NANO LETTERS
Ge1-x Mnx Clusters: Central Structural and Magnetic Building Blocks of Nanoscale Wire-Like Self-Assembly in a Magnetic Semiconductor
2009 Vol. 9, No. 11 3743-3748
D. Bougeard,*,† N. Sircar,† S. Ahlers,† V. Lang,† G. Abstreiter,† A. Trampert,‡ J. M. LeBeau,§ S. Stemmer,§ D. W. Saxey,| and A. Cerezo| Walter Schottky Institut, Technische UniVersita¨t Mu¨nchen, Am Coulombwall 3, D-85748 Garching, Germany, Paul Drude Institut fu¨r Festko¨rperelektronik, HausVogteiplatz 5-7, D-10117 Berlin, Germany, Materials Department, UniVersity of California, Santa Barbara, California 93106-5050, and Department of Materials, UniVersity of Oxford, Parks Road, Oxford OX1 3PH, U.K. Received June 16, 2009; Revised Manuscript Received August 20, 2009
ABSTRACT Controlled nanoscale self-assembly of magnetic entities in semiconductors opens novel perspectives for the tailoring of magnetic semiconductor films and nanostructures with room temperature functionality. We report that a strongly directional self-assembly in growth direction in Mnalloyed Ge is due to a stacking of individual Ge1-xMnx clusters. The clusters represent the relevant entities for the magnetization of the material. They are formed of a core-shell structure displaying a Mn concentration gradient. While the magnetic moments seem to be carried by the shells of the clusters, their core is magnetically inactive.
GeMn alloys have attracted significant interest for applications in the field of semiconductor spintronics.1-6 These materials, fabricated at conditions far from thermodynamic equilibrium, possess above-room-temperature Curie temperatures.1,3 They exhibit a dilute magnetic semiconductor-like undisturbed single crystalline Ge structure2,3,7,8 without precipitation of ferromagnetic intermetallic GexMny phases.9 In addition to high Curie temperatures, Ge1-xMnx single crystalline films reveal promising magnetic and electrical properties10 making them attractive candidates for the realization of Si-compatible room-temperature, all-semiconductor spintronics applications.11 Electron microscopy studies have shown that the alloying of Ge with Mn results in an inhomogeneous distribution of the Mn atoms in the Ge crystal: self-assembled nanometersized Mn-rich regions are embedded into a Ge matrix.1,8,7 Under proper crystal growth conditions in molecular beam epitaxy (MBE), the process of self-assembly can be controlled in Ge1-xMnx,7,9 allowing the possibility of forming nanodiameter structures extending over the whole film * To whom correspondence should be addressed. E-mail: bougeard@ wsi.tum.de. † Walter Schottky Institut, Technische Universita¨t Mu¨nchen. ‡ Paul Drude Institut fu¨r Festko¨rperelektronik. § University of California. | University of Oxford. 10.1021/nl901928f CCC: $40.75 Published on Web 09/14/2009
2009 American Chemical Society
thickness while conserving single crystallinity.1 The material system thus promises the realizability of unique magnetic wires embedded into a semiconductor matrix. Similar observations have also been made in other material candidates envisaged as room temperature magnetic semiconductors,12-14 making Ge1-xMnx a valuable model system for this very recently observed type of self-assembly. Despite the interest in columnar Ge1-xMnx as a potential building block of silicon compatible spintronics devices, fundamental aspects such as the nature of the Mn-rich regions, the driving-forces of the self-assembly and the nanoscale origin of the observed magnetism have not been conclusively determined. In this letter, we combine a nanoscale-resolution chemical and structural study of selfassembly in GeMn MBE films with an analysis of the magnetic properties. We observe a strain and Mn segregationdriven self-assembly of roughly spherical clusters of a Ge1-xMnx solid solution, embedded in a Ge matrix. The clusters nonequidistantly stack in string of pearls-like patterns along the growth direction. Columnar objects in the film are built of closely stacked, individual clusters, making the Ge1-xMnx cluster the relevant magnetic entities in the material. The Mn content increases toward the center of the clusters. The core of the clusters is amorphous and
Figure 2. APT data from a sample with rGe ) 0.25 Å s-1, x ) 2.0% and TS ) 60 °C. (a) Part of a three-dimensional APT reconstruction showing 4% Mn isoconcentration surfaces. Growth direction bottom to top, analysis direction top to bottom. (b) Onedimensional APT Mn concentration profile along a Mn-rich columnar feature. The profile is generated by counting the number of atoms of each species within a slice of reconstructed data. The error bars represent the uncertainty resulting from counting statistics.
