Diffusion and solubility of copper, silver, and gold in germanium

Bracht, H.; Stolwijk, N. A.; Mehrer, H.

doi:10.1103/physrevb.43.14465

Cited by 108 publications

(94 citation statements)

References 29 publications

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“…However, vacancies are generally considered to prevail in Ge under thermal equilibrium conditions. This has been concluded from self-and foreign-atom diffusion studies 7,21,22,[27][28][29][30] and confirmed by atomistic calculations. 15,23,[30][31][32][33] In particular, the simultaneous diffusion of self-and dopant atoms in isotopically controlled Ge heterostructures have revealed that vacancies in Ge are mainly doubly negatively charged under intrinsic and n-type doping conditions.…”

Section: B Motivation Of Diffusion Model and Numerical Simulationsmentioning

confidence: 73%

Intrinsic and extrinsic diffusion of indium in germanium

Kube

Bracht

Chroneos

et al. 2009

Journal of Applied Physics

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Diffusion experiments with indium ͑In͒ in germanium ͑Ge͒ were performed in the temperature range between 550 and 900°C. Intrinsic and extrinsic doping levels were achieved by utilizing various implantation doses. Indium concentration profiles were recorded by means of secondary ion mass spectrometry and spreading resistance profiling. The observed concentration independent diffusion profiles are accurately described based on the vacancy mechanism with a singly negatively charged mobile In-vacancy complex. In accord with the experiment, the diffusion model predicts an effective In diffusion coefficient under extrinsic conditions that is a factor of 2 higher than under intrinsic conditions. The temperature dependence of intrinsic In diffusion yields an activation enthalpy of 3.51 eV and confirms earlier results of Dorner et al. ͓Z. Metallk. 73, 325 ͑1982͔͒. The value clearly exceeds the activation enthalpy of Ge self-diffusion and indicates that the attractive interaction between In and a vacancy does not extend to third nearest neighbor sites which confirms recent theoretical calculations. At low temperatures and high doping levels, the In profiles show an extended tail that could reflect an enhanced diffusion at the beginning of the annealing.

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Section: B Motivation Of Diffusion Model and Numerical Simulationsmentioning

confidence: 73%

Intrinsic and extrinsic diffusion of indium in germanium

Kube

Bracht

Chroneos

et al. 2009

Journal of Applied Physics

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“…The diffusion-reaction form of the Fick's second law has been successfully applied to impurity diffusion in elemental semiconductors -Si:(Au and Zn), Ge:(Co, Cu, Ag, and Au). [11][12][13][14][15][16][17] Before discussing the simulation results, two pertinent analytical solutions are reviewed. 11…”

Section: A General Formulationmentioning

confidence: 99%

“…Diffusion mechanisms are intimately related to the concentrations of intrinsic and extrinsic point defects and their diffusion coefficients. [11][12][13][14][15][16][17] This paper concerns the dissociative diffusion mechanism (alternatively known as the FrankTurnbull mechanism) -where an impurity atom rapidly travels through interstitial sites before reacting with a vacancy -in vacancy-rich materials. 17 Two cases are studied where 1) the impurity interstitial diffusion is sufficiently rapid that vacancies are practically immobile, and 2) impurity interstitial diffusion becomes exceedingly fast that the concentration of impurity atoms in interstitial sites are maintained at the equilibrium value everywhere at all times, leading to the case where vacancy diffusion is the slowest process.…”

Section: Introductionmentioning

confidence: 99%

Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics

et al. 2016

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Two sets of diffusion-reaction numerical simulations using a finite difference method (FDM) were conducted to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,Ga)Se2 (CIGS) and Cu2ZnSn(S, Se)4 (CZTSSe or CZTS) via the dissociative diffusion mechanism where the interstitial diffuser ultimately reacts with a vacancy to produce a substitutional. The first set of simulations extends the standard interstitial-limited dissociative diffusion theory to vacancy-rich material conditions where vacancies are annihilated in large amounts, introducing non-equilibrium vacancy concentration profiles. The second simulation set explores the vacancy-limited dissociative diffusion where impurity incorporation increases the equilibrium vacancy concentration. In addition to diffusion profiles of varying concentrations and shapes that were obtained in all simulations, some of the profiles can be fitted with the constant- and limited-source solutions of Fick’s second law despite the non-equilibrium condition induced by the interstitial-vacancy reaction. The first set of simulations reveals that the dissociative diffusion coefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. In the second set of numerical simulations, impurity-induced changes in the vacancy concentration lead to distinctive diffusion profile shapes. The simulation results are also compared with published data of impurity diffusion in CIGS. According to the characteristic properties of diffusion profiles from the two set of simulations, experimental detection of the dissociative diffusion mechanism in vacancy-rich materials may be possible.

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“…In Ge metals such as gold (Au) and silver (Ag) diffuse via the dissociative mechanism [9][10][11]. In the dissociative mechanism, proposed by Frank and Turnbull [11] there is a requirement for vacancies (V) that excange position with the dopant intersititials (D i ) to form a dopant substitutional to a Ge site (D Ge ) via the relation D i þ V $ D Ge .…”

Section: Introductionmentioning

confidence: 99%

“…Exceptions include copper (Cu), palladium (Pd), Au and Ag (refer to [43] and references therein). Au [10,[44][45][46] and Ag [47,48] diffusion in Ge has been investigated for about six decades. Figure 1 Fig.…”

Section: Introductionmentioning

confidence: 99%

Gold and silver diffusion in germanium: a thermodynamic approach

Panayiotatos

Вовк

Chroneos

2016

J Mater Sci: Mater Electron

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Diffusion properties are technologically important in the understanding of semiconductors for the efficent formation of defined nanoelectronic devices. In the present study we employ experimental data to show that bulk materials properties (elastic and expansivity data) can be used to describe gold and silver diffusion in germanium for a wide temperature range (702-1177 K). Here we show that the so-called cBX model thermodynamic model, which assumes that the defect Gibbs energy is proportional to the isothermal bulk modulus and the mean volume per atom, adequately metallic diffusion in germanium.

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Diffusion and solubility of copper, silver, and gold in germanium

Cited by 108 publications

References 29 publications

Intrinsic and extrinsic diffusion of indium in germanium

Intrinsic and extrinsic diffusion of indium in germanium

Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics

Gold and silver diffusion in germanium: a thermodynamic approach

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