Barrier Potential

Summary

This lecture covers the concept of the built-in potential or barrier potential in a PN junction diode without an applied bias. It explains how diffusion leads to the formation of a depletion layer, which acts as a barrier for further charge movement. The lecture introduces the formula for calculating the barrier potential (V_B = V_T * ln(Na * Nd / Ni^2)), where V_T is the thermal voltage, Na and Nd are acceptor and donor concentrations, and Ni is the intrinsic carrier density. The Boltzmann constant, temperature conversion to Kelvin, and the charge of an electron are also discussed. A numerical example calculates the built-in potential for a silicon PN junction at room temperature.

Takeaways

• 🔋 The built-in potential, also known as barrier potential, is the potential difference created at a PN junction with no applied bias.
• 🌀 Diffusion is the process where free charge carriers recombine, leading to the formation of a depletion layer depleted of free charge carriers.
• 💠 The depletion layer consists of fixed immobile ions with positive and negative charges, which create the barrier potential.
• 🚫 The barrier potential acts as a barrier to the further movement of charge, preventing the recombination of holes and electrons.
• 📘 The expression for barrier potential (V_B) is given by V_B = V_T * ln((n_a * n_d) / ni^2), where V_T is the thermal voltage.
• 🔬 Boltzmann's constant (K) is 1.38066 × 10^-23 J/K, used to calculate the thermal voltage (V_T).
• ⚖️ Absolute temperature (T) is in Kelvin, calculated by adding 273 to the temperature in degrees Celsius.
• ⚡ The charge of one electron (e) is 1.6 × 10^-19 coulombs, used in the calculation of V_T.
• 🔢 At room temperature (27°C or 300K), the thermal voltage (V_T) is approximately 0.026 volts.
• 📌 For a silicon PN junction at room temperature, the barrier potential is approximately 0.757 volts.
• 📚 The barrier potential values for silicon and germanium are often used in semiconductor calculations, with silicon typically at 0.7 volts and germanium at 0.3 volts.

Q & A

What is the built-in potential in a PN junction?

The built-in potential, also known as barrier potential, is a potential difference that arises at the junction of a PN junction diode due to the diffusion of charge carriers and the formation of a depletion layer. It acts as a barrier to the further movement of charge carriers.

What causes the formation of a depletion layer in a PN junction?

The depletion layer forms due to the diffusion process where free charge carriers recombine with each other, leading to the creation of immobile ions. This results in a region depleted of mobile charge carriers, leaving behind a layer of fixed immobile ions with opposite charges on the P and N sides.

Why is the depletion layer called so?

The depletion layer is called so because it is depleted of free charge carriers. It contains only fixed, immobile ions, which are the result of recombination between free charge carriers.

What is the role of the barrier potential in a PN junction?

The barrier potential acts as a barrier to the further movement of charge carriers. The positive layer on the N side repels electrons, and the negative layer on the P side repels holes, preventing further diffusion and maintaining the potential difference across the junction.

What is the expression for barrier potential (V_B)?

The expression for barrier potential (V_B) is given by V_B = V_T * ln((n_a * n_d) / ni^2), where V_T is the thermal voltage, n_a is the acceptor concentration, n_d is the donor concentration, and ni is the intrinsic carrier density.

What is the thermal voltage (V_T) and how is it calculated?

Thermal voltage (V_T) is the voltage equivalent of temperature and is calculated using the formula V_T = (K * T) / e, where K is the Boltzmann constant, T is the absolute temperature in Kelvin, and e is the charge of an electron.

What is the Boltzmann constant and its value?

The Boltzmann constant (K) is a physical constant that relates the energy at the particle level to temperature. Its value is 1.380649 × 10^-23 joules per Kelvin.

How do you convert temperature from Celsius to Kelvin?

To convert temperature from Celsius to Kelvin, you add 273 to the Celsius temperature. For example, 27 degrees Celsius is equal to 300 Kelvin.

What is the charge of an electron?

The charge of an electron (e) is -1.6 × 10^-19 coulombs.

How is the built-in potential of a silicon PN junction calculated at room temperature?

At room temperature (27 degrees Celsius or 300 Kelvin), the built-in potential of a silicon PN junction is calculated using the formula V_B = 0.026 * ln((n_a * n_d) / ni^2), with n_a, n_d, and ni being the acceptor concentration, donor concentration, and intrinsic carrier density, respectively.

What is the typical barrier potential for a silicon PN junction at room temperature?

The typical barrier potential for a silicon PN junction at room temperature is approximately 0.7 volts.