Unlocking extreme doping and strain in epitaxial monocrystalline silicon

Hyperdoping, overcoming the solubility limit of dopants in a crystalline semiconductor, is a fertile method for the enhancement of the electrical, structural and optical devices’ performances and for the exploration of exotic phases such as superconductivity. We demonstrate an unprecedented control on the dopant concentration and lattice deformation via nanosecond laser doping in epitaxial boron doped silicon, achieving record carrier concentrations (8 at.%) and lattice deformations (3 %). Probing the microscopical hyperdoping limitations, we show that the relevant mechanisms are caught by a simple combinatorial model, which quantitatively explains both the experimental carrier concentration and lattice deformation evolution. First principle calculations complete and support such simple model. Indeed, at the high doping levels now attainable, the maximum carrier concentration is inherently limited by the probability of two or three substitutional dopants occupying neighboring lattice sites, forming partially inactive complexes that we detail. This description is valid in the case of perfect layers with no crystallographic defects and a fully substitutional dopant occupation, highlighting the quality of the epitaxial layers realized.

💡 Research Summary

The authors present a comprehensive study on achieving unprecedented levels of boron (B) hyperdoping and associated lattice strain in epitaxial monocrystalline silicon using Gas Immersion Laser Doping (GILD). By exposing a (100) n‑type Si surface to saturated BCl₃ chemisorption and subsequently melting the surface with a 308 nm, 25 ns excimer laser pulse, they create a thin liquid layer whose depth (20–315 nm) is precisely controlled by the laser fluence. In the liquid phase, B diffuses extremely fast (D ≈ 10⁻⁴ cm² s⁻¹) and is trapped during rapid solidification (≈4 m s⁻¹), resulting in a homogeneous, fully substitutional B distribution. Repeating the laser pulse N times (1–700) linearly increases the total B dose, allowing the authors to reach total atomic concentrations C_B up to 8 at.% (≈4 × 10²¹ cm⁻³) while preserving a vertical homogeneity of ±13 % and an interface width of only a few nanometres, as confirmed by SIMS and STEM.

Electrical characterization via Hall measurements on patterned Hall crosses shows that the hole concentration h follows the B concentration almost linearly up to h ≈ 4 × 10²¹ cm⁻³, corresponding to a 100 % activation efficiency (Hall factor γ ≈ 0.7). This performance surpasses that of conventional ion‑implantation followed by rapid thermal annealing (RTA), flash‑lamp annealing (FLA), non‑melting laser annealing (NLA), and even molecular‑beam epitaxy (MBE), which typically exhibit activation efficiencies of 10–60 % at comparable B levels. However, beyond a total B concentration of roughly 5–7 × 10²¹ cm⁻³, the hole concentration saturates, indicating an intrinsic limit to electrical activation.

To explain this saturation, the authors develop a simple combinatorial (binomial) model. Assuming a random distribution of B atoms on the Si lattice, the probability that a given B atom is isolated (i.e., surrounded by four Si atoms) is (1 − p)⁴ with p = C_B/n_Si (n_Si ≈ 5 × 10²² cm⁻³). The concentration of isolated B monomers is therefore B₁ = C_B·(1 − p)⁴. This expression reproduces the experimental h(C_B) curve with less than 5 % deviation up to the onset of saturation, confirming that isolated substitutional B atoms are the sole contributors to free holes. As C_B increases further, the probability of two or three B atoms occupying neighboring lattice sites becomes non‑negligible, leading to the formation of B₂ (dimers) and B₃ (trimers) complexes that are electrically inactive. The non‑active B concentration C_NA = C_B − h follows a quadratic dependence on C_B, consistent with a dominant dimer contribution.

First‑principles density‑functional theory (DFT) calculations complement the statistical model. By constructing random B configurations and evaluating formation energies for complexes containing up to three B atoms within the first (S₁) and extended (S₁.₅) neighbor shells, the authors find that dimers and trimers have relatively low formation energies, especially when a modest B mobility (allowing hopping between first and second nearest neighbours) is permitted. The DFT‑predicted concentrations of B₁, B₁ + B₃, and B₁ + B₂ + B₃ match the experimental data when the diffusion shell S₁.₅ is considered, confirming that the observed activation limit is fundamentally a geometrical constraint rather than a kinetic one.

Structural analysis via X‑ray diffraction (XRD) and scanning transmission electron microscopy (STEM) reveals a linear increase of lattice strain with B content, reaching up to 3 % tensile deformation. This strain originates from both active substitutional B atoms and the inactive B complexes, the latter contributing additional lattice distortion without providing carriers. Thin layers (≈20 nm) remain fully pseudomorphic and defect‑free, whereas thicker layers (≈170 nm) exhibit partial relaxation, cellular breakdown, and the emergence of B‑rich columnar defects at the interface. At the highest doping levels, B‑rich precipitates are observed at the Si:B/Si interface, consistent with the onset of the saturation regime.

In summary, the paper demonstrates that (i) GILD enables controlled incorporation of boron up to 8 at.% with excellent compositional uniformity, (ii) a simple binomial model accurately predicts the carrier concentration and strain evolution by accounting for the statistical occurrence of neighboring B atoms, (iii) DFT calculations validate the formation of electrically inactive B dimers and trimers as the primary mechanism limiting activation, and (iv) the identified “geometrical limit” is intrinsic to the crystal lattice and persists even in the absence of extrinsic defects. These findings provide a universal framework for understanding hyperdoping limits in group‑IV semiconductors and open pathways toward ultra‑low‑resistance contacts, mid‑infrared plasmonics, and potentially superconducting silicon‑based platforms.