iii LIST OF ABBREVIATIONS DFT : Density functional theory GGA : Generalized gradient approximation LDA : Local density approximation MOS : Metal oxide semiconductors SEM : Scanning elec
OVERVIEW
Solution-based thin film technologies
Moore's law indicates that the number of transistors on a microelectronic chip doubles approximately every 18 months; however, chip prices per unit area have remained stable over the past 30 years This stability has spurred the development of innovative and cost-effective technologies, including printing methods Traditional techniques for creating functional inorganic electronic devices involve complex processes like deposition, patterning, and etching, which often rely on multiple photolithography and vacuum-deposition steps, leading to high manufacturing costs In contrast, direct printing of inorganic materials allows for additive patterning and the production of high-performance, cost-effective devices While soluble organic semiconductors have been extensively researched, they often fall short in functional performance and face various process-related challenges, including limited mobility and reliability issues Inorganic semiconductors, on the other hand, remain essential for advanced microelectronic devices.
Inkjet printing for the fabrication of active devices with inorganic materials is a recent advancement compared to the extensive research on organic materials The limited number of inorganic materials suitable for inkjet technology stems from challenges in developing compatible starting materials Additionally, creating functional inorganic materials for applications like thin-film transistors (TFTs) presents significant difficulties due to processing capabilities and material performance However, inkjet printing offers several advantages for electronic circuits, including a digital operation that eliminates the need for masks or screens, an additive process that applies materials only where necessary, and a streamlined approach that enhances efficiency.
Ink-jet technology has been underutilized for producing active devices with inorganic materials, especially when compared to organic materials This is largely due to the difficulties in preparing ink-jet printable precursors, which can hinder the process Additionally, the design ensures that print nozzles do not make contact with the material, protecting delicate surfaces during production.
Thin-film semiconductor devices produced through solution processing hold great potential as affordable and advanced solutions for the future of sustainable information and communication technology A key goal is the development of fully printed devices, which has driven extensive research into materials and the fabrication of n- and p-type semiconductor sheets without the need for precise patterning Alongside material and device advancements, ongoing efforts focus on improving device performance This approach aims to refine and enhance printed devices, ultimately reducing or eliminating unnecessary material consumption.
P-Type Metal Oxide Based TFTs – CuO and transition metal doped CuO thin films…
The success of n-type oxide semiconductors in thin-film transistors (TFTs) has sparked interest in developing p-type oxide semiconductors for similar applications However, a key challenge for p-type oxide TFTs is their low hole mobility, which is typically inferior to the electron mobility found in n-type materials.
In recent decades, transition metal-oxide (TMO) semiconductors have garnered significant attention due to their technological compatibility and wide array of applications Among these, copper oxide (CuO) stands out for its unique optical, electrical, structural, and chemical properties Classified as a p-type semiconductor, CuO is also non-toxic, cost-effective, and environmentally friendly.
In addition, because to its high melting and boiling points, it is considered one of the most hardest substances [14] CuO has a lower-symmetry monoclinic cell that belongs to the
The C2/c space group distinguishes CuO from other transition metal oxides, which typically exhibit a cubic rock salt structure CuO is valued across multiple industries for its unique properties, finding applications in gas sensors, biosensors, batteries, solar energy conversion, high-temperature superconductors, pigments, and catalysis.
Bui Nguyen Quoc Trinh et al (2020) developed a thin film transistor utilizing a solution-processed CuO thin film as the channel layer XRD analysis confirmed the polycrystalline nature and monoclinic structure of the CuO thin films, with grain size increasing alongside solution concentration The film achieved a minimum electrical resistivity of 0.0359 Ωcm at a solution concentration of 0.30 M When employed as a channel layer in thin film transistors, the CuO thin film demonstrated p-type behavior, featuring an on/off current ratio of 10^2 and a saturation mobility of approximately 10^−4 cm^2 V^−1 s^−1.
In recent years, researchers have successfully introduced transition metal impurities, such as manganese, cobalt, nickel, and iron, into CuO to study their effects on its structural, electrical, and optical properties Among these dopants, nickel was chosen due to its ion radius of 0.69 Å, which closely matches the 0.73 Å radius of copper ions, enhancing the effectiveness of the doping process.
