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3.3.2 Bandgap Offsets
The problem to align the bandgaps of two or more different materials is old and
not completely solved [129,130,131] due to the
dependence on the growth conditions. The many suggested approaches mainly
differ in whether to use the electron affinity to align the conduction bands,
whether to align the midgaps, or whether to align the valence band edges. In
MINIMOSNT the last approach is used.
An energy offset,
, is used to align the band edge energies of different
materials.
is an arbitrary value and by changing it consistently for
all materials at the same time the same results are obtained. As a default in
MINIMOSNT for the group IV materials the reference material is Si. The origin of
the energy axis is assumed to be in the middle of the Si bandgap at 300 K. This
corresponds to a fixed value for Si of
eV. For the IIIV
material system GaAs is chosen as the reference material. Therefore, the offset
for GaAs is
eV. The default offsets for other materials,
summarized in Table 3.14, are chosen to give good agreement with reported data from
[108,111,129,130,131].
Table 3.14:
Parameter values for modeling the bandgap energies
Material 
[eV] 
Material 
[eV] 
Si 
0.562 
InAs 
0.286 
Ge 
0.157 
InP 
0.724 
GaAs 
0.712 
GaP 
1.062 
AlAs 
1.008 



The energies of the conduction and valence band edges
are calculated by



(3.66) 



(3.67) 
For alloy materials, the following expressions for the conduction and valence band
energies are often used.



(3.68) 



(3.69) 
The change of the bandgap with the material composition is defined by the ratio
, starting from one of the materials. For example, for
AlGaAs/GaAs interface it is known that this ratio equals 60%.
This means that, with increasing , 60% of the increase of the bandgap
(
) is contributed to the conduction band
() and 40% to the valence band (). The model, being so
formulated, is not symmetric and general enough. However, assuming
is constant for the whole composition range one obtains:
Thus, from (3.68) and (3.70) the ratio
can be expressed as:
Replacing it in (3.68) or (3.70) the offset of alloy material is obtained:
The valence and the conduction band energies are calculated by
(3.66) and (3.67), respectively. Using the default
model parameters in MINIMOSNT ratios
of 0.12 for
SiGe, 0.6 for AlGaAs, 0.5 for InAlAs,
0.6 for InGaAs, InAsP, GaAsP, and 0.3 for
InGaP are obtained, which are in fairly good agreement with
experimental data [110,89,111,108,132].
The complete bandgap alignment of all semiconductor materials presented in
MINIMOSNT is shown in Fig. 3.20.
Figure 3.20:
Bandgaps of all semiconductor materials modeled in MINIMOSNT:
Reference energies for IV group and IIIV group materials are the mid gaps of
Si and GaAs, respectively, placed at 0 eV.

Special attention is paid to the band offsets at the heterointerfaces and
thermionic emission or thermionicfield emission model must be used in
the case of abrupt heterojunctions (see Section 3.1.6).
Next: 3.3.3 Bandgap Narrowing
Up: 3.3 BandStructure
Previous: 3.3.1 Bandgap Energy
Vassil Palankovski
20010228