Fall 2020 441-on-Piazza Compass2g MediaSpace

ECE 441: PHYSICS AND MODELING OF SEMICONDUCTOR DEVICES

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

L1

V1

Essential read

Logistics

Aug 26, 2020 Recap of semiconductor basics--Part II L2 V2

Essential read

Gauss' Law

Aug 28, 2020

Fermi-Dirac statistics;

Free carrier density

L3

V3 Supplementary

Essential read

Reading Material

Aug 31, 2020

Free carrier density continued;

Carrier freezeout

L4

V4

 
Sep 02, 2020

Heavy doping;

Inhomogeneous doping;

Quasi Fermi level

L5

V5 (starts at 3:30 minutes)

Search for bandgap narrowing models in silicon. Example: 

https://www.iue.tuwien.ac.at/phd/palankovski/node39.html

Sep 04, 2020 Generation-recombination introduction

L6 part 1

L6 part 2

V6

 

Sep 09, 2020 Generation-recombination in equilibrium

L7

V7

Non-essential but interesting advanced reading from book 

"Semiconductor Statistics" by J.S. Blakemore

[ISBN 0-486-65362-5, QC611.B52]

Sep 11, 2020 Generation-recombination in out-of-equilibrium (OOE)

L8

V8

Essential read

Appendix (Must follow the calculation for HW-3)

Derivation of U_trap for Et != Ei

Sep. 14, 2020

Low-level injection;

Extraction/generation

L9

V9

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.

Sep. 16, 2020 Carrier dynamics in uniform situation

L10

V10

Essential

Please revise solving 1st order ODEs.

Sep. 18,

2020

Surface recombination due to traps

L11

V11

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

Sep. 21

2020

Introduction to carrier transport

L12

V12

Non-essential read: Concept of phonons and velocity saturation 

Sep. 23

2020

Carrier drift 

Models of mobility and saturation velocity

L13

V13

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 Electronics20(2), 77-89. https://doi.org/10.1016/0038-1101(77)90054-5 

Sep. 25

2020

Carrier diffusion

Current in terms of quasi Fermi level gradient

Non-uniform doping

L14

V14

Essential read

Sample Problems on Carrier Flow

Sep. 28

2020

Carrier distribution in equilibrium

Boltzmann relations

L15

V15

Essential read

M&K Chapter 4, pages 174-181 

Sep. 30

2020

Quasi neutrality condition

Continuity equation

Shockley equations 

L16

V16 

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

L17

V17

 
Oct. 05 2020 Application of Shockley equations to solving minority carrier transport and space charge regions

L18

V18

Essential read

Summary of Shockley equations and various approximations 

Check here.

Oct. 07 2020

Surface continuity eq.

Hot carriers

L19

V19

 

Oct, 09

2020

P-N junction in equilibrium

Qualitative view of band bending

L20

V20

Essential read

Example of difference in transport across QNR and SCR.

Oct. 12

2020

Qualitative view of current conduction

Preliminary derivation of I-V characteristics

L21

V21

Essential read

Qualitative I-V in a p-n junction

 

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

L23

V23

Essential read

P-N junction capacitance details

Oct. 19

2020

Small-signal diode model

Switching characteristics (turn-on and turn-off transient timing)

L24

V24

Essential read from textbook M&K:

Section 5.4, pages 256-261

Section 5.5, pages 262-264

Oct. 21

2020

Secondary effects in a p-n junction diode including (i) short diode and (ii) generation-recombination in SCR.

L25 

V25

Essential read from textbook M&K: 

Sec. 5.3, pages 238-250

Practice problems (solutions discussed during lecture)

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

L26

V26

Essential read from textbook M&K:

Sec. 4.4, pages 203-212

Sec. 4.2, pages 191-194

Non-essential read on avalanche breakdown

https://www.iue.tuwien.ac.at/phd/triebl/node20.html

Oct. 26 

2020

Continued discussion of secondary effects in p-n junction diode

L27

V27

Pending business from Lec. 26

Oct. 28 

2020

Metal semiconductor junction electrostatics

L28

V28

Essential read from textbook M&K:

Sec. 3.1 and 3.2, pages 139-151

Oct. 30

2020

Metal semiconductor junction--current conduction via drift-diffusion

L29

V29

Essential read from textbook M&K:

Sec. 3.3, pages 152-155 (I-V characteristics)

Nov. 02

2020

Current conduction via thermionic emission

Surface effects

 

L30

V30

Essential read from textbook M&K:

Sec. 3.3, pages 155-158 (I-V characteristics)

Sec. 3.5, pages 162-166 (surface effects)

Nov 04

2020

Non-rectifying contacts

Tunneling

Schottky barrier lowering

L31

V31

Pending business from L30 covered

Essential read from textbook M&K

Sec. 3.4, pages 158-162 (Non-rectifying contacts)

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

L32

V32

Essential read from textbook M&K

Sec. 8.1, pages 381-386 

Sec. 8.2, pages 387-390

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

L33

V33

Essential read from textbook M&K

Sec. 8.3, pages 390-396

 

Nov. 11 

2020

Metal-oxide semiconductors electrostatics -- Part III

(i) Quantitative and qualitative analysis of MOS C-V at low frequency

L34

V34

Essential read from textbook M&K

Sec. 8.4, pages 396-402

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

L35

V35

Non-essential read:

Aleksandrov, O. V. "A model of formation of fixed charge in thermal silicon dioxide." Semiconductors 45.4 (2011): 467-473.

Nov. 16

2020

Metal-oxide semiconductors electrostatics -- Part V

(i) Effect of interface traps

(ii) Mobile charges in insulator

L36

V36

Essential read from textbook M&K

Sec. 8.5, pages 402-409

Nov. 18

2020

Metal-oxide semiconductors electrostatics -- Part VI

(i) Polysilicon depletion

(ii) Quantum mechanical effects

L37

V37

 

Nov. 20

2020

MOSFET current conduction

(i) Linear regime and saturation regime

L38

V38

Essential read

Theory of MOSFETS

Nov. 23

2020#

MOSFET current conduction

(i) Saturation regime -- pinch off and velocity saturation

(ii) Output conductance and transconductance

L39

V39

Essential read

Calculation of saturation voltage with velocity saturation

Nov. 25

2020#

Sub-threshold current conduction in MOSFET 

L40

V40

 

Nov. 30

2020

MOSFET current conduction wrap-up

Channel length modulation, drain-induced barrier lowering, body effect, leakage effects

L41

V41

Essential read

Notes on drain-induced barrier lowering 

#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 Nov. 29 HW-Sol-11
12 Homework 12 Dec. 06 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 details will be released later. 

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.