Depletion region, electric field, drift and diffusion currents

Depletion region:
Formation: In a PN junction, the electrons diffuse from N to the P side, leaving behind immobile donor ions, creating a region devoid of mobile charge carriers, known as the depletion region. Similarly, holes diffuse from P to the N side, leaving behind immobile acceptor ions.
Built-in Potential (Vbi):
Vbi = (KT/q)ln(NaNb / ni^2), where N_a and N_b are the doping concentrations of the P and N regions, ni is the intrinsic carrier concentration, K is Boltzmann constant, T is the temperature, and q is the electronic charge.
Relation between Vbi and energy band diagram:
At equilibrium, the bands bend due to the formation of the depletion region, creating a potential barrier known as the built-in potential, which opposes further diffusion of charge carriers across the junction.
Electric field (E) in the depletion region and its direction:
The electric field points from the positive charge (uncompensated donor ions) in the N region to the negative charge (uncompensated acceptor ions) in the P region.
Drift current:
Drift current is the movement of charge carriers due to the influence of an electric field. It is directly proportional to the electric field and the carrier concentration.
Diffusion current:
Diffusion current is the movement of charge carriers from a region of higher concentration to a region of lower concentration. It is directly proportional to the concentration gradient and carrier mobility.

Minority carriers, reverse bias, forward bias, breakdown and device characteristics

Minority and majority carriers:
In a PN junction, the majority carriers in the N region are electrons and holes in the P region. Conversely, the minority carriers in the N region are holes and electrons in the P region.
Reverse bias:
In reverse bias, an external voltage is applied opposite the built-in potential, increasing the depletion region’s width, reducing the chance of carrier recombination, and increasing the reverse bias current.
Forward bias:
In forward bias, an external voltage is applied in the same direction as the built-in potential, reducing the depletion region’s width, increasing the chance of carrier recombination, and dramatically increasing the forward bias current.
Avalanche breakdown:
Avalanche breakdown occurs when the reverse bias voltage is sufficiently high to cause impact ionization, where high-energy carriers collide with lattice atoms, creating additional electron-hole pairs, leading to a rapid increase in current.
Zener breakdown:
Zener breakdown occurs when the reverse bias voltage is sufficiently high to cause quantum tunneling of electrons from the valence band of the P region to the conduction band of the N region, leading to a sudden increase in current.

Reverse bias characteristic:
V-I characteristic shows a small reverse saturation current due to minority carriers.
Forward bias characteristic:
V-I characteristic shows an exponential increase in current with voltage, governed by the diode equation.
Temperature dependence of Vbi:
Vbi decreases with increasing temperature due to the increase in intrinsic carrier concentration.
Applications:
Rectification (converting AC to DC), light-emitting diodes (LEDs), solar cells, transistors, photodiodes, etc.