Bohr radius and quantum confinement
For a nanocrystal, the quantum confinement occurs when the size of the nanocrystal approaches 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)=(4pi epsi _(1)epsi _(0)ℏ^(2))/(e^(2)mu ) where, e is the electron charge, ℏ is the reduced Planck constant, epsi _(0) is the permittivity of free space, and epsi _(1) is the dielectric constant of PbS. mu is the reduced effective mass of the exciton. You can find epsi _(1), 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.