What is the Kronig Penney model What does it represent?

What is the Kronig Penney model What does it represent?

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, k) and the electron density of states.

What are the findings of Kronig Penney model?

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 the basic assumption of Kronig Penney model?

The essential behaviour of electron may be studied by periodic rectangular well in one dimensional which was first discussed by Kronig Penney in 1931. It is assumed that when an electron is near the positive ion site, potential energy is taken as zero.

Why did the Kronig Penney model approximate that an electron moves in a periodically varying square potential?

(a), if an electron moves through these ions, it experiences varying potentials. The potential of an electron at the positive ion site is zero and is maximum in between two ions. So, Kronig and Penney approximated these potentials inside the crystal to the shape of rectangular steps as shown in Fig.

What do you mean by Bloch theorem?

In condensed matter physics, Bloch’s theorem states that solutions to the Schrödinger equation in a periodic potential take the form of a plane wave modulated by a periodic function.

What are ek diagrams?

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 effective mass of electron?

The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. For electrons or electron holes in a solid, the effective mass is usually stated in units of the rest mass of an electron, me (9.11×10−31 kg).

Why Brillouin zone is important?

Brillouin zones play important role in understanding the electronic properties of crystals. The construction of Brillouin zone involves the drawing of perpendicular bisectors to shortest reciprocal lattice vectors of the given crystal. The volume enclosed by the bisectors is called first Brillouin zone.

What is barrier strength in Kronig Penney model?

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 the Bloch Hamiltonian?

The Bloch theorem enables reduction of the eigenvalue problem of the single-particle Hamiltonian that commutes with translational group. The generalized Bloch theorem constrains the form of the Hamiltonian which becomes manifestly invariant under additional symmetries.

What is the Kronig-Penney model (KP model)?

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. Details of the Kronig-Penney model

What does Kronig and Penney mean by height of potential barrier?

In order to make the situation more simple, Kronig and Penney considered the height of the potential barrier is very large. i.eand simultaneously the width of the barrierin such a way that the productremain finite. (15) Where (16) Which is a measure of the areaof the potential barrier.

What is k value of Brillouin zone?

These K value define the boundaries of the first, second and third Brillouin zones. If we consider a line representing K values, divided into energy discontinuities into segments of lengthas shown in Fig. , these line segments are called Brillouin zones.

What are Brillouin zones?

If we consider a line representing K values, divided into energy discontinuities into segments of lengthas shown in Fig. , these line segments are called Brillouin zones. Load more…