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X-ray stress measurements with synchrotron radiation
278
Nuclear
Instruments
and Methods
m Physics Research
A308 (1991) 278-281 North-Holland
Photoelectron yield excited by an X-ray standing wave with synchrotron radiation: energy-dispersive measurements with a magnetic analyzer A.M. Nikolaenko,
M.V. Kovalchuk,
Inmtute of Ctystallography,
Academy
AS. Semiletov
and Yu.N. Shilin
of Scrences of the USSR, Moscow, USSR
E. Michel and G. Materlik HAS YLA B, Hamburg,
Germany
A magnetic solenoldal detector smtable for synchrotron HASYLAB. An energy calibration and energy resolution standmg wave measurements were made for GaAs crystal.
rachatlon was constructed and tested were determined by measurmg spectra
1. Introduction
Energy analysis of photoelectrons considerably expands the possibilities of methods based on the registration of photoemission signals. This applies also to the photoelectron modification of the X-ray standing wave method. The use of synchrotron radiation (SR) in addition to the change of the beam energy makes measurements on anomalous dispersion possible. In previous studies, energy-dispersive photoelectron yield measurements were made using SR [l]. A nondestructive depthselective structure analysis was performed on nearsurface layers of monocrystals. However, the main problem appeared to be the construction of an electron analyzer with enough energy resolution in a wide range of incident beam energy. Two types of dispersive analyzers of electrons are used: magnetic and electrostatic, i.e. the selection of electrons on energy occurs correspondingly in magnetic or electrostatic fields. A dispersive analyzer focuses at one point those electrons which have equal kinetic energies. Magnetic analyzers are preferable to electrostatic ones in the region of high kinetic energies (5 keV and more) for two reasons: Firstly, it is difficult to create and to conserve the field with the required parameters. Secondly, optical systems for the deflection of relativistic electrons are better developed for magnetic fields than for electrostatic fields. Magnetic and electrostatic analyzers have comparable energy resolutions and main characteristics. There is also the problem of the compensation of the external magnetic field that surrounds the analyzer. The main question is the energy resolution, although it does not depend only on the analyzer. One should take into account the intensity 0168-9002/91/$03.50
0 1991 - Elsevler Science Publishers
at an experimental statIon at from various samples. X-ray
of the emitted electrons and that the resolution depends on the angle between the direction of movement of the electron and the direction of the magnetic field and also, naturally, on the size of the electron source. Therefore, such factors as resolution and intensity are in contradiction. From the point of view of the simplicity of construction, the range of electron kmetic energies (l-10 keV) and the possibility of working with conventional X-ray tubes and SR, a magnetic analyzer of the solenoidal type was chosen.
2. Formulae The proposed method for determining photoemission is based on the well-known principle that the focusing of electrons with a specific energy by a homogeneous axially symmetric magnetic field is characterized by a specific value of the induction [2]. Selection of electrons in the energy region of interest to us was ensured by selecting a suitable value of ths magnetic induction, which in turn was governed by the current flowing through the solenoid. The aperture placed inside the vacuum chamber was then “transparent” only to electrons of the selected energy. Here we present some formulae that can help to make a proper choice for the parameters of the analyzer. The trajectory of each electron in accordance with the system of equations that describe the movement of electrons in a magnetic field is a spiral of radius [2] P = (P,/&)
B.V. All rights reserved
sin 0,
A.M. Nlkolaenko
279
et al. / Photoelectron yreld by an X-ray standing wave
The magnetic field in the solenoid is connected current in it in accordance with the equation
where E, = m,c2, e is the charge of the electron, c the velocity of light and p the radius of the solenoid. Thus one can estimate the parameters of the analyzer from these equations. For our case, if we have an electron energy up to 10 keV, we need a magnetic field of about 10e2 T. For a distance between the source and the channeltron of 200 mm and a slit in the diaphragm of 1 mm (see fig. 1) the transparancy ~111 be - 1% and the resolution 5%.
Tt.0Pump Fig. 1 The scheme of the magnetic tron radlatlon
analyzer. beam.
with the
SR 1s the synchro-
3. Construction
where p0 is the impulse of the electron, B, the magnetic induction and 6 the angle between the directions of the electron movement and the magnetic field. The spiral step I is given by I = (2Tp,/B,e)
cos 0.
