Abnormal radiation resistance via direct-amorphization-induced defect recovery in HgTe

Establishing irradiation resistance inside crystalline semiconductors is crucial for their applications as detectors, electronic devices, and photovoltaics under extreme environments, such as space applications, medicine, and the semiconductor industry.^1,2 The compound semiconductors, such as IIIA–VA indium arsenide (InAs) and IIB–VIA mercury telluride (HgTe), turn out as leading materials for mid- and long-wave infrared sensing, photovoltaics, γ-ray detection, and quantum-dot lighting.³ The Hg_xCd_xTe based narrow-bandgap semiconductors have been widely accredited as spintronic devices, laser diodes, infrared detectors,⁴ and magnetoelectric spin–orbit logic.⁵ In addition, HgTe colloidal quantum dots (CQDs) have shown the capability for the highest infrared spectral absorption tunability that covers a majority of atmospheric windows ranged from short-wave infrared⁶ to terahertz,⁷ thus becoming promising candidates for replacing conventional semiconductors. For space applications, in addition to ionization, energetic particles, such as protons and xenons, can cause non-ionization damage, inevitably resulting in generation of interstitials and vacancies, i.e., Frenkel pairs. These surviving defects, depending on their nature and charge states, can act as recombination or trapping centers to decrease mobility of minority-carriers, thus reducing their non-radiative recombination lifetime, which, in turn, decreases quantum efficiency and increases dark-current density. The search for next-generation radiation tolerant semiconductors becomes crucial for designing modern electronics that are capable of continuously operating within the extreme conditions of space.

In this Letter, we present a multiple computational approach to demonstrate that HgTe is strongly resistant to irradiation damage, in a sharp contrast to general mechanisms for conventional compound semiconductors, such as SiC,^8,9 GaN,¹⁰ GaAs, and InAs.¹¹ The damage simulations were carried out by using the molecular dynamics (MD) code-MOLDY¹² that has been modified for HgTe. We apply the periodic boundary conditions in three directions and ensure that the MD cell is large enough to avoid a displacement cascade overlapping with itself. For instance, a crystal consisting of 681 472 atoms (42 $×$ 42 $×$ 42 unit cells) is required to simulate a displacement cascade with the primary-knock-on atom (PKA) energy of 20 keV. The MD block was first equilibrated at 100 K for about 10 ps so as to establish a uniform temperature distribution,¹¹ and then, a cascade is initiated along a randomly selected direction by assigning a kinetic energy to a PKA. The simulation is allowed to evolve for about 40 ps until the surviving defects and defect clusters remain almost unchanged. The PKA energy ranged from 1 to 20 keV is considered in the present study, and 20 cascade events are simulated for each energy in different recoil directions. The interactions between atoms are modeled by using Stillinger–Weber (SW) potentials developed for II–VI elements Zn-Cd-Hg-S-Se-Te,¹³ as detailed in the supplementary material. A two-phase model was utilized to estimate the melting temperature to be 975 K that is slightly higher than the experimental value 946 K (see Fig. S1 in the supplementary material).

In order to understand the radiation resistance, several displacement cascades are randomly selected to study defect annealing. The damaged crystal is rescaled to 600 K with a Nose–Hoover thermostat¹⁴ in order to control temperature, and the constant number of atoms, constant pressure, and constant temperature (NPT) ensemble is employed to simulate defect annealing with a simulation time extended to ∼10 ns. In order to explore varieties of defect diffusion and radiation resistance mechanism, the climbing image nudged-elastic-band (CI-NEB) method¹⁵ combined with empirical potential and density-functional theory (DFT) (see details in the supplementary material) is further employed for determining the minimum energy pathways and activation energies of defects. In light of experimental non-ionizing energy loss (NIEL) measurements, the advanced NIEL model developed previously¹⁶ is applied to calculate the effective NIEL for HgTe.

The numbers of displaced atoms and antisite defects, generated by a Hg 10 keV cascade, in HgTe are shown in Fig. 1 (Multimedia view), where the insets represent the distributions of displacement atoms at the stages of peak and final damages, as indicated by arrows. The atomic configurations are viewed along the ⟨010⟩ direction on the xz plane (⟨101⟩ and ⟨001⟩ directions for x and z), where the PKA position is indicated by a red triangle and its recoil direction is along ⟨315⟩. The number of displacements increases rapidly initially, reaching a peak at 3.2 ps, after which interstitials and vacancies recombine aggressively, and the surviving defects are attained at about 7.3 ps. The cascade morphology in HgTe is different from that in InAs¹¹ and GaAs,¹⁷ where the multiple damage domains are created along a PKA path, but similar to that in GaN,¹⁰ where a large disordered zone is created. In the central damaged regions, the long-range order (LRO) calculated by the Bragg–William approach¹⁷ is almost zero, revealing that LRO is completely lost. However, the calculated short-range order (SRO)¹⁸ is 0.63 (1.0 in a perfect crystal), which demonstrated that the SRO in the central damaged regions of the crystal is preserved. Here, it is important to emphasize that the defects density within the disordered zone of HgTe becomes much higher than that of GaN,¹⁰ producing an amorphous domain, which significantly impacts defect annealing at high temperatures. The formation mechanism of the amorphous domain in HgTe is consistent with the model of direct-impact amorphization mechanism.¹⁹ The number of surviving defects is presented in Fig. 1(b) as a function of PKA energy, and the total numbers of defects turn out much larger than that predicted by the Norgett–Robinson–Torrens (NRT) model.²⁰ This large discrepancy could be attributed to the formation of large amorphous domains.

