Figure 1

Contour map of the (a) equilibrium charge-density distribution $n_0\left(\mathbf{r}\right)$ of valence electrons and (b) potential energy $v_s\left(\mathbf{r}\right)$ for an electron near the Al(100) surface. The $x$ axis is oriented along the $\left[011\right]$ crystal-surface direction and the $z$ axis along the $\left[100\right]$ crystal-surface direction. The contour-line spacing is $0.003$ a.u. in (a) and $-0.086$ a.u. in (b).Reuse & Permissions

Figure 2

(a) Surface Brillouin zone (SBZ) for the unreconstructed Al(100) surface with the three high-symmetry end points $\overline{\Gamma }$, $\overline{X}$, and $\overline{M}$. The main crystallographic directions are along $\overline{\Gamma }\overline{X}$ ([011]) and $\overline{\Gamma }\overline{M}$ ([001]). The edge length of the square Brillouin zone is $2\pi /a_{\left|\right|}=1.16$ a.u., where $a_{\left|\right|}=a_0/\sqrt{2}=5.41$ a.u. is the lattice spacing between Al ionic cores along the $\left[011\right]$ direction. The Cartesian coordinates of the high-symmetry points are $\overline{\Gamma }=(0.00,0.00)$, $\overline{X}=(0.58,0.00)$, and $\overline{M}=(0.58,0.58)$. (b) Band structure ${\varepsilon }_n={\varepsilon }_n\left({\mathbf{k}}_{\left|\right|}\right)$ of the Al(100) surface on a triangle in the SBZ. The crystal momentum ${\mathbf{k}}_{\left|\right|}$ is varied along straight lines connecting the end points $\overline{\Gamma }$, $\overline{X}$, and $\overline{M}$.Reuse & Permissions

Figure 3

Probability density of the orthogonalized AL orbital near an Al(100) surface. The position of the first surface layer $z=0$ is indicated by the dashed line. The projectile (open circle) is at the distance $D=3.5$ a.u. in front of the first surface layer and on top of an Al-ionic core. The positions of a few substrate ionic cores in the first and second surface layers are indicated as dots. The $x$ axis is oriented along the $\left[011\right]$ direction and the $z$ axis along the $\left[100\right]$ direction.Reuse & Permissions

Figure 4

(a) Density of states ${\rho }_a^0(\varepsilon ,D)$ projected onto the H${}^{-}$ AL interacting with an Al(100) surface in fixed-ion approximation. Virtual transitions to the continuum of ionized metal states are neglected. (b) Energy $E_{\mathrm{AL}}^0$ and (c) decay width ${\Gamma }_{\mathrm{AL}}^0$ of the AL resonance in fixed-ion approximation. (d) Density of states ${\rho }_a(\varepsilon ,D)$ projected onto hydrogen AL interacting with an Al(100) surface in fixed-ion approximation. Virtual transitions to the continuum of ionized metal states are included. The energy $E_{\mathrm{AL}}^{\left(\text{LL}\right)}$ and level width ${\Gamma }_{\mathrm{AL}}^{\left(\text{LL}\right)}$ of the long-lived AL resonance are indicated by the upward pointing triangles in (e) and (f), respectively. The energy $E_{\mathrm{AL}}^{\left(\text{SL}\right)}$ and decay width ${\Gamma }_{\mathrm{AL}}^{\left(\text{SL}\right)}$ of the short-lived AL resonance are given by the inverted triangles. The position of the Fermi level is indicated by the solid line in (a), (b), (d), and (e). The dashed curve in (b) and (e) shows the image-potential-shifted energy of the H${}^{-}$ AL ${\varepsilon }_a\left(D\right)$.Reuse & Permissions

