Electronic Stopping Power in Ion-Solid Interactions

When energetic ions penetrate a solid, they lose kinetic energy through interactions with the target’s electrons, a process quantified by the electronic stopping power. This quantity denotes the energy dissipated per unit path length as ions induce electronic excitations and ionisations. Its magnitude depends on ion species, charge state and velocity, as well as the electronic structure and density distribution of the solid. In crystalline materials, trajectories that align with crystallographic channels experience reduced stopping compared with random paths, reflecting local variations in electron density and core‐electron contributions. Understanding electronic stopping power is essential for applications ranging from semiconductor doping and surface analysis to radiation shielding and proton therapy dose planning. Traditional semi-empirical models based on the Bethe formula incorporate corrections for carrier density, shell structure and higher-order charge effects, while modern approaches employ real-time time-dependent density functional theory and advanced binary collision codes to resolve non-adiabatic forces, finite-size effects and trajectory sampling challenges. By integrating experimental measurements with first-principles simulations, researchers are now refining predictive accuracy across energy regimes and materials, thereby improving the design of irradiation protocols and the assessment of radiation damage.

Research from Nature Portfolio

Recent studies have employed real-time time-dependent density functional theory to examine proton stopping in organic polymers, revealing that common assumptions of uniform electron density lead to substantial overestimates of stopping power at energies below 2 MeV. These findings challenge the straightforward application of the Bragg rule in complex compounds and underscore the need for spatially resolved electron-density profiles. Another work has explored non-adiabatic effects by coupling Ehrenfest dynamics with electronic excitation, demonstrating that ionisation of shallow core levels can enhance interatomic forces and boost nuclear and electronic stopping beyond adiabatic predictions. This approach highlights the role of transient electronic excitations in modifying atomic interactions during ion transit and opens new avenues for quantifying energy loss in metallic systems.

Electronic Stopping Power in Ion-Solid Interactions publication trend

The graph below shows the total number of articles in electronic stopping power in ion-solid interactions across all publications each year (not limited to Nature Index journals).

Technical terms

Electronic stopping power: The rate at which an energetic ion loses energy to electrons per unit distance travelled in a material.

Time-dependent density functional theory (TDDFT): A first-principles simulation framework that captures real-time electron dynamics under an external perturbation.

Ion channeling: The phenomenon in which charged particles traverse a crystal along low-index directions, experiencing reduced scattering and energy loss.

Adiabatic approximation: An approach that assumes ions move on a fixed electronic ground-state potential, neglecting instantaneous excitations.

Binary collision approximation (BCA): A simulation model that treats ion–atom interactions as a sequence of independent two-body collisions, incorporating parameterised inelastic losses.

References

1. SBETHE: Stopping powers of materials for swift charged particles from the corrected Bethe formula. Computer Physics Communications (2023).
2. Efficient computational modeling of electronic stopping power of organic polymers for proton therapy optimization. Scientific Reports (2024).
3. Stopping power beyond the adiabatic approximation. Scientific Reports (2017).
4. Trajectory sampling and finite-size effects in first-principles stopping power calculations. npj Computational Materials (2023).
5. Assessing trajectory-dependent electronic energy loss of keV ions by a binary collision approximation code. Physical Review Applied (2024).