Variation in effective energy gap?

[enc08]

Hi,

I've worked out that for the particle-in-a-box model (square well) the energy E

E = 3h^2/8mL^2

where m is the effective mass of the electron.

The next question asks

Hence derive an expression for the variation of the effective energy gap in the quantum dot as a function of its size for a semiconductor material that has a bulk energy gap Eg and electron and hole effective masses of m and m_h.

I haven't studied semiconductor physics in detail so I don't know how to proceed. Thanks for your input.

 

[BigJDubs]

The answer to this question will depend on the exact type of semiconductor material you are looking at. Generally speaking, the energy gap in a quantum dot is related to the bulk energy gap of the material by the following equation: E_dot = Eg - (m+m_h) * h^2 / 8mL^2 Where m is the effective mass of the electron and m_h is the effective mass of the hole. This equation assumes that the size of the quantum dot is much smaller than the length scale of the bulk material. The size of the quantum dot will thus affect the effective energy gap in the quantum dot as the size of the quantum dot gets smaller, the energy gap for the quantum dot will become more negative, and thus the effective energy gap E_dot will become larger.