Three-dimensional modeling of resonant charge transfer between ion beams and metallic surfaces

This study addresses the numerical modeling of resonant charge transfer (RCT) during ion-surface interactions. In our approach we use the original ab initio three-dimensional (3D) time-dependent Schrödinger equation solver in combination with 3D pseudopotentials, which describe the metal structure on the atomic level. Full 3D modeling enables us to reveal such fundamental RCT aspects as anisotropy of electron propagation in the target and electron delay during grazing scattering. We have also refined the theoretical basis for RCT experiments calculations and achieved quantitative correspondence to a large variety of experimental data.

Figure 1

Cu(100), Cu(110), and Cu(111) pseudoponetial dependence on the $Z$ coordinate. One-dimensional pseudopotentials referred to as “Jennings et al.” and “Chulkov et al.” are taken from Refs. [35, 36], respectively.

Figure 2

Comparison of electron decay for ${\mathrm{H}}^{-}$ fixed at distance $Z$ in front of different surfaces (see legend for details). Upper figure shows the energy spectra, lower, the dependence of ${\mathrm{H}}^{-}$ occupation on time.

Figure 3

Illustration of main RCT aspects (details are given in the text).

Figure 4

Ions’ outer electron density distribution in 2D $k$ space inside the target. Left: ${\mathrm{H}}^{-}$ near Cu(110) surface. Right: $\mathrm{L}{\mathrm{i}}^0$ near Ag(111) surface. Ion-surface distance is 7 a.u., interaction time is 100 a.u. Inset illustrates frame transformation (details are given in the text).

Figure 5

Ion-level occupation (population) and decay rate for different systems (see legend for details). The projectile velocity is 0.2 a.u. (1 keV).

Figure 6

Evolution of electron density for Cu(100), left side, and Cu(110), right side. Ion-surface distance is 12 a.u. Figure shows isosurfaces of electron density at sequential time moments (see figure for details). The inset in the center shows electron density distribution in the first surface layer of Cu(110).

Figure 7

Upper: comparison of hydrogen anion decay for different pseudopotentials and surfaces (see legend for details). The figure shows ${\mathrm{H}}^{-}$ ion population as a function of time. Ion-surface distance is 12 a.u. Lower: surface state energy comparison for 1D and 3D pseudopotentials (see legend for details). Ion-surface distance is 47 a.u.

Figure 8

Illustration of electron delay effect with 3D pseudopotential usage. Upper, electron density distribution at $t=150\mathrm{a}.\mathrm{u}.$ for 3D pseudopotential. Lower: ${\mathrm{H}}^{-}$ population as a function of distance from the surface for 3D and 1D pseudopotentials. The ${\mathrm{H}}^{-}$ ion moves away from the Cu(111) surface with $V_{\mathrm{norm}}=0.02\mathrm{a}.\mathrm{u}.$; initial ion-surface distance is 5 a.u. For the upper picture $V_{\mathrm{par}}=0.5\mathrm{a}.\mathrm{u}.$; for the lower picture calculations with different $V_{\mathrm{par}}$ are presented (see $\text{``}v\text{""}$ value in legend). The outgoing trajectory was chosen because it is often used for RCT experiments calculations.

Figure 9

Influence of ion beam energy and orientation on RCT character. Figure shows ${\mathrm{H}}^{-}$ ion population dependence on ion-surface distance for different azimuthal angles [close to $\langle 1\overline{1}0\rangle$ and $\langle 001\rangle$ directions in the Cu(110) crystal] and ion velocities ($V_{\mathrm{par}}=0.5\mathrm{a}.\mathrm{u}.$ vs $V_{\mathrm{par}}=0.25\mathrm{a}.\mathrm{u}.$). The ${\mathrm{H}}^{-}$ ion moves away from the Cu(110) surface with $V_{\mathrm{norm}}=0.02\mathrm{a}.\mathrm{u}.$; initial ion-surface distance is 7.6 a.u.

Figure 10

Comparison of calculation results with experimental data [7]. Figure shows ${\mathrm{H}}^{-}$ fraction as a function of exit angle. The axes scales are chosen according to the original experimental article. Energy of the primary ${\mathrm{H}}^{+}$ ion beam is 1 keV.

Figure 11

${\mathrm{H}}^{-}$ outer electron density distribution in 2D $k$ space inside the Cu(111) for different ion-surface distances.

Figure 12

Comparison of calculation results with experimental data [8]. Figure shows ${\mathrm{H}}^{-}$ fraction as a function of exit angle for several different energies of the primary ion beam (see legend for details). The axes scales are chosen according to the original experimental article. The incidence angle of the primary ${\mathrm{H}}^{+}$ ion beam is 40° to the surface.

Figure 13

Comparison of calculation results with experimental data [5]. Figure shows the $\mathrm{L}{\mathrm{i}}^0$ fraction as a function of primary ion beam energy. The incidence angle of the primary $\mathrm{L}{\mathrm{i}}^{+}$ ion beam is 45° to the surface. Spectra of scattered Li atomic particles ($\mathrm{L}{\mathrm{i}}^{+}$ and $\mathrm{L}{\mathrm{i}}^0$) are measured along the normal to the surface.

Figure 14

Comparison of calculation results with experimental data [6]. Figure shows the $\mathrm{L}{\mathrm{i}}^0$ fraction as a function of primary ion beam energy for different surfaces (see legend). The incidence angle of the primary $\mathrm{L}{\mathrm{i}}^{+}$ ion beam is 45° to the surface. Spectra of scattered Li atomic particles ($\mathrm{L}{\mathrm{i}}^{+}$ and $\mathrm{L}{\mathrm{i}}^0$) are measured along the normal to the surface.

Figure 15

Comparison of calculation results with experimental data [11, 52]. Figure shows a fraction of ${\mathrm{H}}^{-}$ ions, scattered from Al(111) surface, as a function of the primary ion beam parallel velocity value. The normal velocity of the primary ${\mathrm{H}}^{+}$ ion beam is 0.02 a.u.

Figure 16

Comparison of calculation results with experimental data [3, 4, 30]. Figure shows a fraction of ${\mathrm{H}}^{-}$ ions, scattered from the Cu(111) surface, as a function of the primary ion beam parallel velocity value. The normal velocity of the primary ${\mathrm{H}}^{+}$ ion beam is 0.02 a.u.

Figure 17

Illustration of electron propagation anisotropy influence on RCT and ${\mathrm{H}}^{-}$ fraction azimuthal dependence (details are given in the text). Inset shows ${\mathrm{H}}^{-}$ outer electron density distribution in 3D $k$ space inside the Cu(110).

Figure 18

Comparison of calculation results with experimental data [3, 4, 30]. Figure shows a fraction of ${\mathrm{H}}^{-}$ ions, scattered from the Cu(110) surface, for different parallel velocity values of the primary ion beam. The normal velocity of the primary ${\mathrm{H}}^{+}$ ion beam is 0.02 a.u. Calculations 1: data for the $\langle 1\overline{1}0\rangle$ azimuthal direction; Calculations 2: data for $\langle 001\rangle$.