High-energy Electron Diffraction Intensity Oscillations Research Articles

A C++ code for simulations of RHEED intensity oscillations within the kinematical approximation

This paper proposes a new software implementation for the rapid development and deployment of computer simulations of reflection high-energy electron diffraction (RHEED) intensity oscillations during the growth of thin epitaxial films. The calculations are based on the kinematical approximation. In this model the RHEED intensity oscillations from growing layers is considered as an effect of changes of surface roughness. New version program summaryProgram Title: growth22CPC Library link to program files:https://doi.org/10.17632/zkpwhrrfng.1Licensing provisions: GNU General Public License 3Programming language: C++Journal reference of previous version: Computer Physics Communications 170 (2005) 265–286Does the new version supersede the previous version?: YesReasons for the new version:The previous version of the program was written in Object Pascal [1]. This programming language is no longer popular in the scientific community. Responding to user's feedback, the current distribution of the software has been implemented in C++. This version implements improvements for ergonomics, computational performances and code readability. In addition, the output generated by the growth22 (saved in the coverageProfiles.dat file) can be used directly by program [2].Summary of revisions:The growth22 is written in standard C++, therefore one can use the GNU g++ compiler or any ANSI C++ compliant compiler to build the executable program. The code is distributed in the form of one growth22.cpp source file. A Table 1 lists the retired Object Pascal procedures and shows replacements by C++ functions. The present version of the program enables the user to easily manage the input data. Input data are loaded from a manually prepared inputData.dat text file where the user provides information on the parameters of the simulation, i.e. the growth model, the number of growing layers, the upper limit of growth time interval, the values of the phenomenological parameters that measure the net rate of transfer from one layer to the next, and the values of the growth rate for each layer. The user can edit this file as per the requirement of the problem domain. Details of the parameters in the sample inputData.dat file are described in the readme.pdf file provided with the software.The nature of problem:Generally, in order to explain the experimental data two theories—kinematical and dynamical—associated with high-energy electron diffraction in epitaxial layers are used. The dynamical theories take into account multiple scattering within the crystal and are used whenever diffraction from a perfect epitaxial layers is considered [3]. On the other hand, the kinematical theory treats the scattering from each plane in the crystal sample as being independent of others [1,4].In the kinematical theory of RHEED it is assumed that electron wave scatters from atom in the surface layer only once and then interferes with waves scattered on other atoms. This model can be used to describe diffraction effects for small angles of incidence, when the electron beam does not penetrate the deeper layers of the crystal. In the kinematical model the intensity oscillations of specularly reflected electron beam from growing layer is considered as an effect of changes of surface roughness.In this paper we present a time-efficient computer model for kinematical calculations of RHEED intensity oscillations during the growth of thin epitaxial films.The method of solution:According to kinematical approximation the diffracted-beam intensity is given by [4]:(1)I(S‖→=0,Sz)=|∑n=0∞(θn−θn+1)exp(−iSznd)|2 where S→ is the scattering vector, d is the interlayer spacing and n is an integer. θn−θn+1 is the exposed layer coverage which is treated as the atomic distribution function gives the position of surface atoms. For Sz=π/d Eq. (1) simplifies to:(2)I=|∑n=0∞(θn−θn+1)cos⁡(nπ)|2.Variation of the coverage ratio θn of the nth surface layer is modelled by a set of non-linear differential equations [1,4]. The Cash-Karp fifth-order Runge-Kutta method [5] with error estimation and adaptive stepsize control was used for solving initial value problem for non-linear differential equations [6]. The absolute and relative error tolerances and number of integration intervals are fully user-configurable.The proposed code approaches the modelling of RHEED from two different points of view, i.e. the data and functional perspectives. The data perspective (i.e. calculating the layer coverages as a function of their growth time) is used to characterize the data sources of the program whereas the functional perspective includes services provided by the program. It should be noted that the perspective of the data can be expressed by a completely different model introduced by the user.The coverage evolution curves for the diffusive growth model, corresponding kinematical diffracted intensity and total roughness of the surface are shown in Fig. 1. During the numerical calculations showed in Fig. 1 it was assumed that the number of growing layers (numLayers) equals 15, the upper limit of growth time interval (tMax) equals 12, the growth rate equals 1 MLs−1 (for all layers), and the values of the parameter kn (that determines the amount of interlayer diffusion) changing according to the linear relation:(3)kn=k1−(k1−kN)n−1N−1, where N is the total number of growing layers.

