# Trends in Performance Limits of the HOT Infrared Photodetectors
## 4 Interband Quantum Cascade Infrared Photodetectors (IB QCIPs)
The noises suppression for shorter individual absorbers is the advantage of QCIP design. The QCIP detectivity, D+ is influenced by the Johnson and shot noises that is proportional to \(\sqrt{N}\) according to the relation [37]  
\[i_{n}=\sqrt{\frac{4k_{B}T}{NR_{0}A}+\frac{2 qJ_{dark}}{N}}, \tag{12}\]  
where \(N\)--Number of periods and both dynamic resistance, dark current correspond to one QCIP's period. The optimal number of periods is related to the thickness of the single  
Figure 8: Backside illuminated multiple HgCdTe heterojunction devices: (**a**) junction’s planes perpendicular to the surface, and (**b**) 4-cells stacked multiple detector (after reference [8]). absorber, d, and the absorption coefficient and could be expressed as \(N=(2\alpha\text{d})^{-1}\) in the first order approximation. The IB QCIPs (with T2 SLs absorbers) MBE growth process is challenging where many interfaces and strained thin layers are deposited in structures. Nevertheless, the significant progress has been reached for T2 SL based detectors particularly for the LWIR and HOT conditions. They exhibit the capabilities of the IB optical transitions with the exceptional carrier transport properties of the QCIP architectures. Currently, IB QCIPs has two types of configuration: current-matched (designed to have an equal photocurrent in every single stage) and non-current-matched [39]. [PERSON] and [PERSON] described the IB QCIP structure with equal absorbers offering the potential for significant responsivity improvement assuming \(\alpha\)L \(\leq\) 0.2 (\(\alpha\)L--Product of the absorption coefficient and the diffusion length) [40]. From a technological point of view, the non-current-matched IB QCIPs (identical absorber thickness in all stages) are simpler to design and grow in comparison to the current-matched ones. The disadvantage of non-current-matched structure is the limited responsivity due to the significant light suppression along the detector's structure. The high electrical gain, lately observed at HOT conditions in these structures, could at least partially compensate in terms of responsivity reduction [41; 42]. Despite the development of other technologies, HgCdTe is still the most broadly used adjustable gap semiconductor for IR detectors, to include uncooled operation, and stands as a reference for alternative technologies. Figure 10 demonstrates that T2 SL InAs/GaSb IB QCIPs bipolar devices (dashed lines) are proper candidate for HOT conditions. The assessed Johnson-noise limited detectivities under unbiased conditions for IB QCIPs with T2 SL InAs/GaSb absorbers (based on the measured R\({}_{0}\)A product and responsivity) are comparable with commercially available HgCdTe devices. The performance of both types of detectors is comparable only in SWIR range and IB QCIPs outperform uncooled HgCdTe detectors with a similar LWIR cut-off wavelength. Another advantage of IB QCIPs is related to the III-V semiconductors strong covalent bonding allowing for operation at temperatures close to 400 \({}^{\circ}\)C being not possible for HgCdTe. Figure 9: IB QCIP based on T2 SL InAs/GaSb active, GaSb/AlSb tunneling and InAs/AlSb relaxation layers (after reference [38]). In Figure 10, the representative experimental data for 2D material single photodetectors operating in IR spectral range are also marked. It can be seen that in MWIR the performance of black phosphorous-arsenic (bPAs) photodetectors outperforms commercially available uncooled HgCdTe photodiodes, while in LWIR, the detectivity, D\({}^{*}\) of the transition metal dichalcogenide (TMD) photodetectors (PdSe\({}_{2}\)/MoS\({}_{2}\) heterostructure) is the best. More detailed comments about these results are included in Section 5.2. Figure 11 compares the peak detectivity, D\({}^{*}\) for HgCdTe photodiodes [33] and InAs/GaSb T2 SIs IB QCIPs [38] operating at 300 K with bPAs and TMD photodetectors.