Polymer Materials 4471

Transcript Polymer Materials 4471

Special Topic In Polymer Materials (KU 4471)

Lecture #12 Part 1

Professor Kwok Wai Lem Department of Materials Chemistry and Engineering Konkuk University May 18, 2010 Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 1

Special Topic In Polymer Materials (KU 4471)- Outline

Grade (100%) 1. Midterm Exam: 2. Final Exam: 3. Homework: 4. Team Project: 5. *Class Participation: 25% 30% 10% 25%

You Own This!!!

assignments.

10% *Engagement in brainstorming sessions, discussion for project and solution to the homework Schedule Lecture # 1.

10-12 13.

14-15 16.

Contents Introduction - Principles of Functional Polymer Materials and Devices Project Introduction/Dr. Lem's Expectations (Lecture #1) Fundamental of Materials and Value Chain Concept Project Selection Finalize and Team Identify (Lecture #2) Polymer Structural Hierarchy/Properties Polymer and Hybrid Availability Effect of Shape and Size on Properties Polymer Functional Properties Design Tools/Criteria Team Project Interim Report Midterm Devices Design Criteria/Tools Processing of Devices Devices Structure/Properties Market Driven Applications Team Project Final Report Presentation Final Examination

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 2

Final Schedule 1. Lecture 12 – May 18 2. Lecture 13 – May 25 3. Lecture 14 - June 8 4. Final Presentation – June 15 5. Examination - June 15

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 3

Finals

•

Final Project Presentation (15 min)

•

3:00 – 3:20 pm June 15

•

Final Exam (2. 5 hours – Open Book)

•

3:30 – 6:30 pm June 15

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 4

Homework #1 (HW L-12-1 - Due Lecture #13)

Reading Assignments from Organic Electronics (2007)

1. “Organic Materials for Thin Film Transistors” by Z. Bao, pages 4-6 2. “New Conducting And Semiconducting Polymers For Plastic Electronics” by Luebben and Sapp, pages 12-14 3. “Fullerene-Based n-Type Semiconductors in Organic Electronics,” by Kronholm and Hummelenpage, pages 16-20 4. “Achieving High Efficiency In Organic Light-Emitting Devices,” by Polikarpov and Thompson, pages 21-23 5. “Light-Emitting Polymers,” by QB Pei, Pages 26-28

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 5

Special Topic in Polymer Materials (KU 4471) - Project

1. The project aims to challenge and assess your ability to critically evaluate a plastic device that is being sold currently in the marketplace. You are asked to guide the class through a re engineering approach (material tear down, how it was made, etc.) of the material engineered device being explored. This is an exercise that you will encounter over and over again if choose to pursue a career in polymer/plastic materials. 2. Your task is three fold: 1. Select a plastic device and ask the instructor to approve your selection. If you do not have the selection by Lecture #2, the instructor will offer you a set of selections to choose from.

2. Write a report on the article (10 page limit).

3. Make a 12-minute (a) interim and (b) final presentation to the class, respectively. The presentation will be followed by a 3-minute question and answer period from the class. 3. Your report/presentation should contain a brief description of the plastic device, outlining the most significant findings. The main part of the report should discuss the merits of the conclusions of the value of the plastic device in term of cost, material, and technology to meet the market needs. For example: Place these conclusions in the light of other people’s findings. Is there a point that the plastic device failed to meet the requirement to expand market size? What are the technological limits of the described devices? Speculate, on what are the next steps additional developments to make this product/device better to expand the market size by meeting additional customer needs. In essence, tell us how this plastic device contributes to the knowledge of the market it explores.

Due Date: 1. Project Introduction/Dr. KW Lem's Expectations (Lecture #1) 2. Project Selection Finalize and Team Identify (Lecture #2) 3. Project Interim Report Presentation (Lecture #7) 4. Project Final Report Presentation (Lecture # Second to Last)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 6

Team Project – Interim Presentation Class Rep: Kim Seung-Hee 1. Project OLED Displays 2. Team Leader: Lee Seung-Min 3. Members

• Lee Seung-Min

• •

Kim Seung-Hee Lee Tae-Ho Practice - 3:00 PM @ May 18, 2010

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 7

Hybrids Build-up Mechanics

Hybrids/Devices

Hierarchy

Molecules Functional Components Structures Functional Structures Clusters Functional Materials Functional Chemicals Atoms

Features

Ground Work for Continuous Improvement (Kaizen) in Materials Development

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 8

Polymer Structure/Properties

Introduction to High Performance Polymers Structural Hierarchy in Semicrystalline Polymers Structural/Properties in Block Copolymers Structural/Properties in Amorphorous Polymers Structural/Properties in Liquid Crystalline Polymers

Shape and Size: Structural Hierarchy

Polymer and Hybrid Available

Form Shape Size Thermoplastics (Engineering Resins) Thermosets metal/ceramics/organic materials Structural Foam Elastomers Polymers Alloys Liquid Crystal Polymers L/D Ratio Micro vs. Nano

What about the surface?

