Given that the effective mass ratio of the electron is 0.11 and the effective mass ratio of the hole is 0.35, please calculate the ground-state energy (ie: n=1) of the donor and acceptor bands along with their orbital radii.

Complete question:

CdTe has a band-gap energy εg of 1.6 eV and a dielectric constant εr of 10.9.

Given that the effective mass ratio of the electron is 0.11 and the effective mass ratio of the hole is 0.35, please calculate the ground-state energy (ie: n=1) of the donor and acceptor bands along with their orbital radii.

The ground-state energy for donor is 2.6 meV

The ground-state energy for acceptor is 40.1  meV

Explanation:

Given;

effective hole mass, Mh = 0.35

effective electron mass, Me = 0.11

mass of electron, M₀ = 9.11 x 10⁻³¹

dielectric constant,  εr = 10.9

To determine the donor and acceptor energies, we apply the equation below;

E = 1 Rydberg x m*/(m₀εr²)

E = 13.606 eV x m*/(m₀εr²)

The ground-state energy for donor = 13.606 eV x M*/(M₀εr²)

                                                           = 13.606 eV x Me/(εr²)

                                                           = 13.606 eV x 0.11/((10.9)²)

                                                           = 2.6 meV

The ground-state energy for acceptor  = 13.606 eV x M*/(M₀εr²)

                                                                 =  13.606 eV x Mh/(εr²)

                                                                 = 13.606 eV x 0.35/((10.9)²)

                                                                 = 40.1  meV

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