mechanism of channel electron...

IEEE TRANSACTIONS ON NUCLEAR SCIENCE

THE MECHANISM OF CHANNEL ELECTRON MULTIPLICATIONJ. Adams and B.W. Manley

Mullard Research Laboratories,Redhill, Surrey, England

SUMMARY

The paper attempts to relate the importantparameters observed in channelled electron multi-plication to the physical processes involved.Ionic feedback and the effect of channel geometryon it are discussed. Saturation effects occurringin straight channels and curved channels are

described and the different pulse height distri-butions are contrasted.

INTRODUCTION

The channel electron multiplier is now a

well known instrumentl2 which needs only a briefdescription before we discuss its operation indetail.

A channel multiplier is shown in Figure 1.It is a tube of suitably resistive material, witha length which is large compared to its diameter.Between the ends of the multiplying channel a

potential of a few thousand volts is applied invacuum. Electrons or other energetic particlesstriking the low voltage end of the channelrelease secondary electrons with some initialenergy which carries them across the channel.While they traverse the channel the appliedelectric field accelerates the electrons axiallyuntil they collide with the wall with sufficientenergy to release more secondaries. This process

is repeated many times so that a very largenumber of electrons emerge from the output end.The pulse initiated by a single electron may incertain circumstances contain more than 109electrons. The gain obtainable from a channel isa function of a number of parameters: the appliedvoltage, residual gas pressure, the resistanceand geometry of the tube, and pulse repetitionrate.

A channel multiplier amplifies directcurrents and also counts energetic particles byproducing corresponding pulses. This paper isdevoted to pulsed operation.

THE GAIN-VOLTAGE CHARACTERISTIC

We can see intuitively that the energy ofcollision of secondary electrons with the channelwall will increase with the applied voltage butat the same time the number of collisions willdecrease. We thus expect that the gain will riseto a maximum value and then decrease as thevoltage is increased further. An expressionshowing the dependence of gain on the appliedvoltage is derived in Appendix I and is given inequation (1).

4Va2

KV 2 VOG = )

where

.... ... (1)

G is the gainVO is the applied voltageV is the initial energy of the

secondary electroncx is the ratio of length to diameterK is a constant from the relation

= KVc whereis the secondary emission coefficient

and Vc is the collision energy

The theoretical curve in Figure 2 is a plotof equation (1) with reasonable values of theconstants inserted. The experimental curve doesnot show a maximum, but rises to much highergains than are predicted by the model and slowlyflattens out as it approaches some saturationlevel. This is also shown in Figure 2. Thesediscrepancies occur because the simplifiedtheoretical model takes account only of diametrictrajectories. In addition ionic feedback in-creases the gain very considerably in a channelmultiplier.

IONIC FEEDBACKIn any practical system there is always some

residual gas. Some of the gas molecules will beionised by the electrons in the multiplied pulseas it approaches the output end of the tube. Anexpression for the probability of ionisation isderived in Appendix III. The resulting positiveions are accelerated back toward the input endwhere they may strike the wall and producesecondary electrons which re-start the gainprocess. This 'ionic feedback' enhances thegain of the channel very considerably.

Figure 3 shows the result on an oscilloscopeof superimposing a large number of output pulses,each initiated by a single electron. The inter-val between the initiating pulse - the starterpulse - and the rest of the train gives an esti-mate of the charge to mass ratio of the relevantion. The introduction of small amounts of argon

and xenon into the chamber produces the resultsshown in Figure 4(a) and 4(b). The time inter-vals between the starter pulses and the prominentpulses of the trains correspond to A+ and Xe+,respectively accelerated over the full length ofthe channel. In addition, Figure 4(c)+shows a

feedback pulse which corresponds to Hg , pre-

sumably originating from the diffusion pump ofthe vacuum system. These results confirm thatthe multiple pulses are caused by ionic feedback.They also suggest that the first ion to strikethe input end is a hydrogen ion.

88 June

1966 ADAMS AND MANLEY: MECHANISM OF C

Figure 5 shows the gain of the multiplier inboth the starter pulse and the subsequent pulsetrain as functions of voltage. The interestingfeatures of these curves are that the total gainin the pulse is about one or one and a halforders of magnitude greater than that in thestarter pulse, and the gain of the starter pulseis not a function of pressure, whereas the totalgain does increase with pressure. Figure 6 showshow the total gain varies with pressure at a

given multiplier voltage.

