Course Overview: This course focuses on the derivation of models for the terminal currents of the semiconductor devices used in integrated circuits: diode, bipolar junction transistor and MOSFET. Our objective will be to represent the device's steady-state response; however, we will also discuss how to extend the models to the transient case. Throughout the semester, we will study semiconductor physics, focusing on topics such as drift and diffusion, generation and recombination, and avalanche multiplication. In the latter part of the semester, we will explore the motivations behind recent modifications to the basic transistor structures, such as the adoption of high-k gate dielectrics for MOSFETs.
Course Expectations and Outcome: I expect students to do the reading before and after class and monitor all email and online communication related to this class. Ultimately, I want the student to enjoy this course and find it relevant in their career goals. Technical outcomes of this course are:
Section | Time | Room | Instructor | Office Hours | Course Logistics | Piazza |
All |
MWF 10:00-10:50 AM |
Online Click here for zoom login information [Zoom info updated starting Oct. 09] |
Shaloo Rakheja rakheja@illinois.edu |
Thurs 1:00-2:00 PM (zoom info here) or by email appointment also on zoom |
Check here |
Self enroll in Piazza here |
I occasionally need to shift my office hours to accommodate prelim exams, research obligations, firm meetings, etc., so always check the class webpage before coming to office hour on any given day. Any changes to my office hours will be listed under "Announcements." on Piazza. Please drop me an email if you want to meet me outside of office hours.
Teaching Assistants: Ankit Shukla (E-mail: ankits4@illinois.edu) (Use Piazza for quicker response)
Course Outline: Specified Here
Course Material: Lecture notes and slides are based on the material from textbook: Device Electronics for Integrated Circuits, 3rd ed. John Wiley & Sons. Authors: Richard S. Muller and Theodore I. Kamins. However, I will be posting extra reading materials, journal articles, discussion pages on as-needed basis. It is the student's responsibility to go through all the posted materials and ask questions if in doubt. There will be some material that is more advanced and posted only for those interested. You will not be quizzed on it, but feel free to come to office hours to discuss advanced material and research ideas based on it. Lectures will be delivered using a mix of hand written notes and powerpoint slides.
Semiconductor Material Properties: For all HWs and tests, we will use semiconductor material properties given in tables here.
Lecture Date | Title | Lecture Notes (L)/Videos (V) | Reading Materials/Notes |
Aug 24, 2020 | Recap of semiconductor basics--Part I |
Essential read |
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Aug 26, 2020 | Recap of semiconductor basics--Part II | L2 V2 |
Essential read |
Aug 28, 2020 |
Fermi-Dirac statistics; Free carrier density |
Essential read |
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Aug 31, 2020 |
Free carrier density continued; Carrier freezeout |
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Sep 02, 2020 |
Heavy doping; Inhomogeneous doping; Quasi Fermi level |
V5 (starts at 3:30 minutes) |
Search for bandgap narrowing models in silicon. Example: |
Sep 04, 2020 | Generation-recombination introduction |
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Sep 09, 2020 | Generation-recombination in equilibrium |
Non-essential but interesting advanced reading from book "Semiconductor Statistics" by J.S. Blakemore [ISBN 0-486-65362-5, QC611.B52] |
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Sep 11, 2020 | Generation-recombination in out-of-equilibrium (OOE) |
Essential read Appendix (Must follow the calculation for HW-3) Derivation of U_trap for Et != Ei |
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Sep. 14, 2020 |
Low-level injection; Extraction/generation |
Non-essential but highly recommended read. Good discussion on G-R processes can be found in Chapter 5 of "Advanced Semiconductor Fundamentals" by Robert F. Pierret. Full text available on Hathi Trust Digital Library https://catalog.hathitrust.org/Record/000813863? You must login using your Illinois credentials. |
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Sep. 16, 2020 | Carrier dynamics in uniform situation |
Essential Please revise solving 1st order ODEs. |
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Sep. 18, 2020 |
Surface recombination due to traps |
