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Abstract
Antimonide superlattice materials with tunable energy bands, high electron mobility, and easy attainment of good uniformity in large-area materials, are considered to be the material of choice for third-generation infrared photodetectors. Based on energy band engineering, this paper designs a series of long-wave infrared(LWIR) to very-long-wave infrared(VLWIR) photodetectors by employing M-structure superlattice(M-SL) as both absorber layer and barrier layer. The photodetectors’ performances at different temperatures are simulated in this manuscript. At 77K, while minimizing the lattice mismatch, effectively suppresses the dark current of the device which can be as low as 1× 10−8A/cm2, with a quantum efficiency reaching 20.85% and normalized detectivity achieves 4.78×1011 cm·Hz1/2/W for LWIR photodetector with a cutoff wavelength of 11.1 μm. For the VLWIR photodetector with a cutoff wavelength of 16.7 μm, the corresponding figures are 1×10−6A/cm2, 16.77% and 3.09×1010 cm·Hz1/2/W, respectively.
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1. Introduction
long-wave (above 8 $\mathrm{\mu}$m) to very-long-wave (above 12 $\mathrm{\mu}$m) infrared photodetectors have extensive applications in both military and civilian sectors [1–3]. Such as object recognition in military contexts, reconnaissance in harsh environments and detection of blood vessels and diseases in the medical field, among others. Efforts have been made to find materials for infrared photodetectors, and some new semiconductor materials, such as compound semiconductor materials of group II-IV [4] (e.g., HgCdTe) and compound semiconductor materials of group III-V [5] (e.g., InGaAs or antimony compounds) , have been widely studied and applied. Antimony compounds of the 6.1Å series (InAs, GaSb and AlSb) have attracted particular attention, especially the heterostructures formed by combining InAs with two antimonides and their alloys [5,6].
The barrier photodetectors based on InAs/GaSb Type-II superlattice (T2SL) have been extensively developed and utilized [7,8]. A crucial aspect in the design of barrier photodetectors lies in maximizing the conduction band offset (CBO) between the barrier and absorber layers, while minimizing the valence band offset (VBO) [9]. This is done to effectively impede the transport of electrons or holes, thereby reducing dark current. Conventional barrier photodetectors often use bulk materials (such as AlGaSb or AlGaAs) as barrier layer. However, the lattice mismatch between the bulk material and T2SL material used as the absorber layer can impact the performance of the device [10].
The M-structure superlattice, proposed by B-M. Nguyen, M. Razeghi and colleagues in 2007 [11] is a structure built upon the foundation of InAs/GaSb T2SL. In this configuration, a wider bandgap material, AlSb, is introduced into the GaSb layer. This increases the electron effective mass, reduces tunneling probability and diminishes contributions to tunneling current [12] and Auger recombination rate [13]. The effective well becomes narrower, and the hole energy levels become more sensitive to the well dimensions. This design significantly reduces dark current and does not exhibit substantial degradation in the optical characteristics of the device [14]. However, the M-structure superlattice is commonly used as the barrier layer in InAs/GaSb T2SL barrier photodetectors, which can lead to difficulties in controlling the VBO between the two materials. A larger VBO will generate an electric field in the adjacent absorber layer to form a depletion region, contributing to the generation-recombination (G-R) current [15].
In this manuscript, M-SL is utilized as both the absorber layer and barrier layer to minimize lattice mismatch. By adjusting the thickness of the InAs layer within the M-SL (InAs/GaSb/AlSb/GaSb), the cutoff wavelength of the absorber layer is varied while ensuring minimal shift in the valence band position. This enables detection of infrared light ranging from 8 $\mu$m to 20 $\mu$m. Through simulation calculations, at 77K, the quantum efficiency of the LWIR and VLWIR barrier photodetector designed in this paper can reach about 20% and 17%, respectively. The normalized detectivity can reach the order of 10$^{11}$ ${\rm {cm\cdot }}{{\rm {Hz}}^{1/2}}/{\rm {W}}$ and 10$^{10}$ ${\rm {cm\cdot }}{{\rm {Hz}}^{1/2}}/{\rm {W}}$, respectively.
