Conduction, valence bands and band gaps (cont)
Direct gaps are important for most optoelectronic devices They have much stronger optical absorption and emission near the band gap energy Reason - conservation of momentum (photon has small momentum compared to an electron or hole) Transitions are "vertical" on an E vs. k diagram Indirect transitions require additional momentum, usually from a phonon (a crystal lattice vibration), making indirect transitions a three particle process and much weaker
• Black body – T
• Lasers
4) Technologically available materials
Human Eye Response
Lasers and LEDs for displays or lighting must emit in the 430-670 nm wavelength region (bandgaps of 3.0-1.9 eV).
Diamond and Zincblende Lattices Unit cells for silicon (Si) and gallium arsenide (GaAs) Silicon - diamond lattice GaAs - zincblende (cubic zinc sulfide) lattice (most other III-V and many II-VI semiconductors have zincblende lattice) Diamond and zincblende lattice based on tetragonal pattern of bonds from each atom to nearest neighbors-two interlocking facecenteredcubic lattices lattice parameter (or constant), a - repeat length of the unit cells e. g., GaAs, a = 5.65 Å (Angstroms) = 0.565 nm.
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Summary of Course Content Introduction to semiconductor optoelectronic devices for communications and other applications, covering operating principles and practical device features Goals Understand the major semiconductor optoelectronic devices, their operating principles, designs, uses, strengths and weaknesses. Planned topics 1. Review of basic semiconductor physics 2. Heterostructures 3. Optical absorption, emission, and refraction processes 4. Semiconductor pn junction diodes 5. Light-emitting diodes (LEDs) 6. Semiconductor optical detectors 7. Modulators 8. Semiconductor lasers
Conduction, valence bands and band gaps
In the pure, perfect, semiconductor, there is an energy gap, Eg, between highest, filled, “valence” band(s), and lowest energy, empty, “conduction” band(s) In the valence bands, we use the concept of "holes" (positively charged pseudo-particle which is the "absence of an electron") Valence bands in the pure semiconductor are empty of holes Hole energy increases downwards on the E - k diagram Gallium arsenide is a “direct gap” semiconductor lowest “minimum” in the conduction band is directly above the highest “maximum” in the valence band in E vs k (momentum) Silicon is an “indirect gap” semiconductor (Ge is also indirect) lowest CB min. is at zone edge, highest VB max. is at zone center
1. Review of Basic Semiconductor Physics
Crystals
Compound semiconductors
Bloch theorem
Band structure and the Brillouin zone
Effective mass approximation
Wurtzite Lattice
Wurtzite structure Found in AlN, GaN, InN These materials have revolutionized short-wavelength light emitters (e. g., blue and green LEDs) Based on the same tetragonal set of bonds from each atom Two interlocking hexagonalclose-packed lattices of the two different (" dark" and "light") atoms. Note - Wurtzite has different Symmetry properties (e. g., hexagonal,not cubic) and Different band structures from zincblende materials
Kane band theory results
Semiconductor statistical mechanics
Crystals
All materials in this course are crystalline semiconductors Crystal - a structure that can fill all space based on the regular repetition of a particular unit cell Unit cell - unit to construct crystal by regular repetition • Primitive-smallest cell which will replicate the crystal • Larger Cubic-most semiconductors are diamond or zincblende for which the primitive unit cell is complex
Semiconductor Optoelectronics
Prof. Xiaoxia. Zhang
Room 225, School of Opto-Electronic Information
Email: xxzhang@
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First Brillouin zone E vs. k band diagram of zincblende semiconductors
One relevant conduction band is formed from S- like atomic orbitals “unit cell” part of wavefunction is approximately spherically symmetric. The three upper valence bands are formed from (three) P- like orbitals and the spin-orbit interaction splits off lowest, “split-off” hole (i. e., valence) band. The remaining two hole bands have the same energy (“degenerate”) at zone center, but their curvature is different, forming a “heavy hole” (hh) band (broad), and a “light hole” (lh) Band (narrower).