Modern Physics for Engineers and Scientists videos and slides

The lectures are also relatively self-contained in covering the material. The lectures and text introduce (a) quantum mechanics and its use in describing atoms, materials and light, (b) statistical mechanics and its use in underpinning key thermodynamic ideas and in thermal distributions, and (c) applications of these ideas relevant to electronic and optoelectronic devices.

All the lectures for this course are listed below in sequence. Two lists are given: a short list just with built-in links to videos and slides and a full list (further down the page) that includes short abstracts and keywords for each lecture part, together with explicit links. The longer list may help in finding or searching for specific topics and referencing or linking parts of the course content.

Short list of lectures and slides

Lecture 1 Introduction and background

Lecture 1a – Introduction to the class – video and slides MPES 1.1

Lecture 1b – The background to modern physics – video and slides MPES 1.2

Lecture 1c – Transitioning to modern physics – video and slides MPES 1.3

Lecture 1 collected slides

Lecture 2 Oscillations and waves 1

Lecture 2a – Classical mechanics – video and slides MPES 2.2

Lecture 2b – Modes – video and slides MPES 2.3

Lecture 2c – Simple harmonic oscillator – video and slides MPES 2.4

Lecture 2 collected slides

Lecture 3 Oscillations and waves 2

Lecture 3a – Eigen equations and operators – video and slides MPES 2.4

Lecture 3b – The classical wave equation – video and slides MPES 2.5

Lecture 3c – The Helmholtz equation – video and slides MPES 2.6

Lecture 3d – Standing waves – video and slides MPES 2.7

Lecture 3 collected slides

Lecture 4 Oscillations and waves 3

Lecture 4a – A coupled oscillator – video and slides MPES 2.8

Lecture 4b – Inner products, orthogonality, and basis sets – video and slides MPES 2.9

Lecture 4c – Hermitian operators and sets of functions – video and slides MPES 2.9

Lecture 4 collected slides

Lecture 5 The quantum view of the world 1

Lecture 5a – The beginning of quantum mechanics – video and slides MPES 3.1

Lecture 5b – Electrons and atoms – video and slides MPES 3.2

Lecture 5 collected slides

Lecture 6 The quantum view of the world 2

Lecture 6a – Electrons and waves – video and slides MPES 3.2, 3.3

Lecture 6b – Solving Schrödinger’s equation –
a particle in a box – video and slides MPES 3.5

Lecture 6c – Normalization and probability – video and slides MPES 3.5

Lecture 6d – The nature of the particle-in-a-box solutions – video and slides MPES 3.5

Lecture 6 collected slides

Lecture 7 The quantum view of the world 3

Lecture 7a – Waves, diffraction and uncertainty – video and slides MPES 3.6

Lecture 7b – Diffraction by two slits – Young’s slits – video and slides MPES 3.6

Lecture 7c – Young’s slits and quantum mechanics – video and slides MPES 3.6

Lecture 7 collected slides

Lecture 8 The quantum view of the world 4

Lecture 8a – The nature of quantum mechanical particles – video and slides MPES 3.6

Lecture 8b – Waves and measurement – video and slides MPES 3.6

Lecture 8 collected slides

Lecture 9 The quantum view of the world 5

Lecture 9a – Tunneling – video and slides MPES 3.7

Lecture 9b – Solving for barriers of finite height – video and slides MPES 3.7

Lecture 9c – Tunneling through a barrier – video and slides MPES 3.7

Lecture 9 collected slides

Lecture 10 Particles, atoms, and crystals 1

Lecture 10a – The hydrogen atom and center-of-mass
coordinates – video and slides MPES 4.1 – 4.3

Lecture 10b – The hydrogen atom solutions and angular
behavior – video and slides MPES 4.3 – 4.4

Lecture 10c – Spherical harmonics for a classical problem – video and slides MPES 4.4

Lecture 10d – Polar plots of spherical harmonics – video and slides MPES 4.4

Lecture 10e – Spherical harmonics and atomic orbitals – video and slides MPES 4.4

Lecture 10 collected slides

Lecture 11 Particles, atoms, and crystals 2

Lecture 11a – Hydrogen atom radial solutions – video and slides MPES 4.5

Lecture 11b – Hydrogen atom complete solutions – video and slides MPES 4.5-4.6

Lecture 11c – Electron spin and Pauli exclusion – video and slides MPES 4.7

Lecture 11 collected slides

Lecture 12 Particles, atoms, and crystals 3

Lecture 12a – Many-electron atoms – video and slides MPES 4.8

Lecture 12b – Filling “shells” in atoms – video and slides MPES 4.8

Lecture 12c – Fermions and bosons – video and slides MPES 4.9

Lecture 12d – Identical particles – video and slides MPES 4.9

Lecture 12 collected slides

Lecture 13 Particles, atoms, and crystals 4

Lecture 13a – Coupled systems – video and slides MPES 4.10

Lecture 13b – Crystals – video and slides MPES 4.11

Lecture 13c – Emergence of bands – video and slides MPES 4.12

Lecture 13 collected slides

Lecture 14 Particles, atoms, and crystals 5

Lecture 14a – Band structures in crystals – video and slides MPES 4.13

Lecture 14b – The Bloch theorem – video and slides MPES 4.13

Lecture 14c – Solving with periodic boundary conditions – video and slides MPES 4.13

Lecture 14 collected slides

Lecture 15 Particles, atoms, and crystals 6

Lecture 15a – Band structures – video and slides MPES 4.14

Lecture 15b – Crystal momentum and effective mass – video and slides MPES 4.14

Lecture 15c – Band structures in three dimensions – video and slides MPES 4.15

Lecture 15d – Plotting actual band structures – video and slides MPES 4.15

Lecture 15e – Metals, semiconductors and insulators – video and slides MPES 4.16

Lecture 15 collected slides

Lecture 16 Thermal distributions 1

Lecture 16a – Tossing coins, microstates, and macrostates – video and slides MPES 5.2

Lecture 16b – Binomial distribution and Stirling’s
approximation – video and slides MPES 5.2

Lecture 16c – Two-state spin systems and microstates – video and slides MPES 5.3

Lecture 16 collected slides

Lecture 17 Thermal distributions 2

Lecture 17a – Systems in thermal contact – video and slides MPES 5.3

Lecture 17b – Maximizing multiplicities for spin systems – video and slides MPES 5.3

Lecture 17c – Maximizing multiplicity for general systems – video and slides MPES 5.4

Lecture 17 collected slides

Lecture 18 Thermal distributions 3

Lecture 18a – Entropy and temperature – video and slides MPES 5.4

Lecture 18b – Entropy and heat flow – video and slides MPES 5.4

Lecture 18c – Carnot efficiency limit for heat engines – video and slides MPES 5.5

Lecture 18 collected slides

Lecture 19 Thermal distributions 4

Lecture 19a – The Boltzmann factor – video and slides MPES 5.6

Lecture 19b – Chemical potential – video and slides MPES 5.7

Lecture 19c – Chemical potential and the Gibbs factor – video and slides MPES 5.7

Lecture 19 collected slides

Lecture 20 Thermal distributions 5

Lecture 20a – The Fermi-Dirac distribution – video and slides MPES 5.8

Lecture 20b – The Bose-Einstein and Planck distributions – video and slides MPES 5.8

