# Design Consideration & Performance Analysis of MCT Based Dual Band (MWIR/LWIR) Photodetector

**Abstract**

In this paper, a physics based two dimensional (2-D) generic model of dual band mid wavelength and long wavelength infrared (MW-LW) photodetector based on HgCdTe has been reported. The paper discusses variants of the back-to-back diode structure, which allows the detected waveband to be selected simply without changing the polarity of the bias. The structure has been designed by exploiting 2D SILVACO software. A closed form model has been developed for electrical and optical characterization of the device. The model includes all the relevant material physics and solution of non-linear decoupled semiconductor transport and Poisson’s equations. The results obtained on the basis of numerical simulation have been validated with the reported analytical and experimental results by the others. Good agreement is found between both.

**Key words:** Dualband, MWIR, LWIR, Hetero-interface, HgCdTe-MCT.

**1. Introduction**

Mercury-Cadmium-Telluride (HgCdTe) is the dominant material for development of high sensitivity infrared photodetectors for military applications, medical imaging, fire control, environment monitoring and surveillance, and amongst other applications. The adjustable energy gap of HgCdTe with sensitivity spanning from short wavelength (SWIR) to very long wavelength (VLWIR) infrared bands enables it for tremendous potential applications to be realized using advance material growth methods and different detectors design. Significant progress has been made towards the growth of unispectral HgCdTe photodetectors in MWIR and LWIR applications during last five decades. The requirement of the new generation of IR detectors is currently under development, e.g. dual band photodetectors, i.e. two color detection simultaneously. Although unispectral photodetectors can serve separately, but two color detectors offer better performance for same applications.

Initially, the problem in development of dual band photodetector with bias selectable device i.e. independent selection of the optimum bias voltage for both photodiode and substantial medium wavelength (MW) crosstalk in the long wavelength (LW) detector.

These problems associated with dual band detector can be solved by optimizing design guidelines and the device parameters. The dual band detector cannot be designed and optimized by using 1D model because several additional physical phenomena needed to define the mechanisms inside the device. It is important to point out that a very few attempts have been made to perform two dimensional (2-D) simulations of these advanced devices. The biggest challenge is to minimize crosstalk effects within the nearest two photodetectors. It is important to develop a physics based model that can quantitively estimate the cross talk and provide useful design guidelines for minimization of cross talk [1] – [2]

**2. Design and 2-D Simulation of MW/LW Dual Band Detector **

Figure 1a shows the two dimensional cross-sectional view of a dual band photodetector consisting of back-to-back photodiodes. The five layer device composed of two HgCdTe p-n junctions with different energy bandgap. A thin layer has been sandwiched between two diodes. The structure has been designed by using ATLAS framework interfaced with BLAZE of the SILVACO (Figure 1b) for electrical characterization. The Luminous module has been used to design a multi-spectral source and for optical characterization. [3].

Figure 1a. Dual Band (MWIR/LWIR) Photodetector Device Structure. |

Figure 1b. Simulated Energy band diagram. |

The bottom P-N junction (upper case indicate wide bandgap material), has grown such that pixel mesa is square with dimension 45×45 µm and mole fraction (x) of Hg_{1-x}
Cd_{x}Te material is taken for cutoff wavelength 4.3µm. The doping concentrations of P- and N-layers are 1×10^{23} m^{-3} and 2×10^{21} m^{-3} respectively. An n-type buffer layer is deposited over P-N junction. The doping density of the buffer layer is taken to be 1×1021 m-3 with mole fraction x=0.345 to minimize the crosstalk between MW band to LW detector. The narrow bandgap n-type layer is deposited on buffer layer with pixel mesa dimension 45×45 µm followed by deposition of p-type layer over it with mesa pixel dimension 45×45 µm. The cut off wave length of LWIR detector has been tuned 10.34 µm by choosing appropriate mole fraction (x) value.

The p-type layer is etched within structure to make common cathode contact to both detectors. The other two anode contacts have been taken on the bottom of P-type and top of p-type materials. The main advantage of this design was to use narrow gap n-type HgCdTe buffer layer to limit the crosstalk between two photodiodes. The selected mole fraction and doping concentration of all the layers ensure the best compromise between requirements of effective absorption of IR radiation and low thermal generation of charge carriers. The light is incident through MWIR detector.

