CdSe Quantum Wells: Analytical

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Strain Compensation in Single ZnSe/CdSe Quantum Wells: Analytical Model and Experimental Evidence Torsten Rieger,*,† Thomas Riedl,‡ Elmar Neumann,§ Detlev Grützmacher,† Jörg K. N. Lindner,‡ and Alexander Pawlis† †

Peter Grünberg Institute 9 and JARA-FIT, Forschungszentrum Jülich GmbH, Wilhelm Johnen Strasse, 52425 Jülich, Germany Department of Physics, University of Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany § Peter Grünberg Institute 8 and JARA-FIT, Forschungszentrum Jülich GmbH, Wilhelm Johnen Strasse, 52425 Jülich, Germany ‡

S Supporting Information *

ABSTRACT: The lattice mismatch between CdSe and ZnSe is known to limit the thickness of ZnSe/CdSe quantum wells on GaAs (001) substrates to about 2−3 monolayers. We demonstrate that this thickness can be enhanced significantly by using In0.12Ga0.88As pseudo substrates, which generate alternating tensile and compressive strains in the ZnSe/CdSe/ ZnSe layers resulting in an efficient strain compensation. This method enables to design CdSe/ZnSe quantum wells with CdSe thicknesses ranging from 1 to 6 monolayers, covering the whole visible spectrum. The strain compensation effect is investigated by high resolution transmission electron microscopy and supported by molecular statics simulations. The model approach with the supporting experimental measurements is sufficiently general to be also applied to other highly mismatched material combinations for the design of advanced strained heterostructures. KEYWORDS: quantum well, strain compensation, molecular beam epitaxy, geometric phase analysis, molecular statics simulations, critical thickness

1. INTRODUCTION For optically mediated applications, both II−VI colloidal quantum dots1 and planar, epitaxial ZnSe/CdSe quantum wells are in principle capable to cover the whole visible spectrum via a variation of the dimensions (size of the quantum dot or thickness of the quantum well). While the integration of the colloidal quantum dots in devices is challenging, the lattice mismatch between ZnSe and CdSe as well as the typically used GaAs substrates limit the thickness of coherently grown CdSe layers to about 2 monolayers (MLs) in case of epitaxial quantum wells. Between nominal thicknesses of 2 and 3 MLs quantum dots emerge due to the Stranski−Krastanov process and above 3 MLs plastic relaxation takes place.2 Recently Finke et al. managed to obtain efficient light emission from ZnSe/ CdSe quantum wells with CdSe thicknesses as high as 6 MLs.3,4 This became possible by applying a dedicated strain compensation technique involving InxGa1−xAs pseudo substrates. On GaAs substrates, both ZnSe and CdSe are compressively strained. ZnSe layers grown on InxGa1−xAs buffer layers with about 4% Indium are lattice matched and consequently, a high crystalline quality of thick ZnSe layers can be obtained.5 On the contrary, when grown on an InxGa1−xAs substrate with higher Indium content, resulting in a lattice constant in-between those of ZnSe and CdSe, one layer is tensile strained (ZnSe) while the other is compressively strained (CdSe). Strain compensation is widely used in stacked © XXXX American Chemical Society

quantum dots and multiple quantum wells to reduce the overall strain build-up and corresponding relaxation toward the upper layers of the stack.6−12 To analyze the strain components in both directions in nanoscopic layer stacks with a spatial resolution in the range of (sub)nanometers, only few techniques are suitable.13,14 X-ray diffraction15 and Raman spectroscopy16 allow very precise strain resolution but the spatial resolution is limited to some hundreds nanometers. Transmission electron microscopy (TEM) based strain measurements have a significantly higher spatial resolution, while the strain resolution is slightly worse. In the TEM several different techniques are applicable, all having some advantages and disadvantages. For example, convergent electron beam diffraction has a high strain precision but only profiles are possible which require rather long acquisition times. However, TEM investigations of II−VI semiconductors typically require short acquisition times due to potential damage induced by the electron beam.17,18 In contrast, strain determination from high resolution TEM images either in direct (peak fitting19) or reciprocal (geometric phase analysis (GPA)20,21) space is rather fast and provides a good resolution for both the spatial dimensions and the strain. However, the strain is given with Received: December 9, 2016 Accepted: February 13, 2017 Published: February 13, 2017 A

