Vacuum Tubes and Semiconductor Electronics

• Devices use controlled electron flow
• Transistors were discovered in 1948 which changed the game

Vacuum Tubes

• Vacuum tubes, or valves, were common before transistors
• Vacuum diodes have two electrodes: anode and cathode
• Triodes have three electrodes: cathode, anode, and grid
• Tetrodes and pentodes have 4 and 5 electrodes respectively
• In vacuum tubes, a heated cathode supplies electrons
• The controlled flow occurs in a vacuum by varying voltage between electrodes
• Vacuum is required to prevent electrons from losing energy through collisions with air molecules
• Electrons can only flow from cathode to anode
• Vacuum tubes are bulky, consume high power, operate at high voltages (~100V)
• They also have limited life and low reliability

Solid-State Semiconductor Electronics

• The development started in the 1930s
• Some solid-state semiconductors and their junctions can control the number and direction of charge carriers
• Simple excitations like light, heat, or small voltages can change the number of mobile charges
• Charge carriers flow within the solid itself, which is different from vacuum tubes
• Semiconductor devices don't need external heating or large evacuated space
• They are small, consume low power, operate at low voltages
• Semiconductor devices have long life and high reliability
• Liquid Crystal Display (LCD) monitors with solid state electronics are replacing Cathode Ray Tubes (CRT)
• Naturally occurring crystal of galena (Lead sulphide, PbS) with a metal point contact was used as a detector of radio waves

Semiconductor Physics

• Junction diodes (2-electrode device) and bipolar action transistors (3-electrode device) are examples of semiconductor devices

Classification of Metals, Semiconductors, and Insulators

• Classification is based on conductivity or resistivity
• Electrical conductivity (σ) and resistivity (ρ = 1/σ) values of solids have broad ranges

Metals

• Have low resistivity (or high conductivity)
• ρ: 10⁻² - 10⁻⁸ Ωm
• σ: 10² - 10⁸ S m⁻¹

Semiconductors

• Have intermediate resistivity or conductivity
• ρ: 10⁻⁵ - 10⁶ Ωm
• σ: 10⁵ - 10⁻⁶ S m⁻¹

Insulators

• Have high resistivity (or low conductivity)
• ρ: 10¹¹ - 10¹⁹ Ωm
• σ: 10⁻¹¹ - 10⁻¹⁹ S m⁻¹
• Resistivity values are indicative and the differences extend further than just resistivity

Types of Semiconductors

• Elemental semiconductors: Silicon (Si) and Germanium (Ge)
• Compound semiconductors
• Inorganic: CdS, GaAs, CdSe, InP, etc.
• Organic: anthracene, doped pthalocyanines, etc.
• Organic polymers: polypyrrole, polyaniline, polythiophene, etc.
• Most devices are based on elemental semiconductors (Si or Ge) and compound inorganic semiconductors

Organic Semiconductors and Semiconducting Polymers:

• Organic semiconductors and semiconducting polymers mark the beginning of polymer-electronics and molecular-electronics
• Focus is on study of inorganic semiconductors, specifically Si and Ge
• General concept introduced for elemental semiconductors apply to most compound semiconductors

Energy Bands

• In an isolated atom, electron energy depends on its orbit
• When atoms form a solid, outer orbits come close or overlap
• Each electron in the crystal has a unique position with unique surrounding charges
• Each electron then has a different energy level

Energy Bands Explained

• Different energy levels with continuous energy variation form energy bands
• Valence band includes the energy levels of valence electrons
• Conduction band is the energy band above the valence band
• Without external energy, valence electrons stay in the valence band
• If the lowest level in the conduction band is lower than the highest level of the valence band, the electrons move into the conduction band
• Normally conduction band is empty
• If overlap then electrons move freely (metals)
• If there is a gap between the conduction band and valence band, electrons in valence band remain bound (insulators)
• Some electrons gain external energy to cross the energy gap
• They move into the conduction band, creating vacancies in the valence band
• The process allows both electrons and vacancies to conduct

Silicon (Si) and Germanium (Ge) Crystals

• Silicon and germanium crystals contain "N" atoms
• For Si, the outmost orbit is the 3rd orbit (n=3)
• For Ge, the outermost orbit is the 4th orbit (n=4)
• They have 4 electrons in the outermost orbit (2s + 2p electrons)
• Total # of outer electrons is 4N
• The max possible # of electrons in outer orbit is 8
• For the 4N valence electrons, there are 8N available energy states
• The energy band is split into 2 bands separated by energy gap (Eₒ)

Energy Band and Absolute Zero

• The lower band, completely occupied by 4N valence electrons at absolute zero, is the valence band
• The other band consisting of 4N energy states, called the conduction band, is completely empty at absolute zero
• Lowest energy level in conduction band is E
• Highest energy level in the valence band is Eᵥ
• Above E and below Eᵥ are many closely spaced energy levels

Energy Band Gap

• The energy band gap (E) is space between top of valence band and bottom of conduction band
• The energy gap (E) can be large, small, or zero, depending upon the material

