# Trends in Performance Limits of the HOT Infrared Photodetectors
## 2 Trends in Development of Infrared HOT Photodetectors  
As is shown by [PERSON] and [PERSON] [15], the IR detectors performance is limited by statistical character of generation-recombination processes in the material. Thermal processes in the device material limit the detectivity, \(D^{*}\) of an optimized IR detector. It can be given by the following equation  
\[D^{*}=k\frac{\lambda}{hc}\Big{(}\frac{\alpha}{G}\Big{)}^{1/2}, \tag{1}\]  
where \(\lambda\)--Wavelength, \(h\)--Planck's constant, \(c\)--Light speed, \(\alpha\)--Absorption coefficient, \(G\)--Thermal generation in the active detector's region, \(k\)--Coefficient depending on radiation coupling to the detector. \(\alpha/G\) is the absorption coefficient to the thermal generation rate ratio and can be considered as the fundamental figure of merit of any material used for IR detectors (\(\alpha/G\) ratio could be used to evaluate any material). Among different bulk materials, the narrow gap semiconductors are more suitable for the HOT photodetectors than competitive technologies, such as extrinsic devices, Schottky barrier photodiodes, quantum dot infrared photodetectors (QDIP) and quantum well infrared photodetectors (QWIP) [16]. The high performance of intrinsic photodetectors results from high density of states in the conduction and valence bands (contributing to high IR absorption), and long carrier lifetime (contributing to low thermal generation).  
The goal of IR detector technology is the fabrication of HOT photodetector characterized by the dark current lower than the background flux current and 1/f noise negligibly lower than to the background flux shot noise [17; 18].  
In several papers, it was shown that the detector size, d, and F-number (f/#) are the main IR systems parameters [19; 20]. Since they depend on \(F\lambda/d\) (\(\lambda\)--Wavelength), both influence the detection/identification range, as well as the noise equivalent difference temperature (NEDT) [20]  
\[Range=\frac{D\Delta x}{M\lambda}\bigg{(}\frac{F\lambda}{d}\bigg{)}, \tag{2}\]  
\[NEDT\approx\frac{2}{\text{CA}\big{(}\eta\Phi_{B}^{2\pi}\tau_{int}\big{)}} \bigg{(}\frac{F\lambda}{d}\bigg{)}, \tag{3}\]  
where \(D\)--Aperture, \(M\)--Needed number of pixels to identify a target \(\Delta x\), C--Scene contrast, \(\eta\)--Quantum efficiency (QE), \(\Phi_{B}^{2\pi}\)--Background flux into a 2\(\pi\) FOV, \(\tau_{int}\)--Integration time. According to the relations (2) and (3), the \(F\lambda/d\) parameter could be used for IR system optimization. For the f/1 optics, the smallest practicable detector size should be \(\sim\)2 \(\upmu\)m for the MWIR and \(\sim\)5 \(\upmu\)m for the LWIR, respectively [21]. With more realistic f/1.2 optics, the smallest practicable detector size is \(\sim\)3 \(\upmu\)m and \(\sim\)6 \(\upmu\)m for the MWIR and LWIR, respectively.  
[PERSON] claims that the IR system ultimate cost reduction could only be reached by the 300 K operation of depletion-current limited arrays with pixel densities that are fully consistent with background and diffraction-limited performance due to the system optics [20]. The depletion-current limited P-i-N photodiodes demand long Shockley-Read-Hall (SRH)carrier lifetime, marked as \(\tau_{\text{SRH}}\), to meet the requirements of a low dark current. The long HgCdTe SRH lifetime makes this material a great candidate for 300 K condition [20].