Effect of annealing on the depth profile of hole concentration in (Ga,Mn)As
ABSTRACT The effect of annealing at 250 C on the carrier depth profile, Mn distribution, electrical conductivity, and Curie temperature of (Ga,Mn)As layers with thicknesses > 200 nm, grown by molecular-beam epitaxy at low temperatures, is studied by a variety of analytical methods. The vertical gradient in hole concentration, revealed by electrochemical capacitance-voltage profiling, is shown to play a key role in the understanding of conductivity and magnetization data. The gradient, basically already present in as-grown samples, is strongly influenced by post-growth annealing. From secondary ion mass spectroscopy it can be concluded that, at least in thick layers, the change in carrier depth profile and thus in conductivity is not primarily due to out-diffusion of Mn interstitials during annealing. Two alternative possible models are discussed. Comment: 8 pages, 8 figures, to appear in Phys. Rev. B
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ABSTRACT: A modeling approach for standing spin-wave resonances based on a finite-difference formulation of the Landau-Lifshitz-Gilbert equation is presented. In contrast to a previous study [Bihler et al., Phys. Rev. B 79, 045205 (2009)], this formalism accounts for elliptical magnetization precession and magnetic properties arbitrarily varying across the layer thickness, including the magnetic anisotropy parameters, the exchange stiffness, the Gilbert damping, and the saturation magnetization. To demonstrate the usefulness of our modeling approach, we experimentally study a set of (Ga,Mn)As samples grown by low-temperature molecular-beam epitaxy by means of electrochemical capacitance-voltage measurements and angle-dependent standing spin-wave resonance spectroscopy. By applying our modeling approach, the angle dependence of the spin-wave resonance data can be reproduced in a simulation with one set of simulation parameters for all external field orientations. We find that the approximately linear gradient in the out-of-plane magnetic anisotropy is related to a linear gradient in the hole concentrations of the samples.Physical Review B 03/2013; 87(22). · 3.66 Impact Factor
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ABSTRACT: We theoretically investigate the interplay between local lattice distortions around the Mn(2+) impurity ion and its magnetization, mediated through spin-orbit coupling of holes. We show that the tetrahedral symmetry around the Mn(2+) ion is spontaneously broken and that local Jahn-Teller distortions coupled with growth strain result in uniaxial magnetic anisotropy. We also account for the experimentally observed in-plane uniaxial magnetic anisotropy rotation due to variation of hole density. According to this model, lack of inversion and top-down symmetries of (Ga, Mn)As layers lead to in-plane biaxial symmetry breaking in the presence of Jahn-Teller distortions.Journal of Physics Condensed Matter 04/2013; 25(20):206005. · 2.22 Impact Factor
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ABSTRACT: We present the results of combined density functional and many-body calculations of the electronic and magnetic properties of the defect-free digital ferromagnetic heterostructures obtained by doping GaAs with Cr and Mn. While the local-density approximation +U predicts half-metallicity in these defect-free delta-doped heterostructures, we demonstrate that local many-body correlations captured by dynamical mean-field theory induce within the minority-spin channel nonquasiparticle states just above EF. As a consequence of the existence of these many-body states the half-metallic gap is closed and the carriers’ spin polarization is significantly reduced. Below the Fermi level the minority-spin highest valence states are found to localize more on the GaAs layers, being independent of the type of electronic correlations considered. Thus, our results confirm the confinement of carriers in these delta-doped heterostructures, having a spin polarization that follows a different temperature dependence than the magnetization. We suggest that polarized hot-electron photoluminescence experiments might uncover evidence for the existence of many-body states within the minority-spin channel and elucidate their finite-temperature behavior.Physical review. B, Condensed matter 01/2011; 83(12). · 3.77 Impact Factor
arXiv:cond-mat/0503595v1 [cond-mat.mtrl-sci] 24 Mar 2005
Effect of annealing on the depth profile of hole concentration in (Ga,Mn)As
W. Limmer,∗A. Koeder, S. Frank, V. Avrutin, W. Schoch, and R. Sauer
Abteilung Halbleiterphysik, Universit¨ at Ulm, D-89069 Ulm, Germany
K. Zuern, J. Eisenmenger, and P. Ziemann
Abteilung Festk¨ orperphysik, Universit¨ at Ulm, D-89069 Ulm, Germany
E. Peiner and A. Waag
Institut f¨ ur Halbleitertechnik, Technische Universit¨ at Braunschweig, D-38023 Braunschweig, Germany
The effect of annealing at 250◦C on the carrier depth profile, Mn distribution, electrical conduc-
tivity, and Curie temperature of (Ga,Mn)As layers with thicknesses ≥ 200 nm, grown by molecular-
beam epitaxy at low temperatures, is studied by a variety of analytical methods. The vertical
gradient in hole concentration, revealed by electrochemical capacitance-voltage profiling, is shown
to play a key role in the understanding of conductivity and magnetization data. The gradient, ba-
sically already present in as-grown samples, is strongly influenced by post-growth annealing. From
secondary ion mass spectroscopy it can be concluded that, at least in thick layers, the change in
carrier depth profile and thus in conductivity is not primarily due to out-diffusion of Mn interstitials
during annealing. Two alternative possible models are discussed.
