Ab Initio Simulation of Low‑Energy Radiation Response in Si, Ge, and Si/Ge Superlattices

Background

In recent years, the Si/Ge superlattice has emerged as a versatile platform for next‑generation electronic and optoelectronic devices, driven by its tunable band structure and enhanced carrier mobility. Applications span fast photodiodes for optical communication, microelectronics, solar cells, and space‑borne components. However, exposure to high‑energy ions in space can alter the optical and electronic properties of these materials, leading to device degradation. Consequently, understanding the radiation response of Si/Ge SLs under extreme conditions is essential.

Experimental work has documented the superior radiation resistance of Si/Ge SLs compared to bulk Si. For instance, electron irradiation studies on monolayer Ge‑embedded SLs showed reduced photoluminescence degradation relative to bulk silicon, while 2 MeV proton irradiation of Ge quantum‑dot‑in‑SL structures revealed exceptional tolerance. Similar trends were observed in Ge quantum‑well devices on Si/Ge multilayers and in thermoelectric measurements, where ion fluence increased the figure of merit by enhancing phonon scattering and electronic transport. Despite these insights, a comprehensive atomistic understanding of defect formation and evolution in Si/Ge SLs remains lacking.

Ab initio molecular dynamics (AIMD) offers a powerful tool for probing radiation damage at the atomic scale, providing interatomic potentials derived from first‑principles electronic structure calculations. Unlike classical MD, AIMD captures charge transfer and electronic screening effects, enabling accurate determination of threshold displacement energies (E_d) and defect configurations. In this work, we employ AIMD to compare low‑energy displacement events in bulk Si, bulk Ge, and a Si₂/Ge₂ SL, identify the mechanisms underlying their distinct radiation behaviors, and quantify defect formation and migration energetics.

Methods

The displacement cascades were simulated with the SIESTA code. Norm‑conserving Troullier‑Martins pseudopotentials described the ion–electron interaction, while the local‑density approximation (LDA) in the Ceperley–Alder parameterization treated exchange‑correlation effects. Valence states were expanded in a single‑ζ plus polarization (SZP) basis set, with a 1 × 1 × 1 k‑point mesh and a 60 Ry cutoff. The model supercell for the SL comprised 288 atoms arranged in two Si layers alternating with two Ge layers (Si₂/Ge₂). Figure 1 illustrates the geometries of bulk Si and the Si/Ge SL.

A primary knock‑on atom (PKA) was selected and given kinetic energy to initiate a recoil event. If the PKA returned to its lattice site, the simulation was repeated at a higher energy with 5 eV increments; once the PKA remained displaced, the threshold was refined to 0.5 eV precision. For each element, we examined four to five crystallographic directions in the bulk and SL. All runs used the NVE ensemble and were limited to 1.2 ps to avoid numerical instability.

Schematic view of geometrical structures of a bulk Si and b Si/Ge superlattice. The blue and green spheres represent Si and Ge atoms, respectively.

Results and Discussion

The Displacement Events in Bulk Silicon and Germanium

Our AIMD calculations yielded lattice constants of 5.50 Å for bulk Si (matching the experimental 5.43 Å and theoretical 5.48 Å) and 5.71 Å for bulk Ge (in line with the experimental 5.77 Å and theoretical 5.65 Å). Table 1 summarizes the threshold displacement energies (E_d) and the resulting defect structures, while Figures 2 and 3 depict the damage configurations for Si and Ge, respectively.

a–d Schematic view of geometrical structures of damage Si after recoil events. The green and red spheres denote vacancy and interstitial defects, respectively. V_Si: silicon vacancy; Si_int: silicon interstitial.

a–d Schematic view of geometrical structures of damage Ge after recoil events. The red and blue spheres represent vacancy and interstitial defects, respectively. V_Ge: germanium vacancy; Ge_int: germanium interstitial.

For bulk Si, the calculated E_d values are close to experimental measurements: 21 eV for [001], ~47.6 eV for [110], and ~12.9 eV for [111]. The primary defect type in all cases is a Frenkel pair (vacancy plus interstitial). Our E_d for [110] (47 eV) exceeds the classical MD value (24 eV), reflecting the inclusion of charge‑transfer effects in AIMD. The displacement mechanisms vary: along [111], the PKA scatters to an interstitial site while the displaced atom returns to its lattice site; along [001], a more complex sequence of exchanges produces two vacancies and two interstitials; and along [110], multiple collisions lead to a cluster of Frenkel pairs. These results confirm that the [110] direction is the most resistant to displacement in bulk Si.

