Thermodynamic and electro-kinetic aspects of diffusion and migration (charge transfer) of electrons and holes across an n-p-type junction under bias and a photovoltaic cell under illumination

The present article deals with the issue of thermodynamic and electro-kinetic aspects of diffusion and migration (charge transfer) of electrons (e) and holes (h) across an n-type-p-type junction under bias and a photovoltaic cell under illumination from the pedagogical motivation. From the equality of the electrochemical potential of e and h on both sides, it follows that the alignment of the Fermi energy levels gives rise to the separation of the energy bands, causing the build-up of a reversible contact potential. Physical significance of the contact potential has been extensively discussed. Under forward bias, diffusion of the majority carrier electrons in the n-type side has been detailed with simultaneously recombining through the junction “p/n” (p ← n) to the p-type side. Moreover, diffusion of the majority holes in the p-type side has been dealt with in a similar way but in the opposite direction. As a result of under forward bias, the overall resulting current flows in the direction from the p-type to the n-type side. Under forward bias, the contribution of the diffusion current by the majority carriers far outweighs the contribution of the drift current by the minority carriers. In contrast, under reverse bias, the minority electrons created within a diffusion length of e of the transition region on the p side can diffuse to the junction “n/p” (n ← p), and finally, they are swept down before recombining due to the migration (charge transfer) across the junction “n/p” (n ← p) in the direction opposite to the electric field, from p to n, that is, without any barriers. Furthermore, diffusion of the minority holes created within the transition region on the n side to the junction “p/n” (p ← n) has been dealt with likewise across the junction “p/n” (p ← n), but in the direction of the electric field, from n to p. As a result of under reverse bias, the overall resulting current flows in the direction from the n-type to the p-type side. Under reverse bias, the reverse drift current by the minority carriers dominates the diffusion current by the majority carriers. The derivation of a diode equation with bias and another modified equation under illumination necessitates a deep understanding of the Fick’s first law and modified Fick’s second formula. The photo-driven voltaic cell with illumination delivering electric power to the external load is clearly distinguished from the externally driven junction with bias. The delivered current enhanced by the incident light radiation is almost exclusively determined by the drift current by the minority carriers e and h due to their migration (charge transfer) in the direction from the n-type to the p-type. The delivered photovoltage runs in the direction as in the forward bias (from p to n). The photo-enhanced reverse drift current dominates the diffusion current by the majority carriers since the effect of the light quanta radiation is minimal on the change in the majority carrier concentration. Finally, some quizzes are raised with their answers to them, so that the readers facing the problems are motivated to solve them in the instructive perspectives.