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JoshHolloway
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Homework Statement
The donor state for tellurium (Te) in GaAs is 5.9 meV below the conduction band [tex](E=E_{c})[/tex]. At room temperature, what fraction of the states are empty if the Fermi energy lies 0.1 eV below [tex]E_{c}[/tex]
Homework Equations
[tex]E_{c}|_{GaAs}= 1.42eV[/tex]
[tex]E_{d}= [/tex]
[tex]E_{F}= [/tex]
[tex]kT|_{(T=300K)}=0.02585 eV[/tex]
[tex]N_{c}|_{(GaAs)} = 1.04\times10^{19}cm^{-3} [/tex]
Where:
[tex]E_{d}[/tex] is the Donor Energy Level
[tex]E_{f}[/tex] is the Fermi Energy
[tex]T[/tex] is the Temperature
[tex]k[/tex] is the Wave Number
[tex]n_{d}[/tex] is the Density of Electrons in the Donor Energy Level
[tex]N_{c}[/tex] is the Effective Density of States in the Conduction Band[tex]n_{d} = 1 + \frac{1}{2}exp[\frac{(E_{c}-E_{d})-(E_{c}-E_{F})}{kT}][/tex]
The Attempt at a Solution
Ok, so here goes:
[tex]n_{d} = 1 + \frac{1}{2}exp[\frac{( eV - eV) - ( eV - eV)}{0.02585eV}][/tex]
[tex]n_{d} = 1 + \frac{1}{2}exp[\frac{ eV - eV}{0.02585eV}][/tex]
[tex]n_{d} = 1 + \frac{1}{2}exp[\frac{ eV}{0.02585eV}][/tex]
[tex]n_{d} = 1 + \frac{1}{2}exp[-3.64023][/tex]
[tex]n_{d} = 1 + \frac{1}{2}(0.026246)[/tex]
[tex]n_{d} = 1 + (.013123)[/tex]
[tex]n_{d} = 1.013123 cm^{-3}[/tex]
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