Figure 5

(a) Chemisorption shift ${\Lambda }_0\left(\varepsilon \right)$ (45) and width ${\Delta }_0\left(\varepsilon \right)$ (44) functions for the H${}^{-}$ AL near an Al(100) surface in fixed-ion approximation. The ion-surface distance is $D=4$ a.u.. Virtual transitions to the continuum of ionized metal states are neglected. (b) Renormalized chemisorption shift $\Lambda \left(\varepsilon \right)=\mathrm{Re}{\Sigma }_{aa}$ and width $\Delta \left(\varepsilon \right)=-\mathrm{Im}{\Sigma }_{aa}$ functions for the hydrogen AL resonance including virtual transitions to the continuum of ionized metal. The dot in (a) and (b) indicates the approximate energy of the hydrogen AL resonance, as determined by solutions of the equation $\varepsilon -{\varepsilon }_a={\Lambda }_0\left(\varepsilon \right)$ and by $\varepsilon -{\varepsilon }_a=\Lambda \left(\varepsilon \right)$, respectively. The dashed lines in (a) and (b) specify the position of the Fermi level ${\varepsilon }_F=-0.15$ a.u.. The dotted straight lines in (a) and (b) indicate the transition frequencies $\varepsilon -{\varepsilon }_a$. Panels (c),(d) give the unperturbed ${\rho }_a^0\left(\varepsilon \right)$ and renormalized ${\rho }_a\left(\varepsilon \right)$ densities of states projected onto the hydrogen AL, respectively.Reuse & Permissions

Figure 6

Inverse dielectric function ${\epsilon }^{-1}\left(\varepsilon \right)$ for the H${}^{-}$ AL near an Al(100) surface in fixed-ion approximation. The ion-surface distance is (a) $D=4$ a.u., (b) 3 a.u., (c) 2 a.u., and (d) 1 a.u.. The real and imaginary parts of the distribution are indicated by the dashed and solid lines, respectively. The vertical solid line indicates the position of the Fermi level ${\varepsilon }_F=-0.15$.Reuse & Permissions

Figure 7

Time-dependent tunneling density of states $S(\varepsilon ,t)$ for hydrogen atoms normally incident on an Al(100) surface and backscattered as H${}^{-}$ with velocities (a) $v_n=0.02$ (corresponding to a collision energy of 10 eV), (b) $0.045$ (50 eV), (c) $0.1$ (250 eV), and (d) $0.4$ a.u. (4 keV). The time of closest approach to the surface is indicated by the vertical dashed line.Reuse & Permissions

Figure 8

Transient H${}^{-}$ fractions near an Al(100) surface for normally incident hydrogen atoms with impact velocities (a) $v_n=0.02$, (b) $0.045$, (c) $0.1$, (d) $0.4$ a.u., and corresponding collision energies $E$. The time of closest approach to the surface is indicated by the vertical dashed lines.Reuse & Permissions

Figure 9

H${}^{-}$ fraction for H atoms reflected off an Al(100) surface as a function of the exit velocity $v_n$ at normal incidence. The collision energy $E$ is given on the top horizontal axis.Reuse & Permissions

Figure 10

Initial-state-resolved momentum distributions of valence electrons $\sigma (a\leftarrow {\mathbf{k}}_{\left|\right|})$ [Eq. (51)] for normally incident hydrogen atoms backscattered on an Al(100) surface as H${}^{-}$ with exit velocities (a) $v_n=0.4$, (b) 0.2, (c) 0.1, and (d) 0.045 a.u., corresponding to collision energies $E=4000$, 1000, 250, and 50 eV, respectively. The three high-symmetry points in the SBZ are indicated in (a).Reuse & Permissions

Figure 11

Transient H${}^{-}$ fractions for grazingly incident hydrogen atoms specularly reflected on a Al(100) surface along the $\left[001\right]$ crystal-surface direction with kinetic energies (a) $E=1$ keV, (b) 2 keV, (c) 3 keV, and (d) 6 keV, corresponding to parallel velocities $v_{\left|\right|}=0.19$, 0.28, 0.34, and $0.49$ a.u., respectively. The angle of incidence is $\theta =8^{\circ }$ in (a), $5.6^{\circ }$ in (b), $4.6^{\circ }$ in (c), and $3.3^{\circ }$ in (d). The incident and outgoing parts of the trajectory are indicated by the arrows in (a).Reuse & Permissions

