Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
EE 3311/7322 Semiconductor Devices Agendas and Homework Assignments Fall 2016 EE 3311 Oral Exam Groups, Homework and Lab Presentation Schedule Group A Baughman, Alexander Caldwell, Madalene* Campbell, Andrew Group B Chowdhury, Raisa De La Rosa, Daniel Dezfuli, Mary Group C Dhurgude, Vishal El Helou, Assaad Halac, Serdar Group D Herold, Robert Khan, Haider Kim, Sun Woo Group E Lartigue, Robert Matson, Cameron Mauldin, Luke Group F Moody, Scott Patil, Parthivi Pulatie, Robert Group G Rao, Arun Reese, Jennifer* Rinard, Nick Group H Rios, Juan Sakpal, Sahil Scott, Justin Group I Spangler, Adam Templeton, Will Thakur, Sachin Group J Thomas, Krupa Wells, Jakob Woodward, Nathan HW#1 HW#2 Lab#1 HW#3 Lab #2 HW#4 Lab#3 HW#5 Lab#4 HW#6 Lab#5 HW#7 Lab#6 HW#8 Lab#7 HW#9 Lab#8 HW#10 Lab #9 HW#11 Lab#10 HW#12 Lab#11 HW#13 mid#1 mid#2 mid#3 mid#4 previewHW#14part1 previewHW#14part2 Exchange Jennifer Reese with Madelene Caldwell ----------------------------------------------------------------------------------------------------------------------------2016 Laboratory Groups and Times Group 1: Tuesday 8:00am to 10:00am TA's: John & Mary) Students: Sahil Sakpar, Sachin Thakur, Parthivi Patil Group 2: Tuesday 10:00am to 12:00pm TA's: Mary & Freddie Students: Assaad El Hou, Robert Herold, Scott Moody Group 3: Tuesday 12:30pm to 2:30pm TA's: John & Charles Students: Serdar Halac, Arun Rao, Krupa Thomas, Jakob Wells Group 4: Tuesday 3:30pm to 5:30pm TA's: John & Mary Students: Alexander Baughman, Luke Maldin, Cameron Matson, Adam Spangler Group 5: Wednesday 8:00am to 10:00am TA's: Charles & Freddie Students: Vishal Dhurgude, Nick Rinard, Daniel De La Rosa, Justin Scott Group 6: Wednesday 10:00am to 12:00pm TA's: Allison & Freddie Students: Andrew Campbell, Haider Khan, Juan Rios, Raisa Chowdhury Group 7: Wednesday 3:30pm to 5:30pm TA's: Mary & Freddie Students: Jakobus Jordan, Robert Lartigue, Will Templeton, Nathan Woodward Group 11: Thursday 3:30pm to 5:30pm TA's: Charles & John Students: Madelene Caldwell, Sun Woo Kim, Robert Pulatie, Jennifer Reese EE 3311Homework and Lab Report Schedule Baughman, Alexander Caldwell, Madalene Campbell, Andrew Chowdhury, Raisa De La Rosa, Daniel Dezfuli, Mary Dhurgude, Vishal El Helou, Assaad Halac, Serdar Herold, Robert Khan, Haider Kim, Sun Woo Lartigue, Robert Matson, Cameron Mauldin, Luke Moody, Scott Patil, Parthivi Pulatie, Robert HW#1 HW#2 Lab#1 HW#3 Lab#2 HW#4 Lab#3 HW#5 Lab#4 HW#6 Lab#5 HW#7 Lab#6 HW#8 Lab#7 HW#9 Lab#8 HW#10 Rao, Arun Reese, Jennifer Rinard, Nick Rios, Juan Sakpal, Sahil Scott, Justin Spangler, Adam Templeton, Will Thakur, Sachin Thomas, Krupa Wells, Jakob Woodward, Nathan Lab #9 HW#11 Lab#10 HW#12 Lab#11 HW#13 mid#1 mid#2 mid#3 mid#4 previewHW#14part1 previewHW#14part2 Monday, August 24, 2016 Course Philosophy x1. 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. x2. Lab and Lab Safety (J. Kirk), Safety Quiz (see CANVAS) 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. x3. 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 x4. 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. x5. 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) x6. 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. x7. DRAM inventor Robert Denard received an honorary doctorate from SMU in 1997. He received his BSEE and MSEE from SMU in 1954 and 1956. x8. 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. x9. Looking Backwards (mechanical logic and computers to microprocessors) and Forward (silicon photonics): History and Future of Computing (HistoryAndFutureComputingF2014.ppt on CANVAS) x10. JaegerCh01overview2013 powerpoint slides (JaegerCh01overview2013.ppt on CANVAS) 11. How are we going to make a MOSFET? --Overview of Fabrication Process (MOSFETFab_Fall2016withPics 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 x1. Lab sessions (tentatively) start Tuesday, August 30 at 8:30 AM (maybe?) x2. SAFETY QUIZ is due BY FRIDAY, MIDNIGHT, AUGUST 26th, 2016. Apparently you can take the quiz online—no need to download and upload?? x3. Jay Kirk, Lab Instructor—Safety and Laboratory Protocol emphasis on Monday. X(4. Lab Tours (maybe during first lab) --Safety, Safety Quiz and Material Safety Data Sheets (MSDS) To find powerpoint slides and other course material on CANVAS, click on MODULES and then look at Course Documents 2015. Even though this is 2016… From August 22 Agenda: x8. 