Monitoring surface roughness during film growth using modulated RHEED intensity oscillations

Separation of the high- and low-frequency components of Reflection High-Energy Electron Diffraction (RHEED) intensity oscillations during pulsed deposition allows the extraction of a signal that is in phase with the cyclic surface morphology evolution during layer-by-layer growth. Similar to a biased impedance measurement in electricity, the periodic modulation of surface roughness induced by the pulsed deposition probes the differential response of the growth front to changes in step density. This signal does not follow the complex variation of the RHEED oscillation phase with diffraction conditions and surface reconstruction and therefore allows a direct detection of monolayer completion. Off-Laue Circle oscillations show promise to probe the surface morphology evolution at sharply defined in-plane spatial frequencies.

Real-time algorithm to determine the period and phase of Reflection High-Energy Electron Diffraction (RHEED) intensity oscillations during epitaxial growth

We present and discuss an algorithm that reliably determines the period and phase of RHEED intensity oscillations. Based on multiple running averages of the data, this algorithm is not affected by damping or rapid arbitrary changes of the average intensity on a time scale larger than the growth oscillations. It is therefore suitable for a general and precise determination of the deposited layer thickness, at least in homoepitaxy. An additional pre-filtering running average allows the removal of the periodic modulation induced in pulsed laser deposition (PLD).

Hybrid molecular beam epitaxy for the growth of stoichiometric BaSnO3

Owing to its high room-temperature electron mobility and wide bandgap, BaSnO3 has recently become of significant interest for potential room-temperature oxide electronics. A hybrid molecular beam epitaxy (MBE) approach for the growth of high-quality BaSnO3 films is developed in this work. This approach employs hexamethylditin as a chemical precursor for tin, an effusion cell for barium, and a radio frequency plasma source for oxygen. BaSnO3 films were thus grown on SrTiO3 (001) and LaAlO3 (001) substrates. Growth conditions for stoichiometric BaSnO3 were identified. Reflection high-energy electron diffraction (RHEED) intensity oscillations, characteristic of a layer-by-layer growth mode were observed. A critical thickness of ∼1 nm for strain relaxation was determined for films grown on SrTiO3 using in situ RHEED. Scanning transmission electron microscopy combined with electron energy-loss spectroscopy and energy dispersive x-ray spectroscopy confirmed the cube-on-cube epitaxy and composition. The importance of precursor chemistry is discussed in the context of the MBE growth of BaSnO3.

Theoretical analysis of reflection high-energy electron diffraction (RHEED) and reflection high-energy positron diffraction (RHEPD) intensity oscillations expected for the perfect layer-by-layer growth.

Predictions from two theoretical models, allowing one to determine the phase of intensity oscillations, are compared for reflected beams of electrons and positrons. Namely, results of the precise dynamical calculations are compared with results obtained using a simplified approach. Within the simplified model, changes in the specularly reflected beam intensity, expected to occur during the deposition of new atoms, are described with the help of interfering waves and the effect of refraction, and respective approximate analytical formulas are employed to determine the phase of the oscillations. It is found that the simplified model is very useful for understanding the physics ruling the appearance of intensity oscillations. However, it seems that the model with the realistic potential is more suitable for carrying out interpretations of experimental data.

Epitaxial Structures of Band-Gap-Engineered α-(CrxFe1-x)2O3 (0 ≤x≤1) Films Grown on C-Plane Sapphire

Solid solutions of α-Cr2O3 and α-Fe2O3 are novel oxide semiconductors exhibiting narrower band gaps than those of the end members. We have investigated the heteroepitaxial growth and crystalline structure of pulsed-laser deposited α-(CrxFe1-x)2O3 films on c-plane sapphire substrates. Under the growth condition optimized for α-Fe2O3, reflection high-energy electron diffraction intensity oscillations were observable for both α-Fe2O3 and α-Cr2O3, enabling us to control film thickness in a layer-by-layer fashion. The composition dependence of the epitaxial structures, including phase purity, orientation, strain, and in-plane rotation domain, was characterized by X-ray diffraction to reveal a defect-free composition range (0 ≤x ≤0.50). The films with 0.60 ≤x ≤1 were found to have 180°-rotation domains. The absorption spectra of α-(Cr0.50Fe0.50)2O3 solid solution (corundum) and superlattice (nominally composed ilmenite) films are compared with those of end members and an α-Fe2O3/α-Cr2O3 bilayer film to elucidate the origin of the band-gap narrowing.

