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3C3 – Analogue Circuits

Prof J K Vij

jvij@tcd.ie

Lecture 1:

Introduction/

Semiconductors & Doping

Department of Electronic & Electrical Engineering – Trinity College Dublin, 2014

Course Outline – (subject to change)

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Assessment: Examination 85%, Labs (A1 and A2) 15% Module Details

Analogue Circuits is a one semester course taken by Junior Sophister C Stream students. It provides a thorough foundation in analogue circuits as applied to systems used in generating, amplifying and in general processing signals which are continuous functions of time. The course aims to provide students with knowledge of operational principles and practical limitations of analogue circuits at device and circuit level, as well as instructing them in the analysis and design of these circuits. All of the principles and techniques learned are applicable to the design of analogue systems on a wider scale. During the course, students will develop the analytical and synthesis skills needed to design analogue circuits for electronic equipment intended for any modern application area. Electronic Engineering students will use these skills later in further integrated circuit design courses. Reading/Learning Resources

− Microelectronic Circuits, Sedra & Smith (6th edition, 2004). − Electronic Devices, Floyd (9th edition, 2012). − Microelectronic Circuits, Sedra & Smith (5th edition, 2011). − Electronics: a systems approach, Storey (4th edition, 2006). Assessment - Exam Paper: (2 h) Answer 4 Questions out of 6 (100%)

Lecture and Tutorial Times

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Monday 1500-1550h M20

Tuesday 1200-1250h M20

Friday 1000-1050h M21

Thursday 900-950h Panoz L3

Lecture Times

Tutorial Times

Course Outline – (subject to change)

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Topics Subtopics

Physical Operation of Transistors • Basic Semiconductor Concepts • The PN Junction

The Metal Oxide Seminconductor Field Effect Transistor (MOSFET)

• Introduction/Recap • Biasing • Small Signal Analysis • Amplifier Configurations

The Bipolar Junction Transistor (BJT) • Introduction/Recap • Biasing • Small Signal Analysis • Amplifier Configurations

Single Stage IC Amplifiers • Amplifier Configurations

Differential Amplifiers • MOS Differential Pair • BJT Differential Pair • Differential Amps with active Load

Course Outline – (subject to change)

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Topics Subtopics

Multistage Amplifiers • Two-stage CMOS Op Amp • 741 Op Amp – DC Analysis • 741 Op Amp – Small Signal Analysis

Feedback (time permitting) • Introduction • Topologies • Stability

Converter Circuits • D/A Converter Circuits • A/D Converter Circuits

Oscillators • Basic Principles • Op Amp-RC Oscillator Circuits • Other Waveform Shaping Circuits

Filters • Active Filters

Analogue Electronics - What’s the point?

• Almost all electronic signals are now processed using digital electronic circuits.

• Why?

• Noise resistant

• Simpler design

• Greater precision

• Better information storage

• Interface with software

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Analogue Electronics - What’s the point?

• But, some operations have to be done using analogue circuits.

• Most real world signals are analogue!

• To capture them and convert them to the digital domain we need an analogue transducer circuit (analogue front end).

• And, some operations are best performed by analogue circuits.

• Also, many electronics systems include both analogue and digital parts. So, a good electronic engineer must be proficient in the design of both analogue and digital circuits – known as mixed-signal or mixed-mode design.

• Finally, with high-speed digital signal processing, the analogue nature of the digital signals cannot be ignored.

• When speed and power limitations of the technology become the limiting factors for the amount of information that can be processed by a digital system, analog information processing is still an interesting alternative, e.g., mobile phones still have an analog RF receiver.

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Symbol Convention

• Total instantaneous quantities: e.g., ,

• Direct current (DC) quantities: e.g ., ,

• DC Power-supply voltages, e.g.,

• DC current sources, e.g.,

• Incremental signal quantities: e.g, ,

• Sine-wave: e.g., ,

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What you learned about transistors in 2E6

• The n-Channel Transistor

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D

VG= VH= VLVG

S

D

S

D

G

S

This device has three electrical nodes, termed the gate G, the drain D, and the source S. The gate may be regarded as a controlling node, determining the electrical properties of the channel between the drain and source. When operated digitally, ie by VH or VL applied to G, the channel between the D and S nodes behaves like an ideal switch, controlled by the voltage VG applied to the gate. As shown in the diagram:

If VG = VH, then D is essentially connected to S and we say the switch is closed;

If VG = VL, then there is no connection between D and S, and we say the switch is open.

• The p-Channel Transistor

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D

S

D

S

= VLVG VG= VH

S

G

D

This device again has gate G, source S, and drain D nodes in this instance we depict the S node above the D node because it would be normal to find a higher potential on the source than on the drain; the opposite would be the case for the n-channel transistor. The device functions similarly to the n-channel except that the role of the gate is inverted:

If VG = VH, then there is no connection between S and D, and we say the switch is open;

If VG = VL, then D is connected directly to S, and we say the switch is closed.

