Local structure and magnetism of (Ga,Mn)As

Local Structure and Magnetism of (Ga,Mn)As Tiago Abel de Lemos Lima Integrated Masters in Engineering Physics Department of Physics and Astronomy 2014 Advisor João Pedro Araújo, Auxiliar Professor, Faculdade de Ciências Co-advisor Kristiaan Temst, Associate Professor, Faculteit Wetenschappen, KULeuven ii All corrections were determined by the Jury, and only those where performed. President of the Jury, Porto, ______/______/_________ iv Acknowledgments “Sure as I am breathing Sure as I’m sad I’ll keep this wisdom in my flesh I leave here believing more than I had And there’s a reason I’ll be, a reason I’ll be back” – No Ceiling, Into the Wild, Eddie Vedder My MSc ran on more than just the love for physics. A fiery, unbelievable chain of events led me to experience one of the best times in my life so far. Some years back I wouldn’t even believe I would be writing this paragraph in CERN, the most fascinating place for physics research in Europe, if not in the world. All this I owe to the people I acknowledge here and to whom I am very, very grateful. First of all I have to thank my supervisors, Lino and João Pedro, who gave me a fantastic opportunity to move forward in my professional and personal life. All I know about being a physicist I owe it to you, the practical and the theoretical aspects of it, along with all the struggling and failing required for achieving our goals. As in magnetism, some kind of interaction is required for a magnetic state to emerge. Be it through a short-distance mechanism or through a long-distance one, there will always be a regime in which we can achieve such a state. In short, thank you for letting me into this scientific family. I also must thank Kristiaan Temst and André Vantomme for incorporating me into their research group at the Instituut voor Kernen Stralingfysika, KULeuven, Ulrich Wahl for the fruitful insights on the Emission Channeling technique and its intricate theoretical framework, and the EC/ISOLDE collaboration team for providing me the opportunity to dwell into the technical parts behind the technique. Also, a big thanks to my office colleagues at the IKS, Valérie, Koen and Nuno for the friendship and all the help with experimental and analysis procedures, as well as for the ever so useful coffee breaks. v vi None of this would’ve been possible without the support of my friends. Those who grew up in physics with me, specially João and Mafalda, who shared the international experience with me, but also José Valente, Diogo and Artur; thank you all for the incredible moments, useful insights, homework, studying, stressing, despairing and achieving. You made me strive and fight for what I love in science. A very deep and grateful thank you to Máximo (Filipe), who was always by my side and helped me in every personal aspect of my life. Also David, Armando, Artur, Dora and Daniela, and all my other national and international friends, thank you for all the laughs and good times as well as the fantastic experiences. O maior agradecimento devo à minha família. Ao meu pai, mãe, irmão e irmãs devo aquilo que sou, pela confiança que sempre têm em mim; por todo o carinho, amor e saudade, e apoio incondicional, mesmo quando isso envolve estar longe de vocês. Com vocês aprendi a encarar a vida com um sorriso na cara e a tirar partido de todos os momentos da minha vida. E aprendi algo ainda mais importante: a união e o amor conseguem superar qualquer limitação. Muito, muito obrigado! I am mostly grateful to my family, for their trust, care and love, as well as their unconditional support, even when it involved me staying away from you. You taught me to experience life with a smile in my face, enjoying every little and simple moment. With you I learned that love and unity can overcome any limitation. Thank you so much! As Paulo Coelho says in The Pilgrimage,“the boat is safer anchored at the port; but that’s not the aim of boats”, my last and deepest appreciation goes to the person that ultimately made me lift my anchor and set sail. Jana, with you I learned that no distance is large enough and no time is long enough when the wait is worth the price. These last months were filled with work but also with art and music, cuisine and cocktails, trips and tumbles... A compendium of happiness and love in every little moment we shared, and for which I am very grateful. Let’s keep sailing together. They say that sometimes you have to skip a beat to find your rhythm, especially if, like me, you tend to lose it easily. And we all know that the best songs don’t have only one rhythm... Keeping many rhythms is likely to be a challenge, but in the end if you don’t play the song, who will? Tiago September 2014 Abstract Throughout the years, dilute magnetic semiconductors (DMS) have emerged as promising materials for semiconductor-based spintronics. In particular, (Ga,Mn)As has become the model system in which to explore the physics of carrier-mediated ferromagnetism in semiconductors and the associated spintronic phenomena, with a number of interesting functionalities and demonstrated proof-of-concept devices. It constitutes the perfect example of how the magnetic behavior of DMS materials is strongly influenced by local structure. In this thesis, we address key aspects of the interplay between local structure and ferromagnetism of (Ga,Mn)As. We unambiguously identify the lattice site occupied by interstitial Mn as the tetrahedral interstitial site with As nearest neighbors TAs. We show, furthermore, that the TAs is the most energetically favorable site regardless of the interstitial atom forming or not complexes with substitutional Mn. We also evaluate the thermal stability of both interstitial and substitutional Mn sites occupied by Mn for two representative Mn concentrations (1% and 5%), and its influence on the material’s structure and magnetism. We show that compared to the substitutional Mn, interstitial Mn becomes mobile at lower temperatures, for both low (1%) and high (5%) Mn concentration. Moreover, the diffusion temperatures are lower for the high concentration than for the low concentration case. These diffusion temperatures are concentration dependent, with aggregation of impurities occurring for the high concentration at lower temperatures than for the low concentration. These findings translate into two key conclusions: at typical growth temperatures (200-300◦C) the interstitial Mn is mobile for high concentration (5%) but not for low concentration (1%); and substitutional Mn impurities become mobile in a temperature regime that is well below what has been previously reported. We also observe a decrease in the activation energy for the diffusion of both substitutional and interstitial impurities with increasing Mn concentration. This decrease has a different origin for each case: for substitutional diffusion, with activation energies of 2.3-2.6eV at 1% Mn to 1.9-2.0eV at 5% Mn, a vacancy-assisted mechanism occurs that is favored with increasing impurity concentration; for interstitial diffusion, with activation energies of 1.5-2.1eV at 1% Mn to 1.3-1.8eV at 5% Mn, as charge screening effects become stronger with increasing Mn (and consequently carrier) vii viii concentration, interstitial Mn defects are effectively “neutralized”, and therefore experience lower migration barriers. Additionally, we conducted a comprehensive study of the local structure and magnetism in the different diffusion regimes. We show that annealing at 200◦C promotes the passivation of the interstitial Mn for 5% Mn (Ga,Mn)As, as an increase in TC and magnetization is observed. No improvement is observed in the 1% Mn case, which can be understood from the absence of interstitial impurities incorporated during growth for this concentration regime. Annealing at 300◦C induces the precipitation of Mn into Mn-rich regions for both concentrations studied, with no signs of ferromagnetism. Finally, annealing at 600◦C led to the formation of well-defined secondary-phases in both concentrations, consistent essentially of superparamagnetic MnAs nanoclusters of two types: zincblende and hexagonal NiAs-type. The results presented in this thesis are direct evidence for the complex interplay between the local structure and the carrier-mediated ferromagnetism present in this DMS system. It constitutes an important step in the understanding of the fundamental physics behind (Ga,Mn)As, motivating a wider investigation of other dilute magnetic semiconductors within the III-Mn-V family. Key-words Dilute magnetic semiconductors; GaAs; Mn; Emission Channeling; local structure; magnetism; ferromagnetism; superparamagnetism; secondary-phase; clusters; doping; impurities; lattice location; phase-segregation; diffusion; X-ray diffraction; extended X-ray absorption fine structure; magnetometry. Resumo Ao longo dos anos, semicondutores magnéticos diluídos (DMS) aparecem como materiais promissores para a spintrónica baseada em semicondutores. Em particular, (Ga,Mn)As tornou-se o sistema modelo no qual explorar a física do ferromagnetismo mediado por portadores de carga em semicondutores e entre outros fenómenos associados à spintrónica, com uma panóplia de funcionalidades interessantes e dispositivos prototípicos. Este material constitui o exemplo perfeito de como o comportamento magnético de materiais DMS é fortemente influenciado pela sua estrutura local. Nesta tese, abordam-se aspetos sobre a interação entre a estrutura local e o ferromagnetism do (Ga,Mn)As. Em primeira mão, identifica-se inequivocamente a posição ocupada pelo intersticial de Mn na rede cristalográfica como sendo uma posição intersticial coordenada tetraedricamente por átomos de As TAs. Mostra-se, ainda, que esta posição TAs é a posição mais energeticamente favorável, independentemente do interstitial formar complexos com o substitucional ou não. Em segunda mão, averigua-se a estabilidade térmica das impurezas de Mn em ambas as posições substitucional e intersticial para duas concentrações representativas (1% and 5%). Verifica-se que os intersticiais de Mn tornamse móveis a temperaturas mais baixas que o substitucional, para ambas as concentrações. Por outro lado, demonstra-se ainda que as temperaturas de difusão para a mais alta concentração são inferiores às de menor concentração. Estas temperaturas de difusão são então dependentes da concentração, verificando-se que a agregação das impurezas ocorre a temperaturas inferiores para a maior concentração de Mn que para a menor. Duas conclusões chave podem ser daqui retiradas: a temperaturas típicas de crescimento deste material (200-300◦C) o Mn intersticial é móvel para a alta concentração (5%) contrariamente à baixa concentração (1%); e o Mn substitucional começa a difundir num regime de temperaturas bastante inferior ao relatado na literatura. Observa-se ainda um decréscimo na energia de ativação com o aumento da concentração de Mn, para a difusão de ambas as impurezas substitucionais e intersticiais. Este decréscimo tem diferentes origens: no caso da difusão do Mn substitucional, com energias de ativação de 2.3-2.6eV para 1% Mn e 1.92.0eV para 5% Mn, o aumento de concentração favorece a difusão assistida por lacunas ix xvi LIST OF FIGURES 4.11 Reciprocal space maps near the (002) reflections in the 5% Mn (Ga,Mn)As annealed at different temperatures . . . . . . . . . . . . . . . . . . . . . . . . 57 4.12 SR-HRXRD measurements around the (002) peak of GaAs on (Ga,Mn)As . . 58 4.13 SR-GIXRD measurements (Ga,Mn)As samples . . . . . . . . . . . . . . . . . 59 4.14 Fourier transform of the EXAFS spectra . . . . . . . . . . . . . . . . . . . . . 60 4.15 EXAFS analysis: Mn-As NN distance and DW factor . . . . . . . . . . . . . . 61 4.16 Magnetization measurements for as-grown and 200◦C air annealed 1% (Ga,Mn)As 63 4.17 Magnetization measurements for as-grown and 200◦C air annealed 5% (Ga,Mn)As 64 4.18 Magnetization measurements for as-grown and annealed at 200◦C (Ga,Mn)As 65 4.19 Magnetization measurements for 300◦C and 600◦C annealed 1% (Ga,Mn)As 68 4.20 Magnetization measurements for 300◦C and 600◦C annealed 5% (Ga,Mn)As 69 4.21 Magnetization measurements for 300◦C and 600◦C annealed (Ga,Mn)As . . . 70 List of Tables 4.1 Summary of the experimental details of experiments A, B, C and D . . . . . . 28 4.2 Saturation magnetization along four non-equivalent directions at 5 K in (Ga,Mn)As annealed at 200◦Cinair.............................. 32 4.3 Experimental details for 6% Mn (Ga,Mn)As as-grown and annealed at 200◦C 35 4.4 Estimated activation energies for interstitial Mn diffusion . . . . . . . . . . . . 49 4.5 Estimated activation energies for substitutional Mn diffusion . . . . . . . . . . 