Question

For a capacitor of area 100 mm ´100 mm operated at T = 300K, with F_M = 5.2 eV, x_ox = 3 nm, and

N_D = 10¹⁷ cm^-3

a) Calculate the flat band capacitance and treshold voltage

b) Draw the low frequency and high frequency CV curves

Please solve it completely and step by step. I will rate the question

Answer 1

(a) The flatband voltage for a capacitor is the voltage at which there is no charge at the plate of the capacitor, i.e, there is no electric field across the oxide. Flat band voltage of a capacitor can be expressed as;

where is the gate potential and is the potential of silicon substrate. Now for a silicon substrate with doping N_D, can be calculated from following relationship;

where N_D = doner concentration, n_i =intrinsic carrier density, T= absolute temperature, q=charge.

So;

and . So Flatband volatage for the capacitor is;

.

Now the threshold voltage is given by;

where x_ox= oxide thickness = 3 nm, = silicon dielectric constant = and

or .

(b) The Debye length is;

The flat band capacitance per unit area;

The maximum width of the depletion region is given by;

So the semiconductor capacitance per unit area threshold is

The oxide capacitance per unit area is;

So the total capacitance per unit area at threshold is

So the low frequency and high frequency CV curve is as follows;