Ga and In incorporation rates in Ga 1− xIn xAs growth by chemical beam epitaxy

GaAs, InAs and Ga 1− x In x As layers were grown by chemical beam epitaxy (CBE) using triethylgallium, trimethylindium and tertiarybutylarsine as precursors for Ga, In and As, respectively. The growth rate during the homoepitaxial growth of GaAs and InAs, deduced from the frequency of reflection high-energy electron diffraction intensity oscillations, was used to calibrate the incorporation rates for the III elements. The In content of the Ga 1− x In x As layers was measured by Rutherford backscattering spectrometry and compared with the value predicted from the above calibration data; while the measured In mole fraction is close to the predicted value for the samples grown for low In to Ga flux ratios ( x<0.2), the In incorporation is enhanced for larger values of this ratio. The results obtained on layers grown at different substrate temperatures show that In mole fraction is almost constant at growth temperatures in the range 400–500 °C, but a strong dependence on the substrate temperature has been found outside this range. The above results, not observed for samples grown by solid source molecular beam epitaxy, indicate that some interaction between Ga and In precursors at the sample surface could take place during the growth by CBE.

Surface reconstructions and reflection high-energy electron diffraction intensity oscillations during homoepitaxial growth on nonmisoriented GaAs(111)B by MBE

The growth by molecular beam epitaxy of high quality GaAs epilayers on nonmisoriented GaAs(111)B substrates is reported. Growth control of the GaAs epilayers is achieved via in situ, realtime measurement of the specular beam intensity of reflection high-energy electron diffraction (RHEED). Static surface phase maps of GaAs(111)B have been generated for a variety of incident As flux and substrate temperature conditions. The dependence of GaAs(111)B surface reconstruction phases on growth parameters is discussed. The surface reconstruction is identified to be the optimum starting surface for the latter growth of mirror-smooth epilayers. Regimes of growth conditions are optimized in terms of the static surface phase diagram and the temporal RHEED intensity oscillations.

Epitaxial Structure of (001)- and (111)-Oriented Perovskite Ferrate Films Grown by Pulsed-Laser Deposition.

We report epitaxial growth and structures of SrFeO2.5 (SFO) films on SrTiO3 (STO) (001) and (111) substrates by pulsed-laser deposition. Reflection high-energy electron diffraction intensity oscillations were observed during the initial growth on both substrates, reflecting a layer-by-layer growth mode of the formula unit cell. It was found that the films were stabilized with a monoclinic structure that was derived from the original orthorhombic structure of bulk Brownmillerite. Using an X-ray reciprocal space mapping technique, in-plane domain structures and the orientation relationship were investigated. In addition, the impact of laser spot area on the epitaxial structures was studied. For the films grown on the (001) STO, the orientation relationship was robust against the change of the laser spot area: SFO(001)//STO(001) and SFO(100)//STO(100) for the out-of-plane and the in-plane, respectively, with the [001] axis tilted toward the 4-fold a- and b-axes by ∼1.4°, whereas nearly (111)-oriented films were obtained on the (111) STO, exhibiting a complicated manner of tilting that depended on laser spot area. The observed variation in tilting configurations can be understood in terms of possible atomic arrangements at the SFO/STO interface. These results present a guide to control the heteroepitaxial growth and structure of (111)-oriented noncubic perovskites.

Nonpolar 4H-AlN grown on 4H-SiC (11¯00) with reduced stacking fault density realized by persistent layer-by-layer growth

Nonpolar AlN layers were grown on 4H-SiC (11¯00) substrates by plasma-assisted molecular-beam epitaxy. By using SiC substrates with well-formed step-and-terrace structures, stable layer-by-layer growth of 4H-AlN (11¯00) can be realized. The layer-by-layer growth is confirmed by observations of anisotropic two-dimensional AlN islands on the grown surface as well as persistent reflection high-energy electron diffraction intensity oscillations. Cross-sectional transmission electron microscopy observations reveal that stacking fault generation during growth is suppressed and the stacking fault density is reduced to 1×106 cm−1.

