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Bohr radius and quantum confinement
For a nanocrystal, the quantum confinement occurs when the size of the nanocrystal approaching the
Bohr radius of the exciton. A smaller size results in a stronger confinement.
In this task, we will calculate the Bohr radius of the exciton in PbS and discuss what size of the PbS
nanocrystal will start to show quantum confinement.
Here are some tips:
The Bohr radius of the exciton in bulk PbS is,
$a_0 = \frac{4\pi\epsilon_r\epsilon_0\hbar^2}{\mu e^2}$
where, e is the electron charge, \hbar is the reduced Planck constant, \epsilon_0 is the permittivity of free space, and
\epsilon_r is the dielectric constant of PbS. \mu is the reduced effective mass of the exciton. You can find \epsilon_r, and
the effective masses of the electron and the hole from Wise_1997_JOSAB_Electronic structure and
optical properties of PbS and PbSe quantum dots.
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