Exercise 9.1
Assume that the subthreshold current of a MOSFET is given by
−15 VGS ID = 10 exp (2.1)Vt
over the range 0 ≤ VGS ≤ 1 volt and where the factor 2.1 takes into account the effect of interface states. Assume that 106 identical transistors on a chip are all biased at the same VGS andatVDD =5V.
(a) Calculate the total current that must be supplied to the chip at VGS = 0.5, 0.7, and 0.9 V.
(b) Calculate the total power dissipated in the chip for the same VGS values.
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Exercise 9.2
A silicon MOSFET has parameters Na = 4 × 1016 cm−3, tox = 12 nm = 120 ̊A, Q′ss = 4 × 1010 cm−2, and φms = −0.5 V. The transistor is biased at VGS = 1.25 V and VSB = 0.
(a)Calculate∆Lfor(i)∆VDS =1V,(ii)∆VDS =2V,and(iii)∆VDS =4V.
(b) Determine the minimum channel length L such that ∆L/L = 0.12 for VGS = 1.25 V and ∆VDS = 4 V.
Exercise 9.3
Consider an n-channel silicon MOSFET. The parameters are kn′ = 75μA/V2, W/L = 10, and VT = 0.35 V. The applied drain-to-source voltage is VDS = 1.5 V.
(a) For VGS = 0.8 V, find ( i ) the ideal drain current, (ii) the drain current if λ = 0.02 V−1, and (iii) the output resistance for λ = 0.02 V−1.
(b) Repeat part (a) for VGS = 1.25 V.
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Exercise 9.4
(a) What is subthreshold conduction? Sketch a drain current versus gate voltage plot that shows the subthreshold current for the transistor biased in the saturation region.
(b) What is channel length modulation? Sketch an I–V curve that shows the channel length modulation effect.
(c) What is velocity saturation and what is its effect on the I–V relation of a MOSFET?
(d) Sketch the space charge region in the channel of a short-channel MOSFET and show the charge-sharing effect. Why does the threshold voltage decrease in a short-channel NMOS device?
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Exercise 9.5
For a uniformly doped n++p+n bipolar transistor in thermal equilibrium,
(a) sketch the energy-band diagram
(b) sketch the electric field through the device
(c) repeat parts (a) and (b) for the transistor biased in the forward-active region.
Exercise 9.6
What is Early effect? How to minimize it?
Exercise 9.7
(a) From fabrication point of view, why is Si the most commonly used material in semiconductor industry nowadays?
(b) After this course, what did you learn about semiconductors?
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Reference
1. Neamen, Donald A. Semiconductor physics and devices: basic principles. McGraw- hill, 2003.
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