After determining the structure of the dielectric metasurface Si-based InGaAs photodetector, it was necessary to identify the optimal parameters for this structure, which mainly included the shape, period or number, etching depth, side length, and radius. A dielectric metasurface is an array structure composed of multiple identical units arranged according to a certain pattern. This array structure can simultaneously excite electric and magnetic responses, resulting in collective resonance and an array effect, ultimately significantly affecting the resonant peak position and resonance intensity. Therefore, designing these parameters can not only achieve specific electromagnetic properties but also improve the light absorption efficiency of the device structure. This is particularly important for achieving high-performance Si-based InGaAs photodetectors at 1550 nm. In this article, the FDTD Solutions software is used to simulate a photodetector structure to achieve the optimal values of the dielectric metasurface structure at 1550 nm, as well as to determine the optimal shape.
In the simulation of FDTD Solutions, the model structure was mainly divided into a basic structure, network settings, boundary conditions, light source settings, an analysis group (including a power monitor for the measurement of reflectance and transmittance), and a frequency monitor for querying the electric field distribution. Based on the structure, since we epitaxially grew the corresponding structure on Si through ART technology, the Si substrate had low light absorption efficiency within the wavelength range of 1440–1600 nm, and SiO
2 was transparent within this wavelength range. Therefore, the emulation model we chose consisted of a 500 nm InP buffer layer, four cycles of 3 nm/6 nm InGaAs/InP multiple quantum well layers, a 200 nm InP cap layer, and a metasurface structure with a unit cell. The refractive indices of two materials can be queried from [
18]. Mesh settings: Mesh refinement was mainly applied to our emulation area in order to better analyze the field distribution, support more complex simulation scenarios, and improve the reliability of the emulation results. Boundary conditions: Since a dielectric metasurface is composed of periodically arranged unit structures, we chose periodic boundary conditions in the X and Y directions. However, the selected structure satisfied both symmetric and asymmetric conditions, which could be utilized to replace these boundary conditions, thereby reducing the memory required for simulation and accelerating the simulation efficiency. In the Z direction, a Perfectly Matched Layer (PML) was chosen to prevent electromagnetic waves from reflecting back into the computational domain, thereby affecting the accuracy of the results. Light source settings: We chose a plane wave that was vertically incident along the negative half-axis of the Z-axis, with a wavelength range of 1440–1600 nm. The analysis group mainly consisted of two power monitors. In order to detect the reflectance and transmittance, the reflectance monitor was placed above the structure, and the transmittance monitor was placed below the structure. By parameterizing the structure group and coding, it was used to solve the absorption efficiency and subsequent parameter scanning. Frequency Monitor: A frequency monitor was primarily utilized to observe the electric field distribution across different planes and positions. The XY plane was positioned at the location where the electric field was strongest, and the XZ plane was overlaid and aligned with the Z-axis symmetry axis of the circular dielectric metasurface.
3.1. Circular Dielectric Metasurface Structure
As a classic shape for dielectric metasurfaces, a circular structure enhances the optical absorption efficiency of the device structure through Mie resonances and light-scattering processes. Resonance is generated by matching dielectric holes with the incident light frequency. Circular dielectric holes create photon-localized states that confine the optical energy to a specific region, further enhancing light absorption.
Using the above simulation conditions, the initial simulation values for the circular dielectric metasurface were set with a radius of 0.5 μm, a depth of 0.2 μm, and an array period of 1.2 μm. The resulting scan is shown in
Figure 3. As the radius changed, the absorption peaks mainly converged towards the wavelength range of 1530–1540 nm, as shown in
Figure 3a. Under the conditions of a fixed radius and period, the absorption peaks gradually shifted upwards and concentrated near 1530 nm, as shown in
Figure 3b. Under the conditions of a fixed radius and depth, as the period increased, the absorption peaks gradually shifted to the right and their intensities decreased to varying degrees, mainly concentrating within the range of 1530–1540 nm, as shown in
Figure 3c. Finally, through optimized scanning, the optimal radius, depth, and period of the circular dielectric metasurface were determined to be 0.21 μm, 0.207 μm, and 1.2 μm, respectively. The absorption spectra of the metasurface Si-based InGaAs MQW photodetectors and control MQW photodetectors without a metasurface were simulated, as shown in
Figure 3d. The absorption enhancement was wavelength-sensitive, which is a characteristic of metasurface structures. Compared with the control Si-based InGaAs MQW photodetector, the absorption of the metasurface photodetector at 1550 nm was enhanced to 85.9%. Such a high enhancement ratio is promising for efficient photodetection in the 1550 nm band.
