The mid-infrared band comprises two distinct atmospheric windows of 3-5 μm and 8-14 μm. It includes the thermal radiation features of objects and molecular fingerprint regions. Consequently，the mid-infrared band is extensively across various domains，including infrared thermal imaging^［1］，biomedical diagnostics^［2］，and material analysis^［3］. Optoelectronic Integrated Circuits （OEIC） encompass the integration of optoelectronic and microelectronic technologies on a single chip，enabling the consolidation of components for various functions such as generation，transmission，modulation，reception，and processing onto a shared substrate. The advancement of mid-infrared optoelectronic integration is of significant research importance due to its potential to enable the development of compact，chip-level sensors. Waveguide detectors play a crucial role in the integration of optoelectronic devices. In the context of waveguide-integrated detectors，the process of optical signal coupling into the absorption layer occurs gradually as the signals propagate within the waveguide. As light propagates through the waveguide，it is concurrently absorbed within the absorption layer. The direction of light propagation is perpendicular to the direction of transport of photo-generated carriers. This particular design can increase bandwidth while maintaining responsivity at its current level^［4］. It enables efficient absorption along the entire waveguide，providing a larger absorption area. Consequently，it is feasible to sustain a thin absorption layer while ensuring a high quantum efficiency. This design accelerates the transit of photo-generated carriers across the depletion layer，thereby greatly augmenting the bandwidth of the detector. However，the development of mid-infrared waveguide detectors is faced with challenges arising from the integration of infrared-transparent waveguide materials and narrow-bandgap semiconductor detector materials，thereby adding complexity to the process. Penades，J Soler^［5］et al. proposed a silicon slot waveguide on an insulator with a propagation loss of （-1.4±0.2） dB/cm at a wavelength of 3.8 µm. Fangxin Li^［6］et al. reported a low-loss silicon sapphire nanowire with a transmission loss of less than -2 dB/cm at 5.18 μm. Barritault P ^［7］ et al. proposed a waveguide platform with a thick epitaxial silicon-based graded SiGe waveguide. This waveguide demonstrates remarkably low waveguide losses，measuring only -1 dB/cm at 4.5 µm. Aldo Gutierrez-Arroyo et al.^［8］ used the Ge-Sb-Se multilayer structure to make a waveguide，achieving a transmission loss of -2.5 dB/cm at 7.7 µm. Wei Li et al.^［9］ proposed a GON waveguide that grew Ge on Si₃N₄ and had a waveguide loss of -3.35 dB/cm at 3.8 µm. The current focus of waveguide-integrated detector development is mostly on silicon-based materials and focuses on the visible and near-infrared spectrum，with less attention on mid-infrared research. Notable research efforts have been reported，including M. Muneeb^［10］et al.'s integration of PIN photodiodes based on InAs_0.91Sb_0.09 on the SOI platform，achieving a responsivity of 0.3 A/W at 3.8 μm. Zhibo Qu^［11］et al. have reported a waveguide-integrated detector utilizing metal-graphene-metal at 3.8 μm，with a responsivity of 2.2 mA/W. Li Huang^［12］et al. proposed a mid-infrared detector scheme integrating black phosphorus on the SOI platform，achieving a responsivity of 23 A/W at 3.68 μm and 2 A/W at 4 μm，with a noise equivalent power of less than 1 nW/Hz^1/2 at room temperature. Swapnajit Chakravarty^［13］et al. achieved high sensitivity gas sensing by integrating quantum cascade detectors within photonic crystal slot waveguides using the InGaAs/InP material system. They successfully detected 3 ppm of carbon monoxide （CO） at 4.55 μm. In a separate study conducted on the SoS platform ^［14］，they detected 10 ppm of the chemical warfare simulant triethyl phosphate （TEP） at 3.4 μm.

The emergence of InAs/GaAsSb type-II superlattice materials introduces a novel technology for infrared detection and offers new possibilities for mid-infrared waveguide detectors ^［15］. By adjusting the thickness and composition of InAs and GaAsSb layers，it is possible to modify the detection wavelength to cover a wide range from 3 μm to 30 μm. The utilization of lattice-matched GaAsSb as the waveguide layer enables reduced loss within the 3-5 μm spectral range. Growing the waveguide and detector on one chip offers higher integration，eliminating issues associated with device coupling，and aligning with the requirements of OEIC. This study introduces a detector integrated with a mid-infrared waveguide，specifically designed on an InAs substrate. It employs evanescent coupling to effectively direct light into the absorption layer of the InAs/GaAsSb type-II superlattice through the GaAsSb waveguide layer. We presented a simulation of the optical and electrical characteristics of devices. To ensure the accuracy of the computational model，we conducted a comparative analysis with the results of other research teams ^［17］ and found similar approaches，such as simulation of beam propagation and the analysis of quantum efficiency. We conducted an analysis of the factors that influenced the performance of the InAs/GaAsSb superlattice photodetector when integrated with a GaAsSb waveguide.