Enhancement in layer-by-layer growth in heteroepitaxial growth of Co on Au(111) surface by Bi surfactant

The surfactant effect of Bi on the heteroepitaxial growth of Co on the Au(111) surface has been studied. With the predeposition of submonolayer Bi on Au(111) prior to evaporation of Co, more long-lasting reflection high-energy electron diffraction intensity oscillations were observed at room temperature. This implied that Bi enhanced the layer-by-layer growth of Co on the Au(111) surface. The dependence of the Co film growth on the thickness of the Bi surfactant layer suggested that there existed a suitable amount of Bi surfactant that enhanced a smoother layer-by-layer growth. The Auger electron spectra revealed that Bi was segregated at the top of the surface. Therefore, Bi was concluded to be an effective surfactant to enhance the layer-by-layer growth of Co on Au(111).

Influence of atomic hydrogen on step stability during homoepitaxial growth on vicinal GaAs surfaces

We have employed a combination of reflection high-energy electron diffraction intensity oscillations and atomic force microscopy to investigate the effect of atomic hydrogen on the step bunching instability that arises during homoepitaxial growth from molecular beams of Ga and As4 on vicinal GaAs(110) surfaces due to the asymmetric incorporation rates of adatoms to upper and lower step edges. We discuss the variations observed in the GaAs growth mode and in the terrace width distribution of the bunched-step morphology in terms of H-induced changes in the reaction pathway and in the kinetics of adatom migration and incorporation at steps.

Layer-by-layer deposition of epitaxial TiN–CrN multilayers on MgO(0 0 1) by pulsed laser ablation

Titanium nitride (TiN)–chromium nitride (CrN) multilayers were deposited epitaxially on MgO(0 0 1) by pulsed laser ablation combined with nitrogen radical irradiation. High quality TiN film was first deposited on MgO(0 0 1) substrate. During the alternate deposition of six TiN monolayers and three CrN monolayers, reflection high-energy electron diffraction (RHEED) intensity oscillations were observed continuously, showing layer-by-layer growth of a transition metal nitride multilayer structure. An X-ray diffraction peak corresponding to a multilayer periodicity of 2.1 nm was observed. The multilayer sample showed metallic conductivity and ferromagnetic behavior with a Curie temperature of ca. 70 K. The ferromagnetism may be attributable to the formation of a TiN–CrN mixed phase at the multilayer boundaries.

Silicon epitaxial growth on the Si(001)2×1 surface from silane using dynamic Monte Carlo simulations

Dynamic Monte Carlo (DMC) simulations are carried out on silicon (001)2×1 surface under 100% silane gas chemical vapor deposition condition as a function of surface temperature (600–800° C) and pressure (6 and 12 mTorr). The reactant on the surface from gas-phase is assumed to be the silane molecule. The rates and probabilities of surface reactions are determined a priori by recent ab initio calculation results in the literature. The DMC method can reveal not only the short-time microscopic mechanism but also predict the macroscopic phenomena such as deposition. The calculated growth rate and Arrhenius activation energy of growth depending on temperature show good agreement with experimental results. The results suggest that the low activation energy regime above 700 °C is associated with a process controlled by silane dissociative adsorption. In contrast, the higher activation energy regime below 700 °C is supposed to be governed by hydrogen desorption. The periodic change of surface structure that is similar to reflection high-energy electron diffraction intensity oscillation in the process of molecular beam epitaxy is observed. The periodic behavior results from the repeat of a series of hydrogen desorption, silane adsorption, surface incorporation, and adatom diffusion on the growing surface.

Accuracy of AlGaAs growth rates and composition determination using RHEED oscillations

Abstract We investigate the sources of uncertainty in the measurement of the reflection high-energy electron diffraction (RHEED) intensity oscillations during growth of AlAs, GaAs, and AlGaAs on GaAs substrates, and the resulting effects on predicted growth rates and composition. Sources of error examined include beam positioning, flux transients, substrate size, ‘beat’ phenomena in the RHEED oscillations, substrate temperature, and incident beam direction. We find that flux transients and flux nonuniformity are the dominant systematic errors in predicting growth rates and composition with RHEED. From flux uniformity measurements, we estimate the beam positioning error for our growth system to be 0.2–0.6%/mm, and substrate size to impact the uncertainty by as much as several percent. In addition to these errors, flux transients can cause an uncertainty of up to 1%. We also present a procedure that uses the measured variance in the growth rates to calculate the composition with the smallest mean square error.

