Band bending, depletion layer thickness, density of occupie

[Red]

Homework Statement

Consider an n-type Si (Eg =1.1eV, E_D=E_C, ε_r=11.8) with a bulk doping density N_D=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

Q_ss=Q_sc=eN_Dd
band bending, eV_s=e²N_Dd²/2ε_rε₀

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!

 

[Red]

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!