Forward Current Equation of the PN Junction Diode

A PN junction is obtained when a semiconducting material like silicon or germanium is doped with impurities. One side of it has many acceptor impurities and the other side has a large number of donor impurities. 

A donor impurity is diffused to a pure semiconductor to obtain an n-type; likewise, the structure impurity is diffused in a higher concentration to the other side to make it p-type.

A forward-biased PN junction diode is formed when a battery is connected to the ends of the PN junction in such a way that the positive terminal of the battery is connected to the p-side and the negative terminal is connected to the n-side.

Some important terms

1. Diode – Any device that allows the flow of current freely in one direction but does not allow the flow of current in the opposite direction is called a diode. 
2. Depletion layer – The depletion layer is a region in the PN junction diode, where no mobile carrier is found. This layer acts as a barrier that resists the flow of electrons from the n-side and holes from the p-side.
3. Diffusion current – In a PN junction, holes diffuse from p side to n side and electrons diffuse from n-side to the p-side. A potential gradient is generated, which results in the production of a current called diffusion current.
4. Drift current – It is generated due to the creation of electron-hole pairs in the depletion layer, which is under the influence of the electric field. The current flows from the n side to the p side. Drift current and diffusion current are in opposite directions.

Forward bias PN junction diode

• The forward bias PN junction causes the potential of the p-side to increase and hence, the height of the potential barrier decreases.
• The width of the depletion region is reduced in forward bias, due to which more diffusion takes place.
• Therefore, diffusion current is increased by connecting a battery in forward bias.
• The drift current remains constant as the electron-hole pairs are independent of an electric field.
• Here, diffusion current exceeds the drift current, so net current flows from the p-side to the n-side.
• The rate of diffusion increases as the applied potential difference increases along with the decrease in barrier height.
• When the applied potential difference is too high, the potential barrier is reduced to zero.
• The current I in the circuit changes non-linearly with the applied potential difference.
• A PN junction does not obey Ohm’s law.

Forward current equation of PN junction diode

In a p-n junction diode, the current I can be expressed as 

• I represents the current flowing through the diode,
• I0 is the dark saturation current,
• q is the charge on the electron,
• V represents the voltage applied across the diode,
• η is the (exponential) ideality factor.
• (8.6×10−5eVK) is the Boltzmann constant.
• T is the absolute temperature in Kelvin.

Dynamic resistance

Dynamic resistance is the function of operating potential difference. It is equal to the reciprocal of the slope of i-v.

The dynamic resistance of a pn junction diode is given as 

R = vi

Where,

∆v denotes the small change in the applied potential difference.

∆i denotes the corresponding small change in the current.

Examples of forward current equation of PN junction diode and their importance

Light-emitting diode (LED)

The extra energy is emitted in the form of a photon when a conduction electron transitions to the valence band to fill up a hole in the PN junction. The wavelength of this photon is in the visible range (380 nm-780 nm); one can see the emitted light. These kinds of PN junctions are known as light-emitting diodes.

For silicon and germanium, the wavelength of the photons falls in the infrared region.

Junction rectifier

When a potential difference is applied across a PN junction, that device conducts electricity more quickly from one terminal of the applied potential difference than from the other. Thus, a PN junction can serve as a function of a junction rectifier.

Junction laser

A photon is generated when an electron moves from the conduction band to the valence band. This photon stimulates a second electron to enter the valence band, producing a second photon by stimulated emission. A chain reaction of emission occurs, and a current is generated in the circuit. This leads to the generation of laser light. To bring this, the surfaces of the PN junction need to be flat and parallel to reflect the light back and forth within the crystal. Thus, a PN junction can act as a junction laser. 

Conclusion

A PN junction is a single semiconductor crystal with one end doped to form p-type material and the other end to form n-type material. The junction plane is the meeting point of these two types.

Zener diodes, junction rectifier, junction laser and a light-emitting diode are examples of the forward current equation of the PN junction diode.

Forward pn Junction diode has numerous importance; it is used in temperature sensors, reference voltages, solar cells and digital cameras.