In the simulation of energy band of the heterostructure using ATLAS, it is assumed that the ground state degeneracy of conduction band *g _{c}* and valance band

*g*are 2 and 4 respectively. The analysis of energy band diagram of hetero- junction shows that there is energy offset in the conduction ∆

_{v}*E*and valance band ∆

_{C}*E*, due to electron affinity differences and doping concentration gradient and justifies the application of Anderson’s rule. The formation of potential barrier within heterojunction at the buffer layer can be understood in terms of forces that arise due to gradient in electrostatic potential ∇V and electron affinity ∇χ. The electrons will be the dominant current carriers because the barrier is smaller for electrons as compared to holes. The drop in energy band at n-n heterojunction accompanies the potential variation at interface of the junction. The height of the potential barrier at n-n heterojunction depends on the doping profile of the material. [4]- [5]

_{V}In device characterization, (both electrical and optical) the basic non linear decoupled equations have been solved. Numerical simulation has been done for degenerate semiconductor and non-parabolic shape of conduction band. The results presented in this work are obtained with ATLAS (Blaze 2D) software of SILVACO. The Newton-Richardson iteration technique has been used to solve five nonlinear decoupled equations. The Newton-Richardson based method improves the efficiency of the iteration [3].

The doping of the regions has been taken analytically uniform for all regions in the above simulation. In calculation of mobility the concentration dependent ANALYTIC model has been considered. For the simulation of dark current associated with LWIR p-n heterojunction photodetector, AUGER, SRH and OPTICAL (band-to-band) models have been taken into account for recombination mechanisms. Band-to-band standard tunneling and trap assisted tunneling models have been considered for tunneling mechanism. We have taken into account the Fermi-Dirac statistics for non-parabolic shape of conduction band in all the calculations of carrier and doping densities.

**3. Numerical Simulation**

**3.1 Dark Current**

Basic semiconductor transport equations (continuity equations for holes and electrons) and Poisson’s equations have been used for the numerical analysis. The following equation can be given as [5]

Continuity equation for electrons (1)

Continuity equation for holes (2)

Poisson’s equation (3)

where n and p are the electron and hole concentration,* J _{n}* and

*J*are the electron and hole current densities,

_{p}*G*and

_{n}*G*are the generation rates for electron and holes,

_{p}*R*and

_{n}*R*are the recombination rates for electrons and holes, and q is the magnitude of the charge on the electron. V is the electrostatic potential, ε

_{p}*is the local permittivity and ρ is the local space charge density.*

_{s}The solution of equation (1) to (3) involves drift and diffusion components. The current flowing through each heterostructure photovoltaic dualband detector under consideration has three major components:

i) The diffusion current arising from the minority carriers injected from the each neutral p and n regions;

ii) The drift current arising from generation recombination in the depletion region at the each p -n junction and n-n junctions;

iii) The tunneling current across the p-n heterointerface.

The magnitude of total dark current of the photodetector is [5](4)

**3.2 Spectral Response **

The spectral response of the dual band photodetector has been predicted in terms of quantum efficiency. The quantum efficiency can be obtained by using multilayer approach in which the electric field should be matched at the interfaces and structure is supposed to have number of layers with constant complex refractive index. The inter-diffusion layers at each metallurgical interface with continuous variation in the composition, results in cross talk at these interfaces [4] – [5].

Here, quantum efficiency is defined as the ratio of the number of carriers detected at a given photodetector electrode divided by the number of incident photons on the detector. The absorption coefficient ‘α’ is calculated in terms of complex refractive index of each region separately. Different refractive index files have been used for different composition of the MCT materials. The absorption coefficient plays an essential part in deciding the spectral response of the both MW/LW detectors. The available photocurrent within the device can be calculated with the help of absorption coefficient [3].

**4. Results and Discussion**

The simulation of dualband photodetector uses ATLAS tool in conjunction with Blaze module for developing the structure based on compound semiconductors, for electrical characterization and the Luminous module for optical characterization. In the numerical simulation of various characteristics of the heterojunction dualband photodetector, all the calculations have been done by using appropriate material parameters, dependent on the mole fraction (x) of different Hg_{1-x}CdxTe layers are listed in Appendix 1.1.

Numerical computations have been carried out for electrical and optical characterization of dualband heterojunctions p-Hg_{0.75}Cd_{0.25}Te/n-Hg_{0.775}Cd_{0.225}Te/n-Hg_{0.665}Cd_{0.345}Te/N-Hg_{0.68}Cd_{0.32}Te/P-Hg0.55Cd0.45Te/CdZnTe photodetector at 77K for operation at MWIR region (2-5 µm) and LWIR region (8-14µm) simultaneously. The photons with energy higher than the energy gap create electron-hole pairs in each neutral p and n regions as well as in depletion regions formed at the all metallurgical junction.

