HOT mid-wave HgCdTe nBn and pBp infrared detectors

Narrow band gap photon infrared detectors require cryogenic cooling to suppress the noise deteriorating the performance. Among the competitive materials and theoretical predictions favouring type-II superlattices InAs/GaSb, HgCdTe has been still considered as the leader in terms of the fundamental physical parameters. The size, weight, power consumption and multispectral response of the infrared detection system play decisive role in fabrication of the higher operation temperature detectors. Several strategies have been implemented to improve the performance at elevated temperatures. The most efficient and used in HgCdTe technology are: non-equilibrium architectures and currently an idea of the barrier detectors. In this paper we present the comparison of the nBnn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {nB}_\mathrm{n}\hbox {n}$$\end{document} and pBpp(Bn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {pB}_\mathrm{p}\hbox {p}\,(\hbox {B}_\mathrm{n}$$\end{document} and Bp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {B}_\mathrm{p}$$\end{document} stands for n/p-type doped barrier) HgCdTe photodetectors. pBpp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {pB}_\mathrm{p}\hbox {p}$$\end{document} architecture allows to reach higher performance (detectivity ∼109cmHz1/2/W\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sim }10^{9}\,\hbox {cm}\,\hbox {Hz}^{1/2}/\mathrm {W}$$\end{document} for T=200\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T = 200$$\end{document} K) at mid-wave spectrum for wide range of absorber p-type doping 2×1014→1017cm-3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\times 10^{14}\rightarrow 10^{17}\,\hbox {cm}^{-3}$$\end{document} and barrier Cd composition 0.37→0.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.37\rightarrow 0.7$$\end{document}.

nisms leading to long carrier lifetime and high operating temperature. In addition, extremely small change of lattice constant with composition makes it possible to grow high quality layered heterostructures (Norton 2002;Rogalski 2005). Because of its physical properties, HgCdTe has evolved to become the most important and versatile material and can be used for devices operating in various modes: photoconductors, photodiodes and metal-insulatorsemiconductor (MIS) detectors Rogalski 2004, 2007). Additionally HgCdTe has inspired development of four generations of the IR detectors. The IR detector roadmap starting from 1959 when HgCdTe was used for the first time is shown in Fig. 1 (Rogalski 2011). The new concepts of IR technologies are marked in blue to include barrier detectors (barrier infrared detectors-BIRD), multi-stage, photon trapping detectors and type-II superlattices (T2SLs) with their potential to compete with HgCdTe. Third generation HgCdTe systems are now implemented and concept of development of the fourth generation system is undertaken to include: multicolour capability, optical coupling (plasmonic), large number of pixels, high frame rates and high thermal resolution. A revolutionary emergence of focal plane arrays (FPAs) based on thermal detectors (bolometer, pyroelectric) has been observed but these devices are not expected to compete with the highperformance cryogenically cooled arrays or single photon detectors (see Fig. 1).
A number of concepts to improve HgCdTe IR detecors' performance have been proposed, but significant improvements in reduction of the dark current and increasing of the operating temperature has been reached by suppression of Auger thermal generation by implementing non-equilibrium conditions to the detectors structure (Ashley and Elliott 1985;). In practice, most of HgCdTe N + p(π)P + Auger suppressed photodiodes are based on complex graded gap and doping multi-layer structures in which the transport of majority and minority carriers is determined by barriers. Additionally, p-type HgCdTe active regions are characterized by the best compromise between requirement of the high quantum efficiency and a low thermal generation driven by the Auger 7 thermal generation mechanism (Piotrowski et al. 2010). A new strategy to achieve HOT detectors includes barrier structures launched by White and followed by Maimon and Wicks (White 1983;Maimon and Wicks 2006). Potential capability of the simple unipolar BIRD detector is that the generationrecombination (GR) current being dominated by the generation of electrons and holes by Shockley-Read-Hall (SRH) traps in the depletion region may be significantly suppressed by widegap (in relation to absorber and cap layer) barrier implementation to the detector's structure. Assuming that simple BIRD nB n n detector is nearly lacking of depletion region in active layer, the GR contribution to the net dark current from the absorber layer is limited. In low-temperature region (below crossover temperature), the nB n n detector should exhibit a higher signal-to-noise ratio in comparison with a conventional p-n diode operating at the same temperature and should operate at a higher temperature with the same J DARK . Unipolar BIRD architecture was firstly implemented in A III B V bulk materials (InAs, InAsSb), after in T2SLs e.g. InAs/GaSb and finally introduced into HgCdTe by Itsuno et al. in both mid-and long wave ranges (Klipstein 2008;Rodriguez et al. 2007;Itsuno et al. 2011). Growth of BIRD structure exhibiting no valence band offset (VBO) ≈ 0 eV between barrier and absorber for HgCdTe (MWIR HgCdTe-VBO < 200 meV depending on both absorber/barrier composition and doping, T = 200 K) has turned out to be difficult in terms of technology, however the research on this structures has been developing owing to problems