Lecture

Electron Gas and Crystal Lattice

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the behavior of non-interacting electrons in an electron gas, following the Pauli exclusion principle and filling energy levels. It also delves into the periodic arrangement of atoms in crystalline solids, discussing lattice vectors, reciprocal lattice, and Bloch's theorem. The lecture further explores the density of states in 1D, 2D, and 3D systems, including the quantum well, quantum wire, and quantum dot. It concludes with insights into energy bands, excitons, and the density of states in different dimensions.

Official source

Ontological neighbourhood

Physics

Condensed matter physics: Solid-state physics

Related concepts (32)

Quantum dot

Quantum dots (QDs) – also called semiconductor nanocrystals, are semiconductor particles a few nanometres in size, having optical and electronic properties that differ from those of larger particles as a result of quantum mechanics. They are a central topic in nanotechnology and materials science. When the quantum dots are illuminated by UV light, an electron in the quantum dot can be excited to a state of higher energy. In the case of a semiconducting quantum dot, this process corresponds to the transition of an electron from the valence band to the conductance band.

Reciprocal lattice

In physics, the reciprocal lattice represents the Fourier transform of another lattice. The direct lattice or real lattice is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, where refers to the wavevector. In quantum physics, reciprocal space is closely related to momentum space according to the proportionality , where is the momentum vector and is the reduced Planck constant.

Python (programming language)

Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library.

Low-pass filter

A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design. The filter is sometimes called a high-cut filter, or treble-cut filter in audio applications. A low-pass filter is the complement of a high-pass filter. In optics, high-pass and low-pass may have different meanings, depending on whether referring to the frequency or wavelength of light, since these variables are inversely related.

Electronic band structure

In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules.

Related lectures (64)

Density of States in Semiconductor Devices

Explores density of states in semiconductor devices, covering electron gas, energy bands, Fermi-Dirac distribution, and band structures.

Band Structure: Energy Levels and Fermi Sphere

Explains energy levels, Fermi sphere, and periodic potentials in different dimensions.

Dispersion Relationships: Band Structures and Density of States

Discusses dispersion relationships, band structures, and density of states in real crystals and semiconductors.

3, STM / AFM 2024