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Solid State Electronic Devices

Ben G. Streetman, Sanjay Kumar Banerjee

Chapter 7

Bipolar Junction Transistors - all with Video Answers

Educators

Chapter Questions

03:01

Problem 1

Given the data of Prob. $5.2$, plot the doping profiles $N_{a}(x)$ and $N_{d}(x)$ for the following double-diffused transistor: The starting wafer is $\mathrm{n}$ -type $\mathrm{Si}$ with $N_{d}=10^{16} \mathrm{~cm}^{-3} ; N_{s}=5 \times 10^{13} \mathrm{~cm}^{-2}$ boron atoms are deposited on
the surface, and these atoms are diffused into the wafer at $1100^{\circ} \mathrm{C}$ for $1 \mathrm{hr}$ $\left(D=3 \times 10^{-13} \mathrm{~cm}^{2} / \mathrm{s}\right.$ for $\mathrm{B}$ in $\mathrm{Si}$ at $\left.1100^{\circ} \mathrm{C}\right) ;$ then the wafer is placed in a
phosphorus diffusion furnace at $1000^{\circ} \mathrm{C}$ for $15 \mathrm{~min}\left(D=3 \times 10^{-14} \mathrm{~cm}^{2} / \mathrm{s}\right.$ for $\mathrm{P}$ in $\mathrm{Si}$ at $1000^{\circ} \mathrm{C}$ ). During the emitter diffusion, the surface concentration is held constant at $5 \times 10^{20} \mathrm{~cm}^{-3}$. You may assume that the base doping profile does not change appreciably during the emitter diffusion, which takes place at a lower temperature and for a shorter time. Find the width of the base region from plots of $N_{a}(x)$ and $N_{d}(x) .$ Hint: Use five-cycle semilog paper and let $x$ vary from zero to about $1.5 \mu \mathrm{m}$ in steps that are chosen to be simple multiples of $2 \sqrt{D t}$

Chai Santi
Chai Santi
Numerade Educator
00:39

Problem 2

Sketch the ideal collector characteristics $\left(i_{C},-v_{C E}\right)$ for the transistor of Fig. $7-4 ;$ let $i_{B}$ vary from zero to $0.2 \mathrm{~mA}$ in increments of $0.02 \mathrm{~mA}$, and let $-v_{C E}$ vary from 0 to $10 \mathrm{~V}$. Draw a load line on the resulting characteristics for the circuit of Fig. $7-4$, and find the steady state value of $-V_{C E}$ graphically for $I_{B}=0.1 \mathrm{~mA} .$

Chai Santi
Chai Santi
Numerade Educator
03:48

Problem 3

Calculate the minority excess hole distribution $\delta p(x) / \Delta p_{E}$ in the base of a $\mathrm{p}-\mathrm{n}$ -p bipolar junction transistor (BJT), assuming $W_{B} / L_{P}=0.2$ and $0.5$. The calculations have to be carried out for the base distance of $I$ and $2 \pi$

Chai Santi
Chai Santi
Numerade Educator
03:09

Problem 4

Show the bias polarities and depletion regions of an $n p n$ BJT in the normal active, saturation, and cutoff modes of operation. Draw the three sketches one below the other to (qualitatively) reflect the depletion widths for these biases, and the relative emitter, base, and collector doping.

Consider a BJT with a base transport factor of $1.0$ and an emitter injection efficiency of $0.5$.

Calculate roughly by what factor would doubling the base width of a BJT would increase, decrease, or leave unchanged the emitter injection efficiency and base transport factor? Repeat for the case of emitter doping increased $5 \times=$. Explain with key equations, and assume other BJT parameters remain unchanged!

Chai Santi
Chai Santi
Numerade Educator
02:16

Problem 5

An npn BJT has emitter, base, and collector doping levels of $10^{19} \mathrm{~cm}^{-3}$, $5 \times 10^{18} \mathrm{~cm}^{-3}$, and $10^{17} \mathrm{~cm}^{-3}$, respectively. It is biased in the normal active mode, with an emitter-base voltage of $1 \mathrm{~V}$. If the neutral base width is 100 $\mathrm{nm}$, the emitter is $200 \mathrm{~nm}$ wide, and we have negligible base recombination, calculate the emitter current, emitter injection efficiency, and base transport factor. You can assume electron and hole mobility of 500 and $100 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$, respectively, in the emitter, and 800 and $250 \mathrm{~cm}^{2} / \mathrm{V}$ -s in the base. The device gets heated up to $400 \mathrm{~K}$ during operation such that $n_{i}=10^{12} \mathrm{~cm}^{-3}$, and $\epsilon_{\mathrm{t}}=15$. Qualitatively sketch the device structure, the carrier concentrations, and the band diagram under bias below it. Assume that the carrier lifetimes are $0.1 \mu \mathrm{s}$ everywhere.