51 xvii xviii LIST OF TABLES Glossary ADF Annular dark field CERN Centre Européen pour la Recherche Nucléaire DFT Density function theory DMS Dilute magnetic semiconductor DOS Density of states DW Debye-Waller EC Emission channeling ESRF European Synchrotron Radiation Facility EXAFS Extended x-ray absorption fine structure FC Field cool FET Field effect transistor FM Ferromagnetic FWHM Full width at half maximum GIXRD Grazing-incidence diffraction GMR Giant magnetoresistance HDD Hard-drive disk HRXRD High-resolution x-ray diffraction IB Impurity band LED Light emitting diode LT-MBE Low-temperature molecular beam epitaxy MIT Metal-to-insulator transition MTJ Magnetic tunnel junction NRA Nuclear reaction analysis NN Nearest neighbor PIXE particle-induce x-ray emission RBS Rutherford backscattering RKKY Ruderman-Kittel-Kasuya-Yosida SQUID Superconducting quantum interference device xix xx Glossary SP Secondary-phase SPM Superparamagnetic SR-XRD Synchrotron radiation x-ray diffraction STEM Scanning transmission electron microscopy TEM Transmission electron microscopy XAFS X-ray absorption spectroscopy XAFS X-ray absorption fine structure XRD X-ray diffraction ZB Zincblende ZFC Zero-field cool Preface This thesis is the result of experimental research performed at the Instituut voor Kern-en Stralingfysika of KULeuven and is the culminating point of the author’s Integrated Masters on Engineering Physics, taught at the Faculty of Sciences of the University of Porto. It was developed under the supervision of Dr. Lino Pereira (lino.per[email protected]uleuven.be), Prof. Dr. João Pedro Araújo ([email protected]), and Prof. Dr. Kristiaan Temst (kristiaan.tems[email protected]en.be), integrated in the joint research efforts of IFIMUP–IN in Porto, Portugal and IKS in Leuven, Belgium. In the first three chapters the field of diluted magnetic semiconductors is introduced, along with an outline of the research performed in the framework of this MSc. Chapter 4 presents the results obtained for this research and their subsequent analysis. At the end of the thesis, a general conclusion summarizes the results and discusses their implications on the future of the field. xxi xxii Preface Introduction “In a marriage of quantum physics, information theory, and nanoscale engineering, quantum information science endeavors to build machines that can use the power of quantum mechanics for practical purposes.” – David D. Awschalom, 2013 [1] Since the dawn of the humanity, information has been one of the main drives of evolution. Sharing information has led to the creation of numerous languages over time, ever in the way of improving communication between ourselves. For millenia communication between us was of a short-range, requiring a message carrier in order to communicate over long distances, eventually taking days or weeks to deliver a message. In the last century(ies) we have reached a stage where communication has surpassed these physical boundaries, nowadays enabling the sharing of incredibly vast amounts of information, accessible by a simple touch. Digital communication has become a pillar of modern society. Digital communication only became possible due to the technological advances on electronics. The unceasingly increasing amount of transistors in the last 50 years, packed by billions in very small integrated circuits or chips, led to the outstanding speed and performance of every modern electronic device. Processing speed and integration density of silicon chips has been increasing exponentially, doubling every eighteen months according to Moore’s law. However, physical limits are being reached as currently used materials are reaching their functional limits. In other words, the use of electron charge and its transport in conventional electronics, the very same principles as in the first transistor created fifty years ago, is reaching a cul-de-sac. A possible solution comes in upgrading electronics by introducing an additional degree of freedom, such as the electron spin. By using two fundamental properties of the electron or simply by using spin alone, spintronics promises a new generation of devices with various advantages over conventional electronics: non-volatile and faster operating devices, increased integration densities and reduced power consumption along with new ways of xxiii xxiv Introduction processing information [2]. Some examples of spintronic devices are spin-polarized LEDs, spin-field effect transistors (FETs), and spin-based qubits for quantum computing [1]. Spintronics first emerged in 1988, upon the discovery of the giant magnetoresistance (GMR) effect in spin-valve structures by Albert Fert and Peter Grünberg, which earned them the Nobel Prize in Physics in 2007. GMR-based spin-valves quickly made their way into our daily lives in the form of read heads of hard-disks (HDD), revolutionizing data storage technology. These GMR-based spin-valves were quickly replaced in the read-heads of HDDs by magnetic tunnel junctions (MTJ), which are based on the tunnel magnetoresistance effect. These systems are operated in a very close proximity to the spin-valves, with a main difference of using a thin insulator spacer instead of a metallic one. In spite of revolutionizing data storage technology, this first generation of spintronics (magnetoelectronics) has created a bottleneck in the way current devices manage information: data is stored in metal-based magnetic devices, while data processing takes place in semiconductor-based electronic devices. The data exchange between these two units costs time and energy, which could be saved if data storage and processing would be integrated in the same device. However, semiconductors currently used in integrated circuits, transistors and lasers, consist mainly of silicon (Si), gallium arsenide (GaAs) and gallium nitride (GaN) – which are non-magnetic materials – while, on the other hand, digital storage devices resort to ferromagnetic materials such as iron (Fe), cobalt (Co) and nickel (Ni) – non-semiconducting materials. Furthermore, combining the two types of materials into a functional heterostructure has been proven to be difficult due to the different crystal structures of magnetic materials and semiconductor materials [3]. The alternative is then to use materials which combine ferromagnetic and semiconducting behavior [4], i.e. evolving from metal-based to semiconductor-based spintronics. Dilute magnetic semiconductors emerge as a pioneering development in semiconductorbased spintronics: in a similar fashion to electrical doping in insulating or nearly insulating materials to make them conducting, incorporating magnetic ions into non-magnetic semiconductors so that they become ferromagnetic. With already 30 years of an exciting history, generation after generation of ever increasing Curie temperature, dilute magnetic semiconductors have captured the attention of the semiconductor and magnetism communities. Promising and yet puzzling developments, with hundreds of publications every year, led the field to be considered as one of the most controversial research topics in material science and condensed-matter physics today. 1 Literature Review This chapter introduces the field of dilute magnetic semiconductors (dms) and more specifically the properties of narrow-gap DMS (Ga,Mn)As. A short motivation and definition of the field is presented in section 1.1.1, followed by an overview of the history of DMS research motivating the work presented in this thesis (section 1.1.2). In the last section 1.2 we describe the current understanding on structure and magnetism of (Ga,Mn)As. 1.1 Dilute Magnetic Semiconductors 1.1.1 Definition Magnetic semiconductors are materials in which ferromagnetism coexists with semiconducting behavior and have been studied since the 1960s. The first generation is considered by most the true ferromagnetic semiconductors consisting of materials containing magnetic elements in their chemical formula, in which the ferromagnetic order is established in the magnetic (periodic) sublattice. These materials were extensively studied from late 1960s to early 1970s, manifesting various interesting properties, such as red-shift of the bandgap upon the onset of ferromagnetic order, but their crystal structures are incompatible with conventional electronics. Additionally, the synthesis of these materials is rather unwieldy and difficult to reproduce. The low Curie temperatures (TC<100 K) make them of little use in practical applications, which require a ferromagnetic behavior persistent up to typical device operation temperatures (room temperature and above). Dilute magnetic semiconductors (dms) are magnetic semiconductors in which ferromagnetism is introduced by incorporating magnetic atoms into nonmagnetic semiconductors, in similarity with electrical doping, which makes insulating materials conducting by incorporating donor and acceptor impurities. In these materials, magnetic impurities are distributed randomly, substituting a few percent of the atoms in the host matrix of the nonmagnetic semiconductor. Accordingly, a magnetic impurity is an atom or ion of an element which is different from the host’s constituents and carries a non-vanishing magnetic moment. The 1 8CHAPTER 1. LITERATURE REVIEW to the substitutional Mn acceptor concentration, i.e. in weakly compensated systems, with weakly confined holes, TCand electrical conductivity do not tend to zero. This report is not consistent with the picture of a Fermi level located in an isolated impurity band, but with the previously well established p-d Zener model. 1.2.2 Compensation by interstitial Mn Despite this central role in understanding the magnetism in (Ga,Mn)As, and consequently of Mn-doped III-V DMS materials, interstitial Mn is far from being a well understood defect. As seen in the previous section, TCincreases with effective Mn concentration, which takes into account the balance between the fractions of Mn substituting for Ga (Mns) and on the interstitial sites (Mni). Mnsis responsible for the localized magnetic moments and the itinerant holes that mediate the ferromagnetic coupling, whereas Mnihas a two-fold compensation effect: magnetic, as Mnicouples antiferromagnetically with Mns, and electrical, since double donor Mnicompensates Mnsacceptors. As a result, the effective concentration xeff of Mn impurities that effectively contributes to the observable ferromagnetism in (Ga,Mn)As, is smaller than the nominal concentration xby twice the Mniconcentration xi,xeff =x−2xi. Accordingly, the hole concentration pshould be smaller or of the order of this effective concentration, p.x−2xi. Despite the Mn concentration that can be incorporated in high-quality (Ga,Mn)As has been increased throughout the years up to 20%,TCsaturates at ∼200 K for concentrations x= 10% [57]. The highest TCand pvalues achieved in (Ga,Mn)As are obtained after annealing close to growth temperature, around ∼200◦C [11, 58]. Transport measurements have shown a partial activation by annealing that results from the out-diffusion of a compensating defect with a low thermal stability, with an activation energy of Ea= 0.7 eV [44]. This report was supported by ab initio calculations yielding similar activation energy for Mni[17, 44]. In fact, by annealing around this temperature the Mnidiffuses to the surface where it is passivated, partaking in the formation of a antiferromagnetic MnO thin film [13, 44, 59] or an MnAs monolayer, if the surface is capped with an As layer [60]. However, a significant fraction of the introduced Mn still remains inactive, as xeff < x and p < x after annealing. It became generally accepted that Mniwas the low temperature diffuser, establishing the belief that pure substitutional Mn doping can be achieved by low temperature (∼200◦C) thermal annealing. Since then, research focused on increasing the concentration of magnetically active Mn in order to achieve TCabove room temperature, however facing technical challenges in achieving concentrations beyond x≈0.10 with maximum TC= 185 K [11, 14, 17]. 1.2. STRUCTURE AND MAGNETISM OF MN-DOPED GAAS 9 Overcoming this solubility limit with alternate growth and/or post-processing methods would unlock the possibility of increasing TCabove the current maximum, allowing for the realization of possible room temperature ferromagnetism in Ga1-xMnxAs. 