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Theoretical study of pion damage in A3B5 compounds
Nuclear Instruments and Methods in Physics Research A 413 (1998) 242—248
Theoretical study of pion damage in A3B5 compounds S. Lazanu!,*, I. Lazanu", U. Biggeri#, S. Sciortino# ! National Institute for Materials Physics, P.O. Box MG-7, Bucharest-Magurele, Romania " University of Bucharest, Faculty of Physics, P.O. Box MG-11, Bucharest, Romania # I.N.F.N. Firenze and Dipartimento di Energetica, Via S. Marta 3, 50139 Firenze, Italy Received 5 December 1997
Abstract A theoretical study of the radiation effects, from the point of view of the non-ionising energy loss and of the concentration of primary defects, in some A3B5 semiconductors, has been performed. These effects have been analysed for charged pions, in the energy range 50 MeV—50 GeV. The investigated materials have been GaAs, InP, GaP, InAs and InSb, and the results have been compared with silicon, as a reference material, keeping into account the peculiarities of the pion—nucleus interaction, and the recoil energy redistribution in the lattice. The results of the calculations have put in evidence the higher radiation resistance of Si, GaP and GaAs in the whole energy range investigated, with respect to the other analysed materials: InP, InAs and InSb, that proved to be of interest from this point of view only in the intermediate energy region. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 61.82.Fk; 61.85.#p Keywords: Radiation damage; Pions; A3B5 semiconductors
1. Introduction The utilisation of semiconductor materials, as detectors and devices, in high radiation environments (at the future particle colliders, in space applications, in medicine and industry), led to investigations on the mechanisms of radiation damage, to obtain radiation hardner materials. A3B5 compounds are possible candidates for detectors and devices that have to work in pion fields.
* Corresponding author. E-mail: [email protected]/lazanu@ alpha1.infim.ro.
While the studies of materials damage in neutron and proton fields produced results, pion damage investigations are at the initial stages. Up to now, it was stressed that the correlation of damages produced both in different materials by the same particles, and in the same material by different particles, is done by means of the nonionising energy loss (NIEL) [1], that is the rate of energy loss due to atomic displacements, along the particle track inside the material. On the other, the concentration of primary radiation induced defects, vacancy#interstitial, (CPD) in the material bulk is proportional to the NIEL. In this paper, we present the results of a systematic analysis of the damage of some major A3B5
0168-9002/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 6 5 8 - 5
S. Lazanu et al./Nucl. Instr. and Meth. in Phys. Res. A 413 (1998) 242—248
compounds in pion fields, from the point of view of both the non-ionising energy loss and of the concentration of primary radiation-induced defects. The kinetic energy of the incident pions is in the range 50 MeV—50 GeV. The materials investigated are: GaAs, GaP, InP, InAs, InSb, and their behaviour is analysed with reference to silicon. These semiconductors can be grouped in Si, GaAs and InSb, either monoatomic or with constituents very near in charge and mass numbers, that can be approximated with one component materials (Ge and Sn, respectively), and in GaP, InP and InAs, with distant components in the periodic table of elements. The substitution of one of the elements in GaAs and InSb leads to the other three analysed materials, GaP, InAs and InP.
2. Hypothesis and calculations When the pion, with kinetic energy in the range considered in the present paper, hits the semiconductor lattice, it penetrates the atom and interacts with the nucleus. The main interaction processes are: elastic, inelastic and absorption. In this paper, only thin samples made from the above-mentioned materials are considered, so that the light particles resulting from the interaction are supposed to escape without undergoing a second collision, while the recoil nuclei loose all their energy in the lattice by ionisation and atomic motion. The energy lost in non-ionising processes is the source of bulk damage. Details on the NIEL calculations can be found, e.g. in Ref. [2]. The relation between the NIEL and the CPD (n(E) on unit fluence) is n(E)"N
A 1 NIEL(E) ) U(E), N 2E A $
where E is the pion kinetic energy, E is the thre$ shold energy for displacements in the lattice, U(E) the pion fluence in the primary beam, N the atomic density (atoms/cm3) of the target material, A the mass number of the target, and N the A Avogadro number. For compound targets, the result is weighted with the number of atoms in the molecule.
