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. 2023 Jan 23;14(1):361.
doi: 10.1038/s41467-023-36090-2.

The kinetics of carbon pair formation in silicon prohibits reaching thermal equilibrium

Peter Deák  1 , Péter Udvarhelyi  1   2 , Gergő Thiering  1 , Adam Gali  3   4
Affiliations

The kinetics of carbon pair formation in silicon prohibits reaching thermal equilibrium

Peter Deák et al. Nat Commun. .

Abstract

Thermal equilibrium is reached when the system assumes its lowest energy. This can be hindered by kinetic reasons; however, it is a general assumption that the ground state can be eventually reached. Here, we show that this is not always necessarily the case. Carbon pairs in silicon have at least three different configurations, one of them (B-configuration) is the G photoluminescence centre. Experiments revealed a bistable nature with the A-configuration. Electronic structure calculations predicted that the C-configuration is the real ground state; however, no experimental evidence was found for its existence. Our calculations show that the formation of the A- and B-configurations is strongly favoured over the most stable C-configuration which cannot be realized in a detectable amount before the pair dissociates. Our results demonstrate that automatized search for complex defects consisting of only the thermodynamically most stable configurations may overlook key candidates for quantum technology applications.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Fig. 1
Fig. 1. Three configurations of carbon pair defects in silicon.
A, B, and C label the three configurations identified in prior studies. Brown and blues spheres are the carbon and silicon atoms, respectively. The figures are made by Crystal MakerTM.
Fig. 2
Fig. 2. Path for the formation of the A-configuration upon the encounter of a diffusing (C-Si)Si split interstitial and a CSi substitutional.
a initial state, b (near-)saddle-point configuration (c.f. Fig. 4), and c end state of the MEP calculation.
Fig. 3
Fig. 3. Path for the formation of the C-configuration upon the encounter of a diffusing (C–Si)Si split interstitial and a CSi substitutional.
a–f The calculated configurations along the reaction coordinate. Dashed lines indicate bonds in the breaking/forming, and are just guides to the eye.
Fig. 4
Fig. 4. The change of the total energy with respect to the initial state, as a function of the distance travelled by the C-interstitial when a (C–Si)Si split-interstitial approaches a CSi substitutional.
The curves are cubic spline fits, to guide the eye. a The formation of the neutral (red curve) and positive (blue curve) A-configuration. b The formation of the neutral C-configuration.
Fig. 5
Fig. 5. The change of the total energy during the transformation of the A-configuration into the C-configuration in the neutral (red curve) and in the positive (blue curve) charge state.
The configuration coordinate is the sum of the distances the interstitial carbon atom travels in the steps of the transformation.
Fig. 6
Fig. 6. The path of the transformation of the A-configuration into the C-configuration (c.f. Fig. 5).
Dashed lines indicate bonds in the breaking/forming, and are just guides to the eye. a The local minimum. b The saddle point. c The stationary state.
See this image and copyright information in PMC

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