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Abstract
Photocathodes play a crucial role in photoelectronic imaging and vacuum electronic devices. The quantum efficiency of photocathodes, which determines their performance, can be enhanced through materials engineering. However, the quantum efficiency of conventional planar photocathodes remains consistently low, at around 25%. In this paper, we propose what we believe is a novel structure of AlGaN nanowire array to address this issue. We investigate the photoemission characteristics of the nanowire array using the "four-step" process, which takes into account optical absorption, electron transportation, electron emission, and electron collection. We compare the quantum efficiency of nanowire arrays with different structure sizes and Al components. After studying the effect of incident light at various angles on the nanowire array photocathode, we identify the optimal dimensional parameters: a height of 400∼500 nm and a wire width of 200∼300 nm. Furthermore, we improved the collection efficiency of the photocathode by introducing a built-in/external electric field, and obtained a 104.4% enhancement of the collection current with the built-in electric field, meanwhile the photocurrent was increased by 87% compared to the case without the external electric field. These findings demonstrate the potential of optimizing photocathode performance through the development of a novel model and adjustment of parameters, offering a promising approach for photocathode applications.
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1. Introduction
The application of photocathodes in particle accelerators has been a topic of interest for researchers for the past four decades. This interest has been fueled by the development of vacuum electron sources that are based on laser excitation sources [1–3]. The photocathode plays a crucial role as the core element of the particle accelerator. Photocathodes have applications in various devices such as phototubes [4], photomultipliers, image intensifiers [5,6], and ultraviolet (UV) photodetectors [7,8]. Depending on the specific application, different types of photocathodes are manufactured. They can be categorized into metal photocathodes and semiconductor photocathodes. Semiconductor photocathodes can further be divided into positive electron affinity (PEA) potential photocathodes and negative electron affinity (NEA) potential photocathodes based on the surface electron affinity potential [9–11].
Group III nitride materials, such as GaN, AlN, InN, and their alloys, possess semiconducting properties that make them exceptional for optoelectronics, power electronics, and RF devices, as well as direct bandgap properties [12–17]. AlGaN additionally offers the ability to adjust its components for band gap changes and response band regulation, particularly for solar-blind UV detection equipment operating in the range of 200 to 280 nm. Consequently, it is the best-suited material for this application. The photoelectric emission efficacy of current AlGaN-based materials has undergone improvement. However, thin film materials encounter their individual technical bottlenecks defined by inconsistent requirements of photon absorption and electron diffusion concerning material thickness [18–20]. In light of the emergence of nanotechnology and nanomaterials, empirical observations and theoretical studies have both revealed nanomaterials’ ability to surmount the restrictions of thin film materials. Due to the preceding reasons, a fresh configuration has been suggested, specifically, nanowire arrays [21–23]. The nanowire array photocathode reflects, refracts and scatters incident light throughout its microstructure, resulting in the absorption of photons and the transport of electrons being directionally uncertain. Hence, photoelectrons could potentially evade the surface in any direction. Furthermore, the arrays typically have sizes in the range of micrometers or nanometers, with small diameters and large surface areas. Photoelectrons can easily be transported to the surface and tunnel through it, subsequently escaping into the vacuum. Thus, theoretically, photocathodes that utilize AlGaN nanowire arrays offer superior performance [24–26].
The theoretical model of photoelectric emission holds significant research value in the development of photocathodes and experimental mechanisms. Spicer made a significant contribution by proposing a "three-step" model of photoemission, which divides the process into the absorption of energy from photons, excitation of electrons, transfer of energy to the surface, and escape of electrons into the vacuum. Based on this fundamental model, researchers have developed theoretical models applicable to different systems. Zhang et al. utilized a two-dimensional photoemission model and derived a tilted heterojunction nanowire array photocathode with a quantum efficiency of 81.2% at the critical incidence angle [27,28]. Similarly, Xia et al. investigated the quantum efficiency of a nano-array photocathode when exposed to varying incident photon energies by combining the two-dimensional continuity equation for semiconductors with the finite difference method. They determined that the optimal dimensions for the linewidth of the nanoarray were 150-200 nm [22,29]. The significance of these studies lies in their theoretical models of photoelectric emission, which have important implications for the development and practical application of semiconductor photocathodes.
