Electron Spectroscopy (XPS/UPS)
XPS and UPS photoelectrons: kinetic energy E_k = hν − E_B − φ_sp, inelastic mean free path from the TPP-2M equation, sampling depth 3λ cos θ and the kinetic energies from common X-ray and UV sources.
Kinetic Energy E_k
1197.60 eV
hν − E_B − φ_sp
Inelastic Mean Free Path λ
3.08 nm
TPP-2M at hν − E_B, E_p = 24.7 eV
95 % Sampling Depth
9.22 nm
3λ cos θ at θ = 0°
Signal from Top 1 nm
27.7 %
1 − exp(−1 nm/(λ cos θ))
Common Sources for E_B = 284.50 eV
He I (UPS), 21.22 eV
not reached
He II (UPS), 40.81 eV
not reached
Mg Kα, 1253.6 eV
E_k 964.60 eV
λ 2.60 nm
Al Kα, 1486.6 eV
E_k 1197.6 eV
λ 3.08 nm
Ag Lα, 2984.3 eV
E_k 2695.3 eV
λ 5.90 nm (extrapolated)
E_k = hν − E_B − φ_sp, λ = E/{E_p²[β ln(γE) − C/E + D/E²]} (TPP-2M), I(z) ∝ e^(−z/(λ cos θ))
A conducting sample in contact with the spectrometer shares its Fermi level, so the measured kinetic energy depends on the spectrometer's work function, not the sample's; E_B is referred to the Fermi level. In UPS the sample work function is hν minus the spectrum width (secondary-electron cutoff to Fermi edge). Insulators charge, which shifts every peak.
TPP-2M (Tanuma, Powell & Penn 1994) is fitted to IMFPs from optical data for 50–2000 eV, with an RMS deviation of about 11 %; it takes the energy above the Fermi level, hν − E_B (E_k + φ_sp), and fails below 50 eV, where UPS electrons sit (the universal curve puts their IMFP of order 0.5–1 nm). Elastic scattering makes the effective attenuation length 10–30 % shorter than λ, so the depths here are upper estimates.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Fermi-level-referenced binding energy with the spectrometer work function; TPP-2M IMFP at the Fermi-referenced energy hν − E_B (fitted for 50–2000 eV, about 11 % RMS; not given below 50 eV, so not for UPS) and straight-line exponential attenuation, which ignores elastic scattering and so overestimates the sampling depth by 10–30 %.
- Tanuma S., Powell C. J., Penn D. R. (1994). Calculations of electron inelastic mean free paths. V. Data for 14 organic compounds over the 50–2000 eV range. Surf. Interface Anal. 21, 165–176 (TPP-2M). doi:10.1002/sia.740210302
- Tanuma S., Powell C. J., Penn D. R. (2003). Calculation of electron inelastic mean free paths (IMFPs) VII. Reliability of the TPP-2M IMFP predictive equation. Surf. Interface Anal. 35, 268–275. doi:10.1002/sia.1526
- Powell C. J., Jablonski A. (2010). NIST Electron Inelastic-Mean-Free-Path Database, SRD 71, version 1.2: user's guide, Appendix A. nist.gov
- Hüfner S. (2003). Photoelectron Spectroscopy: Principles and Applications, 3rd ed. Springer.