Chai Santi
Chai Santi
Numerade Educator
02:04

Problem 6

Redraw Fig. 7-3 for an $\mathrm{n}^{+}$ -p-n BJT, and explain the various components of current flow and current directions for the normal active mode of operation. Draw the energy band diagram for equilibrium and this bias condition.

Chai Santi
Chai Santi
Numerade Educator
01:40

Problem 7

In a p-n-p transistor emitter, doping is $5 \times 10^{18} / \mathrm{cm}^{3}$, base doping is $10^{17} / \mathrm{cm}^{3}$, base width is $0.985 \mu \mathrm{m}$, diffusion lengths for electrons and holes are the same at $10 \mu \mathrm{m}$. Assume $\tau_{p}=\tau_{n}=10^{-7} \mathrm{sec}$, find the emitter injection efficiency, the base transport factor, and the transistor gains if electron and hole mobility are 1250 and $450 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{sec}$, respectively.

Chai Santi
Chai Santi
Numerade Educator
02:10

Problem 8

(a) In a BJT, we increase the base doping by a factor of 10 and halve the base width. Calculate approximately by what factor the collector current changes in the normal active mode, assuming that everything else stays the same. (b) In a certain BJT, the emitter doping is 100 times greater than the base doping, the emitter width is $0.1$ times the base width, and we can assume both base and emitter widths to be much shorter than the carrier diffusion lengths $L_{n}$ and $L_{p r}$ What is the emitter injection efficiency? What is the base transport factor? (c) Suppose $L_{n}=L_{p}$. Now assuming that both emitter and base are much wider than the diffusion lengths, what is the emitter injection efficiency and base transport factor?

Chai Santi
Chai Santi
Numerade Educator
02:36

Problem 9

The symmetrical $\mathrm{p}^{+}-\mathrm{n}-\mathrm{p}^{+}$ transistor of Fig. $\mathrm{P} 7-7$ is connected as a diode in the four configurations shown. Assume that $V \geqslant k T / q$. Sketch $\Delta p\left(x_{n}\right)$ in the base region for each case. Which connection seems most appropriate for use as a diode? Why?

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
02:01

Problem 10

Derive the expression for the excess minority hole concentration by solving the diffusion equation in a uniformly doped p-n-p bipolar transistor in forward active region having base width $W_{B}$.

Chai Santi
Chai Santi
Numerade Educator
01:42

Problem 11

(a) Find the expression for the current $I$ for the transistor connection of Fig. $\mathrm{P} 7-7 \mathrm{~b} ;$ compare the result with the narrow-base diode problem (Prob. 5.40).
(b) How does the current $I$ divide between the base lead and the collector lead?

Ben Nicholson
Ben Nicholson
Numerade Educator
01:47

Problem 12

For a $\mathrm{p}-\mathrm{n}-\mathrm{p} \mathrm{BJT}$ with $N_{E}>N_{B}>N_{C}$, show the dominant current components, with proper arrows, for directions in the normal active mode. If $I_{E p}=10 \mathrm{~mA}$, $I_{E_{n}}=100 \mu \mathrm{A}, I_{C p}=9.8 \mathrm{~mA}$, and $I_{C n}=1 \mu \mathrm{A}$, calculate the base transport fac-
tor, emitter injection efficiency, common-base current gain, common-emitter current gain, and $I_{C B O}$. If the minority stored base charge is $4.9 \times 10^{-11} \mathrm{C}$, calculate the base transit time and lifetime.

Chai Santi
Chai Santi
Numerade Educator
02:56

Problem 13

A Si p-n-p BJT at $T=300 \mathrm{~K}$ has uniform dopings of $N_{E}=10^{18} / \mathrm{cm}^{3}, N_{B}=10^{16} / \mathrm{cm}^{3}$, and $N_{C}=10^{15} / \mathrm{cm}^{3}$. The metallurgical base width is $1.2 \mu \mathrm{m}$.
(a) Calculate the peak electric field at the $\mathrm{CB}$ junction and the $\mathrm{CB}$ depletion capacitance/unit area for normal biasing, with a $\mathrm{CB}$ bias of $30 \mathrm{~V}$.
(b) Estimate the neutral base width narrowing at this voltage, ignoring the $\mathrm{EB}$ depletion region.