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

Selection of Materials

Mechanical Properties Viscoelastic Behavior Degradations Wear Resistance and Frictional Properties Electrical Properties Optical Properties Magnetic Properties Thermal Properties Barrier Properties Other Functional Properties

Slide # 9

What is a Device?

Source: wordnetweb.princeton.edu/perl/webwn 1. An instrumentality invented for a particular purpose; "the device is small enough to wear on your wrist"; "a device intended to conserve water" 2. Something in an artistic work designed to achieve a particular effect 3. Any clever maneuver; "he would stoop to any device to win a point"; "it was a great sales gimmick"; "a cheap promotions gimmick for greedy businessmen" 4. Any ornamental pattern or design (as in embroidery) 5. An emblematic design (especially in heraldry); "he was recognized by the device on his shield"

Anything Useful is a Device!

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 10

Why Making a Device – First, there is a need! (from a Market Pull)

INPUT MATERIAL DEVICE OUTPUT INPUT

X i Process

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 OUTPUT

f (Xi)

Slide # 11

How to make Device – Must have a need first!

INPUT MATERIAL DEVICE OUTPUT INPUT

X i Process

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 OUTPUT

f (Xi)

Slide # 12

Unmet Needs?

INPUT

X i

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 OUTPUT

f (Xi)

Slide # 13

Making a Better Device is a Continuous Process

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 14

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 15

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 16

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 17

INPUT MATERIAL DEVICE OUTPUT

INPUT OUTPUT Electric Field Magnetic Field Charge Current Permittivity Conductivity Magneto-elect.

effect Magnet ization Electromag.

effect Pemeability Stress Heat Light Piezoelectric effect Pyroelectric effect Photovoltaic effect

Sensor

Piezomagneto effect

Kwok Wai Lem – (KU 4471, Spring 2010)

Strain Converse Piezo-effect Magneto striction Electrocaloric effect Magnetocaloric effect Elastic constant Thermal expansion Photostriction

Actuator

Off-diagonal Coupling:

Smart Materials Lectures #12

Temperature Specific heat Light Electro-opic effect Magneto optic effect Photoelastic effect Refractive index

Slide # 18

Source of Materials to Make Any Device

• Columns: Similar Valence Structure H Li Be Na Mg K Ca Sc Rb Sr Cs Ba Y Fr Ra O F He Ne S Cl Ar Se Br Kr Te I Xe Po At Rn Adapted from Fig. 2.6,

Callister 7e.

Electropositive elements: Readily give up electrons to become + ions.

Kwok Wai Lem – (KU 4471, Spring 2010)

Electronegative elements: Readily acquire electrons to become - ions.

Lectures #12 Slide # 19

Device Build-up Mechanics

Devices Hierarchy Molecules Clusters Functional Components Structures Functional Structures Functional Materials Functional Chemicals Atom s Features

Ground Work for Continuous Improvement (Kaizen) in Materials Development

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 20

Typical TFT Structure

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

A JFET

Slide # 21

Key Difference with CMOS

Si MOSFET A-Si:H TFT Organic TFT Oxide TFT Process Temperature Process Technology Min. Length Substrate Device Type Mobility Cost/Area Lifetime 1000

C Photo lithography <= 65 nm Si Wafer N- & P-type 1500 cm 2 /V-s High Years 250

C Photo lithography 10 μm Glass /Plastic N-type 1 cm 2 /V-s Medium Months Room Temp.

Roll-to-Roll / Ink-Jet 50 μm Plastic/ Metal Foil P-type 0.5 cm 2 /V-s Low Weeks 150

C RF Sputtering 10 μm Glass /Plastic N-type > 10 cm 2 /V-s Low Years Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

Source: Cheng, UCSB, 2009

Slide # 22

Definition of Terms

•

Precision

–

The degree of agreement (or variability) between individual measurements or test results from measuring the same specimen(s)

•

Accuracy (Bias)

–

The difference between the average of the measurement error distribution and the reference value of the specimen measured

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

Source: Luftig, U Colorado at Boulder

Slide # 23

Precision vs. Accuracy

Accuracy

One Thing Only – Focus!

Source: Luftig, U Colorado at Boulder

Slide # 24 Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

Definition of Terms

•

Repeatability

–

The variation in repeated measurements of the same items with a single measurement system

–

Within appraiser/system variation

•

Reproducibility

–

The variation in the average measurements by different appraisers or systems measuring the same items

–

Between appraiser/system variation

Source: Luftig, U Colorado at Boulder

Slide # 25 Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

Measurement Error

Distribution of repeated measures on a single specimen or part

Precision

- Repeatability - Reproducibility

Robust!

