Effects of Different Point Defects on the Electronic Properties of III–V Al_0.5Ga_0.5N Photocathode Nanowires

Abstract

Al_xGa_1−xN nanowires are the key materials for next-generation ultraviolet (UV) detectors. However, such devices have a low quantum efficiency caused by the introduction of defects and impurities throughout the preparation process of nanowires. Herein, the effects of different interstitial defects and vacancy defects on the electronic structure of Al₀.₅Ga₀.₅N nanowires are investigated using density functional theory calculations. Our results successfully discovered that only the formation of an N interstitial defect is thermally stable. In addition, the introduction of different defects makes the different nanowires exhibit n-type or p-type characteristics. Additionally, different defects lead to a decrease in the conduction band minimum in band structures, which is the major cause for the decrease in work function and increase in electron affinity of Al₀.₅Ga₀.₅N nanowires. What is more, the calculation of the partial density of states also proved that the interstitial defects contribute to a re-hybridization of local electron orbitals and then cause more significant movement of the electron density. Our investigations provide theoretical guidance for the pursuit of higher-quantum-efficiency ultraviolet (UV) detectors.

1. Introduction

In recent years, III–V semiconductor nanowires have been intensively selected in the realm of optoelectronic devices such as solar cells, photodetectors, lasers, and other nanoscale devices [1,2,3], owing to their fascinating characteristics [4,5,6,7]. Furthermore, the Al_xGa_1−xN nanowire photocathode has become the most promising candidates for ultraviolet (UV) detectors due to its adjustable band gap, high temperature resistance, and high sensitivity. However, the defects and impurities throughout the growth and preparation process are the main factors affecting the quantum efficiency of photocathodes [8,9,10,11,12]. Additionally, numerous experiments have detected the defects and impurities on the surface of nanowires [13,14,15,16]. Hemesath et al. investigated the incorporation of Au atoms in Si nanowire and proposed new criteria for the stability of planar defects [13]. Biswas et al. discovered that metal impurities in germanium nanowires could substantially alter their electronic and optical properties [14]. Chen et al. studied the incorporation of metal atoms into silicon nanowires and proposed a dimer-atom-insertion kinetic model to explain the impurity incorporation into nanowires [15]. Álvarez et al. found that in InAs nanowires, the surface properties are intimately related to the formation and reaction of surface point defects [16]. However, the experimental studies cannot correctly quantify the variations in nanostructure around the defects and impurities throughout the material growth process. Fortunately, the first-principles calculation method based on density functional theory (DFT) has emerged as an effective means to solve this problem [17,18,19]. A large number of studies have been carried out to analyze the effect of defects on the performance of nanowires by first-principles calculations on the basis of no experiments. For example, Yang et al. found through calculations that the As_Ga point defect is highly stable in the As-rich condition, regardless of whether the GaAs nanowires are exposed or hydrogen-passive. At the same time, the existence of As_Ga point defects inhibits the p-type doping process of GaAs nanowires [20]. Using first principles, Liao et al. found that C_N point defects are more likely to exist on the surface of GaN NWs, and when the defect is closer to the outer side, the effect on the top of the valence band is greater [21]. Kong et al. analyzed first-principles calculations to demonstrate that N vacancy is more likely to exist at the surface of the GaN nanowires and deteriorate the stability [22]. Liu et al. posited that Zn-doped GaAs nanowire suffer more significant surface defects under the same growth conditions due to lower formation energy [23]. Lu et al. explored the optoelectronic properties of native point on GaN nanowires and found that N_Ga substitutional defects are the surface defects with the lowest formation energy [24]. Therefore, it is of great significance to study the effect of defects on the properties of nanowires by first-principles calculations. Nevertheless, there are few investigations into the defects and impurities of the Al₀.₅Ga₀.₅N nanowire surface. Therefore, in this study, according to the first-principles calculation method, we investigated the impact of surface defects on the electronic characteristics of Al₀.₅Ga₀.₅N nanowires.

Herein, interstitial defects and vacancy defects are considered in this study. In addition, in order to maintain the Al composition, only Ga atom and N atom vacancy defects are discussed in this article. The formation energy, work function, electron affinity, geometric structure, Mulliken charge distribution, energy band, and partial density of states are computed and discussed. This study not only explains the physical mechanism of the effect of defects on the Al₀.₅Ga₀.₅N nanowire surface but also provide significant guidance for the preparation of high-performance Al_xGa_1™xN nanowire-based photocathodes.

