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Semiconductor Question

  1. Oct 24, 2007 #1
    1. The problem statement, all variables and given/known data
    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]

    2. Relevant 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]

    [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]

    3. 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]
    Last edited: Oct 25, 2007
  2. jcsd
  3. Oct 25, 2007 #2
    Disregard this post. Sorry.
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