Download EE 3311/7322 Semiconductor Devices

EE 3311/7322 Semiconductor Devices
Agendas and Homework Assignments
Fall 2016
EE 3311 Oral Exam Groups
(Groups of Three To Be Determined from the Class Roster)
----------------------------------------------------------------------------------------------------------------------------2016 Lab Time Possibilities
(Submit your first three choices to Freddie Castillo ([email protected];
The number of groups will be reduced to about 8 groups)
Group 1: Tuesday, 8:00 am - 10:00 am
Group 2: Tuesday 10:00 am - 12:00 pm
Group 3: Tuesday, 12:30 pm - 2:30 pm
Group 4: Tuesday, 3:30 pm - 5:30 pm
Group 5: Wednesday, 8 am - 10 am
Group 6: Wednesday, 10 am to 12: pm
Group 7: Wednesday, 3:30 pm - 5:30 pm
Group 8: Thursday, 8:00 am - 10:00 am
Group 9: Thursday, 10:00 am - 12:00 pm
Group 10: Thursday, 12:00 pm – 2:00 pm
Group 11: Thursday, 3:30 - 5:30 pm
EE 3311Homework and Lab Report Schedule
(Will Be Determined Alphabetically from Class Roster; Each Wednesday one
student will review the laboratory sessions and another student will review the
current homework assignment)
Monday, August 24, 2015
Course Philosophy
1. Review Syllabus (this course may not be for you…)
I have two major objectives for students taking this course:
A. Make working p-channel MOSFET devices. Understand the fabrication process.
Understand the concepts of photolithography, oxidation, diffusion, etching and metallization.
B. Understand how basic semiconductor devices work—in particular how a p-n junction and
a MOSFET transistor works.
2. Lab and Lab Safety (J. Kirk), Safety Quiz (see BlacCANVAS) and Material Safety Data
Sheets (MSDS)
Our plan is to have a maximum of 4 students in each group. For safety reasons, you cannot
enter the clean room without appropriate dress: long pants, covered torso and shoes that
completely cover your feet (no open toes, no sandals).
SAFETY QUIZ MUST BE UPLOADED TO CANVAS BY FRIDAY, MIDNIGHT, AUGUST
26th, 2016.
3. Submit your first, second and third choices for lab times by email to Freddie Castillo
([email protected]) before noon on Wednesday August 24th from the list below.
Lab Time Possibilities (from which we will choose 8 groups)
Group 1: Tuesday, 8:00 am - 10:00 am
Group 2: Tuesday 10:00 am - 12:00 pm
Group 3: Tuesday, 12:30 pm - 2:30 pm
Group 4: Tuesday, 3:30 pm - 5:30 pm
Group 5: Wednesday, 8 am - 10 am
Group 6: Wednesday, 10 am to 12: pm
Group 7: Wednesday, 3:30 pm - 5:30 pm
Group 8: Thursday, 8:00 am - 10:00 am
Group 9: Thursday, 10:00 am - 12:00 pm
Group 10: Thursday, 12:00 pm – 2:00 pm
Group 11: Thursday, 3:30 - 5:30 pm
4. Plagiarism: Not just an ethical question. The internet makes plagiarism easy—and the
internet makes it even easier to detect. Government funding agencies routinely check proposals
and reports for plagiarism. Penalties for plagiarism include banning individuals, institutions and
corporations from applying for grants and contracts.
5. Teaching Baseball or Engineering? “this is the course I would have liked to have had as a
student”
--Old 3311 (all theory) and New 3311 (lab)
--discrete college courses and Boeing 727s…
--New 3311 brings together most everything you have had in all your classes: chemistry,
physics, advanced math, circuits, materials, (thermodynamics, heat transfer, quantum
mechanics, …)
Historical Background (Dallas and SMU related)
6. Jack St. Clair Kilby (November 8, 1923 - June 20, 2005) won the Nobel Prize (with Herbert
Kroemer and Zhores l. Alferov for heterojunctions) in physics in 2000 for his invention of
the integrated circuit during the summer of 1958 at Texas Instruments. He also is credited
with the invention of the handheld calculator and thermal printer. TI Archives and the Jack
St. Clair Kilby Archives are at the DeGolyer Library at Southern Methodist University.
7. DRAM inventor Robert Denard received an honorary doctorate from SMU in 1997. He
received his BSEE and MSEE from SMU in 1954 and 1956.
8. LED inventors Bob Biard and Gary Pittman--Bob Biard received an honorary doctorate from
SMU at the May 2013 graduation ceremony. Gary Pittman could not attend because of poor
health. Pittman received his BS in Chemistry from SMU in 1954. Gary Pittman died
October, 2013.
9. Looking Backwards (mechanical logic and computers to microprocessors) and Forward
(silicon photonics): History and Future of Computing
(HistoryAndFutureComputingF2014.ppt on CANVAS)
10. JaegerCh01overview2013 powerpoint slides (JaegerCh01overview2013.ppt on CANVAS)
11. How are we going to make a MOSFET?
--Overview of Fabrication Process (MOSFETFab_Fall2014.ppt or most recent posted)
12. Basics of Materials: MaterialsBasicsAr12015.ppt
13. What do we need to know to understand how to make a MOSFET?
--thermal oxidation of silicon
--lithography and photoresist
--etching of oxide, metals (and semiconductors)
--diffusion (and ion implantation) of dopants
--testing, packaging
Wednesday, August 24, 2016
Agenda
1. Lab sessions (tentatively) start Tuesday, August 30 at 8:30 AM (maybe?)
2. SAFETY QUIZ MUST BE UPLOADED TO CANVAS BY FRIDAY, MIDNIGHT,
AUGUST 26th, 2016. Safety related articles are on CANVAS in the Safety Information folder
under Course Documents.
