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Directional dependence of energy measurements in Ge(Li) spectrometers
NUCLEAR INSTRUMENTS AND METHODS 116 (1974)
177-179 ; Q NORTH-HOLLAND PUBLISHING CO .
DIRECTIONAL DEPENDENCE OF ENERGY MEASUREMENTS IN Ge(Li) SPECTROMETERS P. C. LICHTENBERGER and I. K. MacKENZIE Physics Department, University of Guelph, Guelph, Ontario, Canada Received 10 December 1973 Precise measurements oftheenergy of gamma rays show variations up to 110eV, depending on the direction from which the radiation is incident on a trapezoidal Ge(Li) detector .
While developing a technique for differential energy spectrometry of annihilation radiation') we encountered significant variations in the apparent energy, depending on the source location. With a particular closed-end cylindrical, coaxial detector we found a centroid shift of 8 eV between two locations which should have been equivalent, judging by external
TABLE I
Centroid variation of three gamma-ray lines, one of which is mobile. Source position (see fig . 1)
geometry . It is, of course, well known that nonuniformity of the Ge stockcan lead to local variations in the lithium drifting process. The resulting departure from cylindrical symmetry in the shape of the undepleted core may produce a lack of radial symmetry in the efficiency of charge collection'). With the belief
5 6 7 8 1 2 2 2 2 9 10
that this type of defect would be magnifiedin adetector with highly non-uniform field strength, we decided to do a more extensive study on a closed-end, trapezoidal detector. A NuclearDiodes detector with an efficiency of 2.3% and a nominal active volume of 20 cm' was used. It is mounted in a conventional cryostat with a vertical
dip-stick, thecore lying in a vertical plane . The resolution with broad-beam radiation incident from above is
Centroid channel number Zero Gain Probe reference reference 54.525 54.524 . 54.533 54.538 54 .536 54.530 54 .533 54 .522 54.527 54 .527 54.530
833.329 833 .336 833.334 833.338 833.339 833.345 833.336 833.343 833.345 833.330 833.341
182.119 182.091 182.346 182.396 182.462 182.279 182.277 182.270 182 .261 182.379 182 .352
Centroid shift (eV) (ref. pos'n9) I -41 -46 -5 +3 +13 -16 -16 -17 -19 0 -4
1 .55 keV on the 514 keV line of "Sr and 2.20 keV on the 1.33 MeV line of 6'Co. The external geometry of the ingot was explored by directing a collimated beam of radiation normal to the end plate of the detector, using the 411 keV line of "'Au . A contour map of count rate in the full-energy peak outlined theshape of
the active region with the results shown in fig . 1 . The dotted lines and associated numbers indicate the directions of subsequent irradiations. It is odd that the angles opposite the curved surface are unequal, since a normal ingot would have such symmetry. We can only conjecture that an accident in fabrication or some visible imperfection persuaded the manufacturer to
Fig. 1 . Horizontal crosssection of thedepleted region as defined by acollimated vertical beam of 411 keVgammarays . The dashed lines and associated numbers give the orientation of horizontal probes . Positions 9 and 10 give thepositions of vertical probes, the former beingthe reference direction.
grind away part of the ingot before drifting. The spectroscopy system, which included a biased amplifier, was conventional in most respects. A dual digital stabilizer was used with relatively high settings on the stabilizer gain, since we were not greatly concerned about stabilizer broadening. In each measure-
177
178
P. C
'LICHTENBERGER AND I. K . MaCKENZIE
TABLE 2 Dependence of centroid position on energy,' collimation and bias . The symbol (c) indicates that the radiation was collimated .
