10. Appendix

A4.1 A Prototypical Deep Center in N-Type Zincblende-Type Semiconductors 677
comes much faster than at low temperatures. The result is a sudden rise in
the capacitance. If the sample is now cooled back to 50 K under zero bias,
the capacitance will follow curve (1) rather than retrace curve (2). The reason
why electrons are not re-captured into the deep centers under zero bias
is because the electrons have to overcome a barrier of 0.2 eV in order to
be re-captured by the deep centers. Thus, at temperatures below 100 K the
capture rate is too small for a significant number of electrons to return to the
deep centers. Curve (3) is obtained by illuminating the sample with a broadband
light source after it has been cooled to low temperature in the dark and
under zero bias. The rise in capacitance indicated by the arrow (labeled hÓ)
in Fig. A4.1(b) suggests that the deep centers are photo-ionized. However,
the capacitance remains high even when the light is turned off. This indicates
that carriers have been photo-excited into a metastable state. If the sample is
now warmed up in the dark, the capacitance will follow curve (3). The sudden
decrease in the capacitance at less than 100 K can be explained by the thermal
activation of the capture of electrons from the metastable state back onto
the deep centers. At still higher temperatures the emission process becomes
thermally activated and results in the rise of the capacitance. Thus, the results
obtained by Lang et al. for the behavior of Te in AlGaAs are completely different
from those expected from shallow donors.
Lang et al. named this newly discovered deep defect the DX center because
they thought that it involved a complex consisting of a donor atom D
and an unknown constituent X. Since this center was first observed in alloys
of AlGaAs only, it was believed that X is an intrinsic defect, such as a vacancy
or an interstitial, which are abundant in alloys. Another characteristic of the
DX centers which distinguishes them from the shallow impurities is that their
optical ionization energy (i.e. the minimum photon energy necessary to ionize
the defect, usually denoted by Eop) is much larger than the thermal ionization
energy. For shallow impurities, these two energies are identical and we have,
therefore, not made a distinction between them. In case of the DX centers Eop
is ∼1 eV as shown in Fig. A4.3.
Lang et al. explained qualitatively many of the unusual properties of the
DX centers with a large lattice relaxation model. We shall discuss this model
in greater detail in A4.1.4. The results of Lang et al. in AlGaAs:Te were soon
confirmed by other authors using different donors. For example, Chand et al.
[Chand84] studied the DX centers in AlGaAs:Si using temperature-dependent
Hall-effect measurements. They determined the thermal activation energy of
the Si DX centers as a function of alloy concentration. They found that the
DX center energy level does not follow the lowest conduction band minima
as a function of Al mole fraction. Instead, it appears to follow the conduction
band minima at the L point of the Brillouin Zone as shown in Fig. A4.4. The
fact that the DX center does not follow the nearest conduction band minimum
suggests that it is not a shallow impurity. Lifshitz et al. [Lifshitz80] made
the interesting observation that pressure has the same effect in converting