10. Appendix

A4.1 A Prototypical Deep Center in N-Type Zincblende-Type Semiconductors 683
independent of their chemical nature. However, there is a “chemical shift” in
their activation energies. For example, Si DX centers have larger activation
energies than Sn. Similarly, S DX centers have larger activation energies than
Te. This chemical shift makes it possible to convert one donor specie into the
deep DX center while a different donor specie remains shallow. When this
shallow-to-deep conversion occurs for one donor specie it can capture free
electrons from the specie which remains shallow. Such a co-doping experiment
was performed by Baj et al. [Baj93]. These authors co-doped a GaAs sample
with both Te and Ge. A hydrostatic pressure of over 1.0 GPa converts Ge into
a DX center while Te remains as a shallow donor level in the gap. Normally
these Ge donors contribute free carriers to the conduction band and the free
electron concentration can be measured accurately by Hall effect (see 5.5.2).
When the Ge donors transform to DX centers there is a drop in the free electron
concentration. This drop should be exactly equal to the Ge concentration
if the deep state captures only one electron per Ge atom. On the other hand,
if the deep state has a negative U then each Ge atom will capture two electrons
with the extra electron coming from the Te donors which remain shallow
at 1 GPa. As a result, the total free carrier concentration will decrease by twice
the total number of Ge donors. Such a co-doping experiment can, therefore,
probe not only the negatively charged DX state but also the neutral A1 state
with small lattice relaxation.
To realize the above idea Baj et al. utilized a combination of light irradiation
and temperature to control the number of electrons trapped on the DX
centers. The Hall effect is used to measure the free carrier concentration as
a function of pressure at 77 K and 100 K, respectively. Light illumination was
used to excite carriers into the persistent photo-conducting states. Their results
are shown in Figure A4.7. Both curves exhibit a step at a pressure between
0.5 GPa and 1.0 GPa. The step in the 77 K curve is smaller and has a magnitude
of ∼ 1 × 10 17 cm 3 . This step is explained by the trapping of electrons
from the conduction band into the shallower A1 level of Ge. Thus, the concentration
of Ge impurities is determined accurately to be 1 × 10 17 cm 3 since
each A1 state captures only one electron. The deeper -U DX level associated
with the Ge impurities does not capture electrons at 77 K because of its large
capture barrier height. However, at 100 K the capture rate of Ge DX center
becomes much larger. If the DX center were really a -U center, then one
would expect to see a bigger drop in the carrier concentration due to trapping
into the DX state. Indeed Baj et al. found that the step in the 100 K curve
in Fig. A4.7 is ∼ 2 × 10 17 cm 3 or exactly twice the Ge impurity concentration.
This experiment unambiguously demonstrates that each DX level of the
Ge impurity in GaAs captures two electrons. The beauty of this experiment
is that the result is independent of the existence of any compensating acceptors.
Also, no prior information on doping concentrations is needed. The only
requirement is that the concentration of the Te shallow donor which provides
the electrons for the Ge DX centers be higher than that of the Ge donors so
that Te can provide enough electrons to fill the -U DX ground states.