How to Calculate Intrinsic Fermi Energy of Silicon?

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SUMMARY

The intrinsic Fermi energy (E_i) of silicon is located at the midpoint of the band gap, which is 1.12 eV wide, placing E_i at 0.56 eV below the conduction band edge and 0.56 eV above the valence band edge. For calculations involving the Fermi level (E_f) in n-type silicon, the relationship E_f - E_i = kT ln(n/n_i) is utilized, where n is the electron concentration and n_i is the intrinsic carrier concentration (1.5 x 10^10 cm³). This equation allows for determining how far E_f is positioned relative to the conduction band edge. The discussion also seeks expressions that relate E_i and the energy gap (E_g) for both intrinsic and extrinsic cases.

PREREQUISITES
  • Understanding of semiconductor physics, particularly intrinsic and extrinsic properties.
  • Familiarity with the concepts of Fermi energy and band gap in semiconductors.
  • Knowledge of the Boltzmann constant (k) and its application in thermal energy calculations.
  • Basic proficiency in logarithmic functions and their application in semiconductor equations.
NEXT STEPS
  • Research the derivation of the relationship between intrinsic Fermi energy and energy gap in semiconductors.
  • Learn about the effects of doping on the Fermi level in n-type and p-type silicon.
  • Study the application of the Boltzmann distribution in semiconductor physics.
  • Explore advanced semiconductor equations that relate E_i and E_g in both intrinsic and extrinsic cases.
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Students and professionals in semiconductor physics, electrical engineers, and anyone involved in the design and analysis of silicon-based electronic devices.

kylie14
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I've tried to look this up online, but I can't find it anywhere. I'm just looking for the intrinsic fermi energy of silicon E_i ?
Can someone maybe direct me towards a website where I could look it up? Either that, or is there a way to calculate it from the energy gap for intrinsic silicon (1.12eV)? I also know the intrinsic carrier concentration n_i (1.5 x10^10 cm^3).
Thanks in advance
 
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If the Si is undoped (i.e. intrinsic), the Fermi energy is in the middle of the band gap. Then the concentration of electrons and holes is equal. Doping the Si moves the Fermi energy toward either the conduction or valence band, depending on the type of dopant,
 
Yes, but how to I find out where the what the energy is at the centre of the band gap?
Thanks for your reply
 
I don't understand your question. What more do you need to know besides, "in the center of the band gap". There is no absolute reference for potential energy, so the value of the energy relative to the band edges is all you ever need to know.
 
I needed it because it appeared in an equation I needed to find how far the fermi energy is below the conduction band in n-type silicon.
I've just found another equation though, and you're right. I can find the distance between E_f and E_i, using
E_f - E_i = kT ln(n/n_i)
and then if E_i is in the middle of the band gap then that tells me how far E_f is below the conduction band edge.
Sorry, I'm with it now, thanks for your help.
 
Ei is in the middle of the band gap. Since the band gap is 1.12 eV wide, as you said, Ei is 0.56 eV below the conduction band edge (and also 0.56eV above the valence band edge). Suppose you have n = 1E18, and ni = 1.5E10. Then the Fermi level at room temperature is kT log(n/ni) = 0.46 eV above Ei, which puts it 0.10 eV below the conduction band edge. Does this do it?
 
Yes, I think that's it. Thanks again!
 
Please help :
Need expression that relates Ei and Eg both intrinsic and extrinsic case
 

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