28Si Crystals Research Articles

Atom probe tomography investigation of highly-enriched 28Si crystal

As part of the Avogadro constant re-determination, the molar mass of a highly-enriched 28Si crystal is being determined using various mass-spectrometry techniques. These calculations rely on the silicon material having high chemical purity, which has been initially assessed by infrared spectrometry. APT is uniquely suited to assess isotopic purity and distribution within a sample, thus ensuring the homogeneity required for precise measurements. In this study, Atom Probe Tomography (APT) is employed to further investigate isotopic composition and elemental purity within the mono-isotopically highly-enriched 28Si crystal (AVO28) and ultra-highly-enriched 28Si (UHP) and contrasted with natural silicon isotopes samples (WASO04, PSM, and SRM990). Reliable silicon isotope ratios are obtained from standard samples through a data processing procedure which utilizes automated mass ranging, background and deadtime corrections. The 29Si/28Si isotope ratios for WASO04, PSM and SRM990 agree with published values. AVO28 and UHP analysis reveals no impurities detected above 2 µg/g, with a uniform distribution of 28Si and 29Si at the nanometer scale. AVO28 exhibits 29Si content of 41 ± 2 µg/g, with no detection of 30Si below 2 µg/g, consistent with SIMS and other international comparisons. This work demonstrates APT’s capability for impurity detection and high-precision isotope analysis, reinforcing the silicon molar mass calculations and supporting Avogadro’s constant redefinition.

Molar mass measurement of a 28Si-enriched silicon crystal with high precision secondary ion mass spectrometry (SIMS)

Several highly-enriched 28Si crystals were produced to enable a better determination of the Avogadro constant through removing the uncertainty associated with the abundance determination of the minor isotopes 29Si and 30Si.

Measurement of miscut angles in the determination of Si lattice parameters

The measurement of the angle between an interferometer’s front mirror and the diffracting planes is a critical aspect of the measurement of Si lattice parameters by combined x-ray and optical interferometry. In addition to being measured offline by x-ray diffraction, it was checked online by moving the analyser crystal transversely and observing the phase shift of the interference fringe. We describe the measurement procedure and give the miscut angle of the 28Si crystal, whose lattice parameter was an essential input datum for the determination of the Avogadro constant in the past and which is now used in the definition of the kilogram, based on counting atoms. These data will benefit others that might wish to repeat the measurement of the lattice parameters of this unique crystal.

Determination of Defect Concentrations in ²⁸Si Crystals Using EPR for the Realization of the Kilogram

To realize the kilogram using the X-ray crystal density method, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">28</sup> Si crystals grown by the floating zone method were employed. Samples cut from two <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">28</sup> Si crystals, the AVO28 crystal (Si28-10Pr11 crystal) and the Si28-23Pr11 crystal, were analyzed by means of an electron paramagnetic resonance (EPR) spectroscopy. The samples were prepared by mirror polishing and subsequent etching using tetramethylammonium hydroxide (TMAH) solution. TMAH etching eliminates signals from the mechanically damaged surface layers of amorphous silicon and allows for the observation of small signals from vacancy defects in bulk crystals. In the study, the signal level of the vacancy defects was below the detection limit of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1 \times 10^{12}$ </tex-math></inline-formula> cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{-3}$ </tex-math></inline-formula> , and the amount of vacancy correction required to realize the kilogram was estimated to be 0.00(23) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{g}$ </tex-math></inline-formula> for both <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">28</sup> Si crystals. Therefore, it was concluded that the 39(21) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{g}$ </tex-math></inline-formula> inconsistency between the kilogram realizations achieved using the two <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">28</sup> Si crystals reported thus far cannot be explained by the existence of vacancy defects that are EPR active in the dark or under illumination.

