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Nature of the Schottky-type barrier of highly dense SnO2 systems ... approached Mott–Schottky model, are used to demonstrate that the potential barriers at the ...
JOURNAL OF APPLIED PHYSICS

VOLUME 88, NUMBER 11

1 DECEMBER 2000

Nature of the Schottky-type barrier of highly dense SnO2 systems displaying nonohmic behavior P. R. Bueno,a) M. R. de Cassia-Santos, E. R. Leite, and E. Longo ˜ o Carlos, C. Postal 676, LIEC—Department of Chemistry, UFSCar—Federal University of Sa ˜ o Carlos, SP, Brazil 13565-905 Sa

J. Bisquert, G. Garcia-Belmonte, and F. Fabregat-Santiago Departament de Cie`ncies Experimentals, Universitat Jaume I, 12080 Castello´, Spain

共Received 6 December 1999; accepted for publication 28 August 2000兲 The electrical characteristics of highly dense SnO2 ceramic varistors are believed to be caused by the existence of potential barriers at the grain boundary. A complex plane analysis technique 共to eliminate the influence of trapping activity associated with the conductance term observed via depression angle of a semicircular relaxation in the complex capacitance plane兲, allied with an approached Mott–Schottky model, are used to demonstrate that the potential barriers at the grain boundary are Schottky-type barriers in SnO2 varistors such as those observed in the traditional ZnO varistor. © 2000 American Institute of Physics. 关S0021-8979共00兲03823-8兴

I. INTRODUCTION

made of the high frequency intercept associated with high frequency relaxation. The presence of the back-to-back Schottky-type barrier is inferred from the voltage dependence of the capacitance. The applied voltage dependence of capacitance can be approximated using the approach of Mukae, Tsuda, and Nagasawa,15 as

Tin oxides are known to display low densification during sintering, leading to the use of this typical n-type semiconductor in highly porous devices such as gas sensors.1 It has been proved that negatively charged oxygen adsorbates, such as O⫺ , O2⫺ , etc., on the surface of SnO2 grain boundaries 共and/or of grains兲, play an important role in detecting inflammable gases.1–3 For this reason, oxygen vacancies and electronic states on SnO2 surfaces have been studied in great detail.2,3 On the other hand, the addition of CoO and MnO2 to SnO2 produces high densification,4–6 allowing for the development of other electronic devices such as varistors.6,7 Other authors, mainly from our own group, have recently reported that dense SnO2 ceramics doped with CoO and small concentrations of Nb2O5 and Cr2O3 display highly nonohmic current–voltage (I – V) characteristics6–9 at room temperature, with electrical characteristics similar to commercial metal oxide varistors, which are also highly dense polycrystalline ceramics composed predominantly of ZnO, with additions of Bi2O3 , Sb2O3 and other oxide constituents. The most appropriate model to explain the nonohmic behavior of ZnO-based varistor systems is based on the presence of an electrostatic potential barrier located in regions of direct ZnO grain-to-grain contact.10–12 This article discusses the capacitance–voltage (C – V) characteristics of highly dense SnO2 varistors, using complex plane analyses. A significant dispersion of metal oxide varistor admittance with ac frequency is typically observed, giving rise to a complex Mott–Schottky response.13–16 The interpretation proposed by Alim14 is applied in this study to characterize the C – V characteristics of the highly dense SnO2 grain boundary, without incorporating other frequencydependent phenomena in the analysis. Calculations were





2



2 共 ␾ ⫹V 兲 , q ⑀ r⑀ 0N d b

共1兲

where q is the electron or elementary charge, ⑀ r is the relative permittivity ( ⑀ r to SnO2 grain is ⬃14兲, ⑀ 0 is the permittivity of free space, N d is the donor concentration, and ␾ b is the barrier height of the system. C 0 and C are the capacitance per unit area of a grain boundary biased, respectively, with zero and V volts. The density of the N IS states at the interface between the SnO2 grain and the intergranular layer was estimated using N IS⫽



2N d ⑀ r ⑀ 0 ␾ b q



1/2

共2兲

.