Lecture 20c – The Maxwell-Boltzmann distribution – video and slides MPES 5.8

Lecture 20 collected slides

Lecture 21 Bands and electronic devices

Lecture 21a – Electrons and holes in bands – video and slides MPES 6.2

Lecture 21b – Semiconductor doping and diodes – video and slides MPES 6.3, 6.4

Lecture 21c – Voltages and Fermi levels – video and slides MPES 6.4 (and 5.7 for equivalent chemical potential definition)

Lecture 21d – Biasing semiconductor devices – video and slides MPES 6.4

Lecture 21 collected slides

Lecture 22 Light and quantum mechanics 1

Lecture 22a – Light, the photoelectric effect, and the
photon – video and slides MPES 7.2

Lecture 22b – Light and modes – video and slides MPES 7.3

Lecture 22c – Thermal radiation – video and slides MPES 7.4

Lecture 22 collected slides

Lecture 23 Light and quantum mechanics 2

Lecture 23a – Black body radiation and Kirchhoff’s law – video and slides MPES 7.5

Lecture 23b – Einstein’s A and B coefficient argument – video and slides MPES 7.6

Lecture 23 collected slides

Lecture 24 Semiconductor optoelectronics 1

Lecture 24a – Optoelectronic devices and photodetectors – video and slides MPES 8.1, 8.2

Lecture 24b – Light emission – video and slides MPES 8.3

Lecture 24 collected slides

Lecture 25 Semiconductor optoelectronics 2

Lecture 25a – Absorption and emission processes – video and slides MPES 8.3

Lecture 25b – Lasers – video and slides MPES 8.3

Lecture 25c – Epilogue – video and slides MPES Chapter 9

Lecture 25 collected slides

Full list of lectures and slides, with abstracts and keywords

Lecture 1 Introduction and background

Lecture 1a – Introduction to the class MPES 1.1

This lecture introduces the motivation for why we need ideas of modern physics so we can understand the world around us and engineer the technologies that make it work. It summarizes the topics to be taught in later lectures, including quantum mechanics and statistical mechanics. Specific topics include the quantum view of the world, particles, atoms and crystals, thermal distributions, bands and electronic devices, light and quantum mechanics, and semiconductor optoelectronics.

Keywords: Physics, Quantum physics, Statistical mechanics, Crystalline semiconductors, Quantum optics, Optoelectronic devices

Video: https://purl.stanford.edu/rs056yh7155 DOI: https://doi.org/10.25740/rs056yh7155

Slides: https://purl.stanford.edu/sq388rv0716 DOI: https://doi.org/10.25740/sq388rv0716

Lecture 1b – The background to modern physics MPES 1.2

This lecture part summarizes the background to modern physics. It starts with early ideas of matter, through the development of the scientific method and its consequences for understanding of matter, and continues with the development of laws of motion. It then introduces the development of physical concepts of light and electromagnetism through to Maxwell’s equations. Finally, it summarizes the history of the understanding of heat and thermodynamics, up to the ideas of the second law of thermodynamics and entropy.

Keywords: History of science, Matter, Laws of motion, Heat, Thermodynamics, Entropy

Video: https://purl.stanford.edu/pd853tx7523 DOI: https://doi.org/10.25740/pd853tx7523

Slides: https://purl.stanford.edu/vb612ph6646 DOI: https://doi.org/10.25740/vb612ph6646

Lecture 1c – Transitioning to modern physics MPES 1.3

This lecture part summarizes the state of our knowledge of what we could call “classical” physics as of about 1870, and our ability to exploit it, including electromagnetism and thermodynamics, and the beginning of the transition to the ideas of modern physics, including the basis of chemistry, the physical processes of light, and what lies behind thermodynamics.

Keywords: Classical physics, Light, Thermodynamics, Chemistry

Video: https://purl.stanford.edu/qm226hf2245 DOI: https://doi.org/10.25740/qm226hf2245

Slides: https://purl.stanford.edu/jy074vx1575 DOI: https://doi.org/10.25740/jy074vx1575

Lecture 1 collected slides

Lecture 2 Oscillations and waves 1

Lecture 2a – Classical mechanics MPES 2.2

This lecture part reminds us of classical mechanics ideas like kinetic energy, momentum, Newton’s second law, potential energy and force, and the relations between these.

Keywords: Kinetic energy, Momentum, Newton’s second law, Potential energy, Force

Video: https://purl.stanford.edu/bf612xk1137 DOI: https://doi.org/10.25740/bf612xk1137

Slides: https://purl.stanford.edu/vr422dz4554 DOI: https://doi.org/10.25740/vr422dz4554

Lecture 2b – Modes MPES 2.3

This lecture part introduces the idea of modes, including simple physical oscillating modes. It emphasizes their generality across many areas of physics and mathematics, including acoustics, mechanical and electrical engineering, quantum mechanics. It introduces examples from musical instruments, acoustics and vibrations, including standing waves.

Keywords: Modes, Standing waves, Oscillations in musical instruments

Video: https://purl.stanford.edu/vr438tv1876 DOI: https://doi.org/10.25740/vr438tv1876

Slides: https://purl.stanford.edu/sy173zy8535 DOI: https://doi.org/10.25740/sy173zy8535

Lecture 2c – Simple harmonic oscillator MPES 2.4

This lecture part introduces the physics and mathematical description of a simple harmonic oscillator, as in a mass on a spring.

Video: https://purl.stanford.edu/cy938rs1418 DOI: https://doi.org/10.25740/cy938rs1418

Slides: https://purl.stanford.edu/tg077df3128 DOI: https://doi.org/10.25740/tg077df3128

Keywords: Simple harmonic oscillator, Oscillator

Lecture 2 collected slides

Lecture 3 Oscillations and waves 2

Lecture 3a – Eigen equations and operators MPES 2.4

Starting with the simple harmonic oscillator as an example, this lecture part introduces the ideas of linear operators and eigen equations.

Video: https://purl.stanford.edu/dy414rr3745 DOI: https://doi.org/10.25740/dy414rr3745

Slides: https://purl.stanford.edu/bt435nk2445 DOI: https://doi.org/10.25740/bt435nk2445

Keywords: Linear operators, Eigen equations, Simple harmonic oscillator

Lecture 3b – The classical wave equation MPES 2.5

This lecture part introduces and derives the classical wave equation, as for a wave on a string

Video: https://purl.stanford.edu/sr153qs8657 DOI: https://doi.org/10.25740/sr153qs8657

Slides: https://purl.stanford.edu/tv859dj3309 DOI: https://doi.org/10.25740/tv859dj3309

Keywords: Wave equation, Wave on a string

Lecture 3c – The Helmholtz equation MPES 2.6

This lecture part introduces the Helmholtz wave equation, which is the classical wave equation for one specific frequency.

Video: https://purl.stanford.edu/hf639rj0381 DOI: https://doi.org/10.25740/hf639rj0381

Slides: https://purl.stanford.edu/cp506cb7154 DOI: https://doi.org/10.25740/cp506cb7154

Keywords: Helmholtz wave equation, Wave equation

Lecture 3d – Standing waves MPES 2.7

This lecture part introduces standing waves on a string stretched between two supports. This also introduces the idea of boundary conditions when solving differential equations.

Video: https://purl.stanford.edu/cj689wp2705 DOI: https://doi.org/10.25740/cj689wp2705

Slides: https://purl.stanford.edu/kd448wh1664 DOI: https://doi.org/10.25740/kd448wh1664

Keywords: Standing waves, Boundary conditions (Differential equations)

Lecture 3 collected slides

Lecture 4 Oscillations and waves 3

Lecture 4a – A coupled oscillator MPES 2.8

This lecture part introduces coupled oscillating systems, using the example of two masses connected by springs in a line between two supports, deriving the resulting oscillating modes as good examples of eigen modes or eigen functions, and preparing for more complicated coupled systems in quantum mechanics and elsewhere.

Video: https://purl.stanford.edu/gj820np3673 DOI: https://doi.org/10.25740/gj820np3673

Slides: https://purl.stanford.edu/mn622wd9822 DOI: https://doi.org/10.25740/mn622wd9822

Keywords: Coupled oscillator

Lecture 4b – Inner products, orthogonality, and basis sets MPES 2.9

This lecture part introduces core mathematical ideas needed to understand oscillating modes and, later, quantum mechanical states. Specifically, it introduces linear algebra ideas of inner products, which generally also define the idea of orthogonality, and basis sets of functions that can be used to describe other functions.

Video: https://purl.stanford.edu/vq983jh7795 DOI: https://doi.org/10.25740/vq983jh7795

Slides: https://purl.stanford.edu/rv182yy1324 DOI: https://doi.org/10.25740/rv182yy1324

Keywords: Inner product, Orthogonality, Basis sets

Lecture 4c – Hermitian operators and sets of functions MPES 2.9

This lecture part starts by introducing key ideas for working with complex matrices, especially the ideas of Hermitian adjoints and Hermitian matrices or, more generally, Hermitian operators. Such Hermitian operators are very useful for describing many physical systems, such as simple oscillators, and also later quantum mechanical systems. Among other properties, their eigenfunctions are orthogonal, and can represent, for example, the modes of many oscillating systems. Such eigenfunctions also generate mathematically complete and orthogonal basis sets for describing their corresponding physical systems – a very powerful property.

Video: https://purl.stanford.edu/pb380yd0294 DOI: https://doi.org/10.25740/pb380yd0294

Slides: https://purl.stanford.edu/sn311ft9797 DOI: https://doi.org/10.25740/sn311ft9797

Keywords: Linear operators, Hermitian adjoint, Hermitian matrix, Complete sets

Lecture 4 collected slides

Lecture 5 The quantum view of the world 1

Lecture 5a – The beginning of quantum mechanics MPES 3.1

This lecture part starts by summarizing many of the puzzles in physics towards the end of the 19th century, including in particular the form in color or wavelength of the light from the sun, electric light bulbs, or more generally the light emission from a hot object if it is perfectly “black” or absorbing at all wavelengths. The resolution of this problem by Max Planck became the start of modern quantum mechanics.

Video: https://purl.stanford.edu/wr173vx1775 DOI: https://doi.org/10.25740/wr173vx1775

Slides: https://purl.stanford.edu/sx884mb7664 DOI: https://doi.org/10.25740/sx884mb7664

Keywords: Quantum mechanics, Spectrum of hot objects

Lecture 5b – Electrons and atoms MPES 3.2

This lecture part summarizes the early ideas to understand the quantum mechanics of atoms, including the Bohr model that, though not correct, gave a first quantum mechanical explanation of aspects of atomic emission lines, and helped lead towards the later correct models.

Video: https://purl.stanford.edu/yy363hk6055 DOI: https://doi.org/10.25740/yy363hk6055

Slides: https://purl.stanford.edu/cp824hf8994 DOI: https://doi.org/10.25740/cp824hf8994

Keywords: Bohr model

Lecture 5 collected slides

Lecture 6 The quantum view of the world 2

Lecture 6a – Electrons and waves MPES 3.2, 3.3

This lecture part introduces the idea of electrons as waves, starting with de Broglie’s hypothesis, and then leading into Schroedinger’s (time-independent) wave equation, briefly summarizing also the subsequent early evidence for electrons behaving as waves.

Video: https://purl.stanford.edu/kc067pb5569 DOI: https://doi.org/10.25740/kc067pb5569

Slides: https://purl.stanford.edu/mn915cg4923 DOI: https://doi.org/10.25740/mn915cg4923

Keywords: de Broglie hypothesis, Electron diffraction, Schrödinger equation

Lecture 6b – Solving Schrödinger’s equation –
a particle in a box MPES 3.5

This lecture part introduces and solves the simple quantum mechanical problem of a particle in a box, illustrating how solving Schrödinger’s equation leads to discrete energy levels and eigen functions that we can think of as wavefunctions.

Video: https://purl.stanford.edu/sz213qv3851 DOI: https://doi.org/10.25740/sz213qv3851

Slides: https://purl.stanford.edu/vs499pp9532 DOI: https://doi.org/10.25740/vs499pp9532

Keywords: Particle in a box, Schrödinger equation

Lecture 6c – Normalization and probability MPES 3.5

This lecture part introduces the idea of “normalization” of a wavefunction, which then means that the modulus squared of the wavefunction directly gives the probability of finding the particle in that vicinity (strictly, the probability density)

Video: https://purl.stanford.edu/xt101qb9456 DOI: https://doi.org/10.25740/xt101qb9456

Slides: https://purl.stanford.edu/jz515cg5099 DOI: https://doi.org/10.25740/jz515cg5099

Keywords: Normalization of the wavefunction, Probability density

Lecture 6d – The nature of the particle-in-a-box solutions MPES 3.5

This lecture part uses the solutions to the particle-in-a-box problem to illustrate several general behaviors found in quantum mechanics, including the notion of only specific allowed energy “states”, quantum numbers that label these states, the notion of “parity” or odd or even symmetry of wavefunctions, and other quantum mechanical behaviors, including “zero-point energy”, and points in space that the electron in a given state will never be found. This particle-in-a-box problem allows simple estimates of the energies of quantum mechanical electron states when the electron is “quantum-confined” in a small space.

Video: https://purl.stanford.edu/qr141gt0040 DOI: https://doi.org/10.25740/qr141gt0040

Slides: https://purl.stanford.edu/fr754sk2761 DOI: https://doi.org/10.25740/fr754sk2761

Keywords: Particle in a box, Zero-point energy, Parity of a wavefunction, Quantum confinement

Lecture 6 collected slides

Lecture 7 The quantum view of the world 3

Lecture 7a – Waves, diffraction and uncertainty MPES 3.6

This lecture part introduces the idea of uncertainty principles, first by using a classical uncertainty principle common for most kinds of waves – the (inverse) relation between the size of an aperture and the diffraction angle or “spread” of the wave. When applied to quantum mechanical waves, we can justify the Heisenberg uncertainty principle. The meaning of the uncertainty principle in quantum mechanics is often unfortunately mixed up with the difficult issue of measurement in quantum mechanics and the “collapse of the wavefunction”.

Video: https://purl.stanford.edu/gt525kd3441 DOI: https://doi.org/10.25740/gt525kd3441

Slides: https://purl.stanford.edu/cg993bh9578 DOI: https://doi.org/10.25740/cg993bh9578

Keywords: Heisenberg uncertainty principle, Diffraction angle, Collapse of the wavefunction, Quantum mechanical measurement

Lecture 7b – Diffraction by two slits – Young’s slits MPES 3.6

This lecture part introduces the classical wave behavior of Young’s slits – two closely spaced slits in a mask that lead to a diffraction pattern behind the mask that, among other things, verifies light is a wave and allows a measurement of its wavelength.

Video: https://purl.stanford.edu/hj539ht2308 DOI: https://doi.org/10.25740/hj539ht2308

Slides: https://purl.stanford.edu/wm946hq0961 DOI: https://doi.org/10.25740/wm946hq0961

Keywords: Young’s slits, Diffraction

Lecture 7c – Young’s slits and quantum mechanics MPES 3.6

This lecture part discusses a classic conundrum in quantum mechanics that is illustrated by Young’s slits. Electrons do diffract as expected by Young’s slits to give an interference pattern, but we apparently cannot “know” which slit the electron went through. In quantum mechanics, in one view that question is meaningless; indeed if we do measure that, we lose the interference pattern.

Video: https://purl.stanford.edu/xg100gf3909 DOI: https://doi.org/10.25740/xg100gf3909

Slides: https://purl.stanford.edu/tw704kw8870 DOI: https://doi.org/10.25740/tw704kw8870

Keywords: Quantum mechanical measurement, Young’s slits

Lecture 7 collected slides

Lecture 8 The quantum view of the world 4

Lecture 8a – The nature of quantum mechanical particles MPES 3.6

This lecture part deals with the nature of quantum mechanical particles, or their “ontology”, pointing out that many of the problems we have with understanding quantum mechanical particles come from us bringing along the ontology of classical particles when we use the word “particle” in quantum mechanics. Many of these problems disappear if we stop doing that, and there are classical analogies that can help with the concepts.

Video: https://purl.stanford.edu/hz252wh8692 DOI: https://doi.org/10.25740/hz252wh8692

Slides: https://purl.stanford.edu/ny971sf7296 DOI: https://doi.org/10.25740/ny971sf7296

Keywords: Ontology and quantum mechanics, Quantum mechanical particles

Lecture 8b – Waves and measurement MPES 3.6

This lecture part discusses the subtle issues of quantum mechanical waves and measurement. Such waves may not themselves be measurable entities, and that resolves some of the apparent contradictions of quantum mechanics. This lecture part extends the discussion of quantum mechanical measurement. It discusses Born’s hypothesis that is essentially that the modulus squared of the wavefunction (not the wavefunction itself) gives probabilities in measurement. This hypothesis is also generalized in quantum mechanics to give probabilities of other quantities after measurement. A brief discussion is also given of the measurement problem more generally – the notion that we may not be able to describe the measurement process using quantum mechanics – and some of the proposed solutions to this problem.

Video: https://purl.stanford.edu/mh418vy8682 DOI: https://doi.org/10.25740/mh418vy8682

Slides: https://purl.stanford.edu/qr315cc5681 DOI: https://doi.org/10.25740/qr315cc5681

Keywords: Measurement problem in quantum mechanics, Born’s rule

Lecture 8 collected slides

Lecture 9 The quantum view of the world 5

Lecture 9a – Tunneling MPES 3.7

This lecture part introduces the idea of quantum mechanical tunneling, in which a particle such as an electron can penetrate into or even through a barrier that is too “high”. This is a core behavior in quantum mechanics and occurs routinely in electronic devices, for example. The problem of an electron and a finite barrier is solved to describe this behavior.

Video: https://purl.stanford.edu/wj806yg0901 DOI: https://doi.org/10.25740/wj806yg0901

Slides: https://purl.stanford.edu/xs652wr9105 DOI: https://doi.org/10.25740/xs652wr9105

Keywords: Quantum mechanical tunneling

Lecture 9b – Solving for barriers of finite height MPES 3.7

This lecture part gives a more detailed solution for an electron tunneling “into” a barrier, including the necessary “boundary conditions” in quantum mechanics for solving the Schroedinger equation in detail for this problem.

Video: https://purl.stanford.edu/bt995tb8796 DOI: https://doi.org/10.25740/bt995tb8796

Slides: https://purl.stanford.edu/dz392qh4115 DOI: https://doi.org/10.25740/dz392qh4115

Keywords: Quantum mechanical tunneling

Lecture 9c – Tunneling through a barrier MPES 3.7

This lecture part shows the solutions for a particle tunneling through a barrier that is too “high”, showing the wave phenomena of both partial transmission and partial reflection.

Video: https://purl.stanford.edu/zj462wx5618 DOI: https://doi.org/10.25740/zj462wx5618

Slides: https://purl.stanford.edu/yf622br4239 DOI: https://doi.org/10.25740/yf622br4239

Keywords: Quantum mechanical tunneling

Lecture 9 collected slides

Lecture 10 Particles, atoms, and crystals 1

Lecture 10a – The hydrogen atom and center-of-mass
coordinates MPES 4.1 – 4.3

This lecture part starts on the quantum mechanical solution of the hydrogen atom, one of the major triumphs of quantum mechanics and the ultimate basis for much of our understanding of all atoms in chemistry. Here the “center of mass” coordinate view of the electron and the proton in the hydrogen atom is constructed as the first part of this solution

Video: https://purl.stanford.edu/zw467cn4933 DOI: https://doi.org/10.25740/zw467cn4933

Slides: https://purl.stanford.edu/vd033ck8060 DOI: https://doi.org/10.25740/vd033ck8060

Keywords: Hydrogen atom, Center of mass coordinates

Lecture 10b – The hydrogen atom solutions and angular
behavior MPES 4.3 – 4.4

This lecture part continues the quantum mechanical solution of the hydrogen atom, starting the discussion of the angular behavior of resulting wavefunction solution, and introducing the so-called spherical harmonics that ultimately lead to the shape of atomic orbitals.

Video: https://purl.stanford.edu/gm561gs5836 DOI: https://doi.org/10.25740/gm561gs5836

Slides: https://purl.stanford.edu/rt925jm7079 DOI: https://doi.org/10.25740/rt925jm7079

Keywords: Spherical harmonics, Hydrogen atom

Lecture 10c – Spherical harmonics for a classical problem MPES 4.4

This lecture part gives a simple visualization of the spherical harmonic functions that form part of the hydrogen atom solution. These functions are also the solutions to some classical problems, including the vibrations of a spherical shell. Visualizing those possible vibrations gives a useful and simple view of the nature of spherical harmonic functions.

Video: https://purl.stanford.edu/qb985kq9531 DOI: https://doi.org/10.25740/qb985kq9531

Slides: https://purl.stanford.edu/sj577wq4370 DOI: https://doi.org/10.25740/sj577wq4370

Keywords: Spherical harmonics, Hydrogen atom

Lecture 10d – Polar plots of spherical harmonics MPES 4.4

This lecture part shows spherical harmonics in so-called “polar” plots, which is the typical way they are shown in discussions of atomic orbitals in chemistry.

Video: https://purl.stanford.edu/jq656hz4970 DOI: https://doi.org/10.25740/jq656hz4970

Slides: https://purl.stanford.edu/sz761sb9879 DOI: https://doi.org/10.25740/sz761sb9879

Keywords: Spherical harmonics, Hydrogen atom

Lecture 10e – Spherical harmonics and atomic orbitals MPES 4.4

This lecture part relates the description of spherical harmonics in terms of quantum numbers (usually l and m in quantum mechanics) to the “spdf” notation common in discussing atomic orbitals in chemistry, and relates them to angular momentum in quantum mechanics.

Video: https://purl.stanford.edu/rq562fh3064 DOI: https://doi.org/10.25740/rq562fh3064

Slides: https://purl.stanford.edu/vr825xw4281 DOI: https://doi.org/10.25740/vr825xw4281

Keywords: Spherical harmonics, Hydrogen atom, Angular momentum

Lecture 10 collected slides

Lecture 11 Particles, atoms, and crystals 2

Lecture 11a – Hydrogen atom radial solutions MPES 4.5

This lecture part shows the radial parts of the solution for the hydrogen atom wavefunction

Video: https://purl.stanford.edu/sd796kz9548 DOI: https://doi.org/10.25740/sd796kz9548

Slides: https://purl.stanford.edu/ks519mh9217 DOI: https://doi.org/10.25740/ks519mh9217

Keywords: Hydrogen atom, Schrödinger equation

Lecture 11b – Hydrogen atom complete solutions MPES 4.6

This lecture part shows simulated images of the shape of the hydrogen atom wavefunctions (or, to be more precise, the probability densities) for various of these “orbitals”. It also summarizes the meaning and use of the three major quantum numbers, n, l, and m, used to describe these wavefunctions or orbitals.

Video: https://purl.stanford.edu/rb635yj1151 DOI: https://doi.org/10.25740/rb635yj1151

Slides: https://purl.stanford.edu/dd805pk8481 DOI: https://doi.org/10.25740/dd805pk8481

Keywords: Hydrogen atom, Schrödinger equation, Hydrogen orbitals

Lecture 11c – Electron spin and Pauli exclusion MPES 4.7

This lecture part introduces the idea of electron spin. Together with the Pauli exclusion principle, which states that only one electron can occupy a given quantum mechanical state, these can explain the occupation of “orbitals” or atomic states in atoms.

Video: https://purl.stanford.edu/jb407pr1284 DOI: https://doi.org/10.25740/jb407pr1284

Slides: https://purl.stanford.edu/yk088ct4957 DOI: https://doi.org/10.25740/yk088ct4957

Keywords: Quantum mechanical spin, Pauli exclusion principle

Lecture 11 collected slides

Lecture 12 Particles, atoms, and crystals 3

Lecture 12a – Many-electron atoms MPES 4.8

This lecture part starts the discussion of atoms other than hydrogen, which are necessarily “many-electron” atoms. Many of the ideas that are exact for the hydrogen atom can be applied approximately to these atoms, including the idea that the potential energy is approximately still “central” (depending approximately only on the distance from the center of the nucleus and approximately not depending on angle).

Video: https://purl.stanford.edu/wz531gj0265 DOI: https://doi.org/10.25740/wz531gj0265

Slides: https://purl.stanford.edu/qy836fd1894 DOI: https://doi.org/10.25740/qy836fd1894

Keywords: Many-electron atoms, Central potential

Lecture 12b – Filling “shells” in atoms MPES 4.8

This lecture part introduces the idea of electrons filling successive “shells” in atoms. This idea helps in understanding chemical properties. A useful rule for the order of the filling of the shells is Madelung’s rule. Though not always correct, it works for most atoms, and is a useful guide. Examples are given.

Video: https://purl.stanford.edu/nd410hn2402 DOI: https://doi.org/10.25740/nd410hn2402

Slides: https://purl.stanford.edu/yc280kj4124 DOI: https://doi.org/10.25740/yc280kj4124

Keywords: Madelung’s rule, Atomic shells, Atomic orbitals, Many-electron atoms

Lecture 12c – Fermions and bosons MPES 4.9

This lecture part introduces the ideas of fermions, which have half integer spin (usually 1/2), and bosons, which have integer spin (for example, 1). Fermions obey Pauli exclusion, but bosons do not. Common misconceptions are also discussed.

Video: https://purl.stanford.edu/xh278hq3961 DOI: https://doi.org/10.25740/xh278hq3961

Slides: https://purl.stanford.edu/fd833vr4122 DOI: https://doi.org/10.25740/fd833vr4122

Keywords: Fermions, Bosons, Pauli exclusion principle

Lecture 12d – Identical particles MPES 4.9

This lecture part describes the quantum mechanical notion of identical particles. Particles in quantum mechanics are identical in the way that dollars in a bank account are identical, in contrast to dollar bills, which are never identical (they have different serial numbers). This leads to quite different counting of possible states of multiple particles.

Video: https://purl.stanford.edu/cn674qm1512 DOI: https://doi.org/10.25740/cn674qm1512

Slides: https://purl.stanford.edu/qf727hz2590 DOI: https://doi.org/10.25740/qf727hz2590

Keywords: Identical particles, Fermions, Bosons

Lecture 12 collected slides

Lecture 13 Particles, atoms, and crystals 4

Lecture 13a – Coupled systems MPES 4.10

This lecture part introduces the idea of coupled systems in quantum mechanics, using the example of two “rectangular” potential wells with a thin barrier between them. What would have been isolated states in two separate wells turn into two coupled states, a “symmetric” one generally with lower energy and an “antisymmetric” one generally with higher energy. These lower and higher energy states introduce an idea common in understanding some kinds of chemical bonds, with these states representing “bonding” and “antibonding” states.

Video: https://purl.stanford.edu/jk870rb4220 DOI: https://doi.org/10.25740/jk870rb4220

Slides: https://purl.stanford.edu/dn955nd5743 DOI: https://doi.org/10.25740/dn955nd5743

Keywords: Chemical bonding, Chemical antibonding, Coupled wells

Lecture 13b – Crystals MPES 4.11

This lecture part introduces the idea of crystals – materials whose properties are periodic in space – together with key concepts like unit cells and crystal lattices. Example lattices in common electronic and optoelectronic devices, such as “zinc blende” and diamond lattices, are shown. The idea of semiconductor alloys – approximately crystalline materials made out of mixtures of atoms – is introduced because of their practical importance in devices. Crystalline growth is briefly discussed.

Video: https://purl.stanford.edu/fb483zt1193 DOI: https://doi.org/10.25740/fb483zt1193

Slides: https://purl.stanford.edu/tb447jx4506 DOI: https://doi.org/10.25740/tb447jx4506

Keywords: Crystals, Crystals > Growth, Diamond lattice, Zinc blende lattice, Epitaxial growth

Lecture 13c – Emergence of bands MPES 4.12

This lecture part illustrates how, when we bring N identical potential wells (or atoms) together, the individual well or atomic energy levels split into N different coupled energy levels, which we can view as forming a “band” of energies or states. These wavefunctions tend to be a product of a “unit cell” function that is approximately the same in each unit cell or period, and a larger envelope function, which is approximately a large sinusoid.

Video: https://purl.stanford.edu/rg362bk0501 DOI: https://doi.org/10.25740/rg362bk0501

Slides: https://purl.stanford.edu/fq775kk6226 DOI: https://doi.org/10.25740/fq775kk6226

Keywords: Band structures

Lecture 13 collected slides

Lecture 14 Particles, atoms, and crystals 5

Lecture 14a – Band structures in crystals MPES 4.13

This lecture part introduces the idea of band structures in crystals and the important “single electron” approximation of presuming that each electron moves in a periodic potential given by all the other electrons and nuclei in the crystal.

