## Description

Ex 7.1

(a) Consider a Schottky diode at � = 300 � that is formed with tungsten on ntype silicon. Use following Fig.1 to determine the barrier height. Assume a

doping concentration of �( = 10*+��./ and assume a cross-sectional area

� = 10.1��2. Given that �∗ = 120�/�2 ⋅ ��2, determine the forward-bias

voltage required to induce a current of

(i) 10��,

(ii) 100��,

(iii) 1��.

(b) Repeat part (a) for a temperature of � = 350�. (Neglect the barrier lowering

effect.)

Figure 1. Experimental barrier heights as a function of metal work functions for GaAs and Si.

Ex 7.2

A pn junction diode and a Schottky diode each have cross-sectional areas of � =

8 × 10.1 ��2. The reverse saturation current densities at � = 300 � for the pn

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junction diode and Schottky diode are 8 × 10.*/ �/��2 and 6 × 10.< A/cm2,
respectively. Determine the required forward-bias voltage in each diode to yields
currents of
(a) 150��,
(b) 700��,
(c) 1.2 ��.
Ex 7.3
The dc charge distributions of four ideal MOS capacitors are shown in the
Following Fig.2. For each case:
(a) Is the semiconductor n or p type?
(b) Is the device biased in the accumulation, depletion, or inversion mode?
(c) Draw the energy- band diagram in the semiconductor region.
Figure 2. Figure for Ex 2.3.
Ex 7.4
(a) Consider an n+ polysilicon–silicon dioxide–n-type silicon MOS structure. Let
�( = 4 × 10*C��/ . Calculate the ideal flat-band voltage for �EF = 20�� =
200�̊.
(b) Considering the results of part (a), determine the shift in flat-band voltage for
(i) �JJ
K = 4 × 10*L��.2, and
(ii) �JJ
K = 10**��.2.
(c) Repeat parts (a) and (b) for an oxide thickness of �EF = 12�� = 120�̊.
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Ex 7.5
The high-frequency C–V characteristic curve of a MOS capacitor is shown in the
following Fig.3. The area of the device is 2 × 10./��2 . The metal–
semiconductor work function difference is �NJ = −0.50�, the oxide is SiO2, the
semiconductor is silicon, and the semiconductor doping concentration is
2 × 10*+��./.
(a) Is the semi- conductor n or p type?
(b) What is the oxide thickness?
(c) What is the equivalent trapped oxide charge density?
(d) Determine the flat-band capacitance.
(e) Indicate which points correspond to flat-band, inversion, accumulation,
threshold, and depletion modes.
Figure 3. Figure for Ex 7.5.
Ex 7.6
The parameters of an n-channel MOSFET are �R
K = 0.6��/�2 and �S = 0.8�.
The drain current is 1�� with applied voltages of �TU = 1.4�, �UV = 0, and
�WU = 4�.
(a)What is the �/� value?
(b)What is the value of �W for �TU = 1.85�, �UV = 0, and �WU = 6�?
(c)Determine the value of �W for �TU = 1.2�, �UV = 0, and �WU = 0.15�.
Ex 7.7
Consider an ideal p-channel MOSFET with the following parameters: �S =
−0.35�, �[ = 210��2/� ⋅ � , �EF = 11 �� = 110 �̊, � = 35��, and � =
1.2��.
(a) Plot �W versus �UW for 0 ≤ �UW ≤ 3 � and for �UT = 0, 0.6, 1.2, 1.8, and
2.4�. Indicate on each curve the �UW(���) point.
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(b) Plot b�W(���) versus �UT for 0 ≤ �UT ≤ 2.4 �.
(c) Plot �W versus �UT for 0 ≤ ��� ≤ 2.4 � and for �UW = 0.1 �.
Ex 7.8
Assume that the subthreshold current of a MOSFET is given by:
�W = 10.*C ���(
�TU
(2.1)�h
)
over the range 0 ≤ �TU ≤ 1 volt and where the factor 2.1 takes into account the
effect of interface states. Assume that 10+ identical transistors on a chip are all
biased at the same �TU and at �WW = 5 �.
(a) Calculate the total current that must be supplied to the chip at �TU = 0.5, 0.7,
and 0.9 �.
(b) Calculate the total power dissipated in the chip for the same �TU values.
Ex 7.9
Consider an n-channel silicon MOSFET. The parameters are �R
K = 75��/�2,
�/� = 10, and �S = 0.35�. The applied drain-to-source voltage is �WU = 1.5 �.
(a) For �TU = 0.8 �, find
(i) the ideal drain current,
(ii) the drain current if � = 0.02�.*, and
(iii) the output resistance for � = 0.02 �.*.
(b) Repeat part (a) for �TU = 1.25�.
Ex 7.10
The parameters of an n-channel enhancement-mode MOSFET are �S = 0.40 �,
�EF = 20�� = 200�̊, � = 1.0��, and � = 10��.
(a) Assuming a constant mobility of �R = 475��2/� ⋅ �, calculate �W for �TU −
�S = 2.0 � when biased at
(i) �WU = 0.5 �,
(ii) �WU = 1.0 �,
(iii) �WU = 1.25 �,
(iv) �WU = 2.0 �.
(b) Consider the piecewise linear model of the carrier velocity versus VDS shown
in the following Fig.4. Calculate �W for the same voltage values given in part (a).
[You may refer to Equation (11.17) in textbook.]
(c) Determine the �WU(���) values for parts (a) and (b).
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Figure 4. Figure for Ex 7.10.