Ionic feedback is a mixed blessing. Wehave seen that it increases the gain consider-ably, but makes it sensitively dependent on

pressure. There are applications in which thepressure sensitivity is an embarrassment and itis then desirable to eliminate ionic feedback.

CURVED CHANNELS

The return of positive ions to the input endof the channel can be prevented by bending it.Evans3 has calculated the minimum curvaturenecessary to eliminate feedback by making theions collide prematurely with the wall. A curvedchannel produces a pulse at the output for eachinput particle as shown in Figure 7. The pulseis 40 nS wide in total.

The expression for the gain of a curvedchannel is derived in Appendix II and is givenin equation (2).

( 211 V= 3

36_V V 2\3 36V/G = K .. .. (2)

where f is the ratio of the length of the channelto its radius of curvature, and the other para-meters are the same as in equation (1).

The theoretical characteristic for a Mullardtype B300A curved channel is shown in Figure 8,together with the experimental relation. Thereis good agreement over several orders of magni-tude until the channel starts to saturate.

It is shown also in Appendix II that formost common curved channel geometries theelectrons do not traverse the diameter of thechannel but simply make repeated collisions withthe outer wall as shown in Figure 18. Thesignificance of this result is that the diameter,and hence the length to diameter ratio, is notimportant in a curved channel. The importantparameter is 3, the included angle of the curve.

This has been verified by operating a curvedchannel multiplier having a value of 3 of 5.2,and a length to diameter ratio, Ot, of 18. Thegain-voltage characteristic for this multiplieris shown in Figure 9, and a photograph of themultiplier is shown in Figure 10.

It has not been possible to operate straighttubes with such a low value of a. A straight

HANNEL ELECTRON MULTIPLICATION 89

channel with Ca = 28 has bees operated to give amaximum gain of only 4 x 10 .

SATURATION EFFECTS

The saturation effects seen in both straightand curved channels are not accounted for by thesimple theories of channel multiplication. Thetwo most probable causes are field distortion andspace charge. The pulse in the curved channel isquite short in time and the maximum gain is lessthan in the straight channel; this suggests thatpulses from curved channels are not limited bythe same mechanism as those from straightchannels.

Saturation in Curved Channels

The mechanism of total pulse saturationsuggested by Evans3 is that the emission ofelectrons from near the end of the channelraises the potential of the channel wall untilthere is a low field region which either main-tains but does not augment the gain process oractually acts as an electron sink. This situ-ation is analogous to that in a conventionalphotomultiplier when a very large light pulsereduces the interstage voltages near the outputend so that the secondary emission coefficientsare reduced. As with the photomultiplier it ispossible to raise the limit on pulse height byconnecting shunt capacitors across the last fewstages. This is done with a channel multiplierby placing an earthed sleeve over the lastcentimetre or so. This sleeve also has the effectof broadening the pulse height distribution.

The pulse height distribution is a functionof pulse repetition frequency. At high fre-quencies the distribution is broad; at low fre-quencies it is narrow. The height of a pulsealso depends on the time interval since the pre-ceding pulse; a pulse following quickly afteranother one will be small. As the resistance ofthe channel is reduced the pulse height distri-bution begins to broaden at progressively higherfrequencies and the recovery time between pulsesfalls. These phenomena are illustrated inFigures 11 and 12. For a multiplier of resistance2 x 101%, the recovery time is about 1 msec. Ifthe resistance is 109 Q the recovery time is about30 ptsec. These figures are consistent with afield distortion model where the equivalentcircuit is a resistance capacity chain as shownin Figure 13.

Since the electron energies emerging from achannel multiplier range up to 100 eV, theeffective capacity of the channel may be consid-ered to be that of the final 100 volt section.Thus with 5 kV applied across a 5 cm long channel,the effective "last stage" is the final 1 mm.The capacity of a cylinder having the dimensionsof such a multiplier is about 4 x 10-12 farads/mm.For a multiplier of total resistance 2 x 1010 Q,the calculated recovery time would thus be 1.6msec. and for a resistance of 109 Q, the recoverytime would be 80 [isecs. The charge in this


capacity is 2.5 x 109 electrons, compared withthe experimentally observed saturated gain ofabout 4 x 109.

Saturation in Straight Channels

There are several pieces of evidence tosuggest that the saturation mechanism in curvedchannels is different from that in straightchannels.

