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Reverse Saturation Current Density in PN Junction Diode Calculator

Reverse Saturation Current Density in PN Junction Diode Calculator

Reverse Saturation Current Density in PN Junction Diode Calculator

Calculate the reverse saturation current density using the equation:
\[ J_{s} = q\, n_{i}^{2}\left(\frac{D_{p}}{N_{D}\,L_{p}} + \frac{D_{n}}{N_{A}\,L_{n}}\right) \] where all parameters are in SI units.

* Enter all values in SI units.

Step 1: Enter Parameters

Example: 1.5e16 m\(^{-3}\) for silicon at 300 K

Example: 0.036 m\(^2\)/s

Example: 0.012 m\(^2\)/s

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

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

Example: 1e-6 m

Example: 1e-6 m

Formula:
\( J_{s} = q\, n_{i}^{2}\left(\frac{D_{p}}{N_{D}\,L_{p}} + \frac{D_{n}}{N_{A}\,L_{n}}\right) \)


Practical Example:
For a silicon PN junction at room temperature with:
\( n_{i} = 1.5\times10^{16} \, \text{m}^{-3} \), \( D_{n} = 0.036 \, \text{m}^2/\text{s} \), \( D_{p} = 0.012 \, \text{m}^2/\text{s} \),
\( N_{A} = 1\times10^{23} \, \text{m}^{-3} \), \( N_{D} = 1\times10^{23} \, \text{m}^{-3} \), \( L_{n} = 1\times10^{-6} \, \text{m} \), and \( L_{p} = 1\times10^{-6} \, \text{m} \):

First, compute the bracket term:
\[ \frac{D_{p}}{N_{D}\,L_{p}} + \frac{D_{n}}{N_{A}\,L_{n}} = \frac{0.012}{1\times10^{23}\times1\times10^{-6}} + \frac{0.036}{1\times10^{23}\times1\times10^{-6}} = 4.8\times10^{-19} \]
Then, using \( q = 1.602\times10^{-19} \) C and \( n_{i}^{2} = (1.5\times10^{16})^{2} = 2.25\times10^{32} \), we get:
\[ J_{s} = 1.602\times10^{-19}\times2.25\times10^{32}\times4.8\times10^{-19} \approx 1.73\times10^{-5}\, \text{A/m}^2 \]
Converting to A/cm2: \(1.73\times10^{-5}\, \text{A/m}^2 \times 1\times10^{-4} = 1.73\times10^{-9}\, \text{A/cm}^2\).

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