Energies of gamma rays (keV) Zero Gain
Bias M
1173 392 392 392 392 392
860 860 860 760 660 510
Probe 1114 411 411 411 411 411
(c) ('c) (c) (c)
1332 514 514 514 514 514
Centroid shift (W) w.r .t. position 9 for position shown 1 5 6 7 8 +71 +39 +13 +8 +39 +55
ment we used two gamma-ray line sources whose positions were fixed rigidly relative to the detector, one line acting as the reference for stabilizing the zero ofthe ADC while the other served for gain stabilization. A third source was moved to irradiate the detector from various directions, ensuring that the total count rate stayed constant to within 1% in order to avoid any spurious shifts due to varying count rates . Table 1 shows the results of a series of measurements using the 392 keV line of t13Sn for zero stabilization, the 514 keV line of 85 Sr for gain stabilization and a collimate? t9sAu source as the probe. The total count rate was 3500 cps and the dispersion was 158 eV per channel. The maximum differences in centroid positions for the reference lines are 2 .53 eV for the gain reference and 2.46 eV for the zero reference . It is notable that, for the four consecutive runs when the probe source was not moved, the centroid of the 411 keV line showed a maximum variation of 2 .84 eV. Based on these observations we expect the standard error in the centroid of a probe line to be about 1 eV, certainly very much smaller than the shifts observed . Table 2 is a condensation of several sets of measurements similar to those detailed in table 1 . The tabulated shifts are relative to the centroid when the source is placed at position 9, i.e . for radiation incident from above into the centre of the detector. The probing was done with uncollimated radiation of 1 .114 MeV from e1Zn and then with uncollimated "'Au in order to study the dependence o .' the asymmetry effect on gamma-ray energy. A collimated source of i9. Au was used next to check the effect of increased localization of the ionization. Finallythe influence of detector bias was checked to see the dependence of the :centroid shifts on electric field strength. The results deviated generally from our expectations which were based on arguments about the variation in
-39 -15 -42 -49 -30 -23
+2 -46
+31 +24 -5
+44 +35 +3
Shift of 5-t . 1 (.V) 110 54 55 57 69 78
the field strengths . These seem to be predictable on the basis of external geometry as indicated by the spatial variation in the timing properties of simil .-r detectors') . We expected that the increased localization of the ionization achieved by lowering the gamma-ray energy and by collimation would enhance the variation in centroid position . It is clear from comparison of rows 1 and 2 of table 2 that the centroid shifts actually increased with energy and were roughly proportional to it. Rows 2 and 3 suggest that collimation did not cause enhanced contrast although it was not equivalent to broad-beam irradiation . The last column in table 2 gives the relative centroid shift between the two directions which usually showed the largest differences . Comparing the last four rows, we see that the relative centroid shifts were not markedly sensitive to detector bias and hence to absolute field strength. The most surprising result, which is apparent from comparison of fig . 1 with both tables, is that the centroid shift did not have the expected correlation with external geometry. One would expect that directions 2; 4, 5 and 7 would be almost equivalent, with appreciable negative shifts for positions 3, 8 and 10. The lack of such a strong correlation, combined with the insensitivity to detector bias, leads us to the conclusion that some other deficiency masked the influence of non-uniformity of the electric field . A possibility, suggested by M . Wormald, is the variation in depth of the undepleted n-type surface. Incomplete charge collection in this layer would not correlate necessarily with detector shape and hence even true coaxial detectors might' display centroid shifts similar in size to those we have observed. The stability of Ge(Li) systems, as indicated in table' 1, justifies the specification of gamma-ray energies to a precision of about 1 eV provided that great care is taken in positioning of all sources used ' in the calibration and measurements . It is, however,
DIRECTIONAL DEPENDENCE OF ENERGY MEASUREMENTS possible to introduce systematic errors of 100eV if the directional dependence of the centroid is ignored. Our studies were limited to a single detector of good quality and to gamma-ray energies of 411 keV and 1 114keV. It is possible that even larger systematic
errors will arise with other detectors and for gamma rays outside theenergy range investigated.
This research is financed by a Grant from the
179
National Research Council of Canada which also provides a fellowship (P .C .L .). References 1) I. K. MacKenzie and P. C. Lichtenberger, submitted to Appl . Phys. 2) P. P. Webb, H. L. Malm, M. G. Chartrand, R. M. Green, E. Sakai and I. L. Fowler, Nucl. Instr. and Meth . 63 (1965) 125. 3) R. L. Graham, 1 . K. MacKenzie and G. T. Ewan, IEEE Trans. Nucl. Sci. NS-13, no . 1 (1966) 72.