Figure 1. Overview Ge 002 dark field TEM images of a sample with rGe ) 0.08 Å s-1, x ) 7.3% and TS ) 60 °C. Bright contrast represents Mn-rich regions.
magnetically inactive. We deduce that the observed magnetic moments are carried by the surface shell of the Ge1-xMnx clusters. GeMn thin films free of intermetallic phases were fabricated by solid source low temperature MBE on Ge (001) substrates. Details of the fabrication procedure are given in ref 9. The investigated Ge flux rates rGe ranged from 0.04 to 0.4 Å s-1 and the Mn content x from 1 to 12%. Mn contents were quantified by secondary ion mass spectrometry (SIMS) using a Mn-implanted GeMn standard. The substrate temperature was TS ) 60 °C. Structural properties were studied by cross-sectional and plan-view diffraction contrast transmission electron microscopy (TEM) and by annular darkfield scanning transmission electron microscopy (STEM) as well as pulsed-laser atom probe tomography (APT).15,16 Samples for TEM and STEM were prepared by standard wedge polishing techniques followed by Ar ion milling. An FEI Titan 80-300 kV S/TEM operating at 300 kV was used for STEM and high resolution TEM (HRTEM) imaging. APT was conducted using an Imago LEAP 3000X HR microscope17 in a pulsed-laser mode. Specimens were maintained at a base temperature of 23 K during the acquisition and the laser pulse energy was minimized in order to avoid atomic diffusion. Magnetic properties were measured in a commercial superconducting quantum interference device (SQUID) magnetometer. A cross-sectional dark field TEM micrograph of a typical GeMn sample is shown in Figure 1. Bright spots correspond to the characteristic self-assembled Mn-rich regions,7 while a dark contrast is obtained for Ge-rich regions. A strong anisotropy of the self-assembly leads to an alignment of Mnrich objects in the [001] growth direction into a string of pearls-like pattern. Furthermore, while the diameter of objects varies only between 3 to 5 nm in the (001) plane, there is a wide range of lengths in the [001] direction. One can observe both roughly spherical objects with dimensions of only a few nanometers as well as columnar objects with an 3744
elongation along the growth direction of several tens of nanometers. An APT analysis confirms the string of pearls-like selfassembly along the growth direction. The nanoscale chemical sensitivity of APT gives access to the composition of the Mn-rich objects observed in TEM. It demonstrates that Ge and Mn assemble into Ge1-xMnx clusters. Figure 2a shows 4% isoconcentration surfaces of Mn in a three-dimensional (3D) reconstruction. The Mn is clearly incorporated into both isolated Ge1-xMnx clusters with dimensions of a few nanometers in all three spatial directions and into columnar objects reaching several tens of nanometers in elongation. Columnar objects are always very irregular and rippled in shape. Figure 2b displays a one-dimensional concentration profile along the axis of such a columnar object more than 20 nm in length. Large variations in the Mn content of the column are observed on the scale of 2 to 3 nm. This variation demonstrates that columnar objects are built from individual, nanometer-sized Ge1-xMnx clusters which are closely stacked. Each Ge1-xMnx cluster appears as a peak in the Figure 2b. Despite the close stacking a low Mn content between individual Ge1-xMnx clusters is clearly visible. The close stacking of individual clusters also explains the very irregular shape of columnar objects seen in the 3D reconstruction in Figure 2a. Both the morphology and the average Mn content