(i) Figure 14 shows the pulses from a

curved channel. At low frequencies the heightsvary over quite a wide range in a random fashion.Unlike the pulses in Figure 11, their height isnot related to the time interval between them.

(ii) The maximum gain8in curved channelsap ears to be about 2 x 10 , compared with 4 x

10 in straight ones.

(iii) Placing a capacitative sleeve round a

curved channel has no effect on the size of themaximum pulse.

Thus it seems unlikely that field distortionis limiting the gain of curved channel multipliers.Bryant and Johnstone4 have considered the effectof space charge in channel multipliers. Theiranalysis is more applicable to straight multi-pliers than to curved ones, but the same generalprinciples apply. The cloud of electrons in thechannel increases in density until it is suffi-cient to drive secondary electrons back into thechannel wall without their acquiring enoughenergy from the field to produce more secondaries.A state of dynamic equilibrium is reached whenthis happens. It follows from Gauss' Law that n,

the number of electrons per cm length uniformlydistributed within a cylinder which will producea voltage depression V volts at the centre of thecylinder is given by n = 7 x 106 V electrons/cm.

Few electrons emerge from the channel withenergies exceeding 100 eV. We may presume there-fore that the maximum collision energy in thechannel is also 100 eV. Channels are invariablyvitreous and since for most glasses the secondaryemission coefficient is unity at about 50 eV, a

reduction in collision energy by a factor 2 wouldinhibit the gain process. It can be shown that a

voltage depression of about 2.8 times the emissionenergy is required to achieve this reduction.This would suggest a maximum charge density ofabout 2 x 107 electrons/cm for 1 volt electrons.The output pulse persists for about 4 x 10-8seconds, and since the mean energy is about 50 eV,the space charge limited gain is about 3 x 108electrons. It should be noted that this is not a

function of tube diameter. This result accordswell with experimental findings.

We can summarise by saying that in curvedchannels the short pulse is limited by space

charge, while in straight channels the long pulsetrain is limited by changes of the potential ofthe channel wall.

PULSE HEIGHT DISTRIBUTION

We have already alluded to the pulse heightdistributions in straight and curved channels.We can now consolidate the discussion of thesephenomena.

In straight channels the pulse heightdistribution at maximum gain is very narrow atlow pulse repetition rates. Figure 15 shows thecontrast between the spread in height of thestarter pulses which did not initiate feedbackand of the larger saturating pulses. It showsthat as the multiplying voltage and thereforethe gain is increased the proportion of starterpulses giving rise to feedback also increases.

As the pulse repetition rate rises, theinterval between pulses becomes shorter than therecovery time of the multiplier. The height ofa pulse therefore becomes a function of the timeinterval since the preceding one, and the pulseheight distribution broadens.

In a curved channel the maximum pulseheight is limited by space charge and this showsitself in the pulse height distribution. Figure16 shows distributions obtained from a MullardB300A multiplier at various applied voltages.The resolution of a distribution is defined as

the ratio of the full width of the distributionat half peak height to the gain at the peakheight. The resolution improves with gain inthe range 105 to 107 but then worsens at about108. The best resolution is about 0.45, whichis to be compared with about 1.5 obtained inconventional multidynode multipliers. Theresolution in a conventional multiplier islimited by the statistical variation of thegain at each stage. According to Lombard andMartin5, a resolution of 1.5 implies a gain per

stage of 5, whereas a resolution of 0.45 wouldrequire a gain per stage of 25. Furthermore thevariation of gain at each collision in a channelwill be greater than that in a conventionalmultiplier, so an even higher mean gain would berequired to account for the resolution of thechannel. Because such high gains per stage donot occur in channels it is evident that thenarrow distribution cannot be accounted forstatistically, but results from the progressiveconstraint which space charge imgoses on the gainprocess when the gain exceeds 10 .

The resolution worsens at gains above 10and as Figure 16 shows, the distribution has a

double peak at 5 KV. This effect is due tosecondary pulses which appear at the tail of thenormal curved channel output pulse. The probabil-ity of occurrence of secondary pulses increaseswith gain and with the length of the straightpart of the channel.

The cause of secondary pulsing thereforeseems to be ionic feedback. It is not clear whythe number of secondary pulses is limited. Ifthe probability of feedback is as high as thepulse height distribution indicates then there

90 June

1966 ADAMS AND MANLEY: MECHANISM OF CHANNEL ELECTRON MULTIPLICATION

ought to be some multiple pulses. All types ofcurved multipliers produce secondary pulses tosome extent, and tertiary and quaternary pulsesare also seen, but they are usually very small,so that they do not make appreciable contribut-ions to the pulse height distribution.

