Ebers-Moll Model
8.8 Consider the excess minority-carrier distribution of a PNP BJT as shown in Fig. 8-28.
(The depletion regions at junctions are not shown.) Assume all
generation-recombination current components are negligible and each region is
uniformly doped. Constant $D_n = 30 \text{ cm}^2/s$ and $D_p = 10 \text{ cm}^2/s$ are given. This device has
a cross-section area of $10^{-5} \text{ cm}^2$ and $N_E = 10^{18} \text{ cm}^{-3}$.
$10^{14} \text{cm}^{-3}$
n'
10
p'
8
6
4
2
0
0
E
1
B
2
C
3 $\mu m$
FIGURE 8-28
18v3.fm Page 322 Friday, February 13, 2009 4:01 PM
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Chapter 8 \textbullet Bipolar Transistor
(a) Find $N_C$, i.e., the dopant concentration in the collector.
(b) In what region of the IV characteristics is this BJT operating? Explain your
answer. (Hints: Are the BE and BE junctions forward or reverse biased?)
(c) Calculate the total stored excess carrier charge in the base (in Coulombs).
(d) Find the emitter current $I_E$.
(e) Calculate $\beta_F$, i.e., the common-emitter current gain when the BJT is operated in
the nonsaturation region (i.e., $V_{EB} > 0.7 \text{ V}$ and $V_{CE} > 0.3 \text{ V}$. Neglect base-width
modulation).
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