Linear Model for Diode;

E L 7 6 D

ELETRÔNICA APLICADA À

ENGENHARIA MECÂNICA MICROELETRÔNICA:

-Semicondutores;

-Diodo Semicondutor.

Aula 02 (10.mar.2020) MICROELETRÔNICA

Dmitri Ivanovic MENDELEIEV (1834-1907)

• CLASSIFICAÇÃO PERIÓDICA

• SEMICONDUTORES

• APLICAÇÃO NA ELETRÔNICA

• ESTRUTURA CRISTALINA

• PORTADORES DE CARGA

• BANDAS DE ENERGIA

• DOPAGEM MICROELETRÔNICA MICROELETRÔNICA

Source: < https://www.coop.com.au/periodic-table-of-elements-reference-card-chm001/5555000095488 > MICROELETRÔNICA

ELEMENTARY CONCEPTS

• Atomic Models Philosophical → Democritus; Lavoiser; Dalton; Avogadro, Brown Subatomic particles → Thomson (“plum-pudding”), Rutherford; Bohr Quantum mechanics → Werner Heisenberg

-19 • Elementary charge → qe = -1,6x10 [C]

-31 • Electron mass → me = 9,1x10 [kg]

• Electron radius → 10-15 [m]

• Atom radius → 10-10 [m] MICROELETRÔNICA

THE STRUCTURE OF MATTER

- Dalton;

- Thomson;

- Rutherford-Bohr;

- De Broglie (modelo quântico). MICROELETRÔNICA

THE NATURE OF THE ATOM Dalton’s Atomic Theory Fonte: < https://www.youtube.com/watch?v=rxltY8HhQkA >

DISCUSSIONS ABOUT DALTON´s ATOMIC THEORY

• Innovatively:

• Setbacks: MICROELETRÔNICA

JOSEPH JOHN THOMSON´s ATOMIC THEORY Thomson's Model of an Atom - Class 9 Tutorial Fonte: < https://www.youtube.com/ watch?v=lLwnACfo7hY >

DISCUSSIONS ABOUT THOMSON´s ATOMIC THEORY

• Innovatively:

• Setbacks: MICROELETRÔNICA

ELECTRONIC STRUCTURE OF THE ELEMENTS (RUTHERFORD) Rutherford's Model of an Atom(US accent) Fonte: < https://www.youtube.com/watch?v=XLaeFUKd2Y4 >

DISCUSSIONS ABOUT RUTHERFORD´s ATOMIC THEORY

• Innovatively:

• Setbacks: MICROELETRÔNICA

THE ENERGY-BAND THEORY (BOHR) Bohr Model of the Hydrogen Atom, Electron Transitions, Atomic Energy Levels, Lyman & Balmer Series

Fonte: < https://www.youtube.com/watch?v=mXxsT1ut35Q >

DISCUSSIONS ABOUT BOHR´s ENERGY-BAND THEORY

• Innovatively:

• Setbacks: MICROELETRÔNICA

DE BROGLIE AND THE QUANTUM MODEL Louis de Broglie's explanation of Bohr's atomic model

Fonte: < https://www.youtube.com/watch?v=oLd-6UytkIU >

DE BROGLIE AND THE QUANTUM MODEL

everything is almost set, but nowadays…

FURTHER DIVING IN THE ATOMIC SCIENCE (With Tyler DeWitt)

Fonte: < https://www.youtube.com/watch?v=NSAgLvKOPLQ > Model of atoms timeline

See more at < http://socratic.org/chemistry > Major discoveries about atom´s structure were performed with study of gases.

But, what about the other states of matter?

Let us take a look… HISTORY CURIOSITY

1.869 – CROOKES (William) and others, invented the Electrical Discharge Tube.

Source: < https://en.wikipedia.org/wiki/File:Crookes_tube_two_views.jpg > HISTORY - CURIOSITY

1.897 – THOMSON (Joseph John) discovered the electron.

Curiosity: in 1.906, Thomson was awarded with the Nobel Prize in Physics.