3. Jay Kirk, Lab Instructor—Safety and Laboratory Protocol emphasis on Monday.
4. Lab Tours (maybe during first lab)
--Safety, Safety Quiz and Material Safety Data Sheets (MSDS)
5. JaegerCh01overview2015 powerpoint slides (JaegerCh01overview2015.ppt on CANVAS)
6. Overview of Fabrication Process (MOSFETFab_Fall2014.ppt or most recent posted)
review 3rd week of class in detail.
7. Basics of Materials: MaterialsBasicsAr12015.ppt
8. What do we need to know to understand how a MOSFET works?
--electrons and holes in semiconductors, doping of semiconductors
--p-n junctions
--resistivity
9. What do we need to know and understand to make a MOSFET?
--thermal oxidation of silicon
--lithography and photoresist
--etching of oxide (dielectrics), metals, and semiconductors
--diffusion (and ion implantation) of dopants
--testing, packaging
Monday, August 29, 2016
Agenda
1. Lab sessions start Tuesday, August 30 at 8:00 AM
---------------------------------------------------------------------------------------------------------------------------------
2. HW#1 due Tuesday, August 29 before 11:59 PM. Review/discussion of HW #1: student
REMINDER: help sessions are every Monday evening in conference room 338 in Junkins.
3. SAFETY QUIZ SHOULD HAVE BEEN UPLOADED TO CANVAS BY FRIDAY,
MIDNIGHT, AUGUST 26th, 2016. Safety related articles are on CANVAS in the Safety
Information folder under Course Documents.
4. Jay Kirk, Lab Instructor—Safety and Laboratory Protocol emphasis (TODAY).
5. Lab Tours (maybe during first lab)
--Safety, Safety Quiz and Material Safety Data Sheets (MSDS)
6. JaegerCh01overview2015 powerpoint slides (JaegerCh01overview2015.ppt on CANVAS)
MOSFET fab traveler; began Basic Materials)
7. Overview of MOSFET Fabrication Process (MOSFETFab_Fall2014.ppt or most recent
posted)
8. Basics of Materials: MaterialsBasicsAr12015.ppt
9. What do we need to know to understand how a MOSFET works?
--electrons and holes in semiconductors, doping of semiconductors
--p-n junctions
--resistivity
10. What do we need to know and understand to make a MOSFET?
--thermal oxidation of silicon
--lithography and photoresist
--etching of oxide (dielectrics), metals, and semiconductors
--diffusion (and ion implantation) of dopants
--testing, packaging
1.
2.
3.
4.
Wednesday, August 31, 2016
Agenda
Professor Ken Springer may (?) talk to the class on Wednesday September 7 about
Writing and Lab Reports
Review/discussion of HW #1: Student name will appear here
JaegerLithographyCh2r1 powerpoint slides
JaegerOxidationCh03r2 powerpoint slides
Monday, September 5, 2016
No Agenda (no class: Labor Day)
Wednesday, September 7, 2016
1.
2.
3.
3.
Agenda
HW #2 review/discussion: Student A; Lab 1 review/discussion: Student B
JaegerLithographyCh2r1 powerpoint slides (review slide 29; look at IBM TEM photo)
Diffusion Concepts2014 powerpoint slides (on CANVAS
JaegerOxidationCh03r2 powerpoint slides (on CANVAS)
Monday, September 12, 2016
Agenda
0. Help session at 5:10 PM or so in Junkins 338 (conference room) every Monday
Wednesday:
Lab 1 Review on Wednesday: student
HW#2 Review on Wednesday: student
1. JaegerOxidationCh03r2 powerpoint slides
2. Jaeger_diffusionCh04r4 powerpoint slides
Wednesday, September 14, 2016
Agenda
1. HW#2 review/discussion:
Lab 1 review;discussion:
2. Why are we diffusing B into Si in the laboratory sessions?
3. Continue Jaeger_diffusionCh04r4 powerpoint slides
Monday, September 19, 2016
Agenda
1. Lab 2 and HW#3 review/discussion on Wednesday
3. Completed Jaeger_diffusionCh04r4 powerpoint slides
Wednesday, September 21, 2016
Agenda
1. Professor Ken Springer: On Writing Lab Reports
2. Homework #4 and Lab 3
3. Begin p-n Junction Slides
Monday, September 26, 2016
Agenda
1. Homework #5 but no Lab this Wednesday?
2. Continue/begin p-n Junction Slides
Wednesday, September 28, 2016
Agenda
1. Homework #5 but no Lab report today
2. Continue p-n Junction Slides
Homework Assignment #1
(due Tuesday, August 30, 2016)
1. In your own words, state the format requirements for homework assignments. What
will happen if homework is turned in that does not satisfy the format requirements?
2. What percentage of homework assignments must be completed and turned in to pass
this course? What percentage of laboratory reports must be completed and turned in to
pass this course?
3. Read Chapter 1 of Introduction to Microelectronic Fabrication. How many inches is a)
100 mm? b) 200 mm? c) 300 mm? d) 400 mm? How many millimeters equal 12
inches? Note: This assignment is an opportunity to show proper use of units when
converting from the metric system to the Imperial (inches, feet, ...) system. You may
want to use an online conversion website as a check on your own calculations.
4. How many complete 1mm x 1mm die can fit on a 100 mm wafer? How many complete 1
cm x 1 cm die can fit on a 300 mm wafer? Assum that the wafer is a complete circle.
