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ECE441

ECE441 (Physics and Modeling of Semiconductor Devices) is a 3 hour senior/graduate level course that satisfies the Technical Electives requirement for ECE majors. It is only offered in the spring.

Content Covered

  • Basic Solid-State Physics
  • Non-Uniform Doping
  • Degenerate/Non-Degenerate Carrier Concentration
  • Generation/Recombination in and out of Equilibrium
  • Carrier Drift/Diffusion
  • Quasi-Neutrality
  • Shockley Equations
  • PN Junctions
  • Metal-Semiconductor Junctions
  • MOSCAPs and MOSFETs
  • BJTs

In many ways, ECE441 can be thought of as ECE340 part two. Many simplifying assumptions that were made before are removed in favor of a more realistic scenario. Topics like partially ionized dopants, or unwanted generation-recombination are explored. This means the math gets substantially more complicated and annoying, but such is the price of realism. The topics covered in ECE441 are almost the exact same as that covered in ECE340, just with more complexity. The class starts with a review of solid-state and semiconductor physics but looking at things like band diagrams and density of states. It then moves to equilibrium semiconductors by looking at things like optically excitation and turn-on/off transient times. Quasi-neutrality and the Shockley equations are then tackled with the class transitioning into a heavy portion of PN junction theory. Non-idealities and non-uniformities within PN junctions are covered, which ECE340 skipped. MOS devices are usually the last thing covered (unless there is time for BJTs) as the course dives more into topics like hysteresis, small/large signal models, and short channel effects.

Prerequisites

ECE340 is the only official prerequisite for ECE441. Most of the topics that overlap between the two courses are quickly reviewed in ECE441, but already having familiarity with these topics from ECE340 allows students to best learn the added complexity.

When to Take it

Ideally, students would take this course ASAP after taking ECE340. The content builds directly off of ECE340, so the fresher it is in your mind the better. Students interested in grad school in the semiconductor field should consider taking this course as it widens your theoretically knowledge and prepares you for the rigorous math to come.

Course Structure

The course has weekly homeworks (although some can take multiple weeks), one midterm, two TCAD projects, and a final. This is usually a fairly small (~20 student) 400-level course, so prepare to be flexible. Assignment and due dates can be pushed back somewhat regularly given the pace of the course and feedback from students, so take all of the dates given in the beginning of the course with a grain of salt.

Homework assignments are not too different in look from those in ECE340. They usually involve the typical calculation based problems, as well as proof-like problems based on topics learned that week in lecture. Some homeworks will include problems that require some experience in Python or Matlab (or some other alternative). These problems normally require very rudimentary graphing or curve fitting, so any level of prior experience should be sufficient. Homework topics are not normally delayed a week, so sometimes certain topics on the homework will not be covered in lecture until a few days before the due date. In certain cases, this can lead to the homework due date being pushed back.

The midterm and final are virtually the same in structure. They are three hour exams that are open notes with calculators. The exams are three to five problems with subparts and the instructor will usually give the topics of each problem before the test (ex. General MCQ, Equilibrium PN Junction, MOSCAP). A practice exam is typically made available the week prior to the tests, and the answers are gone over in the lecture. Even though the tests are open notes and plenty of time is given, they are still very difficult. Most students print out all of the lecture slides to take to the exam, although it is also recommended to build your own cheatsheet(s) as a good way to study and reduce time sifting through papers during the tests.

The TCAD projects use Sentaurus by Synopsys (although previous semesters also permitted nanoHUB) to simulate a basic device. Students are not expected to have any prior experience with TCAD simulations, though anyone who has will find these projects fairly simple. A quick demo session is typically held early in the semester to show students how to use the software, and the instructor and TA can assist students during office hours. The projects involve changing various quantities (dimensions, doping, etc.) and graphing their effects on the characteristics of the device (fields, current, capacitance, etc.). There is usually about one month given for each project, although once students are familiar with the software they could reasonably be knocked out in a weekend. Sentaurus has a fantastic manual that is quite lengthy, so CMD/CTRL+F is your friend.

Instructors

Prof. Leburton is technically the course director, but the professor teaching it each semester has pretty broad control over the course. Prof. Rakheja has taught this course in recent semesters. Prior to her, Prof. Zhu and Prof. Rosenbaum have also taught this course.

Course Tips

SHOW UP TO CLASS. Given the intimate nature of this small course it is a great way to build a relationship with a professor should you desire to get into research or grad school. Professors are also known to be more lenient graders for students that put effort into their learning by attending and participating (asking questions) in lecture.

It is fairly common for homeworks (or even TCAD projects) to have typos or other errors that make them impossible to solve. While you should never assume a hard problem for you is unintentionally impossible, it does happen. Going to office hours or emailing the instructor/TA is the best way to get help for assignments. Also, do not get too frustrated if you start the homework early and find several parts confusing, you probably just have not gone over it in lecture yet.

Life After

ECE441 is not a direct prerequisite for any other classes, but the theory learned is transferable to other semiconductor/IC based courses like ECE444 - Theory and Fabrication of Integrated Circuits, and ECE482 - Digital IC Design. Students interested in the TCAD modeling portion of the class should look into ECE490 - Introduction to Optimization, ECE491 - Numerical Analysis, or ECE492 - Parallel Programing: Science and Engineering. Those interested in grad school who also enjoyed the extended theory component should also look into ECE535 - Theory of Semiconductors and Semiconductor Devices, when offered.

Infamous Topics

  • Density of states: This is where the math starts to get pretty rigorous, study the lecture notes and you'll live.
  • Quasi-Neutrality: Remember when you can assume it, and what it simplifies.
  • PN Junctions: It is a good idea to have a pretty large portion of your cheat sheet dedicated to PN junctions. When doing homework, be wary about assumptions you used to make in ECE340, as some of them (like complete ionization) may not be valid anymore.

Resources

nanohub.org is run by those scumbags at Purdue, and unfortunately it is one of the best semiconductor resources ever created. Not only does it have amazing introductory videos and lectures, it also has a built-in simulation tool to get a "hands on" understanding of semiconductors.

Sentaurus Manual - The version could change, so make sure you are looking at the one provided by the TA. Make sure you search this extensively for any issue you might have before going to the instructor/TA for help with your TCAD project.