- Email: [email protected]
Radiation from axially channeled 1-MeV electrons in germanium
Nuclear Instruments and Methods in Physics Research B33 (1988) 26-29
26
North-Holland, Amsterdam
RADIATION FROM AXIALLY CHANNELED l-MeV ELECTRONS IN GERMANIUM K. KOMAKI and F. FUJIMOTO College of Arts and Sciences, University of Tokyo, Komabq
hero-k~
Tokyo I53, Japan
Y. KAMIYA Toyota Technological Institute, Hisakata,
Tempaku-ky
Nagoya 468, Japan
Energy spectra of the channeling radiation from 0.8 and 1.0 MeV electrons channeled along the (111) axis of a germanium crystal were measured using a high voltage electron microscope attached with a gas flow proportional counter. Subtracting the yield of the Ge L X-rays and bremsstrahlung, the contribution of the channeling radiation was obtained. Peak energy of the radiation at 0.8 and 1.0 MeV and the incident angle dependence of the channeling radiation intensity are in good agreement with calculated ones.
1. Introduction Channeling radiation from relativistic electrons channeled along crystal axes or planes has been extensively investigated both theoretically and experimentally [l]. The energy range of the incident electrons extends from MeV to several hundred GeV and various types of accelerators have been utilized. In the case of low energy axial channeling, transverse motion of channeled electrons is represented by eigenstates indexed by azimuthal and radial quantum numbers. Individual transitions between them are observed as line spectra and photon energies are directly connected to the energy differences of the two states. Observed photon energies were in good agreement with calculated values and provided information on crystal potential shqpes or thermal vibration amplidtudes [2-51. The intensity of the spectral line is proportional to the transition probability and to the initial state population, which is closely related to the shape of the wave function. The observed incident angle dependence of the line intensities showed qualitative agreement with the population change of the initial states of the transitions [2,6]. In the present work, we report the energy spectra and incident angle dependence of the intensity of the channeling radiation measured using a high voltage electron microscope. Use of the electron microscope allows us to choose a small area of sample with various thicknesses and to vary easily such irradiation conditions as the beam position, beam size, beam divergence and incident angle. 0168-583X/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
2. Experimental procedure The experiment was performed using the HUlOOO electron microscope at Nagoya University operated at electron energies of 800 keV and 1 MeV. Fig. 1 shows a
Electron
Source
Condenser
Lens
Specimen Objective
Lens
Intermediate
LA'
Lens
Deflector Projective Fluorescent
Detector
Lens Screen
("r'7) !
f EJ
Fig. 1. Schematic drawing of experimental arrangement.
21
K. Komnki et al. / Axially channeled I MeV electrons
schematic of the apparatus. An electron beam accelerated up to 800 keV or 1 MeV was collimated by a condenser lens system to irradiate a sample with the desired degree of parallelness and beam size. Electrons transmitted through the sample were focussed by objective and intermediate lenses to form either microscopic images or selected area diffraction patterns on the fluorescent screen. A gas flow proportional counter was attached under the camera chamber of the microscope to measure the radiation spectra. The counter was operated with P-10 gas (90% argon and 10% methane) at the atmospheric pressure. The entrance window of the counter was a 1 pm thick polypropylene film. While measuring the photon spectra, the electron beam was deflected by 90“ with a magnetic deflector inserted under the intermediate lens. Energy calibration of the counter system was performed by using the Ge L X-rays. A (111) film of germanium was chemically etched and mounted on the conventional goniometer stage capable of two-axis rotation and two-dimensional translation. The irradiated area of the sample was restricted to 5 pm in diameter. The crystal orientation was controlled by observing the selected area diffraction pattern on the fluorescent screen. The thickness of the area irradiated was chosen to be about 0.4 pm by counting 15k 1 McV
cc
a
AXIS
.;...... .:. ..L..
Ge
800
1 1 BA OFF.. .
5k
.” ;
I
kc’4
;
i“” RANDOM
PHOTON
ENERGY (kc’41
Fig. 2. Energy spectra of emitted photons from 800 keV electrons at incident angles of 18, = 2.57 mrad (0) and 108, (x) relative to the (111) axis of germanium. + : contribution from Zp-1s channeling radiation.
the number of the extinction fringes from the edge of the wedge-shaped specimen. 3. Experimental
results
In fig. 2 is shown a photon spectrum obtained at 800 keV energy under the 220 Bragg reflection condition, 15k
tIn 5 8
Cc
I Me’/
1 BAOFF
b
~..~-.., ... IOk-
..
*... ... ‘..
.. .
-.....
. . . . . . . . k....‘.