At the r, z plane the trajectory of the electron is a sinusoid with an amplitude r,,, = D sin 0 and a halfperiod ITD cos 0, where D = (I/a cos 0). In this plane the focusing of electrons occurs at an angle, the optimum angle being 45 O. The transparency of such a magnetic analyzer is G = (a/2) sin 0, where (Y is the angle of spread of the electron beam (emittance). The relationship between the resolution R and the transparancy G (if the source of electrons is a point) is R = 5G2.
A special magnetic solenoidal analyzer was constructed to perform energy-dispersive measurements of the photoelectron yield at the diffraction incident beam of synchrotron radiation. The analyzer had considerably smaller dimensions and weight compared to its analog [3,41. This analyzer conststs of two coaxial cylinders, one located within the other (fig. 1). The outer hollow cylinder is a solenoid comprising a rigorously fixed number of wire turns. This number and the wire diameter (- 0.7 mm) govern the maximum attainable magnetic field intensity. In our case a field of up to 10e2 T was enough to deflect electrons with kmetic energies up to 10 keV. The current in the solenoid was no more than 4 A. The time constant was about 3 ms. The internal cylinder (with the smaller diameter) represents the working vacuum chamber bounded by flanges at the
Fig. 2 The scheme of the expenment. SR - synchrotron radlatlon; 1 and 2 - crystals of the double-crystals plezodnver; C - capacity-type gauge; I, - lomzatlon chamber; NaI - X-ray detector.
monochromator;
IV. X-RAY
P2 -
DIFFRACTION
280
A M. Nlkolaenko
ef al. / Photoelectron yield by an X-ray standmg woe 10
ends: one of these flanges carried a holder for the mvestlgated crystal and tubes connected to a vacuum pump, whereas the other carried a channeltron for the detection of photoelectrons (diameter 8 mm) and electrical terminals. Inside this chamber was a ring-shaped aperture (size of the slit 1 mm) which is a component of the optical system of the analyzer. The vacuum chamber had two beryllium windows and the solenoid had two cuts to which the incident and dlffracted X-rays were transmitted. This allowed the experiment to be performed in Bragg geometry at angles of 0 to 30 o During the measurements the vacuum inside the chamber was lo-’ Pa.
. . . . . . . . . . . . . . . . . . . 7
6
$ S.
1
6
0-
0
1
Current
4. Results Fig. 4. Electron
As mentioned above, the analogous analyzer was tested with conventional X-ray tubes by an X-ray standing waves method in the case of external photoemlssion. Some possibilities of the analyzer were determined as an analyzer with an energy resolution of about 3-5%. The count rate was 0.1 counts/s. The modlficatlon of the analyzer suitable for SR was tested at the ROM01 station at HASYLAB. The scheme of the experiment is shown in fig. 2. A double-crystal monochromator was used to change the beam energy from 9 to 18 keV. Spectra from GaAs were measured at different energies (fig. 3) to determine an energy calibration for the analyzer (fig. 4) and its resolution. From fig. 4 one can see that the analyzer has a linear dependence in the electron energy region from 2 to 10 keV. By measuring spectra from vanous samples (Ge, Si, GaAs and InAs), the energy resolution of the analyzer was determined. It corresponds to the energy resolution obtained in the
3
2
energy vs current
4
(A) m the magnetic
analyzer.
experiments with conventional X-ray tubes, which indlcates that the analyzer 1s suitable for work with SR sources. The resolution of the analyzer 1s determined by the size of the diaphragm and the width of the entrance slit to the channeltron. With the parameters mentioned above, the resolution was about 5%. The experimental evaluation of the transparency of the analyzer was made in the following way. The channeltron was situated near the sample and the counts were measured without a diaphragm. Then, with the diaphragm in its normal position, the counts were measured again. The ratio of the second value to the first was about 1%. It corresponds to the evaluation of the transparency from geometry considerations. With the help of the magnetic
x
R
2
2
1
Current Fig. 3. GaAs
spectra taken at different bottom
3
(A)
photon energes. to top: E = 13, 15 and 17 keV.