5. Determine the cost per good die for a wafer processing cost of $50,000 and a yield of 95%
for a) a 1mm x 1 mm die size and wafer size of 100 mm? b) for a 2 cm x 2 cm die size and
a wafer size of 300 mm?
6. What is the chemical make up of photoresist? What safety precautions should be used
with photoresist? How and why is photoresist used?
7. Assume that you have a thousand dollars that accrues compound interest of 10% per
time period over 15 time periods. (How many weeks are in this semester?) What is the
accrued value of the thousand dollars after 15 time periods? How much better off will
you be if you work 10% harder each week of this semester?
8. Write a summary of the article “On Physics Education in Brazil,” from the book Surely
You're Joking, Mr. Feynman! (Adventures of a Curious Character), by Ralph Leighton and Edward
Hutchings, 1985. This article can be found on CANVAS under Course Documents or on numerous
sites online.
Homework Assignment #2
(due Tuesday, September 6th, 2016)
1. Evaluate the following integrals:
For problems 2 and 3 recall that the del operator is given by
2. Calculate the divergence (
) of the following vectors:
3. Calculate the curl (
) of the following functions:
4. Below is a list of Maxwell’s Equations in differential form:
One of those equations states that the divergence of the electric displacement vector
D(x,y,z,t) is equal to the charge density (x,y,z,t)—this equation is known as Gauss’s
Law for the electric displacement vector. For problems in space where there is only a
variation in the x direction, show that this equation reduces to the derivative of the
electric field E(x) with respect to x is equal to the charge density divided by the electric
permittivity:
5. The speed of light c = 1/ m oe o , where e o is the permittivity of free space and m o is the
permeability of free space. Show that the units of 1/ m oe o are length/time (or meters/sec).
Using the values of e o and m o , calculate the speed of light.
6. Show that the units of ∇ • 𝐷 = 𝜌 are the same on both sides of the equation.
7. (20 points) What is the oxide thickness on the Si wafer that you are processing? At what
temperature was the oxide be deposited? How long is the deposition process expected to take?
Was the oxide be deposited by a wet or dry process? Using the formulas in your text book
(Jaeger), calculate the theoretical thickness of the first oxide layer grown in the lab. Check your
calculations with the figures in the text book showing oxide thickness as a function of time for
various temperatures.
More about problem #1: See step 1-2 in the traveler, the initial oxidation (Offline)
1000 °C in steam, ~ 5 Hours-target 10,000Å (1 µm). This means that the <100> wafer is put in
the furnace for a 1000 C (wet) for ~ 5 hours. The formula for oxide thickness as a function of
time X(t) is Eq. 3.9 in Jaeger. The oxidation time t is ~ 5 hours. To use Eq. 3.9, you need to
convert Centigrade to Kelvin and you need to find A and B. You can find A and B from Table
4.1 if you know the wafer orientation (100 for this class) and you know if the oxide is deposited
with steam (wet) or dry. So for this problem, you will use an activation energy of 2.05 eV and a
diffusion coefficient of 9.7 x 107 µm/hr to find B/A. That is, B/A = Doexp(-Ea/kT) = (9.7 x 107
µm/hr)exp(-2.05 eV/kT), where T is in Kelvin and k is Boltzman’s constant. After you calculate
B/A, look at Figure 3.5 and see if your calculation agrees with the appropriate curve.
Next you need to find B. From Table 3.1, B = Doexp(-Ea/kT), where the activation energy is
0.78 eV and Do is 386 µm2/hr. After you calculate B, look at Figure 3.4 and see if your
calculation agrees with the curve for H20.
The sentence under Eq. 3.8 in the text explains how to calculate . Explain why for this
particular calculation you can assume no initial oxide thickness. (Note that a freshly cleaned Si
wafer will develop a very thin (~1 to 4 nm) layer of oxide just from being exposed to air.)
Check your final answer for the field oxide thickness with Fig. 3.6.
8. (20 points) In a later laboratory session, the gate oxide for the MOSFET device will be grown
offline. What is the expected thickness of the gate oxide? Will the gate oxide be grown by a
wet or dry process? Why? Using the time and temperature in the MOSFET traveler, calculate
the gate oxide thickness. Check your calculations with the figures in the text book showing oxide
thickness as a function of time for various temperatures. For best theoretical agreement with
experiment, an initial oxide thickness of 25 nm should be used in the calculation—even though
the initial thickness in reality is likely closer to 2.5 nm…
Homework Assignment #3
(due Tuesday, September 13th, 2016)
1. (30 pts) During the processing of your wafer, there are three times that the wafer
is oxidized: a) step 1.2 (in the traveler) which results in a thick field oxide of
about 1 micron; b) a second oxide growth during the boron diffusion (step 2.7 in
the traveler), which provides about 0.5 microns of oxide in the source and drain
region; and c) a final oxide growth for the gate (step 3-17 in the traveler) which
provides about 0.08 microns of oxide in the gate region. Using the time and
temperatures given in the three different oxide growths, calculate the total
thickness of the oxide that surrounds the source and drain regions. Note: The
oxide surrounding the source and drain regions is not ever etched away—and only
becomes thicker with each successive oxide growth that occurs. Check your
numerical calculations with the appropriate figures in the text.