Here, we reveal that the damage in HgTe can be annealed out at low temperatures, thus presenting a strongly resistance to amorphization. To accelerate simulations, the damaged samples are annealed at 600 K, and the simulation time has been extended to several nanoseconds. The numbers of surviving defects generated by a typical 2 keV cascade are presented as a function of annealing time in Fig. 2, while the insets display the defect distributions at the annealing times of 0.0 (a) and 3.5 ns (b). The atomic configurations are viewed in the same directions as those in Fig. 1. The PKA position is indicated by the red triangle, and its recoil direction is along ⟨$2¯3¯$1⟩. Initially, the number of defects decreases rapidly (stage I) for the annealing times up to 400 ps, which is followed by a slow recovery stage (II) to reach a steady state within 800 ps. The fast decrease in defects could be attributed to correlated annihilations, while the slow recovery is associated with uncorrelated annihilations of interstitials resided within the cascade volume. The further annealing results in an even slower decrease in defects. After 3.5 ns annealing, the most survived defects are found to be isolated antisites and 11 Frenkel pairs, which are much smaller than 67 predicted by the NRT model. The annealing of 10 keV and 20 keV cascades at 600 K exhibits a similar tendency for defect reduction but requires significant efforts due to much larger MD simulation cells.

In order to understand detailed mechanisms for radiation tolerance in HgTe, a variety of defect migrations and the corresponding minimum-energy paths are determined by using the CI-NEB method, including vacancies, interstitials, and antisite defects. There are two types of tetrahedral interstitials, one surrounded by four Te atoms (denoted as T₁), whereas the other four Hg atoms (T₂), as seen in Fig. S2 in the supplementary material. The energy barrier for both Te and Hg vacancies is above 1.4 eV, and meanwhile, the energy barrier for Te interstitials becomes much higher than that for Hg interstitials. Several low-energy barriers for interstitials, as well as for two vacancies, and their corresponding paths are plotted in Fig. 3. It is particular interesting to know that Hg interstitial is very mobile with a potential barrier as low as 0.28 eV and migrating from one T₁ position to another equivalent T₁ position. However, the NEB calculation for the Hg interstitial migration from one T₂ to another T₂ position is found not converged, and instead, the interstitial transfers to a lower energy configuration of T₁, as shown by the blue curve in Fig. 3. Moreover, the minimum energy path for Te interstitials is also from one T₁ to another T₁ position, and the relevant potential barrier is 0.68 eV. It is important to point out that the most stable configuration for a Te interstitial is close to the middle point along the path from T₂ to T₂. Based on our computations, it is predicted that the interstitials close to Hg atoms suffer a high-energy barrier in their migration. The energy paths as well as energy barriers of Hg defects calculated by DFT are imposed in Fig. 3, as labeled by the notation (DFT), for comparisons. The minimum energy path for a Hg interstitial is found along the path of T₁-T₁ with an energy barrier of 0.23 eV, but the interstitial at T₂ position becomes unstable, transferring to T₁ configuration. These DFT results are fully consistent with our classical NEB computations, thus confirming that Hg interstitials are indeed very mobile in HgTe. As a whole, a Hg interstitial migrates from a T₁ site to another equivalent T₁ site, while a Te interstitial migrates through the T₂–T₂ path without passing through a T₁ site, which verifies our NEB computations with empirical potentials. Turning to annealing simulations in HgTe, the migration of Hg interstitials is observed at the stage I (see the definition above), which is also consistent with the NEB computations, and therefore, the rapid decrease in the number of defects within the amorphous domains can be attributed to the fast migration of Hg interstitials (for annealing time up to 400 ps), but the Te migration occurs for the time range from 400 ps to 3.5 ns at the stage II, giving rise to a further reduction of defects. It is well known that high-mobile interstitials can escape easily from the amorphization-free cascade volume and change into freely migration defects.²¹ These defects can migrate to microstructural imperfections, such as dislocations and grain boundaries, and provide a possible approach for vacancy-driven microstructural changes. However, the damage structures in HgTe prove that multiple-amorphous domains could be produced along a PKA path. These amorphous domains prevent high mobile defects from leaving the cascade volume due to strain field created at the interfaces between amorphous domains and the perfect matrix, thus restricting defects to migrate within the amorphous domains, and consequently, significantly enhancing defect annihilation. In addition to the high mobility of interstitials in HgTe, direct-impact amorphization provides another important driving force for defect fast recovery. The mechanisms for defect annihilation found in the current study are in sharp contrast with those proposed in previous studies and lead to a unified picture for mitigating displacement damage in semiconductors. As noted above, the cascade morphology in HgTe looks similar to that in GaN, where a large disordered zone can form. To validate the results of HgTe, an annealing simulation is also carried out for the damage produced by a 2 keV displacement cascade at 600 K. The preliminary result shows that the damage in GaN cannot be easily annealed out at 600 K, and most defects are survived at the end of 2 ns annealing, which may be attributed to the low mobility of interstitials in GaN. He et al.²² utilized an ab initio method to investigate the properties of nitrogen interstitials in GaN, including their configuration and migration. In GaN, two migration paths, in-plane and out-of-plane, were considered, and the defect migration exhibits an anisotropic behavior with an additional intermediated rotation process. The migration energy of a neutral Ni interstitial is determined as high as 2.34 eV in-plane and 2.40 eV out-of-plane, which explains well why the annealing behavior of defects in GaN is significantly different from that in HgTe.

