# Trends in Performance Limits of the HOT Infrared Photodetectors
## 3 The Ultimate HgCdTe Photodiode Performance
### Detectivity  
The detector's detectivity, D\({}^{*}\) is related to the current responsivity, \(R_{i}\) [see Equation (13)] and noise current, \(i_{n}\), and can be given by relation  
\[D^{*}=\frac{R_{i}}{i_{n}}. \tag{10}\]  
For the non-equilibrium devices, the \(i_{n}\) value can be calculated assuming thermal Johnson-Nyquist and shot noises contribution by the following expression  
\[i_{n}=\sqrt{\frac{4k_{B}T}{R_{0}A}+2q\int_{dark}}, \tag{11}\]  
where \(k_{B}\)--Boltzmann constant, \(R_{0}A\)--Dynamic resistance area product and \(J_{dark}\)--dark current density.  
The performance of P-i-N MWIR HgCdTe photodiode (\(\lambda_{\text{c}}\) = 5 \(\upmu\)m) is presented in Figure 7.  
Figure 6: The SRRI lifetime versus temperature where fully depleted P-i-N HgCdTe detector depletion dark current equals the background radiation current. The calculations were carried out for SWIR (3 \(\upmu\)m), MWIR (5 \(\upmu\)m), and LWIR (10 \(\upmu\)m) absorbers.  
As is shown in Figure 7a, the Teledyne Judson experimentally measured current densities, at the bias \(-0.3\) V, are close to BLIP (f/3) curve and they are located less than one order of magnitude above this limit [34]. The current density at 300 K is even lower than predicted by Rule 07. The measured current densities presented by VIGO System are close to one order of magnitude higher, however in this case they were measured at lower reverse bias, \(-0.1\) V, with less effective Auger suppression [33]. It is interesting to notice, that the performance of IB QCIP based on T2 SLs InAs/GaSb coincides well with upper experimental data for HgCdTe photodiodes at 300 K [30].  
Figure 7a shows the diffusion and depletion dark current components versus temperature assuming 1 ms SRH carrier lifetime, 5 \(\upmu\)m thick absorber and doping \(5\times 10^{13}\) cm\({}^{-3}\). The diffusion component associated with Auger 1 mechanism is eliminated because of the absence of majority carriers due to exclusion and extraction effects [35; 36]. The background radiation calculated assuming f/3 optics has decisive influence on dark current. It should be mentioned here that the background flux current is determined by the net flux through the optics (limited by f/#) plus the flux from the cold shield. This effect is shown by increased BLIP (f/3) influence on dark current at temperature >220 K.  
Figure 7b shows calculated electricity versus temperature for MWIR P-i-N HgCdTe photodiode assuming identical parameters as taken in calculations presented in Figure 7a (\(\lambda_{\text{c}}\) = 5 \(\upmu\)m, \(\tau_{\text{SRH}}\) = 1 ms, t = 5 \(\upmu\)m, N\({}_{\text{dop}}\) = \(5\times 10^{13}\) cm\({}^{-3}\)). The current responsivity was estimated assuming QE = 1 (however typical QE reaches reasonable value \(\sim\)0.7). As is shown, for MWIR photodiode with 5-\(\upmu\)m cut-off wavelength and low doping in active region, detectivity, D\({}^{*}\) is limited by background and is about one order of magnitude higher than predicted by the Rule 07. The experimental data given for HgCdTe photodiodes in Teledyne Judson and VIGO System catalogues are more than one order of magnitude below background flux limitation for the f/3 optics.