DFT simulation of CuO
Theoretical investigation plays a crucial role in understanding the properties of target materials, complementing experimental studies Density Functional Theory (DFT) is a widely recognized analytical tool that enables the efficient customization of material properties.
The foundation of Density Functional Theory (DFT) is rooted in two essential theorems developed by Kohn and Hohenberg, along with the mathematical framework created by Kohn and Sham in the late 1960s The first theorem, proposed by Hohenberg and Kohn, asserts that the energy of the ground state can be determined from the electron density.
Derived from Schrödinger’s equation, a unique functional of electron density exists, establishing a bijective correspondence between the wave function and the electron density of the lowest energy state.
Hohenberg and Kohn's theorem posits that the ground state's electron density uniquely determines all its properties, including energy and wave function This allows for a reformulation of the Schrödinger equation in terms of electron density, which is a function of three spatial variables, rather than the traditional wave function that relies on 3N variables Thus, "solving the Schrödinger equation" involves accurately calculating the ground-state energy based on this electron density approach.
The initial Hohenberg-Kohn theorem confirms the existence of a functional for electron density that can be used to solve the Schrödinger equation, but it does not specify the nature of this functional The second Hohenberg-Kohn theorem highlights that the electron density yielding the lowest energy of the overall functional is the true electron density corresponding to the complete solution of the Schrödinger equation If the exact form of this functional were known, we could adjust the electron density to minimize the energy, allowing us to determine the correct electron density In practice, the variational principle is often employed using approximate versions of the functional.
Kohn and Sham illustrate that finding the correct electron density can be approached as solving a system of equations, with each equation corresponding to an individual electron The Kohn-Sham equations are presented in a specific mathematical form.
The Kohn-Sham equations bear a resemblance to the Schrödinger equation, with the key difference being the lack of summations in the former This absence of summations in the Kohn-Sham equations is significant, as it simplifies the solutions compared to the full Schrödinger equation.
The Kohn-Sham equations describe single-electron wave functions dependent on three spatial variables, Ψ i (r), and include three key potentials: V, VH, and VXC These potentials illustrate the interactions between electrons and atomic nuclei, with the Hartree potential (VH) accounting for Coulomb repulsion between electrons However, VH also incorporates a self-interaction term, as the electron in the Kohn-Sham framework contributes to its own density, leading to a non-physical self-interaction This self-interaction is addressed within the final potential, VXC, which encapsulates the exchange and correlation effects among electrons VXC is mathematically defined as the functional derivative of the exchange-correlation energy, highlighting its significance in the Kohn-Sham equations.
Kohn, Hohenberg, and Sham's groundbreaking research revealed that achieving the lowest energy state can be accomplished by minimizing a functional's energy through self-consistent solutions for individual particles However, a key challenge in this elegant formulation is the need to explicitly define the exchange-correlation function to effectively solve the Kohn-Sham equations.
Additionally, there are alternative approximations that can be employed to ensure the feasibility of the calculation
Pseudopotentials are essential for managing high-frequency oscillations of plane waves in real space, but they require large energy cutoffs This presents a challenge since core electrons, which are tightly bound and associated with these oscillations, do not significantly influence chemical bonding or the physical properties of materials.
The properties of materials are primarily influenced by their valence electrons, which are less tightly bonded Since the development of plane-wave methods, it has become clear that approximating core electron characteristics can significantly reduce the number of plane waves needed for calculations, leading to considerable computational advantages The main strategy to alleviate the computational burden from core electrons is the use of pseudopotentials, which replace the electron density of core electrons with a smoothed density that retains essential physical and mathematical properties of the actual ion core This approach, known as the frozen core approximation, maintains the characteristics of core electrons constant throughout subsequent calculations Although all-electron calculations that do not utilize a frozen core are less common, pseudopotentials are typically derived from studying individual atoms and can be applied in various chemical environments without further modifications, showcasing their transferability Modern DFT programs provide an extensive array of pseudopotentials for nearly all elements in the periodic table.
