Calculated Results
These results use a MOS inversion-channel model under the gradual channel approximation.
Calculator Inputs
Enter semiconductor and geometry values to estimate local and total inversion charge behavior.
Example Data Table
These example rows show how operating region and local charge vary with geometry and bias.
| Case | Type | εr | tox (nm) | VGS (V) | VTH (V) | VDS (V) | L (µm) | x (µm) | W (µm) | Region | Local Charge Density | Total Channel Charge |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Example 1 | n-channel | 3.9 | 5 | 1.8 | 0.7 | 0.2 | 1.0 | 0.5 | 100 | Linear | -6.906 mC/m² | -0.691 pC |
| Example 2 | n-channel | 3.9 | 4 | 1.6 | 0.6 | 1.2 | 1.2 | 0.8 | 120 | Saturation | -1.727 mC/m² | -0.518 pC |
| Example 3 | p-channel | 3.9 | 6 | 2.2 | 0.8 | 0.6 | 2.0 | 1.0 | 200 | Linear | +6.331 mC/m² | +2.532 pC |
Formula Used
1) Oxide capacitance per unit area
Cox = ε0 × εr / tox
This converts dielectric thickness into gate-oxide capacitance per square meter.
2) Gate overdrive voltage
VOV = VGS − VTH
If overdrive is zero or negative, strong inversion is not established.
3) Local inversion charge density
Q′(x) = s × Cox × max(VOV − V(x), 0)
The sign factor s equals −1 for n-channel and +1 for p-channel.
4) Channel potential approximation
V(x) = VDS × (x / L)
This linear potential profile is used before pinch-off under the gradual channel approximation.
5) Total channel charge
Linear region: Q = s × W × L × Cox × (VOV − VDS/2)Saturation: Q = s × W × L × Cox × VOV2 / (2VDS)
The saturation form integrates only the active inversion section before pinch-off.
6) Sheet carrier concentration
Ns = |Q′(x)| / q
This converts local sheet charge density into carriers per unit area.
How to Use This Calculator
- Choose the channel type so the charge sign follows the selected inversion carrier.
- Enter oxide permittivity and oxide thickness to define gate-oxide capacitance.
- Provide VGS, VTH, and VDS to set the operating point.
- Enter channel length, channel position, and device width in micrometers.
- Press the calculation button to display results above the form.
- Review region, local charge density, total charge, and carrier sheet concentration.
- Use the CSV or PDF buttons to export the latest calculated values.
- Compare your outputs with the example data table to validate expected trends.
Frequently Asked Questions
What does this calculator measure?
It estimates inversion channel charge density for a MOS structure. It also reports oxide capacitance, local sheet charge, average charge density, total channel charge, and sheet carrier concentration.
Which physical model is used here?
The calculator uses the gradual channel approximation. It assumes a long-channel device and linear channel potential variation until pinch-off in saturation.
Why does charge sign change between channel types?
An n-channel uses electron inversion charge, shown as negative. A p-channel uses hole inversion charge, shown as positive. Magnitudes still reflect the same capacitance-based model.
What happens when VGS is below threshold?
Strong inversion is not formed. The calculator blocks the result because the simplified inversion-charge model is intended for above-threshold channel operation.
How is saturation handled?
When VDS exceeds overdrive voltage, the calculator estimates pinch-off position and sets inversion charge to zero beyond that point. Total charge is integrated over the active portion.
Are the outputs suitable for short-channel devices?
Use caution. Velocity saturation, mobility degradation, quantum effects, and short-channel electrostatics can shift real values away from this simplified long-channel estimate.
Why is oxide thickness important?
Oxide thickness directly changes oxide capacitance per unit area. Thinner oxide increases capacitance and therefore increases inversion charge for the same gate overdrive.
Can I export the computed results?
Yes. After calculating, use the CSV or PDF buttons to download the current input values and the derived output metrics for reporting or review.