243
The calculation of the NIEL, and of the CPD, supposes a quantitative understanding of the pion interaction with the nuclei of the host lattice, as well as of the subsequent redistribution of the energy of the recoils in the lattice, in the creation of displacements. The cross-sections used in the present calculations were obtained from the parametrisations of the few experimental data on pion — nucleus cross sections. For each interaction process (i"elastic, absorption, inelastic), and at each energy, a smooth mass number dependence of the cross-section is supposed. Hence, the cross-section was parametrised by a constant times a power of the mass number A, p "p (E) ) Ani(E). i oi The values of p (E) and n (E) have been obtained oi i by a least-square fit on the available data. For all the cases, the s2/degrees of freedom was less than 2.2. For pion kinetic energies in the * resonance 33 range, for all interaction processes, the fit indicates that the interaction takes place at the surface of the nucleus (n (E)+0.66). The contribution of absorpi tion at the interaction has been considered negligible above 1 GeV. At high energies, for absorption and inelastic processes, the pion interacts dominantly at the nucleus surface (n(E)+0.66—0.7) while in the elastic process the pion penetrates the nucleus volume (n(E)+1). The behaviour of the cross-sections for elastic, absorption and inelastic processes versus pion kinetic energy and mass number has been plotted in Ref. [3]. Due to the lack of experimental data on the contribution of different open channels in the cross-sections, we had to model the interaction in each interaction process. In the quantitative calculations for NIEL and for CPD, the most important source of errors is introduced by the pion inelastic interaction, due to the multitude of open channels, corresponding to possible final states. The inelastic interaction has been considered as composed by the knock-out process and the rest of the channels, equivalent to the interaction on an effective number of nucleons. The process of partitioning the energy of the recoil nucleus between electrons (ionisation) and atomic motion (displacements) is described by the
244
S. Lazanu et al./Nucl. Instr. and Meth. in Phys. Res. A 413 (1998) 242—248
Lindhard theory [4], and was kept into account in the present work. Details on the hypothesis and the calculation procedure can be found in the original paper of Lindhard. The factors describing the energy partition between ionisation and displacements for the recoil nuclei in GaP, InAs and InSb have been calculated in this work, and their energy dependence is shown in Fig. 1, together with the Lindhard factors in Si (from Ref. [5]), in GaAs (from Ref. [6]) and in InP (from Ref. [3]). For compound targets, the Lindhard curves have been calculated separately over each element, and the corresponding results have been weighted by the atom density of the element.
3. Results and discussion The results obtained in the present work for the calculated energy dependence of the NIEL in GaP, InAs and InSb are plotted in Fig. 2, together with the same dependence for Si [7], GaAs [7] and InP [3]. From Fig. 2, it could be seen that the energy dependence of the NIEL is for all materials a curve with two maxima, one in the region 100—300 MeV, the other around 1 GeV. Both maxima follow the behaviour of the pion—nucleus total cross-section. The first one is the effect of the * resonance 33 production. For silicon this corresponds to the maximum of the distribution, while for all other heavier materials this is a relative maximum. As we already stressed ([3,7]), the relative importance of the * resonance in the NIEL decreases with the 33 increase of the target mass number. The increase of the NIEL above the * resonance, up to around 33 1 GeV, is roughly due to the inelastic interaction. The energy channelled into displacements, for each pion—nucleus interaction, depends on the value of the recoil energy and on the Lindhard curve. In the region of the * resonance, the recoils 33 have energies in the range 0.1—10 MeV, depending on the nucleus mass number and on the scattering mechanism. By the other side, the Lindhard curves are on their increasing part, with different slopes, depending on the characteristics of the recoil (mass and charge number) and of the medium. Owing to
these facts, it is very difficult to give a direct relation between the NIEL and the mass number. The silicon, GaP and GaAs and, respectively, InP, InAs and InSb have similar behaviours, but different from one group to the other. At high pion kinetic energies, above 1 GeV, when the recoils have enough energy so that all Lindhard curves are on their respective plateau, the energy lost in the creation of atomic displacements is independent on the value of the recoil energy, and proportional to A2 . All NIEL curves have similar !7 shapes, with an evident increase in the NIEL value with the increase of the average mass number (the average mass number being defined as the average of the masses of the two constituents of the host lattice, for compound materials). A general A3@2 de!7 pendence of the NIEL has been obtained for this energy range. The energy dependence of the CPD is represented in Fig. 3. The concentration of primary displacements is a physical quantity that describes better the material degradation with respect to NIEL; it is also nearer to a measurable physical quantity, because the