Charge Accumulation at a Threading Edge Dislocation in GaN Page: 1 of 5
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Charge Accumulation at a Threading Edge Dislocation in GaN
K. Leung, A. F. Wright, and E. B. Stechel'
Sandia National Laboratories, MS 1421, Albuquerque, N.M. 87185
' Ford Motor Company, MD 3028/SRL, Dearborn, MI 48121-2053
(December 19, 1998)
We have performed Monte Carlo calculations to determine the charge accumulation on threading
edge dislocations in GaN as a function of the dislocation density and background dopant density.
Four possible core structures have been examined, each of which produces defect levels in the gap
and may therefore act as electron or hole traps. Our results indicate that charge accumulation,
and the resulting electrostatic interactions, can change the relative stabilities of the different core
structures. Structures having Ga and N vacancies at the dislocation core are predicted to be stable
under nitrogen-rich and gallium-rich growth conditions, respectively. Due to dopant depletion at
high dislocation density and the multitude of charge states, the line charge exhibits complex crossover
behavior as the dopant and dislocation densities vary.
Gallium nitride films grown on sapphire substrates typ-
ically contain between 108 and 1010 threading disloca-
tions per cm2 as a result of the substantial film-substrate
chemical and lattice mismatch.1 Nevertheless, it has been
possible to fabricate bright and efficient light-emitting
diodes from films composed of GaN alloyed with InN and
AIN.2 This success led several researchers to speculate
early on that threading dislocations in GaN might not
act as efficient minority-carrier recombination sites.1 Re-
cent experimental studies, however, have confirmed that
there is significant optical3 and electrical4 activity asso-
ciated with these defects. In particular, results from a
recent scanning-capacitance microscopy study suggest
that dislocations are negatively charged in n-type GaN,
and studies of transverse mobility in n-type GaN films '7
indicate that electrons are scattered from these nega-
tively charged dislocations.
Recent charge-state calculations for AIN and GaN8 in-
dicate that threading edge dislocations produce defect
levels in the forbidden energy gap. These calculations
provide estimates for these defect levels. In agreement
with experimental studies, edge dislocations are pre-
dicted to be negatively charged in n-type GaN. However,
the amount of charge accumulation could not be quan-
tified because electrostatic interactions between charged
defect sites and between defect sites and ionized dopants
were not included in the calculations. In this study, we
treat coulomb interactions explicitly and therefore are
able to predict the amount of charge accumulation on an
edge dislocation under a variety of doping conditions.
We examine the zero-temperature behavior of thread-
ing dislocations using simulated annealing.9 The simu-
lation cell contains one dislocation and is of lateral di-
mension K ,21 where adis is the dislocation density.
Electrons, modelled as point charges, can transfer be-
tween dopants (donors or acceptors) and defect levels
at the dislocation cores, and among the dopants them-
selves. The dislocation consists of 50-1000 defect sites
situated 5.185A apart. We have examined the four dislo-
cation core structures previously considered in first prin-
ciples studies: full core, open core, Ga-vacancy, and N-
vacancy.8 The possible charge states in each core struc-
ture are bracketed by the minimum and maximum values
deduced from first principles calculations. The energy
levels of these charge states, neglecting coulomb inter-
actions, are listed in Table I. The coulomb interactions
among charged defects and ionized dopants are screened
using an empirical, bulk, orientationally averaged static
dielectric constant of ea = 10. Each dopant is randomly
placed within a preassigned volume equal to the inverse
of the dopant density pd. The ionization energy (electron
affinity) of electron donors (acceptors) are taken from ex-
perimental values; see Table I. We apply periodic bound-
ary conditions in all three spatial dimensions and treat
the image charges using the Ewald sum technique. We
find that the effect of dopant positions on simulation re-
sults is negligible. By considering more than one dislo-
cation per simulation cell, we also find that correlation
between dislocations is negligible. We expect the effect of
finite temperature will not be important because defect
levels are widely separated in the band gap.
The existence of multiple charge states suggests that
charge modulation along the dislocation line might be
energetically favorable. For example, in the isolated Ga
vacancy structure, if the charges were discrete, alternat-
ing -3/+3 charges are favored over the 0/0 charge config-
uration by - 0.24 eV per site. However, first principles
studies of core structure cells doubled along the disloca-
tion direction indicate that the excess charges are always
delocalized, due to (1) large dispersions in the low-lying
impurity bands; and (2) unfavorable strain field inter-
actions associated with unlike charge states on adjacent
core structures. Based on the above, we treat the charges
residing in defect levels as delocalized and uniformly dis-
tributed over the length of the dislocation, and we model
these charges as a continuous variable A.
In the limit of small line charge A, our work is similar to
the model derived by Read10 and widely used for making
line charge estimates.' Our model improves upon that
analytical work in that it can treat (1) multiple charge
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Leung, K.; Stechel, E.B. & Wright, A.F. Charge Accumulation at a Threading Edge Dislocation in GaN, article, January 20, 1999; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc679447/m1/1/: accessed February 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.