# Semiconductors

## N-Type semiconductors

n (majority carrier concentration in no of electron in CB/volume)

p (minority carrier concentration in no of holes in VB/volume)

$${ N }_{ D }$$ (donor concentration per unit volume)

## P-Type semiconductors

p (majority carrier concentration in no of holes in VB/volume)

n (minority carrier concentration in no of electrons in CB/volume)

$${ N }_{ A }$$ (donor concentration per unit volume)

NOTE –  CB (conduction band)

VB (valance band)

## Mass Action Law

Mass action law states that Under thermal equilibrium the product of the free electron concentration and the free hole concentration is equal to a constant equal to the square of intrinsic carrier concentration.

It is also known as low of conservation of charges

so mass action law is $$n.p={ n }_{ i }^{ 2 }$$  —————(1)

## Charge Neutrality Equation

Charge neutrality occurs when all the charge in a volume adds to zero, it is neutral, neither positive or negative.

no of +ve charge = no of -ve charge

$$n+{ N }_{ A }=p+{ N }_{ D }$$   —————(2)

Using mass action law and charge neutrality equation we can find the minority charge carrier concentration

### For n-type semiconductor (n>>p)

so using (2) equation   $$n\quad \simeq \quad { N }_{ D }$$

$${ N }_{ A }=0$$

Now by using mass action law

$$p\simeq \frac { { n }_{ i }^{ 2 } }{ { N }_{ D } }$$

### For p-type semiconductor (p>>n)

so using (2) equation $$p\quad \simeq \quad { N }_{ A }$$

$${ N }_{ D}=0$$

Now by using mass action law

$$n\simeq \frac { { n }_{ i }^{ 2 } }{ { N }_{ A} }$$

## Current component in semiconductor

Basically there are two types of current component in semiconductors

1.  Drift current density
2.  Diffusion current density

### Drift current density

• Drift current density is due to free charges or potential gradient

$$E=-\frac { { dv } }{ dx }$$

• It is also known as conduction current density

### Diffusion current density

• Diffusion current density is due to presence of concentration gradient
• It is not present in metal or conductors
• It is only present in semiconductors

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## December 16, 2019

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