Chai Santi
Chai Santi
Numerade Educator
03:17

Problem 14

It is obvious from Eqs. $(7-35)$ and $(7-36)$ that $I_{E O}$ and $I_{C O}$ are the saturation currents of the emitter and collector junctions, respectively, with the opposite junction open circuited.
(a) Show that this is true from Eqs. $(7-32)$.
(b) Find expressions for the following excess concentrations: $\Delta p_{C}$ with the emitter junction forward biased and the collector open; $\Delta p_{E}$ with the collector junction forward biased and the emitter open.
(c) Sketch $\Delta p\left(x_{n}\right)$ in the base for the two cases of part (b).

Chai Santi
Chai Santi
Numerade Educator
03:01

Problem 15

A symmetrical p'np bipolar junction transistor made of $\mathrm{Si}$ has the following specifications:
$\begin{array}{ll}\text { Emitter } & \underline{B a}\end{array}$
$N_{a}=10^{18} / \mathrm{cm}^{3}$
$N_{d}=10^{16} / \mathrm{cm}^{3}$
$\tau_{n}=10^{-6} \mathrm{sec}$
$\tau_{n}=10^{-6} \mathrm{sec}$
$\begin{array}{cc}\mu_{P}=200 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{sec} & \mu_{p}=400 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{sec}\end{array}$
$\mu_{n}=800 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{sec} \quad \mu_{n}=1250 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{sec}$
Base width is $0.8 \mu \mathrm{m}$ and device area is $10^{-4} \mathrm{~cm}^{2}$. Compute the saturation currents and the electron and hole components of emitter current under $0.2 \mathrm{~V}$ of emitter-base applied bias.

Chai Santi
Chai Santi
Numerade Educator
03:32

Problem 16

(a)How is it possible that the average time an injected hole spends in transit across the base $\tau_{t}$ is shorter than the hole lifetime in the base $\tau_{p} ?$
(b) Explain why the turn-on transient of a BJT is faster when the device is driven into oversaturation.

Aman Kumar
Aman Kumar
Numerade Educator
01:11

Problem 17

Use Example $5-7$ to design an $\mathrm{n}$ -p-n heterojunction bipolar transistor with reasonable $\gamma$ and base resistance.

Dominador Tan
Dominador Tan
Numerade Educator
02:10

Problem 18

The current amplification factor $\beta$ of a BJT is very sensitive to the base width as well as to the ratio of the base doping to the emitter doping. Calculate and plot $\beta$ for a p-n-p BJT with $L_{p}^{n}=L_{n}^{p}$, for:
(a) $n_{n}=p_{p}, W_{b} / L_{p}^{n}=0.01$ to 1;
(b) $W_{b}=L_{p}^{n}, n_{n} / p_{p}=0.01$ to 1 .
Neglect mobility variations $\left(\mu_{n}^{p}=\mu_{p}^{n}\right)$.

Chai Santi
Chai Santi
Numerade Educator
03:32

Problem 19

(a) How much charge (in coulombs) due to excess holes is stored in the base of the transistor shown in Fig. $7-4$ at the $\mathrm{d}-\mathrm{c}$ bias given?
(b) Why is the base transport factor $B$ different in the normal and inverted modes for the transistor shown in Fig. $7-5 ?$

Aman Kumar
Aman Kumar
Numerade Educator
03:01

Problem 20

A Si p-n-p transistor has the following properties at room temperature:
$\tau_{n}=\tau_{p}=0.1 \mu \mathrm{s}$
$D_{n}=D_{p}=10 \mathrm{~cm}^{2} / \mathrm{s}$
$N_{E}=10^{19} \mathrm{~cm}^{-3}=$ emitter concentration
$N_{B}=10^{16} \mathrm{~cm}^{-3}=$ base concentration
$N_{C}=10^{16} \mathrm{~cm}^{-3}=$ collector concentration
$W_{E}=$ emitter width $=3 \mu \mathrm{m}$
$W=$ metallurgical base width $=1.5 \mu \mathrm{m}=$ distance between base-emitter junction and base-collector junction $A=$ cross-sectional area $=10^{-5} \mathrm{~cm}^{2}$
Calculate the neutral base width $W_{b}$ for $V_{C B}=0$ and $V_{E B}=0.2 \mathrm{~V}$. Repeat for $0.6 \mathrm{~V}$

Chai Santi
Chai Santi
Numerade Educator
02:10

Problem 21

For the BJT in Prob. $7.20$, calculate the base transport factor and the emitter injection efficiency for $V_{E B}=0.2$ and $0.6 \mathrm{~V}$.