DOI: 10.1021/acsami.6b15824 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces respect to a reference region close to the region of interest. In the direct space analysis, the location of atoms is identified with respect to a reference but the method is rather sensitive to artifacts and noise on the image. Using GPA, two-dimensional strain maps are obtained using the correlation between the phase information on Bragg spots and the displacement field. The method is less sensitive to noise and artifacts due to the applied filtering in the reciprocal space.13 Furthermore, crystallographic defects such as stacking faults and misfit dislocations are directly visualized using HRTEM micrographs. Taking these conditions into account, strain determination from HRTEM micrographs such as GPA is ideally suited. Here, we present TEM-GPA investigations of single strain compensated ZnSe/CdSe/ZnSe quantum wells supported by molecular statics simulations. Moreover, we present a simple analytic set of equations which allows for adapting the properties and thicknesses of alternatingly strained layers on tailored substrates to feature the strain compensation effect.

2. MATERIALS AND METHODS Strain compensated ZnSe/CdSe quantum wells with the structure schematically displayed in Figure 1a were grown by molecular beam epitaxy. The structure consists of a 2 μm thick InxGa1−xAs buffer grown on a GaAs (001) wafer. The Indium concentration is 12%, and the film is relaxed by 74% as determined by X-ray diffraction. Subsequently, a thin ZnSe layer is used for nucleation of the II−VI semiconductor, followed by a 50 nm thick ZnxMg1−xSe barrier. The In0.12Ga0.88As and ZnxMg1−xSe are chosen to be in-plane lattice matched, i.e., a concentration of 10% Mg is used. The ZnSe/CdSe quantum well consists of 11 MLs thick ZnSe claddings and CdSe layers varying between 2 and 5 MLs thickness. Another 50 nm thick Zn0.9Mg0.1Se barrier was deposited on top of the QW to complete the strain compensated structure. The thickness of the quantum well is in situ controlled by RHEED intensity oscillations and ex-situ verified by X-ray diffraction and photoluminescence spectroscopy. Cross-sectional TEM lamellae were prepared by focused ion beam (FIB, FEI Helios NanoLab 600i) using Ga ions where the final thinning took place with an acceleration voltage of 5 kV. High resolution TEM (HRTEM) images were acquired with a FEI Tecnai G2 F2022 transmission electron microscope operated at 200 kV, the samples being aligned along the ⟨110⟩ zone axis. The strain compensation was analyzed applying the GPA to high resolution TEM images.20,21 The basic principle of GPA is the correlation between the phase information Pg( r )⃗ of certain Bragg spots g ⃗ and the local displacement field u ⃗( r ⃗). In practice a Fourier transform of a HRTEM image is calculated and two masks are used to select two nonparallel Bragg reflections. Subsequently, the inverse Fourier transform is calculated and only the phase information is used for the further analysis. Here, an unstrained reference region is required to refine the selected Bragg reflection g⃗. The phase in the reference region is zero. Thus, the reference region has to be close to the region of interest allowing only small structures to be analyzed. The relation between the displacement field u ⃗( r ⃗) and the phase Pg( r )⃗ is given by the following: Pg( r ⃗) = − 2πg ⃗ · u ⃗( r ⃗)

Figure 1. (a) Sketch of the sample structure for strain compensated quantum wells (not to scale). (b) Low resolution TEM micrograph of the entire structure including the In0.12Ga0.88As buffer. (c) TEM micrograph showing the transition from the In0.12Ga0.88As to the II−VI layer stack with threading dislocations changing to stacking faults at the interface. The position of the image is indicated by the red rectangle shown in (b). (d) TEM image of the II−VI layer stack, clearly evidencing the CdSe layer. The green rectangle in (c) indicates the position of the image shown in (d). The inset in (d) displays a HRTEM image of the CdSe quantum well having a thickness of 5 MLs.

reference region close to the region of interest. Here, the reference region is the bottom Zn0.9Mg0.1Se layer and therefore, the relative change in lattice plane spacing across the heterostructure is expressed with respect to the Zn0.9Mg0.1Se, thus the Lagrange strain: Δzz,ZnMgSe =

⎡ ϵxx ϵ=⎢ ⎣ ϵzx

(3)

Here, d(z) is the actual lattice plane spacing and dZnMgSe is the lattice plane spacing in the Zn0.9Mg0.1Se. In order to calculate the atomic positions at minimum energy, molecular statics simulations based on the Tersoff potential23 were performed by using the LAMMPS software.24 For ZnSe and CdSe the parametrization of Benkabou et al.25 was adopted. As there is no parametrization available for Zn 0.9Mg0.1Se we replaced it by In0.1Ga0.9As, which has the same lattice parameter as that observed for the partially relaxed In0.12Ga0.88As buffer and the Zn0.9Mg0.1Se layers. For the atomic interactions between In, Ga and As the parametrization of Hammerschmidt et al. was employed.26 In the x and y directions, periodic boundary conditions were applied, whereas the structure was allowed to relax in +z direction. After conjugate gradient based relaxation of the atom positions the distances between adjacent (001) MLs and the strain in z direction were extracted. Here, either

