http://journa age antum able el 1152 HelpCommentsWelcome Journal of MATERIALS RESEARCH Model for zinc oxide varistor J. D. Santos, E. Longo, and E. R. Leite Departamento de Qu´ımica Universidade Federal de S˜ao Carlos, C.P. 676, 13565-905, S˜ao Carlos, SP, Brazil J. A. Varela Universidade Estadual Paulista, Instituto de Qu´ımica, C.P. 355, 14800-900, Araraquara, SP, Brazil (Received 13 February 1996; accepted 19 December 1997) Zinc oxide varistors are very complex systems, and the dominant mechanism of volt barrier formation in these systems has not been well established. Yet the MNDO qu mechanical theoretical calculation was used in this work to determine the most prob defect type at the surface of a ZnO cluster. The proposed model represents well the semiconducting nature as well as the defects at the ZnO bulk and surface. The mod also shows that the main adsorption species that provide stability at the ZnO surface are O2, O2 2, and O2. a i ri p t ar a e a f b in , ic O h ie n a iz o a be e e a he e- ry ts. lain as by for O of e - s in es, ions the to I. INTRODUCTION The grain boundary strongly affects the electric conductivity of polycrystalline solids.1 The lack of lattice periodicity due to intrinsic defects causes a superfic rearrangement of localized states at the grain bounda Some atomic defects can also be introduced by im rities during processing of powders and segregation the grain boundaries. All these localized defects lead a high density of structural defects that can origina a potential barrier associated to a double space ch distribution. These associated phenomena establish v able resistance as a function of the applied electric fi to the solid. Electronic ceramics based on the grain bound phenomena went through extraordinary advances a studies on the varistor effect of zinc oxide conducted Matsuoka.2 In order to understand the bulk and gra boundary effect on the conductivity of these ceramics is necessary to consider both microscopic and phys chemistry analyses. Two types of point defects are related to the Zn crystal: Frenkel and Schottky defects.3 The predominant defect in the ZnO ceramics has not been well establis yet. According to Mahan4 the predominant defects in ZnO are of the Schottky type where oxygen vacanc are the dominant intrinsic donors. However Schwing a Hoffmann5 proposed that oxygen vacancies are domin only at high temperatures. These defects can be ion and behave like electron donors and acceptors. Interstitial zinc and oxygen vacancies are electr donors and can be single or double ionized and represented by using Kroeger–Vink notation as6: Zni ! Zni ≤ 1 e0, (1) Zni ≤ ! Zni ≤≤ 1 e0, (2) VO x ! VO ≤ 1 e0, (3) VO ≤ ! VO ≤≤ 1 e0. (4) ls.cambridge.org Downloaded: 12 Mar 2014 J. Mater. Res., Vol. 13, No. 5, May 1998 l al es. u- at to e ge ri- ld ry ter y it al ed s d nt ed n re Electron acceptors are zinc vacancies that can single or double ionized: VZn x ! VZn0 1 h≤, (5) VZn 0 ! VZn00 1 h≤. (6) Gupta and Carlson7 proposed a model for the voltag barrier in ZnO varistor in which the negative charg located in the grain boundary is compensated by positive charge at the depletion layer. In this model t negative charges areVZn 0 and VZn 00 and the positive chargesVO ≤, VO ≤≤, Zni ≤≤, Zni ≤, and MZn ≤, where M is Sb or Bi. The varistor degradation is associated with the d crease of the voltage barrier at the grain bounda which is related to the annihilation of trapped defec Several mechanisms have been proposed to exp the degradation phenomena of ZnO varistors, such electron traps, ion migration, and oxygen loss.8–11 The objective of the present study is to determine, quantum mechanical study, the probable mechanism voltage barrier formation and for degradation of Zn varistors. II. MODEL AND QUANTUM MECHANICAL METHOD The calculations were performed with the aid the MNDO12 semiempirical methods included in th MOPAC 5.0 program package.13 The standard parame ters for the zinc atom optimized by Dewaret al.14,15 and Stewart16 were used. The use of cluster models has some advantage chemical analysis, semiconducting analysis of oxid and in adsorption processes. Due to the large dimens of such clusters, a quantum chemical study requires use of semiempirical methods. The MNDO method has been previously used study large silicon clusters (Si)n, with n . 