Source: < https://en.wikipedia.org/wiki/Karl_Ferdinand_Braun > STATES OF MATTER (*)

- Gases;

- Liquids;

- Solids;

- Plasma.

(*) Classical states – see next... FURTHER STATES OF MATTER (**)

- BOSE-EINSTEIN Condensate (BEC);

- Neutron-degenerate matter;

- Quark-gluon plasma.

(**) Non-classical states ... AND FURTHER MORE

- Glass; - Plastic Crystal; - Liquid Crystal states; Also non-classical states - Magnetically ordered; - Microphase-separated; - Superfluid; - Fermionic condensate; - Rydberg molecule; Low-temperature states - Quantum Hall state; (VALIGRA, 2005; MINKEL, 2009) - Photonic matter; - Dropleton; - Degenerate matter; High-temperature states - Quark matter; (FOWLER, 1926; OPPENHEIMER, 1939) - Color glass condensate; - Superglass; - Supersolid; Proposed (MURTHY et. al., 1997) - String-net liquid. Don´t worry at which state you found the matter!!!

See? It´s all about GASES

Atoms are highly energized and therefore, much room is there for relative movement (i.e., vibration) between them. LIQUID

At liquid state, atoms are at an intermediate energized point. There is a plenty room to their vibration, however, they are much more condensed than in gases. SOLID

At solid state, atoms are very, very condensed. There is low enthalpy of the containment system. For all intents and purposes, one can say that only tiny limited atom vibration is allowed (*). PLASMA

Maybe the plasma is the most abundant state of matter in universe although not so abundant in our planet. There is very high enthalpy allowing their atoms become ionized. ... fleetingly ELECTRICAL NATURE OF MATTER

Early experiments: 1. Static electricity (ancient Greece); 2. FARADAY´s unveil (XIX b.C); 3. Conduction of electricity through gases (THOMSON and others). ELECTRICAL NATURE OF MATTER

Although there are electrical charges at matter constituints, conventioned “positive” and “negative”, the matter itself is NEUTRAL. Even so, how can the electricity occur? ELECTRICAL NATURE OF MATTER

The answer, my friend, is NOT blowing in the wind: Faraday´s studies of electrolysis.

Faraday was an excellent experimentalist. Doing so, he early realized that, in particular conditions, external energy could be applied to an environment of electrolysis, causing changes in the distribution of electrical charges. Todays´authors (MILMANN, 1972, p.5) use the terms: “Nature of the atom”. ELECTRICAL NATURE OF MATTER

Since the matter can exist in any state, it is reasonably state that:

Convenient energy exciting an atom can turn possible the movement of electron (negative charge) leading it to that an orbit that allows electricity to flow. Doing so, Regard this view, elements can be stated as: CONDUCTORS NON-CONDUCTORS (“insulators”) ELECTRICAL NATURE OF MATTER

For example: Carbon, Silicon, Germanium, Tin and Lead Although these 5 materials are classified at IVA-Group on Periodic Table of Elements, one can notice that:

• Carbon in its allotropic form “diamond” is non-conductor; • Tin and Lead are both electricity conductors; • Silicon and Germanium are not as good conductors as Sn and Pb. However, they are not electricity insulators. ELECTRICAL NATURE OF MATTER

CHALLENGE:

Acting like your predecessors in scientific experiment, state the properties of “stibium”, Te and Po. THE ENERGY-BAND THEORY Elements like Silicon, Germanium and Arsenic are called “metalloids”, since they occur in environment like crystals(*) and at solid state like majority of metals. Despite this property, they are not as good conductors of electricity and termal energy as metals are.

(*) CRYSTAL is a term used in chemistry to designate a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions (ASHCROFT; MERMIN, 1976). THE ENERGY-BAND THEORY Contrary to that seemed at gases, where the atoms are sufficiently far apart not to exert any influence on one another, the electric potencial for a crystal is a periodic function in space, whose value at any point is the result of contributions from every atom in a crystal structure.