Thus, the interpretation of Alim14 and the approach of Mukae, Tsuda, and Nagasawa15 were used to infer the presence of the Schottky-like barrier and to characterize the nature of the barrier formed in a highly dense SnO2 -based nonohmic ceramic. II. EXPERIMENTAL PROCEDURE

The ceramic samples used in this study were prepared using the ball milling process in an alcohol medium. The oxides used were SnO2 共Merck兲, CoO 共Riedel兲, Nb2O5 共CBMM兲, and Cr2O3 共Vetec兲. The composition of the molar system was 98.95% SnO2 ⫹1.0% CoO⫹X% Nb2O5 ⫹0.05% Cr2O3 共SCNbX%Cr兲, with X equal to 0.035%, 0.050%, and 0.065%. This is one of the best compositions to obtain high nonlinear behavior.6–9 The chemical analysis of SnO2 revealed that the main impurities were Pb 共⬍0.01%兲, Fe 共⬍0.01%兲, Ge 共⬍0.005%兲, and Cu 共⬍0.005%兲, all in

a兲

Author to whom correspondence should be addressed; electronic mail: [email protected]

0021-8979/2000/88(11)/6545/4/$17.00

1 1 ⫺ C 2C 0

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© 2000 American Institute of Physics

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FIG. 1. Experimental I – V characteristics of the SnO2•CoO-based varistor systems. 共䊏兲 SCNb0.035%Cr composition; 共䊊兲 SCNb0.050%Cr composition; 共䉱兲 SCNb0.065%Cr composition. FIG. 2. SEM micrograph of the SCNb0.05%Cr varistor system.

mol%. The powder obtained was pressed into pellets 共11.0 mm⫻1.0 mm兲 by uniaxial pressing 共20 MPa兲, followed by isostatic pressing at 210 MPa. The pellets were sintered at 1300 °C for 1 h, with a cooling rate of 10 °C min⫺1. The mean grain size of the samples was determined by analyzing the scanning electron microscopy 共SEM兲 micrographies 共ZEISS DSM 940A兲 using image analysis software 共PGT— IMIX兲. For the electrical measurements, silver contacts were deposited on the samples’ surfaces, after which the pellets were heat treated at 400 °C for 30 min. Current–voltage measurements were taken using a high voltage measuring unit 共KEITHLEY Model 237兲, while impedance measurements were taken using a frequency response analyzer 共HP 4194 A兲 at frequencies ranging from 100 Hz to 15 MHz, with an amplitude voltage of 1 V. The pellets were placed in a sample holder inside a furnace and measured at temperatures ranging from 25 to 200 °C. The impedance data were analyzed using the EQUIVCRT program.17 III. RESULTS AND DISCUSSIONS

The typical room-temperature I – V characteristic of the systems studied is shown in Fig. 1. The densities of all the systems exceed 98.5% of the theoretical density. Figure 2 presents the SEM micrography of the SCNb0.05%Cr composition, illustrating the microstructure of SnO2•CoO-based varistor systems presented in earlier articles.6–8 The nonohmic coefficients, calculated from 1 mA cm⫺2 of current density up to the last values shown in Fig. 1, can be observed in Table I. The breakdown voltage (E b ) and the barrier voltage per grain (V gb) for these systems, calculated at room temperature, are also given in Table I. Figure 3 shows the complex capacitance of the SCNb0.05%Cr system at room temperature. The total ac electrical data, acquired in the form of the terminal admittance Y * over a large frequency range, is used in the C * plane to represent the best meaning of dispersion. The latter 共the C * plane兲 was used to construct the Mott–Schottky behavior according to Alim,14 allied to

the Mott–Schottky approach of Mukae, Tsuda, and Nagasawa.15 The universal response is given by C *⫽