3.2. Well-Shaped Dielectric Metasurface Structure
A well-shaped dielectric metasurface primarily relies on resonance effects and optical field localization. Each unit of a well-shaped dielectric structure can be regarded as a tiny resonator, which leads to a significant enhancement of the electromagnetic field in the dielectric structure upon resonance, thereby improving the optical absorption efficiency. Additionally, a well-shaped structure is formed by overlapping four identical rectangular prisms. When light is incident on the dielectric holes, it is confined within the structure to multiple scatterings and reflections, which enhances the interaction between light and matter. At the same time, the partial overlap and the presence of many edges and corners strengthen the resonance intensity during electromagnetic resonance to improve the optical absorption efficiency of the device.
Here, the well-shaped dielectric metasurface was composed of four identical rectangular prisms, and the length-to-width ratio of the rectangles was designed to be 5:1. The initial values of side length, depth, and period were set to 0.2 μm, 0.2 μm, and 1.5 μm, respectively, as shown in
Figure 4. Firstly, while keeping the depth and period constant, as the side length increased, the absorption peaks exhibited a rippled trend and gradually shifted to the left, as shown in
Figure 4a. Under the conditions of fixed side length and period, the absorption peaks shifted upwards as the depth increased, as shown in
Figure 4b. Under the conditions of fixed side length and depth, the absorption peaks gradually shifted upwards as the period increased, as shown in
Figure 4c. Subsequently, through optimized scanning, the optimal parameters of the well-shaped metasurface structure were found to be a side length of 0.216 μm, a depth of 0.224 μm, and an array period of 1.41 μm. When compared with the absorption rate of the structure without the dielectric metasurface, the absorption rate reached as high as 67.8% at 1550 nm, as shown in
Figure 4d.
3.3. Triangular Dielectric Metasurface Structure
The periodic arrangement of triangular dielectric metasurfaces can generate collective resonance and absorb specific frequencies of light, similar to a large optical trap. Due to the sharp corners of triangular dielectric holes, the optical field can be effectively captured and concentrated, forming so-called hotspots. In these hotspot regions, there is a strong interaction between light and the medium, which improves the optical absorption efficiency.
In the simulation process, the dielectric metasurface structure was a symmetrical equilateral triangle. The initial side length, depth, and period were set to 1 μm, 0.2 μm, and 1.5 μm, respectively. While keeping the depth and period constant, as the side length increased, the absorption peaks gradually shifted to the left, as shown in
Figure 5a. Under the condition of keeping the side length and period constant, it can be observed that as the depth increased, the absorption peaks gradually shifted upwards, with slight changes in intensity, as shown in
Figure 5b. After determining the side length and depth, the absorption peaks were mainly concentrated near 1560 nm, as shown in
Figure 5c. Through optimized scanning, it was found that the optimized metasurface structure in the simulation had a side length of 1.22 μm, an array period of 1.35 μm, and depth of 0.226 μm. Compared with the absorption rate of the structure without the dielectric metasurface, there was an absorption peak near 1557 nm with the level of intensity reaching 72.9%, as shown in
Figure 5d.
3.4. Square Dielectric Metasurface Structure
In a square dielectric metasurface, light undergoes multiple reflections and scatterings at the interface between the dielectric metasurface and air, as well as inside the dielectric metasurface, increasing the number and paths of interaction between light and the dielectric metasurface, thereby improving the light absorption efficiency. In addition, due to its symmetry, a square dielectric metasurface structure exhibits similar light propagation characteristics in different directions, reducing losses during propagation and making it more conducive to light absorption.
The initial side length, depth, and array period of the square structure were set to 1 μm, 0.2 μm, and 1.5 μm, respectively. As the side length increased, the absorption peak gradually shifted from 1510 nm to 1590 nm, as shown in
Figure 6a. When the depth varied, the absorption peak of the square structure remained relatively stable, as shown in
Figure 6b. As the period increased, the peak gradually shifted downwards, as shown in
Figure 6c. Finally, through optimized scanning, the optimal parameters of side length, depth, and period were determined to be 0.972 μm, 0.2 μm, and 1.374 μm, respectively. As shown in
Figure 6d, when compared with the absorption rate of the structure without the dielectric metasurface, there was a relatively pronounced absorption peak near 1540 nm with an intensity of 67.8%, which was higher than that of the ordinary structure.
3.5. L-Shaped Dielectric Metasurface Structure
By breaking the symmetry of the structure, an L-shaped metasurface excites corresponding electromagnetic responses. Here, electric dipoles and magnetic dipoles with opposite phases interfere with each other, thereby preventing energy leakage, reducing coupling to free space, and minimizing radiation losses. This is the unique bound mode of an asymmetric dielectric metasurface. Furthermore, asymmetric dielectric metasurfaces exhibit different response characteristics to electromagnetic waves with different polarization states and propagation directions. This triggers multiple resonance modes and enables complex electromagnetic field manipulation.