Non-essential Following paper summarizes all our G-R understanding from an experimentalist's perspective: Schroder, Dieter K. "Carrier lifetimes in silicon." IEEE Transactions on Electron Devices 44.1 (1197): 160-170. https://ieeexplore.ieee.org/document/554806 |
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Sep. 21 2020 |
Introduction to carrier transport |
Non-essential read: Concept of phonons and velocity saturation |
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Sep. 23 2020 |
Carrier drift Models of mobility and saturation velocity |
Non-essential Following paper catalogues important models to be used in drift diffusion modeling of silicon: Jacoboni, C., Canali, C., Ottaviani, G., & Quaranta, A. A. (1977). A review of some charge transport properties of silicon. Solid-State Electronics, 20(2), 77-89. https://doi.org/10.1016/0038-1101(77)90054-5 |
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Sep. 25 2020 |
Carrier diffusion Current in terms of quasi Fermi level gradient Non-uniform doping |
Essential read |
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Sep. 28 2020 |
Carrier distribution in equilibrium Boltzmann relations |
Essential read M&K Chapter 4, pages 174-181 |
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Sep. 30 2020 |
Quasi neutrality condition Continuity equation Shockley equations |
Here are in-class notes. |
Non-essential but useful notes on drift diffusion transport model derived from random walk. Check here. |
Oct. 02 2020 |
Application of Shockley equations to solving majority carrier transport | ||
Oct. 05 2020 | Application of Shockley equations to solving minority carrier transport and space charge regions |
Essential read Summary of Shockley equations and various approximations Check here. |
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Oct. 07 2020 |
Surface continuity eq. Hot carriers |
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Oct, 09 2020 |
P-N junction in equilibrium Qualitative view of band bending |
Essential read Example of difference in transport across QNR and SCR. |
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Oct. 12 2020 |
Qualitative view of current conduction Preliminary derivation of I-V characteristics |
Essential read Qualitative I-V in a p-n junction
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Oct. 14 2020 |
Derivation of I-V characteristics and band bending in OOE Introduction to dynamic behavior |
V22 | #No new lecture notes since we wrapped up pending business from L21. |
Oct. 16 2020 |
Junction charge and capacitance Diffusion charge and capacitance Equivalent large-signal circuit model |
Essential read |
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Oct. 19 2020 |
Small-signal diode model Switching characteristics (turn-on and turn-off transient timing) |
Essential read from textbook M&K: Section 5.4, pages 256-261 Section 5.5, pages 262-264 |
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Oct. 21 2020 |
Secondary effects in a p-n junction diode including (i) short diode and (ii) generation-recombination in SCR. |
Essential read from textbook M&K: Sec. 5.3, pages 238-250 |
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Oct. 23 2020 |
Secondary effects in a p-n junction diode including (i) series resistance, (i) junction breakdown (quantitative analysis) and (ii) non-uniform doping |
Essential read from textbook M&K: Sec. 4.4, pages 203-212 Sec. 4.2, pages 191-194 Non-essential read on avalanche breakdown |
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Oct. 26 2020 |
Continued discussion of secondary effects in p-n junction diode |
Pending business from Lec. 26 | |
Oct. 28 2020 |
Metal semiconductor junction electrostatics |
Essential read from textbook M&K: Sec. 3.1 and 3.2, pages 139-151 |
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Oct. 30 2020 |
Metal semiconductor junction--current conduction via drift-diffusion |
Essential read from textbook M&K: Sec. 3.3, pages 152-155 (I-V characteristics) |
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Nov. 02 2020 |
Current conduction via thermionic emission Surface effects
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Essential read from textbook M&K: Sec. 3.3, pages 155-158 (I-V characteristics) Sec. 3.5, pages 162-166 (surface effects) |
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Nov 04 2020 |
Non-rectifying contacts Tunneling Schottky barrier lowering |
Pending business from L30 covered Essential read from textbook M&K Sec. 3.4, pages 158-162 (Non-rectifying contacts) |
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Nov. 06 2020 |
Metal-oxide semiconductors electrostatics -- Part I (i) Band bending (V = 0, V<0, V>0). (ii) Electrical field versus Qs versus surface potential in 3D MOS capacitor |
