139
its vast number of empty levels lies above it. To excite an electron
across the gap requires a photon with an energy at least as great as
the width of the gap, ΔE gap . Thus radiation with photon energy less
than ΔE gap cannot excite electrons; there are no energy states within
the gap for the electron to be excited into. The radiation sees the
material as transparent, offering no interaction of any sort, so it
goes straight through.
Electrons are, however, excited by radiation with photons that
have energies greater than ΔE gap (i.e., higher frequency, shorter
wavelength). These have enough energy to pop electrons into the
conduction band, leaving a “hole” in the valence band from which
they came. When they jump back, filling the hole, they emit radiation of the same wavelength that first excited them, and for these
wavelengths the material is not transparent (Figure 4.69, right
side). The critical frequency ν crit , above which interaction starts, is
given by
h
E
crit
gap
ν = ∆
(4.56)
The material is opaque to frequencies higher than this. Thus Bakelite
is transparent to infrared light because its frequency is too low and
its photons too feeble to kick electrons across the band gap, but
the visible spectrum has higher frequencies with more energetic
photons, exceeding the band-gap energy; they are captured and
reflected.
Although dielectrics can’t absorb radiation with photons of energy
less than that of the band gap, they are not all transparent. Most
are polycrystalline and have a refractive index that depends on
direction; then light is scattered as it passes from one crystal to
another. Imperfections, particularly porosity, do the same. Scattering explains why some polymers are translucent or opaque: Their
microstructure is a mix of crystalline and amorphous regions with
different refractive indices. It explains, too, why some go white
when you bend them; it is because light is scattered from internal
microcracks, or crazes.
Color
If a material has a band gap with an energy ΔE gap that lies within the
visible spectrum, the wavelengths with energy greater than this are
absorbed, and those with energy that is less are not. The absorbed
radiation is reemitted when the excited electron drops back into a
lower energy state, but this might not be the one it started from, so
the photon it emits has a different wavelength than the one that
Optical Behavior
its vast number of empty levels lies above it. To excite an electron
across the gap requires a photon with an energy at least as great as
the width of the gap, ΔE gap . Thus radiation with photon energy less
than ΔE gap cannot excite electrons; there are no energy states within
the gap for the electron to be excited into. The radiation sees the
material as transparent, offering no interaction of any sort, so it
goes straight through.
Electrons are, however, excited by radiation with photons that
have energies greater than ΔE gap (i.e., higher frequency, shorter
wavelength). These have enough energy to pop electrons into the
conduction band, leaving a “hole” in the valence band from which
they came. When they jump back, filling the hole, they emit radiation of the same wavelength that first excited them, and for these
wavelengths the material is not transparent (Figure 4.69, right
side). The critical frequency ν crit , above which interaction starts, is
given by
h
E
crit
gap
ν = ∆
(4.56)
The material is opaque to frequencies higher than this. Thus Bakelite
is transparent to infrared light because its frequency is too low and
its photons too feeble to kick electrons across the band gap, but
the visible spectrum has higher frequencies with more energetic
photons, exceeding the band-gap energy; they are captured and
reflected.
Although dielectrics can’t absorb radiation with photons of energy
less than that of the band gap, they are not all transparent. Most
are polycrystalline and have a refractive index that depends on
direction; then light is scattered as it passes from one crystal to
another. Imperfections, particularly porosity, do the same. Scattering explains why some polymers are translucent or opaque: Their
microstructure is a mix of crystalline and amorphous regions with
different refractive indices. It explains, too, why some go white
when you bend them; it is because light is scattered from internal
microcracks, or crazes.
Color
If a material has a band gap with an energy ΔE gap that lies within the
visible spectrum, the wavelengths with energy greater than this are
absorbed, and those with energy that is less are not. The absorbed
radiation is reemitted when the excited electron drops back into a
lower energy state, but this might not be the one it started from, so
the photon it emits has a different wavelength than the one that
Optical Behavior