Chu’s model [6] has been used to calculate optical absorption coefficients (αn & αp) in determining the imaginary part of the optical index of refraction (k) are given in Appendix 1.1.

The structure under consideration consists of five layers p-n-n-N-P heterostucture based on HgCdTe for MW/LW detection simultaneously is shown in Fig. 1a. The simulated energy band diagram is shown in Fig. 1b. The Anderson type discontinuities have been observed at each hetero-interface. A thin n-type compositional barrier layer is placed between MW and LW absorber layers. This barrier layer forms an n-N heterojunction at the interface. The barrier layer thickness can be optimized such that it would prevent the MW photocarriers from diffusing into the LW absorber layer and prevents LW photocarriers from diffusing into the MW absorber layer. The crosstalk effect between MW and LW bands has been calculated in present model. Under reverse bias photodetector behaves as non-equilibrium device. The analysis has been carried out for non-equilibrium mode by considering quasi-Fermi level into account.

The variation of composition x and doping profile has been depicted in Figure 2. The profile of the electrical potential V across the dualband photodetector at each metallurgical hetero-junction and all neutral regions, in absence of infrared radiation flux and external bias, is shown in Figure 3a. The results have been verified against the theoretical results reported by Rogalski *et. al*., in reference [1].

Figure 2. Simulated Doping & Composition Profile. |

Figure 3a. Simulated Electrical Potential profile in absence of external biasing. |

Figure 3b. Simulated Electrical Field profile in absence of external biasing. |

The electric field associated with the dualband photodetector, gives a perfect triangular shape at each metallurgical junction. The maximum value of electric field (Figure 3b) of the order of 10^{6} V/m is obtained for MW hetero-junction photodetector. A separate peak is observed at n-N isotype hetero-interface due to buffer layer which acts as a barrier in path of carriers diffusing from MW to LW region and vice-versa and minimizes the crosstalk effect. The value of electric field at LW hetero-interface is comparatively low.

The distribution of source photocurrent, available photocurrent (due to absorption of photons) and cathode currents produced within the simulated device has been compared in Figure 4. A multispectral source has also been designed on Luminous platform, for two color detection operation. The power density (P_{opt}) of the source has been kept constant. In the 0.2-10 µm wavelength region source photocurrent and available photocurrent almost overlap on each other. In 0.2-2 µm wavelength region the magnitude of cathode current is almost negligible and shows no influence over available photocurrent. The cathode current increases for the operative wavelength region under zero biasing condition. The available photocurrent suddenly drops after the maximum cutoff wavelength (10.34 µm) of the LW detector because the designing has been done by optimizing the device parameters for operation at MW and LW bands only.

Figure 4. Variation of different currents with operating wavelength. |

The spectral dependence of quantum efficiency, as a function of operating wavelength, for MW and LW photodetector at 77K is shown in Figure 5. It is seen that MW heterojunction P-Hg_{0.55}Cd_{0.45}Te/N-Hg_{0.68}Cd_{0.32}Te photodetector under consideration exhibits almost constant efficiency in entire MWIR region (2.2- 4.3 µm), which is desirable. The maximum internal quantum efficiency exhibited by MW detector is 94%. The quantum efficiency falls very fast beyond the long wavelength cut-off. The LW detector shows almost constant efficiency within wavelength range (4-10.5 µm). The maximum internal quantum efficiency exhibited by LW detector at near cut off wavelength is 86%. The internal quantum efficiency of the both devices has been obtained by rigorous computations. The MW detector shows better spectral response as compared to LW detector. The crosstalk (defined as the ratio of LW available photocurrent to MW available photocurrent in absence of LW radiation) occurs in the LW photodetector, which is less than 4%, and is due to absence of effective barrier for minority carriers (in this case hole of the MW detector. The crosstalk effect has been relatively reduced by optimizing the separation between MW and LW spectral response. A comparison has been made between experimental reported data with the simulation results given in Table 1.

