Strained state of Ge(Si) islands on Si: Finite element calculations and comparison to convergent beam electron-diffraction measurements

Christiansen, Silke; Albrecht, M.; Strunk, H. P.; Maier, H. J.

doi:10.1063/1.111217

Cited by 184 publications

(79 citation statements)

References 12 publications

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“…Experimental studies qualitatively verify the theoretical predictions [12]. It has been shown experimentally that the strain field of a QD extends far into the underlying wetting layer and substrate [17,18]. This strain field surrounding each QD may induce dot-dot interaction that strongly influences the growth of neighboring dots and thus causes short-range ordering of neighboring dots.…”

Section: Introductionsupporting

confidence: 66%

Distribution and shape of self-assembled InAs quantum dots grown on GaAs (001)

Zhang

Falta

Schmidt

et al. 2000

Pure and Applied Chemistry

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Section: Introductionsupporting

confidence: 66%

Distribution and shape of self-assembled InAs quantum dots grown on GaAs (001)

Zhang

Falta

Schmidt

et al. 2000

Pure and Applied Chemistry

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“…Elemental analysis of the film using Rutherford backscattering spectrometry and low temperature photoluminescence spectroscopy of thick relaxed films indicates that the ternary composition of the film is In 0.6 Ga 0. 4 As, corresponding to a lattice mismatch of 4.3% with the GaAs substrate.…”

mentioning

confidence: 99%

“…Finite element analysis (FEA) methods have been widely and successfully used to study the strain field of nanometer-size semiconductor QDs and applied to TEM investigations. For example, Christiansen et al [4] used FEA to obtain the displacement field of Ge(Si) islands grown on Si. Using convergent beam electron diffraction, their study showed that the displacement field obtained in this way is correct.…”

mentioning

confidence: 99%

Indium Segregation and Enrichment in CoherentInxGa1−xAs/GaAsQua

et al. 1999

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Significant differences in the image features of In x Ga 12x As quantum dots (QDs) grown on (001) and vicinal (001) GaAs were seen in [001] on-zone bright-field transmission electron microscope images. Simulated images were obtained by modeling the strain field distribution of the QDs with finite element analysis and then using this model in dynamical electron diffraction contrast simulations. Comparison of the experimental images and the simulated images shows that (i) In segregation exists in the QDs and (ii) the average In content of the QDs is higher than the average In content of the film. [S0031-9007(99)09460-0] PACS numbers: 81.05.Ea, 61.14. Lj, 61.16.Bg, 68.35.Dv The composition, shape, and size of quantum dots (QDs) are essential parameters in determining their optoelectronic properties [1]. Many techniques have been used to study these parameters [2,3]. Among them, transmission electron microscopy (TEM) has been one of the most frequently used. It is well known that, under the usual dynamical two-beam or on-zone axis multibeam imaging conditions, the TEM diffraction contrast image arises largely from the strain field, which is sensitive to the composition, shape, size, and elastic constants of both the substrate and the QD. Consequently, it should be possible to obtain information about the composition, shape, and size of QDs from such images. However, to correctly interpret diffraction contrast images, image simulations are essential [2].Obtaining the strain field distribution within and around the QDs is necessary for image simulations. Finite element analysis (FEA) methods have been widely and successfully used to study the strain field of nanometer-size semiconductor QDs and applied to TEM investigations. For example, Christiansen et al. [4] used FEA to obtain the displacement field of Ge(Si) islands grown on Si. Using convergent beam electron diffraction, their study showed that the displacement field obtained in this way is correct. Rosenauer et al. [3] determined the composition profile of In x Ga 12x As QDs using high resolution TEM and FEA. Benabbas et al.[5] applied FEA to generate strain fields of InAs͞GaAs QDs, and they calculated two-beam dynamical electron diffraction contrast images to study their shape.In this study, we use three dimensional anisotropic FEA to generate strain field distributions of In x Ga 12x As QDs grown on (001) GaAs. We then use these strain field distributions in multibeam dynamical electron diffraction calculations to produce contrast simulations of [001] on-zone bright-field TEM images. An earlier study [6] showed that the [001] on-zone bright-field imaging can be used to estimate the size of the unburied QDs. Here, we show that indium composition plays a role in defining the boundary of the TEM image and in determining several of the image features. Both electron diffraction patterns and comparison of the simulated and experimental images show that the composition of the dots is different from the composition of the thin film alloy from which the QDs formed....

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“…A reason for this may be that the substrate in these regions is "softer," i.e., it allows larger elastic deflections of the Ge͞Si interface from the planar orientation providing a higher degree of the elastic relaxation in the islands. This suggestion is based on recent calculations which show that the elastic displacement fields originating from islands penetrate to substrate depths larger than the island heights [22]. Therefore, since the Si cap thickness in our case is smaller than the island heights, both the Si cap and underlying Si 0.8 Ge 0.2 alloy volumes are involved in the relaxation.…”

mentioning

confidence: 99%