Accuracy

(Bias)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

Reference Value Source: Luftig, U Colorado at Boulder

Slide # 26

Junction Devices

1. Metal/ Metal 2. Metal/ Semiconductors 3. Semiconductor/Semiconductors

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 27

Junction Devices

1. Metal/ Metal 2. Metal/ Semiconductors 3. Semiconductor/Semiconductors

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 28

STANDARD HYDROGEN ELECTRODE

• Two outcomes: -- Corrosion -- Electrodeposition ne e e H 2 ( gas ) 2e Mn+ ions H+ H+ 1M Mn+ 25 °C sol’n 1M H+ sol’n -- Metal is the anode (-)

o metal  0 (relative to Pt) Standard Electrode Potential ne e e Mn+ ions H+ H+ 2e 1M Mn+ 25 °C sol’n 1M H+ sol’n -- Metal is the cathode (+)

o metal  0 (relative to Pt) Adapted from Fig. 16.2,

Callister & Rethwisch 3e

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 29

Example

(a) Briefly explain the difference between oxidation and reduction electrochemical reactions.

(b) Which reaction occurs at the anode and which at the cathode?

Solution

(a) Oxidation is the process by which an atom gives up an electron (or electrons) to become a cation. Reduction is the process by which an atom acquires an extra electron (or electrons) and becomes an anion.

(b) Oxidation occurs at the anode; reduction at the cathode.

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 30

STANDARD EMF SERIES

• EMF series metal Au

o metal +1.420 V Cu Pb Sn Ni Co +0.340

- 0.126

- 0.136

- 0.250

- 0.277

Cd Fe Cr - 0.403

- 0.440

- 0.744

Zn Al Mg Na K - 0.763

- 1.662

- 2.363

- 2.714

- 2.924

o = 0.153V

• Metal with smaller

o metal corrodes.

• Ex: Cd-Ni cell <

o Ni  Cd corrodes Data based on Table 17.1,

Callister 7e

Cd 1.0 M 25 °C Cd 2+ solution 1.0 M + Ni Ni 2+ solution Adapted from Fig. 16.2,

Callister & Rethwisch 3e

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 31



EFFECT OF SOLUTION CONCENTRATION AND TEMPERATURE

• Ex: Cd-Ni cell with • Ex: Cd-Ni cell with standard 1 M solutions non-standard solutions Ni o 

o Cd 

0.153 V

+ -

Ni 

Cd 

Ni o  o

Cd + 

RT nF X ln Y

Cd 25 °C Ni 1.0

M Cd2+ solution 1.0

M Ni 2+ solution

Kwok Wai Lem – (KU 4471, Spring 2010)

T Y

M Ni Cd2+ solution Ni 2+ solution • Reduce

Ni -

Cd -- increasing

by -- decreasing

Lectures #12

-- increasing

T n

= #e per unit oxid/red reaction (= 2 here)

= Faraday's constant = 96,500 C/mol.

Slide # 32

GALVANIC SERIES

• Ranking of the reactivity of metals/alloys in seawater Platinum Gold Graphite Titanium Silver 316 Stainless Steel (passive) Nickel (passive) Copper Nickel (active) Tin Lead 316 Stainless Steel (active) Iron/Steel Aluminum Alloys Cadmium Zinc Magnesium

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

Based on Table 16.2,

Callister & Rethwisch 3e

. (Source of Table 16.2 is M.G. Fontana,

Corrosion Engineering

, 3rd ed., McGraw Hill Book Company, 1986.)

Slide # 33

Fermi Level

• focus on the electrons near the filled/empty boundary.

• each material’s energy state distribution is unique; different E

.

Minimum energy to remove electron from sample E=0 (vacuum level) E F (Fermi level) E F (Fermi level)

Metal 1 Metal 2

• the closer an electron is to the vacuum level, the weaker it is bound to the solid • or, the more energetic is the electron

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

Source: Thomas, U of Guelph

Slide # 34

Two Conductors in Contact

– + – + – + – + – +

electron flow leads to charge separation Contact potential difference Fermi level the same throughout sample

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

Source: Thomas, U of Guelph

Slide # 35

(a) Electrons are more energetic in Mo, so they tunnel to the surface of Pt.

(b) Equilibrium is reached when the Fermi levels are lined up.

When two metals are brought together, there is a contact potential D

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 36

There is no current when a closed circuit is formed by two different metals, even though there is a contact potential at each contact. The contact potentials oppose each other.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 37

Fermi Energy Significance For a given metal the Fermi energy represents the free energy per electron called the electrochemical potential. The Fermi energy is a measure of the potential of an electron to do electrical work (e



V) or nonmechanical work, through chemical or physical processes.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 38

The Seebeck effect. A temperature gradient along a conductor gives rise to a potential difference.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 39

Seebeck Effect

Seebeck effect (thermoelectric power) is the built-in potential difference

V across a material due to a temperature difference

T across it.

 D

Sign of

is the potential of the cold side with respect to the hot side; negative if electrons have accumulated in the cold side.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 40

Seebeck coefficient for metals

   2

eE FO x

Mott and Jones thermoelectric power equation

= a numerical constant that takes into account how various charge transport parameters, such as the mean free path l , depend on the electron energy.

values are tabulated in Table 4.3

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 41

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 42

1. Consider two neighboring regions H (hot) and C (cold) with widths corresponding to the mean Free paths l and l ' in H and C. 2. Half the electrons in H would be moving in the +

x x

direction.

direction and the other half in the – 3. Half of the electrons in H therefore cross into C, and half in C cross into H.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 43

(a) If Al wires are used to measure the Seebeck voltage across the Al rod, then the net emf is zero.