PACS numbers: 75.50.Pp, 61.72.Cc, 81.40.Rs, 78.30.Fs
Keywords: GaMnAs; Annealing; Carrier density; Conductivity; Curie temperature
Semiconductor-based spintronic technology,
both the electrical charge and the spin of carriers are
utilized for signal processing and storage, calls for the
development of new ferromagnetic materials. The III-V
dilute magnetic semiconductor (Ga,Mn)As, being com-
patible with conventional semiconductor technology, is
considered a potential candidate for spintronics and has
been intensely studied during the past few years.1,2,3The
ferromagnetic properties of (Ga,Mn)As, successfully ex-
plained within the Zener mean-field model4, arise from
the S = 5/2 spins of Mn atoms incorporated on Ga lattice
sites. The ferromagnetic Mn-Mn coupling is mediated by
delocalized or weakly localized holes which are supplied
by the Mn atoms acting as acceptors on Ga lattice sites.
The Mn spin system undergoes a ferromagnetic phase
transition at the Curie temperature Tcwhich is suggested
to strongly depend on both, the Mn content and the
hole concentration.4(Ga,Mn)As is grown by molecular-
beam epitaxy (MBE) at low temperatures (∼250◦C). In
most cases, Tcis increased by post-growth annealing at
temperatures near or even below the growth tempera-
ture, resulting in values of up to 160 K in (Ga,Mn)As
single layers, as reported so far.5,6,7,8,9,10,11,12This is
commonly explained by the removal or rearrangement of
highly unstable compensating defects such as Mn atoms
on interstitial lattice sites.10,11,12,13,14The enhancement
of the ferromagnetism associated with low-temperature
(LT) annealing is suppressed in the presence of a thin
GaAs capping layer, indicating that diffusion of defects
towards the surface plays a crucial role in the anneal-
ing process.11,12It has been revealed by electrochemi-
cal capacitance-voltage(ECV) profiling and Raman spec-
troscopy that in general the hole concentration p is not
constant throughout the (Ga,Mn)As layer but exhibits
a vertical gradient.15Starting at the GaAs/(Ga,Mn)As
interface, p monotonously increases and reaches its max-
imum value near the sample surface. This finding is in
agreement with the results of spin-wave resonance exper-
iments which manifest the existence of a gradient in the
For (Ga,Mn)As, it is well known that, within a limited
temperature range, a slight increase of the growth tem-
perature results in a pronounced enhancement of both,
Tcand p.18In addition, a significant increase of the sur-
face temperature, induced by heat radiation from the ef-
fusion cells, has been detected during LT MBE growth
of GaAs.19,20Therefore, we suppose that besides anneal-
ing effects during growth a gradual increase of the sur-
face temperature due do free carrier absorption is likely
to account for the observed gradient. Even though dis-
regarded by most other groups so far, the presence of
the gradient seems to be a general phenomenon, whereas
its specific profile depends on several parameters such as
sample thickness and growth conditions. From the p-
dependence of Tcit becomes obvious that a pronounced
variation in p along the growth direction must have a
strong impact on the electrical and magnetic properties
In this work, the effect of annealing at 250◦C on the
depth profile of hole concentration in (Ga,Mn)As epilay-
ers with thicknesses between 0.2 and 1.2 µm is studied
by ECV profiling, micro-Raman spectroscopy, conduc-
tivity measurements, superconducting quantum interfer-
ence device (SQUID) magnetization measurements, and
secondary ion mass spectroscopy (SIMS). It is shown that
the gradient in the carrier density plays a key role in the
understanding of annealing-induced effects, such as the
increase in conductivity and Curie temperature. From
our SIMS and ECV data we infer that, at least in thick
layers (∼ 1 µm), out-diffusion of Mn interstitials is not
the dominant mechanism for the annealing-induced en-
hancement of the hole density, as recently proposed for
thin layers (≤ 100 nm).10,12While most reports in the
literature are on (Ga,Mn)As epilayers with thicknesses in