1.2.2.1 Lattice Location There are several interstitial sites in the zincblende structure of GaAs – tetrahedral(T), bond centered (BC), anti-bonding (AB) among others (cf. figure 1.2 on the following page). Experimental techniques commonly used to identify lattice sites of impurities in crystalline solids are either based on channeling of charged particles (ions or electrons) or on probing the atomic environment of the impurity atom, e.g. in X-ray absorption fine structure (XAFS) techniques. The first reports on Mn impurities lattice location are on pure Ga-substitutional incorporation (by XAFS [61]) and mixed Ga-substitutional and T interstitial occupancy (by ion channeling [62] and XAFS [63]), with the majority of the atoms in substitutional sites. Although consistent with Mnioccupying tetrahedral (T) interstitial sites, the measurements did not allow to discriminate between the two nonequivalent T sites in zincblende GaAS: coordinated by four Ga atoms (TGa) or by four As atoms (TAs) [64, 65]. More recently, xafs experiments confirmed the mixed occupancy and identified the TGa interstitial site [66, 67]. On the theoretical side, ab initio calculations yielded lower energy for Mn in TAs sites compared to TGa [44], which is consistent with the expectation of having the Mn cations coordinated by As anions. However, XAFS is not well suited to distinguish elements with similar atomic numbers, as is the case for Ga and As, especially in cases of multi-site occupancy (substitutional and interstitial) where the site to be identified is in fact the minority one (interstitial). Transmission electron microscopy measurements using (002) diffracted beam indicated that the Mnipredominantly occupy the TAs site [46]. Pioneering work using X-ray scattering techniques to probe dopant lattice location reported comparable TGa and TAs occupancies [68, 69, 70]. Coexisting TGa and TAs occupancies would suggest that the Mnilattice site depends on the presence of neighboring Mnsatoms, i.e. that isolated Mni and Mniin Mni-Mnspairs occupy different T sites. This is however in contradiction with density functional theory (DFT) calculations which predicted that, for typical ferromagnetic (Ga,Mn)As samples (where the Mnsconcentration is the large majority over that of Mni), TAs is the most stable site for Mniregardless of being isolated, in Mni-Mnspairs, or even in Mns-Mni-Mnstriplets [71]. Solving this inconsistency would allow for a better understanding of the mechanisms of 10 CHAPTER 1. LITERATURE REVIEW SGa SGa SGa SGa SGa SGa SAs SAs TAs TAs TAs TGa TGa ABGa H ABAs BC SPGa SPGa SPAs SPAs CGa CGa CAs YAs YAs YGa YGa CAs CAs <100> <110> Figure 1.2: The {110} plane in GaAs zincblende lattice, showing the following sites: the substitutional Ga (SGa) and As (SAs) sites; the tetrahedral interstitial sites with Ga (TGa) and As (TAs) nearest neighbors; interstitial sites along the <111>direction, i.e. the bond center (BC), antibonding Ga (ABGa), antibonding As (ABAs), and the hexagonal site (H); and the interstitial sites along the <100>direction, in either Ga or As rows, i.e. the split interstitials (SPGa and SPAs), the "C" sites with C2v symmetry (CGa and CAs), and the "Y" sites (YGa and YAs). Along the <100>,<111>,<110>and <211> directions, the rows of Ga and As atoms are indicated (lines), as the rows of the TGa and TAs sites (dashed lines). Note that, along the <111>direction, the substitutional (SGa and SAs) and tetrahedral interstitial (TGa and TAS) sites are all located on the same row; along the <100>direction, SGa is on the same row as TAs, and SAs is on the same row as TGa. electric and magnetic compensation by Mniwhich, as introduced above, plays a central role in the behavior of (Ga,Mn)As. Establishing the lattice location of Mn in (Ga,Mn)As requires the use of a technique which can unambiguously distinguish the two T sites. In fact, the Emission Channeling technique is uniquely suited to address this problem (cf. section 3.2 on page 16), and was used in a recent study on GaAs in the very low concentration regime (x < 0.05 at. %) with different doping (undoped, p-type and n-type) [65, 64] to identify the lattice location and thermal stability of Mn impurities. In these reports, the Mn impurities were found to occupy mainly the substitutional site with a fraction on the TAs interstitial site. This interstitial diffuses around 400◦C, by converting into substitutional Mn, a much higher temperature than reported in literature [44, 17]. However, these experiments were 1.2. STRUCTURE AND MAGNETISM OF MN-DOPED GAAS 11 performed on GaAs within the very low Mn doping regime (x < 0.05 at. %), which has a different local structure than (Ga,Mn)As, i.e. the presence of a higher concentration of Mn impurities might have a strong influence in the diffusion and stability of interstitial Mn. 1.2.3 Mn aggregation and secondary phases formation As mentioned above, annealing Mn-doped GaAs at ∼200 ◦Ctypically increases TC. However, comparing TCafter thermal annealing at temperatures between 160◦C and 220◦C, it was found that TCactually decreases with increasing annealing temperature [11]. Further increasing the annealing temperature (>280◦C) eventually leads to an actual decrease of TC. This is indicative of a second occurring process, with an activation energy slightly above that of the out-diffusion of the compensating defect. This second process has been suggested to be related to Mn aggregation (or segregation). It is however unclear what type of aggregation it is, i.e. whether it is only chemical or also structural. Ion-channeling experiments have shown that part of the substitutional Mn converts to a random fraction at 282◦C, most likely due to cluster formation [62]. This indicates that phase segregation starts already at relatively low temperatures. Ab initio studies on the substitutional Mn diffusion have shown that Ga vacancies act as an efficient trap for Mnsto diffuse and that the clustering rate increases along temperature and/or Mn concentration, effectively decreasing TC[72]. Furthermore, at large Mn concentrations clustering takes place already during sample growth. On the other hand, by annealing at relatively high temperatures (>500◦C) the precipitation of Mn impurities onto a MnAs secondary phase becomes evident [73]. Based on high-resolution X-ray diffraction (HRXRD) and grazing-incidence diffraction (GIXRD) it was reported the co-existence of two different types of MnAs secondary phases [74] in samples annealed at 700 ◦C(Ga,Mn)As: small, coherent with GaAs matrix, zincblende (ZB) MnAs nanoclusters – chemical segregation – and bigger, lattice-distorting, NiAs–type (hexagonal) MnAs nanoclusters – consistent with chemical and structural segregation. In the following years, these two types of clusters have been extensively characterized [75, 76, 77, 78]. Transmission electron microscopy (TEM) experiments [77] and X-ray absorption spectroscopy (XAS) [79] have shown that upon thermal annealing at 500 ◦C, only Mn-rich zincblende (Mn,Ga)As clusters (∼3nm) are formed which are coherent with the GaAs matrix. These coherent (Mn,Ga)As nanoclusters were shown to be ferromagnetic above room temperature, with a TC∼360 K, as the local concentration of Mn reaches the expected x∼20%, that would allow for (Ga,Mn)As to be ferromagnetic at room temperature as well. Annealing at 600◦C has been demonstrated to lead to the precipitation of well defined 12 CHAPTER 1. LITERATURE REVIEW hexagonal NiAs–type MnAs nanoclusters [75, 76, 77, 78]. While these nanoclusters are significantly bigger (20 –45 nm) than the ZB nanoclusters (3–8nm), they are strained in the GaAs structure and also display ferromagnetism, however with a lower Curie temperature (TC∼300 K). Using aberration-corrected tem and aberration-corrected annular dark-field (ADF) STEM it was shown that when annealing (Ga,Mn)As thin films at temperatures above 400◦C both ZB and NiAs–type nanoclusters form along with adjacent As nanocrystals and voids [80, 81]. On another study, the presence of nanoclusters in (Ga,Mn)As was shown to increase in two orders of magnitude the coercivity of the material without significantly reducing TC[82]. All in all, in order to efficiently obtain high-TC(Ga,Mn)As thin films the growth temperature must be decreased as Mn concentration increases [17, 83], in order to avoid secondary phase formation. “The case of (Ga,Mn)As is an optimistic reminder that the complex defect physics of these systems is an opportunity not a warning. The magnetic properties of any diluted magnetic semiconductor ferromagnet can be improved by understanding and learning to control defects.” – A. MacDonald, P. Schiffer and N. Samarth, 2005 [84] 2 Objectives and outline This work addresses the current goals and challenges facing the narrow-gap DMS field, and in particular the research on (Ga,Mn)As ferromagnetic thin films, which were described in section 1.2. The objectives of this work and corresponding research approach are summarized as follows. (A) To determine the lattice location of interstitial Mn in (Ga,Mn)As. The goal is to identify unambiguously the interstitial Mn site in ferromagnetic (Ga,Mn)As, using the emission channeling technique (described in section 3.2). The results and implications on the understanding of the fundamental devices behind the compensation by interstitial Mn in (Ga,Mn)As films are described in section 4.1 on page 27. (B) To study the thermal stability and diffusion of Mn impurities in (Ga,Mn)As. The objective is to investigate the thermal stability of Mn impurities in (Ga,Mn)As doped with different Mn impurity concentrations (1% and 5%), and describe its diffusion behavior upon thermal annealing at various temperatures. Results are presented in section 4.2 on page 41. (C) To investigate the structure and magnetism of annealed (Ga,Mn)As. The aim of is to ascertain the different structural and magnetic properties of (Ga,Mn)As within the ferromagnetic regime (as-grown and annealed at 200 ◦C) and within the secondary phase regime (annealed at 300 ◦Cand at 600 ◦C). Results are presented and discussed in section 4.3 on page 55. 13 14 CHAPTER 2. OBJECTIVES AND OUTLINE 3 Experimental techniques This chapter describes the experimental techniques used in this work. The (Ga,Mn)As samples were grown by low-temperature molecular beam epitaxy (LT-MBE) by the Nottingham group (U.K.) [83]. Sample characterization was carried out using synchrotron radiation Xray Diffraction (SR-XRD) in order to determine the structure and secondary phase formation (cf. section 3.1), Extended X-Ray Absorption Fine Structure (EXAFS) to probe the local structure of Mn impurities, Electron Emission Channeling (EC) to study the lattice location of Mn impurities (cf. section 3.2 on the following page) and Superconducting Quantum Interference Device (SQUID) magnetometry to investigate the magnetic properties (cf. section 3.3 on page 25). Albeit in this chapter we present a description of the experimental setups, only for the Emission Channeling technique a detailed description is given, as it is an unique and unconventional technique. The experimental procedure and data analysis of the EXAFS experiment is not given, since the experiments and subsequent analysis were not performed by the author. The remaining techniques were applied following standard systems and protocols and, therefore, only a small description is provided. 3.1 Synchrotron Radiation X-Ray Diffraction The interaction of X-rays with the crystal lattice of a material allows us to extract information on the lattice. Such is the purpose of X-ray diffraction (XRD) techniques. The most commonly used technique is the θ-2θscan in Bragg-Brentano geometry, where a sample is tilted towards an X-ray beam over an angle θand a detector is rotated over the angle 2θso that the Bragg diffraction criterion is fulfilled for planes that are parallel to the sample stage, provided they have the correct d-spacing determined by the wavelength of the X-rays and the 2θangle of the detector through the Bragg rule 2dsin θ=nλ. However, it is important to be aware of the limitations of this standard technique, as the used geometry will result in a signal which only depends on the crystal planes parallel to the sample stage surface, and thus any information on the occurrence or orientation of other planes is lost. In other 15 16 CHAPTER 3. EXPERIMENTAL TECHNIQUES words, in an epitaxial thin film the diffraction peaks of the substrate and of the film will be much more intense than the peaks from a secondary phase with a random orientation. For the study of materials which can be provided as a powder, this raises no problems, as the statistical distribution of the plane orientations will be uniform (resulting in random orientation of the crystal planes), but for epitaxially grown samples with a secondary phase a lot of information will be missed. In θ-2θgeometry the intensity of a diffraction peak is significantly influenced by the amount of material contributing to the diffraction. In order to probe the orientation of an eventual secondary phase on a single crystal thin film, the use of another diffraction geometry is required. In this work we resorted to the grazing incidence X-ray diffraction (GIXRD) geometry, where the sample is irradiated by X-rays at a small angle, so that these probe only the thin film, effectively increasing the contribution of the thin film to the signal. An advantage of GIXRD is that the electric field at the critical angle is amplified making the signal stronger. In other words, for a single-crystal in GIXRD geometry the Bragg condition is not fulfilled for the substrates peaks. The measurement results then solely on the contribution of diffraction from polycrystalline secondary phases. The XRD measurements presented in this work were performed on the BM20B-Rosendorf beamline [85] at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France, using an incident photon energy of 11.5keV, corresponding to a wavelength of λ= 1.0789 Å. A symmetrical θ-2θscan was performed in the range 15◦-80◦, with a high resolution (HRXRD) scan in the range of the first diffraction of the substrate peak, 20.5◦-22.5◦. Additionally, asymmetrical GIXRD measurements were performed with an incident angle of 1.5◦. Both measurements were recorded using a linear 1D Mythen detector with 1280 channels, with a measurement resolution of 0.01◦. 