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Built-in Potential Barrier Height Calculator

Built-in Potential Barrier Height Calculator

Built-in Potential Barrier Height Calculator

Calculate the built-in potential barrier height using the equation:
\[ V_{bi} = \frac{kT}{q}\ln\left(\frac{N_A\,N_D}{n_i^2}\right) \] where \(T\) is the temperature in Kelvin, \(N_A\) and \(N_D\) are the acceptor and donor concentrations, and \(n_i\) is the intrinsic carrier concentration.

* Enter all values in SI units.

Step 1: Enter Parameters

Example: 300 K

Example: 1×1023 m\(^{-3}\)

Example: 1×1023 m\(^{-3}\)

Example: 1.5×1016 m\(^{-3}\) for silicon at 300 K

Formula: \( V_{bi} = \frac{kT}{q}\ln\left(\frac{N_A\,N_D}{n_i^2}\right) \)


Practical Example:
For a silicon PN junction at 300 K with \(N_A = 1\times10^{23}\) m\(^{-3}\), \(N_D = 1\times10^{23}\) m\(^{-3}\), and \(n_i = 1.5\times10^{16}\) m\(^{-3}\),
we have:
\[ V_{bi} = \frac{(1.380649\times10^{-23})(300)}{1.602\times10^{-19}}\ln\left(\frac{(1\times10^{23})(1\times10^{23})}{(1.5\times10^{16})^2}\right) \]
which evaluates to approximately 0.80 V.

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