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. x9. Looking Backwards (mechanical logic and computers to microprocessors) and Forward (silicon photonics): History and Future of Computing (HistoryAndFutureComputingF2014.ppt on CANVAS) x10. JaegerCh01overview2013 powerpoint slides (JaegerCh01overview2013.ppt on CANVAS) x11. How are we going to make a MOSFET? --Overview of Fabrication Process (MOSFETFab_Fall2016withPics.ppt or most recent posted) x12. Basics of Materials: MaterialsBasicsAr12015.ppt x13. 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 x5. JaegerCh01overview2015 powerpoint slides (JaegerCh01overview2015.ppt on CANVAS) x6. 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 x9. 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 REMINDER: help sessions are every Monday evening in conference room 338 in Junkins. 1. Lab sessions start Tuesday, August 30 at 8:00 AM --------------------------------------------------------------------------------------------------------------------------------- 2. HW#1 due Tuesday, August 30 before 11:59 PM. Wednesday: Review/discussion of HW #1: Baughman, Alexander 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. x4. JaegerCh01overview2015 powerpoint slides (JaegerCh01overview2015.ppt on CANVAS) x5. Overview of MOSFET Fabrication Process (MOSFETFab_Fall2016.ppt) 6. Basics of Materials: MaterialsBasicsAr12015.ppt (stopped at ~ slide 25) 7. What do we need to know to understand how a MOSFET works? --electrons and holes in semiconductors, doping of semiconductors --p-n junctions --resistivity x8. 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 9. JaegerLithographyCh2r1 powerpoint slides Wednesday, August 31, 2016 Agenda 0. Lecture Download Instructions: go to https://lyle.smu.edu/academic/downloads/ You will be prompted for a username and password. Use your 8 digit SMUID for the username. For security and privacy purposes the password will be your My.SMU.edu password. Select the “1167-2016-Fall” folder. Select your Course Number folder. RIGHT click on the file link and select SAVE TARGET AS to save the file to your computer. You can access your Course Downloads within 24 hours of the on-campus course. 1. Professor Ken Springer may (?) talk to the class on Wednesday September 14 about Writing and Lab Reports 2. Review/discussion of HW #1: Baughman, Alexander 3. MaterialsBasicsAr12015.ppt (stopped at ~ slide 32) 3. JaegerLithographyCh2r1 powerpoint slides 4. JaegerOxidationCh03r2 powerpoint slides Monday, September 5, 2016 No Agenda (no class: Labor Day) Wednesday, September 7, 2016 Agenda 0. Bob Biard, inventor of the LED, will visit class Monday, September 19. Here is an abstract of one of his previous talks: “The 2014 Nobel Prize in Physics was awarded for the invention of the blue Light Emitting Diode (LED) to Isamu Akasaki, Hiroshi Amano and Shuji Nakamura. In the early 1960’s, Dr. Bob Biard and Gary Pittman (BS SMU, 1954; selected for SMU Honorary PhD, 2013) were awarded the world’s first patent on LEDs. Bob Biard will talk on his career in semiconductor devices that began in 1957 at Texas Instruments. Bob will share many observations from his long career, such as “don’t listen to experts” (like professors). In addition to the first patent on LEDs, he has been a pioneer in the area of transistor circuits, microwave and optoelectronic components, avalanche photodiodes, silicon MOS technology, and compound semiconductor materials technology and has numerous patents (~80). He is an IEEE Fellow and member of the National Academy of Engineers.” 