(b) The Al and Ni have different Seebeck coefficients. There is therefore a net emf in the Al-Ni Circuit between the hot and cold ends that can be measured.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 44

Thermocouple

We can only measure differences between thermoelectric powers of materials. When two different metals A and B are connected to make a thermocouple, then the net EMF is the voltage difference between the two elements.

V AB

 

T T o



S A



S B



 

T T o S AB dT

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 45

Thermocouple Equation

V AB





( D

) 2 From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 46

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 47

Thermocouples are widely used to measure the temperature.

LEFT: A thermocouple pair embedded in a stainless steel sheath-probe. The thermocouple junction inside the probe is in thermal contact with the probe tip, and, electrically insulated from the probe metal.

| SOURCE: Courtesy of Omega From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 48

Output emf versus temperature (˚C) for various thermocouple between 0 and 1000 ˚ C From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 49

Junction Devices

1. Metal/ Metal 2. Metal/ Semiconductors 3. Semiconductor/Semiconductors

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 50

Formation of a Schottky junction between a metal and an

-type semiconductor when 

> 

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 51

The principle of the Schottky junction solar cell.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 52

Reverse biased Schottky photodiodes are frequently used as fast photodetectors.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 53

Cross section of a typical thermoelectric cooler.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 54

Typical structure of a commercial thermoelectric cooler.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 55

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 56

Junction Devices

1. Metal/ Metal 2. Metal/ Semiconductors 3. Semiconductor/Semiconductors

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 57

The Bipolar Junction Transistor: BJT

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 58

(a) A schematic illustration of the

pnp

regions. bipolar transistor with three differently doped (b) The

pnp

bipolar operated under normal and active conditions.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 59

(c) The common base (CB) configuration with input and output circuits identified. (d) The illustration of various current components under normal and active conditions.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 60

Emitter Junction: The Law of the Junction

Hole concentration just outside the depletion region in the base at the emitter end

p n

( 0 ) 

p no

exp   

eV EB kT

   where

V EB

is the forward bias applied across the emitter-base (EB) junction

Hole concentration just outside the depletion region in the base at the collector end

p n

(

W B

)  0 From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 61

The Emitter Current

Holes diffuse through the base, from the emitter end to the collector end. This diffusion is driven by the hole concentration gradient dp

/dx.

Assume that the hole concentration profile is linear; it decreases from p

(0) to 0 over the neutral base width W

. (Initially, neglect the recombination of holes with electrons in the base.)

I E

 

eAD h dp n dx x



0



eAD h p n

( 0 )

W B

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 62

BJT Common base (CB) dc characteristics

Emitter Current

I E



eAD h W B p no

exp

eV EB kT

where

V EB

is the forward bias applied across the emitter-base (EB) junction and

W B

the neutral base width.

Definition of CB current gain

 

I C I E

Typically  is less than unity, in the range 0.990 - 0.999

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 63

BJT Common base dc characteristics

Total emitter current

I E



I E

( hole ) 

I E

( electron )

Emitter injection efficiency

 

I E

( hole )

I E

( hole ) 

I E

( electron )  1 1 

I E

( electron )

I E

( hole ) From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 64

BJT Common base dc characteristics

Definition of base transport factor





I C I E

( hole ) 



I C E

If the emitter were a perfect injector,

I E

(hole) , then the current gain  would be 

Base minority carrier transit time





W B

2 2

D h

This

diffusion time

is the

transit time

of the minority carriers across the base From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 65

BJT Common base dc characteristics

Base transport factor





I C I E

( hole )  1   

h t

CB current gain

  

    1   

h t

   From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 66

BJT Common base dc characteristics

Base current

I B

    

h t

 

I E

( hole ) 

I E

( electron ) or

I B



I E



I C

   

h t I E

  1   

I E

Base to collector current gain

 

I C I B

  1     

t h

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 67

I-V

characteristics of the pnp bipolar transistor (exaggerated to highlight various effects) From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 68

The Early Effect

The Early effect. When the BC reverse bias increases, the depletion width

W BC

increases to

constant (constant

V EB

), the minority carrier concentration gradient becomes steeper and the collector current

I C

Increases.

which reduces the base width

W B

. As

p n

(0) is From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 69

pnp

transistor operated in the active region in the common base amplifier configuration. The applied (input) signal

v eb

modulates the dc voltage across the

junction and hence modulates the injected hole concentration up and down about the dc value

p n

(0). The solid line shows how

p n

(

) is modulated up and down by the signal veb superimposed on

V EE

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 70

(a) (b) (a) An

npn

transistor operated in the active region in the common emitter (CE) configuration. The dc voltage across the BE junction,

V BE

, controls the current

I E

and hence

I B

and

I C

. The input current is the current that flows between

BE and the base which is (b) DC

I-V I

B . The output current is the current flowing between characteristics of the

npn V

CE and the collector which is

C .

bipolar transistor in the CE configuration (exaggerated to highlight various effects).