3.2 Electron Emission Channeling The electron emission channeling technique has been developed for the study of the lattice site location of impurities in single-crystals and offers a number of advantages when compared to other techniques. Because it relies on the direct comparison between experimental and calculated (2-dimensional) patterns, it provides unambiguous and quantitative lattice location superior to more conventional implementations of ion-channeling techniques such as Rutherford backscattering spectrometry (RBS), particle-induced X-ray emission (PIXE) and nuclear reaction analysis (NRA). Additionally, not relying on elastic recoil like the widely used conventional RBS, it allows a better identification of impurity atoms lighter than the 3.2. ELECTRON EMISSION CHANNELING 17 major constituents of the material, even in cases of multi-site occupancy, with much higher sensitivity (down to 1012 at.cm−2), particularly suited for dilute systems, like the one studied in this work. 3.2.1 Principles The emission channeling technique makes use of the charged particles emitted by a decaying radioactive isotope. These particles are emitted isotropically during decay and are channeled along the screened Coulomb potential of atomic rows and planes. Along lowindex crystal directions of single crystals, this anisotropic scattering results in well-defined channeling or blocking effects. Because these effects strongly depend on the initial position of the emitted particles, they lead to emission patterns which are characteristic of the lattice sites occupied by the probe atoms. Channeling was first introduced by Lindhard in 1965 [86] and is referred to as the mechanism by which atomic rows and planes steer energetic charged particles along major crystal axis and planes. Because the motion of energetic charged particles in a solid is mainly determined by their Coulomb interaction with the (screened) nuclear charges in the lattice, one can expect that particle propagation is very different among these three types of directions. The general principles described for the channeling of heavy, positive ions apply to the channeling of electrons, which are lighter and negatively charged. Changing the sign of the propagating particle’s charge is equivalent to changing the sign of the Coulomb potential: negatively charged particles "see" as channels the rows of nuclear charges instead of the space in between. However, although providing an intuitive insight in the elementary phenomena, the classical approach of Lindhard does not describe quantitatively electron emission channeling, in which quantum effects must be taken in account. Details on the theoretical aspects of emission channeling can be found, for example, in [87]. The principle of emission channeling is slightly different than conventional channeling techniques that rely on the use of an external ion beam and its interaction with the impurity atoms in the host lattice, like RBS, PIXE or NRA, in the sense that the channeled particles are emitted from within the crystal by a radioactive isotope of the impurity element under study. The emission channeling technique can be applied using either αor electron (β− or conversion electrons) emitters. In the latter case, the technique is known as electron emission channeling, for which the requirement of stability 1determines that the channeling 1The principle of stability requires that the particle does not approach the rows of atoms too closely, otherwise, instead of a gentle steering via the interaction with the row of atoms, the particle experiences wideangle deflections in head-on collisions with individual atoms 24 CHAPTER 3. EXPERIMENTAL TECHNIQUES 3.2.4.3 Scattered electron background correction In an emission channeling experiment, two types of electrons reach the detector: direct and scattered electrons. Those with initial direction in the vicinity of the detection axis are direct electrons. The number of direct electrons is roughly given by the ratio between the solid angle Ωspanned by the detector relative to the beam spot and the full 4πsolid angle into which all the electrons are (almost) isotropically emitted, i.e. Ω/4πof the total number of decays. However, the number of detected electrons is always larger than this estimate. The additional scattered electrons are not emitted towards the detector initially, but still reach it after being scattered. The scattering event may occur inside the sample, when an electron is scattered by the host atoms, or outside the sample, by setup parts (including backscattering from sample holder). These scattered electrons constitute an additional isotropic background in the experimental emission yields, which is not taken into account in the theoretical framework of channeling that is implemented in the manybeam program. The problem is different for conversion electrons and β−particles: Conversion electron decay. For a pure conversion electron decay, it is possible to deduce the total scattering background from the experimental energy spectrum. While, for direct electrons, the energy spectrum consists of a set of narrow peaks at well defined energies, the scattered electrons form tails at lower energies due to the energy lost in the scatter process. It is thus possible to correct for this scattering background by estimating (integrating the counts in the tails) and subtracting it from the experimental yields. Beta decay Because such a simple estimate is not possible for β−decays, with continuous energy spectra, De Vries [94] developed the computer program Pad based on the Geant4 toolkit (a set of libraries and tools to simulate the interaction of energetic particles with matter) [95, 96]. Using the Monte-Carlo method, Pad simulates the propagation of electrons emitted from the sample and, among the ones that reach the detector, distinguishes the direct from the scattered ones. This requires detailed input information: the sample’s geometry and composition, the β−decay energy spectrum (isotope-specific) and the exact geometry of the setup, i.e. the position, shape and composition of the setup parts. From the Pad simulations it is possible to estimate the background correction factor fas: f=total electrons total electrons −scattered electrons =total electrons direct electrons.(3.4) 3.3. SUPERCONDUCTING QUANTUM INTERFERENCE DEVICE MAGNETOMETRY 25 This ffactor can be used to correct the experimental patterns before the fitting or, equivalently, as a rescaling factor of the fractions determined from it. 3.2.5 Experimental details In this work, two different types of emission channeling experiments are presented: on-line experiments with implantation of radioactive 56Mn and off-line experiments with implantation of 73As. The on-line experiments where performed using the Emission Channeling – Short Lived Isotopes (EC-SLI) setup and measured in-situ [88]. The radioactive decay mode for 56Mn is presented in equation (3.5). 56Mn →56Fe + β−+νe(3.5) The off-line experiments were performed with the long-lived isotope 73As (decay mode in equation (3.6)), with off-situ measurements. For these experiments the setup described in ref. [97] was used, making use of a detector with a different sensitivity, adjusted to the decay rate of 73As. The specific experimental details for each of the EC experiments performed are presented in the following chapter 4, in the corresponding sections. 73As + β−→73Ge + νe(3.6) 3.3 Superconducting Quantum Interference Device magnetometry DMS materials are usually in the form of thin films (<1µm) or implanted layers, displaying a small magnetic moment which is further decreased by the low concentration of magnetic dipoles and their small magnetic moment (in many cases, only a fraction of a Bohr magneton). The magnetic moment of a typical DMS sample is usually between 10−7and 10−4emu (10−10 and 10−7A m2), thus requiring the high sensitivity of a Superconducting Quantum Interference Device (SQUID) magnetometry. A SQUID magnetometer measures the magnetic moment of a sample by moving it through a superconducting detector coils. The detector coils are connected to the SQUID through superconducting wires, allowing the current from the detection coils to inductively couple to a SQUID sensor (based on a Josephson junction). As the sample moves through the detection coils, the magnetic moment of the sample induces an electric current in the detection coils. The detection coils, the connecting wires and the SQUID input coil form 26 CHAPTER 3. EXPERIMENTAL TECHNIQUES a closed superconducting loop. Any change in the magnetic flux in the detection coils produces a change in the persistent current in the detection circuit, proportional to the change in magnetic flux. Since the SQUID works as a highly linear current-to-voltage converter, the variations in the current in the detection coils produce corresponding variations in the SQUID output voltage which are proportional to the magnetic moment of the sample. In a fully calibrated system, measurements of the voltage variation as the sample is moved through the detection coils provide a highly accurate measurement of the magnetic moment of the sample (with a resolution down to 10−8emu). However, magnetic contamination and measurement artifacts must be carefully taken into account in the range below 10−4emu range. In order for SQUID magnetometry to be used as a reliable tool for the detection of ferromagnetism in DMS materials, it is necessary to develop methods and procedures which ensure that the magnetic signal originating from contamination and other artifacts can be reproducibly kept below a well defined value. Such methods are described in detail in ref. [98]. The SQUID magnetometry measurements presented in this work were performed on rigorously cleaned samples (according to [98]) and consisted mainly in magnetization measurements (a) as a function of applied magnetic field and (b) as a function of temperature. In (a), measurements were performed at 5K and at room-temperature (300 K) along the easy axis ([100] direction) with applied magnetic fields between −2600 mT and 2600 mT. Saturation magnetization was determined by performing a linear fit at high applied magnetic field. All magnetization curves as a function of applied magnetic field presented in this work were subjected to a fit and corrected to the diamagnetic background of the samples. In (b), remanence and zero-field cool/field cool (ZFC-FC) curves were measured with increasing temperature in the range 5-300 K. Remanence was measured at an applied field of 2mT, after cooling in a saturating magnetic field – this magnetic field was applied to compensate an eventual negative residual field in the magnet of the SQUID; the ZFC-FC magnetization curves were measured at an applied magnetic field of 10 mT, with the same magnetic field for the field cooling. 4 Results and discussion This chapter presents the results obtained in this work and their subsequent discussion. It is divided in three parts: first, in section section 4.1, we deal with the identification of the lattice location occupied by the interstitial Mn impurities in ferromagnetic (Ga,Mn)As; second, in section 4.2, we study the thermal stability and diffusion behavior of both substitutional and interstitial Mn impurities in two different concentration regimes – low concentration (1% Mn) and high concentration (5% Mn); and third, in section 4.3, we perform the structural and magnetic analysis of (Ga,Mn)As within the ferromagnetic and secondary-phase regimes (also for 1% and 5% Mn). 4.1 Identification of the interstitial Mn site As seen in section 1.2.2.1, the interstitial Mn impurities in ferromagnetic (Ga,Mn)As occupy mainly T interstitial sites on the zincblende lattice of (Ga,Mn)As. There are, however, two different T sites, coordinated by different nearest neighbor atoms, Ga or As, and the occupancy of these sites by the interstitial Mn is ambiguous. Emission channeling is an unique technique specially suited to tackle this ambiguity as it provides doubtless distinction between TGa versus TAs sites in the GaAs (zincblende) lattice – a direct structural effect related to the mirror-asymmetry of selected crystal axes (typically <211>or <110>) [65]. The EC technique has been previously applied to determine the lattice location of Mn in GaAs in the ultra-low doping regime (<0.05% Mn) [64, 65], showing a major occupancy by the interstitial Mn impurities of the TAs sites when compared to the TGa. In this section we address the first objective outlined in chapter 2, i.e. using the emission channeling (EC) technique (described in section 3.2 on page 16), we pretend to determine the exact lattice site occupied by Mniin ferromagnetic, high Curie temperature (Ga,Mn)As thin films. 