Skip to main content
Sandbox Physics

E63 · Electron excitation and surface spectroscopy

Inverse Photoemission: Empty States

Scan incident electron energy while counting a fixed photon band. Recover two electron-addition peaks from recorded counts, then test photon bandwidth, electron spread, exposure and energy calibration.

Interactive modelInverse Photoemission: Empty States
First count-derived centroid—\text{—}
Second count-derived centroid—\text{—}
Selected stored photon count—\text{—}
Selected surface kinetic energy—\text{—}
Larger centroid error against input—\text{—}
Weaker acquired peak SNR—\text{—}
Acquired electron-energy positions—\text{—}
Combined instrument FWHM—\text{—}
Summed incident dose—\text{—}
Prescribed changed-response fraction—\text{—}
Experiment target—\text{—}

Physics tutorial

Inverse Photoemission: Empty States

BackgroundScan incident electron energy while counting a fixed photon band. Recover two electron-addition peaks from recorded counts, then test photon bandwidth, electron spread, exposure and energy calibration.

Why it mattersTarget: each acquired centroid within 0.12 eV of its undamaged input, peak SNR at least 10, combined instrument FWHM at most 0.8 eV and prescribed changed fraction at most 15 percent.

Start with the essentials

Focus question
What can emitted photons tell us about empty electron states?
One-sentence intuition
The electron supplies energy, the photon leaves with a fixed accepted energy, and their difference locates an unoccupied final state.

Core mathematical model

Electron-addition energy

εf=Ekin+Φ−hνEkin=εf+hν−Φ\begin{aligned}\varepsilon_f&=E_{kin}+\Phi-h\nu\\E_{kin}&=\varepsilon_f+h\nu-\Phi\end{aligned}

Kinetic energy is referenced to the local vacuum; final energy is referenced to the Fermi level. Calibration errors shift the energy axis.

Gaussian instrument resolution

winst=we2+wγ2σ=winst22ln⁡2\begin{aligned}w_{inst}&=\sqrt{w_e^2+w_\gamma^2}\\\sigma&=\frac{w_{inst}}{2\sqrt{2\ln2}}\end{aligned}

Independent Gaussian electron and photon widths add in quadrature; intrinsic state width is additional.

Counted isochromat response

ε0=E+Φ−hνR(E)=∫0∞ρu(u)×Gσ(u−ε0) duμ(E)=bτ+IτeηAγR(E)\begin{aligned}\varepsilon_0&=E+\Phi-h\nu\\R(E)&=\int_0^\infty\rho_u(u)\\&\quad\times G_\sigma(u-\varepsilon_0)\,du\\\mu(E)&=b\tau+\frac{I\tau}{e}\eta A_\gamma R(E)\end{aligned}

The photon passband area increases with bandwidth. The acquired scan is a broadened weighted addition spectrum, not an inverse reconstruction of the ideal input.

Common difficulties

Separate references from data

Typical misconceptionThe ideal input is the inferred result.

Better mental modelGold known-input views are independent audits. The teal result uses stored counts only.

Exposure does not fix every error

Typical misconceptionEnough counts guarantee the right answer.

Better mental modelCounts reduce counting noise, but continuum errors, calibration, finite instrument width and prescribed damage remain.

Run the experiment

  1. 01

    Predict which energy is scanned

    Select a stored electron-energy position and compare its photon count with the energy bookkeeping card.

    What to observe: The detected photon band stays fixed while incident electron energy changes.
  2. 02

    Calibrate the same counts

    Switch the assumed work function from 3.5 to 4.5 eV. Change smoothing and verify that the raw scan stays identical.

    What to observe: A wrong work function shifts both inferred peaks by the same energy.
  3. 03

    Trade throughput for width

    Compare wide photon acceptance with broad incoming electrons. Inspect the count rate and combined FWHM.

    What to observe: More counts do not undo convolution or separate closer unresolved features.
  4. 04

    Recover the two peaks

    Use narrow electron and photon widths, calibrated work function and enough dwell. Compare the centroid energies with the separate reference, then check the target.

    What to observe: The target tests count quality, energy error, instrumental width and prescribed damage.