Progress and Application on the Measurement Technique of Single Crystal Silicon Lattice Spacing

Abstract

Abstract: Lattice spacing of single crystal silicon is the fundamental of measurement of some physical constants. In this paper, the progress of the silicon lattice spacing measurement technique is introduced, including X-ray interferometer for direct measurement and lattice comparator for indirect measurement, and the key factor affecting the uncertainty of lattice spacing measurement are discussed. Due to the development of silicon lattice spacing measurement, the Si lattice spacing is used as a secondary realization of the definition of the metre at nanoscale, approved by BIPM. At last, the application of lattice measurement in metrology and research trends of the traceability system for nano dimension metrology based on the lattice are introduced.

Key words: single crystal silicon, lattice spacing, X-ray interferometer, lattice comparator, nano metrology

CLC Number:

O734
TB383

LI Wei, SHI Yushu, LI Qi, HUANG Lu, LI Shi, GAO Sitian. Progress and Application on the Measurement Technique of Single Crystal Silicon Lattice Spacing[J]. Journal of Synthetic Crystals, 2021, 50(1): 151-157.

References

[1] ANDREAS B, Y AZUMA, G BARTL, et al. Counting the atoms in a ²⁸Si crystal for a new kilogram definition[J]. Metrologia, 2011, 48(2):S1-S3.
[2] WINDISCH D, BECKER P. Silicon lattice parameters as an absolute scale of length for high precision measurements of fundamental constants[J]. Physica Status Solidi (a), 1990, 118(2): 379-388.
[3] DESLATTES R D, HENINS A. X-ray to visible wavelength ratios[J]. Physical Review Letters, 1973, 31(16): 972.
[4] BECKER P, MANA G. The lattice parameter of silicon: a survey[J]. Metrologia, 1994, 31(3):203.
[5] BONSE U, HART M. An X-ray interferometer[J]. Applied Physics Letters, 1965, 6(8): 155-156.
[6] BECKER P, DORENWENDT K, EBELING G, et al. Absolute measurement of the (220) lattice plane spacing in a silicon crystal[J]. Physical Review Letters, 1981, 46(23):1540-1543.
[7] MASSA E, SASSO C P, MANA G, et al. A more accurate measurement of the ²⁸Si lattice parameter[J]. Journal of Physical & Chemical Reference Data, 2015, 44(3):680-365.
[8] SIEGERT H, BECKER P, SEYFRIED P. Determination of silicon unit cell parameters by precision measurements of Bragg plane spacings[J]. Zeitschrift Für Physik B Condensed Matter, 1984, 56(4): 273-278.
[9] KESSLER E G, HENINS A, DESLATTES R D, et al. Precision comparison of the lattice parameters of silicon monocrystals[J]. Journal of research of the National Institute of Standards and Technology, 1994, 99:1(1):1-18.
[10] BECKER, PETER. History and progress in the accurate determination of the Avogadro constant[J]. Reports on Progress in Physics, 2001, 64(12):1945.
[11] KESSLER E G, SZABO C I, CLINE J P, et al. The lattice spacing variability of intrinsic float-zone silicon[J]. Journal of Research of the National Institute of Standards and Technology, 2017, 122: 24.
[12] BECKER P, BETTIN H, DANZEBRINK H U, et al. Determination of the Avogadro constant via the silicon route[J]. Metrologia, 2003, 40(5):271.
[13] VAUDIN M D, KESSLER E G, OWEN D M. Precise silicon die curvature measurements using the NIST lattice comparator: comparisons with coherent gradient sensing interferometry[J]. Metrologia, 2011, 48(3):201-211.
[14] WINDOVER D, GIL D L, HENINS A, et al. NIST high resolution X-ray diffraction standard reference material:SRM 2000[J]. Powder Diffraction, 2009, 24(2):171-171.
[15] WASEDA A, FUJIMOTO H, ZHANG X W, et al. Homogeneity characterization of lattice spacing of silicon single crystals[J]. 29th Conference on Precision Electromagnetic Measurements (CPEM 2014), 2014: 400-401.
[16] Ferroglio L, Mana G, Massa E. Si lattice parameter measurement by centimeter X-ray interferometry[J]. Optics Express, 2008, 16(21):16877-16888.
[17] MASSA E, MANA G, KUETGENS U, et al. Measurement of the lattice parameter of a silicon crystal[J]. New Journal of Physics, 2009, 11(5): 053013.
[18] MARTIN J, KUETGENS U, STUMPEL J, et al. The silicon lattice parameter-an invariant quantity of nature?[J]. Metrologia, 2003, 35(6):811.
[19] DIMIEV A, KOSYNKIN D V, SINITSKII A, et al. Layer-by-layer removal of graphene for device patterning[J]. Science, 2011, 331(6021): 1168-1172.
[20] 罗志勇,王金涛,刘翔,等.阿伏加德罗常数测量与千克重新定义[J].计量学报,2018(3):377-380.
LUO Z Y, WANG J T, LIU X, et al. Avogadro constant determination and kilogram redefinition[J]. Acta Metrologica Sinica, 2018(3): 377-380(in Chinese).
[21] MASSA E, MANA G, KUETGENS U, et al. Measurement of the {220} lattice-plane spacing of a ²⁸Si X-ray interferometer[J]. Metrologia,2011, 48: S37-S43.
[22] BARTL G, BECKER P, BECKHOFF B, et al. A new ²⁸Si single crystal: counting the atoms for the new kilogram definition[J]. Metrologia, 2017, 54(5): 693-715.
[23] MOHR P J, TAYLOR B N, NEWELL D B. CODATA recommended values of the fundamental physical constants: 2006[EB/OL]. 2007: arXiv:0801.0028[physics.atom-ph]. https://arxiv.org/abs/0801.0028.
[24] PISANI M, YACOOT A, BALLING P, et al. Comparison of the performance of the next generation of optical interferometers[J]. Metrologia, 2012, 49(4): 455-467.
[25] 王林,曹芒,李达成.用于纳米测量的扫描X射线干涉技术[J].光学精密工程,1998,6(1):3-5.
WANG L, CAO M, LI D C. Scanning X ray interferometry for nanometer measurement[J]. Optics and Precision Engineering, 1998, 6(1): 3-5(in Chinese).
[26] YACOOT A, KUETGENS U, KOENDERS L, et al. A combined scanning tunneling microscope and X-ray interferometer[J]. Meas Sci Technol. 12001, 12: 1660-1665.
[27] TSAI V W, VORBURGER T, DIXSON R, et al. The study of silicon stepped surfaces as atomic force microscope calibration standards with a calibrated AFM at NIST[J]. AIP Conference Proceedings,1998, 449(1): 839.
[28] CRESSWELL M W, GUTHRIE W F, DIXSON R G, et al. RM 8111: development of a prototype linewidth standard[J]. Journal of Research of the National Institute of Standards and Technology, 2006, 111(3): 187-203.
[29] DAI G L, ZHU F, HEIDELMANN M, et al. Development and characterisation of a new line width reference material[J]. Measurement Science and Technology, 2015, 26(11): 115006.