Answer: Fraction of Empty States in GaAs at Room Temp w/E_{F} 0.1eV Below E_{c}

[JoshHolloway]

Homework Statement

The donor state for tellurium (Te) in GaAs is 5.9 meV below the conduction band (E=E_{c}). At room temperature, what fraction of the states are empty if the Fermi energy lies 0.1 eV below E_{c}

Homework Equations

E_{c}|_{GaAs}= 1.42eV
E_{d}=
E_{F}=
kT|_{(T=300K)}=0.02585 eV
N_{c}|_{(GaAs)} = 1.04\times10^{19}cm^{-3}

Where:
E_{d} is the Donor Energy Level
E_{f} is the Fermi Energy
T is the Temperature
k is the Wave Number
n_{d} is the Density of Electrons in the Donor Energy Level
N_{c} is the Effective Density of States in the Conduction Bandn_{d} = 1 + \frac{1}{2}exp[\frac{(E_{c}-E_{d})-(E_{c}-E_{F})}{kT}]

The Attempt at a Solution

Ok, so here goes:
n_{d} = 1 + \frac{1}{2}exp[\frac{( eV - eV) - ( eV - eV)}{0.02585eV}]

n_{d} = 1 + \frac{1}{2}exp[\frac{ eV - eV}{0.02585eV}]

n_{d} = 1 + \frac{1}{2}exp[\frac{ eV}{0.02585eV}]

n_{d} = 1 + \frac{1}{2}exp[-3.64023]

n_{d} = 1 + \frac{1}{2}(0.026246)

n_{d} = 1 + (.013123)

n_{d} = 1.013123 cm^{-3}

 

[JoshHolloway]

Disregard this post. Sorry.