-:.-
.. . .. .. . .. _..-
.: .. .
PHOTON
PHOTON
ENERGYlkeVl
ENERGY
IkeVI
15k Gc
I
McV
3
BAOFF
... -+.... . . . . . . . . . . . . . . . . . . . . . . C.
5k
...’.
“A.“’
...._/’ .&’ C
+..-“..,
_...5
I
-...* NE T -.+..__4
.-.~~..+.~
1.5 PHOTON
NET __4.y+.+~~.+...~_
. 2
2.5 ENERGY
_; v
3 IkcVl
PHOTON
ENERGY
2.5
3 Ike’41
Fig. 3. Energy spectra of emitted photons from 1 MeV electrons at incident angles of 0 (a), 1 (b, l), 3 (c), 6 (d) and 100, (b, X) with respect to the (111) axis of germanium (f?, = 2.18 mrad). + : contributions from 2p-1s channeling radiation. I. CRYSTAL
ASSISTED PROCESSES
28
K. Komaki et al. / Axially channeled 1 MeV electrons
that is, the incident beam is off axis by a Bragg angle, 8, = 2.57 mrad. A peak at about 1 keV is a superposition of the Ge L X-rays (1.18 keV), the channeling radiation from the 2p-1s transition (in the nl level identifier n is chosen to be greater than I) and background. Photon spectra measured at B = 108,, which consist of the Ge L X-rays and background, are also shown in fig. 2. The main source of the background is considered to be bremsstrahlung in the target. To obtain the channeling radiation contribution from these spectra, the following procedure was adopted. The spectrum for 108, was scaled to the other spectrum so that the high energy side of the peaks coincide with each other and then the scaled spectrum was subtracted from the latter. The resulting spectrum was regarded as the channeling radiation spectrum. The peak energy of the channeling radiation thus obtained was 880 eV. In the case of 1 MeV electrons, photon spectra were measured at incident angles of 0, 1, 3, 6 and 10 8, relative to the (111) axis. The 220 Bragg angle at this energy is 2.18 mrad. By the same procedure as in the case of 800 keV electrons, the channeling radiation spectra were reduced. Observed and reduced spectra are shown in fig. 3. The peak energy of the reduced spectrum was 990 eV. The intensity of the channeling radiation at each incident angle was determined as the counts under the peak in the reduced spectrum normalized to the live acquisition time. The results are shown by the closed circles in fig. 4.
2 2.5: ; 2B Y w 1.56 I: l-
.5t
‘0I
.2
.41
1.2I
INCIDENT
1.4
1.6
1.6
2I
ENERGYIMeVl
The two dimensional continuum potential U(r) was replaced by a muffin-tin potential, UM.,.(r), which is circularly symmetrical within half a distance to the neighboring string and is constant elsewhere. Introducing a single well potential, Usw( r), by extending the constant value of U,,(r) to infinity, the single well wave function q,,,(r) and eigenvalues enl were obtained by numerical integration of the radial wave equation for a single well potential, &w(r)
-Cz,)~nl(r)
=O.
For bound states, the Bloch state wave function qkn,( r) and energy E,,,(k) can be approximated by
4. Calculations Theoretical calculations were carried out using a tight-binding approximation, as described in ref. [3].
4,,,(r)
=+,,,(r)
Ge
and
E,,(k)
= enI.
The energy of photons emitted through nl to n’l’ transitions into the forward direction is given by Eni, = 2y2[E,z,(k)
0.12
I
.EI I
Fig. 5. Incident energy dependence of the photon energy of ) and observed (0). 2p-1s radiation, calculated (-
(T+
p
.6,
-E,/,,(k)],
where y is the Lorentz factor of the incident electron. Fig. 5 shows the photon energy for the 2p-1s transition as a function of the incident energy together with the experimental results. The population, P,,,( 0) of the nl band excited at the entrance of the crystal is given by
1 MeV
P,,(O)
= I G,(K@) I 2>
where K is the longitudinal wave number and
v OO
. 2 INCIDENT
4
6 ANGLE1220
I
6 BRAGG
10 ANGLE1
Fig. 4. Incident angle dependence of intensities of 2p-1s ) and observed (0). channeling radiation, calculated (Experimental points are normalized to the cakulation at tI = 0, = 2.18 mrad.
C,,(k)
= JZ-‘/‘/dr
eik’ ~&~[(r),
s2 being the area of the two-dimensional unit cell. Since the transition matrix element between bound states is almost independent of k, the incident angle dependence of the radiation intensity is identical to that of the initial state population. Numerical result for 2p level population is given in fig. 4.
