# Problem related to nanotechnology

1. Sep 10, 2011

### guptamudit.13

1. In a quantum dot nanostructure having aside of 10 nm has donor concentration 1018
cm-3 . Calculate conduction electron contentin the quantum-dot. Also calculate the
electron content in it if the concentration is1014 .

2. Consider the bulk crystal of GaAs with an electron effective mass m* = 0.067 m0 ,
where m0 is the free-electron mass. Calculate the de Broglie wavelength for free as well as
electron with effective mass m* .

3. Assume that an electron with m0 = 9.8*10-31 kg is placed in a quantum well with two
impenetrable walls and that the distance between the walls is LO = 10 cm. Calculate
the three lowest sub-band bottom energies: ε1 ,ε2 ,ε3. For these stationary states, find the
probability density of finding the electron at the middle of the well at z = 0.

4. Using the lattice constant of silicon, a = 5.43* 10-8 , and the fact that the number of Si
atoms per unit volume, a3 , is eight, calculate the number of atoms per 1 cm3 and the
density of the crystalline silicon ( silicon’s atomic weight is 28.1 g mol-1 ).

5. Assume that the conduction-band offset for an AlGaAs heterojunction is 60% of the difference of the band gaps of these materials. Find the composition of the AlGaAs layer necessary for the resulting heterojunction to have an energy barrier for the
electrons to .3 eV. Calulate the energy barrier for the holes. Given that the band gap energy E of the alloy AlxGa1-xAs is given as Δg = 1.42 + 1.247 x and the
band gap energy for the GaAs is Δg = 1.42 eV.

6. For AlxGa1-xAs alloy, find the composition having an
energy bandgap equal to 2 eV. For this alloy,
determine the effective masses in the Г and X valleys.