ELEG 867 Nanotechnology
Homework #4 - due Wednesday, 10 October 2001

1. Calculate the energy levels in narrow bandgap quantum dots grown on a wide bandgap semiconductor substrate. (a) First assume that the dots are perfect spheres of 5 nm radius, with zero potential energy in the sphere with infinitely high potential barriers. Calculate the energy of the lowest (a₁₀ ) state; (b) calculate the radius of the dot such that the spacing between the first two energy levels (a₁₀ and a₁₁ ) is kT at room temperature (25.8 meV); (c) now assume that the 5 nm radius dots are a material with a bulk energy gap E_g = 1 eV, and effective mass ratios (m^*/m_o) for electrons and holes = 1. Calculate the quantum and Coulombic modifications to the bandgap, using Eqn (1) of L. Brus (chapter 6, p. 264 in Timp). Careful - the third term in Eqn (1) is in CGS units, so you must divide by 4pe_o to convert to MKS units

2.  (a) Calculate the current in a quantum wire of diameter 5 nm and a length of 100 nm, with an applied potential of 1 volt. (b) how many such wires are needed to conduct a current of 1 mA? (c) Using the equations given in class, explain why the conductance, G, is independent of length.

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