i still confused about exciton bohr redius(EBR) in the quantum confinement effect.suppose EBR not exist then how we define the quantum confinement effect??
Quantum confinement is determined by the comparison between the (reduced) size of the material and the characteristic length of the specific physical properties. So for the optical properties of semiconductors, the characteristic length considered is the 'size' of the exciton described by the exciton Bohr radius.
However, if you are considering transport properties the electron mean free path and the Fermi Wavelength are more relevant.
Each of these properties can be calculated for every material.
Dear Wahid,
Exciton Bohr radius can be defined as the separation distance between electron and hole. We all know that the charge carriers can move freely in bulk semiconductor, thus the wavefunction looks much like a hydrogen atom.
As we go from bulk SC to small crystallite, the ability of the exciton to move is impeded, but the total energy of exciton doesn't change until the size of crystallite < than the exciton Bohr radius. So, the hydrogen-like wave fx becomes squished and energy required to create e-h pair starts increasing. This phenomenon of increasing excitation energy with decreasing size of particles is known as quantum confinement. Usually happened in quantum dots.
Quantum confinement effect describes the electron energy, potential energy well, valence band, conduction band, electron energy band gap. The quantum confinement effect is more pronounced in quantum dots in particular with size between 2- 10 nm as the atoms in nanocrystals are few and therefore the quantum effects are not averaged out unlike the material in micro regime. In quantum dots or semiconductor nanocrystals the excitons (electron hole pairs) are tightly confined within the nanocrystals and therefore are defined by discrete energy levels unlike continuum in micro regime. With decrease in the size of the nanoparticles the band gap increases and exhibit more prominent quantum confinement effects. The distance between the electron hole pair is exciton Bohra radius. When the size of nanomaterial is less than exciton Bohr radius the quantum confinement effect is noticed in terms exotic properties such as mechanical, opto-electronic, magnetic, chemical reactivity, color, melting point etc.
Exciton Bohr radius is the separation between electron and hole in an electron-hole pair. A semiconductor quantum dot is dimensionally comparable to exciton Bohr radius, so that quantum confinement of electrons can occur in it.
Dear experts, how can I obtain Bohr exitons experimentally? Is it real that they can be obtained from the smoke of a candle that condenses carbon on a surface?
Dear all,
I ended up in this post trying to find a specific answer to this question. I gather that there is a lot of confusion regarding this topic, mostly related to nomenclature. I'll try to answer to the best of my understanding.
The Bohr radius refers to the natural distance of the electron from the proton in a hydrogen atom. By approximation in semiconductors, thanks to the band structure, the electron can freely move in the space around the quantum dot and can be considered similar to the hydrogen atom from a mathematical standpoint.
Now talking about math, the concept of quantum confined is related to the particle-in-a-box formalism. In such a model, the length of the box is TWICE the Bohr radius.
So be careful, either QDs exhibit quantum confinement at a radius smaller than the Bohr radius, or the particle size (diameter) has to be smaller than TWICE the Bohr radius.
the Bohr radius can be calculated as follow
📷
(although I don't like to use it for scientifical purposes, in case of trouble seeing the image, the English Wikipedia page offer the correct answer https://en.wikipedia.org/wiki/Bohr_radius )
All of this has been drawn by my own study, if more experienced people want to weigh in, please do.
Dear Wahid Qayyum ,
When quantum mechanical particles move in a boundless medium, then their motion will be not confined as they can move as a travelling wave in the boundless space. Once the space in which the particle moves is limited by boundaries, then the motion of the particles will be confined in this bound space. The consequence of this is that the energy and the momentum of the particle will be quantized instead of taking continuous values in free space.
However, the wave mechanical properties become very apparent when the wavelength of the moving particle is in the order of the space in which the particle moves such as the motion of electrons in atoms or molecules or an assembly of atoms such as nanograins.
The wavelength lambda itself is related to the momentum of the particle p according to the De Broglie postulate:
lambda= h/ p,
where h is the Planck's consatnt.
You see as the momentum of the particle decreases by decreasing its mass its wavelength will increase till it reaches the size of the space in which it moves like the motion of electrons in atoms.
In case of exciton, the exciton is an electron hole pair bound to each other by their electrostatic attraction force. Therefor excitons are similar to the hydrogen atom except they move in screening medium while the electron in the hydrogen atom moves in vacuum. This results in a much larger effective Bohr radius which means that the electron hole pairs in the excitons are less confined in space than the hydrogen atom.
More confinement means less occupied space.
More confinement means more observable quantum mechanical behavior.
Less confinement means more free particle behavior.
Best wishes
There is a preferred separation distance between the electron and hole probability distributions in an exciton, and this distance is termed the exciton Bohr radius.
when a particle size of a material becomes comparable with Bohr exicton radius . the electron and holes being small particles resulting in quantum confinement
- Badges
- Science topic
- Similar topics
- Correction