(1)

The strain ϵ is then simply given by the first derivative of the displacement,

⎡ δux δux ⎤ ϵxz ⎤ ⎢ δx δz ⎥ ⎥ ⎥=⎢ ϵzz ⎦ ⎢ δuz δuz ⎥ ⎢ ⎥ ⎣ δx δz ⎦

d(z) −1 d ZnMgSe

(2)

Here, z is the growth direction while x is perpendicular to the electron beam and z. The strain maps are given with respect to the undistorted B


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ACS Applied Materials & Interfaces the distances between the Se atoms or between the Zn/Cd atoms are considered, both producing rather similar results.

along the z-direction and d0 is the ML distance in bulk material. In the CdSe, however, the strain ϵzz reaches up to +8%. As an alternative to complex molecular static simulations, a more simple and intuitive description of the strain situation is obtained by considering the ZnSe/CdSe/ZnSe heterostructure as a pseudo crystal with a lattice constant being the weighted average of the individual layers, t ZnSe tCdSe a ZnSe + aCdSe aeq = t ZnSe + tCdSe t ZnSe + tCdSe (4)

3. RESULTS AND DISCUSSION Figure 1b displays a low resolution TEM micrograph of the entire structure including the In0.12Ga0.88As buffer. The crystal structure is zinc blende. The In0.12Ga0.88As buffer has a high density of threading dislocations caused by the lattice mismatch relative to the GaAs substrate. The II−VI layer stack on top of the In0.12Ga0.88As, however, is almost free of threading dislocations, instead the threading dislocations of the In0.12Ga0.88As buffer turn into stacking faults at the interface to the II−VI layer stack (see Figure 1c and Figure S2 in the Supporting Information). Thus, the interface between the III− V and the II−VI semiconductor acts as a dislocation filter, possibly being caused by the tensile strained ZnSe nucleation layer.27 The interface between the III−V and the II−VI semiconductor has a high crystalline quality, apart from the stacking faults no further defects (such as misfit dislocations) occur. The smooth CdSe quantum well with a thickness of 5 MLs is clearly visible in Figure 1d and the inset showing a low resolution and a high resolution image of the quantum well structure, respectively. The HRTEM image proofs the CdSe layer thickness of 5 MLs. No defects originating from this quantum well or formation of QDs are observed, as shown by Bragg filtered HRTEM micrographs in Figure S5. In contrast, ZnSe/CdSe quantum wells with a CdSe thickness of 3 MLs grown on GaAs without strain compensation evidence a huge amount of defects such as dislocations (encircled area in Figure 2b showing a dislocation half loop) and stacking faults (arrows in Figure 2b) due to beginning plastic relaxation of the CdSe (see Figure 2a,b).

where tZnSe and tCdSe are the thicknesses of the ZnSe and the CdSe, respectively, and aZnSe and aCdSe are the bulk lattice constants listed in Table 1. The average lattice plane distance in z-direction az,eq is then obtained by straining this pseudo crystal with lattice constant aeq to the Zn0.9Mg0.1Se barriers, i.e., ⎛ 2C12,eq ⎞ ⎟(aeq − asub) + asub az,eq = ⎜⎜1 + C11,eq ⎟⎠ ⎝

(5)

