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Systematic measurements of pulse height defects for heavy ions in surface barrier detectors — A comment
Nuclear Instruments and Methods in Physics Research North-Holland, Amsterdam
A257 (1987) 381-383
381
SYSTEMATIC MEASUREMENTS OF PULSE HEIGHT DEFECTS FOR HEAVY IONS IN SURFACE BARRIER DETECTORS - A COMMENT E.C . FINCH University of Dublin, Department of Pure and Applied Physics, Trinity College, Dublin 2, Ireland
Received 16 January 1987 Newly published data on the pulse height defect and its field dependence in heavy ion surface barrier detectors are reported by Oginara et al . to be in conflict with previous models developed by us . We show that this apparent discrepancy is due to the use by them in our models of inappropriately chosen parameters .
Ogihara et al. [1] have recently produced a new experimental and theoretical survey of the pulse height defect produced by various accelerator derived heavy ions in several silicon surface barrier detectors. Extensive comparisons are included with our own surveys made with mass and energy separated fission fragments incident on heavy ion silicon surface barrier detectors [2-4]. Such comparisons are possible because there is considerable overlap between the mass and energy regions studied by Ogihara et al. and by us . The purpose of this comment is to discuss the comparisons which they have made . Our data as given in table 1 of ref. [4] show unambiguously that for all fourteen fragment mass and energy combinations studied the defect decreases for increasing fields. Even our earlier data in ref. [2], while more restricted, nevertheless show that the defect and its mass dependence decrease when the detector applied bias and electric field are raised . This is in distinction to the statement in the introduction of Ogihara that our field dependence data presented in refs . [2] and [4] "are very poor and no clear trend could be established" . Most of the discussion in Ogihara of our work centres on our modelling of the defect, and in particular of that part due to charge recombination through the plasma formed in the wake of a heavy ion. Ogihara is correct in noting that difficulties may arise in the principle of separation of the defect into window dependent, atomic collision and recombination parts; in particular, surface recombination losses are not easy to estimate . The very useful model developed by Wilkins et al . and Steinberg et al. [5,6], for example, envisages that charge recombination occurs in a silicon surface layer behind the entrance window. However, as remarked in ref. [4], the considerable thickness (up to 1 p,m) needed for this layer for fission fragments causes difficulties of 0168-9002/87/$03 .50 C Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
interpretation, and furthermore the predictions are at best confirmed only roughly by some experiments [7,8]. More recently this last conclusion was also reached by Kitahara et al . [9]. We therefore still feel that our modelling of the defect, with its splitting into three components as given above and developed by us in refs . [3] and [4], is a useful alternative concept to pursue . In our previous papers [3,4] we envisaged that the electron-hole plasma formed in the wake of a stopping ion decays through extraction of carriers by the detector depletion layer electric field within the plasma lifetime tp , as described by Tove et al . and Seibt et al. [10,11]. Hence a very simple expression for the recombination defect 4 r is given by eqs. (1) and (2) of ref . [3] or by eq. (3) of ref. [4] as A,/E= tp/tr for
tp << tr,
where t r is the carrier recombination lifetime within the plasma . This model (which we shall here call model A) neglects the radial expansion with time of the plasma column because of the ambipolar diffusion outwards of electrons and holes. Our second model (model B), which is derived from model A, allows for the column radial expansion and leads to the expression . A r/E= (n,o/3?TDaC) ln(4Da tp /rti ),
(2)
which is eq. [13] of ref. [4]. Here njo (m -1 ) is the distance averaged initial linear charge density, Da (m2 s -1 ) the ambipolar diffusion coefficient, ro the plasma column initial radius, C (sm -3 ) = 10 2° to , to (s) is the low density minority carrier lifetime, and 4Da tp >>r:02 . In the derivation of eq . [2] the recombination time t r (<< to) is taken to be inversely proportional to the volume carrier density n, such that t r = C/n . Thus as the column expands n falls and t r rises.
