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.
Answer:
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
