The Mass Action Law

When we are working with doped semiconductors we have to know about the concentration of minority carriers. Since the concentration of majority carriers is known by the amount of doped impurity. The mass action law provides an easy way to derive equation for minority carriers concentration in semiconductors.

Key Questions:

• What is the mass action law?
• How it is helpful in determining the equation for carrier concentration in semiconductors

The Mass Action Law:

This law is used to derive an important relationship between concentration of minority carriers and majority carriers at a constant temperature.

The addition of n-type impurities decreases the number of holes. Similarly, Doping with p-type impurities decreases the concentration of free electrons.

A theoretical analysis lead to the result that under thermal equilibrium, the product of positive and negative charge carriers is a constant, irrespective of the amount of donor and acceptor impurities. This relationship is called the mass action law.

ni2=np ….. (equation 1)

Where ni the intrinsic Carrier concentration is a function of temperature.

Electron and Hole Concentration:

The  mass action law (equation 1) is used to derive the carrier concentration in n-type or p-type material. The amount of majority carriers is approximately equal to the amount of impurity doping is added. The mass action law is used to find out the minority carrier concentration.

According to the principle of electrical neutrality, overall charge on any material should be equal.

So ND+p=NA+n….(equation 2)

Where ND= donor concentration

             NA=Acceptor concentration

             p=hole concentration

             n=electron concentration

Intrinsic Semiconductors

For intrinsic semiconductors ND=NA=0

From equation 2

p=n

By mass action law

np=ni2

p2=n2=ni2

p=n=ni

n-type Semiconductors

For n-type Semiconductors NA=0 and ND=n

From the mass action law

pn=ni2

p=ni2/n

                       p=ni2/ND     equation 3

The above equation is used to calculate the minority carriers concentration (in this case holes) in an n-type semiconductor.

p-type Semiconductors:

For p-type semiconductors ND==0 and NA=p

From the mass action law

np=ni2

n=ni2/p

                         n=ni2/NA       equation 4

The above equation is used to calculate the minority carriers concentration (in this case electrons) in a p-type semiconductor.

According to the law if we increase doping level in the semiconductor material, the concentration of minority carriers would decrease.