The NIEL is one of valuable tools to specify the degree of radiation damage and can be employed to mimic the hash space environment using laboratory setup experiments. Based on MD defect density, the advanced NIEL model¹⁶ has been applied to find the effective NIEL for HgTe under incident particles of proton and xenon, and the obtained results are presented in Fig. 4. In the low-energy regime, the effective NIEL goes up rapidly with an increase in incident-particle energy to a maximum, after which it decreases within the high-energy regime. The computed effective NIEL from the primary damage states in HgTe is usually larger than that in other semiconductors,¹¹ which may be ascribed to the formation of unique large amorphous domains in HgTe. However, the effective NIEL after annealing becomes significantly reduced, particularly at low energies. Experimentally, the degree of radiation on materials can be quantified by measuring the minority carrier recombination lifetime (MCRL), which represents the performance of a detector and can be determined empirically. A variety of mid-wave-infrared space detector, based on III–V nBn and II–VI HgTe semiconductor materials, was irradiated by 63 MeV proton with a fluence up to 7.5 $×$ 10¹¹ cm², and the irradiated samples were measured using time-resolved photoluminescence at 120 K.²³ Our damage-annealing study at 295 K reveals that HgTe based detector materials will acquire a nearly 100% recovery, but only about 50% recovery in III–V samples will be reached under the same condition. It is also of interest to point out that the proton and gamma ray radiation testing of HgCdTe avalanche photodiode (APD) arrays showed that most of the radiation damage, both accumulated as the detector was at cryogenic temperature and the newly released damage at room temperature, can be annealed out by heating the device at 85 °C for several hours.²⁴ The current simulations of HgTe are consistent with these experimental observations, demonstrating a significant radiation tolerance of HgTe-based detector to non-ionizing damage.

A multi-scale computer simulation has been performed to understand defect generation and evolution and explore a pathway to mitigate radiation damage in HgTe. The direct-impact amorphization is one of the major mechanisms to produce amorphous domains in HgTe, and the defect density at the primary damage state is much higher than that in other III–V compound semiconductors. The long-time annealing of damage, the NEB computations, and DFT studies of defect migration reveal that HgTe is strongly resistant to radiation damage. Our findings advocate that the direct-amorphization and fast interstitial migration restricted within the amorphous domains provide driving forces for enhancing fast defect annealing, which provides a common mechanism for drastically recovering radiation damage at low temperatures, notably shedding light on fully understanding the role of direct-amorphization on defect evolution. The effective NIEL determined from the primary damage in HgTe is on the same order of magnitude compared with that in InAs and GaN, but it becomes greatly smaller after short-time annealing. HgTe is one of the most radiation resistant compound semiconductors for detector and high-power applications, and its performance may surpass InAs and GaN for long-term operation in space environments.

See the supplementary material for the details of interatomic potentials used, simulation of melting temperature, DFT approach, and possible interstitial positions in HgTe. In addition, the animation shows the defect generation process in a Hg 10 keV cascade.

This research was supported by Contract No. FA9453-15-1-0084 of the Air Force Research Laboratory. D.H. would like to thank the Air Force Office of Scientific Research for support. Q.P. would like to acknowledge the support by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum Minerals through Project No. DF201020.