Volume determination of two spheres of the new 28Si crystal of PTB

In the scope of the redetermination of Avogadro’s constant NA, a new isotopically enriched silicon crystal has been produced, from which two spheres were manufactured. After the crystal properties, the lattice parameter and molar mass, as well as the masses of the two spheres have been determined, the volume of the spheres was also measured. For this, the sphere interferometer of PTB was used. The methods of the interferometric measurements have been improved and the major contributions to the uncertainty have been investigated thoroughly. As a result, the total uncertainty could be reduced significantly, yielding a substantial impact on the determination of Avogadro’s constant. The mean diameter of each sphere was measured twice with a repeatability of ±2 × 10−10, and the relative uncertainty of the ‘apparent’ volume, which disregards the comparatively small influence of the optical effects of surface layers, was reduced to 7 × 10−9. The final results of the volumes and comments on their uncertainties are given.

Deep carrier traps in as grown isotopically pure 28Si FZ crystal

We studied a distribution of dopants and carrier traps in the FZ grown 28Si crystal. Samples cut‐out from various parts of an as‐grown crystal were analysed by deep level transient spectroscopy (DLTS) and photoluminescence (PL). Several traps were detected at the concentration level of ∼1010 cm−3 by DLTS. Careful analyses of the obtained signals allow attributing the related traps to agglomerates of intrinsic defects. A correlation of the trap concentration to the phosphorus doping, detected by PL and confirmed by electric measurements was also observed. A possible attribution of the traps to the previously reported defects will be discussed.

Storing quantum information for 30 seconds in a nanoelectronic device.

The spin of an electron or a nucleus in a semiconductor naturally implements the unit of quantum information--the qubit. In addition, because semiconductors are currently used in the electronics industry, developing qubits in semiconductors would be a promising route to realize scalable quantum information devices. The solid-state environment, however, may provide deleterious interactions between the qubit and the nuclear spins of surrounding atoms, or charge and spin fluctuations arising from defects in oxides and interfaces. For materials such as silicon, enrichment of the spin-zero (28)Si isotope drastically reduces spin-bath decoherence. Experiments on bulk spin ensembles in (28)Si crystals have indeed demonstrated extraordinary coherence times. However, it remained unclear whether these would persist at the single-spin level, in gated nanostructures near amorphous interfaces. Here, we present the coherent operation of individual (31)P electron and nuclear spin qubits in a top-gated nanostructure, fabricated on an isotopically engineered (28)Si substrate. The (31)P nuclear spin sets the new benchmark coherence time (>30 s with Carr-Purcell-Meiboom-Gill (CPMG) sequence) of any single qubit in the solid state and reaches >99.99% control fidelity. The electron spin CPMG coherence time exceeds 0.5 s, and detailed noise spectroscopy indicates that--contrary to widespread belief--it is not limited by the proximity to an interface. Instead, decoherence is probably dominated by thermal and magnetic noise external to the device, and is thus amenable to further improvement.

Revision of the SI: The Determination of the Avogadro Constant as the Base for the Kilogram

At least four units of the International System of Units (SI) are on the way to a new definition. Especially for the unit of mass, the kilogram, a rigorous change is considered. Instead of the current definition, a 1kg-artifact in form of a Pt-Ir-cylinder, the intended formulation relates the unit of mass to a fundamental constant. In detail this requires in a first step a measurement of the chosen fundamental constant with contemporary lowest uncertainty and best reproducibility. The constant will then be fixed to that value. As an example the metre is related to the fixed constant speed of light.For the kg there are considered two ways: one is a watt balance, which determines the mass in units of the Planck constant, h. While at present the watt balances show a heterogeneous appearance, the second class of experiment the determination of the Avogadro constant, NA, which measures the mass in terms of the number of elementary entities has reached a considerable level of uncertainty and reproducibility. The fundament of the new determination of the Avogadro constant is a highly enriched 28Si crystal. The different working groups of the Avogadro team determine molar mass and lattice parameter of the crystal, and mass and volume of two precision spheres made from different positions, but of the same crystal. All measurements are carried out for both spheres and all measurement quantities are determined at least from two independent working groups, usually of different countries.