However, for the AlGaN nanowires studied in this paper, the photoelectric emission model involves an additional process due to the effect of the array structure on electron collection. This space effect cannot be neglected when compared to thin film materials, and therefore, the electron collection process must be further addressed. Consequently, this paper expands the theory of photoelectric emission into a four-step process: 1) light absorption; 2) electron transportation; 3) electron emission; and 4) electron collection. The transportation of photoelectrons is also expanded to a three-dimensional (3D) scale. Using the 3D-based four-step process developed in this paper, we have gained insights into the complete electron collection process, spanning from excitation to final collection. Our investigations also encompass the optimization of structural and material parameters of AlGaN nano-arrays, including the size of the nanowires and the Al component in the Al$_x$Ga$_{1-x}$N material. This research provides a strong foundation for engineering and conducting experiments with photocathodes utilizing nanostructures.
2. Models and methods
2.1 Optical absorption
The sensitivity and response time of the photocathode are directly influenced by the capability and range of photon absorption. Therefore, it is crucial to enhance the photocathode’s ability to absorb photons in order to improve its performance. In this study, we developed a light absorption model for AlGaN nanowire arrays using the Fluctuating Optics module in COMSOL Multiphysics software. By utilizing the ’periodic boundary conditions’ feature, we transformed the array into a periodic unit for equivalent calculations. Figure 1(a) depicts the simulation area of the AlGaN nanoarray photocathode model, with the simulation area considered as vacuum while the nanowires and substrate are located outside of it. The ports are positioned on the top surface of the nanowire arrays, where incident light vertically illuminates them. To absorb the electromagnetic waves propagating into the AlGaN nanoarray cell, a perfect matching layer (PML) would be applied to the top and bottom of the cell. The simulation domain is then divided into a ’free tetrahedral’ mesh through mesh sizing, which is subsequently used for finite element computations. The reflectivity and absorptivity values obtained from COMSOL will be employed in the carrier concentration equation.
Fig. 1. (a) Schematic diagram of AlGaN nanowire array photocathode. (b) Schematic diagram of the designed AlGaN cross section shape. (c) Top view of AlGaN nanowire photocathode.
2.2 Carrier transportation
2.2.1 Carrier diffusion
When evaluating and designing semiconductor devices with optimized carrier transport, it is crucial to calculate the carrier concentration and distribution. Figure 2(a) illustrates a cross-sectional view of the AlGaN nanowire model in the x-y direction, with its height in the z direction. The model assumes that light incidence is from the x direction. Previous reports have successfully predicted the photoemission property of nano-structured photocathode yet with one-dimensional or two-dimensional models [30,31]. The nanowire has a squared cross-section. This paper’s photoemission model is based on the continuity equation for carrier diffusion. The quantum efficiency of each surface is determined simultaneously with the nanowire’s boundary conditions. The three-dimensional continuity equation for the carrier of an AlGaN nanowire can be expressed as:
where U (x, y, z) is the charge recombination loss, which can be expressed as:In this study, the critical angle of incident light to the array is defined as $\omega =arctan\frac {H}{L}$, as the angle of incident light impacts the variation of the luminous flux of the AlGaN nanowire unit. Assuming $h=Ltan\beta$ when the incident light $\beta$ satisfies $\beta <\omega$, the three-dimensional photoelectron generation function is expressed as follows:
Fig. 2. (a) Schematic of the basic unit of an AlGaN nanoarray photocathode; (b) Internal carrier distribution in the z-direction of the nanowire; (c) Internal carrier distribution in the x-direction of the nanowire; (d) Internal carrier distribution in the y-direction of the nanowire.
For $\beta >\omega$, photoelectron generation function can be expressed as:
2.2.2 Axial exponential doping and carrier drifting
In the theoretical study, it is assumed that all the electrons escaping from the array surface are completely collected, whereas in the experimental process, most of the escaping electrons are secondarily absorbed by the neighbouring nanowires due to the array structure, which causes difficulties in electron collection.