27 28 CHAPTER 4. RESULTS AND DISCUSSION 4.1.1 Experimental details Two separate experiments were performed on the lattice location of radioactive 56Mn (halflife t1/2= 2.56 h) implanted into a (Ga,Mn)As thin film grown by molecular beam epitaxy (MBE) [83]. Experiment A consisted of implanting a Ga0.94Mn0.06As thin film (25 nm thick, grown directly on the GaAs substrate) with 56Mn to a fluence of 2×1012 cm−2, at an energy of E= 40 keV, and a beam angle of 60◦with respect to the surface normal. The high implantation angle was chosen in order to maximize the fraction of 56Mn probes implanted in the (Ga,Mn)As thin film, i.e. minimizing implantation into the substrate. The near-Gaussian depth profile simulated using SRIM-2008 [99] is characterized by a peak concentration xp= 6.2×1017 cm−3(≈0.003 atomic %, i.e. a negligible increase in Mn concentration), a projected range (average depth) of Rp= 17 nm and a straggling of σ= 11 nm, with an estimated <27% of the 56Mn probes implanted into the GaAs substrate. Experiment B consisted of implanting a Ga0.95Mn0.05As thin film (200 nm thick, grown on a 200nm AlAs buffer layer, on a GaAs substrate) with 56Mn to a fluence of 7×1012 cm−2, with an energy of E= 30 keV and an angle of 17◦(resulting in a peak concentration of xp= 2.4×1018 cm−3, a projected range of Rp= 21 nm and a straggling of σ= 11 nm, i.e. with all the 56Mn probes within the film). In order to monitor the degree of disorder upon implantation of the radioactive probes and subsequent annealing, we also determined the lattice location of As using radioactive 73As (t1/2= 80 d) – experiments C and D. These experiments consisted of implanting similar samples as in experiment B with 73As to a fluence of 5×1013 cm−2, with an energy of E= 50 keV and an angle of 10◦(resulting in a peak concentration of xp= 1.5×1019 cm−3, a projected range of Rp= 26 nm and a straggling of σ= 13 nm, i.e. with all the 73As probes within the film). experiment ion annealing E[keV] θ[◦]Rp±σ[nm] xp[cm−3] A56Mn 3h air 40 60 17 ±11 6.2×1017 B56Mn 10 min vacuum 30 17 21 ±11 2.4×1018 C73As 3h air 50 17 26 ±13 1.5×1019 D73As 10 min vacuum 50 17 26 ±13 1.5×1019 Table 4.1: Summary of the experimental details of experiments A, B, C and D. E represents the implantation energy, θis the implantation angle, Rpand σare the projected range and straggling of the implanted ions respectively, xpis the peak concentration of the implanted layer. Emission channeling measurements were carried out in the as-implanted state and after annealing at 200◦C: in air for 3hours in experiments A and C; in vacuum (<10−5mbar) for 4.1. IDENTIFICATION OF THE INTERSTITIAL MN SITE 29 10 min in experiments B1and D. Experiments A and B (with relatively short-lived 56Mn) were performed on-line while experiments C and D (with the longer-lived 73As) were performed off-line. Table 4.1 on the facing page summarizes the experimental details for each of the described experiments. In experiments B, C and D, four axes were measured (<100>,<111>,<110>and <211>), typical of emission channeling experiments on host semiconductors with cubic structure (cf. e.g. [64, 65]). In experiment A, the measurements were limited to the <211>axis, which as will be shown below is sufficient to unambiguously determine the site occupancy (at least when combined with experiment B, where all four axes were measured). The implantation parameters, film thickness and annealing time of experiment A were carefully chosen to allow us to determine the lattice site(s) occupied by interstitial Mn in a stage of annealing for which approximately half had been removed (correlated with magnetic characterization below (cf. section 4.1.3). 4.1.2 Interstitial Mn site As a representative example, in figure 4.1 on the next page, (a-h) shows the experimental β−emission patterns of experiment B after thermal annealing (10 min in vacuum), along the four measured directions (a–d), as well as the best fits of theoretical patterns (e–h). Similarly, in figure 4.1 on the following page, (i-l) compares experimental patterns (i,j) and best fit (k,l) for experiment A (only the <211>direction), both before and after annealing (3h in air). In figure 4.1 on the next page, (m-o) qualitatively illustrates how the mirror asymmetry of the {110}-planar channeling measured in the vicinity of the <211>direction (horizontal plane in the figure) allows us to distinguish between TAs and TGa sites: after subtracting from the experimental data the fitted component occupying the substitutional Ga SGa sites, the asymmetry of the residual {110}-planar channeling corresponds to that of TAs, i.e. stronger channeling on the left versus right in (o) of figure 4.1, which is the opposite of TGa. Quantitative analysis is provided by numerically fitting the data to calculated patterns, as described in section 3.2.4, from which the fractions of the 56Mn atoms in the different lattice sites are obtained – compiled in figure 4.2 (a) for experiments A and B. Here we observe that while the interstitial Mn fraction is unaffected by the 10 min vacuum annealing (experiment 1In this section we consider solely the as-grown and the 200◦C annealing step for the purpose of this experiment. In the next section 4.2 we will consider the remaining annealing steps performed for the detailed diffusion study. 30 CHAPTER 4. RESULTS AND DISCUSSION - 2 - 1 0 1 2 - 2 - 1 0 1 2 {311} {110} {111} {110} {111} {110} {100} {110} 0 . 6 8 1 . 0 2 1 . 3 7 1 . 7 1 2 . 0 6 a2 - 1 0 1 2 e - 3 - 2 - 1 0 12 - 1 0 1 2 b e f o r e annealing e x p e r im e n t b e s t f it 0 . 7 4 1 . 0 1 1 . 2 9 1 . 5 6 1 . 8 4 i - 2 - 1 0 1 2 bb k - 2 - 1 0 1 2 b 0 . 7 4 0 . 9 4 1 . 1 3 1 . 3 3 1 . 5 2 f - 3 - 2 - 1 0 1 a f t e r annealing [deg] jl - 2 - 1 0 1 c 0 . 7 7 0 . 9 5 1 . 1 3 1 . 3 1 1 . 4 9 e x p e r im e n t b e s t f it g - 3 - 2 - 1 0 1 - 0 . 1 4 - 0 . 0 7 0 . 0 0 0 . 0 7 0 . 1 4 m - 2 - 1 0 1 - 1 0 1 2 3 d - 2 - 1 0 1 < 2 1 1 > < 1 1 0 > < 1 1 1 > < 1 0 0 > 0 . 8 1 1 . 0 1 1 . 2 2 1 . 4 2 1 . 6 2 h - 2 - 1 0 1 2 - 3 - 2 - 1 0 1 e x p e r i m e n t a l s u b t r a c t e d o f t h e S G a f r a c t i o n s i m u l a t e d nTG a - 2 - 1 0 1 2 0 . 6 4 1 . 0 1 1 . 3 8 1 . 7 5 2 . 1 2 oTA s Figure 4.1: (a–d) Experimental β−emission patterns of experiment B after thermal annealing (10 min, in vacuum), along the four measured directions, and best fits of theoretical patterns (e–h). The best fit is obtained for 71% of the 56Mn atoms on SGa (MnGa) and 25% on TAs (Mni) sites. (i-l) Experimental patterns (i,j) and best fit (k,l) for experiment A (only the <211>direction), before and after annealing (3h, in air). The best fits are obtained for 64/77% of the 56Mn atoms on SGa (MnGa) and 25/15% on TAs (Mni) sites before/after annealing. (m) Experimental pattern (j) after subtraction of the fitted SGa component. (n,o) Simulated patterns for 56Mn on TGa and TAs sites, respectively. B), annealing for 3hours in air decreases it by almost a factor of 2. This is consistent with our magnetometry measurements (cf. next section 4.1.3), and with the Mniannealing kinetics previously reported based on transport and magnetometry measurements [44, 17]. We also observe an increase in substitutional fraction upon annealing in both experiments A and B, which we attribute to the recovery of disordered regions (created upon implantation), rather than interstitial Mn being converted to substitutional. This is confirmed by experiments C and D, where we see a comparable increase of the substitutional As fractions (cf. section 4.1.4). Figure 4.2 (b) illustrates the technique’s sensitivity specifically for the case of TAs versus TGa occupancy, by showing for experiment A (after annealing) the error associated with the 4.1. IDENTIFICATION OF THE INTERSTITIAL MN SITE 31 - 1 0 1 2 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 f-f0 ( T A s ) [ % ] f ( T G a ) [ % ] 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 χ2-χ20 = 1 0 2 0 4 0 6 0 8 0 100 after annealing i n v a c u u m ( 1 0 m i n ) S G a T A s i n a i r ( 3 h ) S G a T A s s i t e f r a c t i o n f0 [ % ] b e f o r e a b Figure 4.2: a) Fractions of 56Mn atoms on SGa and TAs sites in experiments A and B. b) Error associated with the fit (χ2−χ2 0, with χ2 0being the value for the best fit), for experiment A after annealing, as the fractions fon TAs and TGa sites are varied in the vicinity of the best fit values f0(15% for TAs and 0% for TGa), leaving all other fit parameters free. The contour corresponds to χ2−χ2 0= 1. fit (χ2) as the fractions on TAs and TGa sites are varied in the vicinity of the best fit values (15% for TAs and 0% for TGa, with χ2 0), leaving all other fit parameters free. The contour corresponds to χ2−χ2 0= 1, giving standard deviations of 2% for the TAs fraction and of 0.5% for TGa. Note that the percentages are with respect to all the 56Mn, i.e. even if there is indeed TGa occupancy within the technique’s sensitivity, it is for all purposes negligible. Vanishing TGa occupancy (with comparable standard deviation) is found both before and after annealing, both in experiments A and B. It is important to note that the determined site-fractions correspond to the implanted radioactive 56Mn probes, which are not necessarily (and most likely are not) the same as those of the stable 55Mn atoms incorporated during MBE growth. The goal of these experiments was not to determine the absolute fraction of interstitial Mn in (Ga,Mn)As, but to evaluate the stability of the possibly occupied interstitial sites, which we will discuss in section 4.1.5. 32 CHAPTER 4. RESULTS AND DISCUSSION 4.1.3 Magnetic properties It is well known from literature that the interstitial Mn (Mni) is a double donor [100, 62], with self-compensating effects on (Ga,Mn)As: as a donor impurity it compensates holes created by acceptor impurities and by coupling antiferromagnetically (AFM) with substitutional Mn impurities, it compensates the overall magnetic moment [43, 45, 101], effectively reducing the magnetization and Curie temperature (TC) of the material. As seen in the previous section, by performing post-growth annealing at a temperature around 200◦C, the Mnifraction can be reduced. In experiment A we observe a decrease of the fitted 56Mn interstitial fraction by about a factor of two. In order to correlate this reduction with the magnetic properties we performed SQUID magnetometry measurements on the samples used for experiment A, i.e. on (Ga,Mn)As doped with 6% Mn as-grown and annealed at 200◦C in air. 4.1.3.1 Magnetic anisotropy In order to accurately estimate the interstitial fraction reduction, we first measured the saturation magnetization of the annealed sample along four magnetically non-equivalent directions: [100]/[010], [110], [110] and [001]. direction Msat [µB/Mn] [100]/[010]3.19 [110]3.03 [110]2.61 [001]0.13 Table 4.2: Saturation magnetization Msat measured with applied magnetic field along four non-equivalent directions at a temperature of 5 K in (Ga,Mn)As annealed at 200◦C in air. As shown in table 4.2, the axis in our annealed sample displayed the highest saturation magnetization is the [100]/[010] (in-plane) while the hard axis is out-of-plane [001]. Anisotropy is also found in-plane (cf. sec. 1.2.1): we observe higher saturation magnetization along the [100] direction than the [110] direction. In addition we observe that along two crystallographically equivalent axes we obtain different saturation magnetization values – we observe a higher value for the [110] direction than for the [110] direction. A possible explanation for this puzzling anisotropy between two crystallographically equivalent directions is given in ref. [102]. Figure 4.3 on the next page depicts the nearest neighbor Mn dimers residing along a GaAs 4.1. IDENTIFICATION OF THE INTERSTITIAL MN SITE 33 [110] [110] Ga As Mns Figure 4.3: Mn dimers on the (001) GaAs surface. If residing along the [110] direction, are not bridged by an As atom. Such bonding exists for [110] dimers, resulting in the formation energy. (001) surface along the [110] and [110] axes. In the [110] case the two Mn ions are bound to the same As atom, whereas for the dimer along the [110] axis they are connected to different As atoms, implying that these two directions are not equivalent at the surface. In contrast, for bulk dimers there is an As bridge for these two cases – one below, one above the dimer plane. Since the Mn-Mn interaction is brought about by p-d hybridization (cf. section 1.2.1) one can expect a higher binding energy for the [110] pair compared to the [110] case. Thus, when growing (Ga,Mn)As films, if barriers for Mn diffusion along the surface are sufficiently small, a nonvolatile asymmetry in the pair distribution will set in the whole film during the epitaxy, giving rise to the observed magnetic anisotropy [103]. 4.1.3.2 Saturation magnetization and TC Determined the easy axis, we now proceed with a detailed magnetic characterization of our as-grown and annealed samples. Magnetization measurements as a function of applied magnetic field at a temperature of 5K, and as a function of temperature, with an applied field of 1mT after a field cooling under a saturation field of 100 mT, were performed and are presented in figure 4.4 on the following page. The data presented in this figure has been normalized to the number of Mn atoms present in each of the samples (cf. section 4.1.3.3). In figure 4.4 (a) we observe a clear increase in the saturation magnetization from the asgrown to the annealed sample, which we will discuss next in terms of Mni. In addition, the shape of the hysteresis loop changes, with a dramatic decrease in remanence and coercive field in the annealed sample when compared to the as-grown sample which can be attributed to a changing magnetic anisotropy [54, 103, 104]. In figure 4.4 (b) we represent the measured magnetization as a function of temperature, with an applied field of 1 mT 40 CHAPTER 4. RESULTS AND DISCUSSION 4.2. STABILITY AND DIFFUSION OF MN 41 4.2 Stability and diffusion of Mn Following our work on the identification of the interstitial Mn site in ferromagnetic (Ga,Mn)As we now address the diffusion of both Mnsand Mniin the materials’ matrix in two different concentrations: a low concentration, with 1% Mn, and a high concentration, with 5% Mn. In order to perform such study we resort to the emission channeling (EC) technique (described in section 3.2 on page 16), determining the lattice location and thermal stability of implanted radioactive 56Mn probes at various annealing temperatures. 