the range of 10-200 nm, where the gradient is probably
less pronounced, thicker samples, as considered in this
work, allow to map the depth profiles, e.g., of the hole
and Mn concentration over larger distances, and there-
fore to get more detailed information to the understand-
ing of the defect dynamics. Provided that the fundamen-
tal diffusion processes during annealing are primarily in-
dependent of the layer thickness, the findings reported
in this paper may be helpful in the interpretation of ex-
perimental data obtained from much thinner samples as
II. EXPERIMENTAL DETAILS
(Ga,Mn)As layers were grown in a RIBER 32 MBE
machine on In-mounted semi-insulating VGF GaAs(001)
substrates using a conventional Knudsen cell and a hot-
lip effusion cell to provide the Ga and Mn fluxes, re-
spectively.A valved arsenic cracker cell was used in
the non-cracking mode to supply As4 with a maximum
V/III flux ratio of about 3. First, a GaAs buffer layer
around 100 nm thick was grown at a temperature of Ts
= 585◦C (conventional substrate temperature for GaAs),
then the growth was interrupted and Tswas lowered to
∼250◦C. The Mn concentrations in the 0.2−1.2 µm-thick
(Ga,Mn)As layers under study were determined by flux
measurements, which have been checked by elastic recoil
detection measurements (ERD). For details about ERD,
see Ref. 21.
ECV analyses were performed using a Bio-Rad PN4200
profiler. The electrolyte (250 ml aqueous solution of 2.0
g NaOH + 9.3 g EDTA) is in contact with the semicon-
ductor forming an electrolyte-semiconductor diode. A
low-resistance Ohmic contact can be established to the
(Ga,Mn)As sample without metallization. The poten-
tial of the sample is measured potentiometrically with
reference to a saturated calomel electrode. The admit-
tance Y of the electrolyte-semiconductor contact is de-
termined by ac measurements under reverse bias at ωc.
Additionally, the bias voltage Vmis wobbled at a consid-
erably lower modulation frequency to yield the differen-
tial admittance dY/dV . Vm and ωc are selected to ob-
tain optimum Schottky characteristics of the electrolyte-
semiconductor contact. The corresponding equivalent
circuit which is implemented in the analysis software
consists of the space-charge layer capacitance C and of
resistances Rp and Rs connected in parallel and in se-
ries, respectively. Rs is obtained from the admittance
data measured at two different frequencies ωc. Using Y ,
dY/dV , and Rs, we can determine C and dC/dV yield-
ing the carrier concentration N(wd) at the edge of the
depletion region of width wdaccording to
N(wd) = −C3
where ε (0.12 nF/m) and e are the permittivity of
GaAs and the electron charge, respectively. Controlled
amounts of (Ga,Mn)As are removed in increments of few
tens of nanometers by passing a dc current I between the
anodically polarized semiconductor and a carbon counter
electrode. The removed layer thickness weis calculated
from the accumulated transferred charge using Faraday’s
law of electrolysis:
Idt , (3)
where M (144.6), z (6), ρ (5.36 g/cm3), and F (96490
Asmol−1) denote the molecular weight, effective dissolu-
tion valence, and density of GaAs, and Faraday’s con-
stant, respectively. Additionally, weis controlled by me-
chanical surface tracing. The diode area A of 0.005 to
0.008 cm2is defined by a plastic sealing ring. Normally, A
is not accurately known at the beginning of an ECV pro-
filing run, but is routinely measured subsequently. Rel-
evant recalculation procedures considering the measured
values of A and the series resistance Rsare implemented
in the original Bio-Rad software of the PN 4200 ECV pro-
filer. The measured ECV profiles are reproducible within
an uncertainty in the absolute values of about 15%. More
information about ECV profiling can be found in Ref. 22.
Hole concentrations in (Ga,Mn)As can also be esti-
mated from Raman scattering by coupled plasmon-LO-
phonon modes.23,24Therefore, micro-Raman measure-
ments were performed at room temperature (RT) using
the 514-nm line of an Ar+laser as an excitation source.
