Question

1)For an electron in GaAs with an effective mass of 0.067 m0 , we find λdeB ≈ 42 nm at 300 K. In order to observe quantum confinement effects at room temperature for this material how thick should the structures be?

a) Infinite well b) Finile well T n=2 d .

2)As an example, we consider a typical GaAs/Al0.3Ga0.7As QW with d = 10 nm. The confinement energy is 245 meV for the electrons and 125 meV for the holes. Determine E1 and E2 for electrons and holes in (a) Infinite Well model; (b) Finite Well model.

Answer 1

(1) The energy of the electron is,

hx 3 x 108 hc E = E = 4.733 x 1018 J 42 x 10-9

The energy in the infinite well is given by,

En 2ma

Now to observe quantum confinement effects the energy in infinite well should be equal to the energy of the electron (Let us take n = 1), then we can calculate the thickness required as,

T2(1.05 x 1034)2 (4.733 x 10 2(0.067 x 9.1 x 10-31)a2 18

8.92 x 1037 (4.733 x 10 18) ,2

a4.34 x 100 m4.34A

Hence the thickness of the structure should be in order of 4.34 Angstroms, so as to see quantum confinement effects.