Task 6: Flatband Voltage

The flat band voltage of MOSFET is influenced by the oxide-semiconductor interface and the voltage which when applied to the gate electrode yields a flat energy band. The charge in the oxide or at the interface changes this flatband voltage.As the plot below displays, the capacitance of the flatband would equal to the series of C_ox and C_D.

Firstly, we need to calculate the Debye length which would be 

For ε₀=8.85×10^-12F/m

  ε_s=11.7

kT_t/q=0.026V

N_D=2.7×10²¹

Therefore, L_D =78nm.

Aftwewards, we would calculate the C_D, which is semiconductor capacitance

For For ε₀=8.85×10^-12F/m

ε_s=11.7

L_D=78nm

A=π(d/2)² ,where d=0.58nm

Therefore,C_D=350pF

Finally, we carried out the formula of capacitors in series, and achieved

C_FB=314pF

Then, we find the corresponding voltage in the plot in task 1 and find out the rough voltage is 0.52V.