1. HW #2 review/discussion: Caldwell, Madalene (MOVE TO MONDAY, September 12) Lab 1 review/discussion: Campbell, Andrew 2. JaegerLithographyCh2r1 powerpoint slides (stopped on slide 11 on 9/7/16) 3. Diffusion Concepts2014 powerpoint slides (on CANVAS 3. 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 1. Jay Kirk will talk about vaccum systems (~ 30 minutes) 2. HW and Lab review/discussion: (MOVED FROM WEDNESDAY, September 7) Jennifer Reese HW#2 (replaced Madelene Caldwell) Campbell, Andrew Lab#1 3. Freddie Castillo will preview future homework and review homework if requested/desired Otherwise, will continue with: 3. JaegerLithographyCh2r1 powerpoint slides (stopped on slide 11 on 9/7/16) 4. JaegerOxidationCh03r2 powerpoint slides 5. Jaeger_diffusionCh04r4 powerpoint slides Wednesday, September 14, 2016 Agenda Jin Huang will facilitate the first ½ hour or so of class 1. Homework and Lab review Chowdhury, Raisa HW#3 De La Rosa, Daniel Lab #2 2. Freddie Castillo (or Jin?) will preview future homework and review homework if requested/desired Otherwise, will continue with: 2. JaegerLithographyCh2r1 powerpoint slides (continue or complete) 3. JaegerOxidationCh03r2 powerpoint slides 4. Jaeger_diffusionCh04r4 powerpoint slides 5. Why are we diffusing B into Si in the laboratory sessions? Monday, September 19, 2016 Agenda 1. Lab 3 and HW#4 review/discussion on Wednesday Dezfuli, Mary HW#4 Dhurgude, Vishal Lab#3 2. Speaker: Bob Biard, inventor of the LED, will visit class Monday, September 19. Here is an abstract of one of his previous talks: “The 2014 Nobel Prize in Physics was awarded for the invention of the blue Light Emitting Diode (LED) to Isamu Akasaki, Hiroshi Amano and Shuji Nakamura. In the early 1960’s, Dr. Bob Biard and Gary Pittman (BS SMU, 1954; selected for SMU Honorary PhD, 2013) were awarded the world’s first patent on LEDs. Bob Biard will talk on his career in semiconductor devices that began in 1957 at Texas Instruments. Bob will share many observations from his long career, such as “don’t listen to experts” (like professors). In addition to the first patent on LEDs, he has been a pioneer in the area of transistor circuits, microwave and optoelectronic components, avalanche photodiodes, silicon MOS technology, and compound semiconductor materials technology and has numerous patents (~80). He is an IEEE Fellow and member of the National Academy of Engineers.” (Also an excellent harmonica player!) Wednesday, September 21, 2016 Agenda 1. Professor Ken Springer: On Writing Lab Reports (~ 20 minutes) 2. Homework #4 and Lab 3 Dezfuli, Mary HW#4 Dhurgude, Vishal Lab#3 3. Freddie Castillo will preview future homework and review homework if requested/desired Otherwise, will continue with: 4. JaegerLithographyCh2r1 powerpoint slides (continue or complete) 5. JaegerOxidationCh03r2 powerpoint slides 6. Jaeger_diffusionCh04r4 powerpoint slides 7. Begin p-n Junction Slides Monday, September 26, 2016 Agenda 1. Homework #5 but no Lab this Wednesday? (needed extra off-line time last week?) El Helou, Assaad HW#5 Halac, Serdar Lab#4 (next week?) Where are we?? 2. JaegerLithographyCh2r1 powerpoint slides (completed!) 2.1 Bob Biard; 1964 equation; experts? LED droop? 2.2 “For the first time the Office of General Education is sponsoring awards for writing. Three awards will be offered, one for the best submitted paper in DISC 1312, one for DISC 1313, and one for courses tagged with the Writing Proficiency. If you are teaching any of these courses I hope you will encourage your best writers to apply (see the attached document).” NOTE: In the past there has been a writing competition sponsored by the main library. I will send out information on that competition when I receive the announcement. 2.3 Not sure what the chances are for a technical paper, so for just 3311/7322, we will offer three awards to the top three final reports for 3311: st 1 prize: $100; 2nd prize $75; and 3rd prize $50. 