Band bending, depletion layer thickness, density of occupie

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SUMMARY

The discussion focuses on calculating band bending, depletion layer thickness, and the density of occupied surface states in an n-type silicon (Si) semiconductor with specific parameters: bandgap energy (Eg) of 1.1 eV, doping density (ND) of 1×1017 cm-3, and surface state density of 1×1014 cm-2. The band bending is determined to be 0.55 eV due to the high density of surface states. The depletion layer thickness can be calculated using the equation for band bending, and the density of occupied surface states is derived from the product of ND and the depletion depth.

PREREQUISITES
  • Understanding of semiconductor physics, particularly n-type silicon.
  • Familiarity with band theory and energy band diagrams.
  • Knowledge of depletion region concepts in semiconductor devices.
  • Proficiency in using equations related to charge density and band bending.
NEXT STEPS
  • Study the derivation of the depletion layer thickness in n-type semiconductors.
  • Learn about the effects of surface states on semiconductor behavior.
  • Explore the relationship between doping density and band bending in semiconductor materials.
  • Investigate the role of electric fields in the formation of depletion regions.
USEFUL FOR

Students and professionals in semiconductor physics, electrical engineering, and materials science who are working on device fabrication and characterization of n-type silicon semiconductors.

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Homework Statement


Consider an n-type Si (Eg =1.1eV, ED=EC, εr=11.8) with a bulk doping density ND=1×1017cm-3, a density of acceptor type surface state 1×1014 cm-2 and these states are at the middle of the band gap. Evaluate the amount of:
a) band bending
b)depletion layer thickness
c) density of occupied surface states.

Homework Equations


Qss=Qsc=eNDd
band bending, eVs=e2NDd2/2εrε0

The Attempt at a Solution


I attempted to use equation 2 above but there are 2 unknowns in that equation. Not sure what contributes to the Qss=Qsc.

Thank you very much!
 
Physics news on Phys.org
I just found out that it is very easy! Because of the high surface state density, band bending is simply half of Eg, 0.55eV. Now We can use the second equation in ' Relevant equations' to determine the depletion depth d. And then we can find density of occupied surface states, NDd. And there we have it, the solution to this question! HAHA!
 

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