2. Calculation Models and Method

All calculations were operated in the Vienna ab initio Simulation Package (VASP) program [25,26]. The Heyd–Scuseria–Ernzerhof (HSE06) functional was implemented to handle the electronic exchanges [27,28]. Following a thorough convergence test, the high energy cut-off was determined to be 400 eV, the thickness of the surrounding vacuum layer was determined to 25 Å, and the k-point was determined to be 1 × 1 × 4. The energy change was steady within 10⁻⁴ eV and the force on each atom was less than 0.01 eV, respectively. The valence electrons included: H: 1s¹, N: 2s²2p³, Al: 3s²3p¹, and Ga: 3d¹⁰4s²4p¹.

Initially, the Al₀.₅Ga₀.₅N nanowires were established by replacing half of the Ga atoms with Al atoms based on the principle of lowest energy [17]. The top views of different defect structures are shown in Figure 1. Moreover, H atoms were selected to eliminate the influence of dangling bonds [29]. In this paper, the positions of interstitial defects and vacancy defects of Al₀.₅Ga₀.₅N nanowires were all constructed in the core layer.

3. Results and Discussion

There is no doubt that both interstitial defects and vacancy defects affect the stability of the nanowire structure, and the formation energy can be used to assess the stability of Al₀.₅Ga₀.₅N nanowires with different defects. What is more, the formation energy can be calculated using the following formula [30]:

$$E_f=E_{defect}-E_{perfect}-{\displaystyle \sum }_i{n}_i{\mu }_i$$

(1)

where E_perfect and E_defect represent the total energy of the structures with and without defects, respectively. n_i represents the number of defect atom, and μ_i represents the chemical potential of the defect atom.

Figure 2a shows the calculated formation energies of different structures. It is clear that compared with the original nanowire structure, the formation process of vacancy defects is an endothermic reaction, which contributes to an unstable nanowire structure. The most difficult to survive is the N atom vacancy defect. Surprisingly, for the formation process of Al and Ga interstitial defects, it is also an endothermic process. However, it is easier to survive than the vacancy defect. Then, for the formation process of N interstitial defects, it is stable owing to negative formation energy, which is consistent with the previous conclusion [24]. According to the previous study [24], the formation energy of the outermost surface defects in the GaN nanowire was about 2.64 eV, while in this study, the formation energy of N interstitial defect at the core position is −3.47 eV. The disparity is mainly due to the differences in Al composition and doping position in the simulated nanowire structures.

In order to quantitatively describe the effect of defects on optoelectronic properties, the work function and electron affinity are firstly calculated in this study. The work function (φ) is the energy difference between the vacuum level (E_vac) and the Fermi level (E_f). The electron affinity (χ) is the energy difference between the vacuum level and the conduction band minimum (E_C). The specific formula are as follows [31]:

$$\mathsf{\phi }=E_{vac}-E_f$$

(2)

$$\mathsf{\chi }=E_{vac}-E_C$$

(3)

As is shown in Figure 2b, except for Ga vacancy defects, the introduction of defects contributes to the decrease in surface work function and the slight increase in surface electron affinity. This is mainly attributed to the redistribution of electrons on the nanowire surface caused by the introduction of defects, thereby affecting the transition of photoelectrons. Importantly, it can also be confirmed by the following charge distribution.

On the other hand, the introduction of defects causes changes in the electron density and varying degrees of atom displacements near the defect. Therefore, in order to better understand the effect of introduced defects on the atomic structure and electrons of Al₀.₅Ga₀.₅N nanowires, we estimated the bond length, Barder charge distribution, and lattice constant with different defects. The calculated results are shown in

Table 1. Bond length, Barder charge distribution, and lattice constant of Al_0.5Ga_0.5N nanowires with interstitial defects and vacancy defects.