To reduce the loss caused by mutual blocking of emitted electrons between neighbouring nanowires, there are generally two solutions: (1) designing AlGaN nanowires with axial exponential doping structure, introducing an internal electric field in the axial direction of the nanowires, and accelerating the diffusion or drift of minority carriers to the top surface under the effect of the internal electric field, which in turn reduces the electrons escaping from the lateral side and enhances the electron flow on the top surface (See Supplement 1); (2) the external electric field is introduced by applying a bias voltage, which can both improve the photoelectric emission performance of the AlGaN NWAs and, at the same time, the external electric field can also change the trajectory of the vacuum electrons, and all the escaping electrons are accelerated toward the collection end under the effect of the electric field, and the proportion of the escaping electrons absorbed by the neighbouring nanowires is reduced.In order to enhance the quantum efficiency of the nanowires, we introduced an axial exponential doping structure in the model, which brings in a built-in electric field in the axial direction of the nanowires. The photoelectrons excited by the incident photons diffuse to each side along the x and y directions under the effect of the concentration gradient, and at the same time drift along the z-axis toward the top surface of the nanowire under the effect of the built-in electric field, and the three-dimensional continuity equation of the axially exponentially doped AlGaN nanowire under the irradiation of the incident light can be expressed as follows:
Assuming that carriers are expelled perpendicularly to every surface, the boundary conditions for each face can be expressed as follows (See Supplement 1):
2.3 Electron emission
Photogenerated electrons are able to overcome the surface barrier of the material and enter the vacuum from inside the nanowire. The efficiency of photoelectric emission is directly related to how effectively the surface barrier is overcome. This paper proposes a method to determine the carrier concentration in the nanowire by simultaneously solving Eqs. (1) to (5) using the finite difference method. The currents emitted from each surface of the nanowire, as well as the total currents, can be expressed based on the distribution of carrier concentration within the nanowire:
The total photocurrent emitted from a single nanowire is:
where $J_{emitted}$ is the emission current of a single nanowire, $J_{S_1}$ $J_{S_5}$ are the emission currents corresponding to each side and top face of a single nanowire. The quantum efficiency of the AlGaN nanowire cell can be obtained from the ratio of the emitted current to the incident photon current, which can be expressed as:The AlGaN photocathode surface barrier is depicted in Fig. 3(a), consisting of two approximate triangular barriers (I barrier and II barrier). By determining the shape of the surface barrier, we can calculate the transmission coefficients of photoelectron tunnelling through the surface barrier at different energies by solving the one-dimensional stationary Schrödinger equation. The transfer matrix based on Airy functions is widely applicable to arbitrary segmented linear multi-potential structures, providing an accurate and convenient solution to the one-dimensional stationary Schrödinger equation. By simultaneously solving the equation with the transfer matrix, transmission coefficient can be expressed as:
where $k_3$ and $k_0$ are functions of the shape of the barrier and $M_{11}$ is the first term of the transfer matrix.Fig. 3. (a) Energy band structure of transmissive NEA AlGaN photocathode. (b), (c) Variation curves of transmission coefficients for changing barrier widths.
2.4 Electron collection
The output of the vacuum electron beam is influenced by the presence of other electrons, causing a change in their trajectories, as disciplited in Fig. 4. The previous study of photoemission model for nanoarrays rarely focus on the interaction of free electrons, which will affect the electron collection and QE [32]. In the case of photocurrents emitted from all sides of a single nanowire in a nanoarray, the collect efficiency of electrons is affected by the space charge effect (SCE), even without an external electric field to assist in the collection. The equation below describes the motion of ions in the radial direction at a distance r from the beam center axis:
Fig. 4. Schematic diagram of the influence of space charge effects during electron emission from a NWAs structured photocathode.