Periodic boundary conditions are essential for efficiently studying systems with a large number of atoms using the DFT approach, as calculating the electron configuration of thousands of atoms directly is impractical By implementing periodic boundary conditions, researchers can focus on a smaller unit cell while still allowing for interactions between atoms near the edges and those on the opposite side, effectively simulating an infinite array of identical unit cells This method enables the exploration of mechanisms with larger repeating patterns, achieving a level of accuracy unattainable with smaller unit cells.
Research objectives
This research includes multiple objectives:
• Employ the solution method to make Ni-doped CuO thin films and conduct experimental measurements
To accurately compute the characteristics of CuO, it is essential to select the appropriate functionals, including LDA, GGA, and U values, and compare the results with experimental data These functionals will also be utilized for further calculations on the doped system.
• Examine the mechanism that leads to the p-type conductivity of CuO, and explore the particular experimental circumstances that promote this type of conductivity
• Employ the series of approximations on Ni-doped CuO and compare the calculated band gap values with the experimental data
• Investigate the impact of a doped atom on the conductivity of CuO and provide experimental predictions
METHODOLOGY
Experimental process
The research utilized cupric oxide (CuO) as the host semiconductor and nickel (Ni) as the transition metal dopant in the oxide semiconductor The reaction commenced with solutions of Cu(CH3COO)2.H2O and Ni(CH3COO)2.4H2O, which were combined in ethanol, with MEA serving as a stabilizer throughout the process A comprehensive list of the chemicals required for sample preparation is detailed in Figure 2.1.
Figure 2.1 Chemicals for sample preparation
To prepare the solution, Cu(CH3COO)2.H2O and Ni(CH3COO)2.4H2O were combined in 19.395 mL of absolute ethanol, with nickel added at concentrations ranging from 1% to 4% To prevent agglomeration, 0.605 mL of MEA was introduced into the mixture, which was then covered with plastic wrap After stirring for 15 minutes, the temperature was raised to 75°C, and the mixture was gently stirred for an additional hour to achieve a homogeneous solution before allowing it to cool.
10 temperature and stored in the fridge for 24 hours The resulting solution is completely homogeneous with no precipitation or crystallization of metal compounds observed
Figure 2.2 Precursor solution: CuO (left) and Ni-doped CuO (right)
Figure 2.3 Schematic of precursors synthesis process
Figure 2.3 Schematic of spin coating process for thin film deposition
A 22x22 mm glass substrate is used for the thin film deposition process which refers to the below main steps:
First step: Remove contaminants from glass substrates by applying acetone, ethanol, and distilled water
To enhance the adhesion of the precursor solution to the substrate surface, the second step involves cleaning the substrate with a 2% HF solution, which also helps create a layer of H+ ions.
In the third step, the treated glass substrate undergoes precursor deposition through spin-coating Specifically, 50 μL of precursor is applied to the glass substrate and spin-coated at a speed of 1500 rpm for 50 seconds Following this process, the precursor-coated substrate is dried at 100 °C.
7 minutes and cool down for 5 minutes
To achieve the desired film thickness, repeat the third step three times, ensuring that each coating and drying process is completed After completing the three cycles of coating and drying, the thin-film glass substrate is then annealed in air.
500 °C for 30 minutes to form a crystalline thin film
We used an X-ray diffractometer (XRD, Bruker, D2 phase) with Cu-Kα radiation (λ
= 1.54 cm -1 ) to investigate the crystal structure of thin films
XRD analysis is a crucial technique in materials science for examining the crystal structure of samples This method involves directing an X-ray beam at a crystalline sample, resulting in a scattering pattern that reflects the atomic arrangement within the crystal By analyzing the angle and intensity of the scattered X-rays, researchers can gather essential information regarding crystal structure, phase identification, lattice parameters, and crystalline orientation.
At room temperature, the diffractometer measured reflections between 20° and 80° According to Bragg's Law, represented by the equation nλ = 2dsinθ, the angle of the X-ray impacting the material significantly influences the scattering, where d denotes the inter-planar spacing and λ represents the wavelength of the X-ray.
