224
8 Transport
In Sects. 8.2–8.5 we treat band conductivity, i.e. the transport of charge carriers in extended states, the
conduction and valence bands characterized by an effective mass. Conductivity is then determined by
the carrier concentration (free electrons and holes) and scattering mechanisms (mobility). In disordered
semiconductors such as amorphous material, the charge transport due to hopping between localized
states close to the Fermi level dominates the conductivity which is discussed in Sect. 8.8.
Many semiconductor properties, such as the carrier concentration and the band gap, depend on the
temperature. Thus, device properties will also depend on temperature. During operation of a device
typically heat is generated, e.g. by Joule heating due to finite resistivity. This heat leads to an increase
of the device temperature that subsequently alters the device performance, mostly for the worse.
Ultimately, the device can be destroyed. Thus cooling of the device, in particular of the active area of the
device, is essential. Mostly the thermal management of device heating limits the achievable performance
(and lifetime) of the device. In high-power devices quite high energy densities can occur, e.g. the facet
of a high-power semiconductor laser has to withstand an energy density beyond 10 MW cm
−2 .
8.2 Conductivity
Under the influence of an electric field the electrons accelerate according to (cf. (6.36))
F = m
∗ dv
dt
=
dk
dt
= q E = −e E .
(8.1)
In the following, q denotes a general charge, while e is the (positive) elementary charge. We also
consider an isotropic effective mass m
∗ at first. After the time δt the k vector of all conduction electrons
(and the center of the Fermi sphere) has been shifted by δk
δk = −
e E
δt .
(8.2)
In the absence of scattering processes this goes on further (similar to an electron in vacuum). This regime
is called ballistic transport. In a (periodic) band structure, the electron will perform a closed cycle as
indicated in Fig. 8.1. Such motion is called a Bloch oscillation. However, in a bulk crystal the period T
of such an oscillation eE T / = 2π/a 0 is of the order of 10
−10 s for E = 10
4 V/cm. This time is much
longer than a typical scattering time of 10
−14 s. Thus, in bulk material the Bloch electron cannot reach
the zone boundary. However, in artificial superlattices (cf. Chap. 12) with larger periodicity (≈10 nm),
high electric fields (≈10
6 V/cm) and high quality (reduced collision time) such motion is possible. We
note that in the absence of scattering, electrons also perform a periodic oscillation in a magnetic field
(cyclotron motion).
Fig. 8.1 Schematic
representation of a Bloch
oscillation
/a
/a
8 Transport
In Sects. 8.2–8.5 we treat band conductivity, i.e. the transport of charge carriers in extended states, the
conduction and valence bands characterized by an effective mass. Conductivity is then determined by
the carrier concentration (free electrons and holes) and scattering mechanisms (mobility). In disordered
semiconductors such as amorphous material, the charge transport due to hopping between localized
states close to the Fermi level dominates the conductivity which is discussed in Sect. 8.8.
Many semiconductor properties, such as the carrier concentration and the band gap, depend on the
temperature. Thus, device properties will also depend on temperature. During operation of a device
typically heat is generated, e.g. by Joule heating due to finite resistivity. This heat leads to an increase
of the device temperature that subsequently alters the device performance, mostly for the worse.
Ultimately, the device can be destroyed. Thus cooling of the device, in particular of the active area of the
device, is essential. Mostly the thermal management of device heating limits the achievable performance
(and lifetime) of the device. In high-power devices quite high energy densities can occur, e.g. the facet
of a high-power semiconductor laser has to withstand an energy density beyond 10 MW cm
−2 .
8.2 Conductivity
Under the influence of an electric field the electrons accelerate according to (cf. (6.36))
F = m
∗ dv
dt
=
dk
dt
= q E = −e E .
(8.1)
In the following, q denotes a general charge, while e is the (positive) elementary charge. We also
consider an isotropic effective mass m
∗ at first. After the time δt the k vector of all conduction electrons
(and the center of the Fermi sphere) has been shifted by δk
δk = −
e E
δt .
(8.2)
In the absence of scattering processes this goes on further (similar to an electron in vacuum). This regime
is called ballistic transport. In a (periodic) band structure, the electron will perform a closed cycle as
indicated in Fig. 8.1. Such motion is called a Bloch oscillation. However, in a bulk crystal the period T
of such an oscillation eE T / = 2π/a 0 is of the order of 10
−10 s for E = 10
4 V/cm. This time is much
longer than a typical scattering time of 10
−14 s. Thus, in bulk material the Bloch electron cannot reach
the zone boundary. However, in artificial superlattices (cf. Chap. 12) with larger periodicity (≈10 nm),
high electric fields (≈10
6 V/cm) and high quality (reduced collision time) such motion is possible. We
note that in the absence of scattering, electrons also perform a periodic oscillation in a magnetic field
(cyclotron motion).
Fig. 8.1 Schematic
representation of a Bloch
oscillation
/a
/a