Case 1: Metal

• Metals have the following characteristics:
• Can be a metal if the conduction band is partially filled
• Can be a metal if the valence band is partially empty
• Can be a metal if the conduction band and valence bands overlap
• Overlap allows electrons from valence band to move easily to the conduction band for significant electrical conduction
• Valence band can be partially empty, so a high level can move to a high level which allows for electrical conductivity
• Resistance of metals is low, and conductivity is high

Case II: Insulator

• Insulators have the following characteristics:
• A large band gap exists (E > 3 eV)
• No electrons in the conduction band, then there is no electrical conduction
• Energy gap too large for electrons to move from the valence band to the conduction band by thermal excitation

Case III: Semiconductor

• Semiconductors have the following characteristics:
• A finite but small band gap E_<3 eV exists
• Some electrons from valence band gain energy to cross the energy gap and then enter the conduction band
• Small number of electrons can move into conduction band
• Resistance of semiconductors is not as high as insulators

Intrinsic Semiconductor

• Germanium and silicon are the most common cases
• Lattice structure is called a diamond-like structure
• Each atom is surrounded by four nearest neighbors
• Silicon and germanium have four valence electrons
• In crystal structure, every atom shares one valence electron with each of its four neighbors
• They also, take one electron from each neighbor, making up valence bonds
• The shared electrons move back and forth between the atoms, holding them strongly together

2D Representation of Si or Ge Structure

• Schematic shows a covalent bond
• Shows a picture where bonds are intact
• This happens at low temperatures
• When the temperatures rise, thermal energy becomes available to electrons which then break away becoming free electrons, contributing to conduction
• The thermal energy effectively ionizes a few atoms in the crystal lattice
• Creates a vacancy

Vacancy in the Bond

• Neighbourhood is the vacany the free electron with negative charge which leaves a vacancy with an effect positive charge
• The vacancy with effective positive electronic charge is called a hole
• The hole behaves as an apparent free particle with effective positive charge
• In intrinsic semiconductors, the number of free electrons is equal the number of holes (n = n = n₁)
• n is called intrinsic carrier concentration
• Semiconductors can have holes that move
• If there is a hole at Site 1, an electron from covalent bond at Site 2 may jump to the vacant Site 1.
• Then after the jump, the whole is at Site 2 and Site 1 has an electron
• It seems like the whole has moved from Site 1 to Site 2
• The actual motion of electrons is only a convenient way of describing

Electric Fields and Holes

• There is an empty bond within crystal
• When there is an electric field, the holes move towards negative potential, giving out the hole current
• The total current is the sum of the electron current and the hole current

Generation of Conduction Electrons and Holes

• A process of recombination occurs simultaneously when electrons recombine with holes
• At equilibrium, generation rate and re-combination rates must be balanced
• Recombination occurs due to an electron colliding with a hole
• An intrinsic semiconductor behaves as an insulator at T=0 K

Behavior of Intrinsic Semiconductor at Higher Temperatures

• Thermal energy at higher temperatures excites some electrons from the valence band to the conduction band
• Electrons at higher temperature partially occupy the conduction band
• Some electrons shown in the conduction band come from a valence band which leaves equal number of holes there

Extrinsic Semiconductor

• Conductivity of intrinsic semiconductor depends on the temperature, but the conductivity is low at room temperature
• Extrinsic semiconductors or impurity semiconductors improve conductivity by adding a small amount of suitable impurity known as doping

Dopants

• Dopant atoms do not distort the original pure semiconductor lattice
• A necessary condition to attain this is that the sizes of the dopant and the semiconductor atoms should be nearly the same
• There are two types of dopants used in doping the tetravalent Si or Ge
• Pentavalent (valency 5); like Arsenic (As), Antimony (Sb), Phosphorous (P), etc.
• Trivalent (valency 3); like Indium (In), Boron (B), Aluminum (Al), etc.
• Doping changes the number of charge carriers and hence overall conductivity

n-type Semiconductor

• Silicon or germanium belongs to the fourth group in the periodic table
• Dopant element is taken from the nearby fifth or third group
• It is important to ensure that the dopant atom size remains close to that of silicon and germanium
• If silicon is doped with a pentavalent element, the pentavalent element can occupy the position of an atom in the crystal lattice
• In the crystal lattice, 4 of the 5 electrons bond with four silicon neighbors while the fifth remains weakly bound
• Ionization energy needed to set the electron free is very small
• This electron will be free to move through the lattice of the semiconductor, even at normal temperatures such as room temperature
• Pentavalent dopant donates one extra electron
• Pentavalent dopants are known as donor impurities
• The number of electrons for conduction depends strongly on doping level and is independent of any increase in temperature
• The number of free electrons generated by silicon atoms (with an equal # of holes) increases weakly with temperature

Doped Semiconductor

• In a doped semiconductor, the total number of conduction electrons is due to the electrons contributed by donors
• At the same time, that number is also caused by electrons that are generated intrinsically
• The total number of holes is only due to holes from the intrinsic source
• Rate of recombination of holes increases due to the increase in number of electrons
• With proper doping levels, the number of conduction electrons are made much larger than number of holes
• Semiconductor doped with pentavalent impurity, electrons become the majority carriers and holes the minority carriers
• These semiconductors are known as n-type semiconductors, where n >> n