4.2.1 Experimental details In this section we present two experiments on the lattice location and thermal stability of 56Mn (half-life t1/2= 2.56 h) implanted into (Ga,Mn)As thin films with different Mn concentrations (1% and 5% Mn). The 5% Mn sample was the same as the one used in experiment B described in section 4.1 on page 27 (200 nm thick, grown on a 200 nm AlAs buffer layer, on a GaAs substrate) and the 1% Mn sample consisted of a (Ga,Mn)As film with a thickness of 1500 nm grown directly on a GaAs substrate. Both EC experiments were carried out with the same implantation parameters, i.e. implanting 56Mn to a fluence of 7×1012 cm−2with an energy of E= 30 keV and an angle of 17o (resulting in a peak concentration of xp= 2.4×1018 cm−3, a projected range of Rp= 21 nm and a straggling of σ= 11 nm, i.e. with all the 56Mn probes implanted within the films). As in our previously reported experiments (cf. section 4.1), a control experiment was devised in order to monitor the degree of disorder upon implantation of the radioactive probes and subsequent annealing, i.e. in order to inspect an eventual layer degradation upon annealing. Accordingly, we determined the lattice location and thermal stability of As using radioactive 73As (t1/2= 80 d) implanted into a 5% Mn (Ga,Mn)As sample. The 73As radioactive probes were implanted at a fluence of 5×1013 cm−2, with an energy of E= 50 keV and an angle of 10◦(resulting in a peak concentration of xp= 1.5×1019 cm−3, a projected range of Rp= 26 nm and a straggling of σ= 13 nm, i.e. with all the 73As probes within the film). The emission channeling measurements were carried out in the as-implanted state and in annealing steps of 50◦C (100◦C for the 73As experiment) starting at 100◦C. Each annealing step was performed in vacuum (<10−5mbar) for 10 min. Angular-dependent emission patterns were recorded along four crystallographic axes (<100>,<111>,<110>and <211>). 42 CHAPTER 4. RESULTS AND DISCUSSION 4.2.2 Lattice location and thermal stability 4.2.2.1 Lattice location As in our prior work on 56Mn lattice location in ferromagnetic (Ga,Mn)As (cf. section 4.1 on page 27), the SGa+TAs double occupancy patterns give by far the best fit to experimental data, showing that the probe atoms indeed occupy mainly the substitutional position with only a fraction in the TAs position. Other possibilities for the lattice location of the implanted 56Mn impurities amount to negligible fractions in our fit (<5% overall, <1% for TGa in particular). When investigating the lattice location of the 73As on 5% (Ga,Mn)As, we identified the substitutional SAs site as the best fit to the experimental data, with very small fractions (<5%) in other possible sites. From these lattice site considerations we fitted all the experimental patterns with calculated ones, determining the site fractions as a function of annealing temperatures. In figure 4.8 we compile the fitted fractions for 56Mn and 73As probes. The discontinuities reflect 56Mn re-implantation (discussed in the following). 4.2.2.2 Thermal stability Before proceeding to a detailed analysis of the EC experimental data it is important to note that dechanneling of the emitted β−electrons is enhanced when the radioactive probes diffuse deeper into the bulk of the material. On the other hand, when the radioactive probes diffuse all the way to the surface, channeling breaks down and the β−emission becomes isotropic. Both these phenomena contribute to an increase in the random fraction and a decrease in the fitted fraction. Formation of secondary phases will also lead to dechanneling of the emitted electrons, which also contributes to increasing the random fraction. In figure 4.8 on the facing page we can see that the fitted fractions of the radioactive 73As probes increase up to 300◦C. This increase in the substitutional fraction indicates a recovery of the (Ga,Mn)As structure after the damage caused by implantation. A slight increase in the fitted fractions of 56Mn for both concentrations probed in the same temperature range is also observed. Analogously to our prior experiments in section 4.1, this increase can therefore be attributed to the increased crystallinity after thermal annealing rather than interstitial-to-substitutional 4.2. STABILITY AND DIFFUSION OF MN 43 0 100 200 300 400 500 600 0 2 0 4 0 6 0 8 0 100 1 % M n SG a TA s 5 % M n S G a T A s SA s s i t e f r a c t i o n [ % ] annealing tem perature [oC ] Figure 4.8: Fitted fractions of implanted 56Mn and 73As probes on (Ga,Mn)As samples doped with different concentrations of Mn. The squares represent the fitted substitutional fractions and the circles represent the fitted interstitial TAs fractions on the 56Mn-implanted samples. The triplets represent the fitted substitutional fractions for the 73As-implanted sample. Filled symbols represent the same fitted fractions as above after re-implantation of Mn. conversion. This analysis puts us in a framework in which studying the stability of 56Mn probes in (Ga,Mn)As becomes independent of the structure of the GaAs lattice, which remains unchanged when annealed to temperatures up to 600◦C. In other words, the observed phenomena detailed in the following are intrinsic of the Mn impurities in (Ga,Mn)As. Turning our attention to the other two curves in figure 4.8, we observe that the fitted fractions of implanted 56Mn probes decrease significantly after certain annealing temperature is reached. For the lower concentration, the 56Mn probes occupying substitutional lattice sites start diffusing at a higher temperature (around 400-450◦C in 1% Mn) than for the higher concentration (around 200-250◦C in 5% Mn). The same behavior is observed for the probes occupying the interstitial position. For the 1% Mn case the diffusion temperature is around 300-350◦C and for the 5% Mn case around 200-250◦C. This diffusion behavior will be discussed in more detail in section 4.2.3. 4.2.2.3 Secondary-phases and re-implantation The dramatic decrease in the fitted fractions of the substitutional Mn impurities we observe in figure 4.8 indicates an increase in the random fraction. According to literature, 44 CHAPTER 4. RESULTS AND DISCUSSION (Ga,Mn)As forms nanoscale clusters when annealed at high temperatures [76, 77, 78, 81], and therefore we can then assume that this increase in the random fraction is due to the diffusion of substitutional Mn, eventually leading to the formation of secondary phases. This interpretation is consistent with ref. [11], where an optimal annealing temperature was identified (∼200◦C), above which TCdecreases4. This was attributed diffusion and aggregation of Mns. In section 4.3 on page 55 we address this question in depth. The formation of secondary phases is further supported by the Emission Channeling data at high annealing temperatures, after re-implanting radioactive 56Mn probes in a regime in which the substitutional impurities have already precipitated into secondary phases. When implanting new probes, these will experience a lower effective concentration of Mn (locally). In other words, the local concentration of Mn impurities will be smaller which translates into less efficient segregation of the newly implanted probes, eventually leading to a higher substitutional fraction and a higher thermal stability (higher segregation temperature). This effect is observed in figure 4.8 on the preceding page by discontinuities in the fitted fraction above 450-500◦C, temperatures at which we re-implanted 56Mn. 4.2.3 Diffusion of Mn impurities As seen in section 1.2.2.1, previous emission channeling work [64, 65] addressed the diffusion of Mn in the ultra-dilute regime (<0.05%) in GaAs. In this regime, interstitial Mn (in TAs sites) was found to be a free isolated interstitial, i.e. with no substitutional Mn (Mns) in the first neighbor shell, becoming mobile above 400◦C with an estimated activation energy of Ea= 1.7−2.3eV. In the same studies, the substitutional Mn was found to diffuse at annealing temperatures around 700◦C with an activation energy of Ea= 3 eV. According to our EC experiments described previously, the diffusion of Mn in GaAs doped with several % Mn is strikingly different than for the previously studied case [65]. For increasing Mn concentration in (Ga,Mn)As we observe that both interstitial and substitutional impurities start to diffuse at lower temperatures, with a noteworthy difference between the two regimes under study. We can therefore extrapolate that the mechanism that drives the Mn impurities diffusion is strongly dependent on impurity concentration. In order to study the diffusion mechanisms in our samples, we estimated values for Eafor the interstitial and substitutional Mn cases, following a model similar to the one used for the ultra-dilute case [64, 65]. 4The temperature for which the maximum TCis achieved without secondary phase formation 4.2. STABILITY AND DIFFUSION OF MN 45 4.2.3.1 Interstitial diffusion Arrhenius model for thermally activated migration through interstitial positions Within an Arrhenius model for the thermally activated migration, the change in fraction f(T, t)of Mn on the TAs interstitial sites after an annealing step of duration ∆tat a temperature Tcan be described by: df(T, t) dt =−Nt N(4.3) where Nt=ν∆t, with νthe jump frequency and ∆tthe annealing time, and Nthe average number of jumps a Mniatom must perform until it gets immobilized, i.e. until it does not contribute to the site fraction anymore, by diffusing too close to the surface, into the bulk of the material or by being trapped by a low crystallinity region, where dechanneling takes place. In order to jump from one interstitial site to a neighboring interstitial site, an atom must overcome the potential energy barrier (or migration energy) Ea, as discussed in ref. [71]5. At finite temperatures, the atom will have sufficient thermal energy to overcome a barrier Ea during a fraction of the time exp(Ea/kBT). The jump frequency is then given by: ν=ν0exp −Ea kBT(4.4) where ν0is the attempt frequency, taken as 1012 s−1, i.e. of the order of the lattice vibrations, kBis the Boltzmann constant and Tis the annealing temperature. Applying (4.4) to (4.3) and integrating over the annealing time ∆t, we obtain: f(T, ∆t) = f0exp[−ν0∆t/N exp(−Ea/kBT)] (4.5) where f0is the site (TAs) fraction before the annealing step. By taking f=f0/2,Eacan be estimated through the following expression: Ea=−1 kBTln Nln 2 ν0∆t(4.6) Since no exact value for Twhen freduces to f0/2is directly extractable from our EC data, a lower and upper bound for this value can be taken, leading to an interval for the activation energy Ea. In eq. (4.5) there are two unknown parameters, Nand Ea. These parameters cannot be determined independently and therefore Nhas to be fixed in order to estimate 5For an isolated interstitial the limiting factor to its diffusion is a jump between two interstitial positions. 46 CHAPTER 4. RESULTS AND DISCUSSION Ea.Nis estimated by taking into consideration various diffusion scenarios for interstitial and substitutional impurities. Diffusion mechanisms of Mn interstitials in (Ga,Mn)As When a lattice contains at least two types of atoms A and B randomly distributed over the lattice sites, a type A atom will be in a cluster of one, two, three or more A atoms [106]. When growing (Ga,Mn)As samples in the dilute regime, with several % of Mn, the Mn impurities occupy mainly substitutional positions while a small fraction occupies interstitial positions [17]. With increasing Mn concentration, the probability for Mns–Mni (pairs) and Mns–Mni–Mns(triplets) [44, 71] complexes to be formed increases, leading to different diffusion mechanisms for interstitial Mn. In a concentration regime where both these complexes are present and where sufficient thermal energy has been provided, the interstitial Mn is likely to travel freely through interstitial sites, only becoming trapped when captured by these complexes. This will lead to a hopping behavior of the diffusing Mn between complexes which in turn leads to different activation energies for each trapping mechanism, affecting the effectiveness of the thermal annealing. The number of jumps N will then depend on the diffusion mechanism. In the very low concentration regime [65], the interstitial Mn is predominantly a free interstitial, and the number of jumps Nis given by the number of interstitial sites the impurity goes through until it is immobilized (cf. fig. 4.9a). At a few % Mn, the scenario changes completely as a significant fraction of the interstitial impurities will be in a pair or in a triangle [106] and the impurity will "hop" between these complexes, as demonstrated in figure 4.9b and 4.9c. When considering an interstitial diffusion in which the impurity hops between pairs, the number of jumps Nis given by the number of complexes the impurity goes through until it becomes immobilized. We do not consider the jumps between interstitial sites because in this scenario the energy required to dissociate a pair is much higher than for free interstitial diffusion, i.e. the intermediate jumps between isolated interstitial sites can be neglected. The same reasoning is applied to triplet complexes, as they are expected to have a higher dissociation energy than a pair [71]. 4.2. STABILITY AND DIFFUSION OF MN 47 Free Pairs Triplets a) b) c) Interstitial diffusion Figure 4.9: The different diffusion mechanisms for an interstitial impurity. In blue are the host lattice atoms and in red the impurity atoms. The number of jumps Nis given by the number of a) interstitial sites the impurity runs through until immobilized; the number of "hops" between b) pairs and c) triplets until immobilized. 