Model for zinc oxide varistor
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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 voltage barrier formation in these systems has not been well established. Yet the MNDO quantum mechanical theoretical calculation was used in this work to determine the most probable 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 model also shows that the main adsorption species that provide stability at the ZnO surface are O2 , O2 2 , and O2 . I. INTRODUCTION
The grain boundary strongly affects the electrical conductivity of polycrystalline solids.1 The lack of lattice periodicity due to intrinsic defects causes a superficial rearrangement of localized states at the grain boundaries. Some atomic defects can also be introduced by impurities during processing of powders and segregation at the grain boundaries. All these localized defects lead to a high density of structural defects that can originate a potential barrier associated to a double space charge distribution. These associated phenomena establish variable resistance as a function of the applied electric field to the solid. Electronic ceramics based on the grain boundary phenomena went through extraordinary advances after studies on the varistor effect of zinc oxide conducted by Matsuoka.2 In order to understand the bulk and grain boundary effect on the conductivity of these ceramics, it is necessary to consider both microscopic and physical chemistry analyses. Two types of point defects are related to the ZnO crystal: Frenkel and Schottky defects.3 The predominant defect in the ZnO ceramics has not been well established yet. According to Mahan4 the predominant defects in ZnO are of the Schottky type where oxygen vacancies are the dominant intrinsic donors. However Schwing and Hoffmann5 proposed that oxygen vacancies are dominant only at high temperatures. These defects can be ionized and behave like electron donors and acceptors. Interstitial zinc and oxygen vacancies are electron donors and can be single or double ionized and are represented by using Kroeger–Vink notation as6 : Zni Zni ≤ VO x VO ≤ 1152
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! ! ! !
Zni ≤ 1 e0 , Zni ≤≤ 1 e0 , VO ≤ 1 e0 , VO ≤≤ 1 e0 .
(1) (2) (3) (4)
J. Mater. Res., Vol. 13, No. 5, May 1998
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Electron acceptors are zinc vacancies that can be single or double ionized: VZn x ! VZn0 1 h≤ , VZn 0 ! VZn00 1 h≤ .
(5) (6)
Gupta and Carlson7 proposed a model for the voltage barrier in ZnO varistor in which the negative charge located in the grain boundary is compensated by a positive charge at the depleti
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