From
Fig. 5 Rocking cwve R and photoelectron yield K vs angle @ from GaAs taken at a photon energy E =15 keV; (0) photoelectron curve mostly from Ga atoms, (0) photoelectron curve mostly from As atoms and ( + ) rockmg curve.
A M N~kolaenko et al / Photoelectron yeld by an X-ray srandq
analyzer, X-ray standing wave measurements were made for the GaAs crystal near the absorptron edges. The same experiment was carried out previously without an energy analysis [S] and with an energy analysts of low resolutron [l]. In our case tt is possible to select a signal preferably form Ga or As atoms (see fig. 3, E = 15 keV) and In thts way from the measurements of the photoelectron yteld one can determine the polarity of the crystal on one plate. An example of the measurements of the photoelectron yield excited by X-ray standing waves at a photon energy of 15 keV is shown in fig. 5. One can see a clear difference in the behaviour of curves as a function of the angular posttion of the crystal near the Bragg angle.
5. Conclusion The use of the magnetic analyzer for electrons havmg energies from 2 to 10 keV with the XRSW method should make it possible to extend greatly the possibili-
waue
ties of the depth-selecttve waves.
281
technique
of standing
X-ray
Acknowledgement
One of us (A.M.N.) would like to thank the Alexander von Humboldt Foundation for financial support. References
[II M.J. Bedzyk, G. Materhk
and M.V Kovalchuk, Phya. Rev. B30 (1984) 4881. PI I.G. Kozlov, Modern Problems m Electron Spectroscopy (Atomlzdat, Moscow, 1978) m Russian. [31 M.V. Kovalchuk and AS. Semdetov. Sov. Phys. Solid State 28 (1986) 311. A.S. Semi[41 M.V. Kovalchuk, V.G. Kohn. A.M. Nlkolaenko, letov and I.Yu. Kharltonov, Sov. Phys. Crystallogr 34 (1989) 615. and S. Klkuta, J. Phys. Sot. Jpn. 47 (1979) [I T. Takahashl 620
IV. X-RAY
DIFFRACTION
Nuclear
Instruments
and Methods
m Physics Research
A308 (1991) 278-281 North-Holland
Photoelectron yield excited by an X-ray standing wave with synchrotron radiation: energy-dispersive measurements with a magnetic analyzer A.M. Nikolaenko,
M.V. Kovalchuk,
Inmtute of Ctystallography,
Academy
AS. Semiletov
and Yu.N. Shilin
of Scrences of the USSR, Moscow, USSR
E. Michel and G. Materlik HAS YLA B, Hamburg,
Germany
A magnetic solenoldal detector smtable for synchrotron HASYLAB. An energy calibration and energy resolution standmg wave measurements were made for GaAs crystal.
rachatlon was constructed and tested were determined by measurmg spectra
1. Introduction
Energy analysis of photoelectrons considerably expands the possibilities of methods based on the registration of photoemission signals. This applies also to the photoelectron modification of the X-ray standing wave method. The use of synchrotron radiation (SR) in addition to the change of the beam energy makes measurements on anomalous dispersion possible. In previous studies, energy-dispersive photoelectron yield measurements were made using SR [l]. A nondestructive depthselective structure analysis was performed on nearsurface layers of monocrystals. However, the main problem appeared to be the construction of an electron analyzer with enough energy resolution in a wide range of incident beam energy. Two types of dispersive analyzers of electrons are used: magnetic and electrostatic, i.e. the selection of electrons on energy occurs correspondingly in magnetic or electrostatic fields. A dispersive analyzer focuses at one point those electrons which have equal kinetic energies. Magnetic analyzers are preferable to electrostatic ones in the region of high kinetic energies (5 keV and more) for two reasons: Firstly, it is difficult to create and to conserve the field with the required parameters. Secondly, optical systems for the deflection of relativistic electrons are better developed for magnetic fields than for electrostatic fields. Magnetic and electrostatic analyzers have comparable energy resolutions and main characteristics. There is also the problem of the compensation of the external magnetic field that surrounds the analyzer. The main question is the energy resolution, although it does not depend only on the analyzer. One should take into account the intensity 0168-9002/91/$03.50
0 1991 - Elsevler Science Publishers
at an experimental statIon at from various samples. X-ray
of the emitted electrons and that the resolution depends on the angle between the direction of movement of the electron and the direction of the magnetic field and also, naturally, on the size of the electron source. Therefore, such factors as resolution and intensity are in contradiction. From the point of view of the simplicity of construction, the range of electron kmetic energies (l-10 keV) and the possibility of working with conventional X-ray tubes and SR, a magnetic analyzer of the solenoidal type was chosen.
