- Email: [email protected]
An investigation of the boron electron structure by positron annihilation
Journal of the Less-Common Metals, 67 (1979) 151 - 154 @ Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
AN INVESTIGATION OF THE BORON POSITRON ANNIHILATION*
P. U. ARIFOV, Arifou’s
Institute
A. Z. ILYASOV of Electronics,
151
ELECTRON
STRUCTURE
BY
and A. A. KOTOV Uzbek S.S.R.
Academy
of Sciences,
Tashkent
(U.S.S.R.)
Summary The peculiarities of the electron momentum distribution were investigated by determining the angular correlation function of the y quanta emitted on positron annihilation in various samples of boron (polycrystals; boron films on silicon substrates) and the threshold energies of these electrons were determined.
It is well known that positrons emitted by radioactive sources are thermalized in solids in about lo-l2 s and are then annihilated by the electrons, emitting y quanta [ 1,2] . According to the law of momentum and energy conservation, the information we can obtain from annihilation radiation concerns the energetic state of the positron-electron pairs and this is mainly determined by the electron state (the positron energy at the moment of annihilation is about 0.025 eV). The data obtained from annihilation radiation and their analysis give information about the electron momentum distribution and about the structural peculiarities of the material used; this forms the basis of the positron diagnostic method [ 1, 31. One of the main methods of measuring annihilation radiation is to determine the angular correlation function of the annihilation y quanta, thereby obtaining information about the electron momentum distribution. When the momentum P of the positron-electron pair at the moment of annihilation is zero, annihilation y quanta must be emitted to opposite sides (at a scattering angle OL= n). When the momentum is not zero, then the scattering angle is less than 180” ; this difference is larger when the momentum is larger (6’ = 71- (Y). The momentum PL depends linearly on the angle 8: PL = emc
*Paper presented at the 6th International Varna, Bulgaria, October 9 - 12, 1978.
Symposium
on Boron
and Borides,
152
Thus by measuring the scattering angle of two y quanta it is possible to obtain information about the momentum of the electron which annihilates the positron. A system consisting of two y radiation detectors connected to a coincidence circuit is usually used to measure the angular correlation function of the annihilation y quanta. One of the detectors is motionless and the other moves through a given angle [ 1, 31. The experimental arrangement had point-linear geometry [ 41 and the distance between the source and the y detectors was 2 m. The angular resolution, which was determined by the slit width of the lead collimators in front of the detectors, was 1 mrad. 22NaC1 salt with an activity of 10 mCi was used as the positron source. The sample under investigation and the source were situated in a vacuum chamber evacuated to a pressure of about 10m5 Torr. The whole measurement process was automated. We investigated boron films approximately 3 pm thick deposited both on silicon substrates and on silicon substrates which had been previously oxidized. A clean silicon substrate was also used as a control. We also investigated boron samples obtained by zone melting. One of the samples was prepared from boron powder; it was then sintered and annealed at a temperature of 1800 “C. The samples were prepared by G. V. Pantelejeva. The results were processed in a Minsk-32 computer according to the programme used by Arifov et al. [6] ; using the given model describing the state of the material under investigation this allowed us to obtain information about the momentum distribution, the density of the momentum distribution and the corresponding threshold energy I&, and threshold momentum Pth of the electrons. From this mathematical procedure the momentum distribution function N(P) and the momentum distribution density function p(P) of electrons in boron samples were obtained (Figs. 1 - 4) and showed Fermi steps. The curves of the angular distribution of the annihilation 7 quanta for boron have a large half-height width which is greater than that for silicon; this clearly indicates large values of threshold momentum and threshold energy. The functions p(P) and N(P) for silicon (Fig. 3, crosses, and Fig. 4, crosses) and for boron (Fig. 1, crosses, and Fig. 2, crosses) are also quite different. The curves of angular correlation with a larger intensity in the angular range 8 > 9 mrad indicate that there is a larger probability of positron annihilation by boron valence electrons. The presence of strong directed links also correlates to curve broadening and to the increase in tail intensity. We measured the angular correlation functions of annihilation y quanta in two boron samples obtained by zone melting and in a sample obtained by boron powder pressing. From the rod obtained by boron zone melting in a vacuum a sample was cut off perpendicularly to the direction of the moving zone (Fig. 1, open’circles, and Fig. 2, open circles) and another sample was cut off along the direction of the moving zone to give a longitudinal section (Fig. 1, closed triangles, and Fig. 2, closed triangles). All the curves have smoothed Fermi steps because they are in the region of large angles. These
Fig. 1. The momentum distribution density functions of electrons in boron samples: X, pressed annealed powder;A, boron obtained by zone melting (longitudinal section); 0, boron obtained by zone melting (transverse section); the threshold momentum values Pth are shown by arrows. Fig. 2. The electron momentum distribution symbols are the same as in Fig. 1.
