## What is the nearly free electron model?

In solid-state physics, the nearly free electron model (or NFE model) or quasi-free electron model is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model is closely related to the more conceptual empty lattice approximation.

What is the formula of free electrons?

The calculation is involved even for a crude model, but the result is simple: g(E)=πV2(8meh2)3/2E1/2, where V is the volume of the solid, me is the mass of the electron, and E is the energy of the state. Notice that the density of states increases with the square root of the energy.

### What is the difference between free electron model and nearly free electron model?

The key difference between free electron model and nearly free electron model is that free electron model does not take into account the electron interactions and the potential, whereas the nearly free electron model takes into account the potential.

Which phenomena Drude’s free electron theory Cannot explain?

1) It fails to explain the electrical conductivity of semiconductors and insulators. temperature. 3) It fails to explain the concept of specific heat of metals.

## What is central equation?

• Central equation is the TISE expressed in Fourier series form for a periodic structure. It may not look like the TISE, since the ψ is no longer obviously present. However, remember that ψ is now defined in terms of ck terms: = c ei, which are in there!

What is Brillouin zone in physics?

Brillouin zones are polyhedra in reciprocal space in crystalline materials and are the geometrical equivalent of Wigner-Seitz cells in real space. Physically, Brillouin zone boundaries represent Bragg planes which reflect (diffract) waves having particular wave vectors so that they cause constructive interference.

### What are the assumptions in Drude’s free electron theory?

DC field. The simplest analysis of the Drude model assumes that electric field E is both uniform and constant, and that the thermal velocity of electrons is sufficiently high such that they accumulate only an infinitesimal amount of momentum dp between collisions, which occur on average every τ seconds.

What are the assumptions of free electron theory?

This theory has some assumptions; they are: The valence electrons of metallic atoms are free to move in the spaces between ions from one place to another place within the metallic specimen similar to gaseous molecules so that these electrons are called free electron gas.

## What is the central equation in solid state physics?

Central equation is the TISE expressed in Fourier series form for a periodic structure. It may not look like the TISE, since the ψ is no longer obviously present. However, remember that ψ is now defined in terms of ck terms: = c ei, which are in there!

What is Bragg diffraction and Brillouin zone?

The construction of Bragg Planes in the context of Brillouin zones can be understood by considering Bragg’s Law. λ = 2dsinθ where θ is the angle between the incident radiation and the diffracting plane, λ is the wavelength of the incident radiation and d is the interplanar spacing of the diffracting planes.

### What is the relationship between the Brillouin zone and reciprocal lattice?

The first Brillouin zone is defined as the Wigner–Seitz primitive cell of the reciprocal lattice. Thus, it is the set of points in the reciprocal space that is closer to K = 0 than to any other reciprocal lattice point.

We note that in the free electron model, Within the nearly free electron model we start from the dispersion relation of free electrons and analyze the effect of introducing a weak lattice potential.

Is the nearly-free electron model similar to the tight binding model?

Perhaps surprisingly, we will find that the nearly-free electron model gives very similar results to the tight binding model: it also leads to the formation of energy bands, and these bands are separated by band gaps – regions in the band structure where there are no allowed energy states.

## How do you calculate dispersion in the free electron model?

In the free electron model, the dispersion is E = ℏ 2 | k | 2 / 2 m. The corresponding eigenfunctions | k ⟩ are plane waves with a real-space representation ψ ( r) ∝ e i k ⋅ r.

What is the nearly free electron model of phonons?

Within the nearly free electron model we start from the dispersion relation of free electrons and analyze the effect of introducing a weak lattice potential. The logic is very similar to getting optical and acoustic phonon branches by changing atom masses (and thereby reducing the size of the Brillouin zone).