Hello!(adsbygoogle = window.adsbygoogle || []).push({});

The (potential) energy of an electron in a solid structure is always negative; also the [itex]E_c[/itex] and [itex]E_v[/itex] levels (conduction band and valence band limits) are negative, in the band diagram of a pn junction.

When the junction is built and thermal equilibrium is reached, the depletion region creates an electric field and a potential barrier [itex]\phi_i[/itex].

But I have some doubts about this.

1) First of all,

[itex]\phi_i = \displaystyle \frac{kT}{q} \log \left( \displaystyle \frac{N_D N_A}{n_i^2} \right)[/itex]

where [itex]k[/itex] is Boltzmann's constant, [itex]T[/itex] is the absolute temperature and [itex]q[/itex] is the absolute value of the electron charge. The energy step due to this built-in potential is [itex]q \phi_i[/itex], but why a positive [itex]q[/itex] is used to calculate this step? Given a voltage difference [itex]\Delta V = \phi_i[/itex], the corresponding potential energy difference should be [itex]\Delta U = q \Delta V = - |q| \Delta V[/itex] in the case of an electron.

2) Let's suppose anyway that [itex]q \phi_i > 0[/itex].

In the conduction band of the n-region, just the charge carriers with an energy [itex]E = E_c + q \phi_i[/itex] can cross the junction and diffuse to the p-region. So, I would say that the p-region, with respect to the n-region, is at ahigher potential.

In order to have a reference image, let's consider this document, page 11. Why in the last plot, which shows [itex]V[/itex] as function of position, the n-side is at a higher potential and the p-side at [itex]V = 0[/itex]? (Consider [itex]V_A = 0[/itex], that is the case of thermal equilibrium)

3) What about the vacuum level? It is never depicted in the band diagram of a pn junction; but how is it affected by the built-in voltage?

Thank you anyway for having read.

Emily

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Built-in potential in pn junction

Have something to add?

Draft saved
Draft deleted

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**