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Aharonov-Bohm Interference of Holes at Dislocations in Lattice-Mismatched Heterostructures
T. Figielski, T. Wosiński, A. Mąkosa
To cite this version:
T. Figielski, T. Wosiński, A. Mąkosa. Aharonov-Bohm Interference of Holes at Dislocations in Lattice- Mismatched Heterostructures. Journal de Physique III, EDP Sciences, 1997, 7 (7), pp.1515-1520.
�10.1051/jp3:1997204�. �jpa-00249662�
Aharonov-Bohm Interference of Holes at Dislocations in Lattice-Mismatched Heterostructures
T. Figielski (*), T. Wosifiski and A. M~kosa
Institute of Physics, Polish Academy of Sciences, Al. Lotnik6w 32/46, 02-668 Warszawa, Poland
(Received 30 October 1996, accepted 27 January 1997)
PACS.72.10.Fk Scattering by point defects, dislocations, surfaces and other imperfections PACS.73 40.Kp III-V semiconductor-to-semiconductor contacts, p-n junctions and
heterojunctions
PACS.03 65.Bz Foundations, theory of measurement, miscellaneous theories (including
Aharonov-Bohm effect, Bell inequalities, Berry's phase)
Abstract. We have succeeded in revealing Aharonov-Bohm type interference of holes in
macroscopic semiconductor sample containing an array of straight-line dislocations. This inter- ference has been observed at helium temperatures as oscillations in the forward current flowing through p+-n junction of the lattice-mismatched GaAsi-~Sb~ /GaAs heterostructure while mea- sured as a function of the magnetic field perpendicular to the current. The oscillation cycles
arise when a primary hole wave meeting the Read's cylinder of a misfit dislocation interferes with a wave which circled completely round the cylinder.
1. Introduction
Dislocations are unique defects of crystalline solids as they represent topological faults of Bravais lattice. Therefore they induce some effects on the electronic properties of semiconductor
crystals. The latter are mainly affected by the presence of localised (at least m two dimensions)
electron states in the dislocation core, for instance, those associated with dangling bonds.
Usually, these states accept majority charge carriers from the bulk of material, and then, the
charged dislocation line becomes surrounded by a screening cylinder of opposite-sign charges
associated with ionised donors or acceptors. This (Read's) cylinder is essentially free from the
majority charge carriers in the conduction or valence band of the semiconductor and has well defined edges in heavily doped material at low temperature. In GaAs with carrier concentration of10~~ cm~~ the cylinder diameter is of the order of 100 nm, that is presumably smaller than the phase-coherence length of the charge-carrier wave function at liquid helium temperatures.
The appearance of charge-carrier free cylinders in dislocated semiconductor represents an-
other kind of topological fault affecting charge carrier trajectories. Such a semiconductor may be considered as a multiply connected conductor threaded by cylindrical voids. A conduction
electron (hole) which meets the cylinder has two topologically different paths (clockwise and
counter-clockwise) to pass round this obstacle These paths interfere when meet again behind the cylinder. When a magnetic field is applied along the cylinder axis, its vector potential
(* Author for correspondence (e-mail figieltlifpan.edu,pl) g Les #ditions de Physique 1997
1516 JOURNAL DE PHYSIQUE III N°7
88
Fig. i. Illustration of the Aharonov-Bohm effect in a nonconducting-cylinder geometry. A classical
skipping-orbit trajectory of a hole moving in a high magnetic field along the cylinder periphery is shown. Interference occurs between primary wave which meets the cylinder at a point O and a wave which circled round the cylinder.
causes a phase shift of the wave-function but of opposite sign on each of these two paths. Thus
the magnetic flux penetrating the cylinder changes the resulting interference pattern. This effect, known as the Aharonov-Bohm (AB) direct interference ill, is now widely observed as magnetoresistance oscillations in metallic or doped-semiconductor rings of mesoscopic size at very low temperature [2].
We searched for this type of interference in a macroscopic sample, that is in a piece of semiconductor crystal containing an array of parallel dislocations. We hoped that the effect will manifest itself as a periodic change of the conductance perpendicular to the dislocation lines measured as a function of the magnetic field applied parallel to the dislocations lines. Only recently we succeeded in finding such an effect experimentally. It exhibits specific features
which distinguish it from the AB effect appearing in mesoscopic rings.