177-179 ; Q NORTH-HOLLAND PUBLISHING CO .
DIRECTIONAL DEPENDENCE OF ENERGY MEASUREMENTS IN Ge(Li) SPECTROMETERS P. C. LICHTENBERGER and I. K. MacKENZIE Physics Department, University of Guelph, Guelph, Ontario, Canada Received 10 December 1973 Precise measurements oftheenergy of gamma rays show variations up to 110eV, depending on the direction from which the radiation is incident on a trapezoidal Ge(Li) detector .
While developing a technique for differential energy spectrometry of annihilation radiation') we encountered significant variations in the apparent energy, depending on the source location. With a particular closed-end cylindrical, coaxial detector we found a centroid shift of 8 eV between two locations which should have been equivalent, judging by external
TABLE I
Centroid variation of three gamma-ray lines, one of which is mobile. Source position (see fig . 1)
geometry . It is, of course, well known that nonuniformity of the Ge stockcan lead to local variations in the lithium drifting process. The resulting departure from cylindrical symmetry in the shape of the undepleted core may produce a lack of radial symmetry in the efficiency of charge collection'). With the belief
5 6 7 8 1 2 2 2 2 9 10
that this type of defect would be magnifiedin adetector with highly non-uniform field strength, we decided to do a more extensive study on a closed-end, trapezoidal detector. A NuclearDiodes detector with an efficiency of 2.3% and a nominal active volume of 20 cm' was used. It is mounted in a conventional cryostat with a vertical
dip-stick, thecore lying in a vertical plane . The resolution with broad-beam radiation incident from above is
Centroid channel number Zero Gain Probe reference reference 54.525 54.524 . 54.533 54.538 54 .536 54.530 54 .533 54 .522 54.527 54 .527 54.530
833.329 833 .336 833.334 833.338 833.339 833.345 833.336 833.343 833.345 833.330 833.341
182.119 182.091 182.346 182.396 182.462 182.279 182.277 182.270 182 .261 182.379 182 .352
Centroid shift (eV) (ref. pos'n9) I -41 -46 -5 +3 +13 -16 -16 -17 -19 0 -4
1 .55 keV on the 514 keV line of "Sr and 2.20 keV on the 1.33 MeV line of 6'Co. The external geometry of the ingot was explored by directing a collimated beam of radiation normal to the end plate of the detector, using the 411 keV line of "'Au . A contour map of count rate in the full-energy peak outlined theshape of
the active region with the results shown in fig . 1 . The dotted lines and associated numbers indicate the directions of subsequent irradiations. It is odd that the angles opposite the curved surface are unequal, since a normal ingot would have such symmetry. We can only conjecture that an accident in fabrication or some visible imperfection persuaded the manufacturer to
Fig. 1 . Horizontal crosssection of thedepleted region as defined by acollimated vertical beam of 411 keVgammarays . The dashed lines and associated numbers give the orientation of horizontal probes . Positions 9 and 10 give thepositions of vertical probes, the former beingthe reference direction.
grind away part of the ingot before drifting. The spectroscopy system, which included a biased amplifier, was conventional in most respects. A dual digital stabilizer was used with relatively high settings on the stabilizer gain, since we were not greatly concerned about stabilizer broadening. In each measure-
177
178
P. C
'LICHTENBERGER AND I. K . MaCKENZIE
TABLE 2 Dependence of centroid position on energy,' collimation and bias . The symbol (c) indicates that the radiation was collimated .
