1. 1 Finding missing Si atoms with Cu F. Spaepen, C.Y. Wen, J. Proost Harvard University C. Quétel, V. Aninkevicius, K. Filee, P. Taylor EC - JRC - IRMM

2. 2 How perfect are the Si crystals used for the determination of the Avogadro Constant ?

3. 3  4x10 -6 Do even the best float-zone Si crystals contain voids ? 4x10 -6 deficit, equivalent to 1.7 mm 3 /kg Si How perfect are all these crystals ?

4. 4 Experiments with Cu in Si

5. 5 Diffusion of Cu in Si Diffusivity Cu: fastest diffuser in Si moves interstitially through the lattice Solubility of Cu in Si Cu in solution is interstitial 10 ppb 550 o C

6. 6 Measuring the number of missing Si atoms Heat to 900 o C Saturate with Cu Cu source Cool at 1 K/min Excess Cu precipitates as silicide and fills up voids Clean off surface Cu Anneal at 400 o C Diffuse interstitial Cu to surface Clean off surface Cu Repeat previous step until interstial concentration is negligible Digest sample Determine number of Cu atoms

7. 7 Observing filling of the voids by transmission electron microscopy 200 nm Plan view Voids created by implantation ( 30 keV He 4 nuclei, 3 x 10 16 cm -2 ) and annealing ( 30 min at 700 o C ) of a Si wafer Wafer surface Cross-section All voids are filled with Cu-silicide after heat treatment and cooling

8. 8 Identification of the silicide Electron diffraction pattern [100] direction in the body-centered cubic structure Lattice parameter: 0.2854 nm Two atoms per unit cell, chemically disordered High-resolution electron micrograph showing the lattice planes in the silicide and the Si matrix Si  -Cu 5 Si

9. 9 Cu-Si phase diagram Anneal at 900 o C  -phase forms on cooling

10. 10 Quantitative determination of the amount of Cu in the precipitates and in solution: a challenge ! Very small amounts of Cu ==> minimize blank issues on Si digestion Use Isotope Dilution Mass Spectrometry (IDMS) ==> implement sound protocol at very low content level IRMM Ultra Clean Chemical Laboratory know-how on inorganic analytical chemistry at low level

11. 11 Application in the Avogadro project Boule Avogadro sphere Certify that all test samples have fewer that 10 ppb missing atoms