obtained from APT agree well with TEM and X-ray diffraction estimates in this work as well as previous studies.7,18 APT furthermore reveals that the average Mn content varies from cluster to cluster. The peak concentration measured within the studied clusters was found to vary between 10 and 20%. The concentration of Mn that is incorporated into the Ge matrix is below 0.7 atomic percent. Ge1-xMnx clusters are either very closely stacked or isolated. Isolated clusters can be up to 10 to 15 nm apart. Figure 3a shows a typical one-dimensional profile through a single Ge1-xMnx cluster in the (001) growth plane. Starting from the matrix level below 0.7%, the Mn concentration quickly rises within 1-2 nm toward the cluster center. While it may be possible that ion trajectory aberrations and surface diffusion have some effect on these profiles, similar results Nano Lett., Vol. 9, No. 11, 2009
Figure 3. APT data from a sample with rGe ) 0.25 Å s-1, x ) 2.0% and TS ) 60 °C. (a) One-dimensional concentration profile through a single Ge1-xMnx cluster along a direction in the (001) epitaxial plane. The error bars represent the uncertainty resulting from counting statistics. (b,c) Mn isoconcentration surfaces for 8 and 12% Mn concentration, respectively, in the same region as for Figure 2.
Figure 4. High resolution TEM images of a sample with rGe ) 0.08 Å s-1, x ) 7.3% and TS ) 60 °C recorded on a thicker (a) and thinner (b) part of the same specimen.
are generated when taking concentration profiles along the direction of field evaporation suggesting that a real concentration gradient is present. This presence of a Mn concentration gradient is further illustrated by an extension of the isoconcentration series in 3D reconstruction from Figure 2a in Figure 3b,c. By choosing increasing Mn isoconcentration thresholds the diameter of the Ge1-xMnx cluster reconstructions is decreased. At high concentrations, only the cores of the clusters are visible. The concentration profiles of these clusters thus strongly resemble the distribution of atom species in capped semiconductor islands forming spontaneously in lattice mismatched heterosystems.19 Additionally the presence of a Mn concentration gradient as well as the fact that the Mn content of the cluster core noticeably fluctuates from cluster to cluster leads to the conclusion that the clusters are formed of a random Ge1-xMnx solid solution rather than an intermetallic compound with fixed stoichiometry. To study the structural properties of the Ge1-xMnx clusters, plan view HRTEM were acquired along the growth direction. Figure 4 shows a comparison of HRTEM from (a) thicker and (b) thinner parts of the HRTEM specimen. The micrograph of the thicker part seems to indicate perfect crystal coherence between strings of clusters and the surrounding Ge-rich matrix. On the other hand, in the thinner part it can be seen that the core of the Ge1-xMnx cluster strings is amorphous. Furthermore strain contrast surrounds the cluster strings. The apparent crystallographic coherence in the thick part of the specimen in Figure 4a is an artifact due to overlap of the amorphous clusters with the crystalline Ge matrix in projection. Correct interpretation of the TEM micrographs Nano Lett., Vol. 9, No. 11, 2009
Figure 5. High resolution plan view STEM images of a sample with rGe ) 0.08 Å s-1, x ) 7.3% and TS ) 60 °C. (a) HAADF, inner semiangle 65 mrad and (b) LAADF, inner semiangle 23 mrad. Both images were acquired for the same Ge1-xMnx cluster string. The white circles mark regions with contrast differing from the Ge matrix contrast.