2. Methods
2.1 8-band $k\cdot p$ method
The design of the photodetector depends on the energy band structure of the superlattice. We use the 8-band $k\cdot p$ method [16]. Guided by the Luttinger-Kohn model [17] and the Bir-Pikus model [18] theories, the following eight basis functions can be found in Ref. [19].
Within this framework, the coupling between heavy holes, light holes and the spin-orbit split valence band, along with the interaction between the conduction and valence bands, can be succinctly expressed through an 8$\times$8 Hamiltonian matrix [19–21]:
2.2 Absorption coefficient
The absorption coefficient $\alpha$ (in units of 1/cm) denotes the proportion of photons absorbed per unit distance, relative to the incident light intensity [20]. It can be expressed as follows:
To account for practical considerations, scattering relaxation is included in the calculation of the absorption coefficient. It means the $\delta$ -function can be replaced with the Lorentzian function with a linewidth of $2\gamma$:
A crucial step in calculating the absorption coefficient is determining the band structure and wave functions. The optical matrix elements can be computed using wave functions based on a parabolic band model. Typically, the perturbative $k\cdot p$ method and effective mass theory are employed to study the relevant processes near the band edges in semiconductor quantum structures.
2.3 Carrier densities and current densities
In the calculation of carrier transport, we ues a single-band model, which effectively treats the superlattice structure as a bulk material. The properties of this new bulk material encompass the bandgap size, VBO and carrier effective mass computed from the superlattice band structure. While this method for calculating carrier density is much faster than quantum mechanical approaches, it cannot account for quantum effects such as energy quantization and carrier tunneling through barriers.
The relationship between the total charge density distribution and the electrostatic potential satisfies the Poisson equation:
The continuity equations in the presence of generation or recombination of electron-hole pairs:
Here we only consider stationary solutions and set( $\frac {{\partial n}}{{\partial t}} = \frac {{\partial p}}{{\partial t}} = 0$ ). The current equation can be simplified to:
3. Result and discussion
3.1 Design of the photodetector
The device adopts an nBn structure, as illustrated in Fig. 1(a). It is epitaxially grown on a Te-doped GaSb substrate, with successive layers including a GaSb buffer layer, a bottom contact layer, an absorber layer, a barrier layer, a top contact layer and a cap layer. Notably, the middle three regions all comprise the same M-SL except the periodic thickness of the InAs layer. The detail bandedge structure of the M-SL [22] can be found in the Fig. 1(b).
3.1.1 Band structure of M-SL
All related parameters of M-SL are listed in Table 1. For SL infrared photodetectors, the most important thing is the band engineering of the absorption region. It determines the operating band of the photodetector directly. The band structure of M-SL acting as absorber layers with different InAs thicknesses at 77K is shown in Fig. 2. It can be seen that the bandgap of the M-SL gradually decreases from 113.8 meV to 66.7 meV with the increase of the thickness of the InAs layer while the thickness of the GaSb and AlSb layers remains constant, during which the conduction band edge of the superlattice is gradually shifted downward while the valence band edge remains relatively unchanged. It inspires us to consider the M-SL with a thin layer of InAs as the barrier region and the M-SL with a thick layer of InAs as the absorption region.
Fig. 2. The band structure of the M-SL for different InAs thicknesses. The configuration of the M-SL is as follows:(a)11/4/1/4 (b)11.5/4/1/4 (c)12/4/1/4 (d)12.5/4/1/4 (e)13.5/4/1/4 (f)14/4/1/4 (g)14.5/4/1/4 (h)15/4/1/4 MLs.
In this work, the specific structure of the barrier region superlattice is 5/4/1/4 MLs, which can be controlled with the absorption region of VBO within 10 meV and CBO above 170 meV.
