The effects of doping a grain boundary in ZnO with various concentrations of Bi
Introduction
Zinc oxide is receiving increased interest today due to its range of applications, but it is also considered as a prototype material for studying the properties of metal oxides. The wide direct optical band gap makes single crystalline ZnO suitable for optical applications [1] and the polycrystalline form has been used for a long time in varistors [2]. A varistor is a voltage dependent resistor which exhibits a highly non-linear I–V characteristic [2]. These devices are manufactured by liquid sintering of ZnO mixed with a number of additives such as Bi, Sb, Mo, Co and Cr [3]. The sintering produces a polycrystalline ZnO material where the additives accumulate in the grain boundaries [3], [4]. It is assumed that interface states in the grain boundaries create a depletion region, which leads to the formation of a double Schottky barrier (DSB) [2]. The barrier limits electron transport through the grain boundary but an applied field is able to manipulate the population of the interface states. The non-linearity is therefore the result of the dramatic current increase when the DSB is removed by the applied field.
Bismuth is the most important additive which contributes to the formation of the DSB [2]. A majority of the Bi-atoms accumulate into Bi2O3-phases at the triple junctions between the ZnO grains in varistor materials [5] but the Bi-atoms may also diffuse out to become incorporated in the grain boundaries. These Bi-atoms appear either as isolated Bi atoms decorating the grain boundary [6] or as a thin amorphous Bi2O3-layer [3] depending on the cooling process [2]. It has been debated in the literature which of these two types of Bi configurations give rise to the most pronounced non-linearity.
We have therefore studied the Bi-decoration process in a Σ=13 [0 0 0 1] tilt grain boundary in ZnO by first principles calculations. This particular grain boundary is a convenient model system since its atomic structure has been determined previously by both high resolution electron microscopy (HREM) [7], [8] and first principles calculations [9]. The study involves a systematic investigation of the most favourable substitution sites for the Bi-impurity atoms in the grain boundary and the Bi-induced effects on the electronic structure.
Section snippets
Methods
The first-principles calculations were based on density functional theory (DFT) [10], [11] using the PW-91 GGA exchange-correlation functional [12] implemented in the Dacapo code [13]. A plane wave basis set with an energy cutoff of 300 eV was used together with ultrasoft pseudopotentials [14]. The Σ=13 [0 0 0 1] tilt grain boundary was constructed in the supercell using two unit cells of the coincidence site lattice (CSL) in which the crystals were misoriented by 32.2°. The supercell therefore
Results and Discussion
The results and discussion are divided into two sections. The atomic structures and segregation energies for the Bi impurities in the grain boundary are presented first. This is followed by a description of the impurity induced effects on the electronic structure of the system.
Conclusions
The segregation of Bi-impurities to the Σ=13 tilt grain boundary in ZnO is strongly site dependent. The 3-coordinated sites are favourable for segregation since they provide large freedom for relaxation. Higher Bi-concentrations increase the repulsive Bi–Bi interaction which counteract the energy gain from the improved bonding environment in the grain boundary. The Bi–Bi interaction therefore sets an upper limit for the Bi-concentration in the grain boundary, which is estimated from Fig. 2 to
Acknowledgements
J.C. has been supported by the Swedish Natural Science Research Council and HSD acknowledges grant PRAXIS XXI/BD/13944/97. The calculations were performed using the UNICC resources at Chalmers, Gothenburg, Sweden.
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