Figure 1

(a) The imaginary-frequency dipole polarizability $\alpha \left(i\omega \right)$ of ${\mathrm{He}}^{*}\left(2{}^{3}S_1\right)$ taken from Refs. 31, 32 (dashed line) and the dielectric function $ϵ\left(i\omega \right)$ of silicon (solid line) calculated using Eq. (19) and the values from Ref. 33. We also show the dielectric function of doped silicon with a plasma frequency ${\omega }_p={10}^{14}{\mathrm{s}}^{-1}$ (dash-dot-dot) and ${\omega }_p={10}^{15}{\mathrm{s}}^{-1}$ (dash-dot). The presence of free charges leads to a resonance at zero frequency. (b) The van der Waals potential between a ${\mathrm{He}}^{*}$ atom and a silicon surface. The short-dashed line shows the potential in the case of a perfectly conducting surface. It has been calculated using Eq. (1) and the ${\mathrm{He}}^{*}$ dipole polarizability plotted in (a). This calculation reproduces the values given by Yan and Babb [26] (crosses) with a relative error below 1%. The dashed line is the potential calculated for a dielectric with the frequency-independent dielectric function $ϵ=11.7$ and the solid line is the potential calculated using the frequency-dependent dielectric function of undoped silicon. The latter differ only at very short distances from the surface, where the high-frequency behavior of $ϵ\left(i\omega \right)$ must be considered.Reuse & Permissions

Figure 2

(a) Demonstration of the effect of the conductivity of a solid on the van der Waals potential in the case of silicon and metastable helium $2{}^{3}S_1$. The potential for a perfect conductor is shown by the dotted line. The solid line represents the potential for undoped silicon, which behaves like a dielectric. We also show the potential for doped silicon with plasma frequencies ${\omega }_p={10}^{15}{\mathrm{s}}^{-1}$ (dash-dot) and ${\omega }_p={10}^{16}{\mathrm{s}}^{-1}$ (dash-dot-dot). Note that the effect of free charges appears mainly at a larger distance from the surface. (b) The van der Waals potential between a ${\mathrm{He}}^{*}$ atom and a silicon surface covered with an oxide layer. The silicon oxide is assumed to be a dielectric with constant $ϵ=3.9$. The potentials are shown for undoped silicon (solid line) and layers of thickness of $t=30\mathrm{nm}$ (dash-dot), $t=100\mathrm{nm}$ (dash-dot-dot), and $t=\infty$ (dotted).Reuse & Permissions

Figure 3

Cross-sectional view of the experimental setup.Reuse & Permissions

Figure 4

Measurement of the reflectivity of ${\mathrm{He}}^{*}\left(2{}^{3}S_1\right)$ on a polished $p$-doped silicon plate as a function of the normal incident velocity (error bars). We compare the result to the reflectivities calculated for several potentials. The long-dashed line shows the reflectivity expected for ${\mathrm{He}}^{*}$ on a perfect conductor. The solid line shows the case for undoped silicon (i.e., with low conductivity). The reflectivities expected for a Si surface covered with a 30-nm- (dash-dot) and 100-nm-thick (dash-dot-dot) oxide layer are also shown.Reuse & Permissions

Figure 5

(a) The reflectivity of ${\mathrm{He}}^{*}$ (points) compared to that of ${\mathrm{Ne}}^{*}\left(1s_3\right)$ atoms (solid line), both measured on similar silicon samples as a function of the normal incident velocity. The neon data are taken from Ref. 8. (b) The same data with the normal incident velocities scaled with $v_s^{\mathrm{Ne}}=5.69\mathrm{mm}∕\mathrm{s}$ and $v_s^{\mathrm{He}}=4.89\mathrm{cm}∕\mathrm{s}$, respectively.Reuse & Permissions