Semiconductor Physics and Devices

Donald A. Neamen

Chapter 15

Semiconductor Microwave and Power Devices - all with Video Answers

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Chapter Questions

Problem 1

Sketch the energy band diagrams of a tunnel diode in which both the $\mathrm{n}$ and $\mathrm{p}$ regions are degenerately doped for the case of $(a)$ zero bias, $(b) 0<V<V_{p}$,
(c) $V_{p}<V<V_{x}$, and
(d) $V>V_{v}$

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Problem 2

The parameters in Figure 15.1b are $I_{p}=20 \mathrm{~mA}, I_{v}=2 \mathrm{~mA}, V_{p}=0.15 \mathrm{~V}$, and $V_{v}=0.60 \mathrm{~V}$. Assuming a straight-line approximation to the $I-V$ characteristics between these two points, calculate the value of differential negative resistance.

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Problem 3

For values of $R_{\min }=10 \Omega, R_{p}=1 \Omega$, and $C_{j}=2 \mathrm{nF}$, determine the maximum resistance cutoff frequency of a tunnel diode.

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Problem 4

(a) A GaAs transferred-electron device has a doping concentration of $N_{d}=10^{15} \mathrm{~cm}^{-3} .$ Determine (i) the minimum device length, (ii) the time between current pulses, and (iii) the oscillation frequency (assume $v_{d}=1.5 \times 10^{7} \mathrm{~cm} / \mathrm{s}$ ).
(b) Repeat part
$(a)$ for a doping concentration of $N_{d}=10^{16} \mathrm{~cm}^{-3}$.

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Problem 5

The drift region length of a GUNN diode is $L=15 \mu \mathrm{m}$. The voltage across the diode oscillates between 8 and $10 \mathrm{~V}$. $(a)$ Determine the average electric field in the device. (b) Using Figure $15.3$, find the average electron drift velocity. ( $c$ ) Using the results of part ( $b$ ), find the frequency of oscillation.

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Problem 6

Find the frequency of oscillation of a silicon IMPATT diode with a drift region length of $L=10 \mu \mathrm{m}$.

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Problem 7

Consider the vertical npn power bipolar transistor shown in Figure $15.10 .$ The doping concentrations are $N_{E}=10^{18} \mathrm{~cm}^{-3}, N_{B}=8 \times 10^{15} \mathrm{~cm}^{-3}$, and
$N_{C}=6 \times 10^{14} \mathrm{~cm}^{-3} .$ The neutral base width is $2 \mu \mathrm{m}$, the electron diffusion coefficient in the base is $D_{B}=20 \mathrm{~cm}^{2} / \mathrm{s}$, and the $\mathrm{B}-\mathrm{E}$ cross-sectional area is $0.4 \mathrm{~cm}^{2} .(a)$ The excess electron concentration in the base at the edge of the $\mathrm{B}-\mathrm{E}$ junction is $\delta n_{p}(0)=10^{14} \mathrm{~cm}^{-3} .$ Determine (i) the $\mathrm{B}-\mathrm{E}$ voltage and (ii) the approximate collector current. $(b)$ Determine the (i) $\mathrm{B}-\mathrm{E}$ voltage at the edge of high injection and (ii) the approximate resulting collector current.

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Problem 8

Consider the npn power bipolar transistor described in Problem 15.7. (a) Determine the expected B-C avalanche breakdown voltage. (b) Find the punch-through voltage. ( $c$ ) What is the expected B-E avalanche breakdown voltage?

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Problem 9

A silicon pnp power BJT is to be designed. The base doping concentration is $N_{E}=5 \times 10^{15} \mathrm{~cm}^{-3} .$ The base-collector junction breakdown voltage is to be $B V_{C B O}=1000 \mathrm{~V}$. Determine the maximum collector doping concentration and the minimum base and collector region widths.

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Problem 10

(a) Assume that $B V_{C B O}=300 \mathrm{~V}$ for a power $\mathrm{BJT}$. Determine $B V_{C E O}$ for $(i) \beta=10$ and $(i i) \beta=50 .$ Assume $n=3$ (see Equation (12.63)). (b) Repeat part ( $a$ ) for $B V_{C \text { Co }}=125 \mathrm{~V}$

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Problem 11

The effective $\beta$ of a Darlington pair is found to be $\beta_{e f}=180$. The driver $\mathrm{BJT}, Q_{A}$, has a current gain $\beta_{A}=25 .(a)$ What is $\beta$ of the output transistor $Q_{B} ?(b)$ If the rated collector current of $Q_{B}$ is $I_{C B, \text { mex }}=20 \mathrm{~A}$, what must be the rated collector current of $Q_{A}$ ?