What you learned about transistors in 2E6

• A useful, but overly simple model of the atom where the electrons rotate around the nucleus in discrete shells.

• The quantum model of an atom is more recent and accurate. It includes considerations of wave-particle duality and the Heisenberg uncertainty principle and electrons are considered to occupy a probabilistic cloud around the nucleus.

• Atomic number = number of protons, which is equal to the number of electrons in an electrically balanced atom.

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The Bohr Model of the Atom

Considering the Bohr Model only

• Electrons orbit the nucleus of an atom at certain distances from the nucleus.

• Electrons near the nucleus have less energy than those in more distant orbits.

• Only discrete values of electron energies exist within atomic structures.

• Each discrete distance (orbit) from the nucleus corresponds to a certain energy level. These levels are known as shells.

• The shells are designated 1, 2, 3, and so on, with 1 being closest to the nucleus.

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Bohr model of silicon atom

The Bohr Model of the Atom

Electrons per shell:

• Each shell has a fixed maximum number of electrons.

• The maximum number of electrons (Ne) that can exist in each shell of an atom is a fact of nature and can be calculated by:

where n is the number of the shell.

• Thus for shell 1

for shell 2

for shell 3

for shell 4

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Ne = 2n2

Ne = 2

Ne = 8

Ne = 18

Ne = 32

The Bohr Model of the Atom

• Electrons that are in orbits farther from the nucleus have higher energy and are less tightly bound to the atom than those closer to the nucleus.

• This is because the force of attraction between the positively charged nucleus and the negatively charged electron decreases with increasing distance from the nucleus.

• Electrons with the highest energy exist in the outermost shell of an atom and are relatively loosely bound to the atom.

• This outermost shell is known as the valence shell and electrons in this shell are called valence electrons.

• These valence electrons contribute to chemical reactions and bonding within the structure of a material and determine its electrical properties.

• When a valence electron gains sufficient energy from an external source, it can break free from its atom.

• This is the basis for conduction in materials.

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The Bohr Model of the Atom – Valence Electrons

Insulators, Conductors and Semiconductors

• Consider the representation of an atom as a valence shell and a core that consists of all the inner shells and the nucleus (e.g, carbon)

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• In insulators (which are usually compounds rather than single-element materials), valence electrons are tightly bound to the atoms; therefore, there are very few free electrons. Therefore they have very high resistivities (e.g., rubber, plastics, glass).

• The best conductors are single-element materials (metals) which are characterized by atoms with only one valence electron very loosely bound to the atom. These valence electrons become free electrons and can conduct electricity.

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• A semiconductor is a material that is between conductors and insulators in its ability to conduct electrical current. In its pure (intrinsic) state is neither a good conductor nor a good insulator. Single-element semiconductors include silicon (Si), and germanium (Ge). Several compound semiconductors are also commonly used (e.g., silicon germanium).

• The single-element semiconductors are characterized by atoms with four valence electrons. Silicon is the most commonly used semiconductor.

Insulators, Conductors and Semiconductors

• As already mentioned, when an electron acquires enough additional energy, it can leave the valence shell, become a free electron, and exist in what is known as the conduction band.

• The difference in energy between the valence band and the conduction band is called an energy or band gap. This is the amount of energy that a valence electron must have in order to jump from the valence to the conduction band.

• Once in the conduction band, the electron is free to move throughout the material and is not tied to any given atom.

• The energy gap or band gap is the difference between two energy levels and is “not allowed” in quantum theory.

• In conductors there is no gap meaning electrons can move freely into conduction band.

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Insulators, Conductors and Semiconductors – Band Gap

• A silicon (Si) atom with its four valence electrons shares an electron with each of its four neighbors to form a silicon crystal.

• This effectively creates eight shared valence electrons for each atom and produces a state of chemical stability.

• Also, this sharing of valence electrons produces the covalent bonds that hold the atoms together; each valence electron is attracted equally by the two adjacent atoms which share it.

• An intrinsic crystal is one that has no impurities.

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Semiconductors – Covalent Bonds

• Silicon at 0K has no electrons in the conduction band.

• An intrinsic silicon crystal at room temperature has sufficient thermal energy for some valence electrons to jump from the valence band into the conduction band, becoming free (aka conduction) electrons.

• When an electron jumps to the conduction band, a vacancy is left in the valence band

within the crystal. This vacancy is called a hole.

• For every electron raised to the conduction band by external energy, there is one hole left in the valence band, creating what is called an electron-hole pair.

• Recombination occurs when a conduction-band electron loses energy and falls back into a hole in the valence band.

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Semiconductors – Electron-Hole Pairs

Electron

• When a voltage is applied across a piece of intrinsic silicon, as shown below, the thermally generated free electrons in the conduction band, which are free to move randomly in the crystal structure, are now easily attracted toward the positive end.

• This movement of free electrons is one type of current in a semiconductive material and is called electron current.

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Semiconductors – Electron Current

• Another type of current occurs in the valence band, where the holes created by the free electrons exist. Electrons remaining in the valence band are still attached to their atoms and are not free to move randomly in the crystal structure as are the free electrons.