10 17 and IP address: 200.145.174.165  1998 Materials Research Society http://www.mrs.org/publications/jmr/comments.html http://journals.cambridge.org J. D. Santos et al.: Model for zinc oxide varistor ir h s e e n d d t o d d the he te ) ns. as en he on ce ence en ws rs in large zinc oxide clusters (ZnO)n, with n . 11,18,19 which suggests the possibility of using these semiemp cal methods for investigating even larger clusters. The semiempirical calculations were made using t zinc oxide (ZnO)10 cluster. The structural parameter of the (ZnO)10 cluster used are shown in Fig. 1. Th cluster geometry variables were frozen during all th calculations, whereas the geometry variables correspo ing to the absorbed gas molecules were fully optimize The geometry of various configurations were optimize in order to determine the minimum stationary poin corresponding to the specific active site interaction O2, O21 2 , O22 2 , O2, O22 with the ZnO surface represente by the cluster model (Fig. 2). III. RESULTS AND DISCUSSIONS According to Fujitsuet al.,20 adsorption of oxygen atoms and molecules at the grain boundary of ZnO lea FIG. 1. Structural parameters of the (ZnO)10 cluster used in the MNDO calculation. http://journals.cambridge.org Downloaded: 12 Mar 2014 J. Mater. Res., Vol. 13 i- e d- . f s FIG. 2. Schematic representation of the ZnO cluster showing adsorption of O2, O2 2, O22 2 , O2, and O22 on site A, and interstitial Zni ≤ and Zni ≤≤ on site I. to the formation of the potential barrier and promotes t nonohmic behavior of the ZnO ceramics. To simula the oxygen adsorption at the grain surface, a (ZnO10 model was considered for the theoretical calculatio Adsorption of oxygen atoms and molecules as well the interaction with zinc atoms at the surface was tak into account. Oxygen species used were O2, O21 2 , O22 2 , O2, and O22. Figures 3–8 represent the charge distribution of t (ZnO)10 and (ZnO)10Zn11 with the species O2, O2 2, and O2 at the ZnO surface. It is observed that the interacti of oxygen atoms and molecules at the ZnO surfa increases the negative charge density. As a consequ there is a transfer of negative charge from the oxyg atom or molecule to the cluster surface. This result sho FIG. 3. Charge distribution of the (ZnO)10 cluster showing negative charge at the surface and positive charge in the bulk. The numbe parentheses are the charge value in milielectron. IP address: 200.145.174.165 , No. 5, May 1998 1153 http://journals.cambridge.org h J. D. Santos et al.: Model for zinc oxide varistor h h r io ) a a e and arge The his del on. ar, nd face o FIG. 4. Charge distribution of the (ZnO)10 ? O2 cluster showing that the adsorbed oxygen leads to a negative charge at the surface positive charge in the bulk. The negative charge distribution of t system is higher than that of the (ZnO)10 system. The numbers in parentheses are the charge value in milielectron. FIG. 5. Charge distribution of the (ZnO)10 ? O2 2 cluster showing that the adsorbed oxygen leads to a negative charge at the surface positive charge in the bulk. The negative charge distribution of t system is higher than that of the (ZnO)10 ? O2 system. However, the bulk is lightly positive. The numbers in parentheses