Bulk Ge shows E_d values that align well with experiment and theory: ~18 eV for [001] and 9.5 eV for [111] and [1 1 1]. Displacement along [111] yields a simple interstitial formation, whereas along [110] the PKA exchanges positions with a neighboring Ge atom, creating one vacancy and one interstitial. As in Si, the [110] direction is the most difficult to displace. The overall defect landscape in bulk Si and Ge is dominated by Frenkel pairs.

The Displacement Events in Si/Ge Superlattice

We investigated the Si₂/Ge₂ SL by selecting PKA atoms adjacent to the Si/Ge interface. Table 2 lists the E_d values and associated defects, while Figures 4 and 5 illustrate the resulting configurations.

a–d Schematic view of geometrical structures of damage Si/Ge superlattice after Si recoil events. Blue and green spheres denote Si and Ge atoms; purple and red spheres represent vacancy and interstitial defects. V_X and X_int indicate vacancies and interstitials (X = Si or Ge), while X_Y shows an atom occupying a Y lattice site.

a–e Schematic view of geometrical structures of damage Si/Ge superlattice after Ge recoil events. Blue and green spheres denote Si and Ge atoms; purple and red spheres represent vacancy and interstitial defects. V_X and X_int indicate vacancies and interstitials (X = Si or Ge), while X_Y shows an atom occupying a Y lattice site.

In the SL, Si atoms are highly resistant along the [1 1 1] direction (E_d = 10 eV), while Si[001] and Si[00 1̅] require 46.5 eV and 42.5 eV, respectively, and generate complex antisite clusters. Ge atoms in the SL retain low E_d values along [111] and [1 1 1̅] (≈16 eV) similar to bulk Ge, but display higher thresholds along [001] (≈17 eV) and [00 1̅] (≈18 eV). Importantly, Ge[110] in the SL has a reduced E_d (8.5 eV) and yields a mixed defect cluster (vacancy, antisite, interstitial). These findings confirm that the SL enhances radiation resistance for Si and, to a lesser extent, for Ge, in agreement with previous experimental observations.

The Defect Formation Energy and Migration Barrier in Bulk Si, Ge, and Si/Ge Superlattice

We computed defect formation energies for vacancies, interstitials, and antisites in bulk Si, bulk Ge, and the SL using a 64‑atom supercell, 6 × 6 × 6 k‑point sampling, and a 500 eV cutoff. The results, shown in Table 3, indicate that V_Si (3.60 eV) and V_Ge (2.23 eV) are the most favorable defects in their respective bulk materials, whereas the SL displays slightly higher formation energies for most defects, with V_Ge (2.73 eV) and V_Si (2.85 eV) still being the lowest.

Migration barriers were evaluated for V_Ge and V_Si adjacent to the SL interface using the nudged elastic band method (Table 4). Vacancies migrate more readily along the [111] direction in both bulk and SL, but the barriers are consistently lower in the bulk (e.g., V_Si along [111]: 0.11 eV in bulk vs 0.12 eV in SL). In contrast, migration along [100] and [110] shows modest differences. These results suggest that vacancy mobility is suppressed in the SL, which could reduce defect clustering and swelling under irradiation.

Conclusions

Our AIMD investigation demonstrates that the displacement threshold energies in bulk Si and Ge are strongly anisotropic, with the [110] direction being the most resistant. In the Si/Ge SL, Si atoms exhibit enhanced resistance along [111] and [001] directions, while Ge atoms maintain bulk‑like thresholds except for a reduced value along [110]. Defect formation energies confirm that point defects are more difficult to create in the SL, and migration barriers indicate reduced vacancy mobility, especially along the most favorable [111] direction. These combined effects underpin the superior radiation tolerance of Si/Ge superlattices, making them attractive for devices that must endure harsh radiation environments.

Abbreviations

AIMD:

Ab initio molecular dynamics

E_d :

Threshold displacement energy

FP:

Frenkel pair

Ge:

Germanium

Ge_int :

Germanium interstitial

Ge_Si :

Germanium occupying the silicon lattice site

LDA:

Local‑density approximation

MD:

Molecular dynamics

NVE:

Microcanonical ensemble

PKA:

Primary knock‑on atom

PL:

Photoluminescence

QD:

Quantum dot

QW:

Quantum well

Si:

Silicon

SIESTA:

Spanish Initiative for Electronic Simulations with Thousands of Atoms

Si_Ge :

Silicon occupying the germanium lattice site

Si_int :

Silicon interstitial

SL:

Superlattice

SZP:

Single‑ζ basis sets plus polarization orbital

V_Ge :

Germanium vacancy

V_Si :

Silicon vacancy