Energies of gamma rays (keV) Zero Gain
Bias M
1173 392 392 392 392 392
860 860 860 760 660 510
Probe 1114 411 411 411 411 411
(c) ('c) (c) (c)
1332 514 514 514 514 514
Centroid shift (W) w.r .t. position 9 for position shown 1 5 6 7 8 +71 +39 +13 +8 +39 +55
ment we used two gamma-ray line sources whose positions were fixed rigidly relative to the detector, one line acting as the reference for stabilizing the zero ofthe ADC while the other served for gain stabilization. A third source was moved to irradiate the detector from various directions, ensuring that the total count rate stayed constant to within 1% in order to avoid any spurious shifts due to varying count rates . Table 1 shows the results of a series of measurements using the 392 keV line of t13Sn for zero stabilization, the 514 keV line of 85 Sr for gain stabilization and a collimate? t9sAu source as the probe. The total count rate was 3500 cps and the dispersion was 158 eV per channel. The maximum differences in centroid positions for the reference lines are 2 .53 eV for the gain reference and 2.46 eV for the zero reference . It is notable that, for the four consecutive runs when the probe source was not moved, the centroid of the 411 keV line showed a maximum variation of 2 .84 eV. Based on these observations we expect the standard error in the centroid of a probe line to be about 1 eV, certainly very much smaller than the shifts observed . Table 2 is a condensation of several sets of measurements similar to those detailed in table 1 . The tabulated shifts are relative to the centroid when the source is placed at position 9, i.e . for radiation incident from above into the centre of the detector. The probing was done with uncollimated radiation of 1 .114 MeV from e1Zn and then with uncollimated "'Au in order to study the dependence o .' the asymmetry effect on gamma-ray energy. A collimated source of i9. Au was used next to check the effect of increased localization of the ionization. Finallythe influence of detector bias was checked to see the dependence of the :centroid shifts on electric field strength. The results deviated generally from our expectations which were based on arguments about the variation in
-39 -15 -42 -49 -30 -23
+2 -46
+31 +24 -5
+44 +35 +3
Shift of 5-t . 1 (.V) 110 54 55 57 69 78
the field strengths . These seem to be predictable on the basis of external geometry as indicated by the spatial variation in the timing properties of simil .-r detectors') . We expected that the increased localization of the ionization achieved by lowering the gamma-ray energy and by collimation would enhance the variation in centroid position . It is clear from comparison of rows 1 and 2 of table 2 that the centroid shifts actually increased with energy and were roughly proportional to it. Rows 2 and 3 suggest that collimation did not cause enhanced contrast although it was not equivalent to broad-beam irradiation . The last column in table 2 gives the relative centroid shift between the two directions which usually showed the largest differences . Comparing the last four rows, we see that the relative centroid shifts were not markedly sensitive to detector bias and hence to absolute field strength. The most surprising result, which is apparent from comparison of fig . 1 with both tables, is that the centroid shift did not have the expected correlation with external geometry. One would expect that directions 2; 4, 5 and 7 would be almost equivalent, with appreciable negative shifts for positions 3, 8 and 10. The lack of such a strong correlation, combined with the insensitivity to detector bias, leads us to the conclusion that some other deficiency masked the influence of non-uniformity of the electric field . A possibility, suggested by M . Wormald, is the variation in depth of the undepleted n-type surface. Incomplete charge collection in this layer would not correlate necessarily with detector shape and hence even true coaxial detectors might' display centroid shifts similar in size to those we have observed. The stability of Ge(Li) systems, as indicated in table' 1, justifies the specification of gamma-ray energies to a precision of about 1 eV provided that great care is taken in positioning of all sources used ' in the calibration and measurements . It is, however,
DIRECTIONAL DEPENDENCE OF ENERGY MEASUREMENTS possible to introduce systematic errors of 100eV if the directional dependence of the centroid is ignored. Our studies were limited to a single detector of good quality and to gamma-ray energies of 411 keV and 1 114keV. It is possible that even larger systematic
errors will arise with other detectors and for gamma rays outside theenergy range investigated.
This research is financed by a Grant from the
179
National Research Council of Canada which also provides a fellowship (P .C .L .). References 1) I. K. MacKenzie and P. C. Lichtenberger, submitted to Appl . Phys. 2) P. P. Webb, H. L. Malm, M. G. Chartrand, R. M. Green, E. Sakai and I. L. Fowler, Nucl. Instr. and Meth . 63 (1965) 125. 3) R. L. Graham, 1 . K. MacKenzie and G. T. Ewan, IEEE Trans. Nucl. Sci. NS-13, no . 1 (1966) 72.