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 71

Common Emitter dc characteristics

Active region collector current

I C

 

I B



I CEO

where

I CEO

  1

I CBO

    

I CBO

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 72

Common Base Amplifier

Small signal input resistance

r e

 

V EB



I E



kT eI E

 25

I E

( mA )

CB voltage gain (small signal)

A V



v cb v eb



R C r e

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 73

npn

transistor operated in the active region in the common emitter amplifier configuration. The applied signal

v be

modulates the dc voltage across the BE junction and hence modulates the injected minority concentration up and down about the dc value

n p

(0). The solid line shows

n p

(

) when only the dc bias

V BB

is present. The dashed line shows how

n p

(

) is modulated up by a positive small signal superimposed on

V BB

v be

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 74

Common Emitter dc characteristics

Emitter current and V

I E



I EO

exp

eV BE kT

where

I EO

is a constant

Input resistance (small signal)

r be



v be i b

 



I BE B

  

V BE



I E

  25

I C

( mA ) From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 75

Common Emitter dc characteristics

Transconductance,

g m



i c v be

  

I E V BE



I E

( mA ) 25  1

r e

Voltage gain

A V

  g

m R C

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 76

Low frequency small signal simplified equivalent circuit of the bipolar transistor in the CE configuration with a load resistor

R C

in the collector circuit.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 77

The basic structure of the junction field effect transistor (JFET) with an n-channel. The two p + regions are electrically connected and form the gate.

A simplified sketch of the cross section of a more practical

-channel JFET From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 78

A (b)

V DS

has increased to a value that allows the two depletion layers to just touch, when

V DS

V P

(= 5 V) when the

junction voltage at the drain end,

V GD

= -

V DS

= -

V P

= -5 V.

B C (a) The gate and source are shorted (

V GS

= 0) and

V DS

is small (c)

V DS

is large (

V DS

V P

) so that a short length of the channel is pinched off.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 79

Typical

I D

vs.

V DS

characteristics of a JFET for various fixed gate voltages

V GS

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 80

The pinched-off channel and conduction for

V DS

V P

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

(=5 V)

Slide # 81

(a) The JFET with a negative = 0 case, the same

V DS V GS

voltage has a narrower

-channel at the start. (b) Compared to the

V GS

gives less

I D

as the channel is narrower. (c) The channel is pinched off at 3V sooner than the

V GS

= 0 case where it was

V DS

= 5 V.

V DS

= From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 82

Junction field effect transistor (JFET)

Pinch-off condition

V DS

( sat ) 

V P



V GS

where

V GS

the point

is a negative voltage (reducing

V P

). Beyond pinch-off when where the channel is just pinched still remains at potential

V DS

(sat) , given by the above equation.

V DS

(sat) , From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 83

1. When

V GS

= - 5 V the depletion layers close the whole channel from the start, at

V DS

= 0.

2. As

V DS

is increased there is a very small drain current which is the small reverse leakage current due to thermal generation of carriers in the depletion layers.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 84

(a) Typical

I DS

versus

V GS

characteristics of a JFET. (b) The dc circuit where

V GS

in the gate–source circuit (input) controls the drain current

IDS

in the drain–source (output) circuit in which

V DS

is kept constant and large (

V DS > V P

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 85

Junction field effect transistor (JFET)

Beyond pinch-off

I DS



I DSS

   1  where,

V GS V GS

( off )    2

I DSS

is the drain current when

V GS

= 0

V GS

(off) = –

V p

; the gate-source voltage that just pinches off the channel

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 86

(a) Common source (CS) ac amplifier using a JFET.

Kwok Wai Lem – (KU 4471, Spring 2010)

(b) Explanation of how

I D

by the signal

v gs

is modulated in series with the dc bias voltage

V GG

Lectures #12 Slide # 87

Example - The JFET

Consider an

channel JFET that has a symmetric

p + n

gate-channel structure as shown in Figures A-a and B. Let

be the gate length,

the gate width, and 2

the channel thickness. The pinch-off voltage is given by

V P



eN d

2  

V o

. The drain saturation current,

I DSS

, is the drain current when

V GS

= 0. This occurs when

V DS

(

sat

) =

V P

(Figure C) so

I DSS

V P G

ch , where

ch is the conductance of the channel between the source and the pinched-off point (Figure 6Q30). Taking into account the shape of the channel at pinch-off, if

G ch

is about 1 / 3 of the conductance of the free or unmodulated (rectangular) channel, show that

I DSS



V P

  1 3 (



e N d

)( 2

)

Z L

 

