# Ve320 Introduction of Semiconductor Device Homework 7 solved

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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
2
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�̊. 3 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. 4 (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). 5 Figure 4. Figure for Ex 7.10.