with p-type doping in molecular beam epitaxy (MBE) technology. VBO in HgCdTe-based unipolar BIRD creates several issues limiting their performance. Depending on the wavelength of operation, a relatively high bias, typically greater than the bandgap energy (turn on voltage) is required to be applied to the device in order to collect the photogenerated carriers. This leads to strong band-to-band (BTB) and trap-assisted (TAT) tunneling due to the high electric field at the barrier absorber heterojunction. Proper interface doping at the cap-barrier and barrier absorber heterojunctions should lower VBO (Schubert et al. 1991). Parameters of the MCT devices are still better than devices employing other materials to include A III B V based T2SLs InAs/GaSb. In spite of many advantages, HgCdTe is technologically extremely difficult to grow. Hg bonding reduces strength of a material, resulting in weak mechanical properties and creating difficulties in a material processing. Moreover, the high Hg vapor pressure makes the composition control over a large area difficult (Rogalski 2005). Itsuno et al. (2012) presented nB n n device being a prospect for circumventing of the p-type doping requirements in MBE technology related to an inconvenient ex situ As activation. Since HgCdTe p-type material is much more favorable, metalorganic chemical vapour deposition (MOCVD) growth allowing both in situ donor and acceptor doping seems to be more attractive in terms of growth of pB p p HgCdTe barrier structures. Barrier structures with p-type doped constituent layers grown by MOCVD were presented by Kopytko et al. (2014). The paper presents comparison of the BIRD nB n n and pB p p HgCdTe detectors in terms of dark current and detectivity versus voltage, absorber doping, barrier Cd composition and doping.

Simulation procedure
Both nB n n and pB p p MWIR HgCdTe detectors were simulated with APSYS platform by Crosslight Inc. (APSYS 2014). The structural and simulation parameters were presented in Table 1 while modelled unipolar BIRD structure is shown in Fig. 2a. Interface barrier layers were assumed to be x-graded regions and represent the real structure which profile is shaped by interdiffusion processes during HgCdTe MOCVD growth.
Theoretical modeling of the MWIR HgCdTe barrier detectors has been performed by numerical solving of the Poisson's equation and the carrier current continuity equations by the Newton-Richardson method of nonlinear iterations (APSYS 2014). The applied model incorporates electrical properties to include the influence of radiative (RAD), Auger (AUG), SRH GR at any location within the device and BTB as well as TAT mechanisms at the barrier-absorber heterojunction. For the TAT simulation the Hurkx et al. (1992) model was implemented. We incorporated AUG recombination mechanisms using theory by Casselman and Petersen (1980). APSYS numerical platform requires the HgCdTe's composition,  temperature and doping dependence of the electron affinity, bandgap, intrinsic concentration, mobility and effective masses. Bandgap was obtained from the paper by Hansen et al. (1982). The low-field electron mobility was taken after Scott's study, where the hole mobility was basically taken as 0.01 of the electron mobility (Scott 1972). The intrinsic concentration, composition and temperature dependence was calculated based on the Hansen and Schmidt (1983) model. Although HgCdTe exhibits a non-parabolic conduction band and high carrier degeneracy, computations were performed using the Fermi-Dirac statistics for a non-degenerate semiconductor model with parabolic energy bands (Quan et al. 2007;Wang et al. 2010Wang et al. , 2011. This simplification is valid for a wide range of doping concentrations (Wenus et al. 2001). Absorption was assumed in active region. Ohmic contacts were modeled as Dirichlet boundary conditions-electron and hole quasi-Fermi levels are equal and assumed to be at the voltage of biased electrode, i.e., The noise current was simulated using the following expression that includes both the thermal Johnson-Nyquist noise and electrical shot noise contributions: where A is the area of the detector, RA is the dynamic resistance area product, J DARK is the dark current density, and k B is the Boltzmann constant. Detectivity (D * ) limited by thermal Johnson-Nyquist noise and electrical shot noise could be expressed by relation (where, R i current responsivity): Both nB n n and pB p p detectors require that the valence bands of the three constituent layers line up closely to allow minority carrier transport between the absorber and contact layers. n + extra layer was added to assure proper contact properties to the p-type active layer in pB p p barrier structure. Band diagram of the simulated structures is shown in Fig. 2b. The band energy discontinuity of both barrier layer and absorber layer seems to be the most decisive parameter influencing performance of barrier structure. Similarly to nB n n, for pB p p barrier in conduction band ( E c ) is higher compared to barrier in valence band ( E c > E v ) (see Fig. 2b). At equilibrium both E v (160 meV) and E c (364 meV) for nB n n are higher in comparison to E v (60 meV) and E c (333 meV) for pB p p, at T = 200 K. Dark and photocurrent are effectively blocked for E v ; E c > 3k B T ≈ 50 meV (T = 200 K). J DARK versus voltage is shown in Fig. 3a. pB p p structure reaches lower dark current for > 175 mV. Cap layer's doping to the level of 5 × 10 15 cm −3 and E c dependence on voltage is responsible for the J DARK increase with bias, while for pB p p J DARK saturates. pB p p structure allows operation for unbiased conditions being directly related to E v and E c dependence on voltage ( E v < 3k B T ).
