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Statistics of Transmitted Secondary Electron Multiplication
Statistics of Transmitted Secondary Electron Multiplication W. L. U’ILCOCKt Applied Physics Department, Imperial College University of London, England
The size-spectrum of output light pulses from image intensifiers with five stages of transmitted secondary electron multiplication, when single electrons are emitted from the photocathode, has been examined on a number of occasions,’: and there is general agreement that it approximates more or less closely to an exponential distribution. These observations are of importance in assessing the capabilities of this type of image intensifier as an image-preserving device, but they do not allow reliable inferences to be drawn about the statistics of electron multiplication at a single transmission-type dynode. For one reason, the electron pulses which reach the luminescent screen of the intensifier are the result of a fivefold cascade of multiplication processes, which are not known all to have the same statistical properties. Again, the process of conversion a t the luminescent screen from pulses of electrons t o pulses of photons is itself subject to statistical fluctuations, which become increasingly significant for smaller pulse sizes. Thus, although the measurements which have been made with completed intensifiers are consistent with an exponential probability law for electron multiplication at each transmission-type dynode, they do not prove that such a law is in fact obeyed. To examine this question, it is necessary t o work with a single dynode, and to use some means of detecting the transmitted secondary electrons which is not subject to the large fluctuations associated with multiplication at further dynodes. One such means, which has been employed by Kollatli et aL2* in studies of reflected secondary emission, is a scintillation counter. An alternative, which appears t o be technically preferable and has been used in the present instance, is a silicon surface-barrier detector. The experimental arrangement is shown diagrammatically in Fig. 1. The dynode is held in a continuously pumped tube fabricated from short glass cylinders sealed to Nilo-K rings, to which are attached stainless steel annuli which serve as
t
Now at Physirg Department, ITriiverrJitj College of North Wale8, Bangor. Caerriarvonshire, Web.
$ Seep . 71.
629
630
W. L. WILCOCK
accelerating electrodes. The dynode holder is fitted with an iron slug and pivoted so that the dynode can be removed from the axis of the tube with the aid of an externally held magnet. At one end of the tube is an electron gun to provide primary electrons, which are accelerated to an energy of several keV and focused onto the dynode by the axial magnetic field of a solenoid which surrounds the tube. The transmitted secondary electrons are accelerated to an energy of about 40 keV and similarly focused on the detector. The detector is effectively a solid ionization chamber, of about 3 mm diameter cross-section, in which a 40 keV electron creates on average about lo4 electron-hole pairs. These free charge carriers are
Dynode
4 1 1I 1 I To p u m p s
Fro. 1. Diagram of expcriinental arrangement used to examine statistirs of secondary electron emission from a transmission-type dynode.
separated by an electric field inside the detector, and the resulting current produces a pulse a t the output of the detector, proportional to the number of charge carriers created. When a single primary electron strikes the dynode, the secondary electrons it produces all reach the detector effectively simultaneously, so that the average number of charge carriers created is proportional to the number of secondary electrons arising from the primary. It follows that, when the dynode is bombarded by a stream of single electrons from the gun, the pulse amplitude spectrum from the detector represents the discrete probability distribution for multiplication a t the dynode, modified by the effects of noise in the detector and its associated amplifiers. A typical pulse-amplitude spectrum obtained with a bulk-density potassium chloride dynode is shown in Fig. 2. The broken curve shows the spectrum when the dynode is removed from the axis of the tube, so that the detector is exposed directly to the primary electrons from the
STATISTICS OF TRANSMITTED SECONDARY EMISSION
63 1
gun. Apart from the small amplitude noise pulses from the detector itself, the spectrum consists of a single peak, showing that the gun does indeed furnish single electrons. The contipuous curve is the spectrum when the dynode is inserted. ln addition to a peak corresponding to single secondary electrons, there are additional resolved peaks corresponding to groups of 2 , 3, 4, 5 and 6 secondary electrons.
1'
Pulse h e i g h t ( o r b i t r o r y units ) P I G . 2. Typical pulse amplitude spectra. Rroken rui-ve: spectrum of primary electrons; continuous curve: spectrum of traiisnlitted secondary electrons from a bulkdensity KCI dynode. The single-electron peaks of the two curves are displaced in the horizontal direction because the primary electrons reach the detector with higher energy than the secondaries.
