What is Kronig-Penney equation?

What is Kronig-Penney equation?

The Kronig-Penney model [1] is a simplified model for an electron in a one-dimensional periodic potential. The possible states that the electron can occupy are determined by the Schrödinger equation, In the case of the Kroning-Penney model, the potential V(x) is a periodic square wave.

What is Kronig-Penney equation also discuss its conclusion with the help of diagram?

Hence we conclude that the total number of possible wave functions in any energy band is equal to the number of unit cells N. We have concluded in the Kronig-Penny model that the energy discontinuities in a monatomic one-dimensional lattice occur when k = (nπ/a), where n is any positive or negative integer.

What is Kronig-Penney model and Bloch theorem?

where uk(x) = uk(x + a) represents periodic function and eikx represents plane wave. The above statement is known as Bloch theorem. The Kronig-Penney model demonstrates that a simple one-dimensional periodic potential yields energy bands as well as energy band gaps.

What is KP model in physics?

The KP model is a strongly simplified one-dimensional quantum mechanical model of a crystal. Despite of the simplifications, the electronic band structure obtained from this model shares many features with band structures that result from more sophisticated models.

How Kronig Penney model explain the formation of energy bands?

With increase of αa, the allowed energy states for a electron increases there by increasing the band width of the bands, i.e., the strength of the potential barrier diminishes. This also leads to increase of the distance between electrons and the total energy possessed by the individual electron.

What is Brillouin zone Mcq?

A Brillouin zone is defined as a Wigner-Seitz primitive cell in the reciprocal lattice. The first Brillouin zone is the smallest volume entirely enclosed by planes that are the perpendicular bisectors of the reciprocal lattice vectors drawn from the origin.

What is Bloch theorem and also explain the concept of effective mass?

The Bloch theorem states that if the potential V(r) in which the electron moves is periodic with the periodicity of the lattice, then the solutions Ψ(r) of the Schrödinger wave equation.

What is K in Ek diagram?

the momentum wave number (k) which means k is the measure of the momentum of the particle.

What is Ek diagram explain in detail?

An E-k diagram shows characteristics of a particular semiconductor material. It shows the relationship between the energy and momentum of available quantum mechanical states for electrons in the material.

What is Bloch theorem physics?

Why Ek diagram is parabolic?

Since momentum is proportional to velocity and kinetic energy is proportional to velocity squared, in free space the relationship between E and k depends on the square of k and is thus a parabola with its bottom at k=0.

What are three types of Ek diagram?

THE THREE TYPES OF E-K DIAGRAM ARE:

• PERIODIC ZONE.
• EXTENDED ZONE.
• REDUCED ZONE.

How does Kronig Penney explain the formation of energy bands?

How do you get the Brillouin zone?

Add the Bragg Planes corresponding to the other nearest neighbours. The locus of points in reciprocal space that have no Bragg Planes between them and the origin defines the first Brillouin Zone. It is equivalent to the Wigner-Seitz unit cell of the reciprocal lattice. In the picture below the first Zone is shaded red.

How do you construct a Brillouin zone?

Add the Bragg Planes corresponding to the other nearest neighbours. The locus of points in reciprocal space that have no Bragg Planes between them and the origin defines the first Brillouin Zone. It is equivalent to the Wigner-Seitz unit cell of the reciprocal lattice.

What is Bloch function in physics?

Named after Swiss physicist Felix Bloch, a Bloch wave (also called Bloch State; Bloch Function or Bloch Wave Function), is a type of wave function for a particle in a periodically-repeating environment, for example electrons moving in a semiconductor such as silicon (whose atoms form a crystal lattice).