Attenuation length in ion-induced kinetic electron emission: A key to an understanding of angular-dependent yields

The mean attenuation length, $〈L〉$, of electrons emitted from ion bombarded solids was derived from measured angular-dependent electron yields γ(θ) in combination with Monte Carlo simulations of inelastic (electronic) energy deposition. The transport controlled contributions of excited electrons to the measured electron yields were derived as the integral $g_L$ over $S_e\exp (\text{–}z/L)$, where $S_e(\theta ,z)$ is the electronic energy deposition and $z$ the depth from the surface. The unknown attenuation length $L\equiv 〈L〉$ reflects the average over the energy spectrum and the angular distribution of those internally excited electrons that can reach the solid-vacuum interface and overcome the surface barrier. To determine $L$, the ratios $g_L\left(\theta \right)/g_L\left(0\right)$, calculated for $0⩽L⩽10\mathrm{nm}$, were compared with measured yield ratios γ(θ)/γ(0) for a wide variety of projectile-target combinations and impact energies between 1 and 50 keV (velocity-proportional electronic stopping). The procedure works well at angles at which $S_e$(θ,$z)$ decreases smoothly in the depth region between 1 and 3 nm. The result is $〈L〉=1.5\pm 0.3$ nm, a number basically in accordance with expectation based on estimated data for the inelastic mean free path of low-energy electrons (<25 eV) but a factor of 10 lower than the numbers recently advocated (10–15 nm) to rationalize “internal” electron yields observed with metal-insulator-metal sandwich structures.

Figure 1

Normalized electron yields versus the primary-ion impact angle. From Refs. [13–16] and this work. The gray data highlight “subcosine” cases for which $p$ < 1. Yields due to potential electron emission were not subtracted from the raw data.

Figure 2

(a) Depth dependence of the electronic energy deposition by 10-keV Si and Al normally incident on Si, as calculated with srim-2006 (solid symbols). The open triangles were derived by applying the specified scaling factors to the raw Al data. (b) Ratios of the energy deposition of Si and Al in Si at 70° and 0° versus the reduced depth $z/R_0$, with $R_0$ denoting the mean projectile range at normal incidence.

Figure 3

Depth distribution of inelastic electronic energy losses of (a) 10-keV O on Al and (b) 40-keV Xe on Cu, for different impact angles, as calculated with srim-2006 [number of projectiles $N=30$ 000; step width $\Delta z=0.3$ nm; every second data point skipped in (a) for clarity]. The total losses and the distinctly different contributions due to projectiles and recoils are shown separately (subscripts Σ, p, and r, respectively).

Figure 4

Distributions of (a) electronic energy deposition due to projectiles and (b) projectile ranges of 10-keV O in Au at different impact angles, as calculated with srim-2006 $(N=50$ 000; step width $\Delta z=0.5$ nm). Three-point smoothing of the raw data applied in (b).

Figure 5

(a) Normalized ranges (solid symbols) and half width of the distributions of electronic energy deposition (open symbols and crosses) for different projectile-target combinations versus the cosine of the impact angle. The dash-dotted line denotes direct proportionality. (b) Integral electronic and total energy deposition versus backscattering coefficient, for four different projectile-target combinations. The impact angles in (b) are the same as in (a).

Figure 6

Scaled ratios of the calculated electronic energy losses at the bombarded surface (projectiles: open symbols; total losses: solid symbols) versus the impact angle. Scaled ratios of KEE yields are shown for comparison (lines).

Figure 7

(a) Depth dependence of the total electronic energy deposition for impact of 10-keV O on Mg at normal and oblique incidence (solid symbols). The same data are also shown after application of an exponential attenuation factor, with $L=1$ and 10 nm. (b) Integral electron-yield parameter $g$(θ,$L)$ versus $L$, for two different impact angles.

Figure 8

Depth dependence of calculated ratios of total electronic energy deposition at 70° and 0°, for a variety of projectile-target combinations and impact energies. The black and gray data represent cases in which the angular dependence of electron yields was found to be (inversely) over cosine and under cosine, respectively, see Fig. 1.

Figure 9

Calculated electron-yield ratios $r$ versus the assumed attenuation length $〈L〉$, for different angles of projectile impact; 10-keV O on (a) Mg and (b) Al (Ref. [16]). Solid symbols: total energy deposition, open symbols: projectile contribution. The lines without symbols represent depth-dependent ratios in total energy deposition, ρ, not including attenuation. Horizontal bars: electron-yield ratios derived from experimental data, corrected for potential emission, ${\gamma }_{\mathrm{PEE}}$(Mg) $=0.12,{\gamma }_{\mathrm{PEE}}$(Al) $=0.04$; the gray bars show ratios of raw (uncorrected) data.

Figure 10

The same as Fig. 9, but for (a) 40-keV Xe on Al (Ref. [14]) and (b) 40-keV Xe or Cu on Cu (Ref. [15]). Note the pronounced difference in the calculated yield ratios for total and projectile-only ionization. Corrections were assumed to be negligible in (a), ${\gamma }_{\mathrm{PEE}}⩽0.03$, or not required in (b). To avoid too much overlap of data, $r\left(S_{e,p,{70}^{\circ }}\right)$ is not shown in (b).

Figure 11

The same as Fig. 9, but for He on Cu, (a) 20 keV and (b) 50 keV. Experimental data corrected for potential emission, ${\gamma }_{\mathrm{PEE}}=0.24$ (Ref. [13]).

Figure 12

The same as Fig. 9, but for (a) 10-keV O on Au [13] and (b) 5 and 30-keV Xe on Au. Potential emission considered negligible. Step width in the srim calculations 0.12 nm. Note that the total depth covered in the two panels is only 3.5 nm.