5
p,
hz’
functions
N(P) in boron
samples:
the
fo-J
Fig. 3. The electron momentum distribution density functions p(P) in various systems: X, in silicon; 0, in epitaxial boron films on silicon;A, in epitaxial boron films on silicon oxide substrates; the threshold momentum values Pth are shown by arrows. Fig. 4. The electron momentum are the same as in Fig. 3.
distribution
functions
in laminated
systems:
the symbols
154
curves confirm that positrons are annihilated by strongly fixed electrons. The differences in the curves for the various samples can be explained by the fact that each sample has a structure with one predominant orientation. The parameters of the pressed sample have values which are intermediate between the two zone-melting samples. The presence of micropores and microvoids in a sample strongly influences the shape of the angular correlation curves of the annihilation y quanta and the p(P) and N(P) curves (Fig. 1, crosses, and Fig. 2, crosses). The p(P) and N(P) curves for the silicon samples with epitaxial boron films have shapes characteristic of pure silicon (Figs. 3 and 4); however, the influence of the boron film can still be observed. A boron film on pure silicon leads to a smoothing of the Fermi steps and to an increase in threshold momentum. An oxide film gives the opposite effect. Thus we can conclude that positron annihilation could be an effective new method for investigating the structure of boron and its electron properties.
References 1 V. I. Goldansky, Fizicheskaya Khimiya Positrona i Positroniya, Nauka, Moscow, 1968. 2 E. P. Prokopyev, in Quantovie Svoistva Atomov i Ionov i Positronnaya Diagnostika, Akademii Nauk Usbekskoi S.S.R., Tashkent, 1975. 3 R. N. West, Adv. Phys., 22 (3) (1973) 263. 4 U. Arifov and P. Arifov, Fizika Medlennikh Positronov, Akademii Nauk Usbekskoi S.S.R., Tashkent, 1969. 5 P. U. Arifov, A. Z. Ilyasov, V. A. Kireev and A. A. Kotov, in Quantovic Svoistva Atomov i Zonov i Positronnaya Diagnostika, Akademii Nauk Usbekskoi S.S.R., Tashkent, 1975. 6 P. U. Arifov, V. G. Gontar and S. V. Shevelev, Dokl. Akad. Nauk SSSR, 235 (1977) 313.
AN INVESTIGATION OF THE BORON POSITRON ANNIHILATION*
P. U. ARIFOV, Arifou’s
Institute
A. Z. ILYASOV of Electronics,
151
ELECTRON
STRUCTURE
BY
and A. A. KOTOV Uzbek S.S.R.
Academy
of Sciences,
Tashkent
(U.S.S.R.)
Summary The peculiarities of the electron momentum distribution were investigated by determining the angular correlation function of the y quanta emitted on positron annihilation in various samples of boron (polycrystals; boron films on silicon substrates) and the threshold energies of these electrons were determined.
It is well known that positrons emitted by radioactive sources are thermalized in solids in about lo-l2 s and are then annihilated by the electrons, emitting y quanta [ 1,2] . According to the law of momentum and energy conservation, the information we can obtain from annihilation radiation concerns the energetic state of the positron-electron pairs and this is mainly determined by the electron state (the positron energy at the moment of annihilation is about 0.025 eV). The data obtained from annihilation radiation and their analysis give information about the electron momentum distribution and about the structural peculiarities of the material used; this forms the basis of the positron diagnostic method [ 1, 31. One of the main methods of measuring annihilation radiation is to determine the angular correlation function of the annihilation y quanta, thereby obtaining information about the electron momentum distribution. When the momentum P of the positron-electron pair at the moment of annihilation is zero, annihilation y quanta must be emitted to opposite sides (at a scattering angle OL= n). When the momentum is not zero, then the scattering angle is less than 180” ; this difference is larger when the momentum is larger (6’ = 71- (Y). The momentum PL depends linearly on the angle 8: PL = emc
*Paper presented at the 6th International Varna, Bulgaria, October 9 - 12, 1978.