for this system thus requires thin TEM foils as analyzed in Figure 4b. An annular dark field study in scanning transmission electron microscopy (STEM) on a single cluster string is shown in Figure 5. High-angle annular dark-field (HAADF) imaging in Figure 5a shows decreasing brightness from the Ge matrix toward the center of the string. The low-angle annular dark-field (LAADF) image in Figure 5b reveals dark contrast in the center of the string, surrounded by a brighter halo as identified by the circles in the figure. Within the solid circle amorphous Ge1-xMnx is clearly dominant. While HAADF imaging is chemically sensitive, LAADF images are sensitive to strain. The bright halo delimited by the larger dashed circle in LAADF reveals strain of the matrix in the direct vicinity of the Ge1-xMnx clusters. The presence of local strain confirms earlier work where the average in-plane strain was quantified to be 2%.18 Such strain values are comparable to typical strain values present in lattice mismatched heterosystems exhibiting self-assembled island formation.20 Given the fact that two consecutive Ge1-xMnx clusters are 10 to 15 nm apart at most in the [001] direction, each cluster feels the strain field of its predecessors, as it is known for stacked self-assembled semiconductor islands.21,22 Mn segregation3 combined with strain energy minimization during epitaxy thus leads to a stacking of Ge1-xMnx clusters into a string of pearls pattern. The nonequidistant stacking of the clusters is a consequence of the codeposition of Ge and Mn. Since a Mn concentration gradient has been observed in APT, the decrease of contrast between the two circles in HAADF can be induced both by a progressive increase of Mn content toward the center of the clusters as well as by strained crystalline material. This situation would be indicative of a core-shell structure of Ge1-xMnx clusters, revealing a crystalline, strained shell and an amorphous core which contains most of the Mn. It can be noted that the diameter of the larger, dashed circle agrees with the typical diameter of Ge1-xMnx clusters as determined in APT and TEM. Furthermore, contrast variations surrounding the clusters may also be due to variations in the diameter and overlap with the matrix. 3745
f( µm) )
(
(ln µm - ln m)2 1 · exp 2s2 µms√2π
)
(3)
with m and s being the mean and the standard deviation of the distribution. The expected value of the distribution is the average supermoment per cluster 〈 µm〉 and is given by 〈 µm〉 )
Figure 6. Magnetization loops measured between 50 and 150 K for a sample fabricated with rGe ) 0.08 Å s-1, x ) 7.3% and Ts ) 60 °C. Dotted lines represent log-normal Langevin fits. (Inset) Plot of the fit residual for a single moment Langevin fit (eq 1) and a log-normal fit (eq 2).
In magnetometry measurements, the self-assembly of Ge1-xMnx clusters manifests itself in superparamagnetic signatures of large magnetic supermoments carried by the individual clusters displaying ferromagnetic ordering temperatures above 300 K.7 Such signatures are observed in the whole investigated growth window. The superparamagnetic response is expressed in an s-shaped magnetic field dependence of magnetization as depicted in Figure 6. The free superparamagnetic rotation of the magnetic supermoments with the externally applied magnetic field results in full reversibility and the absence of hysteresis effects. The curves can be fitted in a first approximation by a Langevin function L( y) M(H, T) ≡ M( y) ) nsp µmL( y) µm µ0H 1 , L( y) ) coth( y) y) kBT y
(1)
∫
∞
0
µm f( µm)dµm ) m√exp(s2)
Fits of the experimental data of Figure 6 to eq 2 are indicated by the black lines in the figure. At 50 K, the temperature is high enough to make possible paramagnetic contributions from isolated Mn ions negligible, but low enough to provide a good ratio of magnetic moment magnitudes and thermally induced measurement noise. The fit results in an average supermoment per Ge1-xMnx cluster of 〈 µm〉 ) 360 µB and a volume density of the magnetic clusters of nsp ) 2.4 × 1018 cm-3. As illustrated in the inset of Figure 6, log-normal fits with a finite width of the distribution significantly improve the quality of the fit compared to Langevin fits using a single supermoment value as in eq 1. The fitting parameter s, which represents the width of the log-normal distribution, ranges from 0.3 to 0.5. This indicates the presence of a broad distribution of supermoment magnitudes and therefore corroborates the observation of size fluctuating and nonequidistantly stacked Ge1-xMnx clusters in a [001] string of pearls-pattern. Some of the clusters are stacked closely enough to magnetically couple and to lead to larger supermoments. The number of cluster strings per unit area σ was estimated from plan view TEM data. This areal density σ is connected to the volume cluster density nsp obtained from magnetometry by a line density λ of Ge1-xMnx clusters along a [001] string, nsp ) σ · λ