(graphite)

(diamond) (steel) (glass) THE MILLER INDEX

When studying crystals, the crystallographic directions are fictitious lines linking nodes (atoms, ions or molecules) of a crystal. Similarly, the crystallographic planes are fictitious planes linking nodes. Some directions and planes have a higher density of nodes. These planes have an influence on the behaviour of the crystal:

1. optical properties; 2. adsorption and reactivity; 3. surface tension; 4. dislocations (plastic deformation).

(ASHCROFT; MERMIN, 1976, p.135-44)

THE MILLER INDEX

Silicon and Germanium tetrahedral crystal structure

(BOYLESTAD, NASHELSKY; 1999) THE ENERGY-BAND THEORY In consequence of this observation, when atoms form crystals, the inner-electronic shell (see BOHR atomic model) are poorly affected. However, the outter-shell electrons are dramatically affected, since they are shared by multiple atoms in a crystal. So, there are new values energy associated in comparision to same electron in a gas.

(MILMANN, 1972, p.15) METALS, METALLOIDS, CONDUCTORS, INSULATORS AND SEMICONDUCTORS An excellent conductor of electricity is called a METAL. A very poor conductor of electricity is called an INSULATOR. Finally, a substance whose conductivity lies between these extremes materials is called a SEMICONDUCTOR(*). Depending upon its energy-band structure, the materials used in this subject can be placed in one of these three classes (see below).

(BOYLESTAD, NASHELSKY; 1999, p.16) SEMICONDUCTORS

According to MILMANN, a SEMICONDUCTOR is a substance which

-19 EG (band gap) has at magnitude of about 1 [eV] (i.e., 1,6x10 [J]) at stated temperature. As a matter of fact, according BOYLESTAD:

OBS.: MILMANN considers graphite as a semiconductor. However, band gap for this allotropic form of Carbon is about 0,03 [eV] at room temperature. Hence one must assume that graphite is a conductor!!!

(MILMANN, 1972, p.17) SEMICONDUCTORS

Some semiconductors are most commonly used in construction of electonic devices (BOYLESTAD, 2013).

Singular crystal: i. Ge: in 1939, just after the invention of semiconductor diode, germanium was the first material applied. It occurs in nature bonded to oxygen and it is the 50th element in the Earth´s crost. ii. Si: it is very abundant in nature but only was applied in construct electronic devices after its refine was developed. SEMICONDUCTORS

Compound crystal: i. GaAs

ii. CdS

iii. GaN

iv. GaAsP

All of above are made by two or more semiconductor materials of diferent atomic structures. SEMICONDUCTORS

LET US NOW TAKE A LOOK AT SOME DEFINITIONS... SEMICONDUCTORS

COVALENT BOND It is stated that a covalent bond occurs when atoms share their electrons at valence layer.

Silicon singular crystal GaAs compound crystal (BOYLESTAD, NASHELSKY; 1999, p.5) (BOYLESTAD, 2007, p.4) SEMICONDUCTORS

INTRINSIC MATERIALS All those semiconductors that have been carefully refined to reduce the impurities to a very low level – essentially as pure as can be made available through modern technology. A magnitude sample is some like 1:109. The free electrons in the material due only to “natural”(*) causes are referred to as intrinsic carriers. For example, at room temperature, the intrinsic crystal of germanium will have approximately 2,5x1013 free carriers per cubic centimeter.and intrinsic crystal of silicone 1,5x1010.

(*) such as electric field, light (i.e. photons), thermal energy and so on. SEMICONDUCTORS SEMICONDUCTORS SEMICONDUCTORS SEMICONDUCTORS SEMICONDUCTORS EARTH´S CURIOSITY

(FROLOV, Sergey, University of Pittsburgh, 2015 available at: ) SEMICONDUCTORS

TEMPERATURE BEHAVIOR

As the temperature raises from absolute zero (0 K), an increasing number of valence electrons absorb sufficient termal energy to break the covalente bond and contribute to the number of free carriers. It fair to expect an increase on the conductivity index. In fact, semiconductor materials show a reduction in resistance with increase in temperature. They are said to have a NEGATIVE TEMPERATURE COEFFICIENT.