13 n is an integer that represents the order of the peak (n = 1, 2, 3, …), θ is the incidence angle
Figure 2.5 UV-Vis Spectroscopy (Shimadzu 2450)
Quantitative UV-Vis spectroscopy is utilized to assess optical transmittance and absorption by comparing a sample to a standard reference The data obtained, including transmittance (T%) and absorbance (Abs), are essential for calculating the optical band gap energy An established formula is employed to determine both the optical band gap and the absorption coefficient from these measurements.
The absorption coefficient (α) in the light absorption spectral region is calculated using the Beer-Lambert law, which relates absorbance (A), film thickness (d), and transmittance (T).
The energy of the optical bandgap Eg was determined by considering the relationship between the absorption coefficient (α) and the energy of the incident photons (hv).
Simulation process
All of our calculations are done with the Vienna Ab initio Simulation Package (VASP)
VASP is a computer program used for modeling materials at the atomic scale, specifically for conducting electronic structure computations and quantum mechanical molecular dynamics based on first principles
VASP provides an approximate solution to the many-body Schrödinger equation through methods such as Density Functional Theory (DFT) for Kohn-Sham equations and the Hartree-Fock (HF) approximation for Roothan equations It utilizes plane wave basis sets to represent essential properties, including one-electron orbitals, electronic charge density, and local potential The interaction between electrons and ions is modeled using norm-conserving or ultrasoft pseudopotentials, along with the projector-augmented-wave (PAW) method.
VASP employs advanced iterative matrix diagonalization techniques to determine the electronic ground state, integrating highly effective Broyden and Pulay density mixing methods to enhance the efficiency of the self-consistency cycle.
This thesis utilizes VASP with the projector-augmented wave (PAW) method to perform first-principles calculations based on density functional theory (DFT) The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) is employed to account for exchange and correlation functions The study focuses on the electronic states of valence electrons in copper (Cu: 3d^10 4s^1) and oxygen (O: 2s^2 2p^4).
Ni (3d 8 4s 2 ) are considered The plane-wave basis set and pseudopotential clarified electronic wave structure We use plane-wave cut-off energy of 450 eV
In geometry optimization, the structure's degrees of freedom, such as ionic positions, cell volume, and cell shape, are allowed to vary The optimization process is considered complete when the change in eigenvalues between two steps is less than 10^-5 eV, typically involving 40 to 60 ionic steps.
2.2.1.2 Density of States (DOS) calculation
The electronic density of states (DOS) is a fundamental measure used to describe the electronic state of a material ρ(E)dE = number of electron states with energies in interval (E, E + dE)
After performing a DFT calculation, the electronic density of states (DOS) can be determined by integrating the electron density in k-space Utilizing a high number of k points is essential for accurately calculating the DOS, as the intricate details of the DOS stem from these k-space integrals.
The Density of States (DOS) image reflects energy levels in relation to the Fermi energy (E f), which is the energy of the highest occupied electronic state at absolute zero (0 K) Metals are defined by their non-zero DOS at the Fermi level, indicating the presence of available electronic states When an electric field is applied, electrons gain energy and move more rapidly, allowing them to occupy electronic states just above the Fermi energy This characteristic enhances the conductivity of metals, making them efficient conductors of electricity.
The valence band and conduction band represent distinct regions of the density of states (DOS) in various materials At absolute zero temperature (T = 0 K), all electronic states are filled within the valence band, leaving the conduction band entirely unoccupied The energy gap, known as the band gap, exists between the valence band maximum (VBM) and the conduction band minimum (CBM), indicating the absence of electronic states in this energy range.
When an electric field is applied to certain materials, electron conduction occurs less readily than in metals A material is classified as a semiconductor if its band gap is small, while a wide band gap indicates that the material is an insulator.
Understanding the electronic structure of a material requires knowledge of the significant states near specific atoms A common method to achieve this is through the local (projected) density of states (TDOS/PDOS), which quantifies the number of electronic states at a given energy, weighted by the proportion of total electron density associated with those states in the vicinity of a nucleus.
