Spring 2003
Prof. J. A. del Alamo
6.012 Microelectronic Devices and Circuits
Homework #5 - April 4, 2003
ELEC 310
Due: April 11, 2003 at recitation (Rm. 26-310, 1 PM)
(late homework
will not# be
Homework
4 accepted)
Note: Ignore
points assigned
to problems
below.
Please
writeall your
recitation
session
time on your problem set solution.
1. [30 points] Below is a sketch not to scale of the minority carrier distribution across
the quasi-neutral regions of a forward-biased p-n diode. For this diode, Wp xp = 4 m,
Wn xn = 3 m, Dn = 25 cm2 /s, and Dp = 10 cm2 /s. The area of the junction is 10 m2 .
p-side
n-side
p(xn)=1014 cm-3
n(-xp)=1013 cm-3
p(x)
n(x)
ni2
Nd
ni2
Na
-Wp
xn
-xp
Wn
a) [5 points] Calculate the hole current injected into the n-side of the diode.
b) [5 points] Calculate the electron current injected into the p-side of the diode.
c) [5 points] Calculate the diffusion capacitance associated with carrier storage on the nside of the diode.
d) [5 points] Calculate the diffusion capacitance associated with carrier storage on the
p-side of the diode.
e) [5 points] How much should the voltage across the junction increase if we wish to double
the total current through the diode?
f ) [5 points] If we increase the voltage in the manner suggested in the previous question,
what happens to the total diffusion capacitance of the diode?
g) [5 points] What is the ratio of the doping levels across the junction: Na /Nd ?
h) [5 points] In what direction should Na /Nd change if we wish to redesign the diode so as to
get less diffusion capacitance at the same current level? (Assume that in redesigning
the diode Dn , Dp , Wn xn , and Wp xp do not change).
Choose one: Na /Nd must increase. Na /Nd must decrease. Explain.
2. [40 points] Consider an abrupt asymmetric n+ -p junction diode with a junction area of
100 m2 . All the action in this device is dominated by the lowly-doped p-type region.
Due to processing reasons, the diffusion coefficient of holes across the quasi-neutral p-type
region is not uniform. It suddenly changes half way down the n-QNR at location x1 . As a
at a current level of 400 A, the excess minority concentration in the quasi-neutral
2. result,
Problem
E6.16 of Howe & Sodini.
p-type region has a distribution as sketched below:
See page 4-5 for this problem
n'(x) (cm-3)
n'(xp)=1016
n'(x1)=8x1015
0.1 m
0
xp
x1
wp x (m)
0.2 m
At this bias point:
a) Estimate the electron diffusion coefficient in both portions of the quasi-neutral region.
b) Estimate the total amount of excess minority carrier charge in the diode.
c) Estimate the diffusion capacitance of the diode.
+
d) Estimate the electron diffusion velocity at x
1 and x1 .
3. [30 points] Problem P6.14 of Howe & Sodini. Add one more part to this problem:
c) Plot the conductance of this diode as a function of the applied bias over this voltage
range.
Spring 2003
Prof. J. A. del Alamo
6.012 Microelectronic Devices and Circuits
Homework #6 - April 25, 2003
Due: May 2, 2003 at recitation (Rm. 26-310, 12:55 PM)
(late homework will not be accepted)
Please write your recitation session time on your problem set solution.
Please note difference between Exercises, labeled Ex.y, and Problems, labeled Px.y!
1. [30 points] The figure below shows six possible ways of connecting an npn bipolar
3.
transistor that may yield a diode-like behavior. Using the ideal Non-Linear Hybrid- Model,
calculate the I-V characteristics of the two-terminal device in each configuration. Express
your result as a function of IS , F , and R .
I
V
I
V
V
V
V
B
Which of these configurations exhibit diode-like I-V characteristics?
2. [15 points] Problem E7.2 of Howe & Sodini. Note comment at beginning of Exercises
section.
3. [5 points] Problem E7.4 of Howe & Sodini. Note comment at beginning of Exercises
4.section.
Problem E7.5 of Howe & Sodini. Note comment at beginning of Exercises section.
4. [50 points] Problem P8.10 of Howe & Sodini. Dont do (e). Do instead:
See page 6-7 for this problem
e) Calculate the maximum amplitude of a sinusoidal signal signal applied to the input so
that the output waveform does not clip. What makes the output waveform clip if
this maximum signal is exceeded?
31
E6.16