(BOYLESTAD, NASHELSKY; 1999, p.5) SEMICONDUCTORS

EXTRINSIC MATERIALS Electrical characteristics of semiconductor materials can be altered significantly by the addition of certain impurity atoms into the intrinsic crystal. These impurities, although only added in a order of 1 part per 10 million, can alter the band structure sufficiently to totally change the electrical properties of the material.

This so-obtained material is called EXTRINSIC SEMICONDUCTOR.

The process of adding impurities is called DOPING.

(BOYLESTAD, NASHELSKY; 1999, p.7) SEMICONDUCTORS

EXTRINSIC MATERIALS

There are two kinds of extrinsic materials of immesurable importance to semiconductor device fabrication:

The n-type material

The p-type material

(BOYLESTAD, NASHELSKY; 1999, p.8) MICROELETRÔNICA MICROELETRÔNICA

It is importante to remember that by addition of certain impurities atoms, some properties of semiconductors (notedly that electrical) can be significantly altered.

Although both compound (GaAs, GaAsP, ZnSe, GaSb) and singular crystals (Si,Ge) are used by the semiconductors industry, in our primary studies, we will greatly discuss the silicon-based electronic devices.

(BOYLESTAD, NASHELSKY; 1999, p.8)

MICROELETRÔNICA MICROELETRÔNICA

STUDY OF DIODES • Types of diodes;

• Circuit symbols for diodes;

• Linear model for diode;

• Load Line. TYPES OF DIODES AND THEIR SYMBOLS

1 – Rectifier Diode (or simply “diode”, unless otherwise specified)

2 – Zener Diode

3 – Light Emitter Diode (LED)

4 – Silicon Controlled Rectifier (SCR) TYPES OF DIODES AND THEIR SYMBOLS

5 – Photodiode

6 – Tunnel Diode

7 – Varicap LINEAR MODEL FOR A DIODE

(BOYLESTAD, NASHELSKY; 1999, p.13) LINEAR MODEL FOR A DIODE LINEAR MODEL FOR A DIODE LINEAR MODEL FOR A DIODE LINEAR MODEL FOR A DIODE LINEAR MODEL FOR A DIODE

(BOYLESTAD, NASHELSKY; 1999, p.16)

Despite semiconductor material (Ge vs Si, e.g.) LINEAR MODEL FOR A DIODE

(BOYLESTAD, NASHELSKY; 1999, p.17)

Despite temperature influence LINEAR MODEL FOR A DIODE

(BOYLESTAD, NASHELSKY; 1999, p.18) LINEAR MODEL FOR A DIODE Dynamic (or ac) Resistance

(BOYLESTAD, NASHELSKY; 1999, p.19) LINEAR MODEL FOR A DIODE Signal travelling

(SCHUBERT Jr.; KIM, 2012, p.76) LOAD LINE

When using (or simplifying a) only DC sources, one must use the load line for a diode calculation. See below: LOAD LINE SIMPLIFIED MODELS FOR A DIODE

1 – Ideal diode SIMPLIFIED MODELS FOR A DIODE

2 – Simplified diode SIMPLIFIED MODELS FOR A DIODE

3 – Piecewise linear model DIODE AS A CIRCUIT ELEMENT

1 – Diode as a Rectifier DIODE AS A CIRCUIT ELEMENT

2 – Diode as a Limiter (or Clipper Circuit) DIODE AS A CIRCUIT ELEMENT

3 – Diode as a Clamper (or DC restore circuit) MICROELETRÔNICA RECTIFIERS

Consider an input voltage (vi) given by: vi = A•sin(ωt - 휑) Graphically:

Where: A = maximum (peak) value for vi; ω = angular velocity = 2•휋•f f = angular frequency t = time

휑 = phase shift for vi RECTIFIERS A rectifier circuit applies a semiconductor diode for obtain a non-zero voltage value at the output (also referred as “load”). The simplest of networks to examine with a time-varying signal appears in Fig. 2.43. For the moment we will use the ideal model (note the absence of the Si or Ge label to denote ideal diode) to ensure that the approach is not clouded by additional mathematical complexity.