38 2
E. C Finch / Pulse height defects in surface barrier detectors
These two models fitted well to our own data for the recombination defect (except at very low fields, for reasons described there), as can be seen from figs . 2 and 3 of ref. [4] . However, it appears from fig. 3 in Ogihara [1] that our model B does not fit their own data. There seems to be no reason to doubt that Ogihara's data are, like ours, of good quality. Indeed there is close agreement between our and Ogihara's data for both A r and the total defect as a function of energy at fixed bias around the normal value. This may be verified by comparing our data for 90 and 135 amu fragments (table 1 in ref. [4]) with Ogihara's 79 Br and 1271 results (figs. 1 and 4 in ref . [1]) . This is for Ogihara's detectors 2 and 4 which, like our own, are of low resistivity . It therefore becomes of central importance to determine the cause of the discrepancies described by them . One difference between their work and ours lies in the data used for the plasma lifetime t P . We used our own data [12] for tp rather than Ogihara's procedure of using Seibt's expression (eq . (14) in ref. [111) . Since our data are, as we state in ref. [7], in broad (although not exact) agreement with Seibt's work, we do not expect this difference to explain the discrepancies just described . Ogihara et al . are able to obtain reasonable fits of our model to their data only by introduction of complex empirical assumptions (their eqs. (5)-(11)) about Da , C, t o and t p . As they concede, this is not a very satisfactory procedure . We believe that such assumptions are in fact unnecessary, as we shall show. We fitted the recombination data of our experiment to our expressions (eqs. (1) and (2) above) by rewriting each of them in the form y = mx + c and plotting the appropriate quantities so as to obtain satisfactory straight line least-squares fits (figs . 2 and 3 in ref. [4]) . In addition to demonstrating the general validity of our models, this procedure enabled us to derive from our data appropriate values for, in model A, the minority charge carrier lifetime t o in terms of the constant radius of the plasma column, and, in model B, both t o and the initial column radius ro independently . We discuss this point in more detail later on . The values selected by Ogihara for t o and ro are inappropriate, and are a primary cause of the discrepancies in their fig . 3 between their data for d, and the predictions made by them with our model. We now 'try to explain firstly for t o and then for to why this is so . The expression t o = 52po.6 used by Ogihara in eq . (2) above, where p is the silicon resistivity in fl m and t o is in Its, was taken by them from our earlier ref. [3]. We there described it as an upper limit to the minority carrier lifetime because of several possible effects including, perhaps, the effects of radiation damage caused by an ion inside its own plasma . As Ogihara points out, we produced in ref . [4] some evidence from our data
which supported this suggestion. Unlike Ogihara we did not in fact substitute this expression for to directly in eq. (2) above, both for this reason and also because as stated above we could independently derive appropriate values for t o . These are, as anticipated, less than the value which would be given by t o = 52po.6 for the value of p we quoted . Nevertheless it is clear both from fig. 3 in Ogihara and also from Kitahara [9] that data taken with different resistivity detectors qualitatively follow the trends indicated by our own expression for the upper limit to to . The value of 1 .5 ttm used by Ogihara for to is half that derived by us [4], which as we noted is indeed rather larger than suggested elsewhere . (It is possible because of an ambiguity in Ogihara's wording to infer that this value came from ref. [3], but this is not the case .) However, examination of eq. (2) above shows that a larger value of ro , as was deduced by us by leastsquares fitting to our data, increases the field dependence of this expression for Ar . This is just what is required by the data shown by Ogihara in his fig . 3 . Note that ro , unlike to , does not act as a simple scale factor in eq . (2) above. It would be of great interest to pursue further the fitting of Ogihara's field dependence data to our model and use our linear least-squares fitting procedure . Unfortunately however, Ogihara does not quote the ion energy used for his total and recombination defect field dependence data in his figs . 2, 3 and 5, and this energy appears in a nonlinear fashion (through N o and t p ) in eq . (2) above. As far as we can tell Ogihara's data do not appear to be too dissimilar to our own, and in any case we have already noted the close agreement around normal bias between their data and ours. The important remark of Ogihara that our model A gives predictions for A r half an order of magnitude larger than those from model B needs careful discussion . For a plasma column radius in model A of reasonable magnitude and equal to the initial radius ro in model B this is correct and would be expected. The amount of recombination in model A, where plasma radial expansion is neglected, would then, for the same low density minority carrier lifetime, naturally be larger than in model B - here the volume carrier density decreases and the lifetime increases as the column expands . In contrast, model A becomes a limiting case of model B when (unlike in usual practice) the ambipolar diffusion coefficient Da << ró/4t, as can be deduced from the appendix to ref . [4]. These differences in predictions for 4 r can of course be adjusted by a suitable choice of radius values and low density carrier lifetimes which best fit the data. For example, for the same Ar and low density lifetime the radius from model B is lower than from model A . We have already discussed extensively the interrelation of the best lifetime and radius values [3,4] (see especially
E C Finch / Pulse height defects m surface barrier detectors
above and also the second paragraph of the conclusion to ref. [4]) . In this way there is no problem to fitting either model (not exactly, of course) to our data, even though the initial assumptions for each model are not identical . We are further encouraged in that the resulting radius and lifetime values do not appear unreasonable. Finally, it is of interest to contrast our technique of modelling the defect with the empirical approach proposed by Ogihara in sect . 4.3 of ref. [1]. In the latter the data are fitted with formulae which, while referring to the underlying physics (in a different way from our own), have several empirically determined scale factors and power law dependences. Our approach, by comparison, would seem to be more tightly constrained by the underlying physics through slightly lengthy but basically simple mathematical analyses [3,4]. Such an approach is, we feel, always the more instructive, and in our case when supplied with the appropriate parameters would appear to give results in no way inferior to those from the other, more pragmatic, model. Acknowledgement I would like to thank my colleague Prof. C.F .G . Delaney for a critical reading of this note .