Here is one way to do this problem:
i) You have calculated the oxide thickness outside the source and drain after step 1.2 in
the traveler in HW#2.
ii) Use the (correctly calculated!) thickness (~ 1 micron) of the oxide calculated in HW
#2 for the value of Xi in calculating the total thickness of the oxide that surrounds the
source and drain regions after step 2.7. In other words, use Xi ~ 1.0 micron in the
equation
t=
Xi2
Xi
. Of course, you need to use the values for B and B/A that are appropriate
+
B ( B A)
for the oxide growth of step 2.7. Once you have , then you can use
0.5
éì
ù
ü
B
Xo ( t ) = 0.5A êí1+ 4 2 ( t + t )ý -1ú to find the total thickness of the oxide outside the source and gate
þ
A
êëî
úû
(after step 2.7), again using the appropriate values of B and B/A.
iii) To complete this problem, you need the total thickness of the oxide after step 3-17. Now you need
to calculate  again, but this time you need to use the total thickness Xo that you calculated in step ii) for
Xi. And of course you need to use the appropriate values of B and B/A in this second calculation. The
result of this step is the answer for the total oxide thickness outside the source and drain. You will see
that this answer is different from the answer you would get by (wrongly!) adding the thickness of the
first, second and third oxide growths.
2. In calculating the thickness of thermal oxides, there are two different activation energies and
two different diffusion terms for B and B/A, suggesting that two different physical processes are
involved. In Table 3-1 (Jaeger), we see that for one of the coefficients, the activation energies
and diffusion coefficients do not depend on the orientation of the wafer, while for the other
coefficient, the activation energies and diffusion coefficient do depend on the wafer orientation.
What are some possible mechanisms that might explain the dependence or lack of dependence on
wafer orientation? (Note: the number of Si atoms/cm2 at the surface of a silicon wafer depends
on the orientation.)
3. Read the article by Michael Riordan called “The Silicon Dioxide Solution, (How physicist
Jean Hoerni built the bridge from the transistor to the integrated circuit),” IEEE Spectrum,
December, 2007 (available online at http://spectrum.ieee.org/semiconductors/design/the-silicondioxide-solution or on CANVAS under Course Documents as SiO2_history.pdf).
Write a summary of this article in WORD that includes the advantages and repercusions of
Hoerni’s idea of leaving the oxide on the wafer.
Homework Assignment #4
(due Tuesday, September 20, 2016)
For Problems 1 through 4, review Chapter 4 of the (Jaeger) textbook and the slides on diffusion,
which are posted on CANVAS.
1. Step 2-4 in the MOSFET process traveler is (mostly) a constant source diffusion. For this
case, the solution to Eq. 4.3 in the textbook is given by Eq. 4.4. Calculate the theoretical
diffusion depth of step 2-4 using formulas and graphs in the textbook. Assume that the
surface concentration of this diffusion is equal to the solid solubility limit, which can be obtained
from Fig. 4.6 in the text. You will need to know the background doping of your wafer. The
resistivity of the n-doped substrates used this semester will be obtained in a later lab, but when
we ordered the substrates, we specified that the resistivity be between 1 and 10 ohm-cm. From
past measurements, the resistivity is between 5 and 6 ohm-cm. Using 5.5 ohm-cm as the
resistivity, you can find the background doping from Fig. 4.8 in the text. Now you can set the
constant background doping (NB) equal to the impurity concentration N(x) which is given by Eq.
4.4. The value xj that makes N(xj) = NB is the location of the metalurgical junction or the
location of the p-n junction. Note that you have to calculate a diffusion coefficient D using
Table 1 from the text. Equation 4.4 contains a function called the complimentary error function,
which is plotted in Fig. 4.4.
Fig. P1. Temperature profile for the predeposition step.
2. Step 2-7 in the MOSFET process traveler is a limited-source diffusion. For this case, the
solution to Eq. 4.3 in the (Jaeger) textbook is given by Eq. 4.6. Calculate the theoretical depth
of this step using formulas and graphs in the textbook. A limited-source diffusion assumes
an impulse function representing the total number of boron atoms/cm2 (deposited in step 2-4 of
the MOSFET process traveler) at the silicon surface. The magnitude of this impulse is related to
the total dose (Q) and is given by Eq. 4.5 in the text.
In problem 1 you determined the resistivity and the background doping of your wafer.
Now you can set the constant background doping (NB) equal to the impurity concentration N(x)
which is given by Eq. 4.6. The value xj that makes N(xj) = NB is called the metalurgical junction
or the location of the p-n junction. Note that you have to calculate a diffusion coefficient D
using Table 1 from the text. Equation 4.6 has a Gaussian dependence, which is also shown in
Fig. 4.4.
Fig. P2. Temperature profile for the drive-in step.
3. For this problem it helps to read section 4.2.3 in Jaeger. Calculate the Dt products for the
diffusions in Problem 1 and Problem 2 and compare them. What can you say about the final
profile after the diffusion steps have been performed according to the traveler? Fig. 4.20 of slide
20 of the Diffusion power point slides addresses this issue. Calculate the value of U =
[(D1t1)/(D2t2)]0.5 According to Fig. 4.20, what is the final depth of the junction resulting from
this two-step diffusion?
Fig. P3. Diffusion profiles for various values of U.
4. Show that the expression on the extreme right hand side of Eq. 4.5 in the (Jaeger) text has
units of atoms/cm2.
Homework Assignment #5
(due Tuesday, September 27th, 2016)
1. Read the article “The Accidental Entrepreneur,” by Gordon Moore. Write a summary of this
article in WORD.
2. Calculate the number of Si atoms per cubic centimeter. You can do this by considering the
diamond structure (Fig. 1-8 of the "DiamondLatticeAndSilicon.pdf " notes) as the unit cell. The
lattice constant of silicon is 5.43 Angstroms at room temperature (see Fig. 1-8 again). You also
need to know how many Si atoms are in the diamond unit cell. With a little (or considerable)
thought, you will find that each corner atom contributes 1/8th of an atom/cell (why?). And each
face atom contributes (1/8th?, 1/4th? or ½?) of an atom/cell. And each interior atom contributes
1 atom/unit cell. With this information, you can now calculate the number of Si atoms per cubic
centimeter.
