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

In summary, the donor state for tellurium (Te) in GaAs is 5.9 meV below the conduction band, and at room temperature, approximately 1.31% of the states are empty if the Fermi energy lies 0.1 eV below the conduction band. The relevant equations used are provided, along with their corresponding variables.
  • #1
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]
 
Last edited:
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Disregard this post. Sorry.
 

1. What is the fraction of empty states in GaAs at room temperature with a Fermi energy 0.1eV below the conduction band edge?

The fraction of empty states in GaAs at room temperature with a Fermi energy 0.1eV below the conduction band edge is a measure of the number of unoccupied energy levels in the conduction band at that specific energy level. It is typically expressed as a percentage or decimal value.

2. How is the fraction of empty states determined in GaAs?

The fraction of empty states in GaAs is typically determined using experimental techniques such as temperature-dependent conductivity measurements or theoretical calculations based on the band structure of GaAs.

3. What is the significance of the fraction of empty states in GaAs?

The fraction of empty states in GaAs is an important parameter in understanding the electronic properties of the material. It can affect the conductivity, carrier mobility, and other characteristics of GaAs, making it a key factor in the design and optimization of electronic devices using this material.

4. How does the fraction of empty states change with temperature in GaAs?

The fraction of empty states in GaAs typically increases with temperature, as higher temperatures provide more energy for electrons to occupy higher energy levels in the conduction band. However, this relationship can vary depending on the specific properties of the GaAs sample.

5. Can the fraction of empty states in GaAs be controlled?

Yes, the fraction of empty states in GaAs can be controlled through various methods such as doping, strain engineering, and heterostructure design. These techniques can alter the band structure of GaAs and thus affect the number of empty states in the material.

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