38 3
References [1] M. Ogihara, Y. Nagashima, W. Galster and T. Mikumo, Nucl . Instr. and Meth. A251 (1986) 313. [2] E.C. Finch and A.L . Rodgers, Nucl. Instr. and Meth . 113 (1973) 29. [3] E.C. Finch, Nucl . Instr. and Meth. 113 (1973) 41 . [4] E.C . Finch, M. Asghar and M. Forte, Nucl. Instr. and Meth . 163 (1979) 467. [5] B.D. Wilkins, M.J. Fluss, S.B. Kaufman, C.E. Gross and E.P . Steinberg, Nucl . Instr. and Meth . 92 (1971) 381. [6] E.P . Steinberg, S.B . Kaufman, B.D. Wilkins, C.E. Gross and M.J. Fluss, Nucl. Instr. and Meth . 99 (1972) 309. [7] E.C . Finch, M. Asghar, M. Forte, G. Siegert, J. Greif, R. Decker and the LOHENGRIN collaboration, Nucl . Instr. and Meth. 142 (1977) 539. [8] D.W . Potter and R.D . Campbell, Nucl . Instr. and Meth . 153 (1978) 525. [9] T. Kitahara, H. Geissel, Y. Laichter and P. Armbruster, Nucl. Instr. and Meth . 196 (1982) 153. [10] P.A . Tove and W. Seibt, Nucl . Instr. and Meth. 57 (1967) 261. [111 W. Seibt, K.E. Sundstr6m and P.A . Tove, Nucl . Instr. and Meth. 113 (1973) 317. [12] E.C . Finch, A.A. Cafolla and M. Asghar, Nucl. Instr. and Meth. 198 (1982) 547.
A257 (1987) 381-383
381
SYSTEMATIC MEASUREMENTS OF PULSE HEIGHT DEFECTS FOR HEAVY IONS IN SURFACE BARRIER DETECTORS - A COMMENT E.C . FINCH University of Dublin, Department of Pure and Applied Physics, Trinity College, Dublin 2, Ireland
Received 16 January 1987 Newly published data on the pulse height defect and its field dependence in heavy ion surface barrier detectors are reported by Oginara et al . to be in conflict with previous models developed by us . We show that this apparent discrepancy is due to the use by them in our models of inappropriately chosen parameters .
Ogihara et al. [1] have recently produced a new experimental and theoretical survey of the pulse height defect produced by various accelerator derived heavy ions in several silicon surface barrier detectors. Extensive comparisons are included with our own surveys made with mass and energy separated fission fragments incident on heavy ion silicon surface barrier detectors [2-4]. Such comparisons are possible because there is considerable overlap between the mass and energy regions studied by Ogihara et al. and by us . The purpose of this comment is to discuss the comparisons which they have made . Our data as given in table 1 of ref. [4] show unambiguously that for all fourteen fragment mass and energy combinations studied the defect decreases for increasing fields. Even our earlier data in ref. [2], while more restricted, nevertheless show that the defect and its mass dependence decrease when the detector applied bias and electric field are raised . This is in distinction to the statement in the introduction of Ogihara that our field dependence data presented in refs . [2] and [4] "are very poor and no clear trend could be established" . Most of the discussion in Ogihara of our work centres on our modelling of the defect, and in particular of that part due to charge recombination through the plasma formed in the wake of a heavy ion. Ogihara is correct in noting that difficulties may arise in the principle of separation of the defect into window dependent, atomic collision and recombination parts; in particular, surface recombination losses are not easy to estimate . The very useful model developed by Wilkins et al . and Steinberg et al. [5,6], for example, envisages that charge recombination occurs in a silicon surface layer behind the entrance window. However, as remarked in ref. [4], the considerable thickness (up to 1 p,m) needed for this layer for fission fragments causes difficulties of 0168-9002/87/$03 .50 C Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
interpretation, and furthermore the predictions are at best confirmed only roughly by some experiments [7,8]. More recently this last conclusion was also reached by Kitahara et al . [9]. We therefore still feel that our modelling of the defect, with its splitting into three components as given above and developed by us in refs . [3] and [4], is a useful alternative concept to pursue . In our previous papers [3,4] we envisaged that the electron-hole plasma formed in the wake of a stopping ion decays through extraction of carriers by the detector depletion layer electric field within the plasma lifetime tp , as described by Tove et al . and Seibt et al. [10,11]. Hence a very simple expression for the recombination defect 4 r is given by eqs. (1) and (2) of ref . [3] or by eq. (3) of ref. [4] as A,/E= tp/tr for
tp << tr,