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Problem 12

The maximum current, voltage, and power rating of an npn power $\mathrm{BJT}$ are $2 \mathrm{~A}$, $120 \mathrm{~V}$, and $30 \mathrm{~W}$, respectively. (a) Sketch and label the safe operating area for this transistor using linear current and voltage scales. $(b)$ Determine $R_{L}$ such that the
maximum power is delivered to the load if the quiescent collector-emitter voltage is $60 \mathrm{~V}$. For this value of $R_{L}$, what is the maximum current and maximum voltage?
(c) Determine the value of $R_{L}$ such that the maximum current and maximum power can be obtained. $(d)$ Determine the value of $R_{L}$ such that the maximum voltage and maximum power can be obtained.

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Problem 13

The common-emitter circuit in Figure $15.15$ is biased at $V_{C C}=12 \mathrm{~V}$. The power rating of the transistor is $P_{T}=10 \mathrm{~W}$. ( $a$ ) Determine $R_{L}$ such that the maximum power is delivered to the load. (b) What must be the current rating of the transistor, $I_{C \text { . } \operatorname{mas}}$ ?

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Problem 14

The transistor in the common-emitter circuit in Figure $15.15$ has parameters $P_{T}=2.5 \mathrm{~W}, V_{C \text { ,sus }}=25 \mathrm{~V}$, and $I_{C \max }=500 \mathrm{~mA}$. Let $R_{L}=100 \Omega$. What is the value
of $V_{c c}$ such that the maximum power is delivered to the load?

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Problem 15

A power MOSFET is used in the inverter circuit shown in Figure $15.26$ in which $V_{D D}=200 \mathrm{~V}$ and $R_{D}=100 \Omega$. The on resistance of the transistor is $R_{\mathrm{cn}}=2 \Omega$ at a junction temperature of $25^{\circ} \mathrm{C}$. The on resistance increases linearly with temperature and is $3 \Omega$ at a junction temperature of $100^{\circ} \mathrm{C}$. Plot the power dissipated in the transistor as a function of junction temperature.

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Problem 16

Three MOSFETs are to be used in parallel to sink 5 A of load current when they are on. $(a)$ The on resistances of the three devices are $R_{\text {oel }}=1.8 \Omega, R_{\text {on2 }}=2 \Omega$, and $R_{\mathrm{an3}}=2.2 \Omega$. Calculate the current in each device and the power dissipated in each device. (b) For some unknown reason, the on resistance of the second device increases to $R_{\mathrm{an} 2}=3.6 \Omega .$ Recalculate the current in each device and the power dissipated in each device.

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Problem 17

Consider a silicon DMOS power MOSFET shown in Figure $15.20 .$ The source doping concentration is $5 \times 10^{17} \mathrm{~cm}^{-3}$ and the base doping concentration is $10^{15} \mathrm{~cm}^{-3}$.
(a) Design the drain doping concentration, channel length, and drain drift region width to support a blocking voltage of $200 \mathrm{~V} .(b)$ Repeat part $(a)$ such that the blocking voltage is $80 \mathrm{~V}$.

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Problem 18

A power MOSFET is connected in a common-source configuration as shown in Figure $15.26 .$ The transistor parameters are $K_{n}=0.20 \mathrm{~A} / \mathrm{V}^{2}, V_{T}=2 \mathrm{~V}, I_{D, \text { mas }}=8 \mathrm{~A}$, $B V_{D S s}=80 \mathrm{~V}$, and $P_{T}=45 \mathrm{~W}$. The circuit parameters are $V_{D D}=60 \mathrm{~V}$ and $R_{L}=10 \Omega .(a)$ Sketch and label the safe operating area for the transistor using linear current and voltage scales. Sketch the load line on the same curve. $(b)$ Calculate the power dissipated in the transistor for $V_{a s}=4,6$, and $8 \mathrm{~V}$. Is there a possibility of damaging the transistor? Explain.

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Problem 19

Consider the power MOSFET described in Problem 15.18. (a) For $V_{D D}=60 \mathrm{~V}$, determine the value of $R_{L}$ such that the maximum power is delivered to the load and the transistor remains biased in the safe operating area. For this case, what is the maximum allowed drain current? $(b)$ For $R_{L}=10 \Omega$, determine the maximum value $V_{D D}$ such that the maximum power is delivered to the load and the transistor remains biased in the safe operating area.

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Problem 20

One condition for switching a thyristor is that $\alpha_{1}+\alpha_{2}=1$. Show that this condition corresponds to $\beta_{1} \beta_{2}=1$, where $\beta_{1}$ and $\beta_{2}$ are the common-emitter current gains of the pnp and npn bipolar transistors in the equivalent circuit of the thyristor.

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Problem 21

Explain how a pulse of ionizing radiation could trigger a basic CMOS structure into a high-current, low-impedance state.

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Problem 22

Show that the triac can be triggered into its ON state by gate signals of either polarity and with anode-to-cathode voltages of either polarity. Consider each voltage polarity combination.

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