Figure 5. Variation of theoretically computed quantum efficiency with wavelength. |

Table 1. Comparison between experimental data with the theoretically calculated data. |

The simulated results of relative spectral response of designed MW/LW HgCdTe detector have been compared and contrasted with the experimental reported data [2] is shown in Figure 6. The calculated quantum efficiency depends on the dimension of the shorting contact on which common contact is deposited. Small changes in size affect the quantum efficiency significantly. The average cutoff wavelengths of MW and LW detectors at 77K are 4.3 µm and 10.33µm respectively. The crosstalk effect has been reduced in present modeling of MW/LW photodetector because relative quantum efficiency is very low for wavelengths beyond 4.4 µm, which can be clearly seen from the figure.

Figure 6. Variation of normalized quantum efficiency with operating wavelength. |

The theoretically obtained cross talk (< 4%) effect is consistent with the experimental reported value. The MW to LW cross talk has been seen in 4.0-4.8µm wavelength region. The relative quantum efficiency of MW detector in shorter wavelength region is very low because of high recombination rate of the generated photocarriers at the interface between wide-gap P-type layer. The LW relative spectral response increases sharply beyond 4.0 µm. The value of theoretically predicted relative quantum efficiency is close to experimentally measured values for the both MW and LW detectors.

**6. Conclusion**

In present paper, the performance of simultaneous two-color MWIR-LWIR HgCdTe based photovoltaic detector has been simulated numerically using SILVACO software. The photodetector has been designed and optimized for two colors simultaneously detection applications. A numerical simulation technique has been used to solve the system of decoupled nonlinear equations and Poisson equation. The results of the 2-D simulation of dualband detector show that it is possible to predict the performance of complex detector with fairly good accuracy. The LW detector exhibits lower QE because of much of higher noise current density. The analysis of QE shows that the considerable cross talk between MW band and LW band exists. The simulation of the two color heterojunction photodetector provides useful electrical and optical behavior of the device. The model can be used for optimization of HgCdTe based dualband photodetectors for multi spectral detection application. The magnitude of simulated dark current has a very low value near zero bias. The simulated results can be used as design guidelines by the engineers for developing device prototype which in turn will reduce the number of experimental trails required for the development of improved heterojunction photodetectors based on HgCdTe. Finally, the theoretically predicted spectral characteristics are found to be in good agreement with the reported experimental data.

**Appendix 1.1**

A program has been developed for simulation of two dimensional abrupt p-n heterojunction device based on HgCdTe. The formula used in calculations of band gap energy, effective mass, mobilities of charge carriers, electron affinity, and absorption coefficient (using nonparabolic model) as a function of mole fraction (x) of Cd in HgCdTe alloy and temperature are given below.

(5)

(6)

(7)

(8)

(9)

(10)

The effective Richardson constant is defined as

(11)

The Kramers and Kronig interrelations are usually used to estimate the dependence of refractive index on temperature. For Hg_{1-x}Cd_{x}Te with x from 0.276 to 0.540 and temperatures from 4.2 to 300 K, the following empirical formula can be used

(12)

where

A=13.173-9.852x+2.909

x^{2}+(300-T)10^{-3};B=0.83-0.246x-0.0961

x^{2}+(300-T)8e-4;C=6.706-14.437x+8.531

x^{2}+(300-T)7e-4;D=1.953e-4-0.00128x+1.853e-4x

^{2};

Imaginary part of refractive index can be obtained using following relation

(13)

**Absorption Coefficient**

Investigations of the measured absorption coefficient α of Hg_{1-x}Cd_{x}Te near the band edge show that the frequency dependence of α follows a modified Urbach rule of the form [6]

(14)

where

ln α

_{0}= - 18.5 + 45.68x,E

_{o}= -0.355 + 1.77x,δ /kT= (ln α

_{g}- ln α_{0})/(E_{g}- E_{o}),α

_{g}= -65 + 1.88T+ (8694 - 10.31T)x,E

_{g}(x, T) = -0.295 + 1.87x - 0.28x^{2}+ 10^{-4}(6 - 14x+3x^{2})T + 0.35x^{4}

The meaning of the parameter α* _{g}* is that α = α

*when E = E*

_{g}*, the absorption coefficient at the band gap energy. When E < E*

_{g}*, α < α*

_{g}*, the absorption coefficient obeys the Urbach rule in Eq. (14).*

_{g}The spectral dependence of the absorption coefficient α well above Eg can be defined as follows

(15)

where the parameter β depends on the alloy composition and temperature,

β (T, x)= -1 +0.083T+(21-0.13T)x.

**References**

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