The density of states (DOS) calculation utilizes a Gaussian smearing model along with a Gamma-centered 4x4x4 grid In this thesis, the DOS and projected density of states (PDOS) figures were primarily generated using the Vaspkit code, which automatically sets the Fermi energy to 0 eV.
By analyzing the eigenvalues, we can determine the minimum distance between the highest occupied and the lowest unoccupied energy levels across all k points, which indicates an indirect bandgap, as well as for a single k point, representing a direct bandgap.
Figure 2.6 Indirect and Direct band gap
2.2.1.3 Formation energy of different defects and impurity level calculation
The notation for defect using in this thesis follow Krửger–Vink Point Defect Notation[36] 𝑋 𝑆 𝑞
Where X is the species (element or vacancy)
S is the lattice site (Element symbol of original state)
The variable q represents the electrical charge of the species in relation to the specific location it occupies
The formation energy diagram is essential for assessing defect properties, revealing both the likelihood of defect occurrence and the charge state transition levels The formation energy is affected by the chemical potential of all components involved in defect creation, which can be categorized into two main groups: the chemical potential of elements and the electron's chemical potential, or Fermi level The Fermi level accounts for external influences, such as other defects, on the thermodynamics of electron addition or removal Once a defect is established, the chemical potentials of the involved atoms stabilize, becoming less variable The formation energy of a defect can be mathematically represented by a specific equation.
𝐸 𝑡𝑜𝑡𝑎𝑙 [𝑋 𝑞 ]: the total energy of the defect state with charge q
𝐸 𝑡𝑜𝑡𝑎𝑙 [𝑏𝑢𝑙𝑘]: the total energy of a perfect unit cell (the same size with the defected unit cell)
𝑛 𝑖 𝜇 𝑖 : the reference energy for 𝑛 𝑖 atoms of element 𝑖 that were added at chemical potential 𝜇 𝑖
To determine the formation energy, it is necessary to calculate each of the terms that have been specified previously The procedures are outlined as follows:
• Choose the compound and defect to be examined, as well as the computational model to be employed
• Employ the selected computational model to optimize the pure bulk system
• Calculate the total energy of the bulk for the elements present in the defect
• Calculate 𝐸 𝑡𝑜𝑡𝑎𝑙 [𝑏𝑢𝑙𝑘] and E VBM for the perfect structure
• Begin by introducing the charged defect into the system and then proceed to relax the system in order to obtain 𝐸 𝑡𝑜𝑡𝑎𝑙 [𝑋 𝑞 ]
After got the formation energy of defect, we made the defect formation energy diagram The example of defect formation energy diagram is shown in Figure 2.7
Figure 2.7 Defect formation energy diagram
Electronic carriers, like electrons and holes, are made by charged defects It is not possible for a neutral defect (isoelectronic doping or alloying) to make electronic carriers
In defect diagrams, a positively charged defect exhibits a positive slope and is associated with donor-like characteristics, as it becomes ionized by donating electrons This process gives the defect its donor label, typically imparting n-type properties to the material Conversely, negatively charged defects exhibit acceptor-like properties, often leading to p-type characteristics The classification of a material as n-type or p-type depends on several additional parameters.
To generate a defect formation energy diagram, the initial step involves determining the valence band maximum (VBM) energy (E_v) and the conduction band minimum (CBM) energy (E_c) This is achieved by calculating the total energy differences for a perfect structure across three scenarios: the neutral state (N), the state with one additional electron (N+1), and the state with one electron removed (N-1).
A defect diagram illustrates the correlation between the energy needed to create a defect and the Fermi energy, typically referenced against the highest energy level in the valence band, where E v is set to 0.
RESULTS AND DISCUSSION
Experimental results
The XRD patterns revealed that both pure and Ni-doped CuO films, deposited on glass substrates, displayed excellent crystallinity, as illustrated in Figure 3.1 Notable peaks at 35.57° and 38.60° confirmed the presence of CuO planes (002).
