Activation energy of diffusion determined from a single in-situ neutron reflectometry experiment

Hüger, Erwin; Stahn, Jochen; Schmidt, Harald

doi:10.1080/21663831.2022.2114814

Cited by 4 publications

(27 citation statements)

References 48 publications

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“…As discussed above, eq can be used to approximately calculate the activation energy and the prefactor for small diffusion times (small range of temperatures). Figure shows the variation of the integrated and normalized intensity of the Bragg peak of the experimental data with the annealing time less than 3500 s. It is evident that the integrated and normalized intensity of the Bragg peak is nearly a linear function of the annealing time. According to eq and the experimental data shown in Figure , the term of t 2 in eq is thus negligible.…”

Section: Discussionmentioning

confidence: 99%

“…Using linear-regression fitting to fit the experimental data in Figure , we obtain a slope of −8.6 × 10 –6 s –1 , i.e., χ(593 K) = −8.6 × 10 –6 s –1 , which is comparable to −6.5 × 10 –6 s –1 obtained from eq with D 0 = 19.95 × 10 –4 m 2 /s and Q = 2.20 eV. Note that the numerical values of D 0 = 19.95 × 10 –4 m 2 /s and Q = 2.20 eV fall in the ranges of D 0 = 1.55 –1.3 +18.4 × 10 –4 m 2 /s and Q = 2.29 –0.15 +0.17 eV given by Hüger et al…”

Section: Discussionmentioning

confidence: 99%

“…Introducing a nominal diffusion time of eq , the logarithm of the temporal variation of the intensity of the X-ray peak or Bragg peak for a multilayer structure under continuous heating with a constant heating rate is found to be a linear function of the nominal diffusion time if the diffusion mechanism remains the same for the temperature range under investigation. The experimental results given by Hüger et al support the linear relationship used to determine the activation energy for the diffusion in multilayer structures. From this relationship, a simple method is proposed for the determination of the activation energy of the diffusion in multilayer structures under a small annealing time.…”

Section: Discussionmentioning

confidence: 99%

“…Developing a simple polynomial formulation would make it readily to determine the activation energy from the temporal evolution of the intensity of the Bragg peak. Also, Huger et al 55 and Schmidt et al 37 did not provide detailed information on the derivation of eq 2 theoretically as well as any numerical calculation of the concentration evolution during the diffusion annealing of a multilayer structure.…”

Section: ■ Introductionmentioning

confidence: 99%

“…The multi-isothermal annealing for the determination of the activation energy of atomic motion is timeconsuming and can last more than several hours. 49 To substantially reduce the time needed in the measurement of the temperature dependence of atomic diffusion, Huger et al 55 introduced the concept of increasing temperature at a constant rate in-situ NR measurements for the determination of the temperature dependence of atomic diffusion in solids. They have demonstrated the feasibility of this method in the study of atomic diffusion in amorphous 73 Ge/ nat Ge multilayers.…”

Section: ■ Introductionmentioning

confidence: 99%

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Analysis of the Diffusion in a Multilayer Structure under a Constant Heating Rate: The Calculation of Activation Energy from the In Situ Neutron Reflectometry Measurement

2023

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Understanding mass transport in micro- and nanostructures is of paramount importance in improving the performance and reliability of the micro- and nanostructures. In this work, we solve the diffusion problem in a multilayer structure with periodic conditions under a constant heating rate via a Fourier series. Analytical relation is established between the coefficients of eigenfunctions and the intensity of X-ray or neutron Bragg peak. The logarithm of temporal variation of the intensity of X-ray or neutron Bragg peak is a linear function of the nominal diffusion time, with the nominal diffusion time being dependent on the heating rate. This linear relation is validated by experimental data. The Taylor series expansion of the linear relation to the first order of the diffusion time yields an approximately linear relation between the logarithm of temporal variation of the intensity of X-ray or neutron peak and the diffusion time for small diffusion times, which can be likely used to calculate the activation energy for the diffusion in a multilayer structure. The validation of such an approach is subjected to the fact that the characteristic time for heat conduction is much less than the characteristic time for the ramp heating as well as the characteristic time for diffusion.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

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Analysis of the Diffusion in a Multilayer Structure under a Constant Heating Rate: The Calculation of Activation Energy from the In Situ Neutron Reflectometry Measurement