This particular spectrum was taken with a single-channel pulse-height analyser, which makes severe demands on the current stability of the electron gun. More recently spectra have been taken with a multichannel analyser, which has made it possible to resolve peaks as far as the eighth, and observations have been made on different specimens of dynode and with primary electrons of different energies; but in all cases the spectra obtained are of form similar to that shown. Excluding for the moment the single-electron peak, the distributions appear to obey an exponential law as far as the 4th or 5th peak, but thereafter depart from it in the sense that there is an excess of larger pulses. The relative height of the single-electron peak is found to be
632
W. L. WILCOCK
strongly dependent on the position on the detector of the focal spot for slow electrons. When this spot is near the centre of the detector, the single-electron peak conforms approximately to the exponential law also, but if the spot is displaced to one side the relative height of the single-electron peak increases. It is presumed that this effect is due to the presence of fast electrons from the dynode, which are not focused with the slow secondaries, but reach the plane of the detector a t some distance from the axis. Unfortunately, because of deficiencies in the electron optics, the focal spot in the present tube is nearly 1 mm in diameter, and there is no provision for monitoring its position on the detector whilst the tube is in operation. Further, it is necessary to switch off the high potential whilst the external magnet is used to move the dynode into or out of the beam, and it is found that this operation may shift the position of the focal spot transversely, in an unpredictable way, by an amount comparable to the radius of the detector. It is believed that this shift is due in part to re-distribution of wall charge, and in part to alteration of the magnetization of the Nilo-K rings which form part of the tube structure. Because of this behaviour it has not proved possible to specify the probability distribution completely by measuring the probability that a primary electron will produce no secondaries, nor to establish how the probability distribution for a particular dynode varies with primary energy and mean electron multiplication. These experiments require the dynode to be moved into and out of the beam repeatedly, and the present tube does not give consistent results. It is hoped to investigate these questions with a tube of improved design in the near future.
REFERENCES 1. Emberson, D. L., Todkill, A. and Wilcock, W. L., In “Advances in Electronics
and Electron Physics”, ed. by J . D. McGee, W. L. Wilcock and L. Mandel, Vol. 16, p. 127. Academic Press, New York (1962). 2. Kollath, R. and Simon, I<. H., 2. Phys. 179, 174 (1964). 3. Haussler, P., 2. Phys. 179, 279 (1964).
DISCUSSION c. D . GRAVES: Have you tried using an external magnet to bring the electron beam back into focus at the detector after removal of your dynode? w. L. WILCOCK: It is not possible with the present tube to make use of external trimming magnets because there is no provision for introducing a luminescent screen in front of the detector to show where the beam is when the tube is in operation. This is a desirable modification. E. L. GARWIN: How doe8 the pulse-height distribution curve presented compare with a Poisson diritribution which has the same mean as the average gain of the dynode?
