2.1 Limitations of the Channel
Material InGaAs
To obtain a high conduction band offset DEC
of the channel/barrier interface the In content has to be maximized as
shown in Figure
2.2. A second benefit of a high In mole fraction is an improved transport
behavior as shown in Figure
2.4. The dark shaded area refers to data from [7-9]
obtained from bulk GaAs. The light shaded area comprises data for In0.53Ga0.47As
on InP substrates from different authors compiled in [10].
It shows much higher velocity over the whole electric field range. Unfortunately,
the In content of InGaAs grown on GaAs without dislocations has tight limits
which will be shown in the following.
The lattice constants of GaAs, AlAs, InAs and their alloys are shown in Figure 2.2 versus the band gap along with other important semiconductors. As shown the lattice constants of GaAs and AlAs differ only slightly. Therefore AlyGa1-yAs can be grown in almost arbitrary thicknesses on GaAs for all Al contents without introducing dislocations in the crystal (lattice matched). The lattice constant of InxGa1-xAs is significantly larger than that of GaAs for considerable In contents. Nevertheless, InxGa1-xAs can be grown with moderate In contents in thin strained layers on GaAs substrates without introducing dislocations which is called pseudomorphic growth.
The limitations of the In content and the corresponding thickness of
the layer is given by the critical thickness (dC cr).
If the layers thickness is increased above dC cr an increased
dislocation density has to be expected. dC cr can be
calculated according to the theory of Matthews and Blakeslee [11-13]
by:
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(1)
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(2)
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(3)
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In Figure
2.5 the solutions for the critical thickness dC cr
of (1) are shown. The theory of
Matthews and Blakeslee is confirmed by various data of the literature.
Samples below the critical thickness exhibit a low dislocation density
whereas samples above the critical thickness show a high dislocation density,
i. e. the strained layer starts to relax. The asterisk symbols in
Figure
2.5 represent samples with moderate dislocation density. This shows
that the transition from pseudomorphic growth to relaxation is not abrupt.
Typical channels of pseudomorphic HEMTs have a thickness of 12 nm and an
In content of 20% which is below the critical thickness. But also HEMTs
with other channel thicknesses and compositions have been reported [17,
18].
Next: 2.2 Electron Energy Levels in Strained
Quantum Wells Up: 2 The Principles of a HEMT
Previous: 2 The Principles of a HEMT
Helmut Brech 1998-03-11