Considering the ions on the boundary of the beam, i.e., the envelope of the beam, by assuming that $r=r_0=r_{env}$, one obtains the envelope equation for the transport of a homogeneous beam under a space charge field, which can be expressed as:
The probability that a point on the sidewall can be collected is denoted as $\rho \left (x,y,z\right )$, which can be expressed as:
In semiconductor photoelectric emission materials, the introduction of internal electric field accelerates the movement of carriers within the material along z direction whereas the presence of an external electric field leads to tiny decrease in the surface barrier and affects the trajectory of electrons in a vacuum, reducing the time dispersion of electrons. Photogenerated electrons are vertically displaced by an external electric field. The displacement along z axis can be expressed by:
where v, m respectively denote the velocity and mass of the free electron. Photogenerated electrons on the sidewall can be collected by the anode if the condition $\Delta h(x,y,z)>H-h$ is satisfied, the current that can be collected on each sidewall can be expressed as:3. Results and discussion
In order to understand the photoelectric emission process, we simulated the four steps individually based on the theoretical model of photoelectric emission. Additionally, we optimized the dimensional parameters and component parameters of the nanowires using the four-step process proposed in this paper. The parameters discussed in this paper and their corresponding default values are presented in Table 1.
Table 1. Parameters in the photoemission model
3.1 Optical absorption
The spectral absorbance and reflectance of the Al$_x$Ga$_{1-x}$N nanoarray photocathode vary with different structural parameters such as nanowire diameter, height, and array spacing. Figure 5 illustrates this variation. The default structural parameters of the nanowires can be found in Table 1. To assess the impact of the dimensional parameters on the optical properties, we employ the following equation to calculate the average optical spectral lines: $\bar {R}=\frac {\int _{\lambda _1}^{\lambda _2}R\left (\lambda \right )d\lambda }{\int _{\lambda _1}^{\lambda _2}1d\lambda }$, $\bar {A}=\frac {\int _{\lambda _1}^{\lambda _2}A\left (\lambda \right )d\lambda }{\int _{\lambda _1}^{\lambda _2}1d\lambda }$, where $R\left (\lambda \right )$, $A\left (\lambda \right )$ denotes the reflectance and absorbance of the nanoarray corresponding to the wavelength, and $\bar {R}$, $\bar {A}$ denote the average values of reflectance and absorbance, the results are shown in the insert layer.
Fig. 5. Effect of AlGaN nanoarray photocathodes on light reflection from NWAs with different (a) nanowire diameters, (b) heights, and (c) array spacing.
It can be observed from Figs. 5(a) and (d) that the light-trapping effect of NWAs is enhanced with increasing diameter. The maximum absorption occurs at diameters between 300nm and 400nm. Once the diameter exceeds 300 nm, further increase does not significantly enhance the light-trapping effect, fluctuating within a range of about 5%. On the other hand, the light-trapping effect of NWAs increases as the height increases. Guo et al. [33] conducted simulations on the height of cylindrical nanowires, and the results were similar to Fig. 5(c) in this paper. The absorption of NWAs at a height of 1000 nm increased by 5.9% compared to a height of 400 nm. Due to the complexity of NWAs, an increase in height leads to a higher likelihood of photogenerated electrons on the sidewalls interacting with neighboring nanowires, resulting in a secondary absorption phenomenon. Therefore, the height of the nanowires was fixed at 400 nm. The spacing between neighboring nanowires also affects the light trapping effect, the secondary absorption phenomenon, and the number of array units. Figure 5(c) and (f) demonstrate that the optical properties of NWAs exhibit optimal values between 300 nm and 400 nm, with an optical absorption peak of 91.1% at 200 nm. Considering the number of array units and the optical properties of NWAs, the array spacing was set to 200 nm. In conclusion, the basic structure of the photoemission model established in this paper is fixed as: $D\times H\times L=200\times 400\times 200 \ nm^3$.
3.2 Carrier transportation
3.2.1 Carrier diffusion
After photon excitation, the carriers in a single nanowire exhibit a characteristic distribution. Figure 2(b), (c), (d) illustrates the carrier concentration distribution of an AlGaN nanowire, showing an increase and then decrease in carrier concentration along the z-direction, resulting in a concentration center. The x-z and y-z cross sections reveal that photogenerated carriers are concentrated at the side of light incidence and at the top of the nanowire. This implies that the majority of the photocurrent will originate from the top half of the nanowire, resulting in a significantly larger photocurrent at the light-incidence side compared to the other sides.