are the cha value in milielectron. that a voltage barrier can be formed by the adsorpt of oxygen molecules and atoms in the surface region the ZnO cluster. The charge distribution of the ZnO cluster show that the oxygen species O2, O2 2, and O2 are responsible for the negative state at the ZnO surface (Figs. 4, 6, and 8). Moreover, this negative surface can also analyzed by the total energy calculation of the (ZnO10 cluster interacting with the different oxygen species. To verify which oxygen species lead to major st bility of the system, calculation for each species w considered. Considering the interaction of an oxyg ttp://journals.cambridge.org Downloaded: 12 Mar 2014 1154 J. Mater. Res., Vol. 1 and is and is ge n of s 5, be - s n FIG. 6. Charge distribution of the (ZnO)10? O2 cluster showing that the adsorbed oxygen leads to a negative charge at the surface positive charge in the bulk. The numbers in parentheses are the ch value in milielectron. FIG. 7. Charge distribution of the (ZnO)10 ? Zn11 cluster showing negative charge at the surface and positive charge in the bulk. numbers in parentheses are the charge value in milielectron. molecule on the ZnO surface, the energy value for t adsorption is sZnOd10 1 O2 ! sZnOd10 ? O2 DE ­ 0.78 eV. (7) The experimental value obtained by Binesti21 for this adsorption is 0.8 eV. This indicates that the ZnO mo considered is reasonable for this type of calculati Results for interactions at different sites are simil which leads to charge redistribution in the crystal a the increase of negative charge density at the sur (Figs. 4, 5, and 6). The adsorption of O22 at the surface was als considered leading to: sZnOd10 1 O2 2 1 e0 ! sZnOd10 ? 2O2 DE ­ 6.8 eV . (8) IP address: 200.145.174.165 3, No. 5, May 1998 http://journals.cambridge.org J. D. Santos et al.: Model for zinc oxide varistor rf u ili b th o c a an O e to in n s ti i n c g n o O s e ti h o o f ing by a - r ) the ing et ed r lts of is en he tion e n ng is FIG. 8. Charge distribution of the (ZnO)10 ? Zn11 ? O2 2 cluster show- ing that the adsorbed oxygen leads to a negative charge at the su and positive charge in the bulk. The numbers in parentheses are charge value in milielectron. In this case there is a break of an oxygen molec bond and the system gains an extra electron to stab the reaction. This reaction needs a high energy to completed and the probability that this species is at ZnO surface is very low. The model presented takes into account the n stoichiometry of ZnO by placing an interstitial zin as dominant defect. However, oxygen vacancies also important and should be considered. Gupta co-authors7,9–11 proposed that the degradation of Zn varistors occurs by interstitial zinc diffusion from th depletion layer to the grain boundary. According these authors cooling after sintering leads to freez of interstitial zinc in the depletion layer. The applicatio of an external electric field makes the migration of the ions to the interface possible. The presence of nega charge of the Schottky barrier at the surface leads partial neutralization of the net charge. This effect reversible after elimination of the electric field. Considering the stoichiometric ZnO the charge de sity of the surface is negative. However, the presen of interstitial zinc ions can transform the surface char density to a positive value (Figs. 7 and 8). Compari Figs. 3 and 7 with 5 and 8 a significative increase surface charge density is observed due to adsorbed2 2 and to the positive charge of the interstitial zinc ion These results agree with the model where the oxyg ions and molecules are located at the surface crea a barrier for another neighbor cluster. Moreover, t electron moves more easily inside the cluster due the positive charge generated by