	Bond Length(Å)		Charge Distribution (|e|)			Lattice Constant (Å)
	Ga-N	X-N	Ga	Al	X
Pure	1.986	1.905	+1.37	+2.37	−1.89	a = b = 35.046, c = 5.00
VGa		1.874	+1.36	+2.357	−1.83	a = b = 35.029, c = 5.11
VN			+1.24	+2.35	−1.90	a = b = 34.826, c = 5.14
Ali	1.944	2.506	+1.27	+2.34	−1.90	a = b = 35.033, c = 5.00
Gai	1.919	1.915	+1.25	+2.376	−1.88	a = b = 35.029, c = 5.15
Ni	1.993	1.905	+1.27	+2.37	−1.72	a = b = 35.027, c = 5.11

. As calculated, the bond lengths of Ga-N bonds and Al-N bonds in pure Al₀.₅Ga₀.₅N nanowires are 1.986 Å and 1.905 Å, respectively, which is similar to the previous study [32]. Furthermore, it is clear in Table 1 that the Al interstitial defects lead to a significant extension of the Al-N bond, extending by 0.601 Å. Next, the interstitial defects have little effect on the Ga-N bond. Additionally, the vacancy defects lead to a decrease in Ga-N bond and Al-N bond. What is more, according to the Barder charge distribution, the initial charge values of Ga atoms, Al atoms, and N atoms in the Al₀.₅Ga₀.₅N nanowires without defects are 1.37 eV, 2.37 eV, and −1.89 eV, respectively. Regardless of interstitial defects or vacancy defects, the charge transfer of Al atoms is not obvious, and it is more obvious for Ga atoms and N atoms. Importantly, the N atom vacancy defects greatly reduce the charge of Ga atoms. The introduction of defects also contributes to the reduction in the a-axis and b-axis lattice constant and the increase in c-axis lattice constant, which indicates the closer atomic connections in the horizontal direction of Al₀.₅Ga₀.₅N nanowires.

In order to further understand the effect of defects on the optoelectrical properties of Al₀.₅Ga₀.₅N nanowires, great efforts have been carried out to evaluate the band structures of different models with defects, as shown in Figure 3. It is obvious that the pure Al₀.₅Ga₀.₅N nanowire is a direct band gap semiconductor, with a band gap of 5.43 eV. In Figure 3b,c, the appearance of the acceptor energy level can be clearly observed. Compared with the pure Al₀.₅Ga₀.₅N nanowire, the band structure of Ga vacancy defect exhibits the p-type characteristic. However, for the N vacancy defect, it contributes to the band structure moving toward lower energy direction and then showing the n-type characteristic. It is mainly attributed to the fact that the vacancy atoms reduce the charge density near the defects. Figure 3d–f show that the interstitial defects introduce impurity energy levels near the Fermi level, which are represented as donor or acceptor energy levels in the energy band diagram.

Immediately afterwards, in order to have a deeper understanding of the changes in the band structure, the partial density of states (PDOS) are also considered. Figure 4 shows the PDOS of Al_0.5Ga_0.5N nanowires with different defects. It can be seen from Figure 4a–c that the interstitial defects introduce a new p-type electronic state near the Fermi level and move toward the lower energy direction, thus passing through the Fermi level and showing n-type characteristics. Among them, the influence caused by Al and Ga interstitial defects is the most obvious. As shown in Figure 4d, due to the lack of N atoms, the density of states of Ga atoms moves towards lower energy as a whole and the total electronic states of Ga atoms decrease. As shown in Figure 4e, due to the lack of Ga atoms in the core position, the peak value of the total electronic states of N atoms has been reduced. Meanwhile, the electronic state of the N atom at the Fermi level is no longer zero and has certain p-type structural characteristics.

4. Conclusions

In summary, based on the first-principles calculation method, we have investigated the effects of interstitial defects and vacancy defects on the electronic structure of Al_0.5Ga_0.5N nanowires. From the perspective of formation energy, only the N interstitial defect is an exothermic reaction, which contributes to a thermally stable nanowire structure. In Al_0.5Ga_0.5N nanowire, interstitial defects are more likely to stably exist than vacancy defects. In addition, except for the Ga vacancy defect, other impurity types cause the work function of the nanowire surface to decrease and the electron affinity to increase. This is mainly due to the decrease in the conduction band minimum in band structures caused by the introduction of defects. Furthermore, the introduction of defects cause changes in the electron density and varying degrees of atom displacements near the defects. In others, the introduction of different defects leads to new donor or acceptor energy levels near the Fermi level in the band structures, making the different nanowires exhibit n-type or p-type characteristics. Overall, this research aims to reveal the effect of different defects on the electronic properties of Al_0.5Ga_0.5N nanowires, and to provide systematical guidance for subsequent experimental preparation.