We discuss the optical analogy of reflected electron diffraction from a grating with non-uniform spacing at the nanoscale, and its relationship to another grating with uniform spacing. Two analytical approaches that offer a quantitative solution for the reflected diffraction from a grating are presented. A compact and low-cost experimental kit for demonstrating the physics behind the reflected diffraction from one-dimensional surface structures is described. As an example, the convolution theorem is used to explain the reflected diffraction from a sample consisting of two individual one-dimensional surface structures overlapping orthogonally. This study will broaden students' understanding of the physics behind diffraction.
References
1.
2.
Louis
de Broglie
, “Researches on the quantum theory
,” Ann. Phys.
3
(10
), 22
–128
(1925
).3.
R.
Eisberg
and R.
Resnick
, Quantum Physics: Of Atoms, Molecules, Solids, Nuclei, and Particles
, 2nd ed. (Wiley
, Hoboken, New Jersey
, 1985
).4.
C. J.
Davisson
and L. H.
Germer
, “Reflection of electrons by a crystal of nickel
,” Proc. Natl. Acad. Sci. U. S. A.
14
(4
), 317
–322
(1928
).5.
G.
Wang
, S. K.
Lok
, S. K.
Chan
, C.
Wang
, G. K. L.
Wong
, and I. K.
Sou
, “The formation of an aligned 1D nanostructure on annealed Fe/ZnSe bilayers
,” Nanotechnology
20
, 215607
(2009
).6.
S.
Hasegawa
, “Reflection high-energy electron diffraction
,” Charact. Mater.
3
, 1925
–1938
(2012
).7.
R.
Paschotta
, Encyclopedia of Laser Physics and Technology
, 1st ed. (Wiley-VCH
, Weinheim, German
, 2008
).8.
P. P.
Ewald
, “Introduction to the dynamical theory of X-ray diffraction
,” Acta Crystallogr., Sect. A
25
, 103
–108
(1969
).9.
C.
Kittel
, “Wave diffraction and the reciprocal lattice
,” Introduction to Solid State Physics
, 8th ed. (Wiley
, Hoboken, NJ
, 2004
), Chap. 2.10.
Y. L.
Loh
, “The Ewald sphere construction for radiation, scattering, and diffraction
,” Am. J. Phys.
85
(4
), 277
–288
(2017
).11.
“HKUST eBookshelf-APhO Proceeding 2016,” <http://ebookshelf.ust.hk/flippingbook/G16928/>.
12.
G.
Arfken
, “Convolution theorem
,” Mathematical Methods for Physicists
, 3rd ed. (Academic Press
, Orlando, FL
, 1985
), Chap. 15.13.
See supplementary material at http://dx.doi.org/10.1119/1.5043291 for the detailed and more quantitative description of Ewald's construction and a real-life example of the diffraction phenomenon being studied here in a transmission geometry.
© 2018 American Association of Physics Teachers.
2018
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
