# TCAD Simulation of a Dual Band Monolithic HgCdTe Infrared Photodetector

**Introduction**

Mercury cadmium telluride (HgCdTe) is a semiconductor material
whose material properties are adjustable through altering its constitutive molar
fractions. HgCdTe has found extensive use in optical detection, and in particular
found wide use in infrared photodetectors over the past few decades. Applications
in this area have been the main driving force for research on this material
and for a good review see [1].

HgCdTe has an adjustable bandgap whose value can be altered by varying the stociometric
ratio of Hg and Cd in the form Hg(1-x)CdxTe. This property enables the detection
of multispectral sources through the creation of multispectral infrared detectors
of various bandgaps and in particular dual band photodetection [2]. Dual band
photodetection in the medium wavelength infrared (MWIR) and long wave infrared
atmospheric windows has been performed using HgCdTe photodiodes [e.g. 3] and
for a recent example see [4]. This simulation standard will demonstrate the
simulation of a dual band HgCdTe monolithic photodetector similar to [4]. The
device is suitable for dual band on pixel registered infrared photodetector
arrays in the atmospheric transmission window of 3-5µm and 8-12µm.

**Device Description and Material Properties**

The device is shown schematically in figure 1(a). The device consists of three layers of HgCdTe material with varying x and hence material bandgap situated on top of an CdTe IR transparent substrate. All HgCdTe layers are doped n type. Radiation between 2-5µm now referred to as MWIR (medium wavelength infrared) will pass through CdTe substrate and will not be absorbed due to the high bandgap energy of the CdTe material but will be absorbed by the HgCdTe material in layer 1. Radiation between 6 - 12µm now referred to as LWIR (long wavelength infrared) will also pass through the CdTe and in this case pass through layer 1 and layer 2 as it has insufficient energy to excite any electrons in these materials. However, radiation will be absorbed in layer 3 due to its smaller energy bandgap. As such it is intended that no LWIR or MWIR radiation be absorbed in layer 2, which has the widest bandgap and is referred to as an insulating layer. A simplified band diagram for the structure is shown in figure 1(b). As shown here, the presence of heterojunctions barriers in the valence band will prohibit the flow of photogenerated minority carriers between layers 1 and layer 3 thus confining them to their respective layers.

Figure 1 (a) Schematic diagram of dual band
monolithic HgCdTe

photodetector. (b) Energy band diagram for layer 1, layer 2 and layer 3.

The bandgap of HgCdTe is a function of the fraction of Cd in the composite material. A number of equations have been developed to summarize the empirically measured relationship and of popular choice is the expression developed by Hansen et al [5] which describes the energy bands in a parabolic form where

(1)

Here T is the temperature in degrees Kelvin and x is the molar
fraction, E_{g} is the material bandgap in eV and x is the fractional
composition value. With varying the value of x, the spectral response can be
tailored to detect varying wavelengths. Consequently in order to detect long
wavelength radiation, x must be altered accordingly resulting in a semiconductor
having a very narrow bandgap. Applied formulae describing effective electron
and hole masses are given in equations (2) and (3) respectively. The electron
and hole mobilities are given by equations (4) and (5) respectively. The static
dielectric constant is given in equation (6).

Here is the effective electron mass,

is the effective hole mass,

µ_{e} is the electron mobility in m^{2}/Vs,
µ_{h} is the hole mobility in m^{2}/Vs and _{s}
is the static dielectric constant.

(2)

(3)

(4)

and (5)

(6)

Recombination models are also important to consider and in this example, Auger and radiative recombination are only considered. These expressions have been determined by Wenus et al [6] and have been used for the simulations presented here.

(7)

and (8)

(9)

The Auger recombination rate for electron and holes is given
in equations (7) and (8) respectively. Optical recombination is expressed using
equation (9). Here R_{Ae} is the Auger electron recombination coefficient
in m^{6}/s, R_{Ah} is the Auger hole recombination coefficient
in m^{6}/s, R_{R} is the radiative recombination coefficient
in m^{3}/s, k is Boltzmann’s constant, q is the electron charge
and ni is the intrinsic carrier concentration.

Of critical importance to modelling the absorption of incident radiation is the absorption coefficient. In general this property should be wavelength dependent in order to give realistic behavior similar to a real device. Direct bandgap semiconductors, such as HgCdTe, have a sharp onset of optical absorption as the photon energy increases above the bandgap of the material. The absorption coefficient used should therefore have similar properties to the material of choice.

