ISAT 436 Micro-/Nanofabrication and Applications

1. ISAT 436Micro-/Nanofabrication and Applications Light Absorption in Semiconductors David J. Lawrence Spring 2004

2. Properties of Light (1) • f = frequency (Hz) • lo = wavelength in vacuum or air [usually measured in mm, nm, or Angstroms (Å)] • c = speed of light in vacuum = 3 ´ 108 m/s • c = f lo • n = refractive index of a material (“medium”) • v = c / n = speed of light in material • l = lo / n = wavelength in material • v = f l

3. Properties of Light (2) • E = h f = energy of a photon • h = Planck’s constant = 6.626 ´ 10-34 J-s = 4.136 ´ 10-15 eV-s • E = (h c) / lo • h c = 1240 eV-nm = 1.24 eV-mm • 1 eV = 1.602 ´ 10-19 J • h = h / 2p = 1.055 ´ 10-34 J-s

4. Properties of Light (3) • A useful equation for the energy of a photon: • Rearranged, this gives

5. For the visible portion of the electromagnetic spectrum, the wavelength in vacuum (or in air) ranges from: 400 nm 700 nm to Å 4000 7000 Å to Color lo (nm) f (Hz) Ephoton (eV) red 630-760 ~4.5 x 1014 ~1.9 orange 590-630 ~4.9 x 1014 ~2.0 yellow 560-590 ~5.2 x 1014 ~2.15 green 500-560 ~5.7 x 1014 ~2.35 blue 450-500 ~6.3 x 1014 ~2.6 violet 380-450 ~7.1 x 1014 ~2.9 Properties of Light (4)

6. Properties of Light (5) • Light with wavelength lo< 400 nm is called ultraviolet (UV). • Light with wavelength lo> 700 nm is called infrared (IR). • We cannot see light of these wavelengths, however, we can sense it in other ways, e.g., through its heating effects (IR) and its tendency to cause sunburn (UV).

7. Optical Generation of Free Electrons and Holes • Recall that light can generate free electrons and holes in a semiconductor. • See Photovoltaic Fundamentals, p.12 and p.16. • The energy of the photons (hf) must equal or exceed the energy gap of the semiconductor (Eg) . • If hf > Eg , a photon can be absorbed, creating a free electron and a free hole.

8. Blue l = 475 nm Red l = 650 nm Ec Infrared l = 1200 nm Infrared l = 1100 nm Ev - - - - - - - - - Optical Generation of Free Electrons and Holes • Consider silicon Eg = 1.12 eV

9. Blue l = 475 nm Red l = 650 nm Green l = 555 nm Orange l = 600 nm Ec Infrared l = 1200 nm Ev - - - - - - - - - Optical Generation of Free Electrons and Holes • Consider GaP Eg = 2.26 eV

10. Si Si Si Si Si Si Si free electron Si Si Si Si Si Si Si free hole Si Si Si Si Si Si Si Optical Generation of Free Electrons and Holes - - Bond Model • See Photovoltaic Fundamentals, p.12 and p.16. Photons

11. “Conduction Band” (Nearly) Empty Electron Energy Energy Gap “Forbidden” “Valence Band” (Nearly) Filled with Electrons Optical Generation of Free Electrons and Holes - - Band Model • If a photon has an energy larger than the energy gap, the photon will be absorbed by the semiconductor, exciting an electron from the valence band into the conduction band, where it is free to move. • A free hole is left behind in the valence band. • This absorption process underlies the operation of photoconductive light detectors, photodiodes, photovoltaic (solar) cells, and solid state camera “chips”.