with C11,eq and C12,eq being the weighted averages of the elastic constants of the individual ZnSe and CdSe layers. az,eq is plotted as dashed-dotted lines in Figure 3a,d. Obviously, the lattice mismatch between the equilibrium lattice and the substrate is significantly reduced compared to the pure ZnSe and CdSe. This approach has proven to be suitable for explaining the photoluminescence properties of the strain compensated quantum wells.3 Using the theory for the calculation of the critical thickness developed by Matthews and Blakeslee,28 the critical thickness before strain relaxation takes place is significantly enhanced due to the tensile and compressively strained layer stack. However, more profound knowledge of the strain, roughness, and nanoscale defects of the layers is needed to fully understand it and to be able to explain the photoluminescence properties.3 The results from the molecular statics simulations can be used to create a projection view of the QW structure (see Figure 4a). The projection view can be considered as a simplified TEM images where only the atomic positions are taken into account, other effects such as the sample thickness, defocus, and material contrast are neglected. The out-of-plane lattice plane distances vary according to the molecular statics simulation (Figure 3a,d), while the in-plane distances are constant and equal to those of the Zn0.9Mg0.1Se and the In0.12Ga0.88As buffer. Figure 4a displays such an projection view of a 3 MLs thick CdSe QW embedded in 11 MLs thick ZnSe cladding layers. Two Δzz maps obtained from GPA with different resolutions are displayed in Figure 4b,c. The resolution is given by the size of the mask function used to select the reciprocal fringe vector g:⃗ A large mask radius (inverse of the used resolution) results in a high spatial resolution while a small mask radius gives a higher accuracy of the strain. In Figure 4b, the resolution is 1 nm and the CdSe QW as well as the ZnSe cladding layers are clearly visible. The resolution is changed to 2 nm in Figure 4c and correspondingly, the differently strained layers are slightly smeared out. Δzz profiles obtained from the GPA of the projection view of the 3 MLs and 5 MLs thick QWs are plotted in Figure 3c,f, respectively. In both cases, results from GPA resolutions of 1 and 2 nm are drawn. In general, a compromise between high spatial resolution and high accuracy is needed, which for both the projection view-GPA as well as the experimental analysis is obtained for GPA resolutions of about 2 nm. GPA resolutions of 1.5 nm or better typically gave rise to strong Δzz fluctuations

Figure 2. (a,b) TEM images of ZnSe/CdSe heterostructure with 3 MLs CdSe without strain compensation (i.e., on GaAs substrates) clearly showing strain relaxation via the formation of extended defects (arrow: stacking fault, circle: dislocation half loop). The blue rectangle in (a) denotes the position of the TEM micrograph shown in (b). Colored overlays denote the layer sequence (blue ZnSe, green CdSe).

According to molecular statics simulations the distance between adjacent MLs within the strain compensated II−VI layer stack is found to vary as exemplarily displayed in Figure 3a,d for the 3 MLs and 5 MLs thick quantum wells, respectively. The material specific strain ϵzz and the relative change in lattice plane spacing Δzz (Lagrange strain) are plotted in Figure 3, parts b,e and c,f, respectively. In the xy plane the ZnSe is tensile strained, whereas the compressive out-of-plane strain ϵzz=dz/d0−1 reaches −1%. Here, dz is the ML distance C


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Figure 3. Results from molecular statics simulations showing the distance between adjacent monolayers (a,d), the strain ϵzz within the layers (b,e) and the relative change of the ML distance Δzz,ZnMgSe with respect to the Zn0.9Mg0.1Se, i.e., the Lagrange strain (c,f), for the 3 and the 5 MLs thick quantum wells. The solid lines in (a,d) represent the distance between Se atoms, the dotted lines the distance between Zn(Cd) atoms. The dasheddotted lines in a and d represent the monolayer distance in the pseudo crystal ZnSe-CdSe-ZnSe with lattice parameter az,eq. For comparison, in (c,f) Δzz profiles from GPA of a projection view are shown for two different resolutions. Light blue, dark blue, and green colors denote the Zn0.9Mg0.1Se (replaced by In0.12Ga0.88As as explained in the text), ZnSe and CdSe layers, respectively.

Table 1. Lattice Constants and Elastic Constants of ZnSe and CdSe parameter

ZnSe

CdSe

ref.

a0 (nm) C11 (GPa) C12 (GPa)

0.56686 82.6 49.8

0.6052 74.6 46.1

29,30 29,30 29,30

in the Zn0.9Mg0.1Se, indicating inaccurate measurements of the strain. Resolutions above 2.5 nm resulted in less clear Δzz profiles. Self-evident, the Δxx maps obtained from the projection view do not show any variation of the Lagrange strain. The interface between the In0.12Ga0.88As substrate and the ZnSe/Zn0.9Mg0.1Se layers gives a first indication of avoiding the formation of defects during the nucleation of the II−VI semiconductor stack. Figure 5a,b display the experimental Δxx and Δzz GPA strain maps of the interface superimposed over the respective HRTEM micrographs. It is obvious that Δxx is almost constant along the entire layer stack, demonstrating coherent growth without the formation of defects. This is further supported by the HRTEM micrograph and Bragg filtered images of the interface shown in Figure S1. Contrarily, in the Δzz map a variation is visible: the ZnSe nucleation layer has a smaller lattice plane spacing as compared to the In0.12Ga0.88As and the Zn0.9Mg0.1Se. At the interface between the In0.12Ga0.88As and the ZnSe nucleation layer, a thin region with larger lattice plane spacing is present, probably being associated with the interfacial bonding between Ga/In and Se or Zn and As. We have observed similar thin regions with larger lattice plane spacings also in conventional GaAs/ZnSe heterostructures (see Figure S4), thus we attribute it to an