(111), respectively These results agree well with the published data[28]
Figure 3.1 XRD pattern of CuO and Ni-doped CuO
The experimental findings indicate that nickel (Ni) effectively replaces copper (Cu) in CuO, as evidenced by the similar patterns observed in both materials This suggests that during the simulation process, substituting the Cu atom with a Ni atom in the supercell can be utilized to accurately calculate the properties of Ni-doped CuO.
The UV-vis measurement indicated a bandgap value of approximately 2.77 eV for the CuO thin film, but this may overestimate the actual bandgap Accurately determining the experimental bandgap is essential for this thesis, as it influences the choice of functionals for the simulation process Consequently, I will rely on the bandgap derived from the experimental data.
A study conducted by my research group, detailed in 27 articles, emphasizes the importance of accurate calculations Figure 3.2 illustrates the optical absorbance spectra of pure CuO films alongside nickel-doped copper oxide films, with nickel concentrations varying from 1% to 4%.
CuO 1% Ni 2% Ni 3% Ni 4% Ni
Figure 3.2 UV-vis measurement of Ni-doped CuO [28]
From this spectra, they calculated the band gap energy, and the results of bandgap energy with difference Ni doping concentrations are listed in Table 3.1
Table 3.1 Experimental band gap of CuO and Ni-doped CuO
Sample Band gap energy (eV)
The bandgap energy remained relatively stable as the nickel (Ni) concentration increased from 0% to 3% wt.%, but a notable decrease to 1.88 eV occurred at a doping level of 4 wt.% Ni.
Simulation results
3.2.1 DOS calculation of transition metal oxides
This thesis's first trial systematically and uniformly investigates the properties of the transition metal oxides (TMOs) including NiO, CoO, FeO, and MnO, allowing a prediction for the CuO case
Transition metal oxides (TMOs) are extensively studied materials whose electronic properties are closely interconnected These materials, often classified as wide-gap insulators, are anticipated to display metallic behavior based on traditional density functional theory (DFT) TMOs are distinguished by their insulating characteristics, which are marked by highly localized 3𝑑 magnetic moments.
The calculations for MnO, FeO, NiO, and CoO in the rocksalt structure were performed using experimental lattice values of a = 4.45 Å, 4.26 Å, 4.19 Å, and 4.2615 Å, respectively These calculations incorporate antiferromagnetic ordering, resulting in an R3m space group symmetry, which features two transition metal ions within the unit cells.
Figure 3.3 Structure of transition metal oxide: a) rock-salt structure (Fm3m) and b) rhombohedral structure (R3m) The O, TM with spin up, and TM with spin down are red, blue, and grey, respectively
The density of states (DOS) for transition metal oxides (TMOs), as illustrated in Figure 3.4 using GGA methods, provides immediate insight into whether a material behaves as a metal or an insulator Additionally, the optical band gap, which quantifies the difference between the valence band maximum (VBM) and the conduction band minimum (CBM), is a crucial factor to consider when comparing material properties.
Figure 3.4 Density of states (DOS) of MnO, NiO, CoO and FeO with GGA method
Table 3.2 presents the calculated band gap values derived from the density of states (DOS) alongside the experimental optical band gap values for transition metal oxides (TMOs) including MnO, NiO, CoO, and FeO for comparison purposes.
Material Functional Band gap (eV)
(sta tes /eV ) (sta tes /eV ) (s ta te s/e V )
The analysis reveals a significant gap issue in the normal DFT calculations of GGA, which fail to demonstrate the insulating behavior of CoO and FeO, aligning with existing literature For MnO and NiO, although band gaps are observed, the calculated values of 0.8 eV and 0.5 eV fall short of the experimental values of 3.9 eV and 3.26 eV, respectively These findings underscore the necessity for an additional functional to accurately capture the material properties, as supported by previous studies To address this discrepancy, we employed a Hubbard correction by applying a U value of 6.4 eV to the 3d orbital of the Ni atom, deemed the most suitable for this analysis.