3.1.2 Absorption coefficient
Based on the results of the above band structure calculations, we also calculated the absorption spectrum of the M-SL. Considering the actual working environment of LWIR and VLWIR photodetectors, the operating temperature of the absorption region is set at 77K-120K, and the scattering effect (spectral broadening) needs to be included in the simulation. Fig. 3 depicts the variation of the absorption coefficients of the 8 kinds M-SL with wavelength at different operating temperatures.
The cutoff wavelength of the material increases as both the thickness of InAs increases and the ambient temperature increases. The corresponding cutoff wavelengths are 10.7 $\mu$m, 11.46 $\mu$m, 12.23 $\mu$m, 13.06 $\mu$m, 14.88 $\mu$m, 15.87 $\mu$m, 19.91 $\mu$m and 18.00 $\mu$m, respectively. The cutoff wavelengths align with the band gaps calculated in Fig. 2. It’s attributed to the heightened thermal excitation of charge carriers, resulting in more electrons transitioning from the valence band to the conduction band. Additionally, it leads to a narrowing of the bandgap. The peak absorption coefficients before the cutoff wavelength are all below 2000 cm$^{-1}$. That’s because, for LWIR and VLWIR detection, materials with cutoff wavelengths in the long-wave range have higher effective masses for electrons and holes. It leads to consistently lower absorption coefficients for wavelengths in the long-wave range and beyond. Specifically, it can be analyzed based on the degree of overlapping of the wavefunctions in Fig. 4(a)-(h). The overlap values for each configuration of the M-SL are 0.232, 0.222, 0.212, 0.203, 0.186, 0.179, 0.172, 0.166 as shown in Fig. 4(i). As observed, the magnitude of the absorption coefficient within the M-SL exhibits a positive correlation with the overlap of the electron wave functions and hole wave functions. Notably, an increase in the overlap value is directly associated with the strength of the absorption coefficient.
3.1.3 Band edges of device
Based on the above designed device structure and the band structure of M-SL, the energy band edges of the photodetector at 77K are plotted in Fig. 5. The VBO between the absorber layer and barrier layer for the four devices are 6.12 meV, 6.83 meV, 8.09 meV, and 8.65 meV, respectively, which are all controlled within 10 meV. The CBO are 170 meV, 180 meV, 200 meV, and 210 meV, respectively. The doping levels for the buffer layer, bottom contact layer, top contact layer, and cap layer are all n-type with a concentration of 1$\times$10$^{17}$ cm$^{-3}$. The absorber layer is unintentionally doped, exhibiting a concentration of 1$\times$10$^{16}$ cm$^{-3}$, while the barrier layer is weakly p-type doped with a concentration of 2$\times$10$^{15}$ cm$^{-3}$. The thickness of the GaSb buffer layer is 200 nm, the bottom contact layer has a thickness equivalent to 30 periods, the absorber region spans 200 periods, the barrier region spans 20 periods, the top contact region spans 20 periods, and the cap layer is 30 nm thick.
Fig. 5. The band structure of LWIR to VLWIR barrier photodetectors under 0V bias at 77K. The configuration of the M-SL used as the absorber layer is as follows: (a)11/4/1/4 (b)12/4/1/4 (c)14/4/1/4 (d)15/4/1/4 MLs.
3.2 Performance of the photodetector
For the characterization of IR photodetector performance, the dark current level is used to reflect the impedance. The responsivity, quantum efficiency and normalized detectivity characterize the quality factor of the photodetector.
3.2.1 Dark current density
The dark current is a temperature-sensitive function. Therefore, we calculated the dark current as a function of temperature from 77K to 120K, assuming that the impurities are fully ionized at any temperature, with $N_D$=1$\times$10$^{16}$ cm$^{-3}$ and $N_A$=2$\times$10$^{15}$ cm$^{-3}$. Fig. 6 presents the dark current curves obtained by solving the Poisson and current continuity equations within the single-band model. It depicts the relationship between current density and voltage across the range from −0.5V to 0.1V.