NIEL is related to the energy released in the material by the incident particle, and that goes into the creation of displacements, while the concentration itself gives the number of such primary displacements. On the other hand, the degradation of material and device parameters depends on the number of stable defects in the lattice; these are formed from the interaction of the vacancies and interstitials with the pre-existing defects and impurities of the lattice. Hence, the degradation factors experimentally measured are not directly proportional to the concentration of primary induced defects; in order to do an accurate comparison with experiment, the annealing time constants have to be known. As a first-order approximation, it could be considered that the degradation factors in different materials scale with the concentration of primary radiation-induced defects. The differences between the energy dependencies of NIEL and CPD are due to the different mass numbers of the components, and threshold energies for displacements [8]. The threshold energy for displacements is a factor of two higher in silicon with respect to all the other materials investigated,
S. Lazanu et al./Nucl. Instr. and Meth. in Phys. Res. A 413 (1998) 242—248
245
Fig. 1. Displacement energy versus recoil energy (Lindhard curves) for: (a) Si and its recoil family in the silicon lattice (from Ref. [5]); (b) Ga and P families in GaP; (c) Ga and As families in GaAs (from Ref. [6]); (d) In and P families in InP; (e) In and As families in InAs; (f ) In and Sb families in InSb.
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S. Lazanu et al./Nucl. Instr. and Meth. in Phys. Res. A 413 (1998) 242—248
Fig. 2. (a) Energy and average mass number dependence of the non-ionising energy loss for pions in Si, GaP, GaAs, InP, InAs and InSb. (b) NIEL versus pion kinetic energy.
so that in silicon a factor of two less primary defects are created only due to the difference in the threshold energies. All the investigated materials have a zinc blende structure, but with different lattice constants, and consequently with different concentrations of atoms (see e.g. Ref. [9]), so that the scale factors for the curves are also different. From Fig. 3, it can be seen that Si is characterised by one order of magnitude lower defect concentration with respect to all the other analysed materials.
It can be seen that in the energy range of the * resonance, the same order of magnitude for the 33 CPD in all A3B5 semiconductors investigated has been obtained, while at higher energies, above 1 GeV, the results are very different. So, InP, InAs and InSb are characterised by a pronounced increase CPD for pion kinetic energies higher that 200 MeV. From this point of view, Si, GaAs and GaP are materials that can be used in pion fields in all the calculated energy range, while for InP, InAs
S. Lazanu et al./Nucl. Instr. and Meth. in Phys. Res. A 413 (1998) 242—248
247
and InSb the use up to 200 MeV pion kinetic energy is recommended. We can also observe that in the medium energy range (50—200 MeV), GaP behaves similarly to InP, and GaAs similarly to InAs and InSb. This behaviour can be interpreted as the decisive effect of the light element. At energies in the GeV range, the degradation of all materials is higher, from 1 displacement/cm in GaP, to more than 8 displacements/cm in InSb, and can be attributed to the increase of the mass number (from P to As for the GaAs family, and from P to As and to Sb for the InSb family, respectively). All the above presented results are directly derived from calculations. Unfortunately, there are no experimental data for degradation coefficients of A3B5 materials in pion fields. The concordance of the calculations with experimental data is to be checked.
50 MeV—50 GeV. The behaviour of: GaAs, GaP, InP, InAs and InSb has been analysed with reference to silicon, that has lower mass number, and higher threshold energy for displacements. It has been found that all these materials are characterised by a higher NIEL and in the whole range of energy investigated: 50 MeV—50 GeV. The energy dependence of NIEL and of the CPD presents two maxima, the relative importance of which depends on the target mass number: one in the region of the delta resonance, more pronounced for light elements and for compounds containing light elements, and another one around 1 GeV, more pronounced for heavy elements. At high pion energies, above 1 GeV, a general A3@2 dependence of the NIEL has been obtained, !7 while in the region of the * resonance, it is very 33 difficult to give a direct relation between the NIEL and the mass number. The materials can be grouped in Si, GaP and GaAs and, respectively InP, InAs and InSb with behaviours different from one group to the other. In Si, GaP and GaAs, a slow variation of the primary defect concentration has been found in the whole energy range of interest, in contrast to InP, InAs and InSb, characterised by a pronounced increase of displacements concentration for pion kinetic energies higher than 200 MeV. Due to this fact, Si, GaAs and GaP are materials that can be used in pion fields in all the investigated energy range, while for InP, InAs and InSb the use only up to 200 MeV pion kinetic energy is recommended. A quite different relation between the non-ionising energy losses in these materials and the concentrations of displacements has been found, due to the different materials characteristics.
