JNTU B.Tech IV VLSI DESIGN Previous Question Paper (July - 2021 - R16)

The DC transfer characteristics of a CMOS inverter describe the output voltage (V_out) as a function of the input voltage (V_in). The curve is divided into five distinct regions of operation based on the conduction states of the nMOS and pMOS transistors.

1. Region 1 (V_in < V_tn): The nMOS is in cutoff (OFF) and the pMOS is in the linear region (ON). Since no current flows, V_out = V_DD.
2. Region 2 (V_tn ≤ V_in < V_DD/2): The nMOS turns on and enters saturation, while the pMOS remains in the linear region. V_out begins to drop from V_DD.
3. Region 3 (V_in = V_DD/2): Both transistors are in saturation. This is the transition region where the slope is steepest. The switching threshold voltage V_M is defined where V_in = V_out.
4. Region 4 (V_DD/2 < V_in ≤ V_DD - |V_tp|): The nMOS is in the linear region and the pMOS enters saturation. V_out continues to decrease.
5. Region 5 (V_in > V_DD - |V_tp|): The pMOS is in cutoff (OFF) and the nMOS is in the linear region. V_out = 0V.

The switching threshold V_M is given by the expression:

where k_n and k_p are the transconductance parameters of the nMOS and pMOS transistors respectively. For a symmetric inverter where k_n = k_p and V_tn = |V_tp|, the switching threshold is exactly V_DD/2, providing maximum noise margins and optimal switching performance.

The drain current I_D of an n-channel MOSFET is derived based on the charge induced in the channel by the gate voltage and the drift velocity of carriers under the influence of the lateral electric field.

The charge per unit area in the channel at a distance x from the source is given by:

where C_ox is the gate oxide capacitance per unit area, V_GS is the gate-to-source voltage, V_T is the threshold voltage, and V(x) is the channel potential at x. The drain current is defined by the drift equation:

Substituting Q_ch(x) and integrating from x=0 (where V=0) to x=L (where V=V_DS):

1. Linear (Triode) Region (V_GS - V_T > V_DS):

Performing the integration yields the linear current equation:

2. Saturation Region (V_GS - V_T ≤ V_DS):

As V_DS increases to V_GS - V_T, the channel at the drain end pinches off. The current becomes independent of V_DS. Substituting V_DS = V_GS - V_T into the linear equation:

3. Cut-off Region (V_GS < V_T):

When the gate voltage is below the threshold voltage, no inversion layer is formed, and the drain current is negligible: