Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Recitations: 2 sessions / week, 1 hour / session

Labs: 3 weeks, 5 sessions / week, 1 hour / session


3.012 Fundamentals of Materials Science and Engineering


This course offers a description of how the electronic, optical and magnetic properties of materials originate from their electronic and molecular structure and how these properties can be designed for particular applications, for instance in optical fibers, magnetic data storage, solar cells, transistors and other devices. It also offers experimental exploration of the electronic, optical and magnetic properties of materials, including hands-on experimentation using spectroscopy, resistivity, impedance and magnetometry measurements, behavior of light in waveguides, and other characterization methods, as well as investigation of structure-property relationships through practical materials examples.

Objectives and Approach

There is an emphasis in lectures on fundamental physical models in order to understand and predict electrical, optical and magnetic properties using real world examples and applications, as well as EOM property measurements using state-of-the-art tools and engineering materials properties during lab sessions.

Course Topics

  • Hamiltonian mechanics with application to normal vibrations in crystals
  • Phonons: Dispersion relations, normal modes
  • Introduction to quantum mechanics: Schrödinger's equation
  • Applications to quantum dots, tunneling devices
  • Localized vs. delocalized states: From the free electron to the atom
  • Electronic states in crystals: DOS, bandgaps, interpretation of band diagrams
  • Fermions, symmetrization and Pauli's exclusion principle: Electrons in bands and the classification of solids
  • "Free electron gas" description of carriers
  • The chemical potential: Fermi level, statistics of electron distribution
  • Electronic structure of semiconductors: Intrinsic and extrinsic
  • Semiconductor devices: p-n junctions under illumination and applied voltage
  • Maxwell's equations: Electromagnetic waves in materials
  • Indices of refraction: Reflection and transmission
  • Periodic optical materials: Photonic bands and bandgaps
  • Magnetization in materials: Para-, ferro-, anti-ferro- and ferrimagnets
  • Magnetic domains


6 problem sets 20%
2 quizzes 50%
3 lab reports 30%


Lec 1

Introduction and course overview

The Hamiltonian approach to classical mechanics: Analysis of a simple oscillator

PSet 1 out
Rec 1    
Lec 2 The Hamiltonian approach to classical mechanics: Analysis of vibrations in one-dimensional lattice  
Lec 3 The Hamiltonian analysis of lattice vibrations: Phononic bandgap  
Rec 2    
Lec 4 Introduction to quantum mechanical way of thinking

PSet 1 due

PSet 2 out

Rec 3    
Lec 5 Quantum mechanical systems and measurements: Observables  
Lec 6 Quantum mechanical systems and measurements: Spectral decomposition  
Lec 7 Quantum mechanical measurements: Symmetries, conserved quantities, and the labeling of states  
Rec 4    
Lec 8 Symmetries, conserved quantities, and the labeling of states: Angular momentum  
Lab Week

PSet 2 due

PSet 3 out

Lab report 1 due

Rec 5 Lab recitation  
Lec 9 The hydrogen atom  
Rec 6    
Lec 10 Waves in periodic potentials: Part I  
Lec 11 Waves in periodic potentials: Part II  
Rec 7    
Lec 12 Band gap  
Rec 8    
Lec 13 Band diagrams

PSet 3 due

PSet 4 out

Lec 14 The free electron gas: Density of states  
Rec 9 Midterm exam review  
Midterm Exam
Lec 15 Fermi-Dirac distribution  
Rec 10 Lab recitation  
Lec 16 Carriers in intrinsic semiconductors  
Lab Week Lab report 2 due
Rec 11    
Lec 17 Engineering conductivity through doping  
Rec 12    
Lec 18 The P-N junction (the diode)

PSet 4 due

PSet 5 out

Lec 19 Light emitting diodes  
Rec 13    
Lec 20 Light emitting diodes (cont.)  
Lec 21 Reminder / introduction to wave optics  
Rec 14    
Lec 22 Electromagnetic waves  
Rec 15 Lab recitation  
Lec 23 Layered materials and photonic band diagrams

PSet 5 due

PSet 6 out

Lab Week Lab report 3 due
Rec 16    
Lec 24 Origins of magnetization  
Rec 17    
Lec 25 Hysteresis in ferromagnetic materials PSet 6 due
Lec 26 Magnetic domains  
Rec 18    
Lec 27 Course summary and review for final exam  
Rec 19 Final exam review  
Final Exam