Kronig-Penney Model

1. What are the drawbacks of free electron theory?

The wrong assumptions made by the Drude and Lorentz are the major drawbacks of quantum free electron theory like:

• Electrons inside the crystal, experiences zero constant potential.
• The mutual repulsion between electrons is considered to be zero.

Due to this, the free electron theory does not explains the phenomenon of photoelectric effect, the superconductivity in the metals etc.

2. What is the energy associated with the electron at temperature T?

The energy associated with the electron at temperature T was = 3/2kT and it is related to the kinetic energy with the equation: 3/2kT =1/2mv²_th. Where k = Boltzmann’s Constant

T = Temperature in kelvin

V_th = Thermal velocity of electron

3. How does Kronig-Penney model helps in determining of energy bands?

With the help of their potential well curve, Kronig-Penney describes the concept of allowed and forbidden energy bands. The portion in which Potential V(x) = 0, called forbidden energy gap in which no electrons is allowed to be present inside it. The the portion of curve where potential V(x) ≠ 0 are knows as Valence and Conduction bands.

4. What are the application of kronig-Penney Model?

The real life application of Kronig-Penney model are:

• In the development of Semiconductor chips.
• Used to select the correct material according to the need in the manufacturing of different electronic devices.
• Understanding the behavior of material.
• Identification of nature of material.

When we talk about the conductivity of a material, we generally divide it into three parts: Conductors, Insulators, and Semiconductors. But do you know, which model proves why some materials behave like conductors, insulators, and semiconductors, and what is the reason behind it? This property of a material is verified by Bloch, and two German scientists named Kronig-Penny gave his model to prove it, which is called ” The Kronig-Penney Model”. This model helps in determining the electrical, thermal, and magnetic properties of a solid. In this article, we will discuss this model in detail and understand its advantages, properties, and specific features.