4. Summary
References
The results of a systematic analysis of the damage of some major A3B5 compounds in pion fields are presented, from the point of view of both the non-ionising energy loss and of the concentration of primary radiation induced defects. The kinetic energy of the incident pions is in the range
[1] E. Burke, IEEE Trans. Nucl. Sci. NS-33 (6) (1986) 1276. [2] S. Lazanu, I. Lazanu, U. Biggeri, E. Borchi, M. Bruzzi, Nucl. Phys. B (Proc. Suppl.) 61B (1998) 409. [3] S. Lazanu, I. Lazanu, U. Biggeri, E. Borchi, M. Bruzzi, in: G. Reffo et al., (Eds.), Nuclear Data for Science and Technology, Conference Proceedings, Vol. 59, SiF, Bologna, 1997, p. 1528.
Fig. 3. Concentration of primary displacements induced in the bulk of Si, GaP, GaAs, InP, InAs and InSb by unit pion fluence, versus pions kinetic energy.
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[4] J. Lindhard, V. Nielsen, M. Schraff, P.V. Thomsen, Mat. Phys. Medd. Dan. Vid. Sesk. 33 (1963) 1. [5] G.W. Simon, J.M. Denney, R. Downing, Phys. Rev. 129 (1963) 2454. [6] E.A. Burke, C.J. Dale, A.B. Campbell, G.P. Summers, W.J. Stapor, M.A. Xapsos, T. Palmer, R. Zuleeg, IEEE Tans. Nucl. Sci. NS-34 (1987) 1220.
[7] S. Lazanu, I. Lazanu, U. Biggeri, E. Borchi, M. Bruzzi, Nucl. Instr. and Meth. A 394 (1997) 232. [8] L.W. Aukerman, in: R.K. Willardson, A.C. Beer (Eds.), Semiconductors and Semimetals, vol. 4, Academic Press, New York, 1968, p. 343. [9] S. Adachi, J. Appl. Phys. 58 (1985) R1.
Theoretical study of pion damage in A3B5 compounds S. Lazanu!,*, I. Lazanu", U. Biggeri#, S. Sciortino# ! National Institute for Materials Physics, P.O. Box MG-7, Bucharest-Magurele, Romania " University of Bucharest, Faculty of Physics, P.O. Box MG-11, Bucharest, Romania # I.N.F.N. Firenze and Dipartimento di Energetica, Via S. Marta 3, 50139 Firenze, Italy Received 5 December 1997
Abstract A theoretical study of the radiation effects, from the point of view of the non-ionising energy loss and of the concentration of primary defects, in some A3B5 semiconductors, has been performed. These effects have been analysed for charged pions, in the energy range 50 MeV—50 GeV. The investigated materials have been GaAs, InP, GaP, InAs and InSb, and the results have been compared with silicon, as a reference material, keeping into account the peculiarities of the pion—nucleus interaction, and the recoil energy redistribution in the lattice. The results of the calculations have put in evidence the higher radiation resistance of Si, GaP and GaAs in the whole energy range investigated, with respect to the other analysed materials: InP, InAs and InSb, that proved to be of interest from this point of view only in the intermediate energy region. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 61.82.Fk; 61.85.#p Keywords: Radiation damage; Pions; A3B5 semiconductors
1. Introduction The utilisation of semiconductor materials, as detectors and devices, in high radiation environments (at the future particle colliders, in space applications, in medicine and industry), led to investigations on the mechanisms of radiation damage, to obtain radiation hardner materials. A3B5 compounds are possible candidates for detectors and devices that have to work in pion fields.
