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The properties of semiconductors depend
strongly on the presence of defects, even
in relatively small concentrations. Here,
any break of the lattice periodicity may
be considered as a defect, desired dopants
as well as residual impurities and intrinsic
defects as vacancies and interstitials.
Each defect gives rise for a characteristic
electric field gradient (EFG) at neighbouring
lattice sites, which can be measured with
PAC, e.g. by the 111In probe.
However, an identification of the defect
complexes causing the EFG, i.e. the determination
of the chemical nature and the structure
on an atomic scale, is difficult in many
cases. A theoretical prediction of the EFG
a given defect provokes, is therefore desirable.
For EFG calculation, the linearised augmented
plane wave method (LAPW) within the framework
of density functional theory is very well
suited. Our calculations are performed with
the WIEN97
program package (TU Vienna), where the
LAPW method is implemented. The benefit
of the LAPW calculations is the capability
to analyse structural and electronical properties
of defects theoretically, while experimental
evidence of the assumed defect is given
by the PAC technique via the EFG.
The Group V acceptors N, P, As and Sb form
donor acceptor pairs with 111In
donors in the II-VI semiconductor CdTe;
after the decay to 111Cd, for
each group V acceptor a characteristic EFG
is measured at the NN-Cd site by the PAC
[1]. The results of the present EFG calculations
are published in [2]. The following figure
(created with XCrySDen) shows two of the
32 atomic supercells that are constructed
for the calculation, one wrapped in the
Wigner-Seitz cell of the BCC supercell-lattice.
Blue balls are Cd, yellow are Te, and the
small red ball is N.
It turns out, that taking into account
structural relaxation is crucial for the
accuracy of the calculated EFG: A change
of 1% in the distance of the NN-Cd atom
to the group V acceptor (symbol A in the
figure) leads to a change of about 10% in
the calculated EFG. All atomic positions
up to the 2nd shell about the group V element
are relaxed until the calculated forces
vanish. The following figure shows this
two shells, and the relaxation is sketched.
In the case of N, where the relaxation is
most pronounced, the Cd-N distance is about
20% less than the Cd-Te distance.
Providing the proper, relaxed atomic structure,
the calculated EFG for the ionised state
of the group V acceptors (A) show a very
good agreement with the experimental values
from ref. [1]. Both experimental and calculated
EFG [Vzz in 1021V/m2]
are listed in the following table:
| |
exp. |
CdTe:A- |
CdTe:A0 |
| CdTe:N |
+/-13.95 |
-13.7 |
-13.4 |
| CdTe:P |
+/-10.56 |
-11.2 |
-10.0 |
| CdTe:As |
+/-9.27 |
-9.5 |
-7.7 |
| CdTe:Sb |
+/-7.62 |
-8.1 |
-5.3 |
Along with the sensitivity of the EFG on the
relaxation, the agreement is also evidence
of the accuracy of the calculated lattice
structure. A variety of other calculations,
including intrinsic defects and more complex
cases where two host atoms are replaced in
the supercell by impurities, have also been
finished meanwhile and confirm the universal
applicability of the LAPW method for the calculation
of defect induced EFG in semiconductors.
[1] V. Ostheimer, A. Jost, T. Filz, St.
Lauer, H. Wolf and Th. Wichert, Appl. Phys.
Lett. 69, 2840 (1996).
[2] Stephan Lany, Peter Blaha, Joachim
Hamann, Volker Ostheimer, Herbert Wolf and
Thomas Wichert, Phys. Rev. B 62,
R2259 (2000).
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