PHYS-3301

Nov. 29, 2018

Lecture 25

Chapter. 10Molecules and Solids

Outline:

n10.1 Molecular Bonding and Spectran10.2 Stimulated Emission and Lasersn10.3 Structural Properties of Solidsn10.4 Thermal and Magnetic Properties of Solidsn10.5 Superconductivityn10.6 Applications of Superconductivity

In Chapter 7 & 8, we learned about the properties of individual atoms. This chapter builds on that knowledge to find out what happens when those atoms join together to form molecules & solids.

Stimulated emission:n If the incoming photon has the same energy as the emitted photon:

The result is two photons of the samewavelength and phase traveling in the same direction.Because the incoming photon just triggers emission of the second photon.

Stimulated Emission and LasersIt is possible to make the emission process occur in a more controlled way

Stimulated Emission and Lasers

Laser:n An acronym for “Light Amplification by the Stimulated Emission of Radiation”

Masers:n Microwaves are used instead of visible light.

The first working laser by Theodore H. Maiman in 1960

Stimulated emission is the fundamental physical process in a laser

A schematic diagram of a He-Ne laser. The coherent photon beam escapes through the partially silvered mirror.

It is possible to make the emission process occur in a more controlled way

n The body of the laser is a closed tube, filled with about a 9/1 ratio of helium and neon.

n Photons bouncing back and forth between two mirrors are used to stimulate the transitions in neon.

n Photons produced by stimulated emission will be coherent, and the photons that escape through the silvered mirror will be a coherent beam.

Scientific Applications of Lasers

n An extremely coherent and nondivergent beam is used in making precise determination of large and small distances. The speed of light in a vacuum is defined. c = 299,792,458 m/s.

n Pulsed lasers are used in thin-film deposition to study the electronic properties of different materials.

n The use of lasers in fusion researchq Inertial confinement:

A pellet of deuterium and tritium would be induced into fusion by an intense burst of laser light coming simultaneously from many directions.

Holography

The laser beam is split into two, one known as the object beam and the other as the reference beam. The object beam is expanded by passing it through a lens and used to illuminate the subject. The recording medium is located where this light, after being reflected or scattered by the subject, will strike it. The reference beam is expanded and made to shine directly on the medium, where it interacts with the light coming from the subject to create the desired interference pattern.

Other Laser Applications

n Used in surgery to make precise incisionsEx: eye operations

n We see in everyday life such as the scanning devices used by supermarkets and other retailersEx. Bar code of packaged product

CD and DVD playersn Laser light is directed toward disk tracks that contain encoded

information. The reflected light is then sampled and turned into electronic signals that produce a digital output.

Structural Properties of SolidsCondensed matter physics:n The study of the electronic

properties of solids.

Crystal structure:n The atoms are arranged in

extremely regular, periodic patterns.

n Max von Laue proved the existence of crystal structures in solids in 1912, using x-ray diffraction.

n The set of points in space occupied by atomic centers is called a lattice.

Superconductivity

n Superconductivity is characterized by the absence of electrical resistance and the expulsion of magnetic flux from the superconductor.

It is characterized by some macroscopic features:e.g. zero resistivity

- Onnes achieved temperatures approaching 1 K with liquid helium.

- In a superconductor the resistivity drops abruptly to zero at critical temperature Tc.

- Superconducting behavior tends to be similar within a given column of the periodic table.

The Search for a Higher Tc

n Keeping materials at extremely low temperatures is very expensive and requires cumbersome insulation techniques.

History of transition temperature

Applications of SuperconductivityMaglev:n Magnetic levitation of trains

n In an electrodynamic (EDS) system, magnets on the guideway repel the car to lift it.

n In an electromagnetic (EMS) system, magnets attached to the bottom of the car lie below the guideway and are attracted upward toward the guideway to lift the car.

Applications of SuperconductivityMaglev:n Magnetic levitation of trains

n In an electrodynamic (EDS) system, magnets on the guideway repel the car to lift it.

n In an electromagnetic (EMS) system, magnets attached to the bottom of the car lie below the guideway and are attracted upward toward the guideway to lift the car.

