it was observed only one maximum value of Z'' accompanied by an inflexion point in the Z' curve at the relaxation frequency f0 = 1/2pRC. For this temperature f0 = 40 kHz, corresponding to the maximum in the semicircle of the Fig. 2.



Figure 4 shows the electrical conductivity curves of BGO as a function of the signal frequency. The values of s' were derived from the impedance data using the relation:



BGO electrical conductivity presented a frequency independent part at low frequencies followed by a part in which it obeys approximately the universal power law s'(f) µ wn, where 0 < n <1 9,10. The conductivity value at the plateau (s'p) is interpreted as the dc conductivity11,12.

The behavior of the electrical conductivity with frequency agrees with that predicted for conduction mechanisms over a random distribution of energy barriers in a disordered solid12. For dc conduction the largest energy barriers are overcome, while lower barriers are involved for ac conduction since only a limited distance has to be traveled. At high ac frequencies, the electrical conductivity is increased by the hopping of the charge carrier backward and forward at places with high jump probability. This enhancement in the electrical conductivity continues as long as the frequency of the applied field is lower than the maximum jump frequency in the solid12. In Bi4Ge3O12 structure, the Ge4+ possesses a tetrahedra of coordination quite regular, with ions O2- at a distance of 1.740 Å, but the ion Bi3+ is coordinated by three ions O2- at 2.160 Å and three ions O2- at 2.605 Å, in a very deformed octaedra13. This disorder in BGO structure could account for a distribution of energy barriers for the conduction process, reflected in the dispersion of electrical conductivity values at high frequencies.

The plots in Fig. 4 allow us to evaluate the electrical conductivity s'p in the frequency independent interval. These values were taken at the fixed frequency f = 103 Hz and used to calculate the apparent activation energy of the process. Additionally, the ac conductivity (s'ac) of BGO was determined from the complex impedance diagrams, in which the semicircle diameter stands for the resistivity r = 1/s'ac of the system. From our results, it was verified that both s'p and s'ac were thermally activated according to the Arrhenius law (see Fig. 5):



where s0 is a pre-exponential factor and Ea, k and T represent the apparent activation energy for conduction process, Boltzmann' constant and the absolute temperature, respectively.

The experimental data shown in Fig. 5 were fitted to Eq. 2 and the apparent activation energy Ea = (1.41 ± 0.04) eV was deduced from the slope of the calculated curve. This energy was the same for both sets of s'p and s'ac values, indicating that the ac conductivity in BGO is dominated by a slow, long-range mechanism.

Among the possible defects in the BGO structure, the most probable one is ion substitution14, either in the Bi3+ or Ge4+ sites. Considering that the grouping (GeO4)4- is very stable the charge compensation, if needed, can be supplied either by the removal of some Bi3+ or O2- from their sites or by oxidation of Bi3+ into Bi5+ 14,15. This defect structure results in various trapping centers with different depths since Bi4Ge3O12 lattice structure contains several non-equivalent oxygen sites. Kovács et al.16 have determined a thermoluminescent peak of Bi4Ge3O12 at 130 °C, with activation energy of 0.86 eV, and all the other trap centers of BGO were detected at lower temperatures17,18,19. As the band gap of Bi4Ge3O12 was determined to be 5.0 eV at room temperature20, the activation energy Ea = (1.41 ± 0.04) eV observed in this work could be related to deeper traps than those registered by Kóvacs et al.3z. It can be hypothesized that the conduction mechanism in BGO is due to hopping electrons and that, at low frequencies, it is dominated by the electrons released from these deep traps.

3.2. Dielectric Characterization

In a dielectric under external oscillating field, the answer of the system can be expressed in terms of the complex dielectric permittivity e*:

which is obtained from the complex impedance data Z* by the expression21:

where S is the electrode area,is the pellet thickness and e0 is the vacuum permittivity. The real part e' is the relative permittivity, or dielectric constant, and the imaginary part e'' is the loss factor.

The real and imaginary parts of complex permittivity of BGO were used to evaluate its dependence on frequency. Figure 6 shows log-log plots of e' and e'' at several temperatures. For frequency values higher than 103 Hz, e' presented a weak dependency on the frequency or temperature. The dielectric constant, calculated from the average value over the frequency range of 103 to 106 Hz and several temperatures between 550 and 750 °C, was e' = 20 ± 2. This value is consistent with the value e' = 16 determined by Link et al.6 at f = 103 Hz over the temperature range of 6 to 325 K.



No loss peak was observed in the e'' spectra, characterizing a deviation from the dipolar response of the system, predicted by the Debye theory22. This feature indicates that the applied field interacts with the material not only through reorientation of the electric dipoles9,10,23, but also through the displacement of the charge carriers, in accordance with the hopping-type conduction proposed for BGO in this work.


4. Conclusions

The electrical and dielectric properties of Bi4Ge3O12 single crystals, in the frequency interval of 102 -106 Hz and temperature interval of 500 to 750 °C, were reported by the first time in the present work.

Impedance measurements of Bi4Ge3O12 single crystals allowed us to determine an unique electrical process, identified by a single semicircle in the complex diagrams. The electrical conductivity curves agree with that proposed by Dyre for conduction mechanisms over a random distribution of energy barriers in a disordered solid. Our results provided some evidence that the conduction process is associated to defects in the (BiO6)9- octaedra. As these octaedra are deformed, they can give rise to trapping centers with different depths, which result in a distribution of energy barriers for the conduction process.

The real part of the complex dielectric permittivity was e' = 20 ± 2 for frequency values higher than 103 Hz for all the measured temperatures, and presented a low-frequency dispersion. This feature, combined to the absence of a loss peak in the e'' vs. f curve, characterized a deviation from the dipolar response of the system. Both electrical and dielectric behaviors of BGO are typical of systems in which the charge-carrier polarization dominates the dielectric response.



The authors acknowledge CNPq, CAPES and FAPESP by the financial support.



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Received: February 10, 2003
Revised: September 8, 2003
Trabalho apresentado no V Encontro da Sociedade Brasileira de Crescimento de Cristais, Guarujá - SP, 2002



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