K. Komaki et al. /Axially
5. Discussions The observed photon energies for the 2p-1s transition are in good agreement with the calculation. In the present experiment, a proportional counter was used to detect photons and consequently the energy resolution is not sufficient for more detailed discussions. Experiments with better resolution are in progress using a Si(Li) detector. The incident angle dependence of the radiation intensity also shows good agreement between observation and calculation. Though agreement is satisfactory, there remains room for improvement. Subtraction of the Ge L X-ray and bremsstrahlung contributions from the photon spectra is rather ambiguous especially in such case of poor energy resolution as the present case. In fact peak positon of the channeling radiation component showed considerable shift in cases of low channeling radiation intensity. This may be due to different incident angle dependence of the L X-rays and bremsstrahlung. Measurements with better energy resolution will provide unambiguous subtraction of characteristic X-rays. In the present experiment, the electron dose was determined from the acquisition time. Direct monitoring of the incident beam is desirable.
channeled I MeV electrons
29
6. Conclusions Channeling radiation emitted by the lowest energy electrons was observed in the case of the (111) axis of germanium using a high voltage electron microscope. Photon energy and incident angel dependence of the radiation intensity showed good agreement with calculations. Use of the electron microscope to observe the channeling radiation proved to be advantageous for sample preparation and beam condition adjustments. The authors would like to thank Drs. S. Fukui, N. Horikawa and T. Nakanishi and also C. Morita, I. Arai and T. Goto, Nagoya University. References [1] R. Wedell, Phys. Status Solidi B99 (1980) 11 and refs. therein. [2] J.U. Andersen and E. Lregsgaard, Phys. Rev. Lett. 44 (1980) 1079. [3] K. Komaki, F. Fujimoto and A. Ootuka, Nucl. Instr. and Meth. 194 (1982) 243. [4] J.U. Andersen, E. Bonderup, E. Laegsgaard, B.B. Marsh and A.H. Sorensen, Nucl. Instr. and Meth. 194 (1982) 209. [5] J.U. Andersen, E. Lregsgaard and A.H. Sorensen, Nucl. Instr. and Meth. B2 (1984) 63. [6] N. Cue, E. Bonderup, B.B. Marsh, H. Bakhru, R.E. Benenson, R. Haight, K. IngIis and G.O. Williams, Phys. Lett. 80A (1980) 26.
I. CRYSTAL
ASSISTED
PROCESSES
26
North-Holland, Amsterdam
RADIATION FROM AXIALLY CHANNELED l-MeV ELECTRONS IN GERMANIUM K. KOMAKI and F. FUJIMOTO College of Arts and Sciences, University of Tokyo, Komabq
hero-k~
Tokyo I53, Japan
Y. KAMIYA Toyota Technological Institute, Hisakata,
Tempaku-ky
Nagoya 468, Japan
Energy spectra of the channeling radiation from 0.8 and 1.0 MeV electrons channeled along the (111) axis of a germanium crystal were measured using a high voltage electron microscope attached with a gas flow proportional counter. Subtracting the yield of the Ge L X-rays and bremsstrahlung, the contribution of the channeling radiation was obtained. Peak energy of the radiation at 0.8 and 1.0 MeV and the incident angle dependence of the channeling radiation intensity are in good agreement with calculated ones.
1. Introduction Channeling radiation from relativistic electrons channeled along crystal axes or planes has been extensively investigated both theoretically and experimentally [l]. The energy range of the incident electrons extends from MeV to several hundred GeV and various types of accelerators have been utilized. In the case of low energy axial channeling, transverse motion of channeled electrons is represented by eigenstates indexed by azimuthal and radial quantum numbers. Individual transitions between them are observed as line spectra and photon energies are directly connected to the energy differences of the two states. Observed photon energies were in good agreement with calculated values and provided information on crystal potential shqpes or thermal vibration amplidtudes [2-51. The intensity of the spectral line is proportional to the transition probability and to the initial state population, which is closely related to the shape of the wave function. The observed incident angle dependence of the line intensities showed qualitative agreement with the population change of the initial states of the transitions [2,6]. In the present work, we report the energy spectra and incident angle dependence of the intensity of the channeling radiation measured using a high voltage electron microscope. Use of the electron microscope allows us to choose a small area of sample with various thicknesses and to vary easily such irradiation conditions as the beam position, beam size, beam divergence and incident angle. 0168-583X/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
2. Experimental procedure The experiment was performed using the HUlOOO electron microscope at Nagoya University operated at electron energies of 800 keV and 1 MeV. Fig. 1 shows a
Electron
Source
Condenser
Lens
Specimen Objective
Lens
Intermediate
LA'
Lens
Deflector Projective Fluorescent
Detector
Lens Screen
("r'7) !
f EJ
Fig. 1. Schematic drawing of experimental arrangement.
