STM images of sub-surface Mn atoms in GaAs: evidence of hybridization of surface
and impurity states
J.-M. Jancu1, J.-Ch. Girard1, M. Nestoklon1,2, A. Lemaˆ ıtre1, F. Glas1, Z.Z. Wang1and P. Voisin1
1CNRS-Laboratoire de Photonique et de Nanostructures,
route de Nozay, F-91460, Marcoussis, France and
2Ioffe Physico-Technical Institut, Russian Academy of Science, 194021 St Petersburg, Russia.
(Dated: March 27, 2008)
We prove that scanning tunneling microscopy (STM) images of sub-surface Mn atoms in GaAs
are formed by hybridization of the impurity state with intrinsic surface states. They cannot be in-
terpreted in terms of bulk-impurity wavefunction imaging. High atomic resolution images obtained
using a low-temperature apparatus are compared with advanced, parameter-free tight-binding sim-
ulations accounting for both the buckled (110) surface and vacuum electronic properties.
PACS numbers: 73.20.-r, 71.15.Ap, 73.61.Eyi,71.55-i
The development of scanning tunneling microscopy
has expended the applications of imaging to new ar-
eas of nanosciences and engineering such as atom or
molecule identification, manipulation and nanostructur-
ing [1, 2, 3]. Both spectroscopic and topological infor-
mation is accessible, and quantum-size objects can be
probed in real space with atomic resolution.
ticular, there is growing interest in the STM images of
quantum dots  and sub-surface impurity states in semi-
conductors [5, 6, 7, 8]. Although the well-accepted Ter-
soff and Hamann’s theory  simply relates the tunnel-
ing current to the local density of states (LDOS) at the
tip position, the interpretation of specific experiments
on localized states is still a matter of debate: on the one
hand, the interaction between the surface and the quan-
tum object under investigation must be examined; on the
other hand, particularly in the case of deep bound-states,
the carrier escape toward the extended band states may
play a role . In the last few years, acceptors in GaAs
have attracted much attention because the shape of the
images revealed strong and unexpected chemical signa-
tures: from triangles in the case of shallow acceptors like
carbon  and zinc , to asymmetric butterfly for the
deep acceptor manganese . So far, theoretical work has
concentrated mostly on comparison of STM images with
cross-sections of the bulk impurity wavefunction . In
this letter, we report on new experimental data obtained
with a low-temperature apparatus and compare these re-
sults with advanced TB calculations. We first point that
the STM image cannot reflect the LDOS of the impu-
rity: indeed, empty-state STM images show only the
group-III elements whereas the neutral acceptor wave-
function is distributed over the different chemical species.
In fact, less than 40% of the bulk impurity LDOS shows
up in the STM image. Then we prove that the image
actually results from the hybridization between intrin-
sic surface states and the impurity state. A perturba-
tive model is discussed and indicates that a quantitative
relation between STM images and bulk wave function
is not straightforward. Supercell calculations based on
the sp3d5s∗tight binding model and including the (110)
surface as well as vacuum are performed and reproduce
nicely the experimental images.
The sample used in this study was grown by molec-
ular beam epitaxy on a GaAs(001) substrate at 420 C.
It consists of two 40 nm-thick GaAs layers doped with
2.1018Mn cm−3, embedded between 30 nm-thick GaAs
conducting layers doped with 1.1019Be cm−3. The low
temperature epitaxial growth was chosen in order to min-
imize the segregation of Mn atoms, and the co-doping
was needed because dilute Mn-doped GaAs is insulat-
ing below 77 K. Sample is cleaved in-situ and exposes
in a controlled manner the (110) or (110) surface. Fig-
ure 1a shows a mosaic of three overlapping constant-
current images measured at T=77K with sample-to-tip
voltage Vst=+1.7V and current It=100pA, and Fig. 1b
an atomic-resolution image (Vst=1V, It=100pA) show-
ing a few impurities. Strikingly, the atomic texture of
Fig. 1b shows only a rectangular 5.65 x 4˚ A22 D lat-
tice corresponding to a single species sublattice, while the
(110) surface (Fig. 1d) exposes both Ga and As atoms.