with µm and nsp as the average magnetic supermoment per Ge1-xMnx cluster and the volume density of magnetic clusters, respectively. This equation describes the magnetic response of an ensemble of magnetic clusters with each single cluster carrying exactly the same supermoment µm. To additionally be able to account for magnetic cluster ensembles exhibiting a certain spread in supermoment magnitudes, a supermoment distribution function of the magnetic moments f( µm) is introduced. With the distribution function, eq 1 has to be extended to the continuous summation over all magnetic moments M( y) ) nsp
∫
∞
0
µmL( y)f( µm)dµm
(2)
A distribution function commonly used for small magnetic clusters23 is the log-normal distribution function with the following parametrization, 3746
(4)
(5)
With a value of σ ) 8 × 1011 cm-2 to σ ) 12 × 1011 cm-2 and nsp ) 2.4 × 1018 cm-3, a density of magnetic entities per string of λ ) 2 × 106 to 3 × 106 cm-1 is obtained. For the epilayer depicted in Figure 1, these values correspond to about 40-60 magnetic entities per string. These values are in good agreement with the average amount of Mn-rich regions observed on a string in APT and TEM. Thus magnetometry confirms the picture of self-assembly of Ge1-xMnx clusters in a string of pearls-pattern. It consistently shows that in average, the smallest magnetic entities within each string of pearls are the superparamagnetic, Ge1-xMnx clusters. From the saturation magnetization at 2 and 5 K, the integral magnetic moment of all Mn atoms in the epilayer is calculated. Dividing this value by the overall Mn content in the epilayer as quantified by SIMS analysis, the average magnetic moment per Mn atom µMn, is extracted. The low temperatures between 2 and 5 K were chosen to provide measurement conditions with almost full high field alignment Nano Lett., Vol. 9, No. 11, 2009
of both supermoments and possibly present, isolated paramagnetic Mn ions located for instance in the matrix. Surprisingly, the magnetic moment per Mn atom µMn yields unexpectedly low values ranging from 0.3 to 0.45 µB for the thin films of the investigated growth window. These values are in contrast to values of µMn ) 3 µB per Mn atom predicted for substitutional Mn in a Ge lattice.24-26 It is unlikely that each individual Mn atom exhibits a reduced µMn value. We therefore conclude that a fraction of the Mn ions is magnetically inactive, whereas the other part of the Mn ions exhibits full magnetic activity as expected. For the thin film investigated in Figure 1, the magnetic moment per Mn atom equaling µMn ) 0.35 µB and the expected value being µMn ) 3 µB, it follows that about 88% of the Mn ions are magnetically inactive. One possible location of magnetically inactive Mn ions could be antiferromagnetically coupled Mn-Mn dimers located in the Gerich matrix. Nevertheless, the volume fraction of the matrix, estimated from plan view TEM for the sample shown in Figure 6 under the assumption of continuous cylindrical volumes for the strings of dots, equals roughly 85 to 90% of the total volume. Thus, if all magnetically inactive Mn ions were located in the matrix, about 88% of the total number of Mn ions would have to be distributed across 85 to 90% of the total volume. Such a distribution would correspond to an average matrix Mn content of 7.1 to 7.6%. This value is clearly in contradiction with the matrix Mn concentration below 0.7% as determined in APT. Therefore, Ge1-xMnx clusters must contain magnetically inactive Mn atoms. This observation establishes an evident connection between magnetic activity of Mn atoms and the structural properties of the self-assembled nanostructure. The absence of structural order in the core of the Ge1-xMnx clusters is expected to be the origin of magnetic disorder. This disorder causes the observed magnetic inactivity, for instance through a canting of randomly distributed Mn magnetic moments or antiferromagnetic coupling of subensembles of the Mn moments27 