21
K. Komnki et al. / Axially channeled I MeV electrons
schematic of the apparatus. An electron beam accelerated up to 800 keV or 1 MeV was collimated by a condenser lens system to irradiate a sample with the desired degree of parallelness and beam size. Electrons transmitted through the sample were focussed by objective and intermediate lenses to form either microscopic images or selected area diffraction patterns on the fluorescent screen. A gas flow proportional counter was attached under the camera chamber of the microscope to measure the radiation spectra. The counter was operated with P-10 gas (90% argon and 10% methane) at the atmospheric pressure. The entrance window of the counter was a 1 pm thick polypropylene film. While measuring the photon spectra, the electron beam was deflected by 90“ with a magnetic deflector inserted under the intermediate lens. Energy calibration of the counter system was performed by using the Ge L X-rays. A (111) film of germanium was chemically etched and mounted on the conventional goniometer stage capable of two-axis rotation and two-dimensional translation. The irradiated area of the sample was restricted to 5 pm in diameter. The crystal orientation was controlled by observing the selected area diffraction pattern on the fluorescent screen. The thickness of the area irradiated was chosen to be about 0.4 pm by counting 15k 1 McV
cc
a
AXIS
.;...... .:. ..L..
Ge
800
1 1 BA OFF.. .
5k
.” ;
I
kc’4
;
i“” RANDOM
PHOTON
ENERGY (kc’41
Fig. 2. Energy spectra of emitted photons from 800 keV electrons at incident angles of 18, = 2.57 mrad (0) and 108, (x) relative to the (111) axis of germanium. + : contribution from Zp-1s channeling radiation.
the number of the extinction fringes from the edge of the wedge-shaped specimen. 3. Experimental
results
In fig. 2 is shown a photon spectrum obtained at 800 keV energy under the 220 Bragg reflection condition, 15k
tIn 5 8
Cc
I Me’/
1 BAOFF
b
~..~-.., ... IOk-
..
*... ... ‘..
.. .
-.....
. . . . . . . . k....‘.
-:.-
.. . .. .. . .. _..-
.: .. .
PHOTON
PHOTON
ENERGYlkeVl
ENERGY
IkeVI
15k Gc
I
McV
3
BAOFF
... -+.... . . . . . . . . . . . . . . . . . . . . . . C.
5k
...’.
“A.“’
...._/’ .&’ C
+..-“..,
_...5
I
-...* NE T -.+..__4
.-.~~..+.~
1.5 PHOTON
NET __4.y+.+~~.+...~_
. 2
2.5 ENERGY
_; v
3 IkcVl
PHOTON
ENERGY
2.5
3 Ike’41
Fig. 3. Energy spectra of emitted photons from 1 MeV electrons at incident angles of 0 (a), 1 (b, l), 3 (c), 6 (d) and 100, (b, X) with respect to the (111) axis of germanium (f?, = 2.18 mrad). + : contributions from 2p-1s channeling radiation. I. CRYSTAL
ASSISTED PROCESSES
28
K. Komaki et al. / Axially channeled 1 MeV electrons
that is, the incident beam is off axis by a Bragg angle, 8, = 2.57 mrad. A peak at about 1 keV is a superposition of the Ge L X-rays (1.18 keV), the channeling radiation from the 2p-1s transition (in the nl level identifier n is chosen to be greater than I) and background. Photon spectra measured at B = 108,, which consist of the Ge L X-rays and background, are also shown in fig. 2. The main source of the background is considered to be bremsstrahlung in the target. To obtain the channeling radiation contribution from these spectra, the following procedure was adopted. The spectrum for 108, was scaled to the other spectrum so that the high energy side of the peaks coincide with each other and then the scaled spectrum was subtracted from the latter. The resulting spectrum was regarded as the channeling radiation spectrum. The peak energy of the channeling radiation thus obtained was 880 eV. In the case of 1 MeV electrons, photon spectra were measured at incident angles of 0, 1, 3, 6 and 10 8, relative to the (111) axis. The 220 Bragg angle at this energy is 2.18 mrad. By the same procedure as in the case of 800 keV electrons, the channeling radiation spectra were reduced. Observed and reduced spectra are shown in fig. 3. The peak energy of the reduced spectrum was 990 eV. The intensity of the channeling radiation at each incident angle was determined as the counts under the peak in the reduced spectrum normalized to the live acquisition time. The results are shown by the closed circles in fig. 4.