In this simulation, we created an L-shaped metasurface structure with an initial side length, depth, and period of 0.1 μm, 0.2 μm, and 2 μm, respectively. As seen in
Figure 7a, as the side length increased, the absorption peaks gradually converged towards the range of 1530–1550 nm. Under a constant side length and period, as the depth increased, the absorption peak behaved similarly to the case of varying side length, as shown in
Figure 7b. After determining the side length and depth, as the period increased, the absorption peak shifted significantly towards the blue, and its intensity became lower when approaching 1550 nm, as shown in
Figure 7c. Through optimized scanning, the optimal side length, depth, and period of the L-shaped structure were determined to be 0.85 μm, 0.224 μm, and 2 μm, respectively. Compared with the absorption rate of structures without dielectric metasurfaces, the strength of the L-shaped structure was slightly lower than that of the aforementioned metasurface structures, but still higher than that of structures without dielectric metasurfaces, as shown in
Figure 7d. This indicates that it is still feasible to utilize dielectric metasurfaces to enhance their absorption rates.
Through scanning the parameters of five shapes, it could be observed that the simulation results for each shape parameter varied significantly. The main reason for this is that a multi-layer structure is more realistic compared to the simulation of only a single layer of a dielectric metasurface, making the simulation more convincing. However, this also led to a more complex simulation process, resulting in the aforementioned graphs of the five different shapes. For instance, the three parameters only had a significant effect on the structural absorption rate when their values reached a certain range. This situation can be addressed by improving the simulation grid precision. Additionally, this may also be related to the thickness of the InP cap layer, as its thickness can affect the absorption of light by the absorption layer, resulting in a relatively small influence of the dielectric hole size on the absorption rate to a certain extent. However, beyond a certain threshold, a dielectric metasurface can still significantly improve the light absorption efficiency, as could be observed in all five shapes.
3.6. Optimal Shape Performance Analysis
After the simulation of five different shapes, we found that the circular structure exhibited a relatively high optical absorption rate, as shown in
Figure 8. The analysis can be conducted from the following aspects: Firstly, the circular dielectric metasurface, influenced by its diameter size, is more prone to exhibiting uniform scattering characteristics at specific frequencies. Secondly, due to the smoothness and symmetry of the circular dielectric metasurface, it is easier to achieve efficient focusing and resonance. Lastly, the shape and symmetry of the circular dielectric metasurface minimize light losses during diffraction and scattering processes. Therefore, among the five shapes, the circular dielectric metasurface stood out and was chosen as the optimal shape. Further investigation was conducted to explore the reasons for the high absorption peak near 1550 nm and the physical mechanism behind the improvement in device performance by the dielectric metasurface. To support the idea that the absorption enhancement was due to the resonant metasurface, the distribution of the electric field intensity of the mode at 1550 nm is shown in
Figure 9. When the dielectric metasurface was not added, the electric field distribution of the device was scattered and had a low intensity, resulting in poor light absorption, as shown in
Figure 9a. After introducing the dielectric metasurface, the electric field was mainly confined to between the arrayed dielectric holes. The enhanced mode was attributed to the guided-mode resonance introduced by the dielectric metasurface. When the device was illuminated with broadband light, the metasurface geometry enabled narrow-bandwidth guided-mode resonances, which enhanced the absorption, as shown in
Figure 9c. Subsequently, we introduced the electric field distribution diagrams of the XZ plane, as shown in
Figure 9b,d. When our structure had not yet incorporated the dielectric metasurface, the electric field distribution in
Figure 9b was primarily the result of plane waves undergoing reflection, transmission, and scattering as they passed through various materials. It can be observed that a portion of the light intensity was located within the multi-quantum well layer and the buffer layer, while the remainder existed outside the structure, resulting in a low utilization rate of light, and consequently, low absorption efficiency. After introducing the dielectric metasurface, the light field distribution changed significantly. Although it was still concentrated in the multi-quantum well layer and buffer layer, the light intensity outside the device was significantly reduced, and the light intensity inside the device was enhanced, thereby improving the light absorption efficiency, as shown in
Figure 9d. Therefore, the introduction of the dielectric metasurface not only reduced energy loss but also significantly improved the performance of the device.
To gain insight into the mechanism of the light absorption enhancement within the photodetector, the distributions of the quantum efficiency per unit volume in the metasurface photodetector and the responsivity at the resonance wavelength were simulated. Quantum efficiency is the ratio of the average number of photoelectrons generated by the photoelectric effect to the number of incident photons with a specific wavelength per unit of time, which is used to measure the photoelectric conversion capability of photoelectric devices.