Figure 4. (a) Projection view of the crystal structure with atomic positions being determined from molecular statics simulations, the layer structure with a 3 MLs CdSe quantum well embedded in 11 MLs ZnSe claddings is depicted next to the projection. (b,c) GPA Δzz maps of the projection image with simulated atomic positions shown in (a) with a GPA resolution of 1 nm (b) and 2 nm (c).

interfacial layer between the III−V and the II−VI semiconductor rather than to the presence of In. D


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Figure 5. Δxx (g⃗ = 220) and Δzz (g⃗ = 002) maps obtained from GPA superimposed over HRTEM micrographs for (a,b) the interface between the In0.12Ga0.88As and ZnSe/Zn0.9Mg0.1Se and (c,d) the Zn0.9Mg0.1Se/ZnSe/3 MLs CdSe/ZnSe/Zn0.9Mg0.1Se quantum well structure. (e) Experimental Δzz profile extracted from the Δzz map in (d) (averaged over a lateral distance of 5 nm) in comparison with the theoretical profile obtained directly from molecular statics (MS) simulations and projection view-GPA (with simulated atomic positions). Dotted horizontal lines in (a−e) indicate the positions of interfaces. The inset in (d) shows the Δzz map of a 5 MLs thick CdSe quantum well.

The experimental Δxx map of a ZnSe/CdSe quantum well with 3 MLs CdSe is displayed in Figure 5c, the GPA resolution is 2 nm, i.e., identically to the resolution used in Figure 4c. No gradient in the Δxx map is observed evidencing uniform inplane lattice plane distances. Thus, a coherent growth is obtained, which is similar for the 5 MLs sample (not shown here). In the experimental Δzz map (Figure 5d (3 MLs CdSe) and inset in (d) (5 MLs CdSe)) a gradient is present, i.e., in growth direction Δzz first switches from zero (Zn0.9Mg0.1Se) to negative values (ZnSe, tensile in-plane strain compared to the Zn0.9Mg0.1Se) and subsequently to positive (CdSe, compressive in-plane strain compared to the Zn0.9Mg0.1Se), negative (ZnSe) and zero (Zn0.9Mg0.1Se). The CdSe layer (positive Δzz) has a uniform thickness, no clustering or formation of quantum dots is observed, and even the quantum well with 5 MLs CdSe is smooth. Thus, smooth and coherent ZnSe/CdSe quantum wells with thicknesses larger than the critical thickness for QD formation (∼2 MLs) and even above the critical thickness for plastic relaxation (>3 MLs) are obtained. The experimental Δzz map of the 3 MLs thick CdSe QW is in qualitative agreement with the Δzz map obtained from the projection view based on the molecular statics simulations (Figure 4c). A profile of the experimentally determined Δzz map averaged over a lateral distance of 5 nm in the x direction is displayed in Figure 5e (red full line), clearly evidencing the alternating Δzz values. This profile can be compared with the one obtained directly from the molecular statics simulations (Figure 3c). This comparison is plotted in Figure 5e, the red trace shows the experimental profile while the black dotted line displays the Δzz

profile directly obtained from the molecular statics simulations. A strong deviation between the theoretical and the experimental data is present. However, this is explained by the limited resolution of the GPA, being in the range of few nanometers (here: 2 nm). This is considered by applying a filter with the same size as the mask function used for the experimental GPA to the data obtained directly from the molecular statics simulations via averaging it over the nearest neighbors (7 MLs ≈ 2 nm). Using this method excellent agreement between the filtered molecular statics simulations (black full line in Figure 5e) and the GPA trace (red full line in Figure 5e) is achieved. Furthermore, the experimentally determined Δzz profile is compared with its counterpart from the projection view with the same resolution (2 nm, blue full line in Figure 5e). The Δzz of the projection view-GPA profile is extracted via a linescan from Figure 4c. The experimental GPA profile and the projection view-GPA profile agree well, confirming that the combination of the molecular statics simulations and the projection view analysis is a suitable tool to investigate the strain compensated layer stack. The equilibrium lattice constant aeq as well as the lattice plane distances az,eq in the strained situation are plotted in Figure 6a together with the average distances between the Se or Zn/Cd atoms obtained from the molecular statics simulations. As visible, az,eq and the values from the molecular statics simulations are in excellent agreement, indicating that eqs 4 and 5 represent a good approximation for the strain compensated layer stack. Consequently, the latter equations allow for the specific design of balanced strain compensated thin layer stacks E


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is observed for the quantum wells with larger CdSe thickness (e.g., 5 MLs) is still in the range of the overall accuracy of GPA (≥0.2%),13,14 which can be approximated by the fluctuation amplitude in an unstrained material, i.e., the Zn0.9Mg0.1Se, which is ∼0.5% in this specific case. Furthermore, it is influenced by potential specimen damage during the FIB preparation as well as by the electron beam in the TEM17 and by a partial relaxation of the lamella during thinning.31,32

4. CONCLUSIONS Single ZnSe/CdSe/ZnSe quantum wells with up to 5 MLs CdSe grown on In0.12Ga0.88As pseudo substrates are fully strain compensated and do not evidence a strong roughness of the quantum well or any crystal defects. The In0.12Ga0.88As/ZnSe interface is found to act as a threading dislocation filter due to the slight lattice mismatch. Strain maps of the quantum wells clearly display the uniform in-plane lattice constant, while only the out-of-plane lattice constant varies being a proof of the coherent growth. The experimental Lagrange strain profile is in qualitative agreement with data from molecular statics simulations. Moreover, the strain compensation of the ZnSe/ CdSe/ZnSe layer stack can be nicely described by a pseudo lattice parameter obtained from the weighted average of the individual layers, agreeing well with previously published photoluminescence measurements. The above-mentioned approximation is sufficiently general and valid to be applied to other highly mismatched epitaxial systems for the design of advanced strain compensated heterostructures.

Figure 6. (a) Calculated lattice parameter aeq and az,eq in comparison to lattice plane distances obtained from molecular statics simulations. (b) Average Δzz (average Lagrange strain) from the GPA measurements on HRTEM images in comparison to data from molecular statics simulations (MS) and projection views.

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ASSOCIATED CONTENT

S Supporting Information *

with higher critical thickness depending on elastic constants and thicknesses of the ZnSe and CdSe layers as well as the indium concentration in the InxGa1−xAs pseudo substrate. In general, eqs 4 and 5 may also be directly applied to other highly strained semiconductor heterostructures (e.g., arsenides, tellurides or Si/Ge based combinations). In order to further compare the molecular statics simulations with the experimentally obtained data, the average Δzz (average Lagrange strain in the ZnSe/CdSe/ZnSe layer stack) is calculated from the experimental TEM-GPA profile (black squares), the projection view-GPA profile (red triangles) as well as directly from the molecular statics simulations (blue and green symbols) and is plotted in Figure 6b. Here, data from adjacent Se as well as adjacent Zn/Cd MLs are displayed (blue circles and green diamonds, respectively). In each case, only the relevant resolutions of 2 nm ∼7 MLs are used. Similar as in Figure 5e, the difference between the experimentally determined Lagrange strain and the data obtained directly from the simulations is rather large which is primarily caused by the limited resolution of GPA. Taking this resolution into account, the agreement between the experimental and theoretical data becomes significantly improved. Although, the Lagrange strain profiles obtained directly from the molecular statics simulations reproduce the experimental profiles nicely (see Figure 5e), the average Δzz is typically slightly overestimated. The projection view-GPA data (red triangle) in general exhibit an excellent agreement with the experimentally determined average Δzz, indicating nearly perfect description of the strain compensated ZnSe/CdSe/ ZnSe layer stack. Nonetheless, it should be mentioned that the deviation between the experimental and theoretical data which

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.6b15824. Additional HRTEM micrographs and Bragg filtered images of the InGaAs/ZnSe interface, the GaAs/ZnSe interface, the 5 MLs thick ZnSe-CdSe-ZnSe quantum well, and the conventional ZnSe-CdSe-ZnSe heterostructure without strain compensation (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (T.R.). ORCID

Torsten Rieger: 0000-0003-4873-4022 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The TEM facilities at the Ernst Ruska Centre are gratefully acknowledged. S. Scholz, A. Ludwig, and A. D. Wieck (Ruhr University Bochum) are acknowledged for the growth of the In0.12Ga0.88As buffer. This work was funded by the Volkswagen Foundation (Project No. 88360/90080).

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REFERENCES

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CdSe Quantum Wells: Analytical

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