Essential read from textbook M&K Sec. 8.1, pages 381-386 Sec. 8.2, pages 387-390 |
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Nov. 09 2020 |
Metal-oxide semiconductors electrostatics -- Part II (i) Qualitative discussion of charges, electrostatic potential and electric field in MOS (ii) Threshold voltage definition |
Essential read from textbook M&K Sec. 8.3, pages 390-396
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Nov. 11 2020 |
Metal-oxide semiconductors electrostatics -- Part III (i) Quantitative and qualitative analysis of MOS C-V at low frequency |
Essential read from textbook M&K Sec. 8.4, pages 396-402 |
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Nov 13 2020 |
Metal-oxide semiconductors electrostatics -- Part IV (i) Flatband voltage discussion and its impact on V_T of N-type and P-type transistors |
Non-essential read: Aleksandrov, O. V. "A model of formation of fixed charge in thermal silicon dioxide." Semiconductors 45.4 (2011): 467-473. |
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Nov. 16 2020 |
Metal-oxide semiconductors electrostatics -- Part V (i) Effect of interface traps (ii) Mobile charges in insulator |
Essential read from textbook M&K Sec. 8.5, pages 402-409 |
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Nov. 18 2020 |
Metal-oxide semiconductors electrostatics -- Part VI (i) Polysilicon depletion (ii) Quantum mechanical effects |
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Nov. 20 2020 |
MOSFET current conduction (i) Linear regime and saturation regime |
Essential read |
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Nov. 23 2020# |
MOSFET current conduction (i) Saturation regime -- pinch off and velocity saturation (ii) Output conductance and transconductance |
Essential read Calculation of saturation voltage with velocity saturation For velocity saturation, essential read from textbook M&K Ch. 9, Pages 455-459 |
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Nov. 25 2020# |
Sub-threshold current conduction in MOSFET |
Essential read from textbook M&K Ch. 9, pages 443-446 Read example on page 445 |
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Nov. 30 2020 |
MOSFET current conduction wrap-up Channel length modulation, drain-induced barrier lowering, body effect |
Essential read Notes on drain-induced barrier lowering Essential read from textbook M&K Ch. 9, Sec. 9.2, pages 447-453 |
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Dec. 02 2020 |
Bipolar junction transistor operation and current conduction--Part I |
Essential read |
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Dec. 04 2020 |
Bipolar junction transistor operation and current conduction--Part II | ||
Dec. 07 2020 |
Bipolar junction transistor operation and current conduction--Part III Large-signal equivalent circuit model of a BJT |
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Dec. 09 2020 |
Bipolar junction transistor operation and current conduction--Part IV Recap of equivalent circuit model and discussion of final exam (video is not recorded) |
V45 |
Please revise band diagram of a BJT and minority carrier distribution. Check here. |
#Extra class
Homework: Will be assigned on Piazza under Resources and Compass2g.
HW | Link to HW | Due Date | Solution |
1 | Homework 1 | Sep. 06 | HW Sol-1 |
2 | Homework 2 | Sep. 13 | HW-Sol-2 |
3 | Homework 3 | Sep. 20 | HW-Sol-3 |
4 | Homework 4 | Sep. 27 | HW-Sol-4 |
5 | Homework 5 | Oct. 04 | HW-Sol-5 |
6 | Homework 6 | Oct. 16 | HW-Sol-6 |
7 | Homework 7 | Oct. 25 | HW-Sol-7 |
8 | Homework 8 | Nov. 01 | HW-Sol-8 |
9 | Homework 9 | Nov. 08 | HW-Sol-9 |
10 | Homework 10 | Nov. 22 | HW-Sol-10 |
11 | Homework 11 | Dec. 01 | HW-Sol-11 |
12 | Homework 12 | Dec. 08 | HW-Sol-12 |
Exams: Two midsemester exams and one final exam. Exam dates: October 06, 2020 (midsem exam 1, covers everything up to Oct. 02), November 10 (midsem exam 2).
Note the date of the exams has been changed !!
Midterm exam 2 on Nov. 10 will occur in two time slots: (i) Time slot 1 is from 7:30 AM to 10:30 AM and (ii) Time slot 2 is from 4:00 PM to 7:00 PM.
If you are unable to appear during either of the time slots, please email instructor by EOD Nov. 06 2020.
Final exam is scheduled on Dec. 13th, 5:30 PM to 8:30 PM Central Time. Exam will occur on Zoom. Details will be emailed on the morning of Dec. 13th.
Grading Policy:
Homework | 25% of total |
Midsemester Exams |
45% of total (22.5% each midterm exam) |
Final Exam (comprehensive) | 30% of total |
I encourage active participation in class/online on Piazza. Please ask questions and doubts as often as necessary.