**5. Numerical simulations of barrier detectors**

Theoretical modeling of the HgCdTe barrier detectors has been performed using our original numerical program developed at the Institute of Applied Physics, Military University of Technology (MUT) and the commercially available APSYS platform (Crosslight Inc.). Both programs are based on numerical solution of the Poisson's and the electron/hole current continuity Eqs. (9)–(11). In addition, both programs include the energy balance Eq. (12).

In simulations, we chose HgCdTe barrier detectors with different 50% cutoff wavelengths up to 3.6 μm (MWIR) and 9 μm (LWIR) at 230 K. MWIR devices were investigated by using our original numerical program, while LWIR device was investigated by the APSYS platform. **Table 1** presents selected parameters applied in the numerical modeling of MWIR HgCdTe barrier detectors.


**Table 1.** Parameters taken in modeling of MWIR and LWIR HgCdTe barrier detectors.

#### **5.1. Design and fabrications of HgCdTe barrier detectors**

barrier infrared detector (BIRD) implies that barriers can block one carrier type (electron or hole) but allow the unimpeded flow of the other. Assuming that Simple BIRD nBnn detector can be concluded as a hybrid of a photoconductor and a photodiode. The nBnn detector looks like a photodiode in a part except that the junction (space charge region) is replaced by a unipolar barrier (Bn: n-type doped barrier layer) blocking the electrons, whereas p-contact is replaced by the n-contact. The nBnn detector is nearly lacking the depletion region in an active layer, which leads to the reduction of SRH contribution to the net dark current. In low temperatures (below the crossover temperature), the nBnn detector should exhibit a higher signal-to-noise ratio in comparison with a conventional *p*-*n* photodiode operating at the same

temperature and should operate at a higher temperature with the same dark current.

heterojunction.

80 Modeling and Simulation in Engineering Sciences

barrier detectors.

The idea of the nBnn detector was proposed for bulk III-V materials; however, its introduction to the second type of superlattices has allowed the implementation of the concept of nBnn with a greater control of arrangement of optimal band structure. Contrary to III-V materials, uniformly n-type-doped HgCdTe does not exhibit valence band offset (VBO) *≈* 0 eV between the absorber and the barrier (e.g., MWIR HgCdTe − VBO < 200 meV depending on both the absorber/barrier composition and doping, *T* = 200 K), which is a key limiting detector per‐ formance [26]. Depending on the wavelength of operation, a relatively high bias (so-called "turn on" voltage) is required to be applied to the device to collect the photogenerated carriers. This leads to strong BTB and TAT effects due to a high electric field at the barrier-absorber

Proper p-type doping at the cap barrier and barrier absorber heterojunctions should lower VBO in HgCdTe. However, p-type doping is the technological challenge posed by dopant activation after molecular beam epitaxy (MBE) growth. Metalorganic chemical vapor deposi‐ tion (MOCVD) technology is considered more favorable, which allows both *in situ* donor and acceptor doping. It seems to be more attractive in terms of the growth of pBpn and pBpp (Bp: p-type barrier) HgCdTe barrier structures. Barrier structures with p-type-doped constituent

Theoretical modeling of the HgCdTe barrier detectors has been performed using our original numerical program developed at the Institute of Applied Physics, Military University of Technology (MUT) and the commercially available APSYS platform (Crosslight Inc.). Both programs are based on numerical solution of the Poisson's and the electron/hole current continuity Eqs. (9)–(11). In addition, both programs include the energy balance Eq. (12).

In simulations, we chose HgCdTe barrier detectors with different 50% cutoff wavelengths up to 3.6 μm (MWIR) and 9 μm (LWIR) at 230 K. MWIR devices were investigated by using our original numerical program, while LWIR device was investigated by the APSYS platform. **Table 1** presents selected parameters applied in the numerical modeling of MWIR HgCdTe

layers grown by MOCVD were presented by Kopytko et al. [27, 28].

**5. Numerical simulations of barrier detectors**

The epitaxial structures were grown by MOCVD. Generally, the analyzed MWIR p+ BpnN+ and p+ BppN+ (a capital letter denotes wider band; the symbol "+ " denotes strong doping) structures consists of four HgCdTe layers: p+ -Bp cap-barrier structural unit (highly doped with arsenic ptype cap contact layer and p-type wide bandgap barrier), intentionally undoped (due to donor background concentration with n-type conductivity) or low p-type-doped absorption layer and wide bandgap highly doped N+ bottom contact layer. In the LWIR n+ p+ BppN+ device, the cap contact is a combination of highly doped n- and p-type layers. Such design should create a tunneling junction to allow collection of photogenerated holes. Moreover, the cap n+ layer provides low-resistance ohmic contact. **Figure 2** shows the considered MWIR and LWIR HgCdTe heterostructure with parameters assumed for the growth and modeling.

**Figure 2.** MWIR and LWIR HgCdTe heterostructure with parameters assumed for the growth and modeling. *x* is the alloy composition, *NA* is the acceptor concentration, and *NB* is the donor concentration.

#### **5.2. MWIR HgCdTe barrier detectors**

Our original numerical program incorporates HgCdTe electrical properties to estimate MWIR device performance taking into account Auger, SRH, as well as BTB and TAT tunneling mechanisms. Two types of SRH centers were included in the model: metal site vacancies and dislocation related centers [29, 30]. The two types of centers are characterized by different ionization energies and capture coefficients (**Table 1**).

**Figure 3.** Measured current-voltage characteristics for MWIR HgCdTe (a) p+ BpnN+ and (b) p+ BppN+ barrier detectors operated at 230 K. The experimental data are compared to the theoretical prediction considering overall GR effect and Auger processes.

**Figure 4.** Simulated band diagram for MWIR HgCdTe (a) p+ BpnN+ and (b) p+ BppN+ photodetectors operated at 230 K, unbiased, and under 0.5 V reverse bias.

**Figure 3** presents an example of simulated fitting characteristics of MWIR HgCdTe barrier detectors at a temperature of 230 K. The calculations were made taking into account all considered mechanisms of thermal generation, tunneling, and impact ionization. As we can see, in a wide region of bias voltages, an excellent agreement has been obtained between the experimental and calculated results. What is more, the Auger and the SRH parts of the dark current are clearly visible. The SRH GR process was calculated both for dislocation-free structures and structures containing misfit dislocations. In both types of detectors, the SRH mechanism associated with misfit dislocations has an impact on the dark currents.

**Figure 4** presents the calculated bandgap diagrams of the simulated structures for unbiased and under 0.5 V reverse bias. As expected, the p-type doping of the barrier, with controlled interdiffusion process, and *x*-graded region at the barrier and absorber interfaces introduce a zero offset in the valence band. Bandgap diagrams under reverse bias clearly idicates that in the p+ BpnN+ device a decisive heterojunction is at the barrier and absorber interface while in the p+ BppN+ photodiode at the absorber and highly doped bottom contact layer.

Dislocation-free structures should provide one order of magnitude lower dark currents. For the device with an n-type absorbing layer, saturated dark current is limited by Auger mech‐ anisms. In the case of good-quality p-type HgCdTe, with a reduced number of a structural defect, the influence of exclusion and extraction effects might be more effective than in the ntype material due to a larger diffusion length of electrons than holes. It is apparent that Auger 1 mechanism prevails over Auger 7 mechanism and determines the minority carrier lifetime in intrinsic, n-type, and low-doped p-type materials.
