Electronic – Relation between built in potential and doping

diodes

What is the relationship between the built in potential and the doping concentration of a pn junction diode ? I could only find the relationship between the depletion region width and the doping concentration.

Best Answer

I don't know how you missed the first formula for the built in voltage that I can find.

$$ V_{bi} = V_t\ln(\frac{p_nn_p}{n_i^2}) $$

$$ p_n = \frac{n_i^2}{n_n}$$

$$ n_p = \frac{n_i^2}{p_p}$$

and last but not least:

$$ n_n = N_D - N_A $$

with Nd and Na being the donor / acceptor doping in the n-region

$$ p_p = N_A - N_D $$

with Na and Nd being the acceptor / donor doping in the p-region

Assuming you know algebra you can easily express the built in voltage in terms of the acceptor and donor concentrations.

$$V_0 = V_t \cdot ln\Big(\frac{N_d N_a}{n_i^2}\Big)$$

This equation is what I missed.