Y* Gp ⫽C ⬘ ⫺ jC ⬙ ⫽C p ⫺ j , j␻ ␻

共3兲

where ␻ is the angular frequency (⫽2 ␲ f ) and j⫽ 冑⫺1. The G p parameter includes the dc conductance as well as the relaxation-associated loss.18,19 The diagrams in Figs. 3共a兲 and 3共b兲 show the emergence of part of a circle 共with a tendency for negative capacitance values in the C * plane, as can also be seen in the work of Alim, Seitz, and Hirthe13兲 at higher frequencies. This partial circle results from an LCR resonance series, which is attributed to the external electrode-lead configuration and to the built-in contact inductance of the sample holder. The grain boundary capacity (C BL ) is located in the transition region, while the electrical manifestation of the trapping states of the SnO2 -based varistor system are located at lower frequencies. The corresponding Mott–Schottky plot 共i.e., 关 C BL 兴 ⫺2 vs dc voltage兲 at different temperatures is shown in Fig. 4 for the SCNb0.05%Cr system. A good linear relationship can be seen between the left side of Eq. 共1兲 and the dc voltages, indicating that the barriers formed at the grain boundaries of highly dense SnO2 are of a Schottky nature. This good linear relationship confirms that the shallow donor concentration within SnO2 grains is spatially uniform, as in ZnO.13 The value of the frequency-dependent capacitance, used in conjunction with the information on grain size, reflects the avTABLE I. Nonlinear coefficient values 共␣兲, breakdown voltage (E b ), the barrier voltage per grain (V gb), and mean grain size to the SnO2-CoO-based varistor systems studied.

Nb2O5 mol %

␣ values

E b (V cm⫺1 )

V gb 共V/grain兲

Mean grain size 共␮m兲

0.035 0.050 0.065

33.4 22.2 15.4

3920 6110 11 950

1.5 2.6 3.2

3.72 3.70 3.56

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TABLE II. The ␾ b , N d , and N IS values for a back-to-back Schottky-type potential barrier of SCNbX%Cr varistor systems. These calculations take into consideration the average number of grains between electrodes.

FIG. 3. Complex capacitance behavior of the SCNb0.05%Cr varistor system biased at zero volts. 共a兲 25 °C and 共b兲 200 °C.

eraged Mott–Schottky response13 of any junction within the SnO2 varistor device. Table II presents the ␾ b , N d , and N IS values from this averaged Mott–Schottky response. The behavior of ␾ b as a function of temperature is similar to that of

Nb2O5 /mol %

␾ b /eV

N d (⫻1023)/m⫺3

N IS 共⫻1016兲/m⫺2

0.035 0.050 0.065

0.73⫾0.05 1.01⫾0.06 0.98⫾0.07

13.9 4.82 5.09

3.97 2.75 2.79

the ZnO based varistor, as described in the work of Mantas and Baptista,20 and is shown in Table III for the SCNb0.05%Cr composition. The N d and N IS values obtained in this study cannot be compared to the ZnO-based compositions, since they depend critically on the composition and doping level of varistor systems.21 However, the values obtained for the SnO2 -based varistor system are within the expected interval values of ␾ b , N d and N IS for typical varistor systems.22 These findings are important inasmuch as they offer evidence that the nature of nonlinearity in SnO2•CoO-based varistor systems could be the same as that observed in ZnO•Bi2O3 -based varistor systems, and are related to a Schottky-type barrier at the grain boundary, as shown here using the complex plane analysis technique and the Mott– Schottky approach. Although it is understood that varistor characteristics derive from the existence of trap states at the grain boundary, the chemical species responsible for the formation of these states is still unclear.22 Therefore, it cannot currently be predicted which dopant ions result in any given states of defect.22 Traditional and commercial ZnO•Bi2O3 -based varistor systems have a complex microstructure containing several phases such as a bismuth-rich phase, spinel 共nominally Zn7Sb2O12兲 and pyrochlore 共nominally Zn2Bi3Sb3O14兲, which are determined by the x-ray diffraction method. Moreover, the bismuth-rich phase appears to be particularly important. Previous reports have suggested that varistor characteristics are related to the particular crystalline form that the Bi2O3 takes on,22,23 with oxygen at the grain boundary surface.22 One of the fastest oxygen-ion conductors known, ␦ -Bi2O3 , which is located at the grain boundary region, is essential to obtain a high degree of nonlinear behavior.19 The role of the Bi as the ‘‘grain boundary activator’’ may, in the simplest scenario, be limited to supplying excess oxygen to the grain boundaries.22,23 In contrast to the ZnO•Bi2O3 -based varistor, SnO2•CoO-based varistor systems present only one phase TABLE III. Behavior of ␾ b , N d , and N IS values with temperature for a back-to-back Schottky-type potential barrier of the SCNb0.05%Cr varistor system. These calculations take into consideration the average number of grains between electrodes.