* Corresponding author. E-mail: [email protected]/lazanu@ alpha1.infim.ro.
While the studies of materials damage in neutron and proton fields produced results, pion damage investigations are at the initial stages. Up to now, it was stressed that the correlation of damages produced both in different materials by the same particles, and in the same material by different particles, is done by means of the nonionising energy loss (NIEL) [1], that is the rate of energy loss due to atomic displacements, along the particle track inside the material. On the other, the concentration of primary radiation induced defects, vacancy#interstitial, (CPD) in the material bulk is proportional to the NIEL. In this paper, we present the results of a systematic analysis of the damage of some major A3B5
0168-9002/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 6 5 8 - 5
S. Lazanu et al./Nucl. Instr. and Meth. in Phys. Res. A 413 (1998) 242—248
compounds in pion fields, from the point of view of both the non-ionising energy loss and of the concentration of primary radiation-induced defects. The kinetic energy of the incident pions is in the range 50 MeV—50 GeV. The materials investigated are: GaAs, GaP, InP, InAs, InSb, and their behaviour is analysed with reference to silicon. These semiconductors can be grouped in Si, GaAs and InSb, either monoatomic or with constituents very near in charge and mass numbers, that can be approximated with one component materials (Ge and Sn, respectively), and in GaP, InP and InAs, with distant components in the periodic table of elements. The substitution of one of the elements in GaAs and InSb leads to the other three analysed materials, GaP, InAs and InP.
2. Hypothesis and calculations When the pion, with kinetic energy in the range considered in the present paper, hits the semiconductor lattice, it penetrates the atom and interacts with the nucleus. The main interaction processes are: elastic, inelastic and absorption. In this paper, only thin samples made from the above-mentioned materials are considered, so that the light particles resulting from the interaction are supposed to escape without undergoing a second collision, while the recoil nuclei loose all their energy in the lattice by ionisation and atomic motion. The energy lost in non-ionising processes is the source of bulk damage. Details on the NIEL calculations can be found, e.g. in Ref. [2]. The relation between the NIEL and the CPD (n(E) on unit fluence) is n(E)"N
A 1 NIEL(E) ) U(E), N 2E A $
where E is the pion kinetic energy, E is the thre$ shold energy for displacements in the lattice, U(E) the pion fluence in the primary beam, N the atomic density (atoms/cm3) of the target material, A the mass number of the target, and N the A Avogadro number. For compound targets, the result is weighted with the number of atoms in the molecule.
243
The calculation of the NIEL, and of the CPD, supposes a quantitative understanding of the pion interaction with the nuclei of the host lattice, as well as of the subsequent redistribution of the energy of the recoils in the lattice, in the creation of displacements. The cross-sections used in the present calculations were obtained from the parametrisations of the few experimental data on pion — nucleus cross sections. For each interaction process (i"elastic, absorption, inelastic), and at each energy, a smooth mass number dependence of the cross-section is supposed. Hence, the cross-section was parametrised by a constant times a power of the mass number A, p "p (E) ) Ani(E). i oi The values of p (E) and n (E) have been obtained oi i by a least-square fit on the available data. For all the cases, the s2/degrees of freedom was less than 2.2. For pion kinetic energies in the * resonance 33 range, for all interaction processes, the fit indicates that the interaction takes place at the surface of the nucleus (n (E)+0.66). The contribution of absorpi tion at the interaction has been considered negligible above 1 GeV. At high energies, for absorption and inelastic processes, the pion interacts dominantly at the nucleus surface (n(E)+0.66—0.7) while in the elastic process the pion penetrates the nucleus volume (n(E)+1). The behaviour of the cross-sections for elastic, absorption and inelastic processes versus pion kinetic energy and mass number has been plotted in Ref. [3]. Due to the lack of experimental data on the contribution of different open channels in the cross-sections, we had to model the interaction in each interaction process. In the quantitative calculations for NIEL and for CPD, the most important source of errors is introduced by the pion inelastic interaction, due to the multitude of open channels, corresponding to possible final states. The inelastic interaction has been considered as composed by the knock-out process and the rest of the channels, equivalent to the interaction on an effective number of nucleons. The process of partitioning the energy of the recoil nucleus between electrons (ionisation) and atomic motion (displacements) is described by the
244
S. Lazanu et al./Nucl. Instr. and Meth. in Phys. Res. A 413 (1998) 242—248
Lindhard theory [4], and was kept into account in the present work. Details on the hypothesis and the calculation procedure can be found in the original paper of Lindhard. The factors describing the energy partition between ionisation and displacements for the recoil nuclei in GaP, InAs and InSb have been calculated in this work, and their energy dependence is shown in Fig. 1, together with the Lindhard factors in Si (from Ref. [5]), in GaAs (from Ref. [6]) and in InP (from Ref. [3]). For compound targets, the Lindhard curves have been calculated separately over each element, and the corresponding results have been weighted by the atom density of the element.