STATISTICS OF TRANSMITTED SECONDARY EMISSION
633
What uas thc gain of the tlyiiode used under the same conditions as those prevailuig when the pulse-height spertriim was taken? w. I,. W I L ( ~ O ( ’ R : To aiiswer your seconcl question first, the mean electron gain corrrspontling to t h e pulse spertrum shou 11 u as mc~axuredas 3.0. For A Pi>irsoniiiqtrihiition with mean ii 3 , the probahility p ( n ) of n has the values 0.05, 0.15, 0.25, 0.25, 0.17, for rt = 0, I , 2, 3, 4 rerpertively. If p ( 0 ) is greater than 0 . 0 5 , but t h e tlistr-ibution IS otherwiw Poissonian with mean 3, the most probable value of n is 4 or more. In contrast, all the results so far obtained for t h e transmission secoritlara ernission process give tho emission of 1 secondary rlertron (or possibly no srrondar~ electrons at all) as the most probahle oiitconw o f a primary enrountrr. M. G K E E K : Ha1.e yon made, or do you plan t o make, similar measurements on low density tlynotles? w. L. W I T , ~ ~ O C I CIVe : d o plan to (10 so. ~
The size-spectrum of output light pulses from image intensifiers with five stages of transmitted secondary electron multiplication, when single electrons are emitted from the photocathode, has been examined on a number of occasions,’: and there is general agreement that it approximates more or less closely to an exponential distribution. These observations are of importance in assessing the capabilities of this type of image intensifier as an image-preserving device, but they do not allow reliable inferences to be drawn about the statistics of electron multiplication at a single transmission-type dynode. For one reason, the electron pulses which reach the luminescent screen of the intensifier are the result of a fivefold cascade of multiplication processes, which are not known all to have the same statistical properties. Again, the process of conversion a t the luminescent screen from pulses of electrons t o pulses of photons is itself subject to statistical fluctuations, which become increasingly significant for smaller pulse sizes. Thus, although the measurements which have been made with completed intensifiers are consistent with an exponential probability law for electron multiplication at each transmission-type dynode, they do not prove that such a law is in fact obeyed. To examine this question, it is necessary t o work with a single dynode, and to use some means of detecting the transmitted secondary electrons which is not subject to the large fluctuations associated with multiplication at further dynodes. One such means, which has been employed by Kollatli et aL2* in studies of reflected secondary emission, is a scintillation counter. An alternative, which appears t o be technically preferable and has been used in the present instance, is a silicon surface-barrier detector. The experimental arrangement is shown diagrammatically in Fig. 1. The dynode is held in a continuously pumped tube fabricated from short glass cylinders sealed to Nilo-K rings, to which are attached stainless steel annuli which serve as
t
Now at Physirg Department, ITriiverrJitj College of North Wale8, Bangor. Caerriarvonshire, Web.
$ Seep . 71.
629
630
W. L. WILCOCK
accelerating electrodes. The dynode holder is fitted with an iron slug and pivoted so that the dynode can be removed from the axis of the tube with the aid of an externally held magnet. At one end of the tube is an electron gun to provide primary electrons, which are accelerated to an energy of several keV and focused onto the dynode by the axial magnetic field of a solenoid which surrounds the tube. The transmitted secondary electrons are accelerated to an energy of about 40 keV and similarly focused on the detector. The detector is effectively a solid ionization chamber, of about 3 mm diameter cross-section, in which a 40 keV electron creates on average about lo4 electron-hole pairs. These free charge carriers are
Dynode
4 1 1I 1 I To p u m p s
Fro. 1. Diagram of expcriinental arrangement used to examine statistirs of secondary electron emission from a transmission-type dynode.
separated by an electric field inside the detector, and the resulting current produces a pulse a t the output of the detector, proportional to the number of charge carriers created. When a single primary electron strikes the dynode, the secondary electrons it produces all reach the detector effectively simultaneously, so that the average number of charge carriers created is proportional to the number of secondary electrons arising from the primary. It follows that, when the dynode is bombarded by a stream of single electrons from the gun, the pulse amplitude spectrum from the detector represents the discrete probability distribution for multiplication a t the dynode, modified by the effects of noise in the detector and its associated amplifiers. A typical pulse-amplitude spectrum obtained with a bulk-density potassium chloride dynode is shown in Fig. 2. The broken curve shows the spectrum when the dynode is removed from the axis of the tube, so that the detector is exposed directly to the primary electrons from the
STATISTICS OF TRANSMITTED SECONDARY EMISSION
63 1
gun. Apart from the small amplitude noise pulses from the detector itself, the spectrum consists of a single peak, showing that the gun does indeed furnish single electrons. The contipuous curve is the spectrum when the dynode is inserted. ln addition to a peak corresponding to single secondary electrons, there are additional resolved peaks corresponding to groups of 2 , 3, 4, 5 and 6 secondary electrons.
1'
Pulse h e i g h t ( o r b i t r o r y units ) P I G . 2. Typical pulse amplitude spectra. Rroken rui-ve: spectrum of primary electrons; continuous curve: spectrum of traiisnlitted secondary electrons from a bulkdensity KCI dynode. The single-electron peaks of the two curves are displaced in the horizontal direction because the primary electrons reach the detector with higher energy than the secondaries.
