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: \(1.73\times10^{-5}\, \text{A/m}^2 \times 1\times10^{-4} = 1.73\times10^{-9}\, \text{A/cm}^2\).