where t r is the carrier recombination lifetime within the plasma . This model (which we shall here call model A) neglects the radial expansion with time of the plasma column because of the ambipolar diffusion outwards of electrons and holes. Our second model (model B), which is derived from model A, allows for the column radial expansion and leads to the expression . A r/E= (n,o/3?TDaC) ln(4Da tp /rti ),
(2)
which is eq. [13] of ref. [4]. Here njo (m -1 ) is the distance averaged initial linear charge density, Da (m2 s -1 ) the ambipolar diffusion coefficient, ro the plasma column initial radius, C (sm -3 ) = 10 2° to , to (s) is the low density minority carrier lifetime, and 4Da tp >>r:02 . In the derivation of eq . [2] the recombination time t r (<< to) is taken to be inversely proportional to the volume carrier density n, such that t r = C/n . Thus as the column expands n falls and t r rises.
38 2
E. C Finch / Pulse height defects in surface barrier detectors
These two models fitted well to our own data for the recombination defect (except at very low fields, for reasons described there), as can be seen from figs . 2 and 3 of ref. [4] . However, it appears from fig. 3 in Ogihara [1] that our model B does not fit their own data. There seems to be no reason to doubt that Ogihara's data are, like ours, of good quality. Indeed there is close agreement between our and Ogihara's data for both A r and the total defect as a function of energy at fixed bias around the normal value. This may be verified by comparing our data for 90 and 135 amu fragments (table 1 in ref. [4]) with Ogihara's 79 Br and 1271 results (figs. 1 and 4 in ref . [1]) . This is for Ogihara's detectors 2 and 4 which, like our own, are of low resistivity . It therefore becomes of central importance to determine the cause of the discrepancies described by them . One difference between their work and ours lies in the data used for the plasma lifetime t P . We used our own data [12] for tp rather than Ogihara's procedure of using Seibt's expression (eq . (14) in ref. [111) . Since our data are, as we state in ref. [7], in broad (although not exact) agreement with Seibt's work, we do not expect this difference to explain the discrepancies just described . Ogihara et al . are able to obtain reasonable fits of our model to their data only by introduction of complex empirical assumptions (their eqs. (5)-(11)) about Da , C, t o and t p . As they concede, this is not a very satisfactory procedure . We believe that such assumptions are in fact unnecessary, as we shall show. We fitted the recombination data of our experiment to our expressions (eqs. (1) and (2) above) by rewriting each of them in the form y = mx + c and plotting the appropriate quantities so as to obtain satisfactory straight line least-squares fits (figs . 2 and 3 in ref. [4]) . In addition to demonstrating the general validity of our models, this procedure enabled us to derive from our data appropriate values for, in model A, the minority charge carrier lifetime t o in terms of the constant radius of the plasma column, and, in model B, both t o and the initial column radius ro independently . We discuss this point in more detail later on . The values selected by Ogihara for t o and ro are inappropriate, and are a primary cause of the discrepancies in their fig . 3 between their data for d, and the predictions made by them with our model. We now 'try to explain firstly for t o and then for to why this is so . The expression t o = 52po.6 used by Ogihara in eq . (2) above, where p is the silicon resistivity in fl m and t o is in Its, was taken by them from our earlier ref. [3]. We there described it as an upper limit to the minority carrier lifetime because of several possible effects including, perhaps, the effects of radiation damage caused by an ion inside its own plasma . As Ogihara points out, we produced in ref . [4] some evidence from our data
which supported this suggestion. Unlike Ogihara we did not in fact substitute this expression for to directly in eq. (2) above, both for this reason and also because as stated above we could independently derive appropriate values for t o . These are, as anticipated, less than the value which would be given by t o = 52po.6 for the value of p we quoted . Nevertheless it is clear both from fig. 3 in Ogihara and also from Kitahara [9] that data taken with different resistivity detectors qualitatively follow the trends indicated by our own expression for the upper limit to to . The value of 1 .5 ttm used by Ogihara for to is half that derived by us [4], which as we noted is indeed rather larger than suggested elsewhere . (It is possible because of an ambiguity in Ogihara's wording to infer that this value came from ref. [3], but this is not the case .) However, examination of eq. (2) above shows that a larger value of ro , as was deduced by us by leastsquares fitting to our data, increases the field dependence of this expression for Ar . This is just what is required by the data shown by Ogihara in his fig . 