EE236: Electronic Devices Lab
Lab No. 12
Saptarshi Biswas, 22B1258
November 3, 2024
C-V Characteristics of MOS Capacitor
1 Aim
The objectives of this experiment include the following tasks:
1. Obtain the sub-threshold Id vs Vgs characteristics of an NMOS.
• Objective: Conduct the experiment using an operational ampli-
fier (OP-AMP) that has a low noise figure.
• Goal: Plot the Id versus Vgs characteristics and analyze the re-
sulting plots.
2. Verify the continuity of Id vs Vgs characteristics beyond the
sub-threshold region.
3. Use the NMOS as a Common Source Amplifier within the
sub-threshold region.
2 Theory
An N-channel MOSFET is a type of Field Effect Transistor with four termi-
nals:
1. Drain
1
2. Gate
3. Source
4. Body
The body terminal of the NMOS is connected to the lowest potential in the
circuit, typically ground. To turn on an NMOS, the applied Gate-to-Source
Voltage must exceed the Threshold Voltage Vth . When this voltage is below
Vth , the NMOS is considered ”off.”
However, even below the threshold, the MOSFET allows a minimal cur-
rent flow, as a few electrons are present in the channel. Applying a Drain
Voltage creates a depletion region near the drain junction, with fewer mi-
nority carriers. Electrons near the source junction move towards the drain
through Diffusion, causing Sub-Threshold Current. The Drain current equa-
tion in the Sub-Threshold region is as follows:
Vgs −Vth −Vds
ηVt
Id = I0 e 1−e ηVt
where
µn Cox W 1
I0 = (1 − )
2 L η
and the terms represent:
• Id : Drain Current
• Vgs : Gate to Source Voltage
• Vth : NMOS Threshold Voltage
• Vt : Thermal Voltage
• Vds : Drain to Source Voltage
• µn : Electron Mobility
• Cox : Gate Oxide Capacitance per unit area
• W
L
: Aspect Ratio of the NMOS
• η = 1 + CCoxd , with Cd as the Depletion Capacitance or Sub-Threshold
Slope Factor.
2
Experimental Design Approach
• As seen from the above equation, the drain current equation in the
Sub-Threshold region is complex. Before conducting the experiment,
we aim to reduce one variable, preferably Vds , to simplify plotting Id
versus Vgs characteristics.
• We initially assume η = 10. At room temperature, ηVt is approxi-
mately 0.256. Setting Vds = 2 V allows the exponential term with Vds
to approach zero, simplifying it to 1. Thus, we obtain:
Vgs −Vth
ηVt
Id ≈ I0 e
• Important Note: After completing the experiment, we will calculate
η from the results. If η is close to 10, our assumption is valid, and the
Vds term can be ignored. If η is higher, Vds will be adjusted, and the
experiment repeated.
3
3 Experiment Results
3.1 Part - 1 : Transfer Characteristics of NMOS
Figure 1: Circuit Diagram for Sub-threshold Current Measurement
4
3.2 Part -2 : Graph Continuity
Figure 2: Circuit Diagram for testing continuity of Characteristics
5
3.3 Part -3 : Common Source Amplifier with MOS-
FET in Sub-Threshold
Figure 3: Common Source Amplifier Design
6
4 Simulation Results
4.1 Part - 1 : Transfer Characteristics of NMOS
Figure 4: Id vs Vgs
7
4.2 Part -2 : Graph Continuity
Figure 5: log(Id ) vs Vgs
8
4.3 Part -3 : Common Source Amplifier with MOS-
FET in Sub-Threshold
Figure 6: Vout vs Vin
5 Conclusion and Interpretation
The experiment confirmed that NMOS transistors exhibit distinctive sub-
threshold characteristics, displaying an exponential relationship rather than
the typical linear trend of Id versus Vgs. As Vgs increased, the characteristics
extended beyond the sub-threshold region smoothly. The NMOS, used as a
common source amplifier in the sub-threshold range, demonstrated an ac-
ceptable gain for low-power applications, making it suitable for designs that
prioritize low power dissipation and minimal current draw.
6 Experiment Status
The experiment has been successfully completed.