48 CHAPTER 4. RESULTS AND DISCUSSION Number of jumps for interstitial diffusion Based on these diffusion mechanisms, the number of jumps Ncan now be estimated as follows. From ref. [106] we can obtain an estimate of the fraction of impurities in pairs (xpairs) and in triplets (xtriplets), using the following expressions: xpairs = (1 −x)12 (4.7) xtriplets = 12x(1 −x)18 (4.8) where xis the impurities concentration. Knowing these fractions one can determine the distance between these complexes using: di=3 r1 cMnxi (4.9) where cMn is the concentration of Mn, and i= (pairs,triplets). For a 3–dimensional random walk, the root mean square (rms) distance from the origin after Njumps is given by σ3,i =r21/2=√Ndi(4.10) Within the "thin-film" approximation, the impurity distribution is uniform along two of the three directions, and therefore only the jumps in the last direction will contribute to a net diffusivity, i.e. one third of the jumps N/3. Expression (4.10) then reduces to: σ1,i =rN 3di(4.11) When performing the EC experiment the impurities are implanted at a projected range Rp. Long-range diffusion of the impurities has a strong effect on the fitted fractions, due to exponential dependence of β−dechanneling on the emitter (56Mn) depth. As stated in section 4.2.2.2, the random fraction increases when the probes diffuse closer to the surface or into the bulk. Accordingly, for our impurity probes we will take σ1,i equal to the projected range Rp. We can now estimate the number of jumps Nfor each diffusion mechanisms: N≈3Rp di2 (4.12) 4.2. STABILITY AND DIFFUSION OF MN 49 Activation energies When considering the diffusion mechanisms stated above, the activation energy is given by the sum of a binding energy Eband a migration energy Em. The binding energy Ebis the energy necessary to break the bond between the interstitial Mn and the substitutional Mn in pairs or triplets. The migration energy Emis the energy barrier between interstitial sites (TAs →TGa →TAs). In the very low concentration regime, there is only isolated Mni(Eb= 0) and the interstitial does not share any bond with a substitutional impurity. In this case Ea=Em[65]. At higher concentrations, the increased amount of Mn impurities and the Coulomb attraction between the Mniand Mnsfavors the formation of complexes. In this case the needed activation energy diffuse the interstitial Mn is given by the binding energy Eband the mobility energy Em. Ea=Em+Eb(4.13) Through EC experiments it is not possible to determine Eband Emindependently, but it is possible to estimate Eaand infer how the energies vary with different systems. The estimation of activation energies Eais, however, not so trivial as depicted above, as other effects can take part in the energy barriers considered. Precipitation into secondary phases will have an effect on the number of jumps the interstitial impurities will perform as well as alter the local impurity concentration. Since an estimate for the number of jumps until an impurity is immobilized by a secondary phase is not possible, we consider the limit case N= 1 in our assessment for the activation energies. Activation Energies Ea(eV) % Mn TD(oC)Npairs Ntriplets Nlimit 1 350 −450 1.5−1.7 1.6−1.8 1.9−2.1 5 250 −350 1.3−1.5 1.3−1.5 1.6−1.8 Table 4.4: Estimated activation energies for interstitial Mn diffusion In table 4.4 we compile the estimated values for the activation energy for the interstitial Mn – considering the difference scenarios. We observe that for the 1% Mn sample the activation energies range from 1.5eV to 2.1eV while for the sample with 5% Mn the activation energies are 1.3−1.8eV. For the isolated interstitial in the ultra-low concentration regime [65], the activation energies are 1.7−2.3eV. The different diffusion scenarios that may play a role in (Ga,Mn)As have strong implications 56 CHAPTER 4. RESULTS AND DISCUSSION It is critical to note however, that the diffusion considerations taken in section 4.2 on page 41 were based on the restrictions that come with using radioactive 56Mn in an EC experiment, i.e. the annealing step and subsequent measurements had to be short due to the relatively short lifetime (t1/2= 2.56 h) and in vacuum. Consequently, different annealing times have different impacts on the diffusion of Mn in (Ga,Mn)As, as seen from equation (4.5) on page 45 (cf. section 4.2.3.1). Annealing for a longer period of time will shift to lower temperatures the observed diffusion, while annealing in different atmospheres will only affect the passivation efficiency at the surface. As a result, we studied a set of four samples of each of the concentrations considered in our EC experiment. For each concentration we kept one as-grown sample and subjected three others to thermal annealing at 200◦C and 300◦C for 100 hours in air, and at 600◦C for 10 minutes in vacuum. 4.3.2 Structural characterization Based on our previous EC study of Mn impurity diffusion on (Ga,Mn)As, we expect the structural properties of our samples to vary upon thermal annealing at different temperatures [39, 84, 111]. To investigate these structural changes in (Ga,Mn)As we performed SR-XRD and EXAFS experiments on each of the samples described in sec. 4.3.1. The experimental details of these measurements are portrayed in chapter 3 on page 15. 4.3.2.1 Synchrotron radiation X-ray diffraction (SR-XRD) Various measurements were performed on each of the samples: High-resolution symmetric θ-2θscans between 15◦and 80◦demonstrating the substrate and film peaks with barely no distinction6and θ-2θscans in the vicinity of the (002) peak of GaAs to investigate the film relaxation upon annealing; Grazing Incidence asymmetrical scans to investigate secondary-phase formation upon annealing. Figure 4.11 on the facing page shows the reciprocal space maps near the (002) reflection of GaAs, in 5% Mn (Ga,Mn)As as-grown and annealed at various temperatures. From this 6Only the relevant part of these measurements is shown 4.3. CORRELATING LOCAL STRUCTURE AND MAGNETISM 57 3 7 . 8 3 8 . 0 3 8 . 2 3 8 . 4 - 0 . 0 3 0 . 0 0 0 . 0 3 qω2 θ [102 Å - 1 ] x * - 0 . 0 3 0 . 0 0 0 . 0 3 3 7 . 8 3 8 . 0 3 8 . 2 3 8 . 4 x * 1.0x102 1.4x103 1.9x104 2.6x105 3.6x106 5.0x107 - 0 . 0 3 0 . 0 0 0 . 0 3 3 7 . 8 3 8 . 0 3 8 . 2 3 8 . 4 x * qω2 θ [102 Å - 1 ] qω [102 Å - 1 ] c - 0 . 0 3 0 . 0 0 0 . 0 3 3 7 . 8 3 8 . 0 3 8 . 2 3 8 . 4 - s - - x - - * - s x * qω [102 Å - 1 ] s e c o n d a r y phases s u b s t r a t e l a y e r ab cd Figure 4.11: Reciprocal space maps near the (002) reflections in the 5% Mn samples: a) as-grown, b) annealed at 200 ◦C, c) annealed at 300 ◦C, and d) annealed at 600 ◦C. The symbols X, * and S represent respectively the substrate, layer and secondary phases peaks. reciprocal map we can obtain the high resolution θ-2θscans, shown in figure 4.12 on the next page, for both concentrations – 1% Mn (left) and 5% Mn (right). In this figure, the peaks S, L and SP denote respectively the substrate peak, the (Ga,Mn)As peak and the secondary phases peak. This data will be detailed in sections 4.3.3.1 and 4.3.4.1. Figure 4.13 on page 59 shows the GIXRD measurements with all the identified secondary phases for the samples annealed at 600oC: MnAs in two distinct phases (zincblende and hexagonal) and orthorhombic As. These secondary phases will be discussed in more detail in section 4.3.4.1. 58 CHAPTER 4. RESULTS AND DISCUSSION 2 . 8 0 2 . 8 1 2 . 8 2 2 . 8 3 2 . 8 4 i n t e n s i t y [ a . u . ] d - s p a c in g [ Å ] LS 1 % M n a s - g r o w n 200oC 300oC 600oC 2 . 8 0 2 . 8 1 2 . 8 2 2 . 8 3 2 . 8 4 2 . 8 5 S P LI i n t e n s i t y [ a . u . ] d - s p a c in g [ Å ] S 5 % M n Figure 4.12: SR-HRXRD measurements around the <002>peak of GaAs on (Ga,Mn)As samples with 1% Mn and 5% Mn as-grown and annealed at 200oC,300◦C and 600oC. S, L, I and SP represent respectively the substrate and the film peaks, the interstitial and the secondary phases peaks. 4.3.2.2 Extended X-ray absorption fine structure (EXAFS) The EXAFS experiment was carried out at BM26, ESRF, and consisted on the roomtemperature study of the X-ray absorption near the K-edge of the Mn impurities. Figure 4.14 on page 60 shows the Fourier transform of the isolated fine structure as a function of nonphase corrected radial distance for Mn atoms in a (Ga,Mn)As matrix. Figure 4.15 on page 61 summarizes the outcome of a 1st shell analysis, allowing us to determine the Mn-As NN distance as well as the EXAFS Debye-Waller (DW) factor σ2, which in turn gives us insight into the local structure of Mn impurities in (Ga,Mn)As, in particular, on the local disorder in these systems. 4.3. CORRELATING LOCAL STRUCTURE AND MAGNETISM 59 Figure 4.13: SR-GIXRD measurements (Ga,Mn)As samples with 1% Mn and 5% Mn as-grown and annealed at 200oC,300◦C and 600oC. The emergence of secondaryphases peaks is evident for the samples annealed at 600◦C in the selected scan range and is represented by triangles for NiAs-type MnAs nanoclusters and by squares for zincblende MnAs nanoclusters. A peak corresponding to an orthorhombic As phase is also present and represented with a circle. Only the region of interest is displayed with no more peaks corresponding to secondary phases present in the remaining spectrum. 4.3.2.3 Remarks The results presented in this section (4.3.2) set the ground work for a complete magnetostructural analysis of (Ga,Mn)As with 1% Mn and 5% Mn annealed at various temperatures. As is observable from these results, the structural changes in (Ga,Mn)As in the FM regime are small, since the removal of the interstitial has little effect on the overall structure. Stronger structural modification is observed for the samples annealed at 300◦C and 600◦C. An increase in NN distance as well as in the EXAFS DW factor σ2in the EXAFS analysis (cf. fig. 4.15) indicate the formation of disordered Mn-rich regions at 300◦C and well defined crystallized secondary phases at 600◦C. In the SR-XRD measurements we observe a disappearance of the (Ga,Mn)As peak in the 1% Mn samples at 300◦C and 600◦C, and 60 CHAPTER 4. RESULTS AND DISCUSSION 12345 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 12345 0 . 0 0 . 5 1 . 0 1 . 5 1s t s h e l l a s - g r o w n 200°C 300°C 600°C |χ(R) | [ Å - 3 ] neighbor distance R [ Å ] 1 % M n 5 % M n neighbor distance R [ Å ] Figure 4.14: Spectra of the Fourier transform of the isolated fine structure as a function of non-phase corrected radial distance for Mn atoms in a (Ga,Mn)As matrix for different Mn concentrations. an emergence of a secondary phase peak in the 5% Mn samples at 600◦C (cf. fig. 4.12). These structural changes will be discussed in more detail in the following sections 4.3.3.1 for the ferromagnetic regime and 4.3.4.1 the for the secondary phase regime followed by their implications on the magnetic behavior. 4.3.3 Ferromagnetic regime In section 4.2 we saw that the diffusion of Mnioccurs at lower temperatures than Mns. Annealed below the diffusion temperature of Mns, (Ga,Mn)As should still be ferromagnetic, with small structural changes from the as-grown state. From a magnetic point of view, the interactions that allow the existence of ferromagnetism in each concentration in this regime are different: in the low concentration (x < 1.5%) the holes that mediate the magnetic interactions between Mnsmoments lie in an impurity band [42, 50] while in the higher concentration regime (x > 1.5%) this impurity band is merged with the valence band [50, 112], leading to a ferromagnetic p−dZener exchange interaction. This is however a controversial point in the DMS field, specifically for (Ga,Mn)As [50]. However, in both these regimes the Mn interstitial can be present and couple antiferromagnetically with the substitutional impurities. Within the FM regime we intend to study the Mn 4.3. CORRELATING LOCAL STRUCTURE AND MAGNETISM 61 0 200 400 600 2 . 4 6 2 . 4 8 2 . 5 0 2 . 5 2 2 . 5 4 2 . 5 6 0 200 400 600 0.004 0.006 0.008 0.010 0.012 0.014 b M n - A s N N d i s t a n c e [ Å ] annealing tem perature [°C ] 1 % M n 5 % M n a E X A F S D W f a c t o r σ2 [Å 2] annealing tem perature [°C ] Figure 4.15: a) The best fit distance to the first nearest neighbors of Mn impurities in (Ga,Mn)As as a function of annealing temperature; b) the fitted EXAFS Debye-Waller factors for the first single scattering path of Mn absorbers in a (Ga,Mn)As crystal matrix as a function of annealing temperature. interstitial removal by annealing close to growth temperature (200 oC) in both concentrations and analyzing the material’s structure and magnetism. Therefore, in this section we will distinguish samples by as-grown and annealed, where annealed refers to the samples annealed at 200◦C in air for 100 hours. 4.3.3.1 Structure Within the FM regime we already noted that the structural changes are minimal. However it is worthy to evaluate these changes in order to draw a valid magneto-structural picture of (Ga,Mn)As. From our SR-XRD experiments we observe that the measurements of the as-grown and of the annealed samples held similar results. The GIXRD measurements (figure 4.13 on page 59) showed no secondary phase formation, with no additional peaks present in the full scans, which was expected as in this temperature regime Mnsis not mobile. In figure 4.12 on page 58, however, small changes are observable at 5% Mn. In this concentration we observe that the layer peak (L) becomes sharper upon annealing with better defined interference fringes7. Also, the region where the apparent peak I resides disappears within the fringes. These differences in the experimental curves between the samples seem to indicate a small change in the structure of 5% (Ga,Mn)As when annealed 7These fringes are a result of the interference between the diffracted X-rays from the buffer layer with the diffracted X-rays from the (Ga,Mn)As layer. 