For n-doped GaAs, this feature was explained [10, 11] in
the 1990’s: for positive Vst, electrons flow from the tip
to empty surface states, consisting mostly of empty Ga
dangling bonds, whereas for negative Vst, electrons flow
from occupied surface states (mostly As dangling bonds)
to the tip. This is why the image at positive Vstshows the
rectangular sublattice formed by Ga surface atoms and
not the zig-zag chains of Ga and As atoms along the 
direction, characteristic of a (110) surface. The different
shapes associated with Be (triangle) and Mn (butterfly)
dopants are observed simultaneously in Fig. 1a,b.
Clearly, the texture of image within an impurity is
essentially identical to that in the background.
versely, the LDOS of a neutral acceptor state in bulk
GaAs must be spread over both types of atomic sites
because it is built from zone center valence states that
are known to have 70 % As and 30 % Ga character.
This can be observed in the calculations of ref., and is
further evidenced by the present sp3d5s∗ TB approach.
arXiv:0803.3975v1 [cond-mat.mtrl-sci] 27 Mar 2008
constant-current images measured at T=77K, with sample-
to-tip voltage Vst=+1.7V, current It=100pA . The Be-doped
and Mn-doped GaAs layers are clearly identified.
triangular-shaped and butterfly-like images correspond to Be
and Mn dopants, respectively.
age showing a few impurity states. (c) Typical It(Vst) and
dIt/dVst curves measured at fixed height in the center of a
Mn impurity image. (d) Sketch of atomic arrangement on a
GaAs (110) surface
(color online) (a) Mosaic of three overlapping
(b) Atomic resolution im-
Mn is a deep acceptor whose binding energy (113 meV)
is governed by a strong central cell correction.
TB frame, this local potential is associated with Mn d-
states and their hybridization with p states on neigh-
boring As, a situation often handled perturbatively by
shifting in energy the on-site energy of a virtual group
III element and changing the nearest neighbor interac-
tions. To go beyond this approximation, we constructed
transferable Slater-Koster parameters using an empiri-
cal spd nearest-neighbor model with the nominal atomic
structures: 4s24p14d05s0for Ga, 3d54s24p0for Mn, and
4s24p34d05s0for As. The parameters were optimized to
fulfill the requirement of very good agreement with ab-
initio calculations, keeping unchanged the As one-site pa-
rameters between MnAs and GaAs (including a valence
band offset of 100 meV) for different prototype crystal
structures (hexagonal and cubic). This procedure gener-
ates transferability allowing a precise modeling of the lo-
cal neighborhood of the impurity in the bulk. Electronic
band structure calculations were performed by consider-
ing a 4096-atom supercell of zinc-blende GaAs (45˚ A× 45
FIG. 2: (color online) 3-D plot of the impurity bound state,
and cross sections in the (110) and (110) planes situated 3
atomic planes apart from the impurity center.
˚ A× 45˚ A) in which one Ga atom is replaced by Mn. The
atomic coordinates where relaxed by minimizing the elas-
tic energy using Keating’s valence-force-field approach.
A bound state is found 90 meV above the valence-band
edge, which is in fair agreement with experiment for the
neutral acceptor state of Mn. The following limita-
tions of the present calculations are: i) Coulomb inter-
action between the remote hole and Mn ion is not taken
into account, which is reasonable since the binding en-
ergy is mainly due to the ”central cell” potential; ii) the
short-range p−d exchange interaction giving a magnetic
contribution to the binding energy of 25 meV  is not
considered. A 3 D plot of the resulting state and cor-
responding cross-sections in the (110) and (110) planes
located 3 atomic planes away from the impurity center
are shown in Fig. 2. The similar weights of Ga and As
in the wave function are obvious (see also left column in
Fig. 4). Note that the cross-sections in (110) and (110)
planes obey the rotoinversion symmetry about the impu-
rity center, which is also observed in our measured STM
The strong difference between textures of STM image
and cross-sections of a bulk impurity suggests that the
former is actually formed by hybridization of the impu-
rity and surface states. Providing that the interaction
is weak enough for a perturbative approach to be valid,
we can write the wave function of this mixed state as a
of impurity wavefunction |i? and surface band wave-
function |s,k?. In first-order perturbation theory, ampli-
tude of the admixture of surface band is expressed as:
|ψ? = α|i? +
Ei− Es(k)− I(k)
FIG. 3: (color online) (a) LDOS plot of the surface state
C3, at 0.5eV above the conduction band minimum. LDOS
is calculated at 2˚ A above the surface. (b) Decays of C3 in
crystal and vacuum along the  direction (solid line) and
site-projected anion (dashed line) and cation (dotted line)
where Ei is the impurity level energy and Es(k) the
surface band dispersion.