2023

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Self-Diffusion of Ge in Amorphous Ge_xSi_1–x Films Studied In Situ by Neutron Reflectometry

Hüger,

Stahn,

Schmidt

2024

ACS Mater. Au

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Ge x Si 1−x alloys are gaining renewed interest for many applications in electronics and optics, especially for miniaturized devices showing quantum size effects. Point defects and atomic diffusion play a crucial role in miniaturized and metastable systems. In the present work, Ge self-diffusion in sputter deposited amorphous Ge x Si 1−x alloys is studied in situ as a function of Ge content x = 0.13, 0.43, 0.8, and 1.0 by neutron reflectometry. The determined Ge selfdiffusivities obey the Arrhenius law in the investigated temperature ranges. The higher the Ge content x, the higher the Ge self-diffusivity at the same temperature. The activation enthalpy decreases with x from 4.4 eV for self-diffusion in pure silicon films to about 2 eV selfdiffusion in Ge 0.8 Si 0.2 and Ge. The decrease of the activation enthalpy for amorphous Ge x Si 1−x is similar to the case of crystalline Ge x Si 1−x . Possible explanations are discussed.

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In-situ Neutron Reflectometry to Determine Ge Self-Diffusivities and Activation Energy of Diffusion in Amorphous Ge_0.8Si_0.2

Hüger,

Stahn,

Schmidt

2023

EPJ Web Conf.

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Amorphous Ge-Si solid solutions are an interesting class of materials from the fundamental as well as the technological point of view. Self-diffusion of the constituents is an important process because of the inherent metastability. While self-diffusion was already examined in crystalline GexSi1-x (0 < x <1) this is not the case for the amorphous counterparts. This work reports on Ge self-diffusivities obtained from insitu neutron reflectometry measurements during isothermal annealing of ion-beam sputter-deposited amorphous Ge0.8Si0.2 films. The diffusivities are modified peculiarly fast with annealing time by a maximum factor of two due to structural relaxation. The diffusivities in the relaxed state are lower (higher) than in amorphous germanium (silicon). They follow the Arrhenius law and show an activation energy of (2.06 ± 0.1) eV, which equals that of amorphous germanium, but differs from that of amorphous silicon. Thus, it is concluded that the diffusion mechanism of Ge in amorphous Ge0.8Si0.2 and Ge are similar, despite of the presence of dispersed 20 at.% of Si.

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Activation energy of diffusion determined from a single in-situ neutron reflectometry experiment

Cited by 4 publications

References 48 publications

Analysis of the Diffusion in a Multilayer Structure under a Constant Heating Rate: The Calculation of Activation Energy from the In Situ Neutron Reflectometry Measurement

Analysis of the Diffusion in a Multilayer Structure under a Constant Heating Rate: The Calculation of Activation Energy from the In Situ Neutron Reflectometry Measurement

Self-Diffusion of Ge in Amorphous Ge_xSi_1–x Films Studied In Situ by Neutron Reflectometry

In-situ Neutron Reflectometry to Determine Ge Self-Diffusivities and Activation Energy of Diffusion in Amorphous Ge_0.8Si_0.2

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Activation energy of diffusion determined from a single in-situ neutron reflectometry experiment

Cited by 4 publications

References 48 publications

Analysis of the Diffusion in a Multilayer Structure under a Constant Heating Rate: The Calculation of Activation Energy from the In Situ Neutron Reflectometry Measurement

Analysis of the Diffusion in a Multilayer Structure under a Constant Heating Rate: The Calculation of Activation Energy from the In Situ Neutron Reflectometry Measurement

Self-Diffusion of Ge in Amorphous GexSi1–x Films Studied In Situ by Neutron Reflectometry

In-situ Neutron Reflectometry to Determine Ge Self-Diffusivities and Activation Energy of Diffusion in Amorphous Ge0.8Si0.2

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Product

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About

Self-Diffusion of Ge in Amorphous Ge_xSi_1–x Films Studied In Situ by Neutron Reflectometry

In-situ Neutron Reflectometry to Determine Ge Self-Diffusivities and Activation Energy of Diffusion in Amorphous Ge_0.8Si_0.2