3.2.2 Carrier drifting
Introducing axial exponential doping in AlGaN nanowires is an effective way to enhance their quantum efficiency. This process introduces a built-in electric field in the axial direction of the nanowire, specifically the z-axis. The photoelectric emission model was investigated in this paper by adding a built-in electric field of varying intensity in the z-direction. The results are shown in Fig. 9(a). As the built-in electric field increases, the collection current of the nanowires first increases and then levels off. When the built-in electric field increases from 0 to 1.2V/$\mu$m, the carriers inside the nanowire gradually gather towards the top of the nanowire, at this time most of the emitted current of the nanowire emits from the top, so the collection efficiency of the nanowire is improved, and when the strength of the electric field is greater than 1.2V/$\mu$m, the emitted current gradually decreases, and the value of the collected current increases by 104%. 2V/$\mu$m, the emitted current gradually decreases, and the value of the collected current increases on average by 104.4% with respect to the value of the collected current when there is no built-in electric field. The same phenomenon was observed for the effective quantum efficiency, which leveled off when the electric field strength exceeded 0.7 V/$\mu$m. Therefore adding the built-in electric field can significantly increase the collected current of the nanowires.
3.3 Electron emission
For photoelectron escape at the surface, the surface escape probability is a crucial factor and is primarily determined by the shape of the surface potential barrier. The surface escape probability $P$ depends on the incident electron energy and the shape (height and width) of the surface barriers I and II. In the case of NEA AlGaN photocathodes, the transmission coefficient represents the escape probability $P(E)$ of an electron with a specific energy E tunneling through the surface barrier. In this study, we focus on transmissive cathodes and select electron energies ranging from 1 eV to 1.8 eV due to the concentrated distribution of emitted electron energies. The dual-dipole layer surface model suggests that the cathode’s surface barrier consists of two approximately straight-line segments with different slopes, resulting in two triangular barriers labeled I and II. As shown in Fig. 3(b) and (c), $P(E)$ significantly decreases as the thickness of the I-barrier increases, with a more rapid decrease observed for low-energy electrons. For an emitted electron energy of 1.5 eV, the surface escape probability decreases by 34.2% when the thickness is increased from 1 Å to 3 Å. On the other hand, increasing the thickness of the II barrier slightly decreases $P(E)$ for low-energy electrons, while marginally increasing $P(E)$ for high-energy electrons. Overall, the effect on electron escape is not particularly significant. These findings are consistent with the work of Zou et al. [34]
3.4 Electron collection
3.4.1 Space charge effect
The photocurrent emitted by AlGaN nanowires, in the absence of an external electric field to aid collection, exhibits lower collection efficiency due to the space charge effect. In the simulation of the space charge effect on electron collection, the total current and quantum efficiency emitted by a single AlGaN nanowire are not affected by SCE. Therefore, we investigate the collection current and collection efficiency for the collection process. In this model, the incident luminous flux is calculated as: $S=\left (L+D\right )^2\times sin\beta$, When the incident light is relatively small, the carriers concentrate at the top of the nanowire, allowing for high collection efficiency as most of the photogenerated electrons can be collected. However, with an increase in the incident light angle, the optical flux and collection efficiency exhibit a trend of initially decreasing and then increasing. Additionally, the collection efficiency of the corresponding AlGaN nano-array photocathode shows a higher average value with larger array spacing. This is attributed to the space charge effect primarily affecting the envelope of the emerging electron beam. As the array spacing increases, the envelope expands, resulting in an increased number of photogenerated electrons that can be collected.
Figure 6(b) illustrates that the collection efficiency of NWAs under the space charge effect is only 49.1% at $L$=1000 $nm$. Furthermore, it decreases further with decreasing spacing, reaching as low as below 30% at $L$=100 $nm$. This implies that regardless of the number of array units, the anode will lose more than half of the emitted electrons. The effective quantum efficiency of NWAs ranges from 9% to 11%.
Fig. 6. (a) Collected current, (b) collection efficiency, (c) effective quantum efficiency corresponding to different array spacings without external electric field.
