Calculator Inputs
Example Data Table
| Material | Work Function eV | Temperature K | Field GV/m | β | Expected Trend |
|---|---|---|---|---|---|
| Tungsten | 4.5 | 2500 | 2.5 | 50 | Mixed emission may appear. |
| Molybdenum | 4.6 | 1800 | 4.0 | 120 | Field emission becomes stronger. |
| Low barrier coating | 2.8 | 1100 | 1.5 | 30 | Thermionic emission may increase. |
Formula Used
Field emission is estimated with the Fowler Nordheim relation:
JFE = AFNF² / φ × exp[-BFNφ3/2 / F]
Here, F is the enhanced electric field. It equals βE. The work function φ is measured in electron volts. The constants are AFN = 1.541434E-6 and BFN = 6.830890E9.
Thermionic emission is estimated with the Richardson Dushman relation:
JTE = ART² × exp[-φ / kBT]
Current is found from I = JA. The calculator compares both currents and reports the dominant mechanism. Optional Schottky lowering reduces the effective barrier before both current density estimates are calculated.
How to Use This Calculator
Enter the material work function first. Then add temperature, applied electric field, field enhancement factor, and active emission area. Select suitable units for field and area. Keep β equal to 1 for a broad flat surface. Use a higher β for sharp tips, nanowires, or rough cathodes.
Add the Richardson constant if your material uses a corrected value. Leave the default value for a general estimate. Select Schottky lowering when the barrier reduction from strong fields should be included. Press calculate to compare field emission, thermionic emission, total current, emitted charge, and electron count.
Field Emission vs Thermionic Emission Guide
What the Calculator Measures
Electron emission can happen by different physical routes. Field emission uses a strong electric field. The field narrows the surface barrier. Electrons can then tunnel through it. Thermionic emission uses heat. A hot cathode gives electrons enough energy to rise over the barrier. This calculator compares both effects in one place.
Why Work Function Matters
Work function is the energy needed to remove an electron from a material surface. A high value strongly reduces both emission paths. A low value can increase current by many orders of magnitude. This is why coatings are important in cathode design. Even a small work function change can cause a large output change.
Role of Electric Field
Field emission depends heavily on surface field. Sharp emitters create local field enhancement. The calculator uses β to model this effect. A large β can make tunneling important even when the applied field looks moderate. Flat plates usually need much stronger fields.
Role of Temperature
Thermionic emission rises fast with temperature. The equation includes T squared and an exponential thermal factor. At low temperature, thermionic current can be tiny. At high temperature, it can dominate. Heater design, material stability, and vacuum limits should be considered.
Interpreting the Ratio
The field to thermionic ratio shows which mechanism is stronger. A high ratio means tunneling dominates. A low ratio means heated emission dominates. A near one ratio means both processes may matter. This comparison helps with vacuum tubes, electron guns, microtips, and field emitter arrays.
Important Limits
This calculator is an engineering estimate. Real devices may include space charge, geometry effects, adsorbates, temperature gradients, surface roughness, and material aging. Use the result as a first comparison. Detailed device modeling may need finite element simulation and measured emission data.
FAQs
1. What is field emission?
Field emission is electron tunneling from a surface under a strong electric field. It usually needs high local field and a clean surface.
2. What is thermionic emission?
Thermionic emission happens when heat gives electrons enough energy to escape from a material surface. It rises strongly with temperature.
3. Which formula is used for field emission?
The calculator uses a Fowler Nordheim style equation. It estimates tunneling current density from work function and enhanced electric field.
4. Which formula is used for thermionic emission?
The calculator uses the Richardson Dushman equation. It estimates thermal current density from temperature, work function, and Richardson constant.
5. What does field enhancement factor mean?
Field enhancement factor represents local field increase caused by sharp tips, rough surfaces, or small emitter geometry. Higher values increase field emission.
6. Why include Schottky barrier lowering?
Strong electric fields can reduce the effective emission barrier. This option models that reduction and can increase both estimated emission currents.
7. Why are results sometimes extremely small?
Both formulas contain exponential terms. Small changes in work function, field, or temperature can reduce current by many orders of magnitude.
8. Can this replace lab testing?
No. It provides a theoretical estimate. Real emitters depend on surface condition, vacuum level, space charge, geometry, and material changes.