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Unformatted text preview: June 10, 2002 EEZ
Closed Book Professor Harold Fetterman No calculators, Please write all answers on your
examination papers. Do not write on these sheets. la. In the following figure we have the points labeled A to E. On your
answer paper next to these letters list the proper source numbers.
Indicate in a single sentence the original of each term. 103(1) i. Photogenemtien . Thermai recomoinatioo
in the depiction region ‘5‘ Ideal _ . Avaianching and/or
region Zener process . Lowlevel injection 5. Depletion approximation . Thermal generation in the
I depletion region M_ _ Band bending
. Series resistance
. vA > v51 . Highuicvei injection lb. Two ideal ptn step junction diodes maintained at room temperature
are identical except that Nm m lOls/crn3 and N132 == i017/ern3. Write an
equation for the Current I in the ptn diode in terms of ND. What is the ratio between the currents in the two diodes? Sketch the currents in both
the forward and reverse directions. lc. Write an expression for the dynamic resistance r = 8V/ BE ( both
forward and reverse bias) for an ideal diode. Now derive r for diodes with
either generation or recombination in the depletion region. Finally write an expression for the forward voltage at which the ideal current is 1/ 2
the recombination current. 2a. In the following ﬁgure the three different diodes shown all have
similar lifetimes, areas and dopings. Explain why they have this IV plot.
Assuming that NV and NC are the same for Si and Ge, and taking the same deping concentrations, write an expression for the difference in Vm. Han/1) N u 0.2 0,4 0.5 0.3 1.0
‘24 V] 2b. For the idea} reverse biased diode we have generation in the neutral region. Taking a long base and using gth = pug/12p show that the current is due to thermal generation within a diffusion length of the edge of the
depletion region 2c. In the ﬁgure beiow we show the various components of electric current in the forward biased pn junction. Identify each component
listed. . Vim2 sesame 3a. An interesting diode uses a linearly graded junction, Shown below
9 = qax for»x,,<x<:w;11 p = 0 elsewhere . NA _Nn Charge density 0 for x <xp and x > xn,
find 8hr). Sketch this result as a function of x. part 3a integrate and ﬁnd an expression for
z 0. Also write an expression for W in terms of V. Cd: Es/w Taking the voltage across the diode to be V131 —V. Show how one can ﬁnd
"a" and Vbi by plotting 1/ C3 as a function of voltage. \ .~ .:'4.=§E'Vv{'~‘r"cW—:3€T~$’§33W 4a. in addition to the Wide base diodes we considered the Narrow base
devices. This is when the base length Wn << L3, and WP << Ln. Starting
from the solution to the continuity equation we can expand the exponential terms {On the :1 side) and retain only the ﬁrst two. a” = 3 "" 3n,
, :2 .5: r! x:
AP($)=ACL” +33% Ap(z'):A[l—L—p +8 1+2;
Applying the boundary conditions at x' = 0 and x' 3 Wm show that
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A _ 2 i + W“ B a 2 ( _ W“
This ields: 13' , d Ap
y mm a Mo) (I ~ so) : qop fix, ’ one Wide one. 4%). Using the following figure, for carrier concentrations inside a pn junction diode, identify if the device is forward or reversed biased?
Explain. Do low level carrier injection conditions prevail in the neutral region of
the diode? Determine the applied voltage V and the hole diffusion length L13. L33“? YOUr answer in terms of logs. " 0”)
(log scaie} can write an expression for 8313;; a {qNDxnUes * (qNAanes. Integrate these expressions to ﬁnd the total voltage across this junction
V = Vbi + VR Express Vbi + VR in terms of 8mm; , ND and NA Finally, the breakdown voltage V1,; is the value of VR at which the value of am“ is equal to the critical electric field 8cm. Write an expression for V1,, and Show how it
depends on doping. 1 V~ :: 532mm» JP : Jp(dﬁﬂ) “I” ip(diﬁusion)
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 Spring '07
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 Pn junction, depletion region, forward biased pn, interesting diode uses, ptn step junction

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