Students will learn about the following specific topics:

• energy bands
• band gaps
• effective masses
• electrons and holes
• basics of quantum mechanics
• the Fermi function
• the density-of-states
• intrinsic carrier density
• doping and carrier concentrations
• carrier transport
• generation-recombination
• quasi-Fermi levels
• the semiconductor equations
• energy band diagrams

Among the important learning objectives, the course will introduce learners to the process of drawing and interpreting energy band diagrams. Energy band diagrams are a powerful, conceptual way to qualitatively understand the operation of semiconductor devices. In a concise way, they encapsulate most of the device-relevant specifics of semiconductor physics. Drawing and interpreting an energy band diagram is the first step in understanding the operation of a device.

This course material is typically covered in the first few weeks of an introductory semiconductor device course, but this class provides a fresh perspective informed by new understanding of electronics at the nanoscale.

Week 1: Materials Properties and Doping

• Energy levels to energy bands
• Crystalline, polycrystalline, and amorphous semiconductors
• Miller indices
• Properties of common semiconductors
• Free carriers in semiconductors

Week 2: Rudiments of Quantum Mechanics

• The wave equation
• Quantum confinement
• Quantum tunneling and reflection
• Electron waves in crystals
• Density of states

Week 3: Equilibrium Carrier Concentration

• The Fermi function
• Fermi-Dirac integrals
• Carrier concentration vs. Fermi level
• Carrier concentration vs. doping density
• Carrier concentration vs. temperature

Week 4: Carrier Transport, Generation, and Recombination

• The Landauer approach
• Current from the nanoscale to the macroscale
• Drift-diffusion equation
• Carrier recombination
• Carrier generation

Week 5: The Semiconductor Equations

• Mathematical formulation
• Energy band diagrams
• Quasi-Fermi levels
• Minority carrier diffusion equation