374
12 Heterostructures
If the region of the 2DEG is not doped, the electron gas exists without any dopant atoms and
ionized impurity scattering no longer exists. This concept is called modulation doping. Mobilities
up to 3.1 × 10
7 cm
2 /Vs have been realized (Fig. 12.37). The theoretical limits of mobility in a 2DEG
at modulation-doped (Al,Ga)As/GaAs heterointerfaces are discussed in detail in [1194].
12.3.5 Heterointerface Between Semiconductors with Band Structures of
Different Topology
Let us remember the situation of the topological linear chain developing end states when sandwiched
between trivial material (cf. Sect. 5.2.10). Also surface states develop between a material with nontrivial topological band structure and vacuum (which is trivial) (cf. Sect. 11.6.3). These effects are
expression of the bulk-boundary correspondence, which says that at the interface of topologically
different materials, edge states develop.
If now a semiconductor heterointerface is made up from two topologically differnt materials, a
conductive interface channel is expected. This effect has been found for the HgTe/CdTe system where
HgTe represents the non-trivial material with inverted band structure. (cf. Sect. 6.11). A quantum well
structure was proposed where HgTe is sandwiched between layers of Hg x Cd 1−x Te [1196]. Taking
the electron and hole quantization effects into account, normal band order is present for thickness of
the HgTe layer up to a critical thickness of d c = 6.35 nm (for x = 0.32) and the sample should be
insulating. For thicker QWs, the two-dimensional bands invert and edge states arise. The quantized
electrical conductance due to the edge states was indeed found and measured [1197, 1198].
Fig. 12.36 a Conduction-band edge at a GaAs/Al 0.3 Ga 0.7 As heterointerface (T = 0 K) with two confined states at E 0
and E 1 marked with solid horizontal lines. In the GaAs channel there are 5 × 10 11 cm −2 electrons. The barrier height
is 300 meV, N GaAs
D
= 3 × 10 14 cm −3 . The position of the Fermi level E F is at E = 0 and indicated with a dash-dotted
line. b Envelope wavefunctions φ 0 and φ 1 of the two confined states, dash-dotted line: calculation without exchange and
correlation for state at E 0 . Adapted from [1193]
12 Heterostructures
If the region of the 2DEG is not doped, the electron gas exists without any dopant atoms and
ionized impurity scattering no longer exists. This concept is called modulation doping. Mobilities
up to 3.1 × 10
7 cm
2 /Vs have been realized (Fig. 12.37). The theoretical limits of mobility in a 2DEG
at modulation-doped (Al,Ga)As/GaAs heterointerfaces are discussed in detail in [1194].
12.3.5 Heterointerface Between Semiconductors with Band Structures of
Different Topology
Let us remember the situation of the topological linear chain developing end states when sandwiched
between trivial material (cf. Sect. 5.2.10). Also surface states develop between a material with nontrivial topological band structure and vacuum (which is trivial) (cf. Sect. 11.6.3). These effects are
expression of the bulk-boundary correspondence, which says that at the interface of topologically
different materials, edge states develop.
If now a semiconductor heterointerface is made up from two topologically differnt materials, a
conductive interface channel is expected. This effect has been found for the HgTe/CdTe system where
HgTe represents the non-trivial material with inverted band structure. (cf. Sect. 6.11). A quantum well
structure was proposed where HgTe is sandwiched between layers of Hg x Cd 1−x Te [1196]. Taking
the electron and hole quantization effects into account, normal band order is present for thickness of
the HgTe layer up to a critical thickness of d c = 6.35 nm (for x = 0.32) and the sample should be
insulating. For thicker QWs, the two-dimensional bands invert and edge states arise. The quantized
electrical conductance due to the edge states was indeed found and measured [1197, 1198].
Fig. 12.36 a Conduction-band edge at a GaAs/Al 0.3 Ga 0.7 As heterointerface (T = 0 K) with two confined states at E 0
and E 1 marked with solid horizontal lines. In the GaAs channel there are 5 × 10 11 cm −2 electrons. The barrier height
is 300 meV, N GaAs
D
= 3 × 10 14 cm −3 . The position of the Fermi level E F is at E = 0 and indicated with a dash-dotted
line. b Envelope wavefunctions φ 0 and φ 1 of the two confined states, dash-dotted line: calculation without exchange and
correlation for state at E 0 . Adapted from [1193]