2
3
2
by R. Timm, M. Hjort, A. Fian, B. M. Borg, C. Thelander, J. N. Andersen, L.-E. Wernersson, and
A. Mikkelsen
In our XPS setup, the sample is positioned with its surface parallel to the entrance slit of the electron analyzer, meaning that those photoelectrons leaving the sample perpendicular to its surface are measured. For a planar sample, the XPS signal from the pure InAs is attenuated when passing the surface or interface oxide layer of a constant thickness d
Ox
.
At a NW, however, for most photoelectrons leaving the NW perpendicular to the sample surface the actual attenuation path length upon traveling through the oxide layer is increased, as shown schematically in
Fig. 2(e). When the NW radius R is much larger than the oxide layer thickness d
Ox
, which is the case in our experiment, the effective attenuation length for a photoelectron throughout the oxide can be approximated by 𝑑 𝑒𝑓𝑓
≈ 𝑑
𝑂𝑥
⁄ cos 𝜑 , as can be seen in Fig. 4(b). In order to switch to
Cartesian coordinates, one can use cos 𝜑 = 𝑦 𝑅 and 𝑦 = √𝑅 2 − 𝑥 2
, as defined in Fig. 4(a).
Figure 4 : Sketch of (a) half a NW and (b) a zoom-in, showing the thin oxide layer on the InAs NW. The
NW radius R , the oxide thickness d
Ox
, the effective attenuation thickness d eff
, and the geometrical parameters x , y , and
φ
used for the calculation in the main text are indicated.

With this, the effective attenuation length results in: 𝑑 𝑒𝑓𝑓
= 𝑑
𝑂𝑥
× 𝑅
√𝑅 2 − 𝑥 2
The average effective attenuation length for one complete NW is obtained by integrating over the radius R of the NW and normalizing by 1/ R : 𝑒𝑓𝑓
1
𝑅
∫
0
𝑅 𝑑
𝑂𝑥
√𝑅 2
× 𝑅
− 𝑥 2
𝑑𝑥 = [𝑑
𝑂𝑥
sin −1 𝑥
𝑅
]
𝑅
0
= 𝜋
2
𝑑
𝑂𝑥
Thus, for a NW sample the same oxide layer thickness will lead to an average attenuation length increased by a factor of 1.6 as compared to a planar sample.
The photoemission intensity I
0
corresponding to a pure InAs signal is attenuated – for a planar sample – according to 𝐼 = 𝐼
0
𝑒𝑥𝑝(−𝑑
𝑂𝑥 𝜆 , with the electron inelastic mean free path
λ
.
Assuming an oxide layer thickness of d
Ox
= 1 nm with the InAs oxide stoichiometry as obtained in this work and a kinetic energy of the photoelectrons of about 280 eV (corresponding to photon energies of 320 eV for the As 3d and 730 eV for the In 3d core-levels), the inelastic mean free path amounts to
λ
= 0.82 nm, according to the TPP-2M formula, [1] and the InAs photoemission intensity for the NW sample is obtained as:
𝐼
𝑁𝑊
= 𝐼
0
𝑒𝑥𝑝 (− 𝜋
2 𝑑
𝑂𝑥 𝜆
) = 𝐼
0
𝑒𝑥𝑝 (− ( 𝜋
2
− 1) 𝑑
𝑂𝑥
) 𝑒𝑥𝑝 (− 𝜆 𝑑
𝑂𝑥
) 𝜆
= 𝐼
0
× 0,50 𝑒𝑥𝑝 (− 𝑑
𝑂𝑥 𝜆
) = 0,50 𝐼 𝑝𝑙𝑎𝑛𝑎𝑟
This means that the ratio between the oxide peak and the pure InAs peak in either As 3d or In 3d spectra will appear double as large for a NW sample as for a planar sample.
[1] S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Interf. Anal.
, vol. 21, p. 165, 1994.