9.9 Absorption in the Presence of Free Charge Carriers
293
(a)
(b)
Fig. 9.39 a Optical absorption spectra (at T = 4.2 K) of n-type Ge for various As dopant concentrations as labeled. The
arrow denotes the band edge of undoped Ge, the vertical dashed line the energy for which the free-carrier absorption
is measured in part b. The inclined dashed line visualizes the slope ∝ λ 2 . Curved dashed lines are guides to the eye.
Adapted from [851]. b Free-carrier absorption at λ = 2.4 µm as determined from part a of the figure (blue squares) as a
function of As dopant concentration. Additionally data at 300 K (red circles) from the same samples are included [851].
The dashed lines visualizes the slope ∝ N 1.25
D
Fig. 9.40 a Dielectric
constant for plasmon
oscillations. Shaded area
represents region of
attenuation (negative ). b
Dispersion relation (k in
units of ω p /c, ω in units of
ω p ) in the presence of free
carriers (9.79, for r = 1).
Shaded area represents
forbidden frequency range
for propagating solutions.
Dashed line is photon
dispersion ω = ck
(a)
0
1
2
-2
-1
0
1
/ p
(b)
k
0
1
2
0
1
2
ω
2
= ω
2
p +
c
2 k
2
r
.
(9.79)
For ω > ω p , > 0, thus waves can propagate. For ω < ω p , however, the dielectric constant is negative,
i.e. < 0. For such frequencies waves are exponentially damped and cannot propagate or penetrate
a layer. This effect can be used in a plasmon waveguide or in metamaterials (cf. Sect. 19.1.10). The
expected dependence of the plasmon wavelength on the carrier density λ p = 2πc/ω p ∝ n
−1/2 is
depicted in Fig. 9.41 for GaAs. For semiconductors the plasmon frequency is in the mid-or far-infrared
spectral region.
12
12 The much higher free-electron density in metals shifts the plasma frequency to the UV, explaining the reflectivity of
metals in the visible and their UV transparency.
293
(a)
(b)
Fig. 9.39 a Optical absorption spectra (at T = 4.2 K) of n-type Ge for various As dopant concentrations as labeled. The
arrow denotes the band edge of undoped Ge, the vertical dashed line the energy for which the free-carrier absorption
is measured in part b. The inclined dashed line visualizes the slope ∝ λ 2 . Curved dashed lines are guides to the eye.
Adapted from [851]. b Free-carrier absorption at λ = 2.4 µm as determined from part a of the figure (blue squares) as a
function of As dopant concentration. Additionally data at 300 K (red circles) from the same samples are included [851].
The dashed lines visualizes the slope ∝ N 1.25
D
Fig. 9.40 a Dielectric
constant for plasmon
oscillations. Shaded area
represents region of
attenuation (negative ). b
Dispersion relation (k in
units of ω p /c, ω in units of
ω p ) in the presence of free
carriers (9.79, for r = 1).
Shaded area represents
forbidden frequency range
for propagating solutions.
Dashed line is photon
dispersion ω = ck
(a)
0
1
2
-2
-1
0
1
/ p
(b)
k
0
1
2
0
1
2
ω
2
= ω
2
p +
c
2 k
2
r
.
(9.79)
For ω > ω p , > 0, thus waves can propagate. For ω < ω p , however, the dielectric constant is negative,
i.e. < 0. For such frequencies waves are exponentially damped and cannot propagate or penetrate
a layer. This effect can be used in a plasmon waveguide or in metamaterials (cf. Sect. 19.1.10). The
expected dependence of the plasmon wavelength on the carrier density λ p = 2πc/ω p ∝ n
−1/2 is
depicted in Fig. 9.41 for GaAs. For semiconductors the plasmon frequency is in the mid-or far-infrared
spectral region.
12
12 The much higher free-electron density in metals shifts the plasma frequency to the UV, explaining the reflectivity of
metals in the visible and their UV transparency.