Video: https://purl.stanford.edu/qy203yt0939 DOI: https://doi.org/10.25740/qy203yt0939

Slides: https://purl.stanford.edu/dt345vm5726 DOI: https://doi.org/10.25740/dt345vm5726

Keywords: Band structures, One-electron approximation

Lecture 14b – The Bloch theorem MPES 4.13

This lecture part introduces the Bloch theorem, an important concept that allows us to think of wavefunctions in crystals as a product of a unit cell function that is the same in every unit cell of the crystal and an envelope function with a crystal wavevector. It gives the basic concept necessary for the idea of band structures in crystals.

Video: https://purl.stanford.edu/mq967ch0040 DOI: https://doi.org/10.25740/mq967ch0040

Slides: https://purl.stanford.edu/mx164qy5831 DOI: https://doi.org/10.25740/mx164qy5831

Keywords: Bloch theorem, Band structures

Lecture 14c – Solving with periodic boundary conditions MPES 4.13

This lecture part explains the idea of periodic boundary conditions, which is technically an approximation but which works well in large crystals, and allows the Bloch theorem. This idea also leads an alternate form for the Bloch theorem. An example simple Bloch form wavefunction is shown.

Video: https://purl.stanford.edu/cb769pm7614 DOI: https://doi.org/10.25740/cb769pm7614

Slides: https://purl.stanford.edu/jd092yb8124 DOI: https://doi.org/10.25740/jd092yb8124

Keywords: Bloch theorem, Periodic boundary conditions, Crystals

Lecture 14 collected slides

Lecture 15 Particles, atoms, and crystals 6

Lecture 15a – Band structures MPES 4.14

This lecture part illustrates how a simple band structure is built up by solving for the energies at each of a set of k (wavevector) values. It shows the concept of a Brillouin zone – the range of k required to represent a band structure – as well as concepts like a band gap energy between two bands, and the extended zone scheme, which shows the band structure just repeats for other values of k.

Video: https://purl.stanford.edu/hm072cj4906 DOI: https://doi.org/10.25740/hm072cj4906

Slides: https://purl.stanford.edu/yk259md0718 DOI: https://doi.org/10.25740/yk259md0718

Keywords: Band structure, Brillouin zone, Energy band gap

Lecture 15b – Crystal momentum and effective mass MPES 4.14

This lecture part introduces the ideas of crystal momentum, the effective momentum of the electron in the periodic potential, and effective mass, the apparent mass of the electron because of the band structure. It also introduces the ideas of indirect gap and direct gap materials.

Video: https://purl.stanford.edu/nq967fr6621 DOI: https://doi.org/10.25740/nq967fr6621

Slides: https://purl.stanford.edu/vy907jq6338 DOI: https://doi.org/10.25740/vy907jq6338

Keywords: Effective mass, Crystal momentum, Direct gap, Indirect gap

Lecture 15c – Band structures in three dimensions MPES 4.15

This lecture part formally extends the ideas of band structures and Brillouin zones from the one-dimensional illustrations to three dimensions, as in most actual crystals

Video: https://purl.stanford.edu/tc664jg4027 DOI: https://doi.org/10.25740/tc664jg4027

Slides: https://purl.stanford.edu/vw087nj3876 DOI: https://doi.org/10.25740/vw087nj3876

Keywords: Band structures, Brillouin zones, Crystals

Lecture 15d – Plotting actual band structures MPES 4.15

The lecture part shows how band structures are plotted in practice for real materials, such as silicon and “III-V” (3-5) semiconductors such as Gallium Arsenide, including the concepts of conduction bands and valence bands that are important for devices.

Video: https://purl.stanford.edu/xc935zh6734 DOI: https://doi.org/10.25740/xc935zh6734

Slides: https://purl.stanford.edu/fd348by1209 DOI: https://doi.org/10.25740/fd348by1209

Keywords: Band structures, Silicon, Gallium Arsenide, Conduction band, Valence band, Crystals

Lecture 15e – Metals, semiconductors and insulators MPES 4.16

This lecture part shows how semiconductors, insulators, and metals are distinguished by the different forms of band structures and by the size of bandgap energies.

Video: https://purl.stanford.edu/cd733wr3720 DOI: https://doi.org/10.25740/cd733wr3720

Slides: https://purl.stanford.edu/pc321yn1921 DOI: https://doi.org/10.25740/pc321yn1921

Keywords: Semiconductors, Metals, Insulators, Conduction band, Valence band, Electrons and holes

Lecture 15 collected slides

Lecture 16 Thermal distributions 1

Lecture 16a – Tossing coins, microstates, and macrostates MPES 5.2

This lecture part starts the discussion of statistical mechanics by looking at the outcomes of tossing coins, including the resulting distributions of “heads” and “tails”. It also introduces the concepts of microstates, macrostates, and multiplicity.

Video: https://purl.stanford.edu/fb753nr5592 DOI: https://doi.org/10.25740/fb753nr5592

Slides: https://purl.stanford.edu/pz940zh4180 DOI: https://doi.org/10.25740/pz940zh4180

Keywords: Statistical mechanics, Microstates, Macrostates, Multiplicity

Lecture 16b – Binomial distribution and Stirling’s
approximation MPES 5.2

This lecture part introduces the binomial distribution as the formal description useful for discussing distributions of “heads” and “tails”, for example. It then introduces Stirling’s approximation, which is very useful for large numbers of particles (or coin tosses), and leads to simple formulas. This also gives simple results for how wide we expect the distribution (of multiplicities) to be.

Video: https://purl.stanford.edu/tt799kx6395 DOI: https://doi.org/10.25740/tt799kx6395

Slides: https://purl.stanford.edu/tj109rj4343 DOI: https://doi.org/10.25740/tj109rj4343

Keywords: Binomial distribution, Stirling’s approximation, Statistical mechanics

Lecture 16c – Two-state spin systems and microstates MPES 5.3

This lecture part moves to discussing actual physical systems, here of two-state spin systems (such as electrons), and adds the possibility that the “spin up” and “spin down” states could have different energies. This then gives a model system for introducing many physical concepts and behaviors. It also introduces the concept of accessible microstates and basic assumptions often used in statistical mechanics.

Video: https://purl.stanford.edu/sz568xk7258 DOI: https://doi.org/10.25740/sz568xk7258

Slides: https://purl.stanford.edu/ct742rm1668 DOI: https://doi.org/10.25740/ct742rm1668

Keywords: Electron spin, Statistical mechanics

Lecture 16 collected slides

Lecture 17 Thermal distributions 2

Lecture 17a – Systems in thermal contact MPES 5.3

This lecture part introduces the idea of putting two systems of spins in thermal contact, which means they can exchange energy through some thermally conducting wall, and examines the multiplicities of the combined system.

Video: https://purl.stanford.edu/wh168wn2090 DOI: https://doi.org/10.25740/wh168wn2090

Slides: https://purl.stanford.edu/xy900nx7103 DOI: https://doi.org/10.25740/xy900nx7103

Keywords: Statistical mechanics, Thermal conduction

Lecture 17b – Maximizing multiplicities for spin systems MPES 5.3

This lecture part examines what happens if we maximize the multiplicity of two spin systems joined by a thermally conducting wall. This should correspond to the most likely situation, with the result that the energy per spin becomes the same on both sides of the wall.

