Hello all,

If you remember, most textbooks say that the depletion charge in an N-MOSFET's channel in strong inversion is given by this equation:

Qb = -Sqrt( 2 * q * N_a * Epsilon_Si * 2 * Phi_F), where N_a is the substrate doping, Phi_F is the Fermi potential at the bulk.

The textbooks say that this charge is in the channel exactly when the gate voltage is equal to the threshold voltage (which itself has that charge term in it divided by C_ox). It also says this is the strong inversion charge ( so n-type carriers).

On the other hand, later on when developing the drain characteristics, it says that Q = Cox(Vgs - V_t) (with drain voltage at zero for this example). But if you look at this equation, the charge is exactly ZERO when Vgs = V_t.

How do we solve this apparent contradiction? On the one hand it says that when Vgs is equal to Vt, the charge is given as my first equation. On the other hand the charge is also ZERO when Vgs = Vt for the drain characteristics.

Could it be that even though the channel is inverted at Vgs = Vt, there is still too little charge and so they consider it as ZERO charge? But clearly there isn't zero charge when Vgs = Vt. There should be some charge there, no?

What on earth is going on here?

Thank you so much

If you remember, most textbooks say that the depletion charge in an N-MOSFET's channel in strong inversion is given by this equation:

Qb = -Sqrt( 2 * q * N_a * Epsilon_Si * 2 * Phi_F), where N_a is the substrate doping, Phi_F is the Fermi potential at the bulk.

The textbooks say that this charge is in the channel exactly when the gate voltage is equal to the threshold voltage (which itself has that charge term in it divided by C_ox). It also says this is the strong inversion charge ( so n-type carriers).

On the other hand, later on when developing the drain characteristics, it says that Q = Cox(Vgs - V_t) (with drain voltage at zero for this example). But if you look at this equation, the charge is exactly ZERO when Vgs = V_t.

How do we solve this apparent contradiction? On the one hand it says that when Vgs is equal to Vt, the charge is given as my first equation. On the other hand the charge is also ZERO when Vgs = Vt for the drain characteristics.

Could it be that even though the channel is inverted at Vgs = Vt, there is still too little charge and so they consider it as ZERO charge? But clearly there isn't zero charge when Vgs = Vt. There should be some charge there, no?

What on earth is going on here?

Thank you so much

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