Chai Santi
Chai Santi
Numerade Educator
01:28

Problem 22

For the BJT in Prob. 7.20, calculate $\alpha, \beta, I_{E}, I_{B}$, and $I_{C}$ for the two values of $V_{E B}$ What is the base Gummel number in each case?

Chai Santi
Chai Santi
Numerade Educator
03:01

Problem 23

A Si p-n-p BJT has the following parameters at room temperature. $\begin{array}{llll}\underline{\text { Emitter }} & \underline{\text { Base }} & \underline{\text { Collector }} \\ N_{a}=5 \times 10^{18} \mathrm{~cm}^{-3} & N_{d}=10^{16} & N_{a}=10^{15} \\ \tau_{n}=100 \mathrm{ps} & \tau_{p}=2500 \mathrm{ps} & \tau_{n}=2 \mu \mathrm{s} \\ \mu_{n}=150 \mathrm{~cm}^{2} / V-s & \mu_{n}=1500 & \mu_{n}=1500 \\ \mu_{p}=100 \mathrm{~cm}^{2} / V-s & \mu_{p}=400 & \mu_{p}=450 \\ \text { Base width } W_{b}=0.2 \mu \mathrm{m} & & \\ \text { Area }=10^{-4} \mathrm{~cm}^{2} & & \end{array}$
Calculate the $\beta$ of the transistor from $B$ and $\gamma$, and using the charge control model. Comment on the results.

Chai Santi
Chai Santi
Numerade Educator
01:17

Problem 24

For the BJT in Prob. 7.23, calculate the charge stored in the base when $V_{C B}=0$ and $V_{E B}=0.7 \mathrm{~V}$. If the base transit time is the dominant delay component for this BJT. what is the $f_{r} ?$

Chai Santi
Chai Santi
Numerade Educator
02:34

Problem 25

Consider a Si $\mathrm{n}$ -p-n transistor at $T=300 \mathrm{~K}$ with these specifications: emitter current $\left(I_{E}\right)=1 \mathrm{~mA}$, base width $\left(W_{B}\right)=100 \mathrm{~nm}$, collector-base depletion width $\left(x_{d c}\right)=50 \mathrm{~nm}, C_{\mu}=0.1 \mathrm{pF}, \mathrm{C}_{j e}=1 \mathrm{pF}$, diffusion coefficent for electrons $\left(D_{n}\right)=$
$25 \mathrm{~cm}^{2} / \mathrm{sec}$, collector resistance $\left(r_{C}\right)=20 \Omega$, collector capacitance $\left(C_{s}\right)=0.1 \mathrm{pF}$ and electron saturation velocity $\left(v_{s}\right)=2.3 \times 10^{7} \mathrm{~cm} / \mathrm{sec} .$ Calculate the base transit time for the transistor. Calculate the cut off frequency for the transistor.

Chai Santi
Chai Santi
Numerade Educator
03:41

Problem 26

A n-p-n BJT at room temperature has these data available: emitter diffusion coefficient $\left(D_{E}\right)=10 \mathrm{~cm}^{2} / \mathrm{sec}$, base diffusion coefficent $\left(D_{B}\right)=25 \mathrm{~cm}^{2} / \mathrm{sec}$, base width $\left(W_{B}\right)=0.70 \mu \mathrm{m}$, emitter width $\left(W_{E}\right)=0.50 \mu \mathrm{m}$, emitter doping $\left(N_{E}\right)=$ $10^{18} / \mathrm{cm}^{3}$, base doping $\left(N_{B}\right)=10^{16} / \mathrm{cm}^{3}$, emitter and base recombination lifetimes are $\tau_{E 0}=10^{-7}$ sec and $\tau_{B 0}=5 \times 10^{-7} \mathrm{sec}$, recombination current density $\left(J_{r 0}\right)=5 \times 10^{-8} \mathrm{~A} / \mathrm{cm}^{2}$, and the applied $\mathrm{B}-\mathrm{E}$ bias is $0.5 \mathrm{~V} .$ Calculate
(a) emitter injection efficiency $(\gamma)$,
(b) base transport factor (B),
(c) recombination factor,
(d) CE current gain $(\beta)$,
(e) $\mathrm{CB}$ current gain $(\alpha)$.

Chai Santi
Chai Santi
Numerade Educator