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This paper provides a conceptual analysis of the role of the mathematical continuum versus the discrete in the understanding of randomness as a notion with a physical meaning or origin. The presentation is ‘informal’ as we will not write formulas; however, we will refer to non-obvious technical results from various scientific domains, and we will also propose a conceptual framework for understanding randomness (and predictability), which we believe is, essentially, original. As a matter of fact, unpredictability and randomness may be conveniently identified in various physico-mathematical contexts. This will allow us to explore these concepts in continuous versus discrete frameworks, with particular emphasis on the relationships and differences between classical approaches and quantum theories in Physics.
It is well known that diffusion of deuterium in boron-doped diamond results in the passivation of boron acceptors with the formation of (B,D) complexes. In this work, we show that deuteration of boron-doped diamond can induce a p-type to n-type conversion under certain conditions. The n-type conductivity is governed by the ionization of shallow donors with a ionization energy of 0.34 eV. This is well below the lowest ionization energy of donors found up to now in diamond (0.6 eV for phosphorus donors). The electrical conductivity and the electron mobility can be as high as 6 S/cm and 430 cm2/Vs at 300 K. The reversibility of the effect under thermal annealing and the necessity of excess deuterium to trigger the n-type conductivity suggest that deuterium is involved in the formation of the shallow donors. The present status concerning the understanding of their origin is discussed. In addition, we have found that, contrary to previous conclusions, deuterium can diffuse in type Ib diamond. The conditions where this diffusion is observed are presented.
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