The Raman signals were detected in the backscattering
configuration ¯ z(x,y)z using a DILOR XY 800-mm triple-
grating spectrometer with a confocal entrance optics and
a LN2-cooled charge-coupled device detector.
experimental details of the micro-Raman measurements
are given in Ref. 23.
For the electrical measurements, Hall bars with Ti-
AuPt-Au contacts were prepared on several pieces of the
cleaved samples without annealing. The contacts were
checked to be Ohmic with negligibly low resistance. The
samples were annealed in air using a LINKAM THMS
600 heating chamber equipped with an electrical feed
through, which enabled us to perform in situ measure-
ments of the conductivity. They were mounted on a sil-
ver block which could be heated electrically or cooled by
liquid nitrogen over the temperature range from -200 to
300◦C within 2 minutes.
To measure depth profiles of the Mn fraction, SIMS
experiments were performed using a commercial Cameca
ims4f-E6 spectrometer with Cs+as primary ion beam
(net impact energy 5.5 keV) at a sputter rate of about
1 nm/s. In the absence of appropriate calibration stan-
dards for Mn, the quantitative analysis of the Mn fraction
refers to the flux measurement of sample B313, which
gave us a value of 6%. A detailed introduction into the
SIMS measuring method is given in Ref. 25.
The magnetization measurements were carried out in
a QUANTUM DESIGN MPMS 5 SQUID magnetometer
applying an in-plane magnetic field of 5 mT.
III. RESULTS AND DISCUSSION
The phenomena discussed in this paper have been qual-
itatively observed in all (Ga,Mn)As layers grown at V/III
flux ratios ≤ 3, exhibiting thicknesses between 200 nm
and 1.2 µm. The specific influence of the V/III flux ra-
tio on the structural, electric, and magnetic properties of
(Ga,Mn)As is not subject of this work and will be dis-
cussed elsewhere. In the following we present experimen-
tal results obtained from several pieces of a 1.2-µm-thick
(Ga,Mn)As epilayer with a Mn fraction of 6% (sample
B313) and of a 240-nm-thick epilayer with a Mn fraction
of 4.5% (sample B352). These epilayers are representa-
tive for all other samples investigated so far.
As mentioned above, ECV profiling reveals the pres-
ence of a vertical gradient in the hole concentration. Fig-
ure 1 depicts the ECV profiles of sample B313 before and
after annealing at 250◦C for 30 and 370 min. It is clearly
seen that the gradient, already present in the as-grown
sample, is strongly enhanced by post-growth annealing,
leading to a hole density near the sample surface which is
almost twice as high as near the GaAs/(Ga,Mn)As inter-
face. As a consequence, the electric and magnetic prop-
erties of the (Ga,Mn)As layer are affected in a dramatic
way, as will be shown below. Whereas the total hole con-
centration, averaged over the layer thickness, increases
from (3.8 ± 0.6) × 1020cm−3in the as-grown sample to
(4.3 ± 0.6) × 1020cm−3in the 30-min-annealed sample
and to (4.9 ± 0.7) × 1020cm−3in the 370-min-annealed
sample, the local hole density near the sample surface
almost saturates after annealing for 30 min. The partic-
ular evolution of the carrier depth profile in the course
of the annealing seems to corroborate the assumption
that out-diffusion of compensating defects towards the
surface accounts for the increase in hole density during
The ECV profiles of sample B352, recorded before and
after annealing at 250◦C for 30 min, are shown in Fig. 2.
The gradient in the as-grown sample is much more pro-
nounced than in B313 and flattens upon annealing with
a concomitant increase in the total hole concentration.
The ECV profiles resemble those of sample B313 in the
range from the surface down to ∼ 240 nm after annealing
for 30 and 370 min.
In order to make sure that ECV profiles reflect the
correct depth distribution of the hole concentration, con-
Etch depth (µm)
Hole density (1020cm-3)
annealed (30 min)
annealed (370 min)
6% Mn (B313)
FIG. 1: ECV profiles recorded from sample B313 before and
after annealing at 250◦C for 30 and 370 min.
