In enhancement mode MOSFET the saturation (drain) current is given by (a) \(K\dfrac{W}{L}(V_{gs}-V_{th})^{2}\) (b) \(K\dfrac{W}{L}(V_{gs}-V_{th})(1+\lambda V_{ds})\) (c) \(K\dfrac{W}{L}(V_{gs}-V_{th})^{2}(1+\lambda V_{ds})\) (d) \(K\dfrac{W}{L}(V_{gs}-V_{th})^{2}(1-\lambda V_{ds})\) Out of these
(a) and (c) are correct.
The basic saturation law. Beyond pinch-off the drain current of an enhancement MOSFET depends on the gate overdrive squared and is nearly independent of Vds:
\(I_D=K\dfrac{W}{L}(V_{gs}-V_{th})^{2}\)
That is statement (a), the first-order (long-channel) model.
Adding channel-length modulation. In a real device, raising Vds pushes the pinch-off point back towards the source, shortening the effective channel by ΔL. Since \(I_D\propto1/L_{eff}\), the current creeps up slightly with Vds, giving the saturation characteristic a small positive slope. The effect is modelled by one extra factor:
\(I_D=K\dfrac{W}{L}(V_{gs}-V_{th})^{2}(1+\lambda V_{ds})\)
which is statement (c). So (a) and (c) are the two correct forms — the same law without and with the second-order correction.
Why the other two fail.
Statement (b) loses the square on the overdrive. A linear dependence would describe the triode region, not saturation, and it would wreck the quadratic transfer characteristic that gives the MOSFET its constant transconductance slope \(g_m=2\sqrt{K\frac{W}{L}I_D}\).
Statement (d) has \((1-\lambda V_{ds})\), the wrong sign. That would make the current fall as Vds rises, i.e. a negative output resistance — the opposite of what is observed.
What λ means in practice. It is the reciprocal of the Early-like voltage and sets the output resistance of the device:
\(r_o=\dfrac{1}{\lambda I_D}\)
which is exactly what limits the intrinsic gain \(g_mr_o\) of an amplifier stage. Short-channel devices have larger λ, which is why analog designers deliberately use longer channels where high gain is needed.
Hence, the correct expressions are (a) and (c).
Similar Questions
The threshold voltage of an n-channel MOSFET can be increased by
Assertion (A) : MOS ICs based on MOSFET structure find wide applications in digital field.
Reason (R) : MOS ICs have small size and are easy to fabricate.
In MOSFET, the carrier velocity between constant mobility regime and the saturation velocity can be described as :
If Z × L is the total channel area and C'par is the total input parasitic capacitance, then for microwave performance the cut off frequency can be defined as :
(A) \(\dfrac{g_{m}}{2\pi\left(C'_{ca}+C'_{par}\right)}\)
(B) \(\dfrac{g_{m}}{2\pi C_{gs}}\)
(C) \(\dfrac{g_{m}}{2\pi C_{gd}}\)
(D) \(\dfrac{g_{m}}{2\pi\left(ZLC_{ox}+C'_{par}\right)}\)Choose the most appropriate answer from the options given below :
Consider the following statements :
(A) The origin of the punch through phenomena is the lowering of the barrier near the source.
(B) For a long channel device, a drain bias can change the effective channel length, but the barrier at the source end remains constant.
(C) For a short channel device, this barrier is no longer fixed.
(D) The lowering of the source barrier do not cause any injection of extra carriers.
(E) The punch through condition normally occurs inside the bulk region of the semiconductor.Choose the most appropriate answer from the options given below :
In MOSFET, the linear region current is :
(A) \(\dfrac{\mu_{n}C_{ox}w}{L}\left(V_{gs}-V_{th}-\dfrac{V_{ds}}{2}\right)V_{ds}\)
(B) \(\dfrac{\mu_{n}C_{ox}w}{L}\left(V_{gs}-V_{th}\right)V_{ds}\)
(C) \(\dfrac{\mu_{n}C_{ox}w}{2L}\left(V_{gs}-V_{th}\right)V_{ds}^{2}\)
(D) \(\dfrac{\mu_{n}C_{ox}w}{L}\left(V_{gs}-V_{th}\right)^{2}\)Choose the most appropriate answer from the options given below :
Approximate oxide capacitance value (Cgd) for saturation operating mode of MOS transistor is:
For an n-channel MOS transistor with $\mu_n$ = 600 cm2/Vs, Cox = 7 x 10-8 F/cm2, W = 40 $\mu_m$, L = 4$\mu_m$ and VTO=1.0 V, the value of K parameter is:
In MOS
A. The substrate fermi potential ϕF is negative in NMOS
B. The substrate fermi potential ϕF is positive in NMOS
C. The substrate bias voltage VSB is positive in NMOS, negative in PMOS
D. The substrate bias voltage VSB is negative in NMOS, positive in PMOS.
Choose the correct answer from the options given below:
In a MOSFET the drain saturation current is
Important Questions from MOSFET
The O in a MOSFET stands for _______ layer which provides _______ to the device.
Which industry does aluminium smelting belong to?
In an N-channel MOSFET, the drain current ID increases as _______.
Consider an ideal long channel nMOSFET (enhancement-mode) with gate length 10 µm and width 100 µm. The product of electron mobility (µn) and oxide capacitance per unit area (COX) is µn COX = 1 mA/V2 . The threshold voltage of the transistor is 1 V. For a gate-to-source voltage VGS = [2 − sin (2t)] V and drain-to-source voltage VDS = 1 V (substrate connected to the source), the maximum value of the drain-to-source current is ________.
Given, Vgs is the gate-source voltage, Vds is the drain source voltage, and Vth is the threshold voltage of an enhancement type NMOS transistor, the conditions for transistor to be biased in saturation are