2. Formulae The proposed method for determining photoemission is based on the well-known principle that the focusing of electrons with a specific energy by a homogeneous axially symmetric magnetic field is characterized by a specific value of the induction [2]. Selection of electrons in the energy region of interest to us was ensured by selecting a suitable value of ths magnetic induction, which in turn was governed by the current flowing through the solenoid. The aperture placed inside the vacuum chamber was then “transparent” only to electrons of the selected energy. Here we present some formulae that can help to make a proper choice for the parameters of the analyzer. The trajectory of each electron in accordance with the system of equations that describe the movement of electrons in a magnetic field is a spiral of radius [2] P = (P,/&)
B.V. All rights reserved
sin 0,
A.M. Nlkolaenko
279
et al. / Photoelectron yreld by an X-ray standing wave
The magnetic field in the solenoid is connected current in it in accordance with the equation
where E, = m,c2, e is the charge of the electron, c the velocity of light and p the radius of the solenoid. Thus one can estimate the parameters of the analyzer from these equations. For our case, if we have an electron energy up to 10 keV, we need a magnetic field of about 10e2 T. For a distance between the source and the channeltron of 200 mm and a slit in the diaphragm of 1 mm (see fig. 1) the transparancy ~111 be - 1% and the resolution 5%.
Tt.0Pump Fig. 1 The scheme of the magnetic tron radlatlon
analyzer. beam.
with the
SR 1s the synchro-
3. Construction
where p0 is the impulse of the electron, B, the magnetic induction and 6 the angle between the directions of the electron movement and the magnetic field. The spiral step I is given by I = (2Tp,/B,e)
cos 0.
At the r, z plane the trajectory of the electron is a sinusoid with an amplitude r,,, = D sin 0 and a halfperiod ITD cos 0, where D = (I/a cos 0). In this plane the focusing of electrons occurs at an angle, the optimum angle being 45 O. The transparency of such a magnetic analyzer is G = (a/2) sin 0, where (Y is the angle of spread of the electron beam (emittance). The relationship between the resolution R and the transparancy G (if the source of electrons is a point) is R = 5G2.
A special magnetic solenoidal analyzer was constructed to perform energy-dispersive measurements of the photoelectron yield at the diffraction incident beam of synchrotron radiation. The analyzer had considerably smaller dimensions and weight compared to its analog [3,41. This analyzer conststs of two coaxial cylinders, one located within the other (fig. 1). The outer hollow cylinder is a solenoid comprising a rigorously fixed number of wire turns. This number and the wire diameter (- 0.7 mm) govern the maximum attainable magnetic field intensity. In our case a field of up to 10e2 T was enough to deflect electrons with kmetic energies up to 10 keV. The current in the solenoid was no more than 4 A. The time constant was about 3 ms. The internal cylinder (with the smaller diameter) represents the working vacuum chamber bounded by flanges at the
Fig. 2 The scheme of the expenment. SR - synchrotron radlatlon; 1 and 2 - crystals of the double-crystals plezodnver; C - capacity-type gauge; I, - lomzatlon chamber; NaI - X-ray detector.
monochromator;
IV. X-RAY
P2 -
DIFFRACTION
280
A M. Nlkolaenko
ef al. / Photoelectron yield by an X-ray standmg woe 10
ends: one of these flanges carried a holder for the mvestlgated crystal and tubes connected to a vacuum pump, whereas the other carried a channeltron for the detection of photoelectrons (diameter 8 mm) and electrical terminals. Inside this chamber was a ring-shaped aperture (size of the slit 1 mm) which is a component of the optical system of the analyzer. The vacuum chamber had two beryllium windows and the solenoid had two cuts to which the incident and dlffracted X-rays were transmitted. This allowed the experiment to be performed in Bragg geometry at angles of 0 to 30 o During the measurements the vacuum inside the chamber was lo-’ Pa.