Etch depth (µm)
Hole density (1020cm-3)
annealed (30 min)
as-grown (Raman scattering)
4.5% Mn (B352)
FIG. 2: ECV profiles recorded from sample B352 before and
after annealing at 250◦C for 30 min. Depth-dependent hole
concentrations determined from Raman spectroscopy are de-
picted for comparison.
firmative optical experiments were performed. To this
end, steplike surface profiles with flat terraces at differ-
ent depths below the initial surface were prepared on sev-
eral (Ga,Mn)As layers by wet chemical etching. Micro-
Raman spectra were taken from each of the individual
terraces and the carrier densities, obtained from a line-
shape analysis of the Raman signals, were compared with
the ECV data. Figure 2 shows, as an example, such a
comparison for the as-grown sample B352. Within the
error margin of the two analysis methods, the measured
depth profiles coincide almost perfectly.
The Raman spectra corresponding to the data points
in Fig. 2 are depicted in Fig. 3. The high hole concentra-
tion in (Ga,Mn)As leads to the formation of a phonon-like
coupled mode of the longitudinal optical (LO) phonon
and the overdamped hole plasmon.26With increasing
hole concentration, this mode shifts from the frequency
of the LO phonon to that of the transverse optical (TO)
Raman shift (cm-1)
Raman intensity (arb. units)
4% Mn (B352)
ferent etch depths.
Raman spectra recorded from sample B352 for dif-
mode broadens and shifts to higher frequencies with in-
creasing etch depth, indicating a decrease in the hole con-
centration. At an etch depth of 175 nm, the remaining
layer thickness nearly matches the information depth of
1/2α ≈ 50 nm of the Raman measurement, where α de-
notes the absorption coefficient at 514 nm wavelength
of the Ar+laser. Therefore, the narrow Raman line of
the pure LO-phonon mode in the undoped substrate ap-
pears at 292 cm−1. The values for the hole densities were
obtained from line-shape analyses of the Raman spec-
tra using a value for the hole mobility of 1.6 cm2/Vs.
The calculated line shapes are drawn as solid lines in
Fig. 3. Details concerning the calculation of Raman line
shapes in heavily p-doped semiconductors can be found
in Refs. 23 and 26.
Under the assumption that the hole mobility does not
significantly change during the annealing process, an in-
crease in the hole concentration, as seen from Figs. 1 and
2, should result in an increase in the electrical conductiv-
ity of the (Ga,Mn)As layer. In fact, such an increase has
been observed by several authors.6,7,9,10In the present
work, the effect of annealing at 250◦C on the conductiv-
ity of sample B313 is shown in Fig. 4.
Monitoring the conductivity by an in situ measurement
for 400 min reveals that the conductivity monotonously
rises with a rate that gradually decreases with increasing
annealing time. After total annealing times of 30, 60, and
180 min, the annealing process was interrupted for 10 min
and the temperature was rapidly lowered to 25◦C in order
to probe the RT conductivity (dashed line). During the
first 30 min, the RT conductivity increases from 91 to 103
Ω−1cm−1. After annealing for 370 min, the RT conduc-
It is clearly seen in Fig. 3 that the coupled
Annealing time (min)
6% Mn (B313)
B313 during annealing at 250◦C.
In situ monitoring of the conductivity of sample
tivity has almost saturated at a value of 116 Ω−1cm−1.
According to these values, the conductivity is enhanced
by factors of 1.13 and 1.27 upon annealing for 30 and 370
min, respectively. In contrast to Ref. 6, no decrease of
the conductivity for annealing times longer than 2 h is
observed. Note that the results of our in situ measure-
ments are in qualitative agreement with those obtained
from much thinner (Ga,Mn)As epilayers (10-100 nm) at
lower annealing temperatures (≤ 200◦C).7,10
We may now compare the annealing-induced increase
of the conductivity with that in hole concentration. From
the averaged hole concentrations, derived above from the
ECV profiles in Fig. 1, we obtain an increase in hole
density by factors of 1.13 ± 0.3 and 1.29 ± 0.4, which
are in excellent agreement with the values obtained for
the conductivity. Thus, the assumption of at most a
small change in hole mobility during annealing is clearly
confirmed. From the values of the conductivity and the
averaged carrier concentrations, effective hole mobilities
of 1.5±0.3 cm2/Vs are deduced for the as-grown as well
as for the annealed samples.