Chapter. 11Semiconductor Theory and Devices

Outline:

n11.1 Band Theory of Solidsn11.2 Semiconductor Theoryn11.3 Semiconductor Devicesn11.4 Nanotechnology

In Chapter 10 you learned about structural, thermal, and magnetic properties of solids. In this chapter we concentrate on electrical conduction.

Categories of Solids

n There are three categories of solids, based on their conducting properties: q Conductors, semiconductors, insulators

Categories of Solids

n The electrical conductivity at room temperature is quite different for each of these three kinds of solidsq Metals and alloys have the highest conductivities q followed by semiconductorsq and then by insulators

Semiconductor Resistivity vs. Temperature

Figure 11.1: (a) Resistivity versus temperature for a typical conductor. Notice the linear rise in resistivity with increasing temperature at all but very low temperatures. (b) Resistivity versus temperature for a typical conductor at very low temperatures. Notice that the curve flattens and approaches a nonzero resistance as T → 0. (c) Resistivity versus temperature for a typical semiconductor. The resistivity increases dramatically as T → 0.

n In order to account for decreasing resistivity with increasing temperature as well as other properties of semiconductors, a new theory known as the band theory is introduced.

n The essential feature of the band theory is that the allowed energy states for electrons are nearly continuous over certain ranges, called energy bands, with forbidden energy gaps between the bands.

Band Theory of Solids Band Theory and Conductivity

n Band theory helps us understand what makes a conductor, insulator, or semiconductor.1) Good conductors like copper can be understood using the free

electron.2) It is also possible to make a conductor using a material with its

highest band filled, in which case no electron in that band can be considered free.

3) If this filled band overlaps with the next higher band, however (so that effectively there is no gap between these two bands) then an applied electric field can make an electron from the filled band jump to the higher level.

n This allows conduction to take place, although typically with slightly higher resistance than in normal metals. Such materials are known as semimetals.

Valence and Conduction Bands

n The band structures of insulators and semiconductors resemble each other qualitatively. Normally there exists in both insulators and semiconductors a filled energy band (referred to as the valence band) separated from the next higher band (referred to as the conduction band) by an energy gap.

n If this gap is at least several electron volts, the material is an insulator. It is too difficult for an applied field to overcome that large an energy gap, and thermal excitations lack the energy to promote sufficient numbers of electrons to the conduction band.

n For energy gaps smaller than about 1 electron volt, it is possible for enough electrons to be excited thermally into the conduction band, so that an applied electric field can produce a modest current.

The result is a semiconductor.

Smaller energy gaps create semiconductors

11.3: Semiconductor Devices

pn-junction Diodesn Here p-type and n-type semiconductors are joined

together.

n The principal characteristic of a pn-junction diode is that it allows current to flow easily in one direction but hardly at all in the other direction.

We call these situations forward bias and reverse bias, respectively.

Operation of a pn-junction Diode

Figure 11.12: The operation of a pn-junction diode. (a) This is the no-bias case. The small thermal electron current (It) is offset by the electron recombination current (Ir). The net positive current (Inet) is zero. (b) With a DC voltage applied as shown, the diode is in reverse bias. Now Ir is slightly less than It. Thus there is a small net flow of electrons from p to n and positive current from n to p. (c) Here the diode is in forward bias. Because current can readily flow from p to n, Ir can be much greater than It. [Note: In each case, It and Ir are electron (negative) currents, but Inet indicates positive current.]

Light Emitting Diodesn Another important kind of diode is the light-emitting diode (LED).

Whenever an electron makes a transition from the conduction band to the valence band (effectively recombining the electron and hole) there is a release of energy in the form of a photon (Figure 11.17). In some materials the energy levels are spaced so that the photon is in the visible part of the spectrum. In that case, the continuous flow of current through the LED results in a continuous stream of nearly monochromatic light.

Figure 11.17: Schematic of an LED. A photon is released as an electron falls from the conduction band to the valence band. The band gap may be large enough that the photon will be in the visible portion of the spectrum.