3. Calculate the density of silicon. Hopefully you still have your first year college chemistry
textbook. If so, you will find that
Density = (# of atoms/cm3)*(number of grams/mole)/(number of atoms/mole)
The first term is what you calculated in Problem 1. You can find the number of grams/mole
from looking at Si in the periodic table. The number of atoms/mole is Avagodro's number. If
you do everything right, you should get an answer of about 2 grams/cm3.
4. Find the number of Si atoms/cm2 on the (100) surface of silicon. (Read the appropriate
chapters of Streetman for an understanding of the nomenclature for specifying crystal surfaces
and directions.)
5. Find the number of Si atoms/cm2 on the (110) surface of silicon. (Again, read the appropriate
chapters of Streetman for an understanding of the nomenclature for specifying crystal surfaces
and directions.)
6. Show that the complimentary error function solution to the diffusion equation satisfies the
required boundary conditions. (Note: for problems 6 and 7, see the powerpoint slides on
diffusion.)
7. Show that the gaussian function solution to the diffusion equation satisfies the required
boundary conditions.
8. Recall Problem 3 of HW #4: For this problem it helps to read section 4.2.3 in Jaeger and look
at the CANVAS slides on Diffusion. Calculate the Dt products for the diffusions in Problem 1
and Problem 2 and compare them. What can you say about the final profile after the diffusion
steps have been performed according to the traveler? Fig. 4.20 of slide 20 of the Diffusion
power point slides addresses this issue. Calculate the value of U = [(D1t1)/(D2t2)]0.5 According
to Fig. 4.20, what is the final depth of the junction resulting from this two-step diffusion?
Fig. P3. Diffusion profiles for various values of U.
Now here is the new problem: Calculate U = [(D1t1)/(D2t2)]0.5 and consider where the curve that
corresponds to the value of U should fall on Fig. 4.20. From slide 20, note that the surface
concentration is reduced from No, the solid solubility limit from the pre-dep step, by about 2/.
(This reduction is approximate because of the (1 + U) term in the denominator of the integral and
the actual value of the integral.) Note that the square root of  is just the normalized depth of the
diffusion that is the horizontal variable in both Figs. 4.4 and 4.20. Now the vertical axis of Fig.
4.20 begins at about 10-3 and your value of the surface concentration/NB is likely to be closer to
10-6, so you can use Fig. 4.20 to see where the curve with your calculated value of U occurs
relative to the U = 0 curve (which is equivalent to a Gaussian profile) and the U = infinity curve
(which is equivalent to the complimentary error function profile). Now you can use the relative
placement of your value of U to sketch in a curve in Fig. 4.4 (which has values on the vertical
axis down to 10-6) to find your answer. Now, how does this final answer for the junction depth
compare with the answer for the junction depth obtained for the pre-deposition step?
Homework Assignment #6
(due Tuesday, October 4th, 2016)
1. Calculate the total number of boron atoms that were diffused into one of the
source (or drain) regions of your wafer. You can choose the dimensions of the
source (or drain) of the device (#2) that you photograph during lab sessions.
Recall that you first did a constant source diffusion (Eq. 4.5), which provides you
with the total “dose” Q, which is the number of boron atoms/cm2. To find the total
number of boron atoms diffused into either the source or drain region, you need to
multiply the “dose” by the area of either the source or the drain.
Problem 2. In Problem 8 of HW#5 (and Problem 3 of HW#4) you calculated the
junction depth after the boron diffusion described in the MOSFET traveler.
Compare your answers for the junction depth to the answer obtained from one of
the online calculators for diffusions. A google search produces several, such as
http://fabweb.ece.illinois.edu/utilities/difcad/ (Note: There are no guarantees that these
or other online calculators are accurate…)
Now that you know (within some uncertainty…) the depth of the junction,
calculate the average doping concentration for the source and drain. We will use
the average doping concentration of the p-region and the doping concentration of
the substrate of your wafer in future calculations of the properties of the p-n
junctions formed in your wafer.
3. Read the article “Changing the (Transistor) Channel,” by Richard Stevenson. This article,
which appeared in the July 2013 issue of the IEEE Spectrum, is one person’s view of the future,
and can be found in Course Documents on CANVAS or online at
http://spectrum.ieee.org/semiconductors/design/changing-the-transistor-channel Write a
summary of this article in WORD.
Homework Assignment #7
(due Tuesday, October 11th, 2016)
1. (50 pts) Figure 4.19 illustrates an npn bipolar junction transistor. Design a pnp bipolar
transistor that has a reasonable chance of working. You can also look at Fig. 7-17 (a) on page
369 of “Solid State Electronic Devices,” 6th edition by Streetman and Banerjee. (For this
problem, a “reasonable chance of working” means that the doping of the emitter region is greater
than the doping of the base region, which in turn has a doping level greater than that of the
collector. You do not have to worry (for this problem) about the dimensions of the emitter, base
and collector.) You choose the substrate orientation and doping. You also choose the p and n
dopants and what temperatures and times are used for the diffusions. Give reasons for your
choices. Accurately plot (as opposed to sketch) N(x) for the dopant that you choose for the time
and temperatures that you choose for the diffusions. Your plot should be somewhat similar to
the top plot in Fig. 4.19 above.
