Effective attenuation length of an electron in liquid water between 10 and 600 eV

The absolute values of the effective attenuation length of an electron in liquid water are determined using soft x-ray $\mathrm{O}1s$ photoemission spectroscopy of a liquid beam of water without employing any theoretical estimation or computationally obtained value. The effective attenuation length is greater than 1 nm in the entire electron kinetic energy region and exhibits very flat energy dependence in the 10–100 eV region.

Figure 1

(a) Inelastic mean free path (IMFP) of electron in water. IMFPs are calculated using Mermin's model (IMFP1) and the Ashley model (IMFP2) [6] and a simplified KO model with the e-e dielectric function (IMFP3) [6, 7]. IMFP4 shown as circles is obtained from the electronic inelastic scattering cross section in amorphous ice [5]. (b) Illustration of IMFP and EAL of an energetic electron. (c) Schematic view of the liquid beam x-ray photoelectron spectroscopy. See Fig. 3 for more details of the experimental geometry.

Figure 2

$\mathrm{O}1s$ photoelectron spectra of 0.14 M aqueous NaCl solution observed with 911 eV photon (open circle) and 1140 eV photon (filled square). The inset shows the photoabsorption cross sections for liquid [11] and gaseous [10] water. The cross section of liquid water is normalized for that of the gas in the region over 580 eV. These spectra were measured in the a-branch of BL17SU soft x-ray beamline of SPring-8.

Figure 3

The cut view of the liquid beam in the plane defined by the x-ray propagation direction and the electron detection axis. Illustration of the effective ionization area of vapor and liquid beams for (a) few and (b) many elastic scattering events. $r_0$ and $R$ are the radius of the liquid beam and x ray, respectively, while $l$ represents the visible area for the detector. The gray area indicates the opposite side of the detector.

Figure 4

Effective attenuation length (EAL) as a function of electron kinetic energy (eKE) (also in Table S1 [16]), and thermalization length (TL) and inelastic mean free path (IMFP). The error bars result from data sets on different days. The filled triangles (blue) and filled-inverted triangles (light blue) indicate the EAL, assuming 280 K, with and without the $\pi /2$ geometrical factor. The thick green line is a guide for the eyes as a possible EAL curve affected by the $\pi /2$ factor at high energies. The EAL values reported by Thürmer et al. are indicated by the plus signs. Experimental TL is obtained from the photocurrent in solutions (TL1) [21]. TL2 is the continuous slowing down approximation range [22], and TL3 is the penetration length of an electron [23] in water. The IMFP1 (line) and IMFP4 (circles) are the same as in Fig. 1.