Prof. Jasprit Singh
Fall 2001
EECS 320
Homework 9
This homework is due on November 29, i.e after the thanksgiving
break. Have a great Thanksgiving break!
Problem 1: Consider a npn Si-BJT at 300 K with the following parameters:
1018 cm;3
1017 cm;3
1016 cm;3
30:0 cm2 =s
10:0 m
1:0 m
10 cm2 =s
10:0 m
1:0 m
4:0 10;6 cm2
Nde
Nab
Ndc
Db
Lb
Wb
De
Le
=
=
=
=
=
=
=
=
Emitter thickness =
Device area =
Calculate the emitter eciency and gain when the EBJ is forward biased at
1.0 V and the BCJ is reverse biased at 5.0 V. Calculate the output conductance
of the device de ned by
go = VIC
CB
Problem 2: Consider a npn Si-BJT at 300 K with the following parameters:
Nde
Nab
Ndc
Db
Lb
Wb
De
1
=
=
=
=
=
=
=
1018 cm;3
1017 cm;3
1016 cm;3
30:0 cm2 =s
10:0 m
1:0 m
10 cm2 =s
Le = 5:0 m
electron mobility in the emitter = 500 cm2 V;1 s;1
area = 5:0 10;7 cm2
Calculate the emitter eciency and gain when the EBJ is forward biased at
1.0 V and the BCJ is reverse biased at (a): 5.0 V and (b) 10.0 V.
For high-speed operation, it is found that the BJT discussed above has too
large an emitter resistance. The device designer wants to limit the emitter resistance (keeping the area unchanged) to 2.0 . Calculate the emitter eciency
and for the new device using the case (a) given above.
Problem 3: In a particular BJT the base transit time is 20 % of the total
delay time of charge transport. The base width is 0.5 m and the di usion
coecient is Db = 20 cm2 =s. Calculate the cuto frequency of the device.
Problem 4: Using Eqn. 7.111 of the text calculate the maximum emitter
doping beyond which the emitter eciency of a npn BJT starts to decrease
when the base doping is 1017 cm;3 . Assume that (T=300 K)
De = 10 cm2 =s; Db = 20 cm2 =s; Wbn = 1:0 m; Le = 4:0 =mum
Problem 5: Consider a npn silicon bipolar transistor in which Wb = 2:0
m; Le = Lb = 10:0m and De = Db = 10cm2sec;1 . Assume that Nab = 1016
cm;3 . What is the emitter injection eciency for Nde = 1018; 1019 and 1020
cm;3 when a) bandgap narrowing is neglected, b) when bandgap narrowing is
included?
SOME IMPORTANT ISSUES DISCUSSED THIS WEEK
This week we have nished our discussions on the the operation of the bipolar
junction transistor.
THE BIPOLAR TRANSISTOR
BJT Design Issues: The most important design issues in BJT are high
gain, , (for ampli cation, driving a large number of other devices); excellent
input-output isolation (for applications in digital circuits, for constant current
sources etc.); high switching speed (for digital applications); and excellent high
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frequency response (for microwave devices such as ampli ers and oscillators).
Most of these requirements require selection of device parameters that optimize
performance for one kind of demand but may reduce performance for other
demands. Let us brie y examine the consequences of altering the various device
parameters.
Emitter Doping: The emitter doping should be kept very high since this
improves the emitter eciency e . This allows the device to have a high gain.
However, at very high doping the bandgap of the semiconductor starts to shrink
and as a result the emitter eciency su ers. This is because when the bandgap
of the emitter is smaller than that of the base, the barrier for the electrons (for
an n-p-n device) injected into the base increases while that for the holes to
get into the the base increases while that for the holes to get into the emitter
decreases. As a result the current IEp increases while IEn decreases and e
decreases.
Emitter Thickness: The emitter thickness should be kept as thin as possible
since this adds to the device parasitic resistance and hurts the device high speed
performance. However, we know from our discussion of the narrow diode that if
the emitter thickness becomes smaller than the minority carrier di usion length,
the current owing from the base into the emitter starts to increase since it is
inversely proportional to the emitter thickness in this case. As a result, it is not
possible to reduce the emitter thickness without hurting the emitter eciency.
In the silicon technology, this problem is solved by using polysilicon (heavily
doped) to make the emitter contact. The heavily doped poly allows a very low
emitter resistance. Under the poly is a thin Si emitter. Due to the nature
of poly, the excess minority carrier density does not have to go to zero at the
Si/poly junction as it would for a normal metal contact. Thus the minority
current from the base does not increase even though the emitter thickness has
been reduced.
Base Doping: The base doping has to be maintained at a low value (compared to the emitter doping) for a high emitter eciency. However, if the base
doping is too small, the base resistance can become very large and hurt the device speed performance. Also a low base doping will result in a signi cant change
in the neutral base width. This will change the collector current as the base
collector bias is changed. This, ofcourse, means that the device input-output
isolation is poor. This e ect is called the Early e ect.
Base Width: The base width should be as small as possible so that the base
transport factor, B , is large and the transit time through the base (this time
is important for high frequency performance) is small. Once again a very thin
base will increase the base resistance and any small change in the neutral base
width will have a stronger e ect on the device current.
Collector Doping: The collector doping should be as small as possible compared to the base doping so that the depletion width in the base-collector junction is primarily on the collector side. this would minimize the Early e ect.
Here again we cannot make the doping too small since the collector resistance
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would become too large.
From the discussion above we can see that the device structure has to be
optimized based on the priorities of the various performance demands on the
technology. The BJT technology is almost entirely based on silicon although as
noted above polysilicon is also used to improve the device performance.
Heterojunction Bipolar Transistor: The HBT device in which the
emitter is made from a larger bandgap material allows one to resolve the device
parameter con icts outlined above. This is because the barrier for minority
carrier injection is greatly increased for the carriers coming from the base. As a
result we can have a very large doping in the base without hurting the emitter
eciency. Since the base can be doped heavily, its width can be reduced without
increasing the resistance too much. This solves the problem of base transit time
and the Early e ect. The high performance bipolar technology is therefore based
on the HBT.
TOPICS TO BE COVERED NEXT WEEK
The remainder of the course will be devoted to FETs.
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