in the amorphous cluster core. In turn, unsaturated magnetic moments at the surface of an antiferromagnetic cluster core28-31 or small volumes of dispersed, ferromagnetically ordered Mn atoms in a crystalline shell of a cluster lead to superparamagnetic behavior. From the observation of magnetic supermoments with a magnitude of several hundred Bohr magnetons and the APT and STEM analyses we thus infer that the magnetically active part of Mn is located at the surface, in the shell of the Ge1-xMnx clusters. The magnetic ordering temperatures and moments of Ge alloyed with Mn as well as the perspective of a controllable self-assembly on the nanoscale have led to recent efforts to qualify the material as a promising magnetic semiconductor. Structural and magnetic studies presented here demonstrate that the self-assembly leads to a vertical stacking into a string of pearls-pattern of Ge1-xMnx clusters which carry the relevant magnetic moments in their surface shell. Two rarely considered aspects of this self-assembly are brought out from our study: the degree of crystallinity of the clusters and the strain gradient in the Ge-rich matrix. Nano Lett., Vol. 9, No. 11, 2009
Regarding crystalline order, it is unclear as to whether the nucleus of a Ge1-xMnx cluster, as for example observed by Zeng et al.,3 is formed by random adatoms and is already amorphous or if it adopts the cubic order of the Ge matrix. In (Mn,Ge) codeposition, the first case corresponds to the parallel growth of an amorphous cluster embedded into a crystalline Ge matrix which is seeded by the substrate. The lateral growth of this cluster is then limited by the induced in-plane strain. In the less likely latter case, the in-plane strain induced by the parallel growth of both the Ge matrix and a cubic Ge1-xMnx cluster nucleus would lead to an amorphization of the cluster during the epitaxy of the following layers. An understanding of the thermodynamic driving forces of the early stages of the epitaxy including Mn segregation in (Mn,Ge) codeposition would be extremely beneficial for the improvement of the control of the self-assembly and the crystallinity of the Ge1-xMnx clusters. As the present work shows, such control will have direct consequences on the magnetic properties of the material. Furthermore the degree of crystallinity controls the resulting band structure and thus the electric properties of the material. The in-plane strain distribution in the Ge-rich matrix has been identified as the driving force for the stringlike stacking. Further understanding of the origin of this distribution promises to enhance the control on the homogeneity of the distribution of the Ge1-xMnx cluster along a string. A dense and homogeneous stacking of the clusters on a string would increase the probability of magnetic coupling along a stack and could contribute to global ferromagnetism as for example observed by Jamet et al.1 In summary, we have observed a self-assembly of nanometer-sized Ge1-xMnx clusters in MBE grown GeMn films into string of pearls-like objects. The clusters are the origin of the magnetization of the material. Although showing signs of crystallographic coherence with the Ge matrix in TEM, we present converging evidence for strong structural disorder within these Ge1-xMnx clusters from microscopy and magnetometry. A deeper understanding of the formation mechanism of the clusters seems to be key to a full control of the columnar self-assembly process. Such a directional selfassembly will give a unique access to the realization of stacked nanomagnets and magnetic wires embedded into a Si-compatible material system. Acknowledgment. This work was funded by the German Science Foundation (DFG) via Schwerpunktprogramm SPP 1285 Halbleiter Spintronik, UCSB MRL under NSF MRSEC Program (Award No. DMR05-20415) and the Opal National Atom Probe Facility from the U.K. Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/ 077664/1. D.B. is furthermore grateful for support by Alexander von Humboldt-Stiftung. The authors acknowledge support by the Department of Chemistry, Technische Universita¨t Mu¨nchen and by H. Cerva, Siemens AG, Munich. References (1) Jamet, M.; Barski, A.; Devillers, T.; Poydenot, V.; Dujardin, R.; BayleGuillemaud, P.; Rothman, J.; Bellet-Amalric, E.; Marty, A.; Cibert, J.; Mattana, R.; Tatarenko, S. Nat. Mater. 2006, 5, 653. 3747
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NL901928F
Nano Lett., Vol. 9, No. 11, 2009