Video: https://purl.stanford.edu/bn960qk9816 DOI: https://doi.org/10.25740/bn960qk9816

Slides: https://purl.stanford.edu/fw715fd7177 DOI: https://doi.org/10.25740/fw715fd7177

Keywords: Statistical mechanics, Thermal equilibrium

Lecture 17c – Maximizing multiplicity for general systems MPES 5.4

This lecture part generalizes the idea of maximizing multiplicity by thermal conduction, with a simple result for the quantity that becomes the same on both sides.

Video: https://purl.stanford.edu/pf498qv1024 DOI: https://doi.org/10.25740/pf498qv1024

Slides: https://purl.stanford.edu/gk207pc8527 DOI: https://doi.org/10.25740/gk207pc8527

Keywords: Statistical mechanics, Thermal equilibrium

Lecture 17 collected slides

Lecture 18 Thermal distributions 3

Lecture 18a – Entropy and temperature MPES 5.4

In this lecture part, entropy is defined in terms of the logarithm of the multiplicity. Based on what maximizes the multiplicity in thermal equilibration, and hence what maximizes entropy, in turn that leads to a definition of temperature in terms of entropy. An example system is shown.

Video: https://purl.stanford.edu/dz224jd9442 DOI: https://doi.org/10.25740/dz224jd9442

Slides: https://purl.stanford.edu/vn915mc5638 DOI: https://doi.org/10.25740/vn915mc5638

Keywords: Statistical mechanics, Entropy, Temperature

Lecture 18b – Entropy and heat flow MPES 5.4

This lecture part describes how the flow of heat from hotter to colder bodies leads to an increase in entropy overall, with the entropy of the hotter body decreasing but the entropy of the cooler body increasing by more. A numerical example is given to show just how enormously unlikely it is that even a small amount of heat would instead flow from cold to hot. In turn, this justifies the second law of thermodynamics.

Video: https://purl.stanford.edu/zx615zc5253 DOI: https://doi.org/10.25740/zx615zc5253

Slides: https://purl.stanford.edu/mh342xb8835 DOI: https://doi.org/10.25740/mh342xb8835

Keywords: Statistical mechanics, Second law of thermodynamics, Entropy, Temperature

Lecture 18c – Carnot efficiency limit for heat engines MPES 5.5

Based on the idea that entropy cannot decrease for any large (closed) system, this lecture part derives the so-called “Carnot” limit to the efficiency of any kind of heat engine (examples include steam engines, refrigerators, air conditioners, internal combustion engines, heat pumps).

Video: https://purl.stanford.edu/yn917qh7340 DOI: https://doi.org/10.25740/yn917qh7340

Slides: https://purl.stanford.edu/kb702dz3702 DOI: https://doi.org/10.25740/kb702dz3702

Keywords: Carnot efficiency, Entropy, Second law of thermodynamics

Lecture 18 collected slides

Lecture 19 Thermal distributions 4

Lecture 19a – The Boltzmann factor MPES 5.6

This lecture part introduces the Boltzmann factor, which gives the relative probability of two states of different energies at some temperature.

Video: https://purl.stanford.edu/xw084gh9764 DOI: https://doi.org/10.25740/xw084gh9764

Slides: https://purl.stanford.edu/ym134ms6380 DOI: https://doi.org/10.25740/ym134ms6380

Keywords: Statistical mechanics, Boltzmann factor

Lecture 19b – Chemical potential MPES 5.7

This lecture part introduces the chemical potential, which is the quantity that is equalized when particles are allowed to diffuse through a wall.

Video: https://purl.stanford.edu/xh451ny4159 DOI: https://doi.org/10.25740/xh451ny4159

Slides: https://purl.stanford.edu/xx959cm6376 DOI: https://doi.org/10.25740/xx959cm6376

Keywords: Chemical potential, Statistical mechanics

Lecture 19c – Chemical potential and the Gibbs factor MPES 5.7

This lecture part introduces the Gibbs factor, which gives the relative probability of two states with possibly different energies and different numbers of particles.

Video: https://purl.stanford.edu/wt576sj3412 DOI: https://doi.org/10.25740/wt576sj3412

Slides: https://purl.stanford.edu/vp977ch0604 DOI: https://doi.org/10.25740/vp977ch0604

Keywords: Statistical mechanics, Gibbs factor

Lecture 19 collected slides

Lecture 20 Thermal distributions 5

Lecture 20a – The Fermi-Dirac distribution MPES 5.8

Using the Gibbs factor (and typically calling the chemical potential the Fermi energy instead), this lecture part derives the Fermi-Dirac distribution, which gives the occupation probability of states for fermions (such as electrons) as a function of temperature and Fermi energy.

Video: https://purl.stanford.edu/nz615sh8066 DOI: https://doi.org/10.25740/nz615sh8066

Slides: https://purl.stanford.edu/cc251qv7462 DOI: https://doi.org/10.25740/cc251qv7462

Keywords: Fermi-Dirac distribution, Chemical potential, Fermi energy

Lecture 20b – The Bose-Einstein and Planck distributions MPES 5.8

This lecture part states the Bose-Einstein distribution, which gives the number of bosons that should be expected on average in any given state at a given temperature, and derives the simpler version that is the Planck distribution, which applies to photons in particular, telling us the number of photons expected in a photon mode in thermal equilibrium.

Video: https://purl.stanford.edu/tw706mh0577 DOI: https://doi.org/10.25740/tw706mh0577

Slides: https://purl.stanford.edu/kb974yz8815 DOI: https://doi.org/10.25740/kb974yz8815

Keywords: Bose-Einstein distribution, Planck distribution, Statistical mechanics

Lecture 20c – The Maxwell-Boltzmann distribution MPES 5.8

This lecture part states the Maxwell-Boltzmann distribution, which would be the thermal distribution of non-identical particles. Though quantum mechanical particles of a given kind are actually identical, this distribution is often used in practice in some situations because it gives a simpler mathematical form that is valid anyway as the high-temperature high-energy “tail” of both the Fermi-Dirac and Bose-Einstein distribution.

Video: https://purl.stanford.edu/zs242pm5949 DOI: https://doi.org/10.25740/zs242pm5949

Slides: https://purl.stanford.edu/jh484rj8773 DOI: https://doi.org/10.25740/jh484rj8773

Keywords: Maxwell-Boltzmann distribution, Statistical mechanics

Lecture 20 collected slides

Lecture 21 Bands and electronic devices

Lecture 21a – Electrons and holes in bands MPES 6.2

This lecture part introduces the concept of how electrons and holes move or “transport” in materials, including the “drift” model that leads to conventional electrical resistance. It also expands on the idea of holes and how we view their energy levels.

Video: https://purl.stanford.edu/bp965yk4656 DOI: https://doi.org/10.25740/bp965yk4656

Slides: https://purl.stanford.edu/sz835sz0768 DOI: https://doi.org/10.25740/sz835sz0768

Keywords: Electrons and holes, Drift transport, Semiconductors

Lecture 21b – Semiconductor doping and diodes MPES 6.3, 6.4

This lecture part discusses n-type and p-type doping in semiconductors and the resulting diodes that can be formed in this way. It also discusses that Fermi levels are equalized when such materials are joined together, because of the movement of electrons and holes to equalize their chemical potentials (Fermi levels), and shows the resulting band diagrams for diodes.

