In this course you will learn the following
5.1 Threshold Voltage Calculation
Threshold voltage is that gate voltage at which the surface band bending is twice ,Where
We know that the depth of depletion region for is between 0 and 2 and is given by,
Charge in depletion region at = 2 is given by where
Beyond threshold, the total charge QD in the seminconductor has to balance the charge on gate electrode, Qs i.e. where we define the charge in the inversion layer as a quantity which needs to be determined.
This leads to following expression for gate voltage-
In case of depletion, there in no inversion layer charge, so Qi =0, i.e. gate voltage becomes
but in case of inversion, the gate voltage will be given by :
The second term in second equality of last expression states our basic assumption, namely that any change in gate voltage beyond the threshold requires a change in inversion layer charge. Also from the same expression, we obtain threshold voltage as :
5.2 C-V Characteristics
The low frequency and high frequency C-V characteristics curves of a MOS capacitor are shown in fig 5.2.
Fig 5.2 : Low & High Frequency C-V curves
The low frequency or quasi-static measurement maintains thermal equilibrium at all times. This capacitance is the ratio of the change in charge to the change in gate voltage, measured while the capacitor is in equilibrium. A typical measurement is performed with an electrometer, which measures the charge added per unit time as one slowly varies the applied gate voltage.
The high frequency capacitance is obtained from a small-signal capacitance measurement at high frequency. The bias voltage on the gate is varied slowly to obtain the capacitance versus voltage. Under such conditions, one finds that the charge in the inversion layer does not change from the equilibrium value corresponding to the applied DC voltage. The high frequency capacitance therefore reflects only the charge variation in the depletion layer and the (rather small) movement of the inversion layer charge.
5.3 Oxide Charge Correction
To keep the value of Vr within -1 Volt and +1 Volt, an n-channel device has high Na doping (similarly, p-channel device has high Nd doping).