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A measurement of electron-wall interactions using transmission diffraction from nanofabricated gratings
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10.1063/1.2357000
/content/aip/journal/jap/100/7/10.1063/1.2357000
http://aip.metastore.ingenta.com/content/aip/journal/jap/100/7/10.1063/1.2357000

Figures

Image of FIG. 1.
FIG. 1.

Nanofabricated period grating. Figure courtesy of Tim Savas.

Image of FIG. 2.
FIG. 2.

Geometry of the single slit theory. There are three axes, with depicting the incoherent slit plane, depicting the single slit plane, and depicting the detection plane. The distances between the planes are and . The dashed line is the zero point for the , , and variables. The dotted lines show a few of the possible straight paths that the electron can take. All phases that are accumulated along these paths are stored in the kernel. The position of the initial delta function indicates the location of the incoherent source.

Image of FIG. 3.
FIG. 3.

Cross sectional cut of the nanofabricated grating. The bevel angle of the slit is given by , the electron beam angle with respect to the grating is , the slit width is given as , and the grating thickness is given by .

Image of FIG. 4.
FIG. 4.

Illustration of the experimental setup. The electrons are created in the electron gun using a tungsten filament. The filament is floated at a negative voltage and the electrons are focused using several lenses. After leaving the source the electrons are collimated by 5 and slits. After traveling through the two collimation slits the electrons pass through a metallic coated nanofabricated grating, which can be moved into the beam with a vertical linear feedthrough. After passing through the diffraction grating the diffraction pattern is scanned by either moving a detection slit across the pattern or by rastering the electron beam with deflection plates. The electrons are then detected with an electron multiplier placed behind the detection slit.

Image of FIG. 5.
FIG. 5.

single slit diffraction, taken at . The dots represent the experimental data, and the solid lines represent the results of the path integral model including incoherent averaging over the first slit and convolution over the detection slit. The dashed line represents the Fraunhofer optical diffraction theory with a plane wave illumination of the single slit. The theory is normalized to the experimental data.

Image of FIG. 6.
FIG. 6.

single slit diffraction, taken at . The dots represent the experimental data, and the solid lines represent the results of the path integral model including incoherent averaging over the first slit and convolution over the detection slit. The dashed line represents the Fraunhofer optical diffraction theory with a plane wave illumination of the single slit. The theory is normalized to the experimental data.

Image of FIG. 7.
FIG. 7.

(Color online) Electron diffraction (a) at 900 and (b) . The diffraction patterns are on the left and the beam profiles with the gratings removed are on the right. The solid line is the path integral model with random potential, image charge, and incoherent source.

Image of FIG. 8.
FIG. 8.

Diffraction patterns taken at of grating tilt. Graph (a) is for , (b) is for , (c) is for , and (d) is for . These diffraction patterns taken at have approximately the largest asymmetries of all the tilt angles.

Image of FIG. 9.
FIG. 9.

(Color online) Rocking curves for . The electron transmission into a particular order is given as a function of grating tilt angle. Graph (a) is zeroth order, (b) is the first order, (c) is the second order, (d) is the third order, and (e) is the fourth order. The squares and circles are the +/− orders. The solid line is the model with image charge potential, random potential, and geometry of the grating included.

Image of FIG. 10.
FIG. 10.

(Color online) Rocking curves for . The electron transmission into a particular order is given as a function of grating tilt angle. Graph (a) is zeroth order, (b) is the first order, (c) is the second order, (d) is the third order, and (e) is the fourth order. The squares and circles are the +/− orders. The solid line is the model with image charge potential, random potential, and geometry of the grating included.

Image of FIG. 11.
FIG. 11.

(Color online) Rocking curves for third order. The electron transmission into the third order is given as a function of grating tilt angle. The solid circles are data. The solid line is the model with , the dotted line is with , and the dashed line is with .

Image of FIG. 12.
FIG. 12.

(Color online) Diffraction patterns at . The different coatings are (a) deposition of , (b) deposition of , (c) Ti, and (d) Ni. The open squares are the diffraction pattern, and the solid dots are the associated beam data. The left vertical scales are for the diffraction pattern counts and the right vertical scales are for the beam counts.

Image of FIG. 13.
FIG. 13.

(Color online) STM picture of the coated substrate. The lighter regions are protrusions on the substrate.

Image of FIG. 14.
FIG. 14.

Electron diffraction at . Both plus and minus orders are shown out to approximately 20th order.

Image of FIG. 15.
FIG. 15.

Electron beam diffraction. Electron diffraction from Ni coated gratings presented as a function of position for energies of (a) 125 and (b) . The beam profile without a diffraction grating is shown for comparison.

Tables

Generic image for table
Table I.

Broadening factors (BFs) as a function of different metallic coatings, at electron energy. The broadening factor is defined as , the ratio of the full width at half maximum of the diffraction peaks , over the full width at half maximum of the beam . The symbol denotes the open fraction of the grating which is defined as the slit width divided by the periodicity , where is .

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/content/aip/journal/jap/100/7/10.1063/1.2357000
2006-10-13
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A measurement of electron-wall interactions using transmission diffraction from nanofabricated gratings
http://aip.metastore.ingenta.com/content/aip/journal/jap/100/7/10.1063/1.2357000
10.1063/1.2357000
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