A particular n-channel JFET with a symmetric p

n gate-channel structure has a pinch-off voltage of 3.9 V and an I

DSS

of 5.5 mA. If the gate and channel dopant concentrations are N

= 10 19 cm -3 and N

= 10 15 cm -3 , respectively, find the channel thickness 2a and Z/L. If L = 10



m, what is Z? What is the gate-source capacitance when the JFET has no voltage supplies connected to it? Figure A Figure B

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

, S.O. Kasap (© McGraw-Hill, 2005)

Figure C Slide # 88

Solution (Part a)

Solution

The conductivity of the channel is  =

eN d



The channel width is

and the depth is 2

. Therefore the area

= 2

. The conductance of the channel is given as 1/3 of the conductance of the free channel, therefore Substitute:

G ch

 1 

L G ch

 2 3

eN d



e aZ L

The voltage across the channel is the pinch-off voltage

V P

. At pinch-off the drain current is

I DSS

, given as: 

I DSS

V P G ch I DSS



V P

eN d



e aZ

(1)

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 89

Solution (Part a)

(a) The gate and source are shorted (

V GS

(b)

V DS

has increased to a value that allows the two depletion layers to just touch, when

V DS

(= 5 V) and the

junction voltage at the drain end,

V GD

= 

V DS

= 

V P

=  5 V.

(c)

V DS

is large (

V DS

= 0) and

V DS

is small.

V P

), so a short length of the channel is pinched off.

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 90

Solution (Part a)

Assume temperature

= 300 K and that the JFET is Si. The relative permittivity of Si is 

= 11.9 and the intrinsic concentration is

n i

= 1.0  10 10 cm -3 . The channel donor concentration

N d

is given as 10 15 cm -3 and the gate acceptor concentration

N a

= 10 19 cm -3 . The electron drift mobility with

N d

= 10 15 cm -3 is approximately 

= 1350 cm 2 V -1 s -1 (the dopant concentration is too low to affect 

V o

can be calculated as follows:

V o



kT e

ln  

N d N a n i

2    ( 0 .

0259 V ) ln  10  21 1 .

0 m   3  10 10 16 m 25  3 m  2  3  

V o

= 0.835 V We can calculate

from the given pinch-off voltage,

V P

= 3.9 V:  

V P



eN d

2  

V o a

 2  

V P



V o

 

eN d

2  11 .

9   8  .

854 1 .

602   10

a = 2.50



10 -6 m or 2.50



10  12 F/m  19 C    10 3 .

9 V 21 m  3   0 .

835 V 

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

, S.O. Kasap (© McGraw-Hill, 2005)

Slide # 91

Solution (Part a)

Therefore the

channel width (2a) is 5.00



I DSS

is given as 5.5 mA. The

ratio can then be found from Eqn. (1) above:

I DSS



V P

eN d



e aZ

 

Z Z L L

  2

V P

I DSS eN



d e a

2  3 .

9 V   1 .

602  10  19 C  10 3  21 5 .

5 m  10  3   3 A  0 .

135 m 2 V  1 s  1  2 .

50  10  6 m  

Z L



39.2

The channel length

is given as 10  m, therefore: Z = 39.2(10 

10 -6 m) =

3.92  10 -4 m

392  m

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

, S.O. Kasap (© McGraw-Hill, 2005)

Slide # 92

Solution (Part b)

The gate area is

gate and is equal to



= (3.92  10 -4 m)(10  10 -6 m) = 3.92  10 -9 m 2 . The depletion capacitance per unit area is:

dep 

gate   2 (



N d N



d N N a a

)

V o

  1 2 and the gate capacitance

gate is twice

dep as the JFET is symmetric and the two gates are connected in parallel.

gate  2  3 .

93  10  9 m 2     1 .

602  10  19 C 2   11  10 21 .

9   8 .

m  3 854  10  25 10 m  12  3 F/m    10 21 m 0 .

835 V   3  10 25 m  3    1 2 

gate = 7.9



10 -13 F or 0.79 pF This neglects stray capacitances (e.g. between gate and source leads, gate and drain leads etc.). Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

, S.O. Kasap (© McGraw-Hill, 2005)

Slide # 93

From

Principles of Electronic Materials and Devices, Third Edition

, S.O. Kasap (© McGraw-Hill, 2005)

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 94

JFET Amplifier

Definition of the JFET transconductance (small signal)



dI DS dV GS

 

I DS



V GS



i d v gs

JFET transconductance (small signal)

g m



dI DS dV GS

  2

I DSS V GS

( off )     1 

V GS V GS

( off )     2 

I DSS I DS

 1 / 2

V GS

( off ) From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 95

JFET Amplifier

Small-signal voltage gain

A V



v ds v gs

 

R D i d v gs A V

 

R D

( g

m v gs

)

v gs

  g

m R D

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 96

Example - The JFET Amplifier

Consider an

channel JFET that has a pinch-off voltage (

V P

) of 5 V and

I DSS

in a common source configuration as in Figure A-a in which the gate to source bias voltage ( that

V DD V

= 10 mA. It is used

) is -1.5 V. Suppose = 25 V.

