In an extrinsic semiconductor, two types of charge carriers exist: majority carriers and minority carriers. The majority carriers are produced in large numbers due to impurity doping, while the minority carrier concentration remains very small.
In an n-type semiconductor, electrons are the majority carriers, and holes form the minority carrier concentration. In a p-type semiconductor, holes are the majority carriers, and electrons constitute the minority carrier concentration.
Although small, the minority carrier concentration plays a crucial role in the operation of semiconductor devices such as p–n junction diodes, transistors, and solar cells.
Minority Carrier Concentration in n-Type Semiconductor
In an n-type semiconductor, the majority carriers are electrons, and the minority carriers are holes.
According to the law of mass action, the product of electron concentration n and hole concentration p in thermal equilibrium is constant and is given by
where ni is the intrinsic carrier concentration.
In an n-type semiconductor, the electron concentration is approximately equal to the donor impurity concentration:
Using the mass action law:
Substituting
Thus, the minority carrier concentration (holes) in an n-type semiconductor is inversely proportional to the donor concentration.
Important Observation
As donor concentration increases:
- Electron concentration increases.
Hole concentration decreases.
Minority Carrier Concentration in p-Type Semiconductor
In a p-type semiconductor, the majority carriers are holes, and the minority carriers are electrons.
The hole concentration is approximately equal to the acceptor concentration:Using the law of mass action:
Therefore, $$n=\frac{n_i^2}{p}$$ Substituting $$n=\frac{n_i^2}{N_A}$$ Thus, the minority carrier concentration (electrons) in a p-type semiconductor decreases as the acceptor concentration increases.
Important Observations
Minority carrier concentration is very small compared to the majority carriers.
It depends on the intrinsic carrier concentration.
Increasing impurity concentration decreases minority carrier concentration.
Minority carriers are responsible for important phenomena such as diffusion current and diode operation.
Comparative Summary
| Semiconductor Type | Majority Carrier | Minority Carrier | Minority Carrier Concentration |
|---|---|---|---|
|
n-type |
Electrons |
Holes |
$$p=\frac{n_i^2}{N_D}$$ |
|
p-type |
Holes |
Electrons |
$$n=\frac{n_i^2}{N_A}$$ |
Minority Carrier Diffusion in Semiconductors
Despite their small number, minority carriers play a crucial role in semiconductor devices like solar cells, transistors, and p–n junction diodes.
Minority carriers begin to migrate from the area of higher concentration to the area of lower concentration when their concentration rises in one area of the semiconductor relative to another.
Minority carrier diffusion is the term used to describe this movement of minority carriers caused by a concentration gradient.
Physical Origin of Minority Carrier Diffusion
In thermal equilibrium, the minority carrier concentration remains uniform throughout the semiconductor. When external disturbances such as heat, light, or electrical injection generate additional carriers, the local minority carrier concentration increases.
Due to this concentration gradient, minority carriers diffuse toward regions of lower concentration. During diffusion, many carriers recombine with majority carriers, causing the excess carrier concentration to gradually decrease until equilibrium is restored.
Variation of Minority Carrier Concentration with Distance
The concentration of excess minority carriers decreases exponentially with distance. This variation is expressed as $$\bigtriangleup n(x)=\bigtriangleup n(0)e^{-x/L_n}$$ where:
Δn(x) = excess electron concentration at distance x
Δn(0) = excess electron concentration at x = 0
Ln = diffusion length of electrons
The diffusion length represents the average distance a minority carrier travels before recombination occurs.
Minority Carrier Lifetime
Minority carriers also decay with time due to recombination. The decrease in excess carrier concentration with time is given by $$\bigtriangleup n(t)=\bigtriangleup n(0)e^{-t/\tau_n}$$
where τn = mean lifetime of electrons
The lifetime represents the average time a minority carrier exists before recombining.
Diffusion Length
The diffusion length is related to the diffusion coefficient and carrier lifetime by $$L_n=\sqrt{D_n\tau_n}$$
Similarly, for holes in an n-type semiconductor,
$$L_p=\sqrt{D_p\tau_p}$$
where Dn = diffusion coefficient for electrons and Dp = diffusion coefficient for holes
Importance of Minority Carrier Diffusion
Minority carrier diffusion is a very important process in semiconductor devices because:
It plays a major role in p–n junction formation.
It determines the operation of bipolar junction transistors (BJT).
It is responsible for carrier transport in solar cells and photodiodes.
It influences the current flow in semiconductor devices.
Important Exam Questions
Short Questions
What are minority carriers in semiconductors?
Write the expression for minority carrier concentration in an n-type semiconductor.
What is the minority carrier in a p-type semiconductor?
Long Question
Explain minority carrier concentration in n-type and p-type semiconductors using the law of mass action.
FAQs
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1. What is meant by minority carrier concentration?
"Minority carrier concentration" refers to the number of charge carriers present in a smaller quantity in a semiconductor. In n-type materials, holes are minority carriers, while in p-type materials, electrons are minority carriers.
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2. What are minority carriers in a semiconductor?
Minority carriers are the less abundant charge carriers:
- Electrons in a p-type semiconductor
- Holes in an n-type semiconductor
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3. What is the minority carrier concentration in an n-type semiconductor?
In an n-type semiconductor, minority carriers are holes, and their concentration is given by:
p = nᵢ² / n -
4. What is the minority carrier concentration in a p-type semiconductor?
In a p-type semiconductor, minority carriers are electrons, and their concentration is:
n = nᵢ² / p -
5. Why are minority carriers important?
Even though they are fewer in number, minority carriers play a crucial role in the operation of semiconductor devices like diodes, transistors, and photovoltaic cells.
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6. How does temperature affect minority carrier concentration?
As temperature increases, intrinsic carrier concentration (nᵢ) increases, which leads to an increase in minority carrier concentration.
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7. How does doping affect minority carrier concentration?
Increasing doping raises majority carrier concentration, which decreases minority carrier concentration according to the mass action law.