12.3 Energy Levels in Heterostructures
365
12.3 Energy Levels in Heterostructures
12.3.1 Band Lineup in Heterostructures
In heterostructures, semiconductors with different band gaps are combined. The relative position of
conduction and valence band (band alignment) is determined by the electron affinities χ as shown in
Fig. 12.21. For a semiconductor, the electron affinity is the (positive) energy difference between vacuum
level and conduction band edge. It can lead to different types of heterostructures. Early perspectives of
semiconductor heterostructures are discussed in [1166]. The band alignment can be estimated from the
position of the branch point energies (Sect. 7.8) of the two constituents [699] but additional interface
dipoles may have to be considered.
In Fig. 12.22, the band alignment for type-I, type-II and type-III heterostructures are shown. In the
type-I structure (straddled band lineup) the lower conduction-band edge and the higher valence-band
edge are both in the material with smaller band gap. Thus, electrons and holes will localize there. In
the type-II structure a staggered lineup is present and electrons and holes will localize in different
materials. In the type-III structure, also termed ‘broken gap’ structure, the conduction band of one
material is below the valence band of the other material. The technologically most relevant are type-I
structures. The design of heterostructures to fulfill a certain device functionality or to have certain
physical properties is called ‘band gap engineering’.
Fig. 12.21 Position of
conduction and
valence-band edges for a
variety of semiconductors
(relative to a common
vacuum level at E = 0 eV).
Based on values from
[1167], and from Al 2 O 3
(on InP) [1168], InN on
diamond [1169], InN on
MgO [1170], Ga 2 O 3 on
GaN from [1171], and
In 2 O 3 on Si from [1172,
1173]. On the right hand
side, the work functions of
several metals are shown
for comparison
Fig. 12.22 Position of
band edges (band
alignment) in a type-I, b
type-II and c type-III
heterostructure
E vac
Electron energy
Spatial coordinate
E g2
2
1
E g1
E V
E C
E g2
2
1
E g1
E C,V
E g2
2
1
E g1
(a) type-I
(b) type-II
(c) type-III
365
12.3 Energy Levels in Heterostructures
12.3.1 Band Lineup in Heterostructures
In heterostructures, semiconductors with different band gaps are combined. The relative position of
conduction and valence band (band alignment) is determined by the electron affinities χ as shown in
Fig. 12.21. For a semiconductor, the electron affinity is the (positive) energy difference between vacuum
level and conduction band edge. It can lead to different types of heterostructures. Early perspectives of
semiconductor heterostructures are discussed in [1166]. The band alignment can be estimated from the
position of the branch point energies (Sect. 7.8) of the two constituents [699] but additional interface
dipoles may have to be considered.
In Fig. 12.22, the band alignment for type-I, type-II and type-III heterostructures are shown. In the
type-I structure (straddled band lineup) the lower conduction-band edge and the higher valence-band
edge are both in the material with smaller band gap. Thus, electrons and holes will localize there. In
the type-II structure a staggered lineup is present and electrons and holes will localize in different
materials. In the type-III structure, also termed ‘broken gap’ structure, the conduction band of one
material is below the valence band of the other material. The technologically most relevant are type-I
structures. The design of heterostructures to fulfill a certain device functionality or to have certain
physical properties is called ‘band gap engineering’.
Fig. 12.21 Position of
conduction and
valence-band edges for a
variety of semiconductors
(relative to a common
vacuum level at E = 0 eV).
Based on values from
[1167], and from Al 2 O 3
(on InP) [1168], InN on
diamond [1169], InN on
MgO [1170], Ga 2 O 3 on
GaN from [1171], and
In 2 O 3 on Si from [1172,
1173]. On the right hand
side, the work functions of
several metals are shown
for comparison
Fig. 12.22 Position of
band edges (band
alignment) in a type-I, b
type-II and c type-III
heterostructure
E vac
Electron energy
Spatial coordinate
E g2
2
1
E g1
E V
E C
E g2
2
1
E g1
E C,V
E g2
2
1
E g1
(a) type-I
(b) type-II
(c) type-III