2. Kaitlin Smith (Fall 2012) and Alex Small (Fall 2014) are responsible for these questions: a)
what is the value for a constant source distribution N(x,t) if t = infinity? Why? Show that the
equation for N(x,t) for a constant source distribution satisfies this boundary condition. b) what
is the value for a limited source distribution N(x,t) if t = infinity? Why? Show that the equation
for N(x,t) for a limited source distribution satisfies this boundary condition.
Homework Assignment #8
(due Tuesday, October 18th, 2016)
1. Consider the wafer you are processing in the clean room. Although we know that the value of
the p-doping in the source and drain decreases with depth, approximate the p-doping in the
source and drain as a constant value. Justify (see your previous homework) the value you choose
for your approximation.
2. Consider the wafer you are processing in the clean room. What is the value of the n-doping in
the substrate?
3. Consider the wafer you are processing in the clean room. Calculate the total area of the
depletion region associated with the source or drain.
The value for ni can be obtained from Fig. 3.17 below.
4. Consider the wafer you are processing in the clean room. Calculate and plot the charge
distribution in the vicinity of the junction. Assume abrupt junctions.
5. Consider the wafer you are processing in the clean room. Calculate and plot the electric field
distribution in the vicinity of the junction.
6. Consider the wafer you are processing in the clean room. Calculate and plot the built in
voltage across the junction.
Homework Assignment #9
(due Tuesday, October 25th, 2016)
The first five questions relate to the pn junctions formed by the source (or drain) regions of
device #2 on your 3311 wafer:
1. What is the area of the pn junction?
2. In the equation for the I-V relationship for a pn junction (see below), what are the values of
the minority carriers on either side of the junction? (In the pn junction powerpoint slides
(3311pnJunctions), we show nno*pno = ni2 = npo*ppo (Eq. 29), where nno ~ ND in the n region and
ppo ~ NA in the p region and ni is given in Fig. 3-17 (see HW#8). So you can use Eq. 29 to find
the concentration of minority carriers in the n region from pno = ni2/ND and the concentration of
the minority carriers in the p region is given by npo = ni2/NA.
3. In the equation for the I-V relationship for a pn junction (see below), what values should you
use for the diffusion coefficients and diffusion lengths? (Hint: see Problem #3 a) and b) of your
midterm exam.)
4. Calculate and plot the current flowing through the pn junctions of device #2 on your 3311
wafer as a function of voltage over the range of -3 volts to plus 1.5 (or so) volts.
5. (30 points) On slide 88 or so of the PN junction powerpoint slides, the following equations
appear:
a) For the wafer you are processing in the clean room, calculate EF for the substrate. Using this
value of EF, calculate and plot n(E) = f(E)xNC(E) as a function of electron energy E in the
conduction band and p(E) = [1-f(E)]xNV(E) as a function of hole energy in the valence band.
Note that your plots should look like one of the plots in the fourth column below, which is Fig.
3-16 in Streetman.
b) For the wafer you are processing in the clean room, calculate EF for the average value of the
doping in the source (or drain). Using this value of EF, calculate and plot n(E) = f(E)xNC(E) as a
function of electron energy E in the conduction band and p(E) = [1-f(E)]xNV(E) as a function of
hole energy in the valence band.
6. (20 points) Explain how a pn junction works. Specifically, what happens when you bring
together a block of p-type material and a block of n-type material? Why is a depletion region
formed? Why do we have an electric field with no applied voltage? Why is there a built-in
voltage with no applied voltage? Explain the I-V curve of a pn junction. Note that this question
covers recent lectures that correspond primarily to slides 2 through 31 or so on the powerpoint
slides labeled: “PNjunctions.” This is the same question you may be asked on the oral midterm
and/or oral final exam. Note: a revised version of this write-up should appear as an appendix in
your final MOSFET report.
Homework Assignment #10
(due Tuesday, November 1, 2016)
1. Derive two formulas for the width W (Eq 5-21 and Eq 5-22 in the text) of the
depletion region of an abrupt junction. How does W change if a forward bias is
applied to the pn junction? If a reverse bias is applied? (You may want to look at
Appendix 2 of the power point slides on pn junctions.)
2. Derive the formula xpo for the depletion width on the p-side (see Eq 5-23a in
the text) of the depletion region of an abrupt junction. How does xpo change if a
forward bias is applied to the pn junction? If a reverse bias is applied? (You may
want to look at Appendix 2 of the power point slides on pn junctions.)
3. Derive the formula xno for the depletion width on the n-side (see Eq 5-23a in
the text) of the depletion region of an abrupt junction. How does xno change if a
forward bias is applied to the pn junction? If a reverse bias is applied? (You may
want to look at Appendix 2 of the power point slides on pn junctions.)
4. Expand ex in a Taylor series. Using the first few terms in the Taylor series,
calculate and plot the I-V relationship for the pn junctions of device #2 on your
3311 wafer as a function of voltage, particularly for small positive and negative
values of V. How does this plot of the Taylor series solution compare to the exact
plot for the same values of voltage?
The following is a definition of the Taylor series (from:
http://en.wikipedia.org/wiki/Taylor_series)
The Taylor series of a real or complex function ƒ(x) that is infinitely differentiable
in a neighborhood of a real or complex number a is the power series
which can be written in the more compact sigma notation as
where n! denotes the factorial of n and ƒ (n)(a) denotes the nth derivative of ƒ
evaluated at the point a. The zeroth derivative of ƒ is defined to be ƒ itself and (x
− a)0 and 0! are both defined to be 1. In the case that a = 0, the series is also
called a Maclaurin series.