This particular spectrum was taken with a single-channel pulse-height analyser, which makes severe demands on the current stability of the electron gun. More recently spectra have been taken with a multichannel analyser, which has made it possible to resolve peaks as far as the eighth, and observations have been made on different specimens of dynode and with primary electrons of different energies; but in all cases the spectra obtained are of form similar to that shown. Excluding for the moment the single-electron peak, the distributions appear to obey an exponential law as far as the 4th or 5th peak, but thereafter depart from it in the sense that there is an excess of larger pulses. The relative height of the single-electron peak is found to be
632
W. L. WILCOCK
strongly dependent on the position on the detector of the focal spot for slow electrons. When this spot is near the centre of the detector, the single-electron peak conforms approximately to the exponential law also, but if the spot is displaced to one side the relative height of the single-electron peak increases. It is presumed that this effect is due to the presence of fast electrons from the dynode, which are not focused with the slow secondaries, but reach the plane of the detector a t some distance from the axis. Unfortunately, because of deficiencies in the electron optics, the focal spot in the present tube is nearly 1 mm in diameter, and there is no provision for monitoring its position on the detector whilst the tube is in operation. Further, it is necessary to switch off the high potential whilst the external magnet is used to move the dynode into or out of the beam, and it is found that this operation may shift the position of the focal spot transversely, in an unpredictable way, by an amount comparable to the radius of the detector. It is believed that this shift is due in part to re-distribution of wall charge, and in part to alteration of the magnetization of the Nilo-K rings which form part of the tube structure. Because of this behaviour it has not proved possible to specify the probability distribution completely by measuring the probability that a primary electron will produce no secondaries, nor to establish how the probability distribution for a particular dynode varies with primary energy and mean electron multiplication. These experiments require the dynode to be moved into and out of the beam repeatedly, and the present tube does not give consistent results. It is hoped to investigate these questions with a tube of improved design in the near future.
REFERENCES 1. Emberson, D. L., Todkill, A. and Wilcock, W. L., In “Advances in Electronics
and Electron Physics”, ed. by J . D. McGee, W. L. Wilcock and L. Mandel, Vol. 16, p. 127. Academic Press, New York (1962). 2. Kollath, R. and Simon, I<. H., 2. Phys. 179, 174 (1964). 3. Haussler, P., 2. Phys. 179, 279 (1964).
DISCUSSION c. D . GRAVES: Have you tried using an external magnet to bring the electron beam back into focus at the detector after removal of your dynode? w. L. WILCOCK: It is not possible with the present tube to make use of external trimming magnets because there is no provision for introducing a luminescent screen in front of the detector to show where the beam is when the tube is in operation. This is a desirable modification. E. L. GARWIN: How doe8 the pulse-height distribution curve presented compare with a Poisson diritribution which has the same mean as the average gain of the dynode?
STATISTICS OF TRANSMITTED SECONDARY EMISSION
633
What uas thc gain of the tlyiiode used under the same conditions as those prevailuig when the pulse-height spertriim was taken? w. I,. W I L ( ~ O ( ’ R : To aiiswer your seconcl question first, the mean electron gain corrrspontling to t h e pulse spertrum shou 11 u as mc~axuredas 3.0. For A Pi>irsoniiiqtrihiition with mean ii 3 , the probahility p ( n ) of n has the values 0.05, 0.15, 0.25, 0.25, 0.17, for rt = 0, I , 2, 3, 4 rerpertively. If p ( 0 ) is greater than 0 . 0 5 , but t h e tlistr-ibution IS otherwiw Poissonian with mean 3, the most probable value of n is 4 or more. In contrast, all the results so far obtained for t h e transmission secoritlara ernission process give tho emission of 1 secondary rlertron (or possibly no srrondar~ electrons at all) as the most probahle oiitconw o f a primary enrountrr. M. G K E E K : Ha1.e yon made, or do you plan t o make, similar measurements on low density tlynotles? w. L. W I T , ~ ~ O C I CIVe : d o plan to (10 so. ~