Prior to investigating the effects of introducing a doped atom, it is crucial to understand the underlying mechanism that causes non-doped CuO to exhibit p-type conductivity. It is well known that CuO is a p-type semiconductor. Several mechanism is proposed to explain the p-type conductivity of CuO. Oxygen vacancy VO, copper vacancy VCu, and oxygen interstitial (Oi) are some of the different types of defects that can be found in an intrinsic CuO semiconductor.
The symbols above correspond to the standard interpretation as defined by the Kroger-Vink notations [36]. The value of x (where x might be 0, 1, or 2) represents the level of ionization of the defects, indicating whether they are neutral or mono-/dual-ionized.
There are two types of cation defects, VCu and Oi, that can generate free holes for p-type conductivity. Nevertheless, recent research has established that the primary cause of the p- type properties of CuO is the production of Cu vacancies[61, 62]. Therefore, only this process will be taken into account in the subsequent analysis. Additionally, there is another type of anion defect, known as VO, which acts as a hole suppressor by producing electrons that neutralize the holes. In order to determine the primary defect in CuO, we initially conducted theoretical calculations to determine the formation energy of VO and VCu using first principles, as shown by the reactions (3.1) and (3.2).
O vacancy: CuxOx -> CuxO(x-1) + ẵ O2 (3.3) Cu vacancy: CuxOx -> Cu(x-1)Ox + Cu (3.2)
39 But first, I calculated the formation energy of Cu2O and CuO using below equation and compare it to public paper to ensure the accuracy of formation energy calculation process.
2Cu + ẵ O2 → Cu2O (3.3)
Cu + ẵ O2 → CuO (3.4)
To calculate the formation energy, begin by obtaining the total energy of CuO (Cu2O) on the left side of the equation. Next, subtract the combined total energy of bulk copper and oxygen.
Our calculated formation energies for CuO and Cu2O are -0.6964 and -0.4721 eV, respectively, in agreement with public results of -0.614 eV for CuO and -0.503 eV for Cu2O[43]. These findings indicate that CuO exhibits greater thermodynamic stability than Cu2O, as reported by refs [61, 63], and the ratio of Cu to O is 1:1, indicating that the formation of Cu vacancies in the CuO structure is more difficult than Cu2O. Hence, in addition to the standard circumstances outlined in equation (3.2), it is necessary to introduce further conditions that enhance the probability of generating a vacancy in CuO, thereby explaining the inherent p-type conductivity of CuO. According to Zhiliang Wang, et al.[61]
the application of oxygen to CuO enhances the creation of VCu. Due to the limited volatility of Cu atoms at the given reaction conditions, the Cu atoms will relocate from their initial positions in the lattice to different sites. In this scenario, VCu is formed and extra lattice oxygen is introduced around the newly formed lattice Cu atoms by the reaction with O atoms from atmospheric O2. Following that, we proposed an equation (3.5) for formation of Cu vacancy.
CuxOx + 𝑥
2(𝑥−1) O2 -> 𝑥
𝑥−1 Cux-1Ox (3.5)
40
(states/eV) (states/eV)
Figure 3.8. The schematic illustration for the formation of Cu vacancy in CuO[61].
We then calculated the formation energy and defect level based on the method mention in section 2.2.1.3. The defect formation energy diagram with the DOS structure of Cu and O vacancy in CuO cell are shown in Figure 3.9.
Figure 3.9. The defect formation energy diagram for Cu and O vacancy (a) and DOS of structure with Cu vacancy (b) and O vacancy (c).
c a)
Eq 3.5 Eq 3.1
-5 -4 -3 -2 -1 0 1 2 3 4 5
-2 -1 0 1 2
DOS
Energy (eV)
Cu vacancy
b
41 The formation energy of Cu vacancy in the normal case (calculated from equation 3.1) is 3.1779 eV, higher than 2.0267 eV obtained from the proposed state (calculated from equation 3.5), and even higher than the formation energy of O vacancy, which supports the idea that in the normal condition (Cu-rich condition), CuO is thermodynamically stable.
However, in the situation presented by Zhiliang Wang, et al.[61], referred to as the oxygen rich (O rich) condition, the formation energy of VCu is the lowest at 2.0267 eV. This VCu can then be ionized into VCu' at an energy level of 0.1930 eV above the valence band maximum (VBM), resulting in the generation of free holes. By enhancing the energy to 0.5480 eV compared to VBM, it is possible to create the dual-ionized VCu'' which is more effective in generating holes. The formation energy of VO is higher than that of VCu, approximately 2.7623 eV, resulting in a minimal quantity of VO production. Thus, in an oxygen-rich environment, VCu will be the predominant defect in CuO.
The results for Cu and O vacancies in the DOS exhibit comparable outcomes. When there is a vacancy of Cu, two impurity levels appear and can be identified as acceptor levels.
The energy levels for spin down are observed to be approximately 0.2 eV above the valence band maximum (VBM), whereas for spin up they are roughly 0.7 eV above the VBM. This observation confirms the double acceptor behavior of CuO, which is in line with the defect formation energy. In contract, when an O vacancy is present in the structure, the donor level appears in the DOS figure.