# Modeling of HOT (111) HgCdTe MWIR detector for fast response operation

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## Abstract

The paper reports on photoelectrical performance of the mid-wave infrared (MWIR) (111) HgCdTe high operating temperature detector for the fast response conditions. Detector structure was simulated with software APSYS by Crosslight Inc. The detailed analysis of the time response as a function of device architecture and applied voltage was performed pointing out optimal working conditions. The time response of the MWIR HgCdTe detector with 50 % cut-off wavelength of \(\lambda _{c} \approx 5.3\, \upmu \hbox {m}\) at \(T = 200\) K was estimated at the level of \(\tau _{s} \approx \) 2,500 ps for \(V = 100\) mV and series resistance \(R_{Series} = 510\,\Omega \). The series resistance’s reduction enables to reach \(\tau _{s}\approx 60\!-\!500\) ps.

### Keywords

HOT Time response HgCdTe## 1 Introduction

Higher operation temperature (HOT) condition of the mid-wave (3–8 \(\upmu \hbox {m}\)) photodetectors is one of the most important research areas in infrared technology (Martyniuk and Rogalski 2013). The development of the new detector architectures has been driven by applications requiring fast response operation. This requirement stays in contradiction with reaching high detectivity in terms of detector optimization. Two methods to reach a short response time of the detectors may be listed: high recombination decay in absorber region and fast transport of the photogenerated carriers to contacts. The recombination mechanism is important for forward and weak reverse conditions, while carrier transport is significant for higher reverse voltage. Except of voltage, the drift time strongly depends on thickness of the absorption region. Reducing the thickness of the active region, the short drift times could be reached, but this is not a proper solution to improve the response time of detector because, devices with thin active regions lead to poor quantum efficiency and lower detectivity. Additionally, Hu et al. calculated optimal thickness of absorption layer versus absorption and diffusion lengths showing its dependence on incident light wavelength and minority carrier lifetimes (Hu et al. 2008). In this case, a special heterostructure designs are developed, where \(p\)-type absorber is advantageous due to both high diffusion and drift ambipolar mobility, what is consider as a must to achieve fast and efficient collection of charge carriers. Additionally, in the fundamental approach, \(p\)-type HgCdTe active regions are characterized by the best compromise between obligation of the high quantum efficiency and a low thermal generation driven by the Auger 7 generation-recombination (GR) mechanism (Piotrowski and Rogalski 2007).

In general, most of photodiodes with short time response are based on heterostructures to prevent from parasitic thermal generation at contacts (Ashley and Elliott 1985). A complex multi-layer structure in which the transport of majority and minority carriers is determined by barriers has been used with great success in our laboratory for MWIR photodiodes operating at HOT conditions. The main modification in comparison with the standard three-layer \(\hbox {N}^{+}{\uppi } \hbox {P}^{+}\) structure invented for non-equilibrium conditions is programmed grading of band gap and doping level at heterojunctions (interfaces) (Elliot et al. 1996; Piotrowski et al. 2007a, 2009, 2010).

In this paper we present the theoretical modeling of the photodetector for fast response conditions based on epitaxial HgCdTe multi-layer graded gap architecture. Detector structure was characterized and simulated with software APSYS by Crosslight Inc. The voltage and structural dependence of the dark current and time response characteristics including both trap-assisted (TAT) and band-to-band (BTB) tunneling mechanisms at the graded heterojunctions were simulated. The time response of the MWIR HgCdTe detector with 50 % cut-off wavelength of \(\lambda _{c} \approx 5.3\,\upmu \hbox {m}\) at \(T = 200\) K was estimated at the level of \(\tau _{s} \approx \hbox {2,500}\) ps for \(V = 100\,\hbox {mV}\,(R_{Series} = 510\,\Omega )\). Dark current was found to be driven mostly by TAT/BTB mechanism reaching \(\approx 0.2\,\hbox {A/cm}^{2}\) at 1,500 mV.