. . . . . . . . . . . . . . . . . . . 7
6
$ S.
1
6
0-
0
1
Current
4. Results Fig. 4. Electron
As mentioned above, the analogous analyzer was tested with conventional X-ray tubes by an X-ray standing waves method in the case of external photoemlssion. Some possibilities of the analyzer were determined as an analyzer with an energy resolution of about 3-5%. The count rate was 0.1 counts/s. The modlficatlon of the analyzer suitable for SR was tested at the ROM01 station at HASYLAB. The scheme of the experiment is shown in fig. 2. A double-crystal monochromator was used to change the beam energy from 9 to 18 keV. Spectra from GaAs were measured at different energies (fig. 3) to determine an energy calibration for the analyzer (fig. 4) and its resolution. From fig. 4 one can see that the analyzer has a linear dependence in the electron energy region from 2 to 10 keV. By measuring spectra from vanous samples (Ge, Si, GaAs and InAs), the energy resolution of the analyzer was determined. It corresponds to the energy resolution obtained in the
3
2
energy vs current
4
(A) m the magnetic
analyzer.
experiments with conventional X-ray tubes, which indlcates that the analyzer 1s suitable for work with SR sources. The resolution of the analyzer 1s determined by the size of the diaphragm and the width of the entrance slit to the channeltron. With the parameters mentioned above, the resolution was about 5%. The experimental evaluation of the transparency of the analyzer was made in the following way. The channeltron was situated near the sample and the counts were measured without a diaphragm. Then, with the diaphragm in its normal position, the counts were measured again. The ratio of the second value to the first was about 1%. It corresponds to the evaluation of the transparency from geometry considerations. With the help of the magnetic
x
R
2
2
1
Current Fig. 3. GaAs
spectra taken at different bottom
3
(A)
photon energes. to top: E = 13, 15 and 17 keV.
From
Fig. 5 Rocking cwve R and photoelectron yield K vs angle @ from GaAs taken at a photon energy E =15 keV; (0) photoelectron curve mostly from Ga atoms, (0) photoelectron curve mostly from As atoms and ( + ) rockmg curve.
A M N~kolaenko et al / Photoelectron yeld by an X-ray srandq
analyzer, X-ray standing wave measurements were made for the GaAs crystal near the absorptron edges. The same experiment was carried out previously without an energy analysis [S] and with an energy analysts of low resolutron [l]. In our case tt is possible to select a signal preferably form Ga or As atoms (see fig. 3, E = 15 keV) and In thts way from the measurements of the photoelectron yteld one can determine the polarity of the crystal on one plate. An example of the measurements of the photoelectron yield excited by X-ray standing waves at a photon energy of 15 keV is shown in fig. 5. One can see a clear difference in the behaviour of curves as a function of the angular posttion of the crystal near the Bragg angle.
5. Conclusion The use of the magnetic analyzer for electrons havmg energies from 2 to 10 keV with the XRSW method should make it possible to extend greatly the possibili-
waue
ties of the depth-selecttve waves.
281
technique
of standing
X-ray
Acknowledgement
One of us (A.M.N.) would like to thank the Alexander von Humboldt Foundation for financial support. References
[II M.J. Bedzyk, G. Materhk
and M.V Kovalchuk, Phya. Rev. B30 (1984) 4881. PI I.G. Kozlov, Modern Problems m Electron Spectroscopy (Atomlzdat, Moscow, 1978) m Russian. [31 M.V. Kovalchuk and AS. Semdetov. Sov. Phys. Solid State 28 (1986) 311. A.S. Semi[41 M.V. Kovalchuk, V.G. Kohn. A.M. Nlkolaenko, letov and I.Yu. Kharltonov, Sov. Phys. Crystallogr 34 (1989) 615. and S. Klkuta, J. Phys. Sot. Jpn. 47 (1979) [I T. Takahashl 620
IV. X-RAY
DIFFRACTION