Fig. 6. Dark current simulation results of LWIR to VLWIR photodetectors at 77K-120K. The configuration of the M-SL used as the absorber layer is as follows: (a)11/4/1/4 (b)12/4/1/4 (c)14/4/1/4 (d)15/4/1/4 MLs.
As can be seen in Fig. 6(a) and (b), the dark current densities of the photodetectors with cutoff wavelengths in LWIR region are 0.0085A/cm$^{2}$ and 0.059A/cm$^{2}$ for 77K and 0.5V reverse bias voltage conditions, respectively. For VLWIR photodetectors depicted in Fig. 6(c) and (d), the dark current density is 0.53A/cm$^{2}$ and 2.28A/cm$^{2}$ respectively. These data indicate a significant surge in dark current with the elevation of temperature.
Upon closer examination, it is due to two main factors. On the one hand, the more intense thermal excitation leads to an increase in the intrinsic carrier concentration of the material. On the other hand, the rise in temperature results in an augmented carrier mobility, consequently leading to an escalation in dark current.
Next, it is essential to analyze the components of the dark current. The bulk dark current mainly consists of four types:diffusion current [30], generation-recombination (G-R) current [31], band-to-band tunneling (BTB) current and trap-assisted tunneling (TAT) current [32]. Table 2 provides the necessary values for conducting the analysis of dark current contributions(using the M-SL of 11/4/1/4 MLs as an example). Some of the data were obtained using linear interpolation.Based on the formulas in Ref. [30–32], the dark current components for each structure at 77K are depicted in Fig. 7. The alignment between the dark current density under reverse bias and the data presented in Fig. 6 is clearly apparent. The nBn barrier structure of the photodetector plays a role in suppressing the GR current, leading to a prevalence of diffusion current in the long-wave infrared photodetector at 77K. Carrier tunneling becomes more prevalent as the bandgap of the absorption region decreases, leading to a general increase in tunneling current.
Fig. 7. Dark current analysis results of LWIR to VLWIR photodetectors at 77K. The configuration of the M-SL used as the absorber layer is as follows:(a) 11/4/1/4(b) 12/4/1/4(c) 14/4/1/4(d) 15/4/1/4 MLs.
Due to the fact that in many direct detection applications, the photodiode operates at zero bias voltage, the commonly used approach is to multiply the differential resistance ${R_0}$ at zero bias voltage by the active area $A$ of the diode: ${({R_0}A)^{ - 1}} = {\left. {\frac {{dJ}}{{dV}}} \right |_{V = 0}}$. To maximize the closeness to the actual situation, we use the value at −5 meV to calculate the impedance ${R_0}A$, which are given by: 298.49 $\Omega {\rm {\cdot }}{{\rm {cm}}^2}$,43.01 $\Omega {\rm {\cdot }}{{\rm {cm}}^2}$,0.89 $\Omega {\rm {\cdot }}{{\rm {cm}}^2}$ and 0.26 $\Omega {\rm {\cdot }}{{\rm {cm}}^2}$.
3.2.2 Responsivity and quantum efficiency
The responsivity($R_i$) of an infrared photodetector is defined as the ratio of the root mean square (rms) value of the fundamental component of the electrical output signal of the photodetector to the rms value of the fundamental component of the input radiation power:
At temperatures ranging from 77K to 120K, the responsivity and quantum efficiency curves for long-wave infrared barrier photodetectors with absorption regions consisting of 11/4/1/4, 12/4/1/4, 14/4/1/4 and 15/4/1/4 MLs per period of M-SL are plotted in Fig. 8 and 9. It is evident that the trends in the responsivity and quantum efficiency curves broadly align with the absorption coefficient curves of the absorption region material. This correlation is related to the integral term $\int _0^{{Y_i}} {{P_i}} {\alpha _i}{e^{ - {\alpha _i}y}}dy$ in the photocurrent. At 77K, for the four structures, the responsivity and quantum efficiency both peak at the MSL absorption coefficient maximum, reaching values of 1.8 and 20.85%, 1.9 and 19.13%, 2.15 and 16.77%, and 2.28 and 15.70%, respectively. With increasing temperature and decreasing bandgap, the photodetector’s responsivity tends to increase to some extent, while the quantum efficiency tends to decrease.
