# Microelectronics Questions and Answers – Behaviour of a MOSFET

This set of Microelectronics Multiple Choice Questions & Answers (MCQs) focuses on “Behaviour of a MOSFET”.

1. What happens to the threshold voltage if the doping level in the substrate increases?
a) It decreases
b) It increases
c) It remains constant
d) It is linearly proportional

Explanation: We note that at the threshold voltage, the inversion layer is completely formed in the substrate. If the substrate is very heavily doped, it would take more charges to create the inversion layer. Clearly, we find that the threshold voltage would increase if the doping level in the substrate increases. However, it isn’t linearly proportional since VTH = ΦMS + ΦFP + Qdep/COx and ΦFP = kt / q * ln(Nsubstrate/ni), Qdep=√4q*€Si*|ΦFP|*Nsubstrate). However, this equation does justify the increase in threshold voltage with an increase in substrate doping.

2. In a NMOS, we note that an inversion layer gets created as the gate voltage reaches the threshold voltage. Choose the correct relation which satisfies this condition.
a) ΦS > 2*ΦFP
b) ΦS < 2*ΦFP
c) ΦS = ΦFP
d) ΦS = 2*ΦFP

Explanation: ΦS is the surface potential while ΦFP is the potential difference between the intrinsic fermi level of the p-type substrate and the fermi level of an intrinsic material. As the surface potential decreases, the inversion layer gets accumulated below the gate. When the total no. of electrons in this layer is equal to the total no. of holes in the substrate, the surface potential reaches 2*ΦFP and the gate voltage in this event is defined as the threshold voltage.

3. An NMOS is working in the triode region. What happens to the on-resistance if its width increases by a factor of 2?
a) It doubles
b) It halves
c) It increases by a factor of 4
d) It decreases by a factor of 4

Explanation: In the triode region, the on-resistance of the NMOS is given by 1/μnCOX(W/L)(VGS-VTH). If the width of the MOSFET increases, the on-resistance decreases-in this case, it becomes half. Note that R=ρ*(L/A) where A is Width*thickness – this allows us to conclude further that the resistance decreases with an increase in the width.

4. What happens to the transconductance of a MOSFET if it’s width is multiplied by a factor of 4? Assume that the drain current is constant.
a) It increases by a factor of 2
b) It decreases by a factor of 3
c) It increases by a factor of 4
d) It decreases by a factor of 6

Explanation: The transconductance is proportional to square root of the aspect ratio, for a constant drain current. The transconductance, gm, is given by √μnCOX(W/L)(ID). We readily observe that if the drain current is constant, the transconductance would increase by a factor of 2 when the width is multiplied by a factor of 4.

5. What happens to the transconductance if the overdrive voltage increases by a factor of 4? Assume that the aspect ratio is constant.
a) It increases by a factor of 2
b) It increases by a factor of 6
c) It increases by a factor of 4
d) It increases by a factor of 8

Explanation: The transconductance is directly proportional to the overdrive voltage, for a constant aspect ratio. The transconductance, gm, is given by μnCOX(W/L)(VGS-VTH). We readily observe that if the aspect ratio is constant, the transconductance would increase by a factor of 4 when the overdrive voltage, the term (VGS-VTH), increases by a factor of 4.

6. What would the graph of RON vs VGS represent?
a) A hyperbola
b) A parabola delayed by a threshold voltage
c) A logarithmic function
d) An exponential function

Explanation: RON is the resistance offered by the MOSFET in the triode region. This resistance is inversely proportional to the overdrive voltage for a constant aspect ratio and a graph of RON vs VGS would represent a hyperbola.

7. What happens to the overall transconductance if 10 MOSFETs them are connected in parallel?
a) It decreases by a factor of 10
b) It increases by a factor of 4
c) It decreases by a factor of 5
d) It increases by a factor of 10

Explanation: If 10 transistors are connected in parallel, it can be imagined as the overall width of all the transistors has increased by almost a factor of 10. The overall transconductance thus can be suggested to increase by a factor of 10 for a constant overdrive voltage.

8. What happens to the slope of the graph of ID vs VGS if the width of the MOSFET is doubled? Assume that the transistor is not saturated.
a) It increases rapidly
b) It decreases rapidly
c) It remains the same
d) It increases linearly

Explanation: The slope of the ID vs VGS represents the transconductance of the transistor. The slope will thus increase linearly for an increase in the width of the MOSFET.

9. What happens to the slope of the graph of ID vs VGS if the length of the MOSFET is doubled? Assume that the transistor is not saturated.
a) It increases logarithmically
b) It increases exponentially
c) It increases linearly
d) It decreases linearly

Explanation: The slope is inversely proportional to the length of the transistor. Note that the length of the transistor is the effective channel length between source and drain – we can readily conclude that if the distance between the source and the drain increases, the ability of the transistor to convert voltage into current reduces a bit. Moreover, the slope is given by μnCOX(W/L)(VGS-VTH) and we can readily conclude that for a constant overdrive voltage the slope halves if the length increases by a factor of 2.

10. What happens to the slope of the graph of ID vs VGS if the oxide-thickness of the MOSFET is doubled? Assume that the transistor is not saturated.
a) It increases parabolically
b) It decreases exponentially
c) It increases linearly
d) It decreases linearly

Explanation: The slope is inversely proportional to the oxide thickness. For a constant overdrive voltage, it is given by μnCOX(W/L)(VGS-VTH) and COX=€OX/tOX where tOX is the oxide thickness. Qualitatively, we note that if tOX increases, it would take more voltage to deposit charge on the substrate and create the inversion layer which leads to a decrease in the transconductance.

11. What happens to the slope of the graph of ID vs VDS if the oxide-thickness of the MOSFET is doubled? Assume that the transistor is not saturated.
a) It increases
b) It decreases
c) It decreases proportionately
d) It increases parabolically

Explanation: Before the saturation region, the drain current is a function of the gate and the drain voltage. If the oxide-thickness increases, the slope decreases linearly since ID = $$\frac {1}{2}$$ μnCOX(W/L)[2VDS(VGS-VTH)VDS2].

12. What happens to the slope of the graph of ID vs VDS if the width of the MOSFET is doubled? Assume that the transistor is not saturated.
a) It increases linearly
b) It decreases very fast
c) It decreases proportionately
d) It increases logarithmically

Explanation: Before the saturation region, the drain current is a function of the gate and the drain voltage. If the width increases, the slope increases linearly since ID = $$\frac {1}{2}$$ μnCOX(W/L)[2VDS(VGS-VTH)VDS2].

13. What happens to the slope of the graph of ID vs VDS if the length of the MOSFET is halved? Assume that the transistor is not saturated.
a) It increases
b) It doubles
c) It decreases proportionately
d) It decreases very fast

Explanation: The slope is inversely proportional to the length of the MOSFET. If the length is reduced, the slope gets doubled and we get more drain voltage for less drain current.

14. When the MOSFET is in the triode region, the drain voltage is less than the overdrive voltage.
a) True
b) False

Explanation: If the drain voltage is less than the overdrive voltage, it implies that the channel length still extends upto the drain. The MOSFET is in the amplification region and can also be used as a voltage controlled resistor.

15. When the MOSFET is behaving as a current source, the drain voltage is greater than the overdrive voltage.
a) True
b) False

Explanation: As the drain voltage becomes greater than the overdrive voltage, we find that the channel gets pinched off before the drain and the drain current becomes independent of the gate voltage. The MOSFET behaves as a current source in this region of operation.

Sanfoundry Global Education & Learning Series – Microelectronics.

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