2 2.5: ; 2B Y w 1.56 I: l-
.5t
‘0I
.2
.41
1.2I
INCIDENT
1.4
1.6
1.6
2I
ENERGYIMeVl
The two dimensional continuum potential U(r) was replaced by a muffin-tin potential, UM.,.(r), which is circularly symmetrical within half a distance to the neighboring string and is constant elsewhere. Introducing a single well potential, Usw( r), by extending the constant value of U,,(r) to infinity, the single well wave function q,,,(r) and eigenvalues enl were obtained by numerical integration of the radial wave equation for a single well potential, &w(r)
-Cz,)~nl(r)
=O.
For bound states, the Bloch state wave function qkn,( r) and energy E,,,(k) can be approximated by
4. Calculations Theoretical calculations were carried out using a tight-binding approximation, as described in ref. [3].
4,,,(r)
=+,,,(r)
Ge
and
E,,(k)
= enI.
The energy of photons emitted through nl to n’l’ transitions into the forward direction is given by Eni, = 2y2[E,z,(k)
0.12
I
.EI I
Fig. 5. Incident energy dependence of the photon energy of ) and observed (0). 2p-1s radiation, calculated (-
(T+
p
.6,
-E,/,,(k)],
where y is the Lorentz factor of the incident electron. Fig. 5 shows the photon energy for the 2p-1s transition as a function of the incident energy together with the experimental results. The population, P,,,( 0) of the nl band excited at the entrance of the crystal is given by
1 MeV
P,,(O)
= I G,(K@) I 2>
where K is the longitudinal wave number and
v OO
. 2 INCIDENT
4
6 ANGLE1220
I
6 BRAGG
10 ANGLE1
Fig. 4. Incident angle dependence of intensities of 2p-1s ) and observed (0). channeling radiation, calculated (Experimental points are normalized to the cakulation at tI = 0, = 2.18 mrad.
C,,(k)
= JZ-‘/‘/dr
eik’ ~&~[(r),
s2 being the area of the two-dimensional unit cell. Since the transition matrix element between bound states is almost independent of k, the incident angle dependence of the radiation intensity is identical to that of the initial state population. Numerical result for 2p level population is given in fig. 4.
K. Komaki et al. /Axially
5. Discussions The observed photon energies for the 2p-1s transition are in good agreement with the calculation. In the present experiment, a proportional counter was used to detect photons and consequently the energy resolution is not sufficient for more detailed discussions. Experiments with better resolution are in progress using a Si(Li) detector. The incident angle dependence of the radiation intensity also shows good agreement between observation and calculation. Though agreement is satisfactory, there remains room for improvement. Subtraction of the Ge L X-ray and bremsstrahlung contributions from the photon spectra is rather ambiguous especially in such case of poor energy resolution as the present case. In fact peak positon of the channeling radiation component showed considerable shift in cases of low channeling radiation intensity. This may be due to different incident angle dependence of the L X-rays and bremsstrahlung. Measurements with better energy resolution will provide unambiguous subtraction of characteristic X-rays. In the present experiment, the electron dose was determined from the acquisition time. Direct monitoring of the incident beam is desirable.
channeled I MeV electrons
29
6. Conclusions Channeling radiation emitted by the lowest energy electrons was observed in the case of the (111) axis of germanium using a high voltage electron microscope. Photon energy and incident angel dependence of the radiation intensity showed good agreement with calculations. Use of the electron microscope to observe the channeling radiation proved to be advantageous for sample preparation and beam condition adjustments. The authors would like to thank Drs. S. Fukui, N. Horikawa and T. Nakanishi and also C. Morita, I. Arai and T. Goto, Nagoya University. References [1] R. Wedell, Phys. Status Solidi B99 (1980) 11 and refs. therein. [2] J.U. Andersen and E. Lregsgaard, Phys. Rev. Lett. 44 (1980) 1079. [3] K. Komaki, F. Fujimoto and A. Ootuka, Nucl. Instr. and Meth. 194 (1982) 243. [4] J.U. Andersen, E. Bonderup, E. Laegsgaard, B.B. Marsh and A.H. Sorensen, Nucl. Instr. and Meth. 194 (1982) 209. [5] J.U. Andersen, E. Lregsgaard and A.H. Sorensen, Nucl. Instr. and Meth. B2 (1984) 63. [6] N. Cue, E. Bonderup, B.B. Marsh, H. Bakhru, R.E. Benenson, R. Haight, K. IngIis and G.O. Williams, Phys. Lett. 80A (1980) 26.
I. CRYSTAL
ASSISTED
PROCESSES