. If a small signal voltage gain of 10 is needed, what should be the drain resistance (

R D

)? What is

V DS

.If an ac signal of 3 V peak-to peak is applied to the gate in series with the dc bias voltage, what will be the ac output voltage peak-to peak? What is the voltage gain for positive and negative input signals? What is your conclusion?

From Figure A

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 97

Solution (Part a)

Solution

Given,

V P

= 5 V,

I DSS

= 10 mA,

V GS

V GG

=  1.5 V.

If a small signal voltage gain of 10 is needed, what should be the drain resistance (

R D

I DS



I DSS

   1   

V GS



V P

     2  ( 10 mA  )  1    1 .

5 5 V V   2 = 4.90 mA 

g m



dI DS V GS

 2

I DSS V P

   1   

V GS



V P

      2 ( 10 mA ) 5 V   1   1 .

5 V  5 V   = 2.80  10 -3 A/V The small signal voltage gain

A V

g m R D

, so that

R D

A V

g m

= (10)/(2.80  10 -3 A/V) =

3571



V DS

is given by (

I DS

= 4.9 mA):

V DS

V DD



I DS R D



V DS

= 25 V



(4.9



10 -3 A)(3571



) =

7.50 V From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 98

Solution (Part b)

b. V

is given as 25 V. Let

R D

= 3571  . Negative input signal: When

signal =  1.5 V at the input then,

V GS

min =

V GG

signal =  1.5 V  1.5 V =  3 V  

I DS

min 

I DSS

   1   

V GS



V P

     2  ( 10 mA )   1    3 5 V V   2 = 1.60 mA

V DS

max

= V



DSmin

R D

= (25 V)



(1.60 mA)(3.571 k



) =

19.29 V For negative going signals, the gain is,

A V -

 Change in output vol tage Change in input volt age 

V DS

max 

signal

V DS

 19 .

29 V   7 1 .

5 V .

51 V 

A V-

=  7.85

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 99

Solution (Part b)

Positive input signal: When

signal = +1.5 V at the input then,

V GS

max =

V GG

signal =  1.5 V + 1.5 V = 0 V 

I DS

max 

I DSS

   1   

V GS



V P

     2  ( 10 mA )   1   0 5 V V   2 = 10.0 mA 

DSmin

V DD



I DS

max

R D

= 25 V  (10.0 mA)(3.571 k  ) = 

10.7 V

This is nonsense as

V DS

min can not be below zero. The peak to peak voltage is then 19.3 V  0 V = 19.3 V. Therefore the JFET has saturated with

V DS

 0 and the voltage across

R D

being

V DD

. This occurs when

I DS

sat . The JFET amplifier saturates when

I DS

sat 

V DD

R D

= 25 V / (3.571 k  ) = 7.00 mA For positive going signals the output eventually becomes saturated and the gain is, 

A A V V

 +  Change in output vol tage Change in input volt age =  5.00 

V DS

min 

signal

V DS

 0  7 .

5  1 .

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

Slide # 100

Solution (Part b)

The JFET amplifier is operating non-linearly. The negative going

output

signal will be clipped for the positive going

input

signal. The negative sign in both cases represents a phase shift of 180  . Can we find the signal

signal for this saturation (clipping) condition in the positive going input signal? Normally this would be done using a

load line

with the JFET characteristics (as in electronics circuits courses). It may be thought that we can at least estimate

V GS

min from

I DS



I DSS

   1   

V GS



V P

     2

with I

= I DSmax to find the required V GSmin . However this equation is not valid when V

< V DS(sat) , see Figure B, which will be the case when the drain current drops V

across R

. As a very rough estimate, using the above equation with I DSmax = 10 mA, gives V GSmin =



0.82 V which can be interpreted as a rough condition for approaching saturation (clipping). Thus when V

+ v signal

 

0.82 V, the output should be approaching saturation, or when v signal



+0.68 V. Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

Slide # 101

Solution (Part b)

Figure B:

Typical

I D

versus

V DS

characteristics of a JFET for various fixed gate voltages

V GS

. 19.3 7.5

0  1.5 –1.5 Figure C From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12

time time

Slide # 102

The Field Effect

(a) In a metal-air-metal capacitor, all the charges reside on the surface (b) Illustration of field penetration into a

-type semiconductor (c) As the field increases eventually when

> conduction electrons.

V th

an inversion layer is created near the surface in which there are From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 103

The basic structure of the enhancement MOSFET and its circuit symbol.

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 104

SEM cross section of a MOS Transistor |SOURCE: Courtesy of Don Scansen, Semicondutcor Insights, Kanata, Ontario, Canada

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 105

The MOSFET

I D

vs.

V DS

characteristics From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 106

The MOSFET

I D

vs.