The optical detection of the waveguide detector was simulated using the finite element method. Figure 1 shows the simulation structure of the waveguide-integrated detector and the simulated propagation of the optical beam. External optical signals are coupled into the GaAs_0.09Sb_0.91 waveguide and subsequently detected by the photodiode following propagation. Due to the comparable refractive index of the absorption layer and the waveguide layer，light can penetrate the waveguide layer and enter the absorption layer. Once light is absorbed，it initiates the generation of electron-hole pairs，with electrons and holes being collected by the n-type and p-type contact layers，respectively. It is assumed that the absorption of each photon leads to the generation of an electron-hole pair，thereby establishing a direct relationship between the absorption rate of the absorption layer and its quantum efficiency. The refractive index of GaAsSb is 3.75 at 4.6 μm，allowing for negligible absorption. A heavily doped InAs layer is positioned beneath the GaAsSb waveguide layer，with a refractive index of 3.1 ^［18］，in order to effectively inhibit the leakage of light towards the substrate. The absorption coefficient and refractive index of the InAs/GaAs_0.09Sb_0.91 （2.1 nm InAs/2.1 nm GaAs_0.09Sb_0.91） superlattice material are illustrated in Fig. 2.

Devices with different thicknesses and lengths of the absorption layer were simulated，and the quantum efficiency was calculated. From the obtained results，the responsivity of the device，represented as R，can be expressed as：

where Ip is the average output current，P0 is the average input power. Ip can be expressed as：

where q is the electronic charge，η is the quantum efficiency at the wavelength of λ，h is the Planck constant and c is the speed of light in vacuum. By combining Eqs. （1） and （2），it can be concluded that：

In the context of free-space detection，it is observed that the signal-to-noise ratio （SNR） exhibits a proportional relationship with the square root of the detector area. In the case of waveguide-integrated detectors，the distribution of the optical signal across the surface of the detector is not uniform as the light propagates through the waveguide towards the detector. In this scenario，the relationship between SNR and the square root of the detector area is no longer valid. Therefore，the noise equivalent power （NEP） is used as a characterization of SNR，replacing detectivity （D*） as the evaluation metric for the device ^［19］. At ambient temperature，the dark current of the device is primarily dominated by the diffusion current. The diffusion current density can be approximated by the following expression^［20］：

where Ln is the diffusion length，as the absorption layer of the waveguide detector is relatively thin，typically Ln > d，gth is the thermal generation rate of minority carrier，gth=n0τ，n0 is the concentration of minority carrier ，τ is the carrier lifetime of minority carrier，V is the working voltage，d is the thickness of the absorption layer，T is the working temperature，and K is the Boltzmann constant. The expression for NEP is：

where RI is the current response，in¯2 is the mean square noise current，assuming that only the current generated by the shot noise is considered here，under reverse bias：

where I0 is the dark current，∆f is the bandwidth. Based on the above equation，it can be concluded that^［21］：

where A is the area of the detector.

It's essential that the waveguide exhibits excellent transmission capabilities for optical interconnects between the detector and other devices. Therefore，it's desirable for the GaAsSb waveguide layer exposed to air to support single-mode propagation in order to minimize transmission losses. By utilizing Maxwell's equations and boundary continuity conditions，the characteristic equation for the TE mode can be obtained：

where κ is the phase constant of GaAsSb waveguide layer in the x-direction，d is the thickness of GaAsSb layer，n1，n2，n3 are the refractive indices of GaAsSb waveguide layer，the doped InAs lower cladding layer and air. K0 is the wave number in vacuum. The value range of m is an integer starting from 0，representing the order of the mode. When 0.38μm<d<1.57μm，the fundamental mode exists and the first-order mode is cut off.

As shown in Fig. 3（a），it can be observed that for waveguide thicknesses below 0.9 μm，the waveguide loss exceeds -1 dB/cm. This is attributed to insufficient confinement of light by the waveguide layer. The refractive indices of the waveguide and the integrated detector are comparable. When the thickness of the waveguide is comparable to the detector，it satisfies the phase-matching condition for mode coupling. As a result，light can be coupled from the lower waveguide to the upper absorption zone with minimal loss，resulting in a high quantum efficiency. Therefore，both the issue of loss and detector performance should be considered in the selection of waveguide thickness. When the thickness of waveguide layer is 1 μm，the waveguide satisfies the conditions for single-mode transmission，resulting in lower transmission losses （~ -0.67 dB/cm）. Although the current quantum efficiency is not at its maximum，it still exceeds 97%. We have selected a waveguide with a thickness of 1 μm for the subsequent design. Figure 3（b） illustrates an absorption layer waveguide detector with a length of 200 μm and a thickness of 0.55 μm. It shows the variation of quantum efficiency and responsivity with wavelength. The operational range of the detector is below 5 μm，owing to the influence of InAs/GaAsSb superlattice material. Figure 3 （c） shows the loss of the waveguide with wavelength. The waveguide loss is 0.36 dB/cm at 3 μm. As the wavelength increases，there is a decrease in the effective refractive index of the waveguide，resulting in a reduction in the confinement of light and an increase in the distribution of evanescent fields outside the waveguide. This results in greater energy loss，with a waveguide loss of 0.79 dB/cm at a wavelength of 5 μm. Overall，the working wavelength and loss characteristics of the 1 μm-thick GaAsSb waveguide align well with the specified requirements for waveguide detectors.

