IntRoduction to solid state physics

Week 3: p-n Junctions - Basic Structure and Operation

Lecture Topics:

1. Introduction to the p-n Junction

   • Definition and importance of a p-n junction: A junction formed by joining p-type and n-type semiconductors.

   • The p-n junction is the basic building block of semiconductor devices such as diodes, transistors, and solar cells.

   • Formation of the depletion region: When the p-type and n-type materials come into contact, electrons from the n-side recombine with holes from the p-side near the junction, leaving behind ionized donor and acceptor atoms that form a region devoid of free charge carriers, called the depletion region.

2. Band Structure of the p-n Junction

   • Energy band diagram of the p-n junction before contact:

     • The Fermi level of the n-type semiconductor is close to the conduction band, while the Fermi level of the p-type semiconductor is close to the valence band.

   • After the junction is formed, the Fermi levels of the two regions align, leading to a band bending at the junction.

   • Formation of a built-in potential V0, which creates an electric field in the depletion region.

3. Depletion Region and Built-in Potential

   • The depletion region is created due to the diffusion of electrons and holes across the junction.

   • Characteristics of the depletion region:

     • It is free of mobile charge carriers (electrons and holes) and contains only fixed ionized donor and acceptor atoms.

     • The width of the depletion region depends on the doping levels of the p-type and n-type materials.

   • Built-in potential V0:

• where NA and ND​ are the acceptor and donor concentrations, and ni is the intrinsic carrier concentration.

p-n Junction under Equilibrium Conditions

• At equilibrium, the diffusion of electrons and holes is balanced by the drift current due to the electric field in the depletion region.

• The current at equilibrium is zero because the diffusion and drift currents cancel each other out.

• Explanation of how the built-in electric field in the depletion region prevents further diffusion of carriers, maintaining equilibrium.

p-n Junction under Bias

• Forward bias: When a positive voltage is applied to the p-side and a negative voltage to the n-side:

  • The applied voltage reduces the built-in potential, allowing electrons to move from the n-side to the p-side and holes from the p-side to the n-side.

  • This results in a current flow across the junction.

• Reverse bias: When a negative voltage is applied to the p-side and a positive voltage to the n-side:

  • The applied voltage increases the built-in potential, widening the depletion region and preventing current flow.

  • Only a small reverse saturation current flows due to minority carriers.

Current-Voltage (I-V) Characteristics of the p-n Junction

• Forward bias: The current increases exponentially with applied voltage. The I-V relationship is given by the Shockley diode equation:

• where I0​ is the reverse saturation current, V is the applied voltage, q is the electron charge, kB is Boltzmann’s constant, and T is the temperature.

• Reverse bias: The current is very small and approximately constant, known as the reverse saturation current I0​.

Examples:

• Derivation of the built-in potential V0​ for a p-n junction given the doping concentrations NA​ and ND​.

• Calculation of the width of the depletion region for a given p-n junction under equilibrium conditions.

• Plotting the I-V characteristics of a p-n junction in both forward and reverse bias.

Homework/Exercises:

1. Calculate the built-in potential for a silicon p-n junction with doping concentrations NA=10^17 /cm^3 and ND=10^16 /cm^3 at room temperature.

2. Derive the width of the depletion region for an unbiased p-n junction and explain how it changes under forward and reverse bias.

3. Plot the I-V characteristics of a p-n junction diode and explain the behavior in forward and reverse bias.

Suggested Reading:

• Charles Kittel, Introduction to Solid State Physics, Chapter 8: Semiconductors (continued).

Key Takeaways:

• A p-n junction forms a depletion region with a built-in potential that prevents charge carriers from flowing across the junction in equilibrium.

• The behavior of the p-n junction under forward and reverse bias is fundamental to the operation of diodes and other semiconductor devices.

• The I-V characteristics of a p-n junction diode show exponential growth in forward bias and a very small current in reverse bias.

This week introduces the fundamental structure and operation of the p-n junction, a critical component in semiconductor devices. Understanding its behavior under different bias conditions is key to analyzing diodes and other electronic components.