the interstitial zinc i These results are in agreement with the proposition Gupta7,9,10 in which the role of the positive charge is t neutralize the negative surface charge. http://journals.cambridge.org Downloaded: 12 Mar 2014 J. Mater. Res., Vol. 1 ace the le ze e e n- re d g e ve to s - e e g f . n ng e to n. of Takahashiet al.22 suggested that at least part o the surface charge is due to oxygen ions. Consider that the degradation of ZnO varistors occurs mainly the liberation of oxygen, it is reasonable to propose reaction of the interstitial zinc ions (Zn12) and ad- sorbed oxygens (O22). However, this reaction is endo thermic and involves 8 eV, which is not very likely fo this system. Therefore, the adsorption of O2, O2 2, and O2 species was considered in a stoichiometric (ZnO10 model and in a nonstoichiometric (ZnO)10Zn1. The results showed that to adsorb an oxygen molecule in stoichiometry model, 0.78 eV are necessary accord to reaction (7). The system (ZnO)10O2 can be reduced leading to: sZnOd10 ? O2 1 e0 ! sZnOd10 ? O2 2 DE ­ 21.7 eV. (9) Then for the oxygen adsorption and reduction the n reaction is: sZnOd10 1 O2 1 e0 ! sZnOd10 ? O2 2 DE ­ 20.92 eV . (10) Then the reverse reaction (10) indicates the ne of 0.92 eV to liberate an oxygen from the ZnO cluste surface. This result is close to the experimental resu obtained by Leiteet al.23 during degradation of a ZnO varistor (0.98 eV). For the nonstoichiometric system the adsorption oxygen is given by: sZnOd10 ? Zn1 1 O2 ! sZnOd10 ? Zn1 ? O2 DE ­ 0.78 eV , (11) sZnOd10 ? Zn1O2 1 e0 ! sZnOd10 ? Zn1 ? O2 2 DE ­ 22.07 eV . (12) The net variation of reactions (11) and (12) DE ­ 21.3 eV, indicating that the interstitial zinc ions are located near the surface. In this case the oxyg adsorption will be higher in this system compared to t stoichiometric system. As a consequence the degrada phenomena will be more difficult. There is also th possibility of the existence of double charged oxyge at the ZnO surface that is represented by the followi reactions: sZnOd10 ? O2 1 2e0 ! sZnOd10 ? O22 2 DE ­ 0.7 eV, (13) sZnOd10 ? O2 2 1 e0 ! sZnOd10 ? O22 2 DE ­ 1.6 eV. (14) By analyzing Eq. (14) it is observed that there a very high energy barrier to reduce O2 2 to O22 2 . According to Shih-Chia Chang,24 this reaction should IP address: 200.145.174.165 3, No. 5, May 1998 1155 http://journals.cambridge.org J. D. Santos et al.: Model for zinc oxide varistor t ) s yer en . e w e O rs, d by O ct ere y r cts he e nc dis- f have a double ionization leading to O2 adsorbed at the surface. The EPR data, however, agree with theoretical calculation of Eq. (13). The O2 2 adsorption at the ZnO surface is als possible and is represented by: sZnOd10 1 O2 2 ! sZnOd10 ? O2 2 DE ­ 0.43 eV , (15) sZnOd10 ? Zn1 1 O2 2 ! sZnOd10 ? Zn1 ? O2 2 DE ­ 0.05 eV . (16) Moreover, by analyzing Table I the formation o oxygen and zinc vacancies in distinct sites can inferred. The oxygen vacancies (VO ≤ and VO ≤≤) are located at the surface cluster and the zinc vacancies (VZn 0 and VZn 00) inside the cluster. Considering that the energy calculated for (ZnO10 cluster is 23499.608 eV, for sZnOd9Zn ? VO ≤ ? O2 is 23499.632 eV, and forsZnOd9O ? VZn 0 ? Zn≤ is 23499.449 eV, we may conclude that the creation oxygen vacancies is a spontaneous characteristic of n-type semiconducting behavior of ZnO. According to Edaet al.25 and Gupta and Carlson,26 the most probable mechanism for potential barrier sta lization is interstitial diffusion of zinc through the ZnO crystal to the grain boundary. The theoretical resu confirm this premise for interstitial zinc ions (Zni ≤ and TABLE I. Stability of zinc and oxygen vacancies in the (s) surface of ZnO grain and (i) inside the ZnO grain. ZnO clusters 2E (eV) Energy gap (eV) sZnOd9O ? VZn 