Raman spectra, recorded from sample B313 before and
after annealing at 250◦C for 30 and 370 min, are shown
in Fig. 5. Whereas a strong increase in the hole con-
centration within the first 30 min of annealing can be
deduced, the Raman spectrum recorded from the 370-
min-annealed sample does not significantly differ from
that of the 30-min-annealed sample. This is in agree-
ment with the ECV profiles in Fig. 1, which reveal that
near the sample surface the hole density is only slightly
enhanced by annealing for more than 30 min. For the
interpretation of the Raman spectra one should keep in
mind that the Raman signal, as already mentioned above,
stems from the near-surface region. The solid lines repre-
sent model calculations of the Raman line shapes using a
hole mobility of µ = 1.2 cm2/Vs and hole concentrations
of 4.3×1020cm−3and 7.8×1020cm−3for the as-grown
and the annealed samples, respectively.
Raman shift (cm-1)
Raman intensity (arb. units)
annealed 30 min
annealed 370 min
6% Mn (B313)
and after annealing at 250◦C. The solid lines are calculated
Raman spectra recorded from sample B313 before
According to the relation4
Tc∝ x × p1/3
between Curie temperature Tcand hole density p, with
x denoting the concentration of magnetically active Mn
ions on Ga sites, an increase in the hole density should
result in an enhancement of the Curie temperature. In
fact, such an enhancement is shown by the SQUID mag-
netization curves in Fig. 6, recorded from sample B313
before and after annealing at 250◦C for 30 and 370 min.
Note that the curves are normalized to the values at 5
K, and thus, cannot be used to obtain information about
the influence of post-growth annealing on the saturation
magnetization. We suggest that the extended tails of the
magnetization curves arise from the vertical gradient of
the hole density p in the (Ga,Mn)As layer. According
to Eq. (4), this gradient results in a depth-dependent
Curie temperature Tc, and thus the curves in Fig. 6 can
be viewed as superpositions of individual magnetization
curves. Then, the values of Tcindicated by arrows have
to be attributed to the near-surface region, similar to the
hole densities obtained from the Raman measurements.
Whereas a Curie temperature Tcof 60 ± 5 K is deduced
for the as-grown sample, a constant value of 100 ± 5 K
is obtained for the two annealed samples, yielding an
increase of Tcby a factor of 1.7±0.3. In contrast, an en-
hancement of Tcby a factor of only 1.2±0.1 would have
been expected from Eq. (4) and the ECV data measured
near the sample surface, yielding an increase of the local
hole density by a factor of 1.7±0.5. The discrepancy be-
tween the two values may be explained by a reduction of
the number of antiferromagnetically ordered Mn atoms14
The increase in hole density, conductivity, and Curie
temperature upon post-growth annealing is commonly
Magnetization (arb. units)
6% Mn (B313)
FIG. 6: Normalized magnetization of sample B313 as a func-
tion of temperature before and after annealing.
explained by the removal of compensating defects in
(Ga,Mn)As. The results of ion channeling experiments
point to a reduction of Mn interstitials (MnI), acting as
compensating double donors.13Based on the observation
of Mn accumulation at the sample surface and on theo-
retical calculations, this reduction has been traced back
to an out-diffusion of MnI towards the surface followed
by oxidation.10,12,27In order to verify the latter sugges-
tion for the thick (Ga,Mn)As layers under study, the Mn
depth profiles of the as-grown and the annealed samples
were experimentally determined by SIMS measurements
recorded from the same sample pieces as used for ECV
profiling. The Mn profiles are depicted in Figs. 7 and 8
for B352 and B313, respectively. Whereas Fig. 7 suggests
a slight annealing-induced lowering of the Mn fraction
in the 240-nm-thick sample, no significant difference be-
tween the three profiles of the 1.2-µm-thick sample can
be identified in Fig. 8. Inevitably the question arises if
an out-diffusion of MnI, necessary to completely account
for the observed ECV profiles, would result in a signifi-
cant and measureable change in the Mn depth profile at
all. Therefore, simple considerations are made in the fol-
lowing to estimate the annealing-induced changes in the
Mn depth profiles expected for the extreme case that the
increase in the hole densities in Figs. 1 and 2 was entirely
due to the out-diffusion of MnI.
The hole concentration p is given by the density
[MnGa] of substitutional Mn acceptors (MnGa) minus
the total density of compensating donors:
p = [MnGa] − C × [MnI] − d , (5)
where [MnI] denotes the density of MnI and d the den-
sity of all other compensating defects.
terms in Eq. (5) are local quantities which may in gen-
eral vary with depth within the sample. The factor C
accounts for the fraction of MnIacting as donors as well
as for the corresponding valency (2 for double donors).