Figure 12

Asymptotic tunneling density of states $S(\varepsilon ,t\to \infty )$ projected onto the hydrogen AL [cf. Eq. (16)]. Results for grazingly incident hydrogen atoms that are specularly reflected on an Al(100) surface along the $\left[001\right]$ crystal-surface direction with kinetic energies (a) $E=1$ keV, (b) 2 keV, (c) 3 keV, and (d) 6 keV, corresponding to parallel velocities $v_{\left|\right|}=0.19$, 0.28, 0.34, and $0.49$ a.u., respectively. The angle of incidence is $\theta =8^{\circ }$ in (a), $5.6^{\circ }$ in (b), $4.6^{\circ }$ in (c), and $3.3^{\circ }$ in (d). The position of the Fermi level is indicated by the vertical solid lines.Reuse & Permissions

Figure 13

H${}^{-}$ fractions as a function of the parallel velocity $v_{\left|\right|}$ for incident H atoms that are specularly reflected on an Al(100) surface along the $\left[001\right]$ crystal-surface direction with fixed exit-velocity component normal to the surface $v_n=0.028$ a.u.. The corresponding collision energies $E$ and the incidence angles $\theta$ are indicated along the top horizontal axis.Reuse & Permissions

Figure 14

Initial-state-resolved valence-electron distribution $\sigma (a\leftarrow {\mathbf{k}}_{\left|\right|})$ for grazingly incident hydrogen atoms reflected as H${}^{-}$ on an Al(100) surface with kinetic energies (a) $E=500$ eV, (b) 2 keV, (c) 4 keV, and (d) 6 keV, corresponding to parallel velocities $v_{\left|\right|}=0.14$, 0.28, 0.39, and 0.49 a.u., respectively. The angles of incidence are (a) $\theta =11.5^{\circ }$, (b) $5.6^{\circ }$, (c) $4^{\circ }$, and (d) $3.3^{\circ }$. The high-symmetry points in the SBZ are indicated in (d). The arrows show the surface-projected collision velocity ${\mathbf{v}}_{\left|\right|}$.Reuse & Permissions

Figure 15

Surface-orientation dependence of the H${}^{-}$ fraction $n_a(E,\theta ,\phi )$ after the reflection of hydrogen atoms on an Al(100) surface. The angle of incidence $\theta$ is measured relative to the surface plane. $\phi$ is the angle between the surface-projected impact velocity ${\mathbf{v}}_{\left|\right|}$ and the $\left[011\right]$ crystal-surface direction. (a) Azimuthal variation of the H${}^{-}$ yield at a collision energy of 1 keV for incidence angles $\theta =6^{\circ }$ (inverted triangles) and $8^{\circ }$ (upward-pointing triangles). (b) Azimuthal variation of the H${}^{-}$ yield at a collision energy of 4 keV and incidence angles $\theta =4^{\circ }$ (inverted triangles) and $5^{\circ }$ (upward-pointing triangles).Reuse & Permissions

Figure 16

Percentage H${}^{-}$ yields on an Al(100) surface as functions of the exit-velocity component perpendicular to the surface $v_n$ for collision energies of (a), (c) 1 keV and (b), (d) 4 keV in comparison with experimental results of Ref. [1]. The experimental H${}^{-}$ fractions are indicated by the dots (with interpolated solid black lines). $\phi$ is the angle between the surface-projected projectile velocity ${\mathbf{v}}_{\left|\right|}$ and the $\left[011\right]$ crystal-surface direction. (a), (b) Anion yields including ($n_a$) and excluding ($n_a^0$) transitions to ionized metal states for $\phi ={45}^{\circ }$. The anions yields are calculated for the substrate work function $W_{\mathrm{theor}}=4$ eV. The top horizontal axis gives the exit angle with respect to the surface ${\theta }_{\mathrm{exit}}$. (c), (d) Anion yields $n_a$ for $\phi ={35}^{\circ }$ calculated for both $W_{\mathrm{theor}}=4$ eV and the measured work function $W_{\mathrm{expt}}=4.4$ eV.Reuse & Permissions