Photovoltaic Cellsn An exciting application closely related to the LED is the solar cell, also known as the

photovoltaic cell. Simply put, a solar cell takes incoming light energy and turns it into electrical energy. A good way to think of the solar cell is to consider the LED in reverse (Figure 11.18). A pn-junction diode can absorb a photon of solar radiation by having an electron make a transition from the valence band to the conduction band. In doing so, both a conducting electron and a hole have been created. If a circuit is connected to the pn junction, the holes and electrons will move so as to create an electric current, with positive current flowing from the p side to the n side. Even though the efficiency of most solar cells is low, their widespread use could potentially generate significant amounts of electricity. Remember that the �solar constant� (the energy per unit area of solar radiation reaching the Earth) is over 1400 W/m2, and more than half of this makes it through the atmosphere to the Earth�s surface. There has been tremendous progress in recent years toward making solar cells more efficient.

Figure 11.18: (a) Schematic of a photovoltaic cell. Note the similarity to Figure 11.17. (b) A schematic showing more of the working parts of a real photovoltaic cell. From H. M. Hubbard, Science 244, 297-303 (21 April 1989).

n Another use of semiconductor technology is in the fabrication of transistors, devices that amplify voltages or currents in many kinds of circuits. The first transistor was developed in 1948 by John Bardeen, William Shockley, and Walter Brattain (Nobel Prize, 1956). As an example we consider an npn-junction transistor, which consists of a thin layer of p-type semiconductor sandwiched between two n-type semiconductors. The three terminals (one on each semiconducting material) are known as the collector, emitter, and base. A good way of thinking of the operation of the npn-junction transistor is to think of two pn-junction diodes back to back.

Transistors

Figure 11.22: (a) In the npn transistor, the base is a p-type material, and the emitter and collector are n-type. (b) The two-diode model of the npn transistor. (c) The npn transistor symbol used in circuit diagrams. (d) The pnp transistor symbol used in circuit diagrams.

n Consider now the npn junction in the circuit shown in Figure 11.23a. If the emitter is more heavily doped than the base, then there is a heavy flow of electrons from left to right into the base. The base is made thin enough so that virtually all of those electrons can pass through the collector and into the output portion of the circuit. As a result the output current is a very high fraction of the input current. The key now is to look at the input and output voltages. Because the base-collector combination is essentially a diode connected in reverse bias, the voltage on the output side can be made higher than the voltage on the input side. Recall that the output and input currents are comparable, so the resulting output power (current � voltage) is much higher than the input power.

Transistors

Figure 11.23: (a) The npn transistor in a voltage amplifier circuit. (b) The circuit has been modified to put the input between base and ground, thus making a current amplifier. (c) The same circuit as in (b) using the transistor circuit symbol.

Field Effect Transistors (FET)

n The three terminals of the FET are known as the drain, source, and gate, and these correspond to the collector, emitter, and base, respectively, of a bipolar transistor.

Figure 11.25: (a) A schematic of a FET. The two gate regions are connected internally. (b) The circuit symbol for the FET, assuming the source-to-drain channel is of n-type material and the gate is p-type. If the channel is p-type and the gate n-type, then the arrow is reversed. (c) An amplifier circuit containing a FET.

Semiconductor Lasersn Like the gas lasers described in Section 10.2, semiconductor lasers

operate using population inversion—an artificially high number of electrons in excited states

n In a semiconductor laser, the band gap determines the energy difference between the excited state and the ground state

n Semiconductor lasers use injection pumping, where a large forward current is passed through a diode creating electron-hole pairs, with electrons in the conduction band and holes in the valence band.

A photon is emitted when an electron falls back to the valence band to recombine with the hole.

Semiconductor Lasers

n Since their development, semiconductor lasers have been used in a number of applications, most notably in fiber-optics communication.

n One advantage of using semiconductor lasers in this application is their small size with dimensions typically on the order of 10−4 m.

n Being solid-state devices, they are more robust than gas-filled tubes.

