Energetics of intrinsic defects and their complexes in ZnO investigated by density functional calculations

Abstract

Formation energies of various intrinsic defects and defect complexes in ZnO have been calculated using a density-functional-theory-based pseudopotential all-electron method. The various defects considered are oxygen vacancy ( Upon comparing the formation energies of these defects, we find that V O would be the dominant intrinsic defect under both Zn-rich and O-rich conditions and it is a deep double donor. Both Zn O and Zn i are found to be shallow donors. The low formation energy of donor-type intrinsic defects could lead to difficulty in achieving p-type conductivity in ZnO. Defect complexes have charge transitions deep inside the band gap. The red, yellow, and green photoluminescence peaks of undoped samples can be assigned to some of the defect complexes considered. It is believed that the red luminescence originates from an electronic transition in V O , but we find that it can originate from the antisite Zn O defect. Charge density and electron-localization function analyses have been used to understand the effect of these defects on the ZnO lattice. The electronic structure of ZnO with intrinsic defects has been studied using density-of-states and electronic band structure plots. The acceptor levels introduced by V Zn are relatively localized, making it difficult to achieve p-type conductivity with sufficient hole mobility.

Electrical degradation of double-Schottky barrier in ZnO varistors

“…As the Fermi level is generally accepted to lie itself 0.067 eV below the CBM in the grain boundary region 33 of ZnO varistor, the individual Zn i in the 1+ state is favored since, for instance, the (1+/0) and (2+/1+) transition levels are located at 0.05 and 0.16 eV respectively below the CBM in Zn-rich n-type ZnO as suggested by Vidya et al, 64 while the V O is neutral simultaneously. 64,66 Specifically, we adopt the proposal by Kim and Park 76 in this paper in favor of the novel interaction between component point defects inside the complex donor (V O 0 -Zn 2+ i ), 64,76 i.e. the strong attractive interaction between V O 0 and Zn 2+ i caused by quantum mechanical hybridization significantly lowers the formation enthalpy of the V O 0 -Zn 2+ i pairs, which makes it possible for Zn 2+ i to be generated in large quantities in DSB region.…”

“…4,6,57,[59][60][61] However, recent atomic-scale investigations focused on point defects in ZnO materials that use first-principles calculations methods have brought to attention refreshed and distinct insight into the properties of defects. Even though various researches carried out by different groups could show certain disparities in predicting the characteristics of native defects inside periodic-structure ZnO system, [62][63][64][65][66][67][68][69][70][71][72][73][74] owing to employing different exchange-correlation approximations, numbers of k-point sampling for Brillouin-zone integration, supercell sizes, corrections for spurious defect interactions, and so forth, meaningful and significant conclusions can still be extracted for native donor defect: (i) V O is the lowest-energy donor defect which means it can be generated in large concentration, whereas it is surprisingly a deep donor, i.e. its (2+/0) transitional level lies ∼1 eV below the conduction band minimum (CBM) and V O at 1+ charge state is unstable; (ii) the formation energy of shallow-donor Zn i is higher compared to V O , and its thermal-dynamic (1+/0) and (2+/1+) transitional levels are predicted as 0.05 and 0.16 eV below the CBM by R. Vidya, 64 and as ∼ 0.05 and ∼ 0.1 eV by F. Oba.…”

“…More first-principles calculations have suggested that the formation energy of native defects (especially Zn i ) can be significantly reduce when undoped grain boundary exists due to the interactions between defects and boundary, 75 and if captured by other point defect or impurity defect to form complex defect, the formation energy of Zn i can be further lowered. 64,76 Hence, it is argued here that the accumulation of native donors in depletion layers is believed to be facilitated by the Bi-or Pr-doped grain boundary and by forming certain complex donor defects, and then the remained issue is how to identify the dominant mobile donor ions based on the long-term aging simulation method described below.…”

“…In the simulation, three different kinds of native donor defects are considered as potential mobile ion: the V O of a neutral charge state (V O 0 ), Zn i in a 1+ charge state (Zn 1+ i ) and Zn 2+ i from a complex defect (V O 0 -Zn 2+ i ), which are selected for they are more stable or energetically easier to be generated [64][65][66]68,69,76 when compared to other charge states. As the Fermi level is generally accepted to lie itself 0.067 eV below the CBM in the grain boundary region 33 of ZnO varistor, the individual Zn i in the 1+ state is favored since, for instance, the (1+/0) and (2+/1+) transition levels are located at 0.05 and 0.16 eV respectively below the CBM in Zn-rich n-type ZnO as suggested by Vidya et al, 64 while the V O is neutral simultaneously. 64,66 Specifically, we adopt the proposal by Kim and Park 76 in this paper in favor of the novel interaction between component point defects inside the complex donor (V O 0 -Zn 2+ i ), 64,76 i.e.…”

“…the strong attractive interaction between V O 0 and Zn 2+ i caused by quantum mechanical hybridization significantly lowers the formation enthalpy of the V O 0 -Zn 2+ i pairs, which makes it possible for Zn 2+ i to be generated in large quantities in DSB region. Even though the V O 0 owns the lowest formation energy among various individual donor defects, [64][65][66]68,69 it must be excluded prior to the simulation because of its deep-donor nature in n-type ZnO (i.e. make no contribution to the degradation of DSB).…”