3.2.3 Normalized detectivity
In addition to responsivity and quantum efficiency, the normalized detectivity ($D^*$) is also a crucial metric for assessing the photodetector’s performance [33]. Fig. 10 depicts the wavelength-dependent normalized detectivity for LWIR to VLWIR barrier photodetectors with absorption regions composed of 11/4/1/4, 12/4/1/4, 14/4/1/4 and 15/4/1/4 MLs per period of M-structure superlattice. Taking 77K as an example, in Fig. 10(a), the peak $D^*$ reaches 4.78$\times$10$^{11}$ ${\rm {cm\cdot }}{{\rm {Hz}}^{1/2}}/{\rm {W}}$, in Fig. 10(b), the peak $D^*$ is 1.9$\times$10$^{11}$ ${\rm {cm\cdot }}{{\rm {Hz}}^{1/2}}/{\rm {W}}$, the maximum value in Fig. 10(c) is 3.09$\times$10$^{10}$ ${\rm {cm\cdot }}{{\rm {Hz}}^{1/2}}/{\rm {W}}$. Finally, in Fig. 10(d), the peak $D^*$ is 1.78$\times$10$^{10}$ ${\rm {cm\cdot }}{{\rm {Hz}}^{1/2}}/{\rm {W}}$. For an ideal photovoltaic photodetector operating at zero bias, where the dark current is very close to zero, Johnson noise $i_{{\rm {thermal\ }}}^2 = \frac {{4kT}}{{{R_d}}}\Delta f$, becomes the dominant mechanism. Therefore, the formula for normalized detectivity can be simplified to:
Additionally, to enhance device performance, it is recommended to prioritize optimizing quantum efficiency and R$_{0}$A product. Moreover, for LWIR to VLWIR photodetectors, it is crucial to ensure that the operating environment maintains a suitably low temperature.
3.3 Performance comparison
To provide a more intuitive view of the data, the four barrier photodetectors designed in this paper are simulated at different operating temperatures. The radar chart Fig. 11 illustrates the peak wavelength of the absorption coefficient, quantum efficiency, responsivity, normalized detectivity and dark current density at a reverse bias voltage of 500 mV. When the temperature increases, the cutoff wavelength, responsivity and dark current of the photodetector increase significantly. However, the quantum efficiency and peak of the normalized detectivity decrease. In addition, the comparison of data between this paper and several other references is shown in Fig. 12. The devices we have designed demonstrate commendable performance, particularly in the realm of long-wave to very-long-wave detection. Nevertheless, there is potential for enhancement in the domain of quantum efficiency.
4. Conclusion
In this manuscript, we focus on assessing the impact of varying the thickness of the InAs layer in the InAs/GaSb/AlSb/GaSb M-SL on the vacuum bandedges. Specifically, our proposed simultaneous use of M-SL as absorber layer and barrier layer is feasible for infrared barrier photodetectors, which ensures the VBO for absorber layer and barrier layer can be controlled within a relatively small range. Based on this idea, we calculated the absorption coefficients and wavefunctions’ overlap values of the M-SL, which in turn led to the calculation of a series of performance parameters of the devices. Simulation results show that such a design is favorable for dark current density, quantum efficiency, responsivity, and detectivity. In the results of the simulation, at 77 K, the values of responsivity, quantum efficiency, and detectivity for the LWIR barrier detector with a cutoff wavelength of 11.1 $\mu$m, for example, are 1.8 A/W, 20.85%, and 4.78$\times$10$^{11}$ ${\rm {cm\cdot }}{{\rm {Hz}}^{1/2}}/{\rm {W}}$, and the corresponding values for the VLWIR barrier detector with a cutoff wavelength of 16.6 $\mu$m are 2.15 A/W, 16.7%, and 3.09$\times$10$^{10}$ ${\rm {cm\cdot }}{{\rm {Hz}}^{1/2}}/{\rm {W}}$ respectively.
