We perform first-principles calculations based on density functional theory (DFT) to study the electronic properties of HgCdTe alloys for infrared detection applications. The Heyd, Scuseria, and Ernzerhof (HSE) and the modified Becke-Johnson (mBJ) functionals are employed to predict the bandgap of the ternary alloy over the full composition range. Due to the disordered nature of ternary alloys, we compute the bandgap values by enumerating all distinct atomic arrangements of supercells up to 16 atoms. By using the alloy composition to tune the HSE and mBJ functionals, we show that both functionals successfully produce bandgap values in good agreement with the experimental data. Subsequently, we apply the developed model to study the electronic structure properties of the alloy and its binary compounds under biaxial strain. Our results show that biaxial strain leads to a reduction in the bandgap in CdTe. In contrast, HgTe transitions from a semimetal at its equilibrium geometry to an indirect gap semiconductor under the same strain conditions. For the ternary alloys, we examine alloy compositions for applications in the long and mid-wavelength infrared detection regimes. Strain was applied to 32-atoms representative supercells for Cd compositions of 21 % and 31 %, which were obtained using the Special Quasirandom Structure (SQS) method. For both compositions, all strain configurations lead to a reduction in the bandgap. However, bandgap narrowing exhibits a stronger dependence on the strain magnitude in the case of tensile strain compared to compressive strain.
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