Integrated Circuits

n The most important use of all these semiconductor devices today is not in discrete components, but rather in integrated circuits commonly called chips.

n Some integrated circuits contain a million or more components such as resistors, capacitors, transistors, and logic switches.

n Two benefits: miniaturization and processing speed

Moore�s Law and Computing Power

Figure 11.29: Moore�s law, showing the progress in computing power over a 30-year span, illustrated here with Intel chip names. The Pentium 4 contains over 50 million transistors. Courtesy of Intel Corporation. Graph from http://www.intel.com/research/silicon/mooreslaw.htm.

11.4: Nanotechnology

n Nanotechnology is generally defined as the scientific study and manufacture of materials on a submicron scale.

n These scales range from single atoms (on the order of 0.1 nm up to 1 micron (1000 nm).

n This technology has applications in engineering, chemistry, and the life sciences and, as such, is interdisciplinary.

Carbon Nanotubes

n In 1991, following the discovery of C60buckminsterfullerenes, or �buckyballs,� Japanese physicist Sumio Iijima discovered a new geometric arrangement of pure carbon into large molecules.

n In this arrangement, known as a carbon nanotube, hexagonal arrays of carbon atoms lie along a cylindrical tube instead of a spherical ball.

Structure of a Carbon NanotubeFigure 11.30: Model of a carbon nanotube, illustrating the hexagonal carbon pattern superimposed on a tubelike structure. There is virtually no limit to the length of the tube. FromChris Ewels/www.ewels.info

Carbon Nanotubes

n The basic structure shown in Figure 11.30 leads to two types of nanotubes. A single-walled nanotube has just the single shell of hexagons as shown.

n In a multi-walled nanotube, multiple layers are nested like the rings in a tree trunk.

n Single-walled nanotubes tend to have fewer defects, and they are therefore stronger structurally but they are also more expensive and difficult to make.

Applications of Nanotubes

n Because of their strength they are used as structural reinforcements in the manufacture of composite materialsq (batteries in cell-phones use nanotubes in this way)

n Nanotubes have very high electrical and thermal conductivities, and as such lead to high current densities in high-temperature superconductors.

Nanoscale Electronics

n One problem in the development of truly small-scale electronic devices is that the connecting wires in any circuit need to be as small as possible, so that they do not overwhelm the nanoscale components they connect.

n In addition to the nanotubes already described, semiconductor wires (for example indium phosphide) have been fabricated with diameters as small as 5 nm.

Nanoscale Electronics

n These nanowires have been shown useful in connecting nanoscale transistors and memory circuits.

These are referred to as nanotransistors.

Graphene

n A new material called graphene was first isolated in 2004. Graphene is a single layer of hexagonal carbon, essentially the way a single plane of atoms appears in common graphite.

n A. Geim and K. Novoselov received the 2010 Nobel Prize in Physics for �ground-breaking experiments.�Pure graphene conducts electrons much faster than other materials at room temperature.

n Graphene transistors may one day result in faster computing. Figure 11.33 Schematic diagram of graphene-based transistor developed at the

University of Manchester. The passage of a single electron from source to drain registers 1 bit of information—a 0 or 1 in binary code.

Graphene

Quantum Dotsn Quantum dots are nanostructures made of

semiconductor materials.q They are typically only a few nm across, containing up to 1000

atoms. q Each contains an electron-hole pair ]confined within the dot�s

boundaries, (somewhat analogous to a particle confined to a potential well discussed in Chapter 6.

n Properties result from the fact that the band gap varies over a wide range and can be controlled precisely by manipulating the quantum dot�s size and shape.q They can be made with band gaps that are nearly continuous

throughout the visible light range (1.8 to 3.1 eV) and beyond.

Nanotechnology and the Life Sciences

n The complex molecules needed for the variety of life on Earth are themselves examples of nanoscale design.

Examples of unusual materials designed for specific purposes include the molecules that make up claws, feathers, and even tooth enamel.

Information Science

n It�s possible that current photolithographic techniques for making computer chips could be extended into the hard-UV or soft x-ray range, with wavelengths on the order of 1 nm, to fabricate silicon-based chips on that scale.

n In the 1990s physicists learned that it is possible to take advantage of quantum effects to store and process information more efficiently than a traditional computer. To date, such quantum computers have been built in prototype but not mass-produced.