• However, a valence electron can move into a nearby hole with little change in its energy level, thus leaving another hole where it came from. So effectively the hole has moved from one place to another in the crystal structure, as illustrated below.

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• Although current in the valence band is produced by valence electrons, it is called hole current to distinguish it from electron current in the conduction band.

Semiconductors – Hole Current

• We can contrast the two types of charge movement in a semiconductor with

the charge movement in a metallic conductor, such as copper (atomic number 29).

• Copper atoms form a different type of crystal in which the atoms are not covalently bonded to each other but consist of a “sea” of positive ion cores, which are atoms stripped of their valence electrons.

• The valence electrons are attracted to the positive ions, keeping the positive ions together and forming the metallic bond.

• The valence electrons do not belong to a given atom, but to the crystal as a whole.

• Since the valence electrons in copper are free to move, the application of a voltage results in current.

• There is only one type of current—the movement of free electrons—because there are no “holes” in the metallic crystal structure.

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Semiconductors – Electron & Hole Current

Semiconductor Doping

• Since semiconductors are generally poor conductors, their conductivity can be drastically increased by the controlled addition of impurities to the intrinsic (pure) semiconductive material.

• This process, called doping, increases the number of current carriers (electrons or holes).

• The two categories of impurities are n-type and p-type.

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N-Type Semiconductors

• To increase the number of conduction-band electrons in intrinsic silicon, pentavalent impurity atoms are added.

• These are atoms with five valence electrons such as arsenic (As), phosphorus (P), bismuth (Bi), and antimony (Sb).

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• As illustrated on the right, each pentavalent atom (Sb, in this case) forms covalent

bonds with four adjacent silicon atoms.

• Four of the antimony atom’s valence electrons are used to form the covalent bonds with silicon atoms, leaving one extra electron.

• This extra electron becomes a conduction electron because it is not involved in bonding.

• Because the pentavalent atom gives up an electron, it is often called a donor atom.

• The number of conduction electrons can be carefully controlled by the number of impurity atoms added to the silicon.

• A conduction electron created by this doping process does not leave a hole in the valence band because it is in excess of the number required to fill the valence band.

• Since most of the current carriers are electrons, silicon doped with pentavalent atoms is an n-type semiconductor (n stands for the negative charge on an electron).

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• The electrons are called the majority carriers in n-type material. Although the majority of current carriers in n-type material are electrons, there are also a few holes that are created when electron-hole pairs are thermally generated.

• These holes are not produced by the addition of the pentavalent impurity atoms.

• Holes in an n-type material are called minority carriers.

N-Type Semiconductors

• To increase the number of holes in intrinsic silicon, trivalent impurity atoms are added.

• These are atoms with 3 valence electrons, e.g., boron (B), indium (In), and gallium (Ga).

• As shown on the right, each trivalent atom (B, in this case) forms covalent bonds with four adjacent silicon atoms.

• All three of the boron atom’s valence electrons are used in the covalent bonds; and, since four electrons are required, a hole results when each trivalent atom is added.

• Because the trivalent atom can take an electron, it is often referred to as an acceptor atom.

• As before, the number of holes can be carefully controlled by the number of trivalent impurity atoms added to the silicon.

• A hole created by this doping process is not accompanied by a conduction (free) electron.

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P-Type Semiconductors

• Since most of the current carriers are holes, silicon doped with trivalent atoms is called a p-type semiconductor.

• The holes are the majority carriers in p-type material.

• Although the majority of current carriers in p-type material are holes, there are also a few conduction-band electrons that are created when electron-hole pairs are thermally generated.

• These conduction-band electrons are not produced by the addition of the trivalent impurity atoms.

• Conduction-band electrons in p-type material are the minority carriers.

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P-Type Semiconductors

• NB: N- and P-Type Semiconductors are not negatively and positively charged!!

• Adding pentavalent atoms to (electrically neutral) silicon means adding atoms with 5 electrons in their valence shell. But these atoms have equal numbers of electrons and protons, i.e., they are electrically neutral too. So they add no net charge to the silicon.

• So, even though there are free electrons, the net overall charge is zero.

• Same story for trivalent atoms added to silicon to form p-type: electrically neutral.

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N- and P-Type Semiconductors

What we covered in this lecture

• Course outline – subject to change…

• Analogue electronics – what’s the point?

• Symbol convention – slide 8 for reference…

• Reminder of transistor introduction from 2E6.

• Revision of the Bohr Model of the atom, including:

• Shells, i.e., discrete energy levels.

• Definition of valence shell and valence electrons.

• Discussion of insulators, conductors and semiconductors in terms of valence electrons.

• Introduction of the notion of the band gap.

• Revision of covalent bonds.

• Notion of the creation of electron-hole pairs.

• Definition of electron current and hole current.

• Introduction of the notion of semiconductor doping, both n-type and p-type.

• Noted that denoting n-type and p-type semiconductors with n and p does not imply that they are negatively and positively charged.

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