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Maximum Space Charge Width of a MOSFET Calculator

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Maximum Space Charge Width of a MOSFET Calculator

Maximum Space Charge Width of a MOSFET Calculator

Calculate the maximum space charge width using the equation:
\[ W_{max} = \sqrt{\frac{4\,\epsilon_s\,\phi_F}{q\,N_A}} \] where:
– \(\epsilon_s\) is the semiconductor permittivity, – \(\phi_F\) is the Fermi potential, and – \(N_A\) is the acceptor doping concentration.

* Ensure all inputs use consistent SI units.

Step 1: Enter Parameters

Example: 1.04e-10 F/m (for silicon)

Example: 0.3 V

Example: 1e23 m\(^{-3}\)

Formula: \( W_{max} = \sqrt{\frac{4\,\epsilon_s\,\phi_F}{q\,N_A}} \)


Practical Example:
For \(\epsilon_s = 1.04 \times 10^{-10}\) F/m, \(\phi_F = 0.3\) V, and \(N_A = 1 \times 10^{23}\) m\(^{-3}\), the maximum space charge width is calculated as:
\[ W_{max} = \sqrt{\frac{4 \times 1.04 \times 10^{-10} \times 0.3}{1.602 \times 10^{-19} \times 1 \times 10^{23}}} \approx 8.82 \times 10^{-8}\, \text{m} \quad (0.0882\,\mu\text{m}) \]