Electron spectrometer calibration method
The present invention concerns an energy dispersion calibration method for calibrating an electron spectrometer of an electron spectrometer system including at least one electron emission source, electron optics and the electron spectrometer. The method comprising: obtaining, providing or receiving at least one electron energy loss spectrum produced by electrons of the electron spectrometer system exchanging energy with at least one resonant optical mode of an optical resonator into which light at a resonant wavelength is coupled; calculating or providing a Fourier transform of the at least one electron energy loss spectrum or a part of the at least one electron energy loss spectrum; determining or providing an energy dispersion (ΔE) of the electron spectrometer according to the equation Δ E = f E hc λ N or Δ E = f E E p N .
1 . An energy dispersion calibration method for calibrating an electron spectrometer of an electron spectrometer system including at least one electron emission source, electron optics and the electron spectrometer, the electron spectrometer system being configured to produce an electron energy spectrum electrons received by the electron spectrometer, the election energy spectrum including a plurality of channels defining an electron energy range the electron energy spectrum, the method comprising:
providing an optical resonator configured to exchange energy with the electrons of the electron spectrometer system;
obtaining, using the electron spectrometer, at least one electron energy loss spectrum produced by electrons of the electron spectrometer system exchanging energy with at least one resonant optical mode of the optical resonator into which light at a resonant wavelength is coupled;
calculating a Fourier transform of the at least one electron energy loss spectrum or a part of the at least one electron energy loss spectrum;
determining an energy dispersion ΔE of the electron spectrometer according to the equation
Δ
E
=
f
E
hc
λ
N
or
Δ
E
=
f
E
E
p
N
where λ is the resonant wavelength of the light coupled into the optical resonator, h is Planck's constant, c is the speed of light in vacuum, E p is the resonant photon energy of the light coupled into the optical resonator, N is the number of channels or data points along an energy axis of the at least one electron energy loss spectrum used in determining the Fourier transform of the at least one electron energy loss spectrum or a part thereof, and f E is the number of reciprocal energy space data points or coordinates between (i) a DC spectral component peak of the Fourier transform of the at least one electron energy loss spectrum or a part thereof and (ii) a sideband peak or a center of a sideband peak of the Fourier transform (FT) of the at least one electron energy loss spectrum or a part thereof, the sideband peak originating from electron energy exchange with the at least one resonant optical mode of the optical resonator, the determined energy dispersion ΔE defining an incremental energy value of the plurality of channels defining the election energy range of the election energy spectrum or an incremental energy value of a subset of the plurality of channels used to calculate the Fourier transform of the part of the at least one electron energy loss spectrum; and
using the determined energy dispersion ΔE to provide calibrated electron energy spectrum when the electron spectrometer system is used to perform electron spectroscopy.
2 . The energy dispersion calibration method according to claim 1 , wherein the center of the sideband peak is determined by fitting the sideband peak with a peak fitting function, the center of the sideband peak being determined to be the center of the peak of the fitted peak fitting function.
3 . The energy dispersion calibration method according to claim 1 , further including determining or providing an accuracy or error value SAE of the energy dispersion AE determined according to the equation
δΔ
E
=
(
δ
f
E
f
E
)
2
+
(
δλ
λ
)
2
·
Δ
E
where ΔE is the energy dispersion,
δλ is an accuracy or error value of the wavelength value or wavelength measurement of the resonant wavelength of the light coupled into the optical resonator λ, and
δf E is an accuracy or error value of a determined center of the side peak f E of the Fourier transform of the at least one electron energy loss spectrum or a part thereof.
4 . The energy dispersion calibration method according to claim 3 , wherein the accuracy or error value δf E of a determined position of a center of the side peak is determined as half of the width of a confidence interval of the mean value of the peak fitting function.
5 . The energy dispersion calibration method according to claim 4 , wherein the confidence interval is set to be between a 90% confidence interval and a 99% confidence interval.
6 . The energy dispersion calibration method according to claim 1 , further including determining spectrometer or system calibration nonlinearities by calculating or providing a Fourier transform of a plurality of spectral subsets or spectral windows of the at least one electron energy loss spectrum by displacing at least one spectral subset or spectral window across the at least one electron energy loss spectrum, and determining an energy dispersion AE of channels within each of the plurality of spectral subsets or spectral windows to determine an energy dispersion ΔE of a plurality of different regions across the channels of the electron spectrometer.
7 . The energy dispersion calibration method according to claim 6 , further including applying a nonlinearity calibration correction to the determined energy dispersion ΔE of the electron spectrometer, the calibration nonlinearity correction being based on the determined energy dispersion ΔE of the plurality of different regions across the channels of the electron spectrometer, the nonlinearity calibration correction including a calibration that compensates for nonlinearities of the system.
8 . The energy dispersion calibration method according to claim 1 , wherein the electron spectrometer system is set at a specific electron energy for exchanging energy between an electron and light propagating in the optical resonator.
9 . The energy dispersion calibration method according to claim 8 , wherein an electron velocity is matched with a phase velocity of the light resonating in the optical resonator.
10 . The energy dispersion calibration method according to claim 9 , wherein an alignment of the electron spectrometer system concentrates the electron beam in the vicinity of the optical resonator in which an optical power contained therein creates an electron energy loss spectrum containing a plurality of sideband peaks populating the entire range of the spectrometer energy scale to assure higher precision of dispersion calibration and determination of the spectrometer non-linearities.
11 . The energy dispersion calibration method according to claim 10 , wherein the electron spectrometer system comprises a transmission electron microscope.
12 . The energy dispersion calibration method according to claim 1 , further comprising providing an optical device holder configured to hold or holding the optical resonator.
13 . The energy dispersion calibration method according to claim 1 , further comprising providing a calibration device or system including the optical device holder configured to hold or holding the optical resonator, at least one optical waveguide configured to provide light to the optical resonator, an optical wavelength determiner and a resonance wavelength determiner configured to determine wavelength matching of light coupled to the optical resonator with a resonance wavelength or mode of the optical resonator.
14 . The energy dispersion calibration method according to claim 13 , further comprising providing at least one light source, at least one controller, at least one processor, and a computer program including program instructions, which when executed by the at least one processor cause the at least one controller to:
adjust a wavelength generated by the at least one light source,
monitor or process data or a signal representative of a light intensity signal provided to the optical resonator, and
identify or determine a decrease in the light intensity signal or a signature representing a reduction in the optical power representing a resonance condition at which a wavelength of light coupled to the optical resonator matches a resonance wavelength or mode of the optical resonator.
15 . The energy dispersion calibration method according to claim 1 , wherein the determined energy dispersion ΔE is used to modify a nominal energy dispersion value of the electron energy spectrum of the electron spectrometer to provide a recalibrated electron energy spectrum when the electron spectrometer system is used to perform electron spectroscopy.