PX262 - L3 - p-n junction

• it occurs at the boundary of one region doped with p-type impurities and another with n-type impurities
• the current flow is given by:

where, $i_s$ is the saturation current

• this acts as a one way device

• when two regions are in equilibrium, they must have the same chemical potential

• applying this to p-type semiconductor in contact with an n-type:

• in equilibrium, there is no net current through the junction, but carriers cross back and forth
• when first connected, the many holes in the p-region diffuse across the junction, into the n-region, where they can recombine with some of the many free electrons
• similarly, electrons diffuse from the n to the p-region
• this sets up an electric field, ${\overrightarrow{\epsilon }}_{elec}$
• the potential energy associated with this field raises the energy levels in the p-region relative to those in the n-region so that the chemical potentials align
• the upward shift (AB) $\simeq \mathrm{\Delta }$

• in equilibrium, there are four currents across the junction
• the diffusion processes lead to a recombination of holes and electrons: $i_{pr}$ and $i_{nr}$
• at the same time, electron-hole pairs are generated by thermal excitation: $i_{pg}$ and $i_{ng}$
• the electric field, ${\overrightarrow{\epsilon }}_{elec}$ sweeps them out of the junction
• at equilibrium, these currents balance:

• note:

  • $i_{ng}\propto \exp (-\mathrm{\Delta }/k_{B}T)$, ie. the probability of exciting a minority carrier in the p-region ($e^{-}$)
  • $i_{nr}\propto \exp (-{\mathrm{\Delta }}_{AB}/k_{B}T)$, ie. the probability of a majority carrier flowing from the n-region (hole), or, the probability that a majority carrier has enough energy to surmount the barrier, ${\mathrm{\Delta }}_{AB}$, where $\mathrm{\Delta }\simeq {\mathrm{\Delta }}_{AB}$

• applying a forward bias (positive potential difference) across the junction

• the electric field, ${\overrightarrow{\epsilon }}_{elec}$, and the difference between the energy levels in the p-region and the n-region are reduced by: $\mathrm{\Delta }E=-e{V}_{applied}$

• it becomes easier for the electrons in the n-type region to climb the potential barrier and diffuse into the p-region, and for the holes in the p-region to diffuse into the n-region
• both recombination currents $i_{nr}$ and $i_{pr}$ are increased by: $\exp (e{V}_{applied}/k_{B}T)$
• the generation currents, $i_{ng}$ and $i_{pg}$, do not change
• the net hole current:

• similarly, the net electron current:

• therefore, the total current:

where, $i_s=|i_{pg}|+|i_{ng}|$

• therefore, this diode effectively allows current in the forward direction only
  j