Carrier Density Input Form
Use conductivity with mobility, or enter Hall coefficient only.
Carrier Density Trend Graph
The graph shows density variation against mobility scaling.
Example Data Table
| Material | Conductivity (S/m) | Mobility (cm²/V·s) | Hall Coefficient (cm³/C) | Estimated Density (cm⁻³) |
|---|---|---|---|---|
| Silicon, lightly doped | 5800 | 1350 | -3.20 | 2.68 × 1013 |
| Germanium | 2200 | 3900 | -1.60 | 3.52 × 1012 |
| Gallium arsenide | 8500 | 8500 | -0.85 | 6.24 × 1012 |
| ITO thin film | 120000 | 40 | -0.015 | 1.87 × 1020 |
Formula Used
Where:
- n = carrier density
- σ = conductivity
- q = elementary charge, 1.602176634 × 10-19 C
- μ = mobility
- RH = Hall coefficient
- ρ = resistivity
- Rs = sheet resistance
- t = film thickness
- J = current density
- vd = drift velocity
This tool supports two practical methods. The first uses conductivity and mobility. The second uses Hall coefficient magnitude. Both are common in semiconductor transport analysis.
How to Use This Calculator
- Enter conductivity in siemens per meter.
- Enter mobility in square centimeters per volt-second.
- Optionally provide Hall coefficient for comparison.
- Add thickness for sheet resistance estimation.
- Add current and area for drift velocity.
- Click the calculation button.
- Review the result panel above the form.
- Export your output as CSV or PDF.
Frequently Asked Questions
1. What does carrier density represent?
Carrier density measures how many free charge carriers exist within a material volume. These carriers are usually electrons or holes in semiconductors and conductors.
2. Why is mobility important here?
Mobility shows how easily carriers move under an electric field. Higher mobility means the same conductivity can occur with fewer carriers.
3. When should I use Hall coefficient input?
Use Hall coefficient when Hall measurement data is available. It provides an independent carrier density estimate and can indicate dominant carrier polarity.
4. Why are units important in this calculator?
Carrier density calculations are very sensitive to unit conversion. Conductivity, mobility, area, and thickness must follow the stated units for correct results.
5. What is sheet resistance used for?
Sheet resistance is useful for thin films, transparent conductors, and deposited layers. It helps compare films without requiring full three-dimensional geometry.
6. Can this be used for intrinsic materials?
Yes, but the input values must still reflect measured transport properties. Intrinsic samples usually have much lower carrier concentrations than doped materials.
7. Why might conductivity and Hall methods differ?
They may differ because of mixed carriers, measurement uncertainty, temperature variation, scattering effects, or inaccurate mobility assumptions used in calculations.
8. What does the graph show?
The graph illustrates how estimated carrier density changes when mobility changes while conductivity stays fixed. It is useful for sensitivity checks.