(BOYLESTAD, NASHELSKY; 1999, p.71) RECTIFIERS HALF-WAVE RECTIFIER:

VDC = Vm / π RECTIFIERS FULL-WAVE RECTIFIER (Type I – Center tap transformer)

(BOYLESTAD, NASHELSKY; 1999, p.74)

VDC = 2 • (Vm / π ) RECTIFIERS FULL-WAVE RECTIFIER (Type II – Bridge network)

(BOYLESTAD, NASHELSKY; 1999, p.74)

VDC = Vm / π RECTIFIERS RECTIFIERS AND POWER SUPPLIES

(BOYLESTAD, NASHELSKY; 2013, p.654) RECTIFIERS RECTIFIERS AND POWER SUPPLIES

(BOYLESTAD, NASHELSKY; 2013, p.656) RECTIFIERS RECTIFIERS AND POWER SUPPLIES

(BOYLESTAD, NASHELSKY; 2013, p.657) RECTIFIERS RECTIFIERS AND POWER SUPPLIES - NETWORKS

PI-filter

(BOYLESTAD, NASHELSKY; 1999, p.789) RECTIFIERS RECTIFIERS AND POWER SUPPLIES - NETWORKS

T-filter CLIPPERS* As their name states, “CLIPPERS” are circuits that employ rectifier diodes to “clip” off a portion of the input signal without distorting the remaining part of the alternating waveform. The half-wave rectifier is an example of the simplest form of diode clipper (one resistor and one diode). Depending on the orientation of the diode, the positive or negative region of the input signal is “clipped” off.

There are two general categories of clippers: series and parallel. The series configuration is defined as one where the diode is in series with the load, while the parallel variety has the diode in a branch parallel to the load.

* (Também chamados de “Ceifadores”) CLIPPERS*

(BOYLESTAD, NASHELSKY; 2013, p.70)

* (Também chamados de “Ceifadores”) CLIPPERS*

(BOYLESTAD, NASHELSKY; 2013, p.73) * (Também chamados de “Ceifadores”) CLAMPERS**

The clamping network is one that will “clamp” a signal to a different dc level. The network must have a capacitor, a diode, and a resistive element, but it can also employ an independent dc supply to introduce an additional shift. The magnitude of R and C must be chosen such that the time constant RC is large enough to ensure that the voltage across the capacitor does not discharge significantly during the interval the diode is nonconducting. Throughout the analysis we will assume that for all practical purposes the capacitor will fully charge or discharge in five (5) time constants.

** (Também chamados de “Grampeadores”) CLAMPERS** The network of Fig. 2.89 will clamp the input signal to the zero level (for ideal diodes). The resistor R can be the load resistor or a parallel combination of the load resistor and a resistor designed to provide the desired level of R.

** (Também chamados de “Grampeadores”) CLAMPERS**

** (Também chamados de “Grampeadores”) MICROELETRÔNICA MICROELETRÔNICA

REFERÊNCIAS BIBLIOGRÁFICAS

BELL, David A. Electronic devices & Circuits, 2nd ed. Virginia : Reston (Prentice-Hall), 1980, 493p., 28cm. ISBN 0-8359-1634-0.

BOYLESTAD, Robert Louis; NASHELSKY, Louis. Dispositivos eletrônicos e teoria de circuitos, 11ª. ed. São Paulo : Pearson, 2013, 766p., 28cm. ISBN 978-85-64574-21-2.

MILLMAN, Jacob; HALKIAS, Christos C. Integrated electronics: analog and digital circuits and systems. Tokyo : McGraw-Hill, 1972, 911p., 21cm. Library of Congress Catalog Card Number 79-172657.

PIERRET, Robert F. Semiconductor device fundamentals. Massachusetts : Addison-Wesley, 1996, 793p., 24cm. ISBN 0-201- 54393-1.