I(k) = ?s,k|i? and V (k) =
?s,k|Ui|i? (where Ui(r) is the impurity potential)are the
overlap and perturbation integrals, respectively.
should be small compared to unity in any situation where
the perturbative approach is valid. Conversely, evalua-
tion of V (k) requires precise knowledge of the impurity
potential and detailed description of the surface band
structure. Equation 2 provides insight into the mixing
between surface bands and impurity level, but does not
bring a quantitative information.
necessary to simulate the physical situation numerically.
We first prove that the present TB approach accounts
fairly well for the surface states by calculating the elec-
tronic properties of a superlattice where 40 monolayers
of GaAs alternate with 3 nm of vacuum. Here vacuum is
described in terms of a zinc-blende crystal with TB pa-
rameters reproducing the dispersion of the free electron,
and having a dielectric constant equal to unity. As dis-
cussed in ref. , the sp3d5s∗model is close enough to
numerical completion to allow for such folding of the free
electron band structure. The rearrangement of surface
atoms known as the buckling relaxation which prevents
the formation of surface states inside the gap [11, 14] was
taken into account in the calculation. The band structure
and LDOS of buckled GaAs(110) surface are found in ex-
cellent agreement with ab initio results, as evidenced in
Fig. 3 for the first empty dangling-bond state C3 [11, 14].
The calculation closely reproduces the general properties
of C3 obtained from ab initio modeling in terms of energy,
the strong Ga contribution to the surface wave-function,
and attenuation within the crystal and vacuum. The slow
decay of surface states inside the crystal certainly plays
a major role in their strong interaction with sub-surface
Next, a Mn dopant is added in the GaAs slab, in the
nth plane below the surface. In Fig. 4, the cross-sections
of the corresponding states in the first plane of ”vacuum
atoms” (i.e. 2˚ A above the surface  are compared with
experimental results and cross-sections of the bulk impu-
To go beyond it is
rity for n=3 to n=5. For these depths, the calculated
acceptor binding energy shows little change (from 90 to
85 meV). For n= 2 and n=1, the decrease of binding en-
ergy is more pronounced while for the surface impurity,
we find a large increase due to complete change of local
environment. Discussion of n=0 to 2 is beyond the scope
of this Letter. All the images have an horizontal mirror
symmetry axis, but for even n, this axis corresponds to a
row of Ga atoms while for odd n, it goes through a row
of As atoms. Major differences between the two types of
theoretical images are clearly observed. The most strik-
ing discrepancy concerns the respective weights of anion
and cation sites: to be specific, we focus the discussion
on the case of n = 4. The bulk impurity cross-section
(BICS) in that case is centered on a Ga site, and one
easily checks that most of the bright spots correspond to
As sites. More precisely, the As sites dominate strongly
the left part of the image, while Ga and As have similar
weights in the right part. Conversely, in the simulated
STM (SSTM) image, the Ga sites clearly dominate and
As show up only in the nearest vertical rows on the left
of the impurity. Similar conclusions are drawn for the
n=3 and n=5 cases, with the difference that correspond-
ing images appear centered on an As site. The inten-
sity distributions near the image center also differ signifi-
cantly, with a very sharp peak on odd-n BICS and a more
(BICS)(left), simulated (SSTM)(center) and experimental
(right) STM images of a Mn neutral acceptor located n mono-
layers (n=3 to 5) below the (110) surface. BICS is calculated
in a 110 plane, n atomic planes away from the impurity, and
SSTM 2˚ A above the surface. Note that As rows are on the
right side of Ga rows.