Since both HgCdTe n/p-type barrier height in conduction band was estimated to be within the range of ∼400 meV, the SRH GR contribution is evident in HOT conditions. Crossover temperature (T C -temperature where diffusion component is balanced by GR component) for nB n n was estimated at T C ≈ 152 K, while for pB p p T C ≈ 164 K. (Fig. 3b. Barrier x Cd composition influence on J DARK and J PHOTO is presented in Fig. 3c. Barrier x Cd has no influence on J PHOTO for pB p p which indicates that E v has no influence on the transport of the photogenerated carriers, while for nB n n this behavior is observed for x Cd > 0.5. pB p p J DARK saturates reaching ∼ 3 × 10 −4 A/cm 2 for x Cd > 0.49, while for nB n n this effect is observed for x Cd > 0.66. nB n n J DARK and J PHOTO versus absorber doping for two selected barrier doping N D = 7 × 10 14 and 10 16 cm −3 are presented in Fig. 4a. For B-N D = 10 16 cm −3 , J DARK keeps constant ∼ 10 A/cm 2 for absorber N D = 0.01 →1 cm −3 , while above slight increase of the dark current is observed. For B-N D = 7 × 10 14 cm −3 J DARK increases three orders of magnitude (2 × 10 −3 →2 A/cm 2 ), J PHOTO stays constant to N D = 10 16 cm −3 . Opposite trend is observed for J PHOTO (2 ×10 −1 → 8 × 10 −5 A/cm 2 ) in analyzed active layer doping range. Figure 4b presents pB p p J DARK and J PHOTO dependence on absorber doping for B-N A = 7 × 10 14 cm −3 . J PHOTO stays constant for analyzed absorber doping range, while J DARK increases sharply for N D > 10 16 cm −3 .
Detectivity calculated according to relation (1) versus temperature is presented in Fig. 5a. nB n n reaches background limited photodetector (BLIP) conditions at ∼175 K, while for pB p p at ∼200 K. D * for BLIP condition was calculated for background temperature, T B = 300 K and field of view, FOV = 20 • . Detectivity dependence on barrier composition is presented   Fig. 5b. Barrier x Cd should be higher than 0.49 for pB p p structure, where D * saturates, while for nB n n, D * increases with x Cd (for x Cd > 0.49). D * versus active layer doping for two selected barrier's doping, B-N D/A = 7 × 10 14 and 10 16 cm −3 (barrier x Cd = 0.6) are presented in Fig. 5c. For absorber's N D within 10 14 → 10 17 cm −3 , D * decreases almost four orders of magnitude. Barrier doping also influences D * (the higher barrier doping the lower D * may be reached for N D > 2 × 10 14 cm −3 , while below oppo- site trend is observed). D * for nB n n (∼10 8 cm Hz 1/2 /W) and pB p p (∼10 9 cm Hz 1/2 /W) BIRD structures could be increased by nearly 10 times by growth of the structures on GaAs substrates.

Conclusion
The barrier structure has been introduced to simplify the detector fabrication process and increase detector's operating temperature. Depending on the growth method, particular HgCdTe barrier architectures are favorable nB n n -MBE, both nB n n and pB p p -MOCVD. pB p p architecture allows to reach higher performance at MWIR spectrum for wide range of absorber doping N D/A = 2 × 10 14 → 10 17 cm −3 and barrier x Cd composition. Simulations indicate that pB p p structure is not that sensitive to the barrier and absorber doping changes in comparison to nB n n detector. Further strategy in development of HgCdTe BIRD detectors should focus on decreasing or even removing the VBO at the barrier-absorber heterojunction, which will result in lower operating bias, lower dark current, and ability to operate at higher temperatures. Theoretically estimated D * for both nB n n and pB p p BIRD detectors could possibly reach ∼10 9 and ∼10 10 cmHz 1/2 /W by growth on GaAs substrates.