3. Results and discussion The results obtained in the present work for the calculated energy dependence of the NIEL in GaP, InAs and InSb are plotted in Fig. 2, together with the same dependence for Si [7], GaAs [7] and InP [3]. From Fig. 2, it could be seen that the energy dependence of the NIEL is for all materials a curve with two maxima, one in the region 100—300 MeV, the other around 1 GeV. Both maxima follow the behaviour of the pion—nucleus total cross-section. The first one is the effect of the * resonance 33 production. For silicon this corresponds to the maximum of the distribution, while for all other heavier materials this is a relative maximum. As we already stressed ([3,7]), the relative importance of the * resonance in the NIEL decreases with the 33 increase of the target mass number. The increase of the NIEL above the * resonance, up to around 33 1 GeV, is roughly due to the inelastic interaction. The energy channelled into displacements, for each pion—nucleus interaction, depends on the value of the recoil energy and on the Lindhard curve. In the region of the * resonance, the recoils 33 have energies in the range 0.1—10 MeV, depending on the nucleus mass number and on the scattering mechanism. By the other side, the Lindhard curves are on their increasing part, with different slopes, depending on the characteristics of the recoil (mass and charge number) and of the medium. Owing to
these facts, it is very difficult to give a direct relation between the NIEL and the mass number. The silicon, GaP and GaAs and, respectively, InP, InAs and InSb have similar behaviours, but different from one group to the other. At high pion kinetic energies, above 1 GeV, when the recoils have enough energy so that all Lindhard curves are on their respective plateau, the energy lost in the creation of atomic displacements is independent on the value of the recoil energy, and proportional to A2 . All NIEL curves have similar !7 shapes, with an evident increase in the NIEL value with the increase of the average mass number (the average mass number being defined as the average of the masses of the two constituents of the host lattice, for compound materials). A general A3@2 de!7 pendence of the NIEL has been obtained for this energy range. The energy dependence of the CPD is represented in Fig. 3. The concentration of primary displacements is a physical quantity that describes better the material degradation with respect to NIEL; it is also nearer to a measurable physical quantity, because the NIEL is related to the energy released in the material by the incident particle, and that goes into the creation of displacements, while the concentration itself gives the number of such primary displacements. On the other hand, the degradation of material and device parameters depends on the number of stable defects in the lattice; these are formed from the interaction of the vacancies and interstitials with the pre-existing defects and impurities of the lattice. Hence, the degradation factors experimentally measured are not directly proportional to the concentration of primary induced defects; in order to do an accurate comparison with experiment, the annealing time constants have to be known. As a first-order approximation, it could be considered that the degradation factors in different materials scale with the concentration of primary radiation-induced defects. The differences between the energy dependencies of NIEL and CPD are due to the different mass numbers of the components, and threshold energies for displacements [8]. The threshold energy for displacements is a factor of two higher in silicon with respect to all the other materials investigated,
S. Lazanu et al./Nucl. Instr. and Meth. in Phys. Res. A 413 (1998) 242—248
245
Fig. 1. Displacement energy versus recoil energy (Lindhard curves) for: (a) Si and its recoil family in the silicon lattice (from Ref. [5]); (b) Ga and P families in GaP; (c) Ga and As families in GaAs (from Ref. [6]); (d) In and P families in InP; (e) In and As families in InAs; (f ) In and Sb families in InSb.