3 . Note that ro , unlike to , does not act as a simple scale factor in eq . (2) above. It would be of great interest to pursue further the fitting of Ogihara's field dependence data to our model and use our linear least-squares fitting procedure . Unfortunately however, Ogihara does not quote the ion energy used for his total and recombination defect field dependence data in his figs . 2, 3 and 5, and this energy appears in a nonlinear fashion (through N o and t p ) in eq . (2) above. As far as we can tell Ogihara's data do not appear to be too dissimilar to our own, and in any case we have already noted the close agreement around normal bias between their data and ours. The important remark of Ogihara that our model A gives predictions for A r half an order of magnitude larger than those from model B needs careful discussion . For a plasma column radius in model A of reasonable magnitude and equal to the initial radius ro in model B this is correct and would be expected. The amount of recombination in model A, where plasma radial expansion is neglected, would then, for the same low density minority carrier lifetime, naturally be larger than in model B - here the volume carrier density decreases and the lifetime increases as the column expands . In contrast, model A becomes a limiting case of model B when (unlike in usual practice) the ambipolar diffusion coefficient Da << ró/4t, as can be deduced from the appendix to ref . [4]. These differences in predictions for 4 r can of course be adjusted by a suitable choice of radius values and low density carrier lifetimes which best fit the data. For example, for the same Ar and low density lifetime the radius from model B is lower than from model A . We have already discussed extensively the interrelation of the best lifetime and radius values [3,4] (see especially
E C Finch / Pulse height defects m surface barrier detectors
above and also the second paragraph of the conclusion to ref. [4]) . In this way there is no problem to fitting either model (not exactly, of course) to our data, even though the initial assumptions for each model are not identical . We are further encouraged in that the resulting radius and lifetime values do not appear unreasonable. Finally, it is of interest to contrast our technique of modelling the defect with the empirical approach proposed by Ogihara in sect . 4.3 of ref. [1]. In the latter the data are fitted with formulae which, while referring to the underlying physics (in a different way from our own), have several empirically determined scale factors and power law dependences. Our approach, by comparison, would seem to be more tightly constrained by the underlying physics through slightly lengthy but basically simple mathematical analyses [3,4]. Such an approach is, we feel, always the more instructive, and in our case when supplied with the appropriate parameters would appear to give results in no way inferior to those from the other, more pragmatic, model. Acknowledgement I would like to thank my colleague Prof. C.F .G . Delaney for a critical reading of this note .
38 3
References [1] M. Ogihara, Y. Nagashima, W. Galster and T. Mikumo, Nucl . Instr. and Meth. A251 (1986) 313. [2] E.C. Finch and A.L . Rodgers, Nucl. Instr. and Meth . 113 (1973) 29. [3] E.C. Finch, Nucl . Instr. and Meth. 113 (1973) 41 . [4] E.C . Finch, M. Asghar and M. Forte, Nucl. Instr. and Meth . 163 (1979) 467. [5] B.D. Wilkins, M.J. Fluss, S.B. Kaufman, C.E. Gross and E.P . Steinberg, Nucl . Instr. and Meth . 92 (1971) 381. [6] E.P . Steinberg, S.B . Kaufman, B.D. Wilkins, C.E. Gross and M.J. Fluss, Nucl. Instr. and Meth . 99 (1972) 309. [7] E.C . Finch, M. Asghar, M. Forte, G. Siegert, J. Greif, R. Decker and the LOHENGRIN collaboration, Nucl . Instr. and Meth. 142 (1977) 539. [8] D.W . Potter and R.D . Campbell, Nucl . Instr. and Meth . 153 (1978) 525. [9] T. Kitahara, H. Geissel, Y. Laichter and P. Armbruster, Nucl. Instr. and Meth . 196 (1982) 153. [10] P.A . Tove and W. Seibt, Nucl . Instr. and Meth. 57 (1967) 261. [111 W. Seibt, K.E. Sundstr6m and P.A . Tove, Nucl . Instr. and Meth. 113 (1973) 317. [12] E.C . Finch, A.A. Cafolla and M. Asghar, Nucl. Instr. and Meth. 198 (1982) 547.