5. (70 points) Read the following articles related to blue LEDs and the 2014 Nobel
prize:
a PrefaceBookNakamuraALL
b
c
d
e
f
BlueChipScientificAmerican
BlueAboutJapan
Interview Nakamura
BenjaminGross How America Lighted the Way for a Japanese Nobel
NichiaNakamura
g Nobel Prize snub: Professor Nick Holonyak questions why blue LED is
worthy while his - the very first - was not
After reading these articles, write down your thoughts and comments. Be prepared
to discuss the articles in class.
Homework Assignment #11
(due Tuesday, November 8th, 2016)
1. Show that under equilibrium conditions, the Fermi level in a semiconductor is
invariant (has a constant value) throughout the semiconductor. Consider two
regions of a semiconductor with one region having a density of states N1(E) and a
Fermi distribution f1(E) that is adjacent to another region having a density of states
N2(E) and a Fermi distribution f2(E). (You may want to look at Appendix 1 of the
power point slides on pn junctins.)
2. Draw a complete band diagram for the p region (source and drain) of your
class wafer. Assume an average value for the p-dopant (you have done this in
previous homework assignments). You need to calculate the Fermi level for the
p-region. You can use Figure 4-9 of your textbook to find the acceptor level. Show
EC, EV, EF, Ei, EG, EG /2 and EA. Hints: Ei is calculated on slide 96 of the pn
junction slides. You can use either equation 3-25b or 3-19 (Streetman) to find EF.
3. Draw a complete band diagram for the n region (source and drain) of your
class wafer. You need to calculate the Fermi level for the n-dopant. Assume
that the n-substrate is doped with Arsenic. You can use Figure 4-9 of your
textbook to find the donor level. Show EC, EV, EF, Ei, EG, EG /2 and ED. Assume
the n-doping is Arsenic. Hints: Ei is calculated on slide 96. You can use either
equation 3-25a or equation 3-15 (Streetman) to find EF.
Your sketch should look something like this:
4. Draw the band diagram for the p-n junctions that exists in the wafer you are
processing in the clean room by appropriately combining the band diagrams you
made in problems 2 and 3. Include this drawing of the pn junctions formed in your
wafer in an Appendix of your Final Report.
5. Consider the total depletion widths and the depletion widths on the p- and nsides the p-n junctions that exists in the wafer you are processing in the clean
room. Calculate these depletion widths at equilibrium (0 applied volts); in reverse
bias for voltages of 5, 4, 3, 2, and 1 Volts; and in forward bias for voltages of 0.5,
1.0 and 1.5 Volts. Plot the depletion widths as a function of voltage.
6. An alternative to doping semiconductors by diffusion (the method we used in
the lab) is a process called ion-implantation. Ion implantation is discussed in
Chapter 5 of the Jaeger textbook and briefly in Chapters 5 (the physical process)
and 6 (for adjustment of the threshold voltage of MOSFETs) of the Streetman and
Bannerjee text. After reviewing these sections of the text, answer the following
questions:
a) what parameter determines the location of the peak concentration of the dopant
in the semiconductor?
b) what parameter determines the width of an implant performed at a single beam
acceleration energy?
c) for an implant that is fully contained within a semiconductor, what is the doping
profile?
7. The same technology that is used for implanting dopants in semiconductors is
the best technology (in my non-medical opinion) for treating many types of cancer.
Read the following articles: “Radiation in the treatment of cancer,”Arthur L.
Boyer, Michael Goitein, Antony J. Lomax, and Eros S. Pedroni; Physics Today
55(9), 34 (2002); and “Imaging particle beams for cancer treatment,”Jerimy C.
Polf and Katia Parodi; Physics Today 68(10), 28 (2015). If you don’t get
cancer (approximately 1 in 6-7 males get prostate cancer over their lifetime
and about 1 in 6-8 females get breast cancer over their lifetime), you almost
certainly will have a close friend or relative that does get cancer at some time
in your life. Answer the following questions:
a) give a rough/crude explanation of how radiation kills cells.
b) sketch the absorption of photon (X-ray) radiation as a function of depth in
water (or gelatin, or human tissue).
c) On the same graph as b), sketch the distribution of protons as a function of
depth in water (or gelatin, or human tissue).
d) Explain how the use of a particle beam of radiation can deliver the same
total dose to a cancerous tumor as a photon (X-ray) beam of radiation, but do
much, much less damage to healthy tissue and organs that surrounds the
tumor.
NOTE 1: There are about 20 centers in the US that provide proton beams for cancer
treatment. One of the most recent opened in the last year or so in the Dallas area. The
oldest hospital center began treating cancer with protons in 1992 at Loma Linda University
Medical Center in Loma Linda, CA.
NOTE 2: Further details related to the treatment of prostate cancer by proton beams are
contained in the powerpoint slides “ProstateSMUFeb28_2014rsR1,” “EvansInterview,” and
“Prostate Cancer AbstractR2,” all of which are available on CANVAS.
Homework Assignment #12
(due Tuesday, November 15th, 2016)
Problem 1. (30 points) Plot the I-V characteristics of a JFET using equations
15 and 16 below (which are Eqs. 6-9 and 6-10 in Streetman). In your early
circuits courses, resistors are assumed to be ideal and to have a constant value,
independent of the current flowing through the resistor or the voltage across the
resistor. However the channel of a JFET and MOSFET has a varying resistance
whose value depends on current flowing through the channel, the voltage across
the channel and the gate voltage. For such a "non-linear" resistor, we can consider
a differential resistance (Rd = dV/dI) and an average resistance (R = V/I). For a
linear resistor, the differential and average resistances are equal. Use the following
JFET formulas to plot the I-V characteristics:
Equation 15 is valid up to pinch-off, after which the drain current is constant and given by
where
(11)
(12)
For this assignment you can choose your own values for a, Z, L and the doping of the
channel. However, if you use the following values:
a = 100 nm, Nd = 7 x 1017 cm-3, Z = 100 microns, L = 5 microns you should end up with the
plot shown below for the drain current as a function of drain voltage as the gate voltage VG
has the values 0, -1, -2, -3, -4 and -5 volts.
