P-N junction, injected carrier profile, diffusion length L, electron/hole currents vs X, Kirchhoff

In a p-n junction under forward bias, majority carriers injected across the barrier become minority carriers and recombine with majority carriers. For example, electrons injected from the n-type region to the p-type region combine with holes. The electrons fall off exponentially as they go deeper into the p region. Like a radioactive element, the rate at which electrons disappear by recombination is proportional to the number of them present.

In a graph of the injected electron concentration, the X-distance decay constant is called the diffusion length, equal to the square root of the electron diffusion constant multiplied by the average electron lifetime. One diffusion length can be microns to hundreds of microns long, hundreds to times longer than depletion region width.

The non-uniform carrier concentrations result in diffusion currents, which are proportional to the slopes of the concentration curves.

The total current through the semiconductor consists holes moving in the direction of the current and electrons moving in the opposite direction. In the steady state, with a constant forward bias voltage, the total current is constant across all values of X, a requirement of Kirchhoff's current law. Thus, the electron and hole currents are complementary, adding up to the same constant value.

In most of the n-type side, all the current is due to electrons. As the electrons approach the junction, they start to recombine with holes injected from the other side; the electron current decreases as the hole diffusion current increases. Electrons injected past the junction soon recombine with majority holes, and the electron current drops to zero.

In most of the p-type side all the current is due to holes. As holes approach the junction, they recombine with electrons injected from the left side. Holes injected past the junction soon recombine with majority electrons, and the hole current drops to zero.

When the applied voltage is lowered by 0.06 volts, the carrier concentrations, diffusion current, and total current decrease to one-tenth of what they were. Conversely, increasing the applied voltage by 0.06 volts increases all those quantities by a factor of 10. This is the exponential characteristic of diode forward bias.

Applying a negative voltage has the opposite effect, reducing the minority charge carriers near the junction. This is called minority carrier extraction, which is important in bipolar junction transistors.

The bipolar transistor has three adjacent doped regions, called the emitter, base, and collector; for example, n-type, p-type, and n-type, respectively. With the transistor operating in the "active" region (as an analog amplifier), the emitter-base junction is forward biased, which injects minority carriers into the base, while the base-emitter junction is reverse-biased, which extracts minority carriers from the base. The base is made thin enough that it greatly exceeds the diffusion length in the base, so a large current can flow between the emitter and collector. The base-emitter forward voltage controls this current. A small base current is amplified linearly to make the large emitter-collector current.

The next video in the series describes the I-V characteristics of the p-n diode and shows how the p-n junction can operate as a solar cell or light-emitting diode.

This is the fourth of several videos describing the p-n junction physics and electrical characteristics. The following viewing sequence is recommended.

P-N Junctions 1 -- Semiconductor P-N junction, electron/hole diffusion & drift, non-uniform doping profile:    • Semiconductor P-N junction, electron/...  

P-N Junctions 2 -- Depletion region, electric field barrier, built-in potential, reverse bias:    • P-N junction, depletion region, elect...  

P-N Junctions 3 -- Forward bias, Boltzmann, majority & minority injected carrier concentration profiles:    • P-N junction forward bias, Boltzmann,...  

P-N Junctions 4 (this video) -- Injected carrier profile, diffusion length L, electron/hole currents vs X, Kirchhoff current law:    • P-N junction, injected carrier profil...  

P-N Junctions 5 -- Electron/hole flow, exponential diode equation, diode as valve, photovoltaic solar cell, LED:    • P-N junction, electron/hole flow, exp...  

If you are not already familiar with the concepts of mobile electrons and holes in semiconductors, start with:    • Electrons and holes in semiconductors...  

For energy band model (conduction band, valence band, Fermi level), see https://www.chu.berkeley.edu/wp-conte...

For a detailed analysis of p-n junctions (Poisson’s equation, capacitance, charge storage, tunneling/avalanche junction breakdown, quasi-equilibrium boundary, laser diodes, Schottky diodes, optoelectronics), see https://www.chu.berkeley.edu/wp-conte...