FIG. 4. Mott–Schottky behavior without charge transport influence 共true Mott–Schottky behavior兲 of the SCNb0.05%Cr varistor system at different temperatures.

Temperature/°C

␾ b /eV

N d (⫻1023)/m⫺3

N IS 共⫻1016兲/m⫺2

25 50 100 150 200

1.01⫾0.06 1.12⫾0.09 1.09⫾0.07 0.98⫾0.07 0.94⫾0.06

4.82 5.13 5.09 8.87 6.86

2.75 2.99 2.93 3.68 3.16

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with x-ray precision, in which CoO forms a solid solution by the substitution of Sn⫹4 ions for Co⫹2 or Co⫹3 ions, as reported and discussed in previous articles.4,6 A CoSnO3 -precipitated phase at the grain boundary is determined only when the energy dispersive spectroscopy stage attached to the high resolution transmission electron microscopy and electron diffraction is used.5 The absence of experimental evidence for a eutectic liquid suggests that the densification observed in this system is not associated with liquidphase sintering and that the sintering of the SnO2•CoO-based system is controlled by solid state diffusion. Other constituents of SnO2 -based varistors, such as Nb2O5 and Cr2O3 , are present in small concentrations 共⬃0.05 mol %兲; however, they are sufficient and necessary to render the behavior of this material highly nonlinear.6 The microstructural difference between the above described SnO2 - and ZnO-based varistor ceramics appears to suggest that the mechanism of electrostatic barrier formation at the grain boundary could be different, but the C – V characteristics reveal that their physical nature is the same. Although there are evident chemical differences between SnO2 and ZnO-based varistors, the response of the C – V characteristics suggests that, at the grain boundary, the chemistry of the interface is similar in both types of varistors, and could be intrinsic to nonlinear behavior in metal oxide semiconductors. There is evidence indicating that the chemistry of the grain boundaries in these materials is similar in terms of the presence of oxygen.22,24–26 The evidence of oxygen species 共that generate trapping states兲 present at the grain boundary surface of nonohmic ceramic materials22,24,25 may lead to a reasonable physicochemical model to explain the varistor behavior in SnO2 , 9 ZnO22,24 and SrTiO3 . 25 Oxygen vacancies and electronic states on SnO2 surfaces are related to each other22,27 and have been exhaustively studied.2,3 Oxygen plays a key role in ZnO22 and SrTiO3 25 varistor grain boundaries,27 since it indicates that the chemistry of grain boundaries determines the material’s electrical nature 共nonohmic behavior兲. An absorbed layer of bismuth with a thickness of about ⬃5 Å in a ZnO-based varistor is necessary to create potential barriers at grain boundaries, and the height of these potential barriers largely depends on the excess amount of oxygen present at the interface between grains in ZnO varistors.22 Similar results have been observed in our laboratory for the SnO2 varistor,28 indicating that the amount of oxygen present at the interface between grains may determine the formation of the potential barrier. Thus, SnO2 - and ZnO-based varistor grain boundaries display similarities in their physical and chemical features. Because the microstructure of the SnO2•CoO-based varistor is simpler and more homogeneous than the ZnO•Bi2O3 -based varistor system, we believe it may be a good material for a detailed study of the nature of the Schottky-type barrier formation mechanism in polycrystalline semiconductor systems, possibly contributing toward a deeper understanding of the exact role of chemical constituents in nonlinear behavior and in the mechanism of degradation.

IV. CONCLUSION

To conclude, the main objective of this work was to characterize the nature of the potential barrier in SnO2 -based varistor systems using a complex plane analysis technique and a Mott–Schottky approach to demonstrate that these systems have a Schottky-type nature 共electrostatic potential barrier兲, i.e., the same nature frequently reported on in the traditional ZnO-based varistor system.

ACKNOWLEDGMENTS

The financial support of this research project by the Brazilian research funding agencies FINEP/PRONEX, CNPq and FAPESP is gratefully acknowledged.

1

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