# Trends in Performance Limits of the HOT Infrared Photodetectors
## 3 The Ultimate HgCdTe Photodiode Performance
### Dark Current Density
At very low level of n-type doping (about 10\({}^{13}\) cm\({}^{-3}\)) the P-i-N photodiode ultimate performance is influenced by SRH recombination and neither Auger recombination nor Auger suppression. As is shown in Figure 4, for the sufficiently long SRH carrier lifetime in HgCdTe, the internal photodiode current is limited, and the performance is contributed by the background radiation. Its influence is shown for four background temperatures: 300, 200, 100 and 50 K. [PERSON] et al. suggested to replace Rule 07 by Law 19 corresponding exactly to the background limited curve for room temperature [25]. The internal photodiode current may be several orders of magnitude below Rule 07 versus given cut-off wavelength and operating temperature. It can be also seen that Rule 07 coincides well with theoretically predicted curve for the Auger-suppressed p-on-n photodiode with absorber doping concentration N\({}_{\rm d}\) = 10\({}^{15}\) cm\({}^{-3}\). The experimental data for p-on-n HgCdTe photodiodes (Teledyne Technologies) [25] and for III-V barrier detectors (Raytheon Technologies [28] and SCD SemiConductor Devices [29]) operating at about 80 K, and 300 K IB QCIP [30] are presented in Figure 4. It is easy to notice that experimental data for III-V barrier detectors are slightly worse than the p-on-n HgCdTe photodiodes, but III-V IB QCIPs operating at 300 K are even better in LWIR. Figure 4 shows also representative data for both InSb (\(\lambda_{\rm c}\) = 5.3 \(\mu\)m, T = 78 K) and InGaAs (\(\lambda_{\rm c}\) = 1.7 and 3.6 \(\mu\)m, T = 300 K) photodiodes. InSb detector is characterized by several orders higher dark current density than HgCdTe one, however for optimal InGaAs detectors the dark current density is close to HgCdTe data [31]. The theoretical simulations presented in Figure 4 indicate that the background limited performance (BLIP) has the most impact on detector's current density for small 1/(\(\lambda_{\rm c}\)T) products; in other words for photodiodes operating in LWIR and H  
Figure 4: Current density of p-on-n HgCdTe photodiodes versus 1/(\(\lambda_{\rm c}\)T) product (adapted after reference [25]). Experimental data is gathered for Teledyne Technologies and alternative technologies [22; 25; 28; 29; 30; 31]. photodiodes operating at low temperature become generation-recombination limited due to the SRH centers influence the lifetime in the millisecond range. Figure 5 shows the current density calculated using Rule 07 (determined for diffusion limited P-on-n photodiodes) and Law 19 (which exactly equals to the background radiation current density) versus temperature for short-wave infrared (SWIR: \(\lambda_{\text{c}}\) = 3 \(\upmu\)m), MWIR (5 \(\upmu\)m), and LWIR (10 \(\upmu\)m) absorber. If the fully depleted P-i-N detector is influenced by the background current, a certain minimal value of SRH lifetime is required. The SRH lifetime calculations were made under condition where depletion dark current equals the background radiation current  
\[J_{dep}=J_{BLIP}. \tag{9}\]  
It was assumed that the 5-\(\upmu\)m thick absorber is fully depleted. The SRH lifetime at which the fully depleted P-i-N photodiode reaches the BLIP limit is presented in \[\tau_{A1}=\frac{2\tau_{A1}^{i}n_{i}^{2}}{n(n+p)}, \tag{5}\]0 As shown, the SRH lifetime required to reach BLIP limit decreases versus temperature (nevertheless fully depleted P-i-N photodiodes are particularly interesting in HOT conditions). What more, for LWIR detectors, it is possible to reach BLIP for shorter carrier lifetimes. At 300 K and 5-\(\upmu\)m fully depleted thick absorber, these carrier lifetimes are 15 ms for SWIR, 150 \(\upmu\)s for MWIR and 28 \(\upmu\)s for LWIR, respectively. The Teledyne Technologies experimentally measured SRH lifetimes for 10-\(\upmu\)m cut-off HgCdTe are higher than 100 ms (extracted at 30 K) [26].