Skip to main content
Sandbox Physics

E50 · Electron imaging / spectroscopy

Photoemission & Hemispherical Analyzer

Illuminate a grounded specimen and follow emitted electrons through a transfer lens, entrance slit and concentric hemispheres. Resolve a synthetic doublet while trading pass energy, slit width, angular acceptance and exposure.

Interactive modelPhotoemission & Hemispherical Analyzer
Sample-vacuum kinetic energy0 eV0\,\mathrm{eV}
Analyzer kinetic energy0 eV0\,\mathrm{eV}
Contact energy shift0 eV0\,\mathrm{eV}
Retarding potential0 V0\,\mathrm{V}
Instrumental FWHM0 eV0\,\mathrm{eV}
Expected integrated count rate0 s−10\,\mathrm{s^{-1}}
Expected integrated counts00
Selected-state emission—\text{—}
Experiment task—\text{—}

Physics tutorial

Can you separate two peaks without losing all the counts?

BackgroundIlluminate a grounded specimen and follow emitted electrons through a transfer lens, entrance slit and concentric hemispheres. Resolve a synthetic doublet while trading pass energy, slit width, angular acceptance and exposure.

Why it mattersConnect the instrument setting to a measured result before interpreting the specimen.

Start with the essentials

Focus question
Can you separate two peaks without losing all the counts?
One-sentence intuition
Lower pass energy and a narrower slit sharpen the response but reduce transmission. Sample-vacuum kinetic energy differs from analyzer kinetic energy when the work functions differ.

Core mathematical model

Two vacuum references

Ekin,s=hν−ϕs−EB,Ekin,a=hν−ϕa−EBE_{\mathrm{kin,s}}=h\nu-\phi_s-E_B,\quad E_{\mathrm{kin,a}}=h\nu-\phi_a-E_B

Assumes grounded electrical contact and no sample charging or external bias.

First-order energy width

ΔEa≃Ep(s2R0+α24),ΔE=ΔEa2+ΔEγ2\Delta E_a\simeq E_p\left(\frac{s}{2R_0}+\frac{\alpha^2}{4}\right),\quad \Delta E=\sqrt{\Delta E_a^2+\Delta E_\gamma^2}

The slit term uses a 150 mm mean radius; angular half-acceptance is in radians.

Noise and throughput

Nˉ=N˙(Ep,s,α,θ) τ,σN=Nˉ\bar N=\dot N(E_p,s,\alpha,\theta)\,\tau,\quad \sigma_N=\sqrt{\bar N}

The rate is an empirical teaching law, not a commercial instrument specification.

Common difficulties

Interpretation trap

Typical misconceptionSample work function shifts every binding-energy peak in a properly grounded, calibrated analyzer.

Better mental modelThe contact-potential difference changes the local vacuum reference. Binding-energy calibration uses the analyzer work function when the Fermi levels align; emission threshold still depends on the sample.

Run the experiment

  1. 01

    Predict the result

    Predict whether the fastest collection preset can separate the doublet. Compare Fast survey and Resolve doublet using the fixed intrinsic reference.

    What to observe: Lower pass energy and a narrower slit sharpen the response but reduce transmission. Sample-vacuum kinetic energy differs from analyzer kinetic energy when the work functions differ.
  2. 02

    Operate and check

    Resolve the 0.25 eV doublet with instrumental FWHM below 0.10 eV and at least 500 expected integrated counts. The selected state must also be able to escape.

    What to observe: Use the numerical target, then compare the linked instrument and data views.
  3. 03

    Explain the limitation

    Change only the sample work function. Compare surface kinetic energy with analyzer kinetic energy, then reduce photon energy until emission stops.

    What to observe: Ideal central-field dispersion and first-order analyzer resolution for an assumed 150 mm mean radius. The analyzer work function is fixed at 4.5 eV; electrical contact aligns Fermi levels. Gaussian line response and empirical transmission are teaching assumptions, with no material-specific cross sections, space charge or detailed lens solver.