Therefore, the inequality C ≤ 2 holds, where the sign of
equality applies for the case that all MnI act as double
Note that the
Depth z (µm)
Mn fraction (%)
4.5% Mn (B352)
annealed (30 min)
annealing at 250◦C for 30 min measured by SIMS. The dashed
line represents the calculated Mn profile of the annealed sam-
ple using Eqs. (7) and (8).
Mn depth profiles of sample B352 before and after
Depth z (µm)
Mn fraction (%)
6% Mn (B313)
annealed (370 min)
annealed (30 min)
annealing at 250◦C for 30 and 370 min measured by SIMS.
The dashed and dotted lines represent the calculated Mn pro-
files of the 30-min and 370-min-annealed sample, respectively,
using Eqs. (7) and (8).
Mn depth profiles of sample B313 before and after
donors. The total density [Mn] of Mn atoms is given by
[Mn] = [MnGa] + [MnI] + [Mnia] , (6)
with [Mnia] denoting the density of electrically inactive
Mn atoms. Let us now consider the hypothetical case
that the increase in p, revealed by ECV profiling, is
solely due to out-diffusion of MnI and that inside the
(Ga,Mn)As layer d, [MnGa], and [Mnia] remain unaf-
fected upon annealing. Then, using Eqs. (5) and (6), the
local density [Mn]annof Mn atoms inside the annealed
sample (z > 0) is given by
[Mn]ann= [Mn]ag− (pann− pag)/C ,(7)
where the subscripts ann and ag stand for annealed and
as-grown, respectively. The increase in the Mn concen-
tration on the surface (z=0) due to the accumulation of
out-diffused MnIcan be calculated from the conservation
of the total amount of Mn as follows:
([Mn]ann− [Mn]ag)z=0×δ =
dz(pann−pag)/C , (8)
where t denotes the thickness of the as-grown (Ga,Mn)As
epilayer and δ the thickness of the Mn surface layer,
which is of the order of nm.
The dashed and dotted lines in Figs. 7 and 8 represent
the calculated Mn profiles for the 30-min and 370-min-
annealed samples, respectively, using Eqs. (7) and (8)
with C = 2, and taking into account that a Mn frac-
tion of 1% corresponds to a concentration of Mn atoms
of 2.2 × 1020cm−3. For [Mn]ag, the experimental SIMS
profiles of the as-grown samples were used, while pagand
pannwere taken from Figs. 1 and 2. In the case of sample
B352 the calculated [Mn]anncurve inside the (Ga,Mn)As
layer has qualitatively the same form as the measured
Mn profile, but quantitatively the annealing-induced de-
crease in Mn fraction is about twice as strong.
that our estimate would yield an even more pronounced
reduction of the Mn fraction if a value less than 2 had
been used for the factor C. Thus, it seems that in the
240-nm-thick sample only a small portion of the enhance-
ment in hole density is actually due to MnIout-diffusion.
In the case of sample B313 the calculated [Mn]anncurves
inside the epilayer show a clear deviation from the Mn
distribution in the as-grown sample, beginning at a depth
of about 0.5-0.7 µm and increasing strongly towards the
surface. This behavior is not even qualitatively reflected
by the measured Mn profiles. Therefore, we conclude
that at least in thick (∼ 1 µm) samples the observed in-
crease in hole concentration in the bulk is not primarily
due to out-diffusion of MnI. This finding is in agree-
ment with the low diffusivity of MnI at 250◦C derived
in Ref. 10. Moreover, the calculated narrow peaks at the
surfaces, arising from the accumulation of out-diffused
MnI, are not seen in the measured SIMS profiles. Calcu-
lation yields ([Mn]ann− [Mn]ag)z=0≥ 6% for B352 and
([Mn]ann− [Mn]ag)z=0≥ 11% for B313 with δ ≤ 10 nm.
Note however that the SIMS data presented in Fig. 7 and
8 may be too rough to resolve an extremely thin Mn-rich
oxide layer on the surface, if present.
Our findings discussed above do not contradict the
model deduced for much thinner (Ga,Mn)As layers (?
100 nm) that out-diffusion of MnIplays a dominant role.
