Large-scale production of highly enriched²⁸Si for the precise determination of the Avogadro constant

Abstract

An attempt is described to replace the present definition of the kilogram with the mass of a certain number of silicon atoms. A prerequisite for this is that the Avogadro constant, N A , is determined with a relative uncertainty of better than 2 × 10 −8. For the determination, silicon crystals are used. However, the difficulty arising thereby is the measurement of the average molar mass of natural Si. Consequently, a worldwide collaboration has been launched to produce approximately a 5 kg 28 Si single crystal with an enrichment factor greater than 99.985% and of sufficient chemical purity so that it can be used to determine N A with the targeted relative measurement uncertainty mentioned above. In the following, the first successful tests of all technological steps will be reported (enrichment of SiF 4 , distillation into silane and chemical purification, chemical vapour deposition of polycrystalline 28 Si, floating zone growth of a dislocation-free single crystal) and new equipment for the production of high-purity 28 Si with an enrichment of not less than 99.99% will be described. All steps are well defined by a Technical Road Map (TRM28) and all key results are measured by new mass spectrometric, IR spectroscopic and other chemical and physical methods, such as Hall effect, photoluminescence, laser scattering and x-ray topographic methods (TRM for Analytical Monitoring and Certification, TRM28-AMC). The initial enrichment of the gas is >0.999 95 and the depletion during the entire process is <0.000 05. The isotopic homogeneity is checked by natural Si crystal growth and does, in the enriched sphere, not

Isotope engineering of silicon and diamond for quantum computing and sensing applications

“…The electrons bound to the phosphorus donors mediate the 31 P-31 P nuclear spin interactions between the adjacent qubits. The nuclear spin state for each 31 P qubit is read out at the end of the calculation by detecting the single-electron tunneling current using a single-electron transistor (SET). Kane's vision has triggered many proposals that use the electron spins in donors imbedded in silicon as qubits.…”

“…[31,32] The silicon crystals fabricated for the Avogadro measurement were shaped into precise spheres and the sawn-off pieces generated during the shaping process were used to perform basic characterization on the crystal. Some pieces were also used in some of the silicon quantum information research described below.…”

“…Additionally, the mass difference between the stable isotopes changes the bond lengths (the local lattice strain), leading to perturbation of the hyperfine interactions between the electron spin and the 31 P nuclear spin in each phosphorus atom. This could lead to a shift in the NMR frequencies of the 31 P between different donors, making each phosphorus atom distinguishable and the ensemble of phosphorus donors would not be able to be manipulated all together. Moreover, there was a random distribution of 29 Si that changes the local magnetic field near each phosphorus donor.…”

Impurity absorption spectroscopy of the deep double donor sulfur in isotopically enriched silicon

“…The 28Si material used for this study was obtained from the Avogadro Project [23], an effort to redefine the kilogram in terms of the Avogadro constant. This material had previously proven to be of excellent quality [24,25], both in terms of isotopic enrichment as well as chemical purity.…”

Realization of the kilogram by the XRCD method

“…In order to overcome this bottleneck in the determination of N A , isotope enrichment of Si was undertaken [17]. The International Avogadro Coordination (IAC) project was launched in 2004 to reduce the uncertainty in N A using a crystal highly enriched in 28 Si.…”