Compared with the traditional design scheme, our approach solves the problems of lattice matching and band-order matching. Although there is still room for further improvement in the performance of the device, this implies a new idea of the barrier photodetector.
Funding
National Natural Science Foundation of China (62274190, 61934007); National Key Research and Development Program of China (2021YFB2800304).
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.
References
1. P. Klipstein, “XBn barrier photodetectors for high sensitivity and high operating temperature infrared sensors,” Proc. SPIE 6940, 69402U (2008). [CrossRef]
2. H. Martijn, C. Asplund, R. M. von Würtemberg, et al., “High-performance MWIR type-II superlattice detectors,” Proc. SPIE 8704, 87040Z (2013). [CrossRef]
3. Y. Karni, E. Avnon, M. B. Ezra, et al., “Large format 15μm pitch XBn detector,” Proc. SPIE 9070, 90701F (2014). [CrossRef]
4. C. Grein, P. Young, M. Flatté, et al., “Long wavelength InAs/InGaSb infrared detectors: Optimization of carrier lifetimes,” J. Appl. Phys. 78(12), 7143–7152 (1995). [CrossRef]
5. H. Kroemer, “The 6.1 Å family (InAs, GaSb, AlSb) and its heterostructures: a selective review,” Phys. E: Low-dimensional Syst. Nanostructures 20(3-4), 196–203 (2004). [CrossRef]
6. G. Sai-Halasz, R. Tsu, and L. Esaki, “A new semiconductor superlattice,” Appl. Phys. Lett. 30(12), 651–653 (1977). [CrossRef]
7. A. Rogalski, “Infrared detectors: an overview,” Infrared Phys. Technol. 43(3-5), 187–210 (2002). [CrossRef]
8. J.-B. Rodriguez, E. Plis, G. Bishop, et al., “nBn structure based on InAs/ GaSb type-II strained layer superlattices,” Appl. Phys. Lett. 91(4), 043514 (2007). [CrossRef]
9. M. Pitrowski and R. Antoni, “Performance comparison of barrier detectors and HgCdTe photodiodes,” Opt. Eng. 53(10), 106105 (2014). [CrossRef]
10. A. Jang, H. J. Lee, Y. H. Kim, et al., “Effect of barrier layer on InAs/GaSb type-II superlattice nBn detector,” in 2021 International Conference on Electronics, Information, and Communication (ICEIC), (IEEE, 2021), pp. 1–3.
11. B. Nguyen, M. Razeghi, V. Nathan, et al., “Type-II M structure photodiodes: an alternative material design for mid-wave to long wavelength infrared regimes,” Proc. SPIE 6479, 64790S (2007). [CrossRef]
12. D. Smith and C. Mailhiot, “Proposal for strained type II superlattice infrared detectors,” J. Appl. Phys. 62(6), 2545–2548 (1987). [CrossRef]
13. H. Mohseni, V. Litvinov, and M. Razeghi, “Interface-induced suppression of the Auger recombination in type-II InAs/GaSb superlattices,” Phys. Rev. B 58(23), 15378–15380 (1998). [CrossRef]
14. B.-M. Nguyen, D. Hoffman, P.-Y. Delaunay, et al., “Band edge tunability of M-structure for heterojunction design in Sb based type II superlattice photodiodes,” Appl. Phys. Lett. 93(16), 163502 (2008). [CrossRef]
15. H.-J. Lee, A. Jang, Y. H. Kim, et al., “Comparative advantages of a type-II superlattice barrier over an AlGaSb barrier for enhanced performance of InAs/GaSb LWIR nBn photodetectors,” Opt. Lett. 46(16), 3877–3880 (2021). [CrossRef]
16. Y. Livneh, P. Klipstein, O. Klin, et al., “k·p model for the energy dispersions and absorption spectra of InAs/GaSb type-II superlattices,” Phys. Rev. B 86(23), 235311 (2012). [CrossRef]
17. J. M. Luttinger and W. Kohn, “Motion of electrons and holes in perturbed periodic fields,” Phys. Rev. 97(4), 869–883 (1955). [CrossRef]