TOWARD THE REDEFINITION OF THE KILOGRAM FROM THE 28Si INTERNATIONAL RESEARCH PROJECT

In the international system of units, the kilogram in the only SI base unit still defined by a material artefact. In order to redefine this unit with a fundamental physical constant, an international research project was launched in 2004 for determining the Avogadro constant, NA, by counting the atoms in an isotopically enriched 28Si crystal. The counting procedure relies on the measurements of the molar and atomic volumes of 1 kg spheres made of the 28Si crystal. In 2011, the project succeeded in measuring the Avogadro constant with a smallest standard uncertainty, 3.0 × 10−8 NA. Because of an unexpected metallic contamination at the surface of the spheres, the measurement uncertainty was larger than the target of the project by a factor of 1.5. In order to further reduce the uncertainty, a new international research project was launched in 2012. Outline of the new project and the improvements of the measurements will be introduced at the forum. Note from Publisher: This article contains the abstract only.

The new kilogram definition based on counting the atoms in a 28Si crystal

The kilogram is the only unit of measure still defined by a physical object. Now, a marathon effort to tie the kilogram to a constant of nature is nearing the finish line. This paper concerns an international research project aimed at determining the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The counting procedure was based on the measurement of the molar volume and the volume of an atom in two 1 kg crystal spheres. The novelty was the use of isotope dilution mass spectrometry as a new and very accurate method for the determination of the molar mass of enriched silicon. Because of an unexpected metallic contamination of the sphere surfaces, the relative measurement uncertainty, , results were larger by a factor 1.5 than that targeted. The measured value of the Avogadro constant, mol–1 is the most accurate input datum for the kilogram redefinition and differs only by from the CODATA 2010 adjusted value. This value is midway between the watt-balance values.

Elemental characterization of the Avogadro silicon crystal WASO 04 by neutron activation analysis

Impurity measurements of the 28Si crystal used for the determination of the Avogadro constant are essential to prevent biased results or underestimated uncertainties. A review of the existing data confirmed the high purity of silicon with respect to a large number of elements. In order to obtain direct evidence of purity, we developed a relative analytical method based on neutron activation. As a preliminary test, this method was applied to a sample of the Avogadro natural silicon crystal WASO 04. The investigation concerned 29 elements. The mass fraction of Au was quantified to be (1.03 ± 0.18) × 10−12. For the remaining 28 elements, the mass fractions were below the detection limits, which ranged between 1 × 10−12 and 1 × 10−5.

Density Comparison of Isotopically Purified Silicon Single Crystals by the Pressure-of-Flotation Method

An isotopically purified silicon crystal has recently been synthesized to enable the Avogadro constant to be determined more accurately. To perform new density comparison measurement by the pressure-of-flotation method, the effective compressibility of a liquid is reevaluated. Density comparison measurement is performed for purified 28Si crystals, and the relative density difference of Avo28-S5 and Avo28-S8 28Si spheres is evaluated.

Measurement of the {2 2 0} lattice-plane spacing of a 28Si x-ray interferometer

The spacing of the {2 2 0} lattice planes of a 28Si crystal, used to determine the Avogadro constant by counting silicon atoms, was measured by combined x-ray and optical interferometry to a relative accuracy of 3.5 × 10−9. The result is d2 2 0 = (192 014 712.67 ± 0.67) am, at 20.0 °C and 0 Pa. This value is greater by (1.9464 ± 0.0067) × 10−6d2 2 0 than the spacing in natural Si, a difference which confirms quantum-mechanics calculations. This result is a key step towards a realization of the mass unit based on a conventional value of the Planck or the Avogadro constant.

Counting the atoms in a 28Si crystal for a new kilogram definition

This paper concerns an international research project aimed at determining the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The counting procedure was based on the measurement of the molar volume and the volume of an atom in two 1 kg crystal spheres. The novelty was the use of isotope dilution mass spectrometry as a new and very accurate method for the determination of the molar mass of enriched silicon. Because of an unexpected metallic contamination of the sphere surfaces, the relative measurement uncertainty, 3 × 10−8 NA, is larger by a factor 1.5 than that targeted. The measured value of the Avogadro constant, NA = 6.022 140 82(18) × 1023 mol−1, is the most accurate input datum for the kilogram redefinition and differs by 16 × 10−8 NA from the CODATA 2006 adjusted value. This value is midway between the NIST and NPL watt-balance values.