The performance of waveguide detectors is influenced by the thickness and length of the absorption layer. Figures 4 （a） and 4 （b） show the variations in quantum efficiency and responsivity，respectively，as a function of the thickness and length of the absorption layer at 4.6 μm. The responsivity exhibits a positive correlation with both the thickness and length of the absorption layer. Even when the absorption layer is of minimal thickness，it is still possible to achieve a quantum efficiency close to 100% by ensuring an adequate length. The maximum current response exhibits a value of 3.7 A/W at 4.6 μm.

Figures 5（a） and 5（b） represent the variation of NEP with absorption layer thickness and length at 4.6 μm. Combining the information from Fig. 4 and Fig. 5，when the quantum efficiency is less than 70%，increasing the length and thickness of the absorption layer results in a reduction in NEP. However，when the quantum efficiency exceeds 70%，further increases in length or thickness lead to a higher quantum efficiency that has a less impact on NEP compared to the increase in dark current，causing NEP to increase.

We found that a waveguide detector with an absorption layer length of 50 μm and a thickness of 0.3 μm has the lowest NEP at 0.39，with 68.9% quantum efficiency and 2.55 A/W responsivity. The methodology for calculating the propagation of optical power along the waveguide and its coupling into the integrated detector is shown in Fig. 6. Optical power absorption predominantly takes place within a relatively short distance. After traversing a distance of 30 μm through an absorbing medium，the optical power decreases by 50%. After a distance of 50 μm，there is a decrease of 70%，and after a distance of 125 μm，there is a decrease of 90%. The light coupling efficiency from the waveguide into the integrated component exceeds 99.9%. There is minimal loss observed during the propagation of light within the waveguide，as it is absorbed by the absorption layer. As the thickness of the absorption layer increases，there is an observed increase in both the dark current and the transit time of carriers. Consequently，this results in a reduction in the bandwidth of the detector. Combined with the analysis of NEP，the impact of absorption layer length on dark current is much smaller than thickness，and it does not have a significant inhibitory effect on the bandwidth. To simultaneously achieve high responsivity，low dark current，and high bandwidth，it is advisable to increase the length of the detector. Therefore，waveguide detectors generally necessitate absorption layers that are thinner and longer. To achieve a high quantum efficiency，it is necessary to decrease the thickness of the waveguide in order to enhance the coupling efficiency between the waveguide layer and the absorption layer. However，this will inevitably lead to increased transmission losses. Therefore，in forthcoming investigations，there is a plan to develop waveguides with varying thicknesses for transmission and coupling. Additionally，tapered couplers will be implemented at the connections to decrease transmission losses and enhance coupling efficiency.

This paper introduces a novel design for a mid-infrared waveguide utilizing heavily doped InAs and GaAs_0.09Sb_0.91 materials. The transmission loss within the wavelength range of 3-5 μm is consistently below -1 dB/cm，with a loss of -0.67 dB/cm at 4.6 μm. This waveguide not only matches the current mainstream silicon-based waveguide in terms of performance，but also offers the advantage of easier integration with high-performance Ⅲ-V group semiconductor detectors. Based on the waveguide provided，an integrated InAs/GaAs_0.09Sb_0.91 type-II superlattice detector is implemented，with an absorption layer length of 50 μm and a thickness of 0.3 μm. At 4.6 μm，the quantum efficiency is 68.9%，the responsivity is 2.55 A/W，and NEP is 0.39. With the new type-II superlattice material and long absorption distance，a significant enhancement in quantum efficiency has been achieved，resulting in a response rate more than twice that of most currently available mid-infrared detectors. At the same time，it has been observed that the dark current diminishes as the cascade order of the absorption region increases. Consequently，the NEP of the detector in question is smaller compared to that of conventional mid-infrared detectors. We conducted simulations to evaluate the impact of structural parameters of the absorption layer on quantum efficiency. Mathematical modeling was subsequently utilized to calculate the responsivity，dark current，and NEP of the integrated device. An analysis of the impacts of various structural parameters is provided. The simulations presented in this study propose a novel concept for mid-infrared waveguide-integrated detectors. The findings provide reference data and theoretical foundations for subsequent experimental designs.