62 CHAPTER 4. RESULTS AND DISCUSSION close to the growth temperature. As seen in section 1.2, interstitial Mn does not form when growing (Ga,Mn)As for concentrations below 2% Mn. Therefore, no change is expected in the material when annealed at 200 oC. This is also visible in our HRXRD data, in figure 4.12 on page 58 where the as-grown and annealed scans display the same peaks with similar intensities. 4.3.3.2 Magnetism By performing SQUID magnetometry measurements we are able to analyze the magnetic properties of our samples, most importantly the Curie temperature TC, saturation magnetization, remanence and coercivity. In order to determine these properties, we measured for each sample the magnetization as a function of applied magnetic field at 5K and at 300 K, the magnetization as a function of temperature at an applied field of 10 Oe after cooling under a saturating field (remanence curves), and magnetization as a function of temperature at an applied field of 100 Oe after a zero-field cooling and a 100 Oe field-cooling at the same magnetic field. All measurements were performed along the same direction as the applied magnetic fields, the [100]/[010]. For each concentration we obtained different results and accordingly we will divide the analysis in low concentration (1% Mn) and high concentration (5% Mn). Low concentration In figure 4.16 we can observe the M-H and M-T curves measured for 1% Mn in the FM regime. The as-grown sample as well as the annealed sample display ferromagnetic behavior with a saturation magnetization of 3.5µB, very close to the magnetization of uncompensated substitutional Mn, 4µB(cf. [49]). Both the ZFC-FC curves and the remanence present a peak in magnetization at around 17 K. This may be due to a changing magnetic anisotropy, which has been shown to be temperature dependent [102, 103]. No significant change is visible in the magnetic properties of 1% (Ga,Mn)As when comparing the as-grown with the annealed sample: the saturation magnetization remains the same (Msat = 3.5µB) as well as the Curie temperature (TC= 20 K) at which the paramagnetic transition occurs. This further supports our emission channeling conclusion (cf. section 4.2.4) that interstitial Mn impurities do not form upon growth for this concentration 4.3. CORRELATING LOCAL STRUCTURE AND MAGNETISM 63 -2000-1000 0 1000 2000 - 4 - 3 - 2 - 1 0 1 2 3 4br e m a n e n c e Z F C - F C ( 1 0 0 O e ) m a g n e t i z a t i o n [ µB/ M n ] m a g n e t i c f i e l d [ m T ] a s - g r o w n annealed T = 5 K a 0 - 3 - 2 - 10123 0 1 0 2 0 3 0 4 0 5 0 0 1 2 m a g n e t i z a t i o n [ µB/ M n ] t e m p e r a t u r e [ K ] 0 1 0 2 0 3 0 4 0 0 . 0 0 . 5 1 . 0 1 . 5 Figure 4.16: (a) Magnetization as a function of applied magnetic field; (b) ZFC-FC curves and remanence (inset) as a function of temperature for as-grown and 200◦C air annealed 1% (Ga,Mn)As. regime8, and therefore no Mniimpurities are there to be removed when annealing. High concentration Figure 4.17 displays the results of SQUID magnetometry on the 5% Mn samples in FM regime. We observe a considerable increase in saturation magnetization from 2.4µBto 3.6µBfrom the as-grown to the annealed sample, accompanied by an enhancement of TC from 50 K to 100 K (cf. figure 4.17b). This is due to the removal of Mnifrom the complexes considered in section 4.2.3.1), leaving more substitutional Mn impurities isolated, which in turn contribute to the net magnetization of the material. The coercive field as well as the shape of the hysteresis loops change significantly, indicating the changing magnetic anisotropy upon annealing. As we can see in the metallic regime, post-growth annealing close to growth temperature can effectively promote the out diffusion and passivation of Mnicontributing to an activation of the substitutional Mn and enhancing the magnetization and Curie Temperature. 8as it is not mobile at temperatures around 200◦C 64 CHAPTER 4. RESULTS AND DISCUSSION - 4 0 - 2 0 0 2 0 4 0 - 4 - 3 - 2 - 1 0 1 2 3 4br e m a n e n c e Z F C - F C ( 1 0 0 O e ) m a g n e t i z a t i o n [ µB/ M n ] m a g n e t i c f i e l d [ m T ] annealed a s - g r o w n T = 5 K a 0 50 100 150 200 0 1 2 3 4 m a g n e t i z a t i o n [ µB/ M n ] t e m p e r a t u r e [ K ] 0 5 0 1 0 0 0 1 2 3 Figure 4.17: (a) Magnetization as a function of applied magnetic field; (b) ZFC-FC curves and remanence (inset) as a function of temperature for as-grown and 200◦C air annealed 5% (Ga,Mn)As. 4.3.3.3 Concentration dependence In section 4.2.2 we saw that by annealing at a temperature around 200◦C the substitutional Mn impurities are not completely mobile for both concentrations under inspection, i.e. while in the 1% Mn samples the Mnsis not mobile at 200◦C, in the 5% Mn samples some residual precipitation may have already occurred. We also note that, as seen in section 1.2.2, annealing at this temperature will promote the diffusion of the interstitial Mn, passivating it at the surface and thereby we expect to see an increase in the net magnetization of our samples as well as their Curie Temperatures. In figure 4.18 we compare the obtained magnetization curves for both concentrations for as-grown samples as well as for annealed samples within the FM regime. We observe that the 1% FM samples have a comparable net magnetization to the 200◦C annealed 5% Mn sample. As seen in sec. 4.2.4 and according to literature [17, 44], for Mn impurity concentration below 2% Mn the interstitial impurity does not form. With no self-compensation by the Mniimpurities in the 1% Mn samples, the total magnetic moment per Mn impurity shall be close to the theoretically predicted value of 4µB[105]. However, in a low concentration regime, where the sample is insulating, the amount of holes to mediate the ferromagnetism is smaller than at higher concentrations, therefore limiting the net magnetization of the sample. Also, the lower concentration of Mnsdefects results in a lower TC, as seen in figure 4.18. 4.3. CORRELATING LOCAL STRUCTURE AND MAGNETISM 65 -800 -400 0 400 800 - 4 - 3 - 2 - 1 0 1 2 3 4 1 % M n a s - g r o w n annealed 5 % M n a s - g r o w n annealed r e m a n e n c e Z F C - F C ( 1 0 0 O e ) m a g n e t i z a t i o n [ µB/ M n ] m a g n e t i c f i e l d [ m T ] T = 5 K a - 4 0 - 2 0 0 2 0 4 0 - 4 - 2 0 2 4 0 40 80 120 160 200 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 b m a g n e t i z a t i o n [ µB/ M n ] t e m p e r a t u r e [ K ] 0 7 0 1 4 0 0 . 0 0 . 8 1 . 6 2 . 4 3 . 2 Figure 4.18: Magnetization curves for 1% and 5% (Ga,Mn)As samples as-grown and annealed respectively at 200◦C. Another noteworthy observation is the anisotropy of the system in the two different concentration regimes: along [100]/[010] the magnetic hysteresis is disparate for the 1% Mn samples from the 5% Mn samples. The different magnetic anisotropy properties of the samples in both concentrations are mostly due to the different magnetic ordering mechanisms as described in section 4.3.3. 4.3.4 Secondary-phase regime 4.3.4.1 Structure While for higher temperature annealing temperatures (500◦-600◦C) it is generally accepted that Mn precipitates into a secondary phase [76, 82], the low temperature regime (between 200◦C and 400◦C) is still poorly understood. For the samples annealed at 300◦C, the GIXRD measurements did not reveal additional peaks, and the HRXRD measurements show the disappearance of the film peak L in the 1% Mn sample when compared to the samples within the FM regime9. This is indicative of a relaxation of the film to the GaAs lattice constant. Indeed, in figure 4.15 on page 61 we observe a slight increase in Mn-As NN distance, with a significant increase on the DW factor σ2, which together indicate that the Mn impurities are forming disordered Mn-rich 9This measurement shows a higher background noise than all the others due to experimental difficulties during alignment 72 CHAPTER 5. CONCLUSION (ii) substitutional Mn impurities become mobile at lower temperatures than those previously reported. Finding (i) sheds new light on the formation mechanism of interstitial Mn during LT-MBE growth. It shows that interstitial Mn only forms for Mn concentrations at which it is mobile during growth. As such, this finding constitutes strong experimental evidence for a previously proposed (but never demonstrated) mechanism in which interstitial Mn is not incorporated simultaneously with substitutional Mn but by diffusion of Mn atoms from the sample surface into the bulk of the film (which can only occur if the interstitial is mobile in the film bulk at the growth temperature). Finding (ii) uncovers an unexpectedly low temperature regime in which the Mn impurities become mobile at high impurity concentrations, i.e. annealing at temperatures as low as 200-250◦C induces Mn diffusion and segregation. In (3) we conducted a comprehensive study of the interplay between local structure and magnetism in the different annealing regimes considered in (2). Annealing at ∼200◦C resulted in the reduction of interstitial Mn fraction only for the high Mn concentration, leading to an increase in TCand magnetization, while for the low concentration no improvement in ferromagnetic behavior is observed, further supporting the scenario in which the interstitial Mn does not form during LT-MBE growth for Mn concentrations below 2%. Complementing result (ii) in (2), annealing at ∼300◦C induced precipitation of Mn into disordered Mnrich regions for both concentration regimes, effectively annihilating the ferromagnetism. Additionally, annealing at a temperature of 600◦C led to the formation of a well defined secondary-phases, consisting of superparamagnetic MnAs nanoclusters of mainly twotypes: zincblende, coherent to the GaAs matrix, and hexagonal NiAs-type, strained and not coherent with host matrix. This comprehensive study revealed itself as a powerful complement to the emission channeling technique in order to explore and investigate the structural and magnetic properties of (Ga,Mn)As. This toolset of characterization techniques presents itself as a dynamic and thorough investigation method for studying dilute magnetic systems, such as the case of dilute magnetic semiconductors and oxides. Outlook The main implications of the results presented in this thesis concern the influence of the local structure on ferromagnetic (Ga,Mn)As. For low impurity concentrations the impurities are essentially substitutional, with high thermal stability allowing for a full activation of the magnetic moments. Increasing concentration lowers the mobility threshold, increasing diffusion, leading to the formation of interstitials upon growth, which compensate substitutional 73 Mn both magnetically and electrically. Passivating the interstitial Mn by annealing at low temperatures increases the magnetization and Curie temperature. However, with increasing concentration, the temperature gap interstitial removal and Mn segregation narrows down significantly, requiring a careful design of the activation annealing procedure (temperature and duration). This increased understanding of the complex interplay between local structure and ferromagnetism in (Ga,Mn)As has the potential to inspire new strategies to increase the substitutional Mn concentration and consequently the Curie temperature of this model DMS system. Such strategies may include development of improved sample preparation methods and/or post-growth treatment for more efficient incorporation of Mn in substitutional sites as well as minimization of interstitial Mn. Also, the intricate physics uncovered on this specific system motivates a wider investigation of the III-Mn-V DMS family, where one can evaluate e.g. the effect of the III-V band-gap, the position of the Mn acceptor level and the degree of hole localization. Unraveling the interplaying mechanisms between the structural and magnetic properties of these DMS materials constitutes an important step in the understanding of the fundamental physics that lie behind them and the technological applications that lie beyond. “It might be, therefore, expected that studies of magnetically doped semiconductors (...) will continue to bring unanticipated and inspiring discoveries in the years to come.” Tomasz Dietl and Hideo Ohno, 2014 [39] 74 CHAPTER 5. CONCLUSION Publications Articles submitted or to be submitted to international, peer-reviewed journals • “Unambiguous identification of the interstitial Mn site in ferromagnetic (Ga,Mn)As” L.M.C. Pereira, T. Lima, U. Wahl, V. Augustyns, J.G. Correia, K.W. Edmonds, B.L. Gallagher, R.P. Campion, J.P. Araújo, K. Temst, A. Vantomme Submitted to Applied Physics Letters • “Concentration-dependent thermal stability of Mn impurities in (Ga,Mn)As” T. Lima,U. Wahl, V. Augustyns, J.G. Correia, K.W. Edmonds, B.L. Gallagher, R.P. Campion, J.P. Araújo, K. Temst, A. Vantomme, L.M.C. Pereira To be submitted to Physical Review B • “Concentration and temperature dependent Mn segregation in (Ga,Mn)As” T. Lima, V. Augustyns, K.W. Edmonds, B.L. Gallagher, R.P. Campion, D. Banerjee, C. Baehtz, M.J. Van Bael, J.P. Araújo, K. Temst, A. Vantomme, L.M.C. Pereira To be submitted to Journal of Applied Physics Communications in international, peer-reviewed conferences • “Lattice location and thermal stability of Mn in ferromagnetic (Ga,Mn)As” L.M.C. Pereira, T. Lima, U. Wahl, V. Augustyns, J.G. Correia, K.W. Edmonds, B.L. Gallagher, R.P. Campion, K. Temst, A. 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