When a p-type and n-type semiconductor are joined, then due to the concentration gradient between the n and p regions, charge carriers start diffusing across the junction. As electrons and holes recombine near the junction, only positive immobile ions on the n-side and negative immobile ions on the p-side are left behind near the junction. This region is called the depletion region.
Due to these immobile ions, an internal electric field is created near the junction. This field produces a voltage across the junction called the potential barrier or built-in potential.
The potential barrier plays a very important role because it opposes further diffusion of majority carriers across the p–n junction and helps maintain equilibrium at the junction. It also determines the diode’s behavior when an external bias is applied.
The potential barrier is defined as
The potential difference produced across the depletion region of a p–n junction diode due to the internal electric field created by immobile acceptor and donor ions is called the potential barrier.
Typical values of the potential barrier at room temperature are the following:
- Silicon ≈ 0.7 V
- Germanium ≈ 0.3 V
Derivation of Potential Barrier
The following figure shows the energy band diagram of a p-n junction diode, highlighting the potential barrier VB.
The potential barrier (the built-in potential) VB can be derived using the electron concentration in the n and p regions of the junction diode. The electron concentration in the conduction band of the n region is given by
$$n_n=N_cexp\left[ -\left( E_{cn}-E_{Fn} \right)/kT \right] ———(1)$$
Similarly, the electron concentration in the conduction band of the p region is given by
$$n_p=N_cexp\left[ -\left( E_{cp}-E_{Fp} \right)/kT \right] ———-(2)$$
Since the bottom of the conduction band in the p region is at Ecn + eVB. Therefore, equation (2) becomes,
$$n_p=N_cexp\left[ -\left( E_{cn}+eV_B-E_{Fp} \right)/kT \right] ———(3)$$
Dividing equation (1) by equation (3), we get
$$\frac{n_n}{n_p}=exp\left( \frac{eV_B}{kT} \right)$$ (Since at equilibrium EFn = EFp)
This equation is called Boltzmann’s equation.
Taking the logarithm on both sides of the above equation, we get
$$V_B= \frac{kT}{e}\log_e\left( \frac{n_n}{n_p} \right)$$
We can write the above equation as
$$V_B= \frac{kT}{e}\log_e\left( \frac{n_np_p}{n_pp_p} \right)———(4)$$
Since at room temperature all impurity atoms are ionized, therefore
$$n_n=N_D \quad and\quad p_p=N_A$$
where
ND = donor concentration
NA = acceptor concentration
And from the law of mass action, nppp = ni2
Hence, now equation (4) becomes
$$V_B= \frac{kT}{e}\log_e\left( \frac{N_DN_A}{n_i^2} \right)$$
This is the final expression for the built-in potential of a p–n junction diode.
Where:
VB = built-in potential (potential barrier)
k = Boltzmann constant
T = absolute temperature
e = electronic charge
NA = acceptor concentration
ND = donor concentration
ni = intrinsic carrier concentration
Physical Interpretation of Potential Barrier
For a higher doping concentration (NA or ND), there is a higher potential barrier, whereas a higher concentration of intrinsic carriers lowers the potential barrier. An increase in temperature modifies the barrier slightly.
Importance of Potential Barrier
The potential barrier is an essential part of a p-n junction because it controls the flow of charge carriers across the junction. It prevents further diffusion of the majority charge carriers from the p-region to the n-region and vice versa, thereby helping maintain thermal equilibrium.
The barrier also regulates the behavior of the diode when an external voltage is applied. Under forward bias, the potential barrier decreases, making it easier for current to flow.
Under reverse bias, the barrier increases and restricts current flow. Therefore, the potential barrier is essential to the proper operation of semiconductor devices.
Important Examination Questions
Short Answer
- Define potential barrier.
- Write the expression for built-in potential.
Long Answer / Derivation
- Derive the expression for the potential barrier in a p–n junction diode.
- Explain the formation of the built-in potential using an energy band diagram.
Conclusion – Potential Barrier (Built-in Potential)
The potential barrier is the internal voltage that forms in a p–n junction to control the movement of charge carriers. It plays a key role in diode operation by regulating current flow under different biasing conditions and forms the basis of semiconductor device behavior.
FAQs
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1. What is potential barrier in a p–n junction?
The potential barrier is the voltage difference that develops across the junction of p-type and n-type semiconductors when they are joined. It acts as an internal electric field that prevents further movement of charge carriers across the junction.
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2. How does potential barrier form in a p–n junction?
When the p-region and n-region come into contact, electrons and holes start diffusing across the junction due to concentration differences. This diffusion leaves behind charged ions, creating an electric field that opposes further diffusion. This opposition results in the formation of the potential barrier.
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3. What is formula for potential barrier?
The built-in potential of a p–n junction is given by:
where is Boltzmann's constant, is temperature, is the charge of an electron, and are doping concentrations, and is intrinsic carrier concentration.
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4. What is the typical value of potential barrier in semiconductors?
For silicon, the potential barrier is usually around 0.6 to 0.7 V, while for germanium it is approximately 0.2 to 0.3 V at room temperature.
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5. How does temperature affect the potential barrier?
As temperature increases, the potential barrier slightly decreases because more charge carriers are generated, which reduces the strength of the built-in electric field.
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6. What is potential barrier and depletion region?
The depletion region is the area around the junction where mobile charge carriers are absent, while the potential barrier is the voltage developed across this region that opposes carrier movement.
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7. Can the potential barrier be controlled?
Yes, it can be controlled by applying an external voltage (biasing). Forward bias reduces the barrier, whereas reverse bias increases it.
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8. What is another name for barrier potential?
Another name for barrier potential is built-in potential.
It is also sometimes referred to as:
Junction potential
Contact potential
Among these, built-in potential is the most commonly used term in semiconductor physics.
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9. Why is it called a barrier?
It is called a “barrier” because it acts like an obstacle that prevents charge carriers from freely crossing the p–n junction.