Symposium
on Boron
and Borides,
152
Thus by measuring the scattering angle of two y quanta it is possible to obtain information about the momentum of the electron which annihilates the positron. A system consisting of two y radiation detectors connected to a coincidence circuit is usually used to measure the angular correlation function of the annihilation y quanta. One of the detectors is motionless and the other moves through a given angle [ 1, 31. The experimental arrangement had point-linear geometry [ 41 and the distance between the source and the y detectors was 2 m. The angular resolution, which was determined by the slit width of the lead collimators in front of the detectors, was 1 mrad. 22NaC1 salt with an activity of 10 mCi was used as the positron source. The sample under investigation and the source were situated in a vacuum chamber evacuated to a pressure of about 10m5 Torr. The whole measurement process was automated. We investigated boron films approximately 3 pm thick deposited both on silicon substrates and on silicon substrates which had been previously oxidized. A clean silicon substrate was also used as a control. We also investigated boron samples obtained by zone melting. One of the samples was prepared from boron powder; it was then sintered and annealed at a temperature of 1800 “C. The samples were prepared by G. V. Pantelejeva. The results were processed in a Minsk-32 computer according to the programme used by Arifov et al. [6] ; using the given model describing the state of the material under investigation this allowed us to obtain information about the momentum distribution, the density of the momentum distribution and the corresponding threshold energy I&, and threshold momentum Pth of the electrons. From this mathematical procedure the momentum distribution function N(P) and the momentum distribution density function p(P) of electrons in boron samples were obtained (Figs. 1 - 4) and showed Fermi steps. The curves of the angular distribution of the annihilation 7 quanta for boron have a large half-height width which is greater than that for silicon; this clearly indicates large values of threshold momentum and threshold energy. The functions p(P) and N(P) for silicon (Fig. 3, crosses, and Fig. 4, crosses) and for boron (Fig. 1, crosses, and Fig. 2, crosses) are also quite different. The curves of angular correlation with a larger intensity in the angular range 8 > 9 mrad indicate that there is a larger probability of positron annihilation by boron valence electrons. The presence of strong directed links also correlates to curve broadening and to the increase in tail intensity. We measured the angular correlation functions of annihilation y quanta in two boron samples obtained by zone melting and in a sample obtained by boron powder pressing. From the rod obtained by boron zone melting in a vacuum a sample was cut off perpendicularly to the direction of the moving zone (Fig. 1, open’circles, and Fig. 2, open circles) and another sample was cut off along the direction of the moving zone to give a longitudinal section (Fig. 1, closed triangles, and Fig. 2, closed triangles). All the curves have smoothed Fermi steps because they are in the region of large angles. These
Fig. 1. The momentum distribution density functions of electrons in boron samples: X, pressed annealed powder;A, boron obtained by zone melting (longitudinal section); 0, boron obtained by zone melting (transverse section); the threshold momentum values Pth are shown by arrows. Fig. 2. The electron momentum distribution symbols are the same as in Fig. 1.
5
p,
hz’
functions
N(P) in boron
samples:
the
fo-J
Fig. 3. The electron momentum distribution density functions p(P) in various systems: X, in silicon; 0, in epitaxial boron films on silicon;A, in epitaxial boron films on silicon oxide substrates; the threshold momentum values Pth are shown by arrows. Fig. 4. The electron momentum are the same as in Fig. 3.
distribution
functions
in laminated
systems:
the symbols
154
curves confirm that positrons are annihilated by strongly fixed electrons. The differences in the curves for the various samples can be explained by the fact that each sample has a structure with one predominant orientation. The parameters of the pressed sample have values which are intermediate between the two zone-melting samples. The presence of micropores and microvoids in a sample strongly influences the shape of the angular correlation curves of the annihilation y quanta and the p(P) and N(P) curves (Fig. 1, crosses, and Fig. 2, crosses). The p(P) and N(P) curves for the silicon samples with epitaxial boron films have shapes characteristic of pure silicon (Figs. 3 and 4); however, the influence of the boron film can still be observed. A boron film on pure silicon leads to a smoothing of the Fermi steps and to an increase in threshold momentum. An oxide film gives the opposite effect. Thus we can conclude that positron annihilation could be an effective new method for investigating the structure of boron and its electron properties.
References 1 V. I. Goldansky, Fizicheskaya Khimiya Positrona i Positroniya, Nauka, Moscow, 1968. 2 E. P. Prokopyev, in Quantovie Svoistva Atomov i Ionov i Positronnaya Diagnostika, Akademii Nauk Usbekskoi S.S.R., Tashkent, 1975. 3 R. N. West, Adv. Phys., 22 (3) (1973) 263. 4 U. Arifov and P. Arifov, Fizika Medlennikh Positronov, Akademii Nauk Usbekskoi S.S.R., Tashkent, 1969. 5 P. U. Arifov, A. Z. Ilyasov, V. A. Kireev and A. A. Kotov, in Quantovic Svoistva Atomov i Zonov i Positronnaya Diagnostika, Akademii Nauk Usbekskoi S.S.R., Tashkent, 1975. 6 P. U. Arifov, V. G. Gontar and S. V. Shevelev, Dokl. Akad. Nauk SSSR, 235 (1977) 313.