Video: https://purl.stanford.edu/tc688np4377 DOI: https://doi.org/10.25740/tc688np4377

Slides: https://purl.stanford.edu/bx769xf8457 DOI: https://doi.org/10.25740/bx769xf8457

Keywords: Semiconductor diodes, n-type doping, p-type doping, Fermi levels

Lecture 21c – Voltages and Fermi levels MPES 6.4 (and 5.7 for equivalent chemical potential definition)

This lecture part shows why it is that, when we apply a voltage to a diode, we separate the Fermi levels on the two sides by an amount equal (in electron-volts) to the applied (“bias”) voltage. This will allow us to understand biasing of diodes.

Video: https://purl.stanford.edu/dg178rw7394 DOI: https://doi.org/10.25740/dg178rw7394

Slides: https://purl.stanford.edu/tv852qw4189 DOI: https://doi.org/10.25740/tv852qw4189

Keywords: Fermi levels, Semiconductor diodes

Lecture 21d – Biasing semiconductor devices MPES 6.4

This lecture part shows what happens when we apply “bias” voltages to diodes. Then, using the statistical mechanics of electrons and holes in the Maxwell-Boltzmann approximation, we are able to derive the ideal diode current-voltage characteristic, giving a good example of putting together many different ideas.

Video: https://purl.stanford.edu/nd351qg2808 DOI: https://doi.org/10.25740/nd351qg2808

Slides: https://purl.stanford.edu/sv627gw7791 DOI: https://doi.org/10.25740/sv627gw7791

Keywords: Semiconductor diodes

Lecture 21 collected slides

Lecture 22 Light and quantum mechanics 1

Lecture 22a – Light, the photoelectric effect, and the
photon MPES 7.2

This lecture part describes the photoelectric effect and how Einstein’s proposal of the photon led to its explanation.

Video: https://purl.stanford.edu/ww801fb8540 DOI: https://doi.org/10.25740/ww801fb8540

Slides: https://purl.stanford.edu/zb916cm8302 DOI: https://doi.org/10.25740/zb916cm8302

Keywords: Photoelectric effect

Lecture 22b – Light and modes MPES 7.3

This lecture part introduces one way of understanding how many “modes” of light there are, modes that can be occupied by photons.

Video: https://purl.stanford.edu/hm042vn5425 DOI: https://doi.org/10.25740/hm042vn5425

Slides: https://purl.stanford.edu/qn632qm6607 DOI: https://doi.org/10.25740/qn632qm6607

Keywords: Quantum mechanics of light, Optical modes

Lecture 22c – Thermal radiation MPES 7.4

This lecture part derives Planck’s description of the black-body radiation spectrum (as seen in the sun and in incandescent light bulbs, for example) that triggered much of modern quantum mechanics. It continues to derive the Stefan-Boltzmann law for the amount of energy in a light field in thermal equilibrium, which also explains why hot objects radiate so much light.

Video: https://purl.stanford.edu/rr796xy3214 DOI: https://doi.org/10.25740/rr796xy3214

Slides: https://purl.stanford.edu/yk746kv0769 DOI: https://doi.org/10.25740/yk746kv0769

Keywords: Black body radiation, Stefan-Boltzmann law

Lecture 22 collected slides

Lecture 23 Light and quantum mechanics 2

Lecture 23a – Black body radiation and Kirchhoff’s law MPES 7.5

This lecture part shows how to envisage a perfect black body for thought experiments and derivations, and goes on to derive Kirchhoff’s radiation law, which states that the “absorptivity” of an object (the fraction of incident light it absorbs) must equal its emissivity (the amount of light it emits at a given temperature as a fraction of the light a perfect black body would emit).

Video: https://purl.stanford.edu/dy762sz3700 DOI: https://doi.org/10.25740/dy762sz3700

Slides: https://purl.stanford.edu/cf521rq1709 DOI: https://doi.org/10.25740/cf521rq1709

Keywords: Kirchhoff radiation law, Black body radiation

Lecture 23b – Einstein’s A and B coefficient argument MPES 7.6

This lecture part derives Einstein’s “A & B coefficient” argument, which predicts the existence and strength of stimulated emission, the kind of emission we get from lasers.

Video: https://purl.stanford.edu/pm246kg9828 DOI: https://doi.org/10.25740/pm246kg9828

Slides: https://purl.stanford.edu/jg412dd7396 DOI: https://doi.org/10.25740/jg412dd7396

Keywords: Einstein A and B coefficient argument, Lasers

Lecture 23 collected slides

Lecture 24 Semiconductor optoelectronics 1

Lecture 24a – Optoelectronic devices and photodetectors MPES 8.1, 8.2

This lecture part introduces semiconductor optoelectronic devices, the devices that convert light to electricity and electricity to light. Devices include photoconductors, photodiodes.

Video: https://purl.stanford.edu/hg132hn9284 DOI: https://doi.org/10.25740/hg132hn9284

Slides: https://purl.stanford.edu/gp544zn8910 DOI: https://doi.org/10.25740/gp544zn8910

Keywords: Semiconductor optoelectronic devices, Photoconductors, Photodiodes

Lecture 24b – Light emission MPES 8.3

This lecture part introduces both thermal (e.g., incandescent light bulb) and non-thermal (e.g., light-emitting diodes and lasers) light sources. It goes on to consider the light emission from semiconductors, especially the strong emission from direct-gap semiconductors, and explains the light emission from semiconductor light-emitting diodes (LEDs).

Video: https://purl.stanford.edu/vf654xr7507 DOI: https://doi.org/10.25740/vf654xr7507

Slides: https://purl.stanford.edu/sm396gq4063 DOI: https://doi.org/10.25740/sm396gq4063

Keywords: LEDs (Light emitting diodes), Direct gap semiconductors, Light emission

Lecture 24 collected slides

Lecture 25 Semiconductor optoelectronics 2

Lecture 25a – Absorption and emission processes MPES 8.3

This lecture part introduces the absorption and emission processes, both spontaneous and stimulated, from a quantum mechanical point of view of transitions between energy levels.

Video: https://purl.stanford.edu/yg356fd8716 DOI: https://doi.org/10.25740/yg356fd8716

Slides: https://purl.stanford.edu/vf719nt6353 DOI: https://doi.org/10.25740/vf719nt6353

Keywords: Optical absorption, Spontaneous emission, Stimulated emission

Lecture 25b – Lasers MPES 8.3

This lecture part introduces how lasers work, including the ideas of population inversion and 3-level and 4-level laser systems, and semiconductor lasers in particular.

Video: https://purl.stanford.edu/sn066wc4638 DOI: https://doi.org/10.25740/sn066wc4638

Slides: https://purl.stanford.edu/mp376pd2384 DOI: https://doi.org/10.25740/mp376pd2384

Keywords: Lasers, Semiconductor lasers, Population inversion

Lecture 25c – Epilogue MPES Chapter 9

This lecture part is a short epilogue to the entire course of Modern Physics for Engineers and Scientists.

Video: https://purl.stanford.edu/tf597tt5819 DOI: https://doi.org/10.25740/tf597tt5819

Slides: https://purl.stanford.edu/gf324tw8036 DOI: https://doi.org/10.25740/gf324tw8036

Keywords: Modern physics

Lecture 25 collected slides