3. Basic Diffusion Concept 4. Begin JaegerOxidationCh03r2 powerpoint slides (stopped on 7/52) 5. Then: Jaeger_diffusionCh04r4 powerpoint slides 6. Then: p-n Junction Slides Wednesday, September 28, 2016 Agenda Announcements: a) Friday, October 21st at 10:00 AM: Anticipated tour of Texas Instruments’ RFAB facility b) Any students graduating at the end of this semester? Openings for several technicians to work at Finisar in Allen, TX (testing semiconductor lasers called VCSELs). Also openings at Finisar in Fremont, CA. 1. Homework #5 but no Lab report today since no Lab last week (right?) El Helou, Assaad HW#5 Halac, Serdar Lab#4 (next week) x2. Basic Diffusion Concept 3. Continue JaegerOxidationCh03r2 powerpoint slides (start about slide 7) 4. Then: Jaeger_diffusionCh04r4 powerpoint slides 5. Then: p-n Junction Slides Monday, October 3, 2016 Agenda Announcements: a) Friday, October 21st at 10:00 AM: Anticipated tour of Texas Instruments’ RFAB facility b) Any students graduating at the end of this semester? Openings for several technicians to work at Finisar in Allen, TX (testing semiconductor lasers called VCSELs). Also openings at Finisar in Fremont, CA. 1. Homework #6; Lab#4 (?) [NOTE: New homework assignments after #6—some changes to the assignments below] Herold, Robert HW#6 Halac, Serdar Lab#4 x2. Basic Diffusion Concept 3. Continue JaegerOxidationCh03r2 powerpoint slides (start about slide 20) 4. Then: Jaeger_diffusionCh04r4 powerpoint slides (stopped at slide 30) 5. Then: 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? Assume 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? You can use the appropriate figure from Chapter 1 of Jaeger as a check to see if your answer is reasonable. 6. What is the chemical make-up of the photoresist used in the SMU clean room for opening the source and drain areas in the silicon dioxide layer? 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 (go to MODULES first) 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 ( 3. Calculate the curl ( ) of the following vectors: ) 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 #7: 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 3.1 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 Xi2 Xi . Of course, you need to use the values for B and B/A that are appropriate t= + 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 (revised) (due Tuesday, October 11th, 2016) 1. 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. 2. Consider the wafer you are processing in the clean room. The source and drain are p-regions and of course the substrate is n-type. a) what is a reasonable number to use for an average value of the p-doping of the source and drain. (You can use the answer to Problem #2 of HW#6 if you believe your answer.) b) what is the doping level of 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. Using a formula above, calculate the built-in voltage associated with the source to substrate p-n junction. 5. Consider the wafer you are processing in the clean room. Using a formula above, calculate the depletion width on the p-side, the depletion width on the n-side, and the total depletion width associated with the source to substrate p-n junction. Homework Assignment #8 (to be revised “soon”) (due Tuesday, October 18th, 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. 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 (to be revised “soon”) (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 (to be revised “soon”) (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 (to be revised “soon”) (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 (to be revised “soon”) (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 (to be revised “soon”) (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 qs and qm and how are they defined? Do they change with applied voltage? What is the significance of qF 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 qs (not the same as qs) 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 (to be revised “soon”) 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.