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Fig. 2. (a) Energy and average mass number dependence of the non-ionising energy loss for pions in Si, GaP, GaAs, InP, InAs and InSb. (b) NIEL versus pion kinetic energy.
so that in silicon a factor of two less primary defects are created only due to the difference in the threshold energies. All the investigated materials have a zinc blende structure, but with different lattice constants, and consequently with different concentrations of atoms (see e.g. Ref. [9]), so that the scale factors for the curves are also different. From Fig. 3, it can be seen that Si is characterised by one order of magnitude lower defect concentration with respect to all the other analysed materials.
It can be seen that in the energy range of the * resonance, the same order of magnitude for the 33 CPD in all A3B5 semiconductors investigated has been obtained, while at higher energies, above 1 GeV, the results are very different. So, InP, InAs and InSb are characterised by a pronounced increase CPD for pion kinetic energies higher that 200 MeV. From this point of view, Si, GaAs and GaP are materials that can be used in pion fields in all the calculated energy range, while for InP, InAs
S. Lazanu et al./Nucl. Instr. and Meth. in Phys. Res. A 413 (1998) 242—248
247
and InSb the use up to 200 MeV pion kinetic energy is recommended. We can also observe that in the medium energy range (50—200 MeV), GaP behaves similarly to InP, and GaAs similarly to InAs and InSb. This behaviour can be interpreted as the decisive effect of the light element. At energies in the GeV range, the degradation of all materials is higher, from 1 displacement/cm in GaP, to more than 8 displacements/cm in InSb, and can be attributed to the increase of the mass number (from P to As for the GaAs family, and from P to As and to Sb for the InSb family, respectively). All the above presented results are directly derived from calculations. Unfortunately, there are no experimental data for degradation coefficients of A3B5 materials in pion fields. The concordance of the calculations with experimental data is to be checked.
50 MeV—50 GeV. The behaviour of: GaAs, GaP, InP, InAs and InSb has been analysed with reference to silicon, that has lower mass number, and higher threshold energy for displacements. It has been found that all these materials are characterised by a higher NIEL and in the whole range of energy investigated: 50 MeV—50 GeV. The energy dependence of NIEL and of the CPD presents two maxima, the relative importance of which depends on the target mass number: one in the region of the delta resonance, more pronounced for light elements and for compounds containing light elements, and another one around 1 GeV, more pronounced for heavy elements. At high pion energies, above 1 GeV, a general A3@2 dependence of the NIEL has been obtained, !7 while in the region of the * resonance, it is very 33 difficult to give a direct relation between the NIEL and the mass number. The materials can be grouped in Si, GaP and GaAs and, respectively InP, InAs and InSb with behaviours different from one group to the other. In Si, GaP and GaAs, a slow variation of the primary defect concentration has been found in the whole energy range of interest, in contrast to InP, InAs and InSb, characterised by a pronounced increase of displacements concentration for pion kinetic energies higher than 200 MeV. Due to this fact, Si, GaAs and GaP are materials that can be used in pion fields in all the investigated energy range, while for InP, InAs and InSb the use only up to 200 MeV pion kinetic energy is recommended. A quite different relation between the non-ionising energy losses in these materials and the concentrations of displacements has been found, due to the different materials characteristics.
4. Summary
References
The results of a systematic analysis of the damage of some major A3B5 compounds in pion fields are presented, from the point of view of both the non-ionising energy loss and of the concentration of primary radiation induced defects. The kinetic energy of the incident pions is in the range
[1] E. Burke, IEEE Trans. Nucl. Sci. NS-33 (6) (1986) 1276. [2] S. Lazanu, I. Lazanu, U. Biggeri, E. Borchi, M. Bruzzi, Nucl. Phys. B (Proc. Suppl.) 61B (1998) 409. [3] S. Lazanu, I. Lazanu, U. Biggeri, E. Borchi, M. Bruzzi, in: G. Reffo et al., (Eds.), Nuclear Data for Science and Technology, Conference Proceedings, Vol. 59, SiF, Bologna, 1997, p. 1528.
Fig. 3. Concentration of primary displacements induced in the bulk of Si, GaP, GaAs, InP, InAs and InSb by unit pion fluence, versus pions kinetic energy.
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S. Lazanu et al./Nucl. Instr. and Meth. in Phys. Res. A 413 (1998) 242—248
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