3.4.2 External field assistance
To improve the collection efficiency of NWAs, an external electric field is commonly used. In this study, we modified the collection model to consider the space charge effect between the vacuum electron streams and the impact of the external electric field. The electric field strength was set to 2 $V/\mu m$ to prevent the generation of field-emitting dark current. The results, presented in Fig. 7, demonstrate the significant enhancement of electron collection with the presence of the external electric field. At $L$ = 500 $nm$, the collection efficiency of NWAs reached 94.6%, and the average effective quantum efficiency increased by 87% compared to the absence of an external electric field.
Fig. 7. (a) Collected current, (b) collection efficiency, (c) effective quantum efficiency (c) considering SCE enhanced by external electric field.
3.4.3 Collection model optimization
Based on the aforementioned study, we have made additional enhancements to the electron collection model. Specifically, we have found that the influence of the space charge effect can be disregarded when an applied electric field is present. When we applied an external electric field of 2 $V/\mu m$ to the NWAs without considering the space charge effect, the results depicted in Figure 8 indicate that the collection efficiency can reach a maximum value of 99.1%, while the average value of the effective quantum efficiency can reach 20.2%.
Fig. 8. (a) Collected current, (b) collection efficiency, (c) effective quantum efficiency considering SCE enhanced by external electric field.
We introduce an enhancement factor $f_{En}=E_{C}^{w}/E_{C}^{w/o}$ to analyze the impact of space charge effects on the collection efficiency of the photocathode. This factor compares the collection efficiency with an external field ($E_{C}^{w}$) and without an external field ($E_{C}^{w/o}$). Fig. 9(b) demonstrates that the space charge effect is not prominent when both the external electric field and space charge effect are present. The enhancement factor reaches 116.8% at $L = 1000 \ nm$, while the lowest value is only 101.9%. These findings indicate that the space charge effect impacts electron collection without the assistance of an external electric field. Furthermore, the presence of an external electric field significantly enhances the collection efficiency of NWAs, thereby increasing the effective quantum efficiency of the device.
Fig. 9. (a)Variation curves of photocathode collection current versus effective quantum efficiency at different built-in electric field strength, (b)Variation of enhancement coefficients with/without consideration of space charge effects after addition of external electric field.
In the study on optimizing the AlGaN nanowire structure, an electric field of 2 $V/\mu m$ will be applied by default to assist the collection. The influence of the space charge effect is considered negligible, and for the sake of simplifying the calculation, it will be ignored.
3.5 Nanowire parameter optimization
3.5.1 NWAs height
Carrier diffusion in AlGaN nanowires exhibits diffusion in all directions, not just vertically on the surface. The transport of carriers within the nanowire is considered in a multidimensional space. This study investigates the impact of height, diameter, and array spacing of AlGaN nanowires on the photoemission model, focusing on the diffusion process in the cross-section and vertical cross-section. The default nanowire structure is $200\times 400\times 200 \ \textit {nm}^3$ (Diameter$\times$Height$\times$Array Spacing) with the other two parameters remaining constant as the height changes. The results, shown in Fig. 10(a), (b), (c), indicate a positive correlation between the collected current and nanowire height, while the collection efficiency is negatively correlated with the height.
Fig. 10. (a) Collected current, (b) collection efficiency, (c) effective quantum efficiency at different NAWs height.
Nanowires with a height of 1000 nm exhibited a 31.3% increase in the maximum value of the total collected current compared to nanowires with a height of 400 $nm$. However, once the height reaches 800 nm, further increasing the height does not significantly enhance the collection current. This can be attributed to the fact that as the nanowire’s height increases, the complexity of the NWAs’ structure enhances the secondary absorption phenomenon, resulting in a decrease in the absorption efficiency of the device. Consequently, the effective quantum efficiency of the device decreases as well.