Growth and structure of L10 ordered FePt films on GaAs(001)

The structural properties of epitaxial L10 ordered FePt(001) films, grown bymolecular beam epitaxy (alternating deposition of Fe and Pt atomic layers) onbuffer-Pt/seed-Fe/GaAs(001) have been studied by in situ reflection high-energyelectron diffraction and by ex situ x-ray scattering as a function of the growthconditions. Reflection high-energy electron diffraction intensity oscillations measuredduring FePt layer growth provide evidence for island growth at Ts = 200°C and quasi layer-by-layer growth at Ts = 350° C.From small-angle and wide-angle x-ray scattering it was found that the degree ofepitaxy depends critically on morphology of the seed layer and the substrateroughness. X-ray diffraction analysis showed that the long-range order parameterincreases from near zero for films grown at 200°C to 0.65 for films grown at 350°C.This confirms the fact that the order parameter is mainly determined by thesurface mobility of the atoms which is controlled experimentally by the substratetemperature.

Correlation of surface chemistry of GaAs substrates with growth mode and stacking fault density in ZnSe epilayers

We report on the correlation of surface chemistry of GaAs substrates with growth mode and stacking fault density in ZnSe epilayers. High quality ZnSe epilayers with low stacking fault density have been directly grown on commercial epiready GaAs (001) substrates without GaAs buffer layer growth. It is found that proper pregrowth treatments of epiready GaAs (001) substrates to obtain clean surfaces are crucial to two-dimensional layer-by-layer growth and suppression of generation of stacking faults. The surface oxide layers of epiready GaAs substrates before and after chemical etching using a NH4OH-based solution are carefully characterized by angle-resolved x-ray photoelectron spectroscopy. The surface oxide layer is composed of Ga2O3 and As2O3. The chemical etching is found to reduce not only the thickness of the oxide layers but also the ratio of Ga2O3 to As2O3 to about half of that before etching. A clean GaAs (001) surface typically characterized by a (4×1) reconstruction is obtained in the present case after thermal cleaning. Prior to ZnSe growth Zn preexposure is carried out. Reflection high-energy electron diffraction intensity oscillations with more than 50 periods are observed even from the beginning of ZnSe growth on such cleaned GaAs substrates. High quality ZnSe layers with a stacking fault density of low-105 cm−2 range are grown.

Gas Source Molecular Beam Epitaxy Growth of TlInGaAs Layers on GaAs Substrates

New alloy semiconductor TlInGaAsN/AlGaAs heterostructures for fabricating 1.3–1.55 µm wavelength laser diodes with temperature-stable threshold current and temperature-stable lasing wavelength are proposed. TlInGaAs/GaAs and InGaAs/GaAs double-hetero (DH)-, multi-hetero (MD)- and single-quantum-well (SQW) structures were grown on GaAs substrates by gas source molecular beam epitaxy. Incorporation of Tl into TlInGaAs was confirmed up to 9% with reflection high-energy electron diffraction intensity oscillation. Red shift of the photoluminescence peak energy was also observed for TlInGaAs/GaAs DH, MH and SQW samples, which agrees with the incorporation of Tl.

First successful growth of TlInGaAs layers on GaAs substrates by gas source MBE

To realize the temperature-stable threshold-current and lasing-wavelength 1.3–1.5 μm laser diodes, TlInGaAsN/AlGaAs heterostructures were proposed. As a first step, TlInGaAs was successfully grown, for the first time, on GaAs substrate by molecular beam epitaxy. The incorporation of Tl was confirmed with reflection high-energy electron diffraction intensity oscillation measurement. Photoluminescence (PL) measurements were conducted on the TlInGaAs/GaAs and InGaAs/GaAs heterostructure samples and the red shift of the PL peak energy was observed for the TlInGaAs/GaAs samples, as expected.

Valuing of the critical layer thickness from the deading time constant of RHEED oscillation in the case of In xGa 1− xAs/GaAs heterojunction

In this work, we have looked for the correlation between the observed decay of reflection high-energy electron diffraction intensity oscillation and the critical layer thickness in the case of strained In x Ga 1− x As/GaAs heterojunctions. The value of deading time constant of oscillation depends on the mismatch and on growth parameters, too. The decay of oscillation was described by two deading time constants which are responsible for the influences of the parameters mentioned above. The critical layer thickness was valued from the deading time constant responsible for the influence of mismatch only. The critical layer thickness determined this way shows good agreement with the theoretical model.