V DS

characteristics From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 107

(a) Typical

I D

V DS

characteristics of an enhancement MOSFET (

V) for various Fixed voltages

th V

= 4

(b) Dependence of

I D V GS

at a given

V DS V DS

(

sat

) ) on (> From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 108

Example -Ultimate limits to device performance

. Consider the speed of operation of an

channel FET-type device. The time required for an electron to transit from the source to the drain is 

v d

, where

is the channel length and

v d

is the drift velocity. This transit time can be shortened by shortening

and increasing

v d

. As the field increases, the drift velocity eventually saturates at about

v dsat

= 10 5 m s -1 when the field in the channel is equal to

E c

 10 6 V m -1 . A short 

requires a field that is at least

E c

. 1. What is the change in the

of an electron when it traverses the channel length

from source to drain if the voltage difference is

V DS

? 2. This energy must be greater than the energy due to thermal fluctuations, which is of the order of

. Otherwise, electrons would be brought in and out of the drain due to thermal fluctuations. Given the minimum field and

V DS

, what is the minimum channel length and hence the minimum transit time?

. Heisenberg's uncertainty principle relates the energy and the time duration in which that energy is possessed through a relationship of the form D

>  . Given that during the transit of the electron from the source to the drain its energy changes by

eV DS

, what is the shortest transit time,  , satisfying Heisenberg's uncertainty principle? How does it compare with your calculation in part (

c. How does electron tunneling limit the thickness of the gate oxide and the channel length in a MOSFET? What would be typical distances for tunneling to be effective?

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 109

Solution (Part a)

Solution

Assume temperature

= 300 K. The saturation velocity is given as

v dsat

= 10 5 m/s and the saturation field is given as

E c

= 10 6 V/m.

(1) The change in the

is D

. This is the charge times the voltage, i.e. D

eV DS

. (2) The lower limit to D

due to thermal fluctuations is

. Therefore, substituting into the equation above: 

eV DS

kT V DS

= (1.381  10 -23 J/K)(300 K)/(1.602  10 -19 C) = 0.02586 V This is the lower limit to

V DS

. The minimum channel length

can now be found from the minimum electric field, given by

E c

V DS

:  The minimum transit time 

is then,

V DS

E c

= (0.02586 V)/(10 6 V/m) =

2.59



10 -8 m



v dsat

= (2.586  10 -8 m)/(10 5 m/s) =

2.59



10 -13 s The above limit is the thermal fluctuation limit (thermal noise limit).

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 110

Solution (Part b & c)

Consider the Heisenberg uncertainty principle. Let  = D

be the transit time. During this time the energy changes by D

eV DS

. We are given D

>  , therefore, substituting for the shortest transit time:

eV DS

 =     

eV DS

  1 .

602 1 .

055  10  19  10 C    34 J s 0 .

02586 V  =

2.55



10 -14 s

The uncertainty limit allows a shorter transit time down to 0.0255 ps. Thus thermal fluctuation limit will operate at room temperature.

If the oxide becomes too thin then the electron tunneling will allow gate charge to tunnel into the channel. This will lead to a gate current. The field effect will fail. Similarly, if the source and drain are very close there will then be a tunneling current, a drain current, even when the transistor is off, one can guess that the thickness should be less than 1 nm or 10 Å depending on various material properties. The same order of magnitude also applies to the minimum source drain separation.

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 111

Enhancement NMOSFET

Enhancement NMOSFET constant





 2

ox where 

is the electron drift mobility in the channel,

and

are the length and width of the gate controlling the channel, and  and

ox are the permittivity ( thickness of the oxide insulation under the gate 



) and

Enhancement MOSFET

I DS





V GS



th   1  

V DS

 Where  is a constant that is typically 0.01 V -1 .

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 112

voltage:

Q mi

(a) The threshold voltage and the ideal MOS structure. (b) In practice, there are several charges in the oxide and at the oxide-semiconductor interface that effect the threshold = Mobile ionic charge (e.g. Na + ),

Q ot

= Trapped oxide charge,

Q f

= Fixed oxide charge,

Q it

= Charge trapped at the interface.

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 113

Schematic illustration of ion implantation for the control of

V th

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 114

(a) There is an overlap of the gate electrode with the source and drain regions and hence Additional capacitance between the gate and drain.

(b)

+ type ion implantation extends the drain and source to line-up with the gate.

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 115

The poly-Si gate technology. (a) Poly-Si is deposited onto the oxide and the areas outside the gate dimensions are etched away. (b) The poly-Si gate acts as a mask during ion implantation of donors to form the

+ source and drain regions. (c) A simplified schematic sketch of the final poly-Si MOS transistor.

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 116

(a) The energy band diagram of a

+ (heavily

-type doped) junction without any bias.

Built-in potential

V 0

prevents electrons from diffusing from (b) The applied bias reduces

V 0 n

+ to

side. and thereby allows electrons to diffuse, be injected, into the

-side. Recombination around the junction and within the diffusion length of the electrons in the

-side leads to photon emission.

From

Principles of Electronic Materials and Devices, Third Edition

Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 117

Special Topic In Polymer Materials (KU 4471)

Lecture #12 Part 2

Professor Kwok Wai Lem Department of Materials Chemistry and Engineering Konkuk University May 18, 2010 Kwok Wai Lem – (KU 4471, Spring 2010) Lectures #12 Slide # 118