3.5.2 NWAs diameter
The simulation carried out for the nanowire diameter shows that the number of nanowires per unit area in the photocathode of the AlGaN nanowire array changes. The results are shown in Fig. 11(a). From the figure, it can be observed that increasing the nanowire line width enhances the collected current per unit area. However, the peak collection current at $D$=100 nm only increases by 32.3% compared to the peak collection current at $D$=500 nm. Additionally, the collection efficiency decreases by 10.3% to 13.5%. Therefore, increasing the nanowire line width is not a feasible method to increase the collection current.
Fig. 11. (a) Collected current, (b) collection efficiency, (c) effective quantum efficiency per unit area for different diameter as a function of incident angle.
3.5.3 Array spacing
The number of nanowires in the unit area of the AlGaN nanoarray photocathode is influenced by the array spacing of the nanoarrays, as well as the diameter of the nanowires. To determine the collection current per unit area, instead of considering the collection current of a single nanowire unit, the collected current per unit area is used. Figure 12(a) illustrates that as the array spacing increases, the collected current per unit area initially increases and then decreases. To visually represent these changes, the peak value of the collected current is combined with its corresponding array spacing, as shown in the insert layer. The results indicate that the peak value of the collected current per unit area occurs between 200 nm-300 nm, and the collected current per unit area decreases with further increases in the array spacing. Therefore, an optimal nanowire array spacing of 200 nm-300 nm is identified.
Fig. 12. (a) Collected current, (b) collection efficiency, (c) effective quantum efficiency per unit area for different spacing as a function of incident angle.
3.5.4 Al component
The absorption coefficients of different Al components are obtained from literature [35]. Figure 13 demonstrates that at an incident light photon energy of 4.0 eV, NWAs with an Al component of 0.2 exhibit significantly better performance compared to other components. The collected current can reach 1.78 (a. u.), and the collection efficiency is improved by 9.7% compared to the maximum value at x=0 for the Al component. Additionally, the average value in the effective quantum efficiency fraction is also 9.8% higher.
Fig. 13. (a) Collected current, (b) collection efficiency, (c) effective quantum efficiency per unit area for Al components.
3.5.5 Surface emission velocity
For the study of surface emission coefficients as shown in Fig. 14(a), (b), (c) for different surface emission rates of $10^4$ $cm/s$, $10^5$ $cm/s$, $10^6$ $cm/s$, $10^7$ $cm/s$. The collected photocurrent decreases at lower surface emission rates, and the impact on the total photocurrent is less pronounced when Se is increased. When the incident photon energy is 4.0 $eV$, the effective quantum efficiency increases by 0.3% for a surface emission rate of $10^7$ $cm/s$ compared to $10^6$ $cm/s$. It can be observed that the effective quantum efficiency of the nanowire slightly decreases with an increase in the surface emission rate.
Fig. 14. (a) Collected current, (b) collection efficiency, (c) effective quantum efficiency for different emission velocity.
4. Conclusion
In this paper, we investigate the photoemission model of AlGaN NWAs by simulating the nanowire structure and material parameters using a four-step process. Our findings reveal that there exists an optimal range of dimensional parameters for AlGaN nanowires to achieve the best performance. Specifically, a height of 400-500 nm, diameter of 200-300 nm, and optimal values of array spacing between nanowires of 200-300 nm are crucial. Furthermore, we demonstrate that adjusting the array spacing between the nanowires can improve device performance by modifying the critical angle of the photocathode incidence angle. For instance, in a 1:1 duty cycle nano-array, the optimum angle of incidence is 45$^{\circ }$. We also explore the practicality of applying an external electric field to enhance electron collection, which results in a significant 48.2% improvement in collection efficiency.We simultaneously introduced a built-in electric field and enhanced the collection current of the nanowires by an average of 104.4% by designing an axial exponential doped photoemission model. Moreover, we observe that the performance of an AlGaN photocathode is greatly influenced by different absorption coefficients corresponding to different Al components. By adjusting the Al components, we can enhance the performance, providing a theoretical basis for the axial exponential doped AlGaN nanowire array structure photocathode. Therefore, in practical applications, improving the photoelectric conversion efficiency requires comprehensive consideration of various parameters.
Funding
National Natural Science Foundation of China (12374257, 62201253); Nanjing University of Aeronautics and Astronautics (xcxjh20232112).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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