Quantum-Dot Fluorescence - Hypothetical Semiconductor

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Homework Statement



Consider a hypothetical semiconductor with band gap 1eV, Relative electron mass is 0.05 and relative hole mass is 0.5.
In a cube-shaped quantum dot of this material with side length L = 3nm, what is the energy associated with a transition from (2 1 1) electron state to the (1 1 1) hole state?

Homework Equations



confinement energy of a particle trapped in a 3D box:

[itex] E_n = \left(\frac{h^2}{8mL^2}\right)\left(n_x^2 + n_y^2 + n_z^2\right)[/itex]


The Attempt at a Solution



so, an electron has been excited into the a higher energy state (2 1 1) from (1 1 1) producing an exciton, the hole remains in state (1 1 1).

the band gap energy [itex]E_g = 1eV[/itex]

the recombination energy is [itex]E_r[/itex]

i have a formula which says that:

[itex]E_r = E_g + E_e + E_h[/itex]

where Ee and Eh are confinement energies of the electron and hole respectively.

do i just sum up Eg Eh and Ee to get the recombination energy?
I would have thought i'd need to work out the difference between the (2 1 1) and (1 1 1) state of the electron.
 

Answers and Replies

  • #2
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Just summing them up like the formula says, i get 1.525eV for the recombination energy. My quantum is pretty waek, is this right?
 

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