4: (color online)Bulk impuritycross section
distributed maximum in corresponding SSTM, while the
opposite holds for even-n images. Altogether, these fea-
tures can be summarized by stating that hybridization
filters out the As component from BICS. This finding is
by no way trivial: building on the perturbative model,
one might have expected that impurity state interacts
preferentially with energetically closer valence-type sur-
face states that have a strong As component in vacuum
. There are also more subtle and counter intuitive fea-
tures: while the decay of intensity with distance to center
is roughly monotonic in BICS, one observes bright spots
in SSTM and experimental images. This is particularly
obvious on the last visible vertical row on the right of the
images. The distance between these bright spots gives a
direct and non-ambiguous measurement of the impurity
depth: it is equal to n times the surface lattice spac-
ing along the  axis, or, equivalently, the number of
weak spots between the two bright ones is equal to n-
1. It is also noteworthy that the global aspect ratio of
the experimental images is better reproduced in SSTM
than in BICS, which indicates that part of the STM im-
age asymmetry arises from the interaction with surface
states. A small remaining discrepancy can be observed as
one more vertical row appears on the left of experimental
images, compared to simulation. In fact, this discrepancy
is of the order of differences between similar experimen-
tal images and is likely due to uncontrolled variations of
impurity environment. Electric field due to tip induced
band bending might for instance play a role. It should
also be noted that we compare constant current images
with constant-height calculated LDOS, which certainly
contributes to small distortions of experimental vs simu-
lated images. Also, it is possible and would certainly be
interesting to include in the theoretical model Coulomb
and p-d exchange interactions, but since the agreement is
already within experimental fluctuations, their influence
on the STM images is likely limited and at most simi-
lar to that of uncontrolled parameters. Finally, we insist
that in the theoretical images of Figs. 3 and 4, the anions
rows are on the right side of cation rows. The agreement
with observed STM images implies that it is also the case
experimentally. From a crystallographic point of view,
this depends on an arbitrary convention regarding the
identification of  vs  directions, and there are
conflicting discussions in the literature [17, 18] regarding
this point. In our experiment (see Fig. 1) the growth axis
direction is unambiguously identified, and we can state
firmly that for the cleavage surface showing the asym-
metrical butterfly with a stronger left wing, the anions
are on the right side of cations. According to commercial
wafer specification, this is the (110) surface.
We finally comment spectroscopic data on these im-
It(Vst) curves at fixed height were recorded on
many images, and a typical spectrum is shown in Fig.
1c. These curves show a threshold whose position varies
between 100 mV and 600 mV. A clear correlation be-
tween threshold voltage and distance to the heavily p-
doped layer is observed, suggesting that variations of the
tip-induced band bending is the main cause of threshold
variation. Images of a given impurity show essentially no
dependence on Vstuntil Vstexceeds 1.5 V and Itstarts
integrating contributions from tunneling to conduction
band states. We point that STM measures basically a
DC current, that can flow only if the tunneling electron
escapes out of the bound state at a rate faster than the
injection rate . Since when changing Vst, one changes
the electrostatic environment of the impurity from hole
depletion to hole accumulation, the very mechanism of
electron escape probably changes while the image is not
affected. This strongly suggests that in our sample the
voltage threshold merely corresponds to a condition for
the impurity to be effectively in an A0state, or for the
electron to escape fast enough. The detailed mechanisms
of electron escape towards extended band states in STM
spectroscopy certainly deserves more attention, but in
the present case it does not seem to influence the image
In conclusion, we have shown that STM images of sub-
surface impurities are formed due to hybridization of im-
purity and intrinsic surface states. These features are
general and apply to other types of near-surface localized
states like images of shallow impurities (like Be in Fig.
1b)and quantum dots. Realistic tight-binding calcula-
tions including the surface allow comparison with exper-
iment at an unprecedented level of precision. The method
can be extended to many different nanometer-sized ob-
jects, up to a present limit of a few million atom super-
cells. More fundamentally, our analysis suggest that the
well understood bulk impurity state acts as an inner ex-
perimental probe of surface states and their extension in
Acknowledgement: The authors thank Dr. L. Largeau
for valuable discussions and C. David for technical assis-
tance. Calculations were performed at the IDRIS-CNRS
supercomputing center under project ”CAPnano”. One
of us (JMJ) is supported by the SANDIE NoE of the EC,
and one of us (MN)by the ”Dynasty” foundation.
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