2. Fundamentals of the Elfect
The direct AB interference, mentioned in the Introduction, will hardly give rise to observable current oscillations in the case being of our interest, since then, there is a very large number of different paths that circumscribe the impenetrable Read's cylinder. The magnetic field, B,
will cause different phase shift for paths enclosing different area, and so, their contribution to
the AB oscillations at low magnetic fields will be averaged toward zero. But this situation
can change at high magnetic fields when the magnetic length, (hleB)~/2, becomes shorter than the cylinder radius R. Then, charge carriers which experience the Lorentz force bending
their trajectories toward the cylinder axis, are forced to circle along the cylinder circumference via skipping orbits; Figure I. In this case, a primary electron (hole) wave which meets the
cylinder at a point O, interferes with a wave which circled completely around the cylinder.
This gives rise to a hole trapping on a quasi-stationary orbit encircling the cylinder. Now, the
magnetic flux enclosed by the charge carrier trajectories is well defined by the cylinder radius:
4lB = 7rR2B. In the present approximation we neglect an additional flux enclosed between the skipping-orbit trajectory and the cylinder circumference and also ignore effects associated with coherent charge-carrier focusing [3] The squared modulus of the wave function at the point O, ~lbs, which results from the interference between the primary wave, ~lo, and the wave
which circled once around the cylinder, ific, can be written as:
j~~~j2 m j~o + ~cj2
m 2j~oj2ii + cos(2~rpR/h + 2~r~~ /~o)j, (i)
where p is the charge-carrier kinetic momentum and 4l0 " hle. '
Fig 2. Planar cathodoluminescence micrograph of the interface of GaAso ggsbo oi/GaAs hetero- structure revealing misfit o and fl dislocations as horizontal and vertical, respectively, dark lines.
Thus the probability of hole trapping will exhibit oscillations as a function of the magnetic flux enclosed inside the cylinder, with the period 4l0 " hle (the same as in the case of direct
interference). But here, in distinction from the direct-interference case, an additional phase factor, 27rpR/h, appears in argument of the cosine function describing the oscillations, which depends on the charge carrier wavenumber. So, in principle, a monochromatic electron (hole)
wave is required to observe the AB oscillations in this case, since contribution of different wave-
lengths will cause different phase shifts which will tend to smear out the oscillations. On the other hand, this dependence on the charge carrier wavenumber offers additional experimental possibilities which could be the source of complementary information.
3. Samples
The object of our investigations were p+-n junctions fabricated by liquid-phase-epitaxy growth
of n-type GaAsi-zsb~ layers on (001) oriented p+-type GaAs:Zn substrates. We studied
samples with three different contents of Sb in the epilayer: ~
= 0.01, 0.02 and 0.03, and, in
addition, a reference sample free from Sb. The results presented in this paper refer to the sample with ~
= 0.01 for which the lattice mismatch between the substrate and epilayer is of the order 0.I$lo. Results obtained for samples with a higher mismatch could hardly be analysed
because of their complicated behaviour. A two-dimensional array of
a and fl dislocations lying along two different orthogonal ii lo) directions at the interface has been generated by the lattice
mismatch in the heterostructures. The presence of such dislocation array was revealed with spatially resolved cathodoluminescence [4]; Figure 2.
4. Experimental Results
We examined the forward current flowing through the junction at temperatures down to 1.8 K in a magnetic field transverse with respect to the current. The current is mainly due to the diffusion of injected holes. The most important finding has been the discovery of fine
oscillatory structure in the current measured as a function of the magnetic field. It is absent at low magnetic fields and only appears for B > 3 T. This structure is clearly seen at 1.8 K while
measuring the derivative of the current with respect to the bias voltage (Fig. 3). The same
1518 JOURNAL DE PHYSIQUE III N°7
T =1.8 K
~
~
~
~i
2
(al
~j ]
8
.
I
ui#
~ c~
I
~§ g
~ ~AB
ill
$l
2
6 7 8 9 10 11 12 13
B (T)
Fig. 3 High-magnetic-field part of the derivative of the current density with respect to the voltage
us magnetic field perpendicular to the current, measured at a temperature of1.8 K a) Magnetic field parallel to the misfit a dislocations. b) Magnetic field parallel to the misfit fl dislocations Vertical lines indicate the oscillatory structure with a period of 0 39 T (a) and 0 48 T (b). Inset in 16) power
spectral density, estimated by the maximum entropy method, of the data presented in 16) from the range 7-12 T.
structure has been obtained by computing the derivative of the current with respect to the
magnetic field. The apparent period of the oscillations is about 0.5 T. This principal period has been determined more precisely using the
mamm~m entropy method which has also exhibited
the presence of subsidiary periods (inset in Fig. 3b). The exact shape of the observed fine structure, but not the principal period, is very" sensitive function of the bias voltage applied
to the junction. This fine structure disappears after elevating the temperature above
r~ 8 K
and does not appear at all when the magnetic field is parallel to the current. It has been also
absent in the reference sample free from misfit dislocations.