## 2 Simulation procedure

Theoretical modeling of the HgCdTe heterostructures has been performed by numerical solving of Poisson’s and the electron/hole current continuity equations. The commercially available APSYS platform (Crosslight Inc.) was implemented in our simulation procedure. APSYS uses the Newton-Richardson method of nonlinear iterations. The applied model incorporates both HgCdTe electrical and optical properties to estimate device performance taking into consideration radiative (RAD), Auger (AUG), Shockley Read-Hall (SRH) GR and BTB as well as TAT tunneling mechanisms. In TAT simulation the Hurkx et al. model was implemented (Hurkx et al. 1992). The TAT mechanism was found to be important by assuming trap concentration \(N_{Trap} = 10^{10}\,\hbox {cm}^{-3}\) at the tunneling interfaces 1 and 3. The absorption was only assumed in active layer region. The HgCdTe absorption coefficient was estimated according to Kane model including its composition, doping and temperature dependence \((\alpha = \hbox {3,390}\,\hbox {cm}^{-1}, \lambda _{c} = 5.3\,\upmu \hbox {m}, T = 200\,\hbox {K})\).

It must be stressed that HgCdTe is a narrow-gap semiconductor that exhibits a non-parabolic conduction band and high carrier degeneracy. These conditions are very difficult to fulfil because of numerical problems with computation of the Fermi-Dirac integral for non-parabolic model. Quan et al. and Wang et al. have proposed approximations to this expression, however mentioned solution have only been validated for \(T = 77\!-\!120\,\hbox {K}\) (Quan et al. 2007a, b; Wang et al. 2010, 2011). Since HgCdTe device studied in this work operates at increased temperatures 200 K and proposed approximations has not been fully validated for HOT conditions yet, computations were performed using the Fermi-Dirac statistics for a non-degenerate semiconductor model with parabolic energy bands. Such simplification gives quite good results in a broad range doping concentrations (Wenus et al. 2001).

Parameters taken in modeling of MWIR HgCdTe heterostructure

Barrier layer | Active layer | Barrier layer | Contact layer | |
---|---|---|---|---|

Doping, \(N_{A}; N_{D} [\hbox {cm}^{-3}]\) | \(50 \rightarrow 0.5 \times 10^{16}\) | \(0.4 \rightarrow 0.8 \rightarrow 2 \times 10^{16}\) | \(2\rightarrow 10 \rightarrow 1 \times 10^{16}\) | \(3\rightarrow 30 \times 10^{16}\) |

Doping Gauss tail, | 0.05 | |||

Composition, \(x\) | \(0.34\rightarrow 0.27\) | \(0.27\rightarrow 0.325\) | \(0.15 \rightarrow 0.4\) | 0.15 |

Geometry, \(d [\upmu \hbox {m}]\) | 9.9 | 6 | 2.25 | 0.85 |

Electrical area, \(A [\upmu \hbox {m}^{2}]\) | \(100\times 100\) | |||

Overlap matrix, \(F_{1}F_{2}\) | 0.2 | |||

Trap energy level, \(E_{Trap}\) | \(0.33\times \hbox {E}_{\mathrm{g}}\) | |||

Trap concentration, \(N_{Trap}[\hbox {cm}^{-3}]\) | \(10^{10}/2.3\times 10^{13}\) | |||

SRH \(\frac{\upsigma _{\mathrm{n}}}{\upsigma _{\mathrm{p}}}[\hbox {cm}^{-2}\)] | \(5\times 10^{-15}\) | |||

Incident power density, \(\varPhi \) [\(\hbox {W/m}^{2}\)] | 50 |

## 3 Simulation results

## 4 Conclusion

The time response characteristics were theoretically simulated showing its TAT/BTB and \(R_{Series}\) dependence. The proper fitting to the experimental results was achieved using the presented models. The appropriate controlling of \(R_{Series}\) (detector *processing*) and the tunneling effects at interface 1 and 3 allows to decrease the \(\tau _{s}\) below 500 ps. Theoretical simulations indicates that assuming proper TAT/BTB mechanism and \(R_{Series}\) the shorter response times could be obtained even for interfaces’ composition higher than nominal, assumed in growth procedure.

## Notes

### Acknowledgments

We acknowledge support by National Centre of Research and Development-the Grant No. PBS 1/B5/2/2012.

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