Subthreshold Slope Equation Calculator

Model subthreshold swing with flexible physics inputs. See thermal limits, body factors, and slope trends. Create reports, review examples, and visualize performance clearly today.

Calculator Inputs

Use one method at a time. Capacitance inputs only need consistent units because the ratio determines the body factor.

Plotly Graph

The chart compares the ideal thermal limit with the currently selected body-factor trend.

Showing a default trend using n = 1.20.

Formula Used

Definition

S = dVG / d(log10ID)

Weak-inversion equation

S = n × ln(10) × kT / q

Body-factor relation

n = 1 + Cdep / Cox

Measured sweep form
S = ΔVg / log10(I2/I1)

Where S is the subthreshold slope in volts per decade, n is the body factor, k is the Boltzmann constant, T is absolute temperature, and q is the electron charge.

For an ideal conventional MOSFET at 300 K, the lower thermal limit is near 60 mV/dec. Higher depletion effects or non-ideal electrostatics increase the slope.

How to Use This Calculator

  1. Select a calculation method that matches your data source.
  2. Enter the device temperature in kelvin.
  3. For the capacitance method, enter Cdep and Cox using matching units.
  4. For the body-factor method, enter the known value of n.
  5. For measured data, enter the gate-voltage change and current ratio.
  6. Click the calculate button to show the result above the form.
  7. Review the plotted slope trend and compare it with the ideal limit.
  8. Use the CSV or PDF buttons to export the current report.

Example Data Table

Temperature (K) Cdep Cox n Ideal S (mV/dec) Actual S (mV/dec)
300 0.20 1.00 1.20 59.53 71.44
325 0.15 1.00 1.15 64.49 74.16
350 0.10 1.00 1.10 69.45 76.39

Frequently Asked Questions

1. What does subthreshold slope measure?

It measures how much gate voltage is needed to change drain current by one decade in weak inversion. Lower values mean sharper switching and usually better low-voltage behavior.

2. Why is 60 mV/dec important?

At about 300 K, a conventional MOSFET has an ideal thermal lower limit near 60 mV/dec. This comes from Boltzmann carrier statistics in the subthreshold region.

3. Why do Cdep and Cox affect the slope?

They set the body factor n. A larger depletion contribution makes n bigger, which directly raises the subthreshold slope and weakens switching sharpness.

4. Do Cdep and Cox need absolute units?

They only need consistent units because the capacitance method uses the ratio Cdep/Cox. Per-area units are common, but any matching units work.

5. How does temperature change the result?

Subthreshold slope scales roughly linearly with absolute temperature in the ideal model. Higher temperature increases the thermal voltage and usually increases the slope.

6. When should I use the measured sweep method?

Use it when you already have two current points and the gate-voltage difference between them. It extracts slope directly from measured transfer data.

7. Can this calculator model non-classical steep-slope devices?

It is intended for conventional weak-inversion style analysis. Exotic devices that beat the thermal limit need different physical models and extraction methods.

8. Why export the results?

CSV files help with spreadsheets and lab logs. PDF files help with reports, sharing, and documenting assumptions, trends, and final extracted values.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.