A direct evidence for the connection of the fine oscillatory structure with the dislocation array has been found by changing the angle, ~J, betv.een the magnetic field direction and dislocation
axes. When
~J = 45°, the principal period of the oscillations is 1.4 re II cos(45°) of its value at ~J = 0° (or 90°). Accepting that the oscillations are due to the AB effect caused by holes,
r~
which is a reasonable value.
More careful analysis of the experimental results has revealed a systematic difference between the principal periods measured in two different configurations of magnetic field, that is of B
directed along either a or fl dislocation axis. The periods in these two configurations are
0.39 and 0.48 T, which correspond to the Read's cylinder radii of a and fl dislocations equal
l16 and 105 nm, respectively. This result shows that larger positive charge is accepted by o
than by fl dislocations under the same conditions. Consequently, hole traps of a dislocations have to be deeper in the band gap than those of fl dislocations. This is in agreement with our
earlier determination, by means of Deep-Level Transient Spectroscopy (DLTS), of energy levels associated with both types of dislocations in GaAs [5]. The concluded above difference in Read's
cylinder radii of o and fl dislocations is also consistent with the higher recombination activity of
a dislocations as against that of fl dislocations. The latter relation was demonstrated by means of Electron-Beam-Induced Current (EBIC) contrast investigations of dislocations introduced by micro-indentation in n-type GaAs [6, 7].
5. Conclusions
In conclusion, we have observed the Aharonov-Bohm interference occurring at misfit disloca- tions in semiconductor heterostructure. This quantum interference is complementary, to the
conventional AB effect appearing in metallic or semiconductor rings of mesoscopic size. While the latter effect is suppressed in intense magnetic fields [8], the present phenomenon only ap-
pears there. This phenomenon, despite its own physical significance, can also be exploited
as a tool for the investigation of misfit dislocation features inaccessible by other methods.
Another significant effect found in these investigations, that is a complete suppression of the current flowing through the junction at very high transverse magnetic fields, will be discussed elsewhere.
Acknowledgments
The authors would like to thank Dr J. Raczyliska (Military University of Technology, Warsaw)
for growing the investigated heterostructures, Professor A. Zozime (LPSB-CNRS, Bellevue)
for cooperation in the cathodoluminescence measurements and Dr. W. Dobrowolski (Institute
of Physics, Warsaw) for cooperation in the magneto-transport measurements. This work was partly supported by the State Committee for Scientific Research of Poland under grant N°2
P302128 07.
References
iii Aharonov Y. and Bohm D., Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115 (1959) 485-491.
[2] Appenzeller J., Schipers Th., Hardtdegen H., Lengeler B. and Lbth H., Aharonov-Bohm effect in quasi-one-dimensional InGaAs/InP rings, Phys. Rev. B 51 (1995) 4336-4342.
[3] Beenakker C-W-J- and van Houten H., Skipping orbits, traversing trajectories, and quan- tum ballistic transport in microstructures, S~perlatt. Microstr. 5 (1989) 127-132.
1520 JOURNAL DE PHYSIQUE III N°7
[4] Wosifiski T., Mjkosa A., Figielski T. and Raczyfiska J., Deep levels caused by misfit dislocations in GaAssb/GaAs heterostructures, Appl. Phys. Lett. 67 (1995) l131-l133.
[5] Wosifiski T. and Figielski T., Energy levels and electrical activity of dislocation electron
states in GaAs, Acta Phys. Polon. A 83 (1993) 51-58.
[6] Sieber B., Farvacque J.L. and Carton P., EBIC contrast study of the recombination mech- anism at dislocations in GaAs, J. Phys. III France 2 (1992) 325-333.
[7] Wosifiski T., Zozime A., RiviAre A. and Vermeulin C., EBIC investigation of a and fl dislocations in GaAs, Phys. Stat. Sol. (a)142 (1994) 347-355.
[8] Timp G., Behringer R.E., Westerwick E.H. and Cunningham J.E., Transport in an electron
waveguide, in "Quantum Coherence in Mesoscopic Systems", B. Kramer, Ed. (Plenum Press, New York, 1991) pp. l13-lsl.