18. G. L. Bir and G. E. Pikus, Symmetry and strain-induced effects in semiconductors (Wiley, New York, 1974).
19. G. Liu and S.-L. Chuang, “Modeling of Sb-based type-II quantum cascade lasers,” Phys. Rev. B 65(16), 165220 (2002). [CrossRef]
20. S. L. Chuang, Physics of photonic devices (Wiley, New York, 2009).
21. M. A. Kinch, State-of-the-art infrared detector technology (SPIE, 2014).
22. A. W. Rogalski, M. E. Kopytko, and P. M. Martyniuk, Antimonide-based infrared detectors: a new perspective (SPIE-The International Society for Optics and Photonics, 2018).
23. I. Vurgaftman, M. P. Lumb, and J. R. Meyer, Bands and Photons in III-V Semiconductor Quantum Structures, vol. 25 (Oxford University, 2020).
24. P.-F. Qiao, S. Mou, and S. L. Chuang, “Electronic band structures and optical properties of type-II superlattice photodetectors with interfacial effect,” Opt. Express 20(3), 2319–2334 (2012). [CrossRef]
25. J. Glennon, F. Bertazzi, A. Tibaldi, et al., “Extraction of Mobility from Quantum Transport Calculations of Type-II Superlattices,” Phys. Rev. Appl. 19(4), 044045 (2023). [CrossRef]
26. P. Martyniuk, A. Rogalski, and S. Krishna, “Interband quantum cascade infrared photodetectors: Current status and future trends,” Phys. Rev. Appl. 17(2), 027001 (2022). [CrossRef]
27. W. Huang, L. Li, L. Lei, et al., “Minority carrier lifetime in mid-wavelength interband cascade infrared photodetectors,” Appl. Phys. Lett. 112(25), 251107 (2018). [CrossRef]
28. S.-N. Cui, W.-Q. Chen, D.-W. Jiang, et al., “Dark current simulation and analysis for InAs/GaSb long wavelength infrared barrier detectors,” Infrared Phys. Technol. 121, 104006 (2022). [CrossRef]
29. D. Neamen, Semiconductor physics and devices (McGraw-Hill, Inc., 2002).
30. X. Li, D. Jiang, Y. Zhang, et al., “Investigation of dark current mechanisms on type-II InAs/GaSb superlattice very long wavelength infrared detectors,” J. Phys. D: Appl. Phys. 49(16), 165105 (2016). [CrossRef]
31. Q. Yang, F. Fuchs, J. Schmitz, et al., “Investigation of trap-assisted tunneling current in InAs/(GaIn) Sb superlattice long-wavelength photodiodes,” Appl. Phys. Lett. 81(25), 4757–4759 (2002). [CrossRef]
32. J. Nguyen, D. Z. Ting, C. J. Hill, et al., “Dark current analysis of InAs/GaSb superlattices at low temperatures,” Infrared Phys. Technol. 52(6), 317–321 (2009). [CrossRef]
33. R. C. Jones, “Phenomenological description of the response and detecting ability of radiation detectors,” Proc. IRE 47(9), 1495–1502 (1959). [CrossRef]
34. D. Hoffman, B.-M. Nguyen, E. K.-w. Huang, et al., “The importance of band alignment in vlwir type-ii inas/gasb heterodiodes containing the m-structure barrier,” Proc. SPIE 7222, 722215 (2009). [CrossRef]
35. L. Wenjing, Z. Lianqing, Z. Dongliang, et al., “Optimization of nBn dual-band mid-/long-wavelength detector based on InAs/GaSb superlattice,” Infrared Laser Eng. 52, 20220837 (2023). [CrossRef]
36. A. Haddadi, G. Chen, R. Chevallier, et al., “InAs/InAs1-xSbx type-II superlattices for high performance long wavelength infrared detection,” Appl. Phys. Lett. 105(12), 121104 (2014). [CrossRef]