In Eqs. 15 and 16 above, you need to calculate the resistivity of the channel, which is the
reciprocal of the conductivity, so the channel resistivity is given by
 = 1/ = 1/(qµnNd)
2. In the above problem, the resistivity was calculated using  = 1/ = 1/(qµnNd) using Fig. 3-23
(in Streetman) for the mobility. How does this calculation compare to the value of the resistivity
shown in Fig. 4.8 in Jaeger? (This problem is brought to you by Nicole Hartman, EE 3311 Fall
2014).
Homework Assignment #13
(due Tuesday, November 29, 2016)
Problem 1. Read Chapter 6 in Streetman and Banerjee. What is VT? How is it
defined? What is the equation for VT in the ideal case? What are the modified
work functions qs and qm and how are they defined? Do they change with
applied voltage? What is the significance of qF and how is it defined? What is the
best criterion for strong inversion of the surface of a semiconductor? What is the
resulting equation that indicates strong inversion? What is qs (not the same as
qs) and how is it defined? What is Ci and how is it defined? What is VFB and
how is it defined?
Problem 2. List the key concepts that explain how a MOSFET transistor works.
Problem 3. Read Chapter 7 in Jaeger. Define the term “Al spiking” and explain
how it is prevented.
Problem 4. Define the term “electromigration” and explain how the result of
electromigration is reduced when using Al as a contact to silicon.
Homework Assignment #14
Also known as
EE 3311 Final Exam, Fall 2016
Report Must Be Uploaded to
CANVAS On Or Before (Need to Check)
Problem 1. (20 points) Si is an n-dopant in GaAs at very high temperatures but
becomes a p-dopant in GaAs at lower temperatures. Provide an explanation of
how Si could be an n-dopant or a p-dopant in GaAs. (Hint: What happens when a
Si atom replaces a Ga atom? Or an As atom? Also recall that GaAs crystalizes in
the same configuration as Si.)
Problem 2. (20 points) The first semiconductor laser demonstrated in 1962 at
General Electric was a pn homojunction device and only operated in short pulses at
liquid nitrogen temperatures. The first semiconductor laser operated continuously
at room temperature in June, 1970 at Bell Laboratories and had a double
heterostructure configuration. Explain how a double heterostructure laser has both
carrier confinement and optical confinement and how these improvements allow
continuous room temperature operation.
Problem 3. (20 points) Starting from Eg = Ephoton = hf = hc/(wavelength), show that the
formula for the wavelength that corresponds to the bandgap of a semiconductor is given by
 (microns) = 1.24/(Eg (eV). Note that h is Planck’s constant, f is the frequency of the photon
and c is the speed of light.
Problem 4. (20 points) In present high performance computers, a) approximately how many
floating point operations per second (FLOPS) are performed? b) how many FLOPS are predicted
to be occur in high performance computers in the year 2020? c) how many fiber optic cables are
used in present day high performance computers? d) explain why many researchers believe
incorporating optics into microelectronic chips is a way to continue Gordon Moore’s 1965
prediction of continued exponential growth in semiconductor chip performance for perhaps
another decade or so.
Problem 5. (20 points) Consider the bandgap energy versus lattice constant curves shown in
Fig. FE-1.
a) What range of wavelengths can be emitted by the direct bandgap region of AlxGa(1-x)As as the
mole fraction of Al (x) varies from 0 (GaAs) to about 0.4 (Al0.4Ga0.6As)?
b) What range of wavelengths can be emitted by a quaternary compositions of InxGa(1-x)AsyP(1-y)
(the green line in Fig. FE-1) as x and y are chosen to range from InP (x = 1, y = 0) to
In0.53Ga0.47As (x = 0.53, y = 1)?
c) What wavelength corresponds to the bandgap of AlInP lattice matched to GaAs?
d) What wavelength corresponds to the bandgap of InGaP lattice matched to GaAs?
The attached chart shows the band gap energy of different semiconductors such Si, GaAs, AlAs,
and InP and their lattice constant. All of the semiconductors just mentioned have the diamond
structure. Note that there is a line connecting AlAs and GaAs and that line spans an energy
range of 1.435 eV (GaAs) to 2.16 eV (AlAs). GaAs and AlAs are called binary compounds.
The line connecting these two binary compounds represents AlxGa(1-x)As, a ternary compound.
(A binary compound contains, two elements, a ternary compound contains three elements and a
quaternary compound has four elements and so on...) Also note that a curved line connects
GaAs to InAs and the connecting curve represents InGaAs, another ternary compound. There is
a green line that connects InGaAs to InP on the graph. The green line represents the quaternary
compounds of InGaAsP that are lattice matched to InP.
The band gap energy Eg is the difference between the bottom of the conduction band Ec and the
top of the valance band Ev: Eg = Ec - Ev. When an electron in the conduction band recombines
with a hole in the valance band, a photon with energy Eg can be produced. The wavelength of
that photon is related to the band gap energy by Eg = hc/(wavelength).
So by choosing a particular binary, ternary or quaternary material, a specific bandgap can be
achieved that gives off a particular wavelength of light.
Fig. FE-1. Band gap energies and lattice constants for numerous semiconductor
compounds.