Calculator Inputs
Example Data Table
These values are illustrative reference examples for quick comparison.
| Material | Typical electron mass (m*/m₀) | Band note | Use case |
|---|---|---|---|
| Silicon transverse | 0.19 | Light transverse conduction response | Mobility-oriented transport studies |
| Silicon longitudinal | 0.92 | Heavier longitudinal conduction response | Anisotropic valley analysis |
| Germanium | 0.12 | Relatively light conduction mass | Carrier transport estimates |
| Gallium arsenide | 0.067 | Very light conduction electron mass | High-speed device calculations |
| Indium arsenide | 0.023 | Extremely light conduction response | Narrow-gap semiconductor analysis |
Formula Used
Primary curvature relation: m* = ħ² / (d²E/dk²).
Mobility relation: μ = qτ / m*, so m* = qτ / μ.
Cyclotron relation: ωc = qB / m*, so m* = qB / (2πf).
Three-point fit: fit E(k) = ak² + bk + c, then d²E/dk² = 2a.
Density-of-states mass: mdos = (|mx my mz|)^(1/3).
Conductivity mass: mcond = 3 / (1/|mx| + 1/|my| + 1/|mz|).
How to Use This Calculator
- Select the method that matches your available data.
- Enter curvature, transport, resonance, or E-k fit values.
- Optionally add x, y, and z curvatures for anisotropy.
- Press the calculation button to place results above the form.
- Review the graph, compare values, and export CSV or PDF.
FAQs
1. What does effective mass represent?
Effective mass describes how a carrier responds to forces inside a crystal. It replaces free-electron mass in band-structure problems and can be much lighter or heavier.
2. Why can the result be negative?
Negative electronic effective mass appears near valence-band maxima because curvature is negative. In practice, this is often interpreted as positive hole mass with opposite charge behavior.
3. When should I use the curvature method?
Use curvature when you have band-structure data or a fitted E-k relation near a minimum or maximum. It is the most direct definition-based method.
4. When is the mobility method useful?
Use it when transport measurements provide mobility and an estimated scattering time. It is practical for device analysis, but depends on the quality of the scattering-time assumption.
5. What does the cyclotron method measure?
Cyclotron resonance gives the mass linked to orbital motion in a magnetic field. It is valuable for clean experimental characterization of semiconductor carriers.
6. Why offer a three-point E-k fit?
Three nearby E-k points can estimate a local parabola when a full band dataset is unavailable. This is useful for quick checks around a band extremum.
7. What are density-of-states and conductivity masses?
They summarize anisotropic directional masses into compact values. Density-of-states mass affects carrier statistics, while conductivity mass is useful for transport averaging.
8. Can I export the calculation results?
Yes. After a successful calculation, use the CSV button for spreadsheet work or the PDF button for clean reporting and documentation.