The U value for NiO was adjusted to align the band gap with the experimental value, resulting in a band gap increase to 3.53 eV using the GGA+U approach, as illustrated in Figure 3.5 This value is in close agreement with the experimental measurement of 3.6 eV, demonstrating the effectiveness of the Hubbard approach in correcting the gap error in NiO Furthermore, this success indicates its potential applicability to CuO as well.
Figure 3.5 DOS structure of NiO applied +U method
3.2.2 LDA+U and GGA+U calculation of CuO
In this section, we start with the primitive cell of CuO, which has four Cu atoms in the unit cell Cu atoms are arranged with an antiferromagnetic spin (Figure 2.9.) [38]
To determine the density of states (DOS) of CuO, we utilized the Generalized Gradient Approximation (GGA) and Local Density Approximation (LDA), both established methods in Density Functional Theory (DFT) studies Subsequently, we implemented the GGA+U and LDA+U techniques to further validate our findings.
(sta tes /eV ) (sta tes /eV )
(sta tes /eV ) (s ta te s/e V )
The U method significantly influences the outcomes for CuO, as illustrated in Figure 3.6 The optimized Cu-O bond lengths and the corresponding band gap energy values are detailed in Table 3.3.
Figure 3.6 DOS of CuO calculated using GGA+U and LDA+U
Table 3.3 Cu-O length and band gap calculates with GGA+U and LDA+U method
Band gap/eV LDA+U No band gap
The standard Density Functional Theory (DFT) calculations using Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA) fail to accurately predict the insulating behavior of CuO, as indicated by the Fermi level crossing the peak in the density of states (DOS) structure Even with an applied U value of 3 eV, this issue persists However, increasing the U value to 5 eV results in the emergence of a small bandgap energy, measuring 0.17 eV for LDA+U and 0.47 eV for GGA+U Further raising the U value to 7 eV leads to a broader bandgap energy of 0.71 eV for LDA+U and 1.11 eV for GGA+U.
The experiment reveals that in CuO, the Cu-O bond lengths are measured at two shorter distances of 1.95 Å and two longer distances of 1.96 Å A comparison of the Cu-O distances in the primitive cell with experimental values is presented in Table 3.3, showing a 2.7% underestimation in bond length using the LDA method, consistent with previous studies indicating that LDA results yield shorter bond lengths than experimental data In contrast, the GGA method provides theoretically calculated Cu-O bond lengths that closely align with experimental values, exhibiting only about a 0.5% difference.
The analysis of band gap energy and Cu-O bond length indicates that the GGA method yields superior results compared to LDA Consequently, GGA+U will be utilized for subsequent calculations Additionally, the findings demonstrate that the +U approach significantly improves the characterization of the electronic structure of CuO.
3.2.3 Effect of the U value on CuO properties
One major drawback of the DFT + U method is the uncertainty in selecting the U parameter, which is usually fitted based on experimental data or higher-order functionals In this study, we demonstrate how we determine the U value for CuO, testing values ranging from 1 to 9 eV This determined U value is subsequently applied to investigate other relevant systems, including the p-type conductivity of CuO and transition metal-doped CuO films.
Phuc et al highlight the significant impact of spin configuration on the properties of CuO Their findings indicate that utilizing a small unit cell is insufficient for accurately representing Type II spin, leading to unreliable results To address this issue, I expand the Type I cell (Figure 2.9) to a 2x1x2 configuration, resulting in a supercell containing 16 Cu atoms, aligning it with the characteristics of Type II spin.
The total energy comparison between Type I and Type II reveals that Type I has a total energy of -125.597 eV, which is higher than Type II's -125.870 eV This slight difference indicates that Type II is more stable under normal conditions, making it the focus for examining bandgap energy across various U values.
The Cu–O bond length, the spin moment on the Cu d-orbital, the indirect bandgap, and the direct bandgap at the G-point are all presented in Table 3.4 as a function of U
Table 3.4 presents a comparison of the Cu-O bond length, the spin moment on the Cu d-orbital, and the band gap energy (both indirect and direct at the Gamma point) for CuO (Type II), highlighting theoretical estimates alongside experimental findings.
Functional U/eV |Cu - O|/ Å Mcu / à B Eg/eV