We used the built-in quantum efficiency model in FDTD Solutions to simulate the radiation and scattering of electromagnetic waves through dipoles, in response to electromagnetic waves. In the simulation, we simplified the photoelectric conversion process into the behavior of multiple dipoles and theoretically calculated the specific value of quantum efficiency through the dipole method. This simplification may have ignored the trap effect and carrier recombination, which would have had a certain impact on the numerical results. However, we mainly focused on the impact of ART technology and whether the introduction of dielectric metasurfaces affected the device performance.
Responsivity is also an important parameter used to measure the photoelectric conversion capability. It has a certain relationship with quantum efficiency, which can be expressed as follows:
where λ is the wavelength of the incident light and η is the quantum efficiency.
Through the simulation of the above quantum efficiency model,
Figure 10a,b was obtained, showing that the trends of the two parameters were similar and that the performance of both was improved after introducing the dielectric metasurface. However, there was a trough near 1520 nm, which was because the absorption efficiency and quantum efficiency were negatively correlated to a certain extent, so the quantum efficiency exhibited a trough at the point where the absorption efficiency was highest. Additionally, the relatively high quantum efficiency of the structure without a dielectric metasurface was due to the influence of the quantum well structure on parameters such as quantum efficiency. However, across the entire wavelength range, the dielectric metasurface structure outperformed the structure without a dielectric metasurface.
In order to further study the device performance, we combined the photoelectric simulation through FDTD Solutions and Lumerical CHARGE solver. We calculated the light-generation rate of the absorption layer in this model through optical simulation and imported it into CHARGE to perform electrical stimulation. In steady-state and small-signal AC modes, the photocurrent and dark current parameters were obtained. Please note that to solve for the dark current, the import of the source needed to be disabled first, and then re-enabled to complete the simulation of photocurrent, resulting in
Figure 10c.
From the figure, we can observe that within the main operating range of −3 V to 0 V, the dark current remained stable at 10−4 mA, while the photocurrent was approximately 1 mA. This indicates that the device possesses a low dark current and good detection capability for optical signals. At 0 V, the device exhibited the lowest dark current, but as the bias voltage increased, the dark current rose sharply and became comparable to the photocurrent. This is because photocurrent is primarily determined by the light intensity and quantum efficiency, and continuously increasing the bias voltage does not necessarily increase the photocurrent indefinitely. Instead, as the bias voltage increased, the electric field inside the detector was enhanced, making it easier for thermally excited carriers to be collected at the electrodes, resulting in an increase in dark current. For subsequent device fabrication, to reduce the impact of dark current, we can passivate the device with a layer of SiO2 to mitigate the dark current.
To demonstrate the superior performance of the device we studied, several III-V photodetectors prepared by heteroepitaxy and selective heteroepitaxy methods are listed in
Table 1. As can be seen from the literature comparison, in the C-band, the theoretical responsivity of the device structure we proposed was as high as 1.11 A/W, with a dark current as low as 10
−4 mA, which was superior to other device structures. Therefore, our proposed dielectric metasurface-enhanced Si-based InGaAs photodetector is theoretically feasible and possesses certain advantages.
We have also formulated a technological process for the preparation of Si-based InGaAs photodetectors utilizing ART technology, as shown in
Figure 11. The first step is to deposit SiO
2 along the (110) direction on a Si (001) substrate by MOCVD, and then form a high-aspect ratio trapping structure with Si material at the bottom by the ICP dry etching of SiO
2. The second step involves growing the corresponding epitaxial structure layer using MOCVD epitaxial equipment, as shown in Step 2 of
Figure 11. The third step involves etching away the SiO
2 on the sidewalls using HF solution to prepare for the subsequent deposition of electrodes and the fabrication of the dielectric metasurface structure. The fourth step involves using electron beam lithography to pattern a specific structure on the top layer, followed by ICP etching to form the dielectric metasurface structure. The fifth step involves depositing a layer of Au on both the substrate surface and the top layer using magnetron sputtering technology as electrodes, preparing for subsequent experimental testing. In addition, the advantages of the heterogeneous epitaxy of III-V materials on silicon substrates through ART technology mainly include the following: the convenient integration of various high-mobility III-V materials and device structures; the easy realization of Si-based monolithic integration; patterned substrates can be prepared using STI templates, facilitating large-scale integration; excellent optoelectronic properties. Therefore, we intend to utilize ART epitaxy technology to grow high-quality InGaAs/InP multiple quantum well materials, with the goal of minimizing the influence of defects and lattice mismatch on device performance. Subsequently, leveraging the design parameters of dielectric metasurfaces obtained through simulation, we will design a high-performance Si-based InGaAs photodetector. This is precisely the reason why we have chosen to simulate the entire epitaxial layer produced by ART epitaxy technology, aiming to make the simulation more closely align with actual conditions and thereby thoroughly preparing for the subsequent device fabrication process.