Oxide Layer Mass Determination at the Silicon Sphere of the Avogadro Project

Within the International Avogadro Project, two spheres of highly enriched 28Si crystals have been produced to perform new determination of Avogadro constant NA. The mass of the oxide layer of the spheres has to be measured as one of the critical tasks. For this purpose, a method consisting of precise thickness measurements and density determinations is proposed and tested. Part of this procedure is the thermal oxidation of the Si spheres to produce a SiO2 layer with a well-defined structure and stoichiometry. Consecutively, its thickness is determined by a combination of X-ray reflectometry (XRR) for absolute thickness determination and spectral ellipsometry for mapping. Starting with the analysis of the assumed uncertainty budget, the allowed uncertainties of each part of the procedure were estimated to realize the required uncertainty in an oxide layer mass of 10 mug. The measurements at the test spheres have been carried out to show that an uncertainty of u(d) = 0.1 nm for the thickness measurements directly at the silicon spheres can be achieved, e.g., the thickness of the SiO2 layer at the PTB-01 sphere at a (100) lattice plane has been determined to be d = 6.2(1) nm. The second major part of the procedure described in this paper is the determination of the density of the oxide layer of the sphere by pressure of floatation at an additional test sphere. A value of rho = 2228(18) kg/m3 has been determined and confirmed in a remeasurement, with the resulting value of rho = 2223(15) kg/m3.

High Purity Isotopically Enriched 29Si and 30Si Single Crystals: Isotope Separation, Purification, and Growth

We report the successful isotope separation and bulk single crystal growth of 29Si and 30Si stable isotopes. The isotopic enrichments of the 29Si and 30Si single crystals determined by mass spectrometry are 99.23% and 99.74%, respectively. Both crystals have the electrically active net-impurity concentration less than 1015 cm-3. Thanks to the result of this work and the 28Si crystals we grew previously, high quality single crystals of every stable Si isotope (28Si, 29Si, and 30Si) have been made available for a wide variety of basic research and industrial applications.

Impurity absorption spectroscopy in 28Si: the importance of inhomogeneous isotope broadening.

We report high-resolution infrared absorption spectra of the neutral donors phosphorus and lithium, and the neutral acceptor boron, in isotopically pure 28Si crystals. Surprisingly, many of the transitions are much sharper than previously reported in natural Si. In particular, the 2p(0) line of phosphorus in 28Si has a full width at half maximum of only 4.2 microeV, about 5 times less than the narrowest 2p(0) line previously reported for natural Si, making it the narrowest shallow impurity transition yet observed. The widely held assumptions that the impurity transitions previously reported in high quality samples of natural Si revealed the true, homogeneous linewidths, are thus shown to be incorrect. The sharper transitions in 28Si also reveal new substructures in the boron and lithium spectra.

Anomalous isotopic effect on the lattice parameter of silicon.

The difference Delta(a)=a(30)-a(28) of the lattice parameter of 30Si and 28Si crystals is measured over a temperature range from 4.7 to 700 K. In disagreement with existing knowledge, the strongest isotopic effect is not detected at the lowest achieved temperature T=4.7 K. An anomalous behavior is observed: The relative difference |Delta(a)/a| attains its maximum value of 56.8(5) ppm at T=75(10) K. The anomalous behavior is attributed to the influence of phonon modes with negative Grüneisen parameters. At T=700 K the effect still amounts to 30% of the maximal value. The experimental data are consistent with an approach based on the density-functional perturbation theory.

Simulations and comparisons of channeling spectra in the p+ 28Si system in the backscattering geometry

Energy spectra of protons channeling along the 〈1 1 1〉 plane of a 28Si crystal in the energy region E p=1.7–2.4 MeV in a backscattering geometry were taken and analyzed. Computer simulations based on the assumption that the dechanneling of protons follows an exponential law are in excellent agreement with the measured spectra. Differences between the 〈1 0 0〉 and the 〈1 1 1〉 axis in the silicon crystal and their subsequent effect on the stopping power of channeled protons are described.