Pre-equilibrium stopping and charge capture in proton-irradiated aluminum sheets

We present a first-principles study of pre-equilibrium stopping power and projectile charge capture in thin aluminum sheets irradiated by 6–60 keV protons. Our time-dependent density functional theory calculations reveal enhanced stopping power compared to bulk aluminum, particularly near the entrance layers. We propose the additional excitation channel of surface plasma oscillations as the most plausible explanation for this behavior. We also introduce a technique to compute the orbital-resolved charge state of a proton projectile after transmission through the sheet. Our results provide insight into the dynamics of orbital occupations after the projectile exits the aluminum sheet and have important implications for advancing radiation hardness and focused-ion beam techniques, especially for few-layer materials.

Figure 1

Illustration of our simulation cell at a time of 0.75 fs after a proton with a velocity of 1 at. u. impacts a four-layer thick aluminum sheet. A slice of the electron density is overlaid with projected positions of aluminum atoms in gray and the projectile along with its trajectory in red. Electron density has been emitted into the vacuum and captured by the projectile. Dashed yellow lines indicate the aluminum-vacuum boundaries used for calculating the sheet's dipole moment, and the 5 ${\mathrm{a}}_0$ projectile radius [55] used to compare our charge capture method with volume partitioning is indicated by the red dashed circle (see Sec. 3 of this paper and Sec. SIII of Ref. [58]).

Figure 2

Curve fitting used to determine the orbital occupations of the proton projectile and to calculate the charge it captured. Red circles show simulation results for the radial distribution of the electron density around the projectile (1 at. u. of velocity) 1.2 fs after it exits from a four-layer aluminum sheet. Least squares fits to this data using different analytic hydrogen orbitals and a uniform background charge are shown in green, blue, and purple. Radial distributions for analytic $1s, 2s$, and $2p$ hydrogen orbitals are shown in gray; they are scaled by their respective occupations as obtained from the $1s+2s+2p+\mathrm{uniform}$ fit, which describes the simulation results very well.

Figure 3

Electronic stopping as a function of kinetic energy of a proton projectile in a four-layer aluminum sheet (green) is higher than in bulk aluminum (TDDFT results [26] in orange and SRIM data [80] in blue). Inset: Electronic stopping of a 25 keV proton (velocity of 1 at. u.) for different aluminum sheet thicknesses. Dashed lines indicate bulk values from TDDFT [26] (orange) and SRIM [80] (blue). For each sheet, average stopping is computed across the two middle layers as the most bulklike region.

Figure 4

Instantaneous electronic stopping (red) and effective projectile charge state from DDEC6 analysis [70, 71] analysis (blue) for a proton projectile with 1 at. u. of velocity traversing aluminum sheets that are four, six, and eight layers thick (solid, dashed, dotted, respectively). The entrance layer of aluminum atoms is located at 0 ${\mathrm{a}}_0$.

Figure 5

Average electron density located within a 1 ${\mathrm{a}}_0$ radius of the proton's trajectory for the ground-state initial condition (dashed black) and when the proton, approaching with 1 at. u. of velocity, is 3.5 ${\mathrm{a}}_0$ away from impacting a four-layer aluminum sheet (solid red). Dotted blue shows the difference between the average densities just before impact and in the ground state. The positions of the aluminum atoms (proton projectile) are indicated in gray (gold).

Figure 6

Fourier transform of the time-dependent out-of-plane dipole moment in the aluminum sheets after impact by a proton with 1 at. u. of velocity. Only data at least 0.7 fs after the projectile exits the material was analyzed in order to isolate plasma oscillations and exclude contributions from emitted electrons. The dashed (dotted) lines indicate the theoretical (experimental) energies of the bulk and surface plasmons [81, 82, 83].

Figure 7

(a) Total charge captured by the projectile, decomposed into occupations of the $1s$ and $2s+2p$ hydrogen orbitals, after a proton with 1 at. u. of velocity impacts aluminum sheets of different thickness. Error bars indicate standard deviations of these time-dependent values. (b) The same quantities are shown as a function of projectile velocity for protons impacting four-layer aluminum.

Figure 8

Average number of electrons captured by the proton projectile inside (blue triangles) and after exiting (purple squares) a four-layer aluminum sheet. The difference between these two quantities, the number of electrons stripped at the exit-side surface, is shown in orange exes. Error bars indicate standard deviations of the time-dependent quantities.

Figure 9

Time-dependent hydrogen orbital occupations after a proton projectile with 1 at. u. of velocity traverses a four-layer aluminum sheet. The number of electrons within 5 ${\mathrm{a}}_0$ of the projectile is included for reference.