In fact, the experimental data available so far suggest
that, due to the low diffusivity of MnIat 250◦C, a signif-
icant out-diffusion of MnI occurs in the near-surface re-
gion, whereas in the bulk the highly unstable MnIatoms
rearrange and form electrically inactive randomly dis-
tributed precipitates, as proposed in Ref. 13.
the framework of our simple considerations above, this
means that in the bulk the rise in hole concentration p is
mainly due to a local increase of [Mnia] and/or [MnGa]
at the expense of [MnI]. From the ECV profiles in Fig. 1
it follows that this rearrangement of [MnI] does not take
place homogeneously throughout the whole (Ga,Mn)As
layer, leading to an overall upshift of the hole density,
but exhibits a pronounced dependence on sample depth.
At present, there is no final explanation for this partic-
ular evolution of the carrier depth profile on annealing
which seems to be governed by a diffusion-based mecha-
nism. Further experiments such as depth-resolved inves-
tigations on the MnIdistribution and theoretical studies
have to be performed in the future to clarify this point.
Yet, we finally close with a brief discussion of two poten-
The first mechanism is based on a weak depth-
dependent diffusion of MnI towards the surface associ-
ated possibly with a change of lattice site location. Ini-
tiated by an out-diffusion of MnI in the near-surface re-
gion, MnI atoms deeper in the bulk successively diffuse
towards the surface while forming electrically inactive Mn
clusters and/or MnAs. Due to the low diffusivity of MnI,
this process gradually becomes ineffective with increasing
sample depth. Thus, depending on the annealing time,
different diffusion-like profiles of MnIevolve which result
in the hole density profiles shown in Figs. 1 and 2. This
explanation also accounts for the fact that, compared to
the total amount of Mn inside the (Ga,Mn)As layer, only
a negligibly small fraction of Mn effectively migrates out
of the bulk.
The second mechanism is more hypothetical and rests
upon an assumed out-diffusion of highly mobile, pos-
sibly compensating, defects other than MnI, acting at
least partially as a trigger for the rearrangement of MnI.
Arsenic located in interstitial positions (AsI) may be a
potential candidate for such a defect.
GaAs28,29,30the LT MBE growth of (Ga,Mn)As leads
to the incorporation of excess As up to 2%, acting at
least partially as compensating donor defects.3,13Even
though controversially discussed, several authors suggest
that in LT GaAs a considerable fraction of the excess
As atoms is located in interstitial positions, acting as
highly mobile defects, while the rest of the excess As is
believed to be in antisite positions (AsGa).31,32,33AsGa
defects are known to remain stable up to 450◦C and are
therefore not expected to play a significant role in the
physical processes taking place at 250◦C.34Whereas a
rearrangement of MnI could be revealed in (Ga,Mn)As
Similar to LT
by combined channeling Rutherford backscattering and
by particle-induced x-ray emission experiments13, out-
diffusion of As is difficult to verify.
diffuse from interstitial sites to the sample surface dur-
ing annealing, efficiently desorb at the surface and are
therefore hardly detected by surface sensitive methods.
As atoms, which
The depth profile of the hole concentration in thick
(≥ 200 nm) MBE-grown (Ga,Mn)As layers, measured by
ECV profiling, as well as its strong change upon post-
growth annealing at 250◦C has been shown to play a key
role in the interpretation of conductivity and magnetiza-
tion data. The annealing-induced increase in the total
hole concentration, derived from ECV profiling, is in ex-
cellent quantitative agreement with the change in elec-
trical conductivity measured in situ during annealing.
The pronounced enhancement of the hole density near
the sample surface, confirmed by micro-Raman measure-
ments, is accompanied by a distinct increase of the Curie
temperature. The particular evolution of the measured
ECV profiles under continued annealing suggests that
diffusion processes play a major role in the post-growth
annealing of (Ga,Mn)As. From a comparison between
the ECV profiles and the Mn distributions determined
by SIMS, it is concluded that, in contrast to thin layers,
the increase in hole density upon post-growth annealing
in thick (∼ 1 µm) samples is not primarily due to out-
diffusion of MnI. We suppose that a depth-dependent
rearrangement of MnI in the bulk, initiated by an out-
diffusion of MnI from the near-surface region, accounts
for the change in the hole-density profile. Alternatively, a
process based on the out-diffusion of other highly mobile
defects, such as AsI, has been tentatively discussed.
The authors acknowledge financial support by the
Deutsche Forschungsgemeinschaft, DFG Wa 840/4.
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