Pn Junction : Basic theory

Pn junctions are formed by joining two different type of semiconductor material i.e. p-type semiconductor on one side and n-type semiconductor on another side. In this article, we are going to explain you about p-n juenction formation, phenomena of p-n junction formation and basic equations. Have a look at it.

Pn junction image

It is discovered by the American physicist Russell Ohl at Bell laboratories. In p-type semiconductor holes are majority carriers and electrons are minority carriers while in n-type semiconductor electrons are majority carriers and holes are minority carriers i.e. one end has excess of electrons and other has excess of holes.

P-n junction formation:

As we know the elements around us are classified into three categories i.e. insulator, conductor, semiconductor etc depending upon their electrical conductivity. The conductivity of semiconductors lies between the conductor and insulator i.e. conductors have high electrical conductivity and insulators have low electrical conductivity. The most common semiconductors we are using for the formation of PN junction are Germanium and silicon because of its electrical properties. Before proceeding further, we recommended reading semiconductor basics and its types for proper understanding.

PN junction formation image

Generally, there are several different ways to make a p-n junction. For the ease of understanding, we explain it in a simpler way by taking an example. We usually make it using a single wafer of Silicon or Germanium. For the formation of p-n junction, we firstly convert a silicon wafer to a p-type semiconductor by doping it with a trivalent impurity i.e. aluminium, gallium etc on one side. Then we dope this p-type semiconductor with a pentavalent impurity i.e. antimony, phosphorus etc to form an n-type region on the same wafer. Thus, through this, we made p-type and n-type semiconductors on the same wafer which results in the formation of the junction.

Phenomena’s occur during the  p-n junction formation:

At the time of PN junction formation we observe different phenomena occur like the movement of the majority and minority carriers, region formation etc.

Pn junction phenomena

[Image source]

Three important phenomena occur during the formation of p-n junction are:

(a) Diffusion:

In a silicon wafer when the junction is formed, a concentration occurs between p-type and n-type materials. This results in movement of electrons from n-side to p-side and holes from p-side to n-side through the junction. When a hole is diffused to n-side it leaves behind an ionised acceptor at the p-side and when the electron leaves the n-side region, it leaves behind an ionised donor at the n-side. This movement of electrons from n-side to p-side and the holes from p-side to n-side is called diffusion which results in diffusion current.

(b)Depletion region formation:

As we know, when more and more electrons leave the n-region and more and more holes leave the p-region then a region of positive and negative charges is formed at the junction. Negative charges get deposited near the p-side junction and the positive charges get deposited near the n-side junction. The region where negative and positive charges get deposited on one of the sides is known as depletion region.

(c) Drift:

When the negative charges get deposited near the p-side junction and the positive charges get deposited near the n-side junction then the electric field is generated. This electric field causes electrons to move from p-side to n-side and the holes from n-side to p-side. This motion of charge carriers due to the electric field is known as drift and the current resulting from the flow of electrons and holes is known as drift current.

Note: Drift current is opposite in direction to diffusion current.

Basic Equations of P-n junction:

In p-n junction, the size of depletion region depends on  the movement of the majority and minority carriers. Here we explain it with the help of mathematical equation.

Size of depletion region:

Let Ca and Cd be the concentration of acceptor and donor atoms and let No and Po be the equilibrium concentration of electrons and holes. As per the poison’s equation:

-d2 V / dx2 = ƿ / ϵ

 = q / ϵ [ (No – Po) + (Ca – Cd )

Where,

V= Electric potential

Ƿ = Charge Density

ϵ = Permittivity

q = Magnitude of electron charge

As we know, the total charge on either side of the depletion region must cancel out. Therefore, the multiplication of the width and the concentration on the p side and the n side become equal i.e

 dp Ca = dn Cd

dp = width of depletion region within the p-side

dn = width of depletion region within the n-side

After the movement of majority and minority carriers, the entire depletion region and potential difference across the p-n junction can be calculated as given below;

∆ V = ʃD ʃ   q / ϵ [ (No – Po) + (Cd – Ca ) dx dx

= (Ca Cd / (Cd – Ca ) )x (2q (dp + dn )2 / ϵ )

As we know in the depletion region,  No and Po is equal to zero. Therefore, the total width of the depletion region can be defined as:

d = √ (2 ϵ (Ca + Cd )/ q Ca Cd ) x ∆V

where ∆V can be written as ∆Vo + ∆Vext i.e. it is split into the voltage difference into the equilibrium plus external components.

Check animation of PN junction to gather more information: PN junction video

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