00ssd 3464.620 4.8 sZnOd9O ? VZn 00sid 3468.337 6.6 sZnOd9O ? VZn 0ssd 3466.443 2.3 sZnOd9O ? VZn 0sid 3469.235 2.0 sZnOd9Zn ? VO ≤≤ssd 3159.558 3.2 sZnOd9Zn ? VO ≤≤sid 3158.275 5.5 sZnOd9Zn ? VO ≤ssd 3170.989 1.7 sZnOd9Zn ? VO ≤sid 3169.505 3.1 sZnOd9 ? VO ≤sid ? VZn 0ssd 3139.549 4.1 sZnOd9 ? VO ≤sid ? VZn 0sid 3142.607 2.8 sZnOd10Zni ≤≤ssd 3503.859 2.6 sZnOd10Zni ≤≤sid 3491.927 4.5 sZnOd10Zni ≤ssd 3514.404 3.7 sZnOd10Zni ≤sid 3504.415 3.1 Mean value of energy gap 3.6. http://journals.cambridge.org Downloaded: 12 Mar 2014 1156 J. Mater. Res., Vol. 1 he o f be of the bi- lts Zni ≤≤) as seen in Table I. These interstitial zinc ion create a positive charge density in the depletion la (Figs. 7 and 8). This layer would be associated to oxyg vacancies (VO ≤ and VO ≤≤) that migrate to the surface This fact would facilitate the oxygen adsorption at th crystal surface. However, the results of Table I sho that zinc vacancies (VZn 0 and VZn 00) are located inside the ZnO cluster and would not directly participate in th superficial charge formation. Considering that the nonohmic properties of Zn varistors are due to the Schottky type potential barrie the grain boundary negative charges are compensate positive charges located at the depletion layer of Zn grains. In this way the grain boundary atomic defe model is proposed to represent the ZnO varistor, wh negative superficial charge states are O2, O2, and O2 2 and positive states areVO ≤, VO ≤≤, Zni ≤ and dopants VM ≤, VM ≤≤ (Fig. 9). This model is basically similar to that proposed b Gupta25 with the addition of oxygen ions and molecula oxygen adsorbed at the grain boundary. These defe together with interstitial zinc ions (Zni ≤≤ andZni ≤) and oxygen vacancies (VO ≤ and VO ≤≤) are responsible for the ZnO grain boundary atomic defects. The above defects form the depletion layer at t grain boundary region of zinc oxide, increasing th nonohmic behavior of this oxide. Previous theoretical cluster calculations of the zi oxide surfaces and adsorption process include the crete variational (DV)x-a model,27,28 semiempirical (INDO/S),29 and extend H¨uckel methods30 of the en- ergy gap HOMO-LUMO. The theoretical calculations o FIG. 9. Atomic defect model for ZnO grain boundary. TABLE II. Theoretical and experimental results from the literature for the HOMO-LUMO gap of different ZnO clusters. Exp. DV-Xa DV-Xa INDO/S EHT MNDO (this work) Gap (eV) 3.3 3.2 1.2 4.4 3.0 3.6 Cluster · · · Zn7O11 Zn3O10 Zn13O13 Zn9O9 Zn10O10 ? x Ref. 31 27 28 29 30 x ­ VZn 00, VZn 0, VO ≤≤, VO ≤, Zni ≤≤, andZni ≤. IP address: 200.145.174.165 3, No. 5, May 1998 http://journals.cambridge.org J. D. Santos et al.: Model for zinc oxide varistor t g t t a e t e o s 3). alk, em. J. ics 5). . A. Refs. 27 and 30 in Table II agree with the experimen value of the crystal bulk (3.3 eV).31 In the present work the mean value for the ener gap calculated for the 14 ZnO clusters is 3.6 eV agreement with experimental data. This result shows to simulate the energy gap of a crystalline solid n only the defect concentration (vacancies and intersti ions) should be considered, but also its position (surf or bulk). IV. CONCLUSIONS The theoretical calculations lead to the followin conclusions: (1) The ZnO proposed model represents very w the semiconducting properties of this oxide in bo surface and bulk. (2) The interstitial Zn1 species near the grain boundary decrease the negative surface state du redistribution of charge and favor the adsorption oxygen. (3) The adsorption of O2, O2 2, and O2 at the ZnO surface stabilizes the ZnO system, increasing the vari properties. The desorption of these species leads to Z varistor degradation. REFERENCES 1. G. E. Pike and C. H. Seager, J. Appl. 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