(10)

The absorption coefficient is given in [7] and has been used in this work expressed in the form of equation (10). Here a is the absorption coefficient in m-1, l is the incident wavelength in meters, h is Plank’s constant, t is the electron lifetime in seconds, c is the speed of light and lg is the cut-off wavelength determined by the bandgap of the material.

**Device Simulations and Results.**

* ATLAS* has been modified to include
the mathematical definitions of the material parameters set out here. Each expression
has been implicitly coded using the C-interpreter that is an ANSI C compatible
environment consistent within the

*framework. All calculations were performed at 77K. The photodiode was backside illuminated through the transparent CdTe substrate. Surface power density of incident radiation was set to 0.1W/cm*

**ATLAS**^{2}. Each simulation was performed with the LWIR and MWIR electrode held at 0.1V with respect to ground.

Figure 2(a) shows the x compositional value through the device. Figure 2(b) shows the corresponding energy band diagram in eV for the x compositional values as based on equation (1). It is clear that three distinct energy bands are present. Layer 1 which has x=0.21 has the smallest band gap and is suitable for LWIR detection. Layer 3 which has x=0.29 has a larger band gap and is suitable for MWIR detection. Layer 2 has x=0.7 and as such has a significantly larger band gap thus acting as an electrically and optically isolating layer.

Figure 2. (a) One dimensional cutline showing fractional
composition x through device. (b) Corresponding one dimensional cutline
display for the energy band diagram through the device. |

Figure 3 shows the photogeneration of electrons within the device for two different wavelengths. It is clear that two distinct cases are present. At a wavelength of 4.5mm the photogeneration rate is approximately three orders of magnitude higher in the MWIR detector compared to the LWIR detector. As the wavelength is increased to 9.5mm, the photogeneration rate in the MWIR detector is reduced. In contrast to this, the photogeneration rate in the LWIR detector with the lowest fractional compositional of x is seen to increase dramatically. Figure 4 details the spectral response of the device. It is clear that two distinct areas of device responsivity exist. As the wavelength is increased from 0um the current in the MWIR detector increases. This current reaches a maximum at approximately 5um then falls sharply to a smaller value. In contrast, the LWIR response in negligible in the wavelength range 0 to 5 um. As the wavelength is increased further the LWIR detectors response increases and reaches a maximum at approximately 9.5 um. The LWIR current then reduces in a similar fashion as the MWIR detector.

Figure 3. One dimensional cutline showing photo generated
carriers within the LWIR and MWIR detector for 4.5µm and 9.5µm
of incident radiation. |

Figure 4. Spectral response of LWIR and MWIR current as a function of wavelength. |

**Conclusion**

A dual band monolithic HgCdTe material has been successfully
simulated and is shown to be capable of detecting infrared radiation. It is
clear that two distinct bands of radiation, medium wavelength infrared 2-5 um
and long wavelength infrared 5-12 um are easily detectable using the device
described here. Non-standard expressions have been incorporated into the simulation
domain through the use of a ANSI C c-interpreter which has a seamless link with
** ATLAS**. Effective simulations have been incorporating
advanced expressions for recombination mdels as a function of compositional
fraction.

**References**

- Norton P., Optoelectronics review vol. 10, (3) p159-174 (2002).
- Blazejewski E.R., Arias J.M., Williams G.M., McLerige W., Zandian M., Pasko J., J. Vac. Sci. Technol. B., vol. 10, p1626 (1992).
- Reinie M.B., Norton P.W., Starr R., Weiler M.H., Kestigian M., Musicant B.L., Mitra P., Schimert T., Case F.C., Bhat I.B., Ehsani h., Rao V., J. Electron. Matter., vol. 24, p669, (1995).
- Parish G., musca C.A., Siliquini J.F., Dell J.M., Nener B.D., Faraone L., Gouws G.J., IEEE Electron Device Letters, vol. 18, no7, p352-354 (1997).
- Hansen G.L., Schmit J.L., Casselman T.M., J. Appl. Phys. vol 53, p7099-7101 (1982).
- Wenus J., Rutkowski J., Rogalski A., IEEE Trans. On elecron devices, vol. 48, 7, p1326-1332 (2001).
- Hess G.T., Sanders T.J., Newsome G., Fischer T., Modeling and simulation of microsystems, p542-545 (2001).

```
```