Calculating Fermi Energy Shift in a GaN Semiconductor

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In summary: X.In summary, the Fermi energy in a GaN semiconductor with a band gap energy of 3.45 eV and an intrinsic concentration of 1e-14 cm-3 must move towards the valence band edge by 1.725 eV to result in 1 hole per cm3, when acceptors are added to the material. This can be calculated using the equation EF = ET + kTln(NV/ni), where NV is the effective density of states in the valence band and ni is the intrinsic carrier concentration.
  • #1
ashkash
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Homework Statement



A GaN semiconductor (EG=3.45 eV, intrinsic concentration is ni=1e-14 cm-3) is initially barely doped n-type so that the electron concentration is 1 electron/cm3. Acceptors are added to the material. How far (in energy) and in what direction (in energy) must the fermi energy move
to result in 1 hole per cm3.


Homework Equations





The Attempt at a Solution



I do not even know where to begin. Any help would be appreciated. thanks.
 
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  • #2




Thank you for your question. The movement of the Fermi energy in a semiconductor can be calculated using the equation: EF = ET + kTln(NV/ni), where EF is the Fermi energy, ET is the intrinsic energy level, k is the Boltzmann constant, T is the temperature, NV is the effective density of states in the valence band, and ni is the intrinsic carrier concentration.

In this case, we can calculate the effective density of states in the valence band as NV = 2*(2πm*kT/h2)3/2, where m is the effective mass of the holes in the valence band, k is the Boltzmann constant, T is the temperature, and h is the Planck's constant.

Since the material is initially barely doped n-type, the Fermi energy is close to the conduction band edge. To result in 1 hole per cm3, the Fermi energy must move towards the valence band edge by an amount equal to the energy difference between the conduction band edge and the top of the valence band. This energy difference can be calculated using the band gap energy (EG) of the material.

Therefore, the Fermi energy must move by an amount of EG/2, towards the valence band edge, to result in 1 hole per cm3. This corresponds to a movement of 1.725 eV in the energy direction.

I hope this helps. Let me know if you have any further questions. Good luck with your studies!
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  • #3


To calculate the Fermi energy shift in a GaN semiconductor, we can use the following equation:

EF = (1/2) * (EC + EV) + (kT/2) * ln(NV/NC)

Where EF is the Fermi energy, EC and EV are the conduction and valence band energies, k is the Boltzmann constant, T is the temperature, and NV and NC are the effective densities of states in the valence and conduction bands, respectively.

In this case, we are starting with an n-type GaN semiconductor with an electron concentration of 1 electron/cm3. To achieve a hole concentration of 1 hole/cm3, we need to add acceptors to the material. This will shift the Fermi energy towards the valence band, since acceptors create holes in the valence band.

To calculate the Fermi energy shift, we first need to determine the effective densities of states in the valence and conduction bands. This can be done using the following equations:

NV = 2 * (2πm*kT/h^2)^(3/2) * e^(EV/kT)

NC = 2 * (2πm*kT/h^2)^(3/2) * e^(EC/kT)

Where m is the effective mass of the carriers, k is the Boltzmann constant, T is the temperature, and h is the Planck constant.

Once we have determined NV and NC, we can plug them into the equation for EF and solve for the Fermi energy shift. The direction of the shift will depend on the relative values of NV and NC. If NC > NV, then the Fermi energy will shift towards the conduction band. If NV > NC, then the Fermi energy will shift towards the valence band.

I hope this helps. Good luck with your calculations!
 

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