366
12 Heterostructures
(a)
(b)
Fig. 12.23 a XPS measurements of InN and GaN and a InN/GaN heterostructure. The vertical dashed lines indicate
the core level positions in the bulk (black) and the heterostructure (red). The valence band offset is given by V =
core,HS − core,bulk (when E V is set to zero for both the bulk materials). b Schematic band lineup of the type-I
InN/GaN heterojunction (all energies in eV). Adapted from [1174]
In a type-I heterostructure, the conduction- and valence-band discontinuities are given, respectively, by
C = χ 1 − χ 2
(12.3a)
V = (χ 1 + E g 1 ) − (χ 2 + E g 2 ) .
(12.3b)
Experimentally, the valence band offset can be determined using X-ray photoelectron spectroscopy
(XPS) probing the filled states; together with the band gap then also the conduction band offsets are
obtained. As example, in Fig. 12.23a the binding energies of an indium and a gallium core level are
shown with the valence band edges of InN and GaN, respectively, set to zero energy. Both core levels
are then also investigated in a 5 nm InN on GaN heterostructure (the InN layer is sufficiently thin to
allow photoelectrons to escape from the GaN underneath). The sum of the shifts represents the valence
band offset ( V = 0.58(8) eV from the analysis of several core levels [1174]). Together with the band
gaps, the conduction band offset results in V = 2.22 eV as schematically depicted in Fig. 12.23b.
Depending on the layer sequence of high- and low-bandgap materials various configurations, as
shown in Fig. 12.24 have obtained special names, such as single heterointerface, quantum well (QW),
multiple quantum well (MQW), superlattice (SL). In the extreme case the layer is only one monolayer
thick (Fig. 12.25) and the concept of layer and interface blurs. Such atomically precise layer sequences
are mastered nowadays for a variety of material systems such as (Al,Ga)As/GaAs/InAs, InP/(In,Ga)As,
Si/SiGe, ZnO/(Mg,Zn)O and also BaTiO 3 /SrTiO 3 .
The abruptness of interfaces is determined by the epitaxial machine through the switching precision
of the incoming material flux and fundamentally limited by segregation phenomena which can be
modeled with a segregation coefficient [1175] (cmp. Sect. 4.2.4). As shown in Fig. 12.25c, In has
the tendency to be carried into the following GaAs layer. A quantitative evaluation is possible using
aberration-corrected scanning transmission electron microscopy [1176].
12 Heterostructures
(a)
(b)
Fig. 12.23 a XPS measurements of InN and GaN and a InN/GaN heterostructure. The vertical dashed lines indicate
the core level positions in the bulk (black) and the heterostructure (red). The valence band offset is given by V =
core,HS − core,bulk (when E V is set to zero for both the bulk materials). b Schematic band lineup of the type-I
InN/GaN heterojunction (all energies in eV). Adapted from [1174]
In a type-I heterostructure, the conduction- and valence-band discontinuities are given, respectively, by
C = χ 1 − χ 2
(12.3a)
V = (χ 1 + E g 1 ) − (χ 2 + E g 2 ) .
(12.3b)
Experimentally, the valence band offset can be determined using X-ray photoelectron spectroscopy
(XPS) probing the filled states; together with the band gap then also the conduction band offsets are
obtained. As example, in Fig. 12.23a the binding energies of an indium and a gallium core level are
shown with the valence band edges of InN and GaN, respectively, set to zero energy. Both core levels
are then also investigated in a 5 nm InN on GaN heterostructure (the InN layer is sufficiently thin to
allow photoelectrons to escape from the GaN underneath). The sum of the shifts represents the valence
band offset ( V = 0.58(8) eV from the analysis of several core levels [1174]). Together with the band
gaps, the conduction band offset results in V = 2.22 eV as schematically depicted in Fig. 12.23b.
Depending on the layer sequence of high- and low-bandgap materials various configurations, as
shown in Fig. 12.24 have obtained special names, such as single heterointerface, quantum well (QW),
multiple quantum well (MQW), superlattice (SL). In the extreme case the layer is only one monolayer
thick (Fig. 12.25) and the concept of layer and interface blurs. Such atomically precise layer sequences
are mastered nowadays for a variety of material systems such as (Al,Ga)As/GaAs/InAs, InP/(In,Ga)As,
Si/SiGe, ZnO/(Mg,Zn)O and also BaTiO 3 /SrTiO 3 .
The abruptness of interfaces is determined by the epitaxial machine through the switching precision
of the incoming material flux and fundamentally limited by segregation phenomena which can be
modeled with a segregation coefficient [1175] (cmp. Sect. 4.2.4). As shown in Fig. 12.25c, In has
the tendency to be carried into the following GaAs layer. A quantitative evaluation is possible using
aberration-corrected scanning transmission electron microscopy [1176].