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Hemispherical electron energy analyzer

Hemispherical electron energy analyzer is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hemispherical electron energy analyzer rather than just read about it. In short: A hemispherical electron energy analyzer or hemispherical deflection analyzer is a type of electron energy spectrometer generally used for applications where high energy resolution is needed—different varieties of electron spectroscopy such as angle-resolved photoemission spectroscopy (ARPES), X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) or in imaging applications such as photoemissio…

Hemispherical electron energy analyzer — main illustration
Hemispherical electron energy analyzer — illustration

Key takeaways

  • Hemispherical electron energy analyzer belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Hemispherical electron energy analyzer to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Hemispherical electron energy analyzer from memory before moving on to harder problems.

Reference excerpt

A hemispherical electron energy analyzer or hemispherical deflection analyzer is a type of electron energy spectrometer generally used for applications where high energy resolution is needed—different varieties of electron spectroscopy such as angle-resolved photoemission spectroscopy (ARPES), X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) or in imaging applications such as photoemission electron microscopy (PEEM) and low-energy electron microscopy (LEEM). It consists of two concentric conductive hemispheres that serve as electrodes that bend the trajectories of the electrons entering a narrow slit at one end so that their final radii depend on their kinetic energy. The analyzer, therefore, provides a mapping from kinetic energies to positions on a detector.

Function

An ideal hemispherical analyzer consists of two concentric hemispherical electrodes (inner and outer hemispheres) of radii R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} held at proper voltages. In such a system, the electrons are linearly dispersed, depending on their kinetic energy, along the direction connecting the entrance and the exit slit, while the electrons with the same energy are first-order focused.

When two voltages, V 1 {\displaystyle V_{1}} and V 2 {\displaystyle V_{2}} , are applied to the inner and outer hemispheres, respectively, the electric potential in the region between the two electrodes follows from the Laplace equation:

V ( r ) = − [ V 2 − V 1 R 2 − R 1 ] ⋅ R 1 R 2 r + c o n s t . {\displaystyle V(r)=-\left[{\frac {V_{2}-V_{1}}{R_{2}-R_{1}}}\right]\cdot {\frac {R_{1}R_{2}}{r}}+const.}

The electric field, pointing radially from the center of the hemispheres out, has the familiar planetary motion 1 / r 2 {\displaystyle 1/r^{2}} form

| E ( r ) | = − [ V 2 − V 1 R 2 − R 1 ] ⋅ R 1 R 2 r 2 {\displaystyle |\mathbf {E} (r)|=-\left[{\frac {V_{2}-V_{1}}{R_{2}-R_{1}}}\right]\cdot {\frac {R_{1}R_{2}}{r^{2}}}}

The voltages are set in such a way that the electrons with kinetic energy E k {\displaystyle E_{k}} equal to the so-called pass energy E P {\displaystyle E_{\textrm {P}}} follow a circular trajectory of radius R P = 1 2 ( R 1 + R 2 ) {\displaystyle R_{\textrm {P}}={\tfrac {1}{2}}(R_{1}+R_{2})} . The centripetal force along the path is imposed by the electric field − e E ( r ) {\displaystyle -e\mathbf {E} (r)} . With this in mind,

V ( r ) = E P e R P r + c o n s t . {\displaystyle V(r)={\frac {E_{\textrm {P}}}{e}}{\frac {R_{\textrm {P}}}{r}}+const.}

The potential difference between the two hemispheres needs to be

… excerpt ends here. Continue reading the full article.

Illustrations

Hemispherical electron energy analyzer: Hemispherical electron energy analyzer.
Hemispherical electron energy analyzer.
Hemispherical electron energy analyzer: Main parts of a hemispherical electron energy analyzer.
Main parts of a hemispherical electron energy analyzer.
Hemispherical electron energy analyzer: Calculated trajectories for three different kinetic energies and four starting positions within the slit. Slit width maps directly into energy detection channels, worsening the resolution. ρ = r 0 − R P {\displaystyle \rho =r_{0}-R_{\textrm {P}}}
Calculated trajectories for three different kinetic energies and four starting positions within the slit. Slit width maps directly into energy detection channels, worsening the resolution. ρ = r 0 − R P {\displaystyle \rho =r_{0}-R_{\textrm {P}}}
Hemispherical electron energy analyzer: Calculated trajectories for five different kinetic energies and five initial angles. Initial angular spread, dependent on the chosen slit and aperture width, worsens the energy resolution.
Calculated trajectories for five different kinetic energies and five initial angles. Initial angular spread, dependent on the chosen slit and aperture width, worsens the energy resolution.
Hemispherical electron energy analyzer: Distance from the central trajectory at the exit of a hemispherical electron energy analyzer depending on the electron's kinetic energy, initial position within the 1 mm slit, and the angle at which it enters the radial field after passing through the slit. Dispersion is nearly linear in energy, linear in initial position, and quadratic in angle. The latter two map into energy channels of the detector, spoiling the resolution. Data was calculated for Rp=100 mm. Note orders of magnitude different scales on the vertical axes.
Distance from the central trajectory at the exit of a hemispherical electron energy analyzer depending on the electron's kinetic energy, initial position within the 1 mm slit, and the angle at which it enters the radial field after passing through the slit. Dispersion is nearly linear in energy, linear in initial position, and quadratic in angle. The latter two map into energy channels of the detector, spoiling the resolution. Data was calculated for Rp=100 mm. Note orders of magnitude different scales on the vertical axes.

Worked examples

Example 1 — a first encounter with Hemispherical electron energy analyzer

Start with the simplest possible case. Write down what Hemispherical electron energy analyzer claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hemispherical electron energy analyzer before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hemispherical electron energy analyzer ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hemispherical electron energy analyzer

In research
Hemispherical electron energy analyzer appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Hemispherical electron energy analyzer in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Hemispherical electron energy analyzer is common in secondary-school and first-year university syllabi. It links to neighbouring topics Electron spectroscopy, so understanding it makes those chapters shorter.
In everyday life
Look for Hemispherical electron energy analyzer outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Hemispherical electron energy analyzer in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Hemispherical electron energy analyzer means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Hemispherical electron energy analyzer out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hemispherical electron energy analyzer in simple terms?

A hemispherical electron energy analyzer or hemispherical deflection analyzer is a type of electron energy spectrometer generally used for applications where high energy resolution is needed—different varieties of electron spectroscopy such as angle-resolved photoemission spectroscopy (ARPES), X-ra…

Why does Hemispherical electron energy analyzer matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hemispherical electron energy analyzer?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hemispherical electron energy analyzer.

Tags

  • Electron spectroscopy

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