The distribution broadens slightly as therepetition frequency increases and the relation-ship between pulse height and time between pulsesbecomes more systematic. This is similar to thesaturation effect seen in straight channels.

OPERATIONAL CONSIDERATIONSIt is now possible to indicate some oper-

ational characteristics of channel multipliers.A channel multiplier will detect any radiationwhich will excite electrons from the channel wall.Of course the channel entrance may be suitablytreated to increase its detection efficiency forcertain types of radiation. It is not an energysensitive device in the sense that a sodiumiodide crystal is for example. The pulses fromthe multiplier signify only that an input eventhas been detected.

It is possible to make straight multipliershaving a sharp pulse height distribution up totens of kilocycles/sec by using resistive layersof about 109 Q. Straight multipliers have thedisadvantage that the gain depends upon gaspressure.

Curved multipliers have a broader pulseheight distribution in general, although it isnarrower than that obtained from a conventionalphotomultiplier. The highest detectable countrate is determined by the resistance of thechannel and by the noise level in the multiplier-pulse counter system. The choice of resistanceis determined by the available power and the needfor the channel material to satisfy certainrequirements. It must be stable, for example,and it should have a reasonably high secondaryemission coefficient. It is necessary to fabri-cate channels in a variety of shapes and sizes,therefore the channel material must be easilyworked. Count rates of the order of 105 pulses/sec above a 5 mV threshold are currentlyavailable.

Gain maintenance is an important character-istic of channel multipliers but by the nature ofthe problem, experimental evidence accumulatesrather slowly. Deterioration of gain does takeplace and seems to be due to a combination ofmaterial changes and surface contamination.

Because of changes in electron trajectoriesin channel multipliers it is not possible tooperate them in magnetic fields of more than afew hundred gauss.

CONCLUSION

The channel multiplier is a useful researchtool for detecting fluxes of energetic particlesand radiation up to 105 output pulses/sec. Atlower count rates it is possible to obtain gainsof over 109 in straight channels and 108 incurved ones. The limitation on gain is probablyspace charge in curved channels and fielddistortion effects in straight ones.

ACKNOWLEDGMENTSThe authors wish to thank the Directors of

Mullard Ltd. for permission to publish and theproprietors of "Electronic Engineering" in whichFigures 1 and 7 were previously published. Theyare also grateful to Mr. R. Speer of the MullardSpace Laboratory, University College, London andMr. C. Casemore, of Mullard Research Laboratoriesfor many of the experimental measurements.

APPENDIX I

Electron Trajectories in Straight ChannelsThe distance S travelled down the tube

between collisions is given by

S = 1E et2 m

E is the axial electric field.t is the time between collisions.

t = d m2eV

.... ... (1)

. .... .. (2)

V is the initial energy in volts, of an electronemitted normally from the channel wall.

d is the channel diameter.

The collision energy, Vc. is given by

V E Sc

v 20

_ o

4 VIa2where V is the total voltage applied to the

0channel,

and a is the length to diameter ratio.

Let the secondary emission coefficient 6obey the relation

6 = KVc K is a constant

The gain G is given by

G = n

cdwhere n = S

91


24 V aX2KV 2 VHence G = 0 0

4Vz2

APPENDIX 11

Electron Trajectories in Curved Channels

Consider an electron emitted normally fromthe outer wall of the channel towards the centreof curvature of the channel, with an initialvelocity a. We want to find h, the height of theelectron trajectory and the value of 6 at whichit strikes either wall.

The equations of motion are

r e) + 2 r 3= E m

it '2r = re

.... ... (1)

. . .. .. (2)

where E, the electric field is parallel to theaxis of the channel. In equation (1) r 6 isalways small compared with e and can be neglected.The tube diameter d is small compared with Ro andwe may assume r is constant and equal to Ro.

Equations (1) and (2) can then be integratedwith the initial conditions

r = -a r = R + d0

e E=o0the resulting expressions are

At3r = 3R - a

0

where A = E-m

A2t4and r = R

0+ d +12R - at

0

3From (3) and (4) rmin= R0 + d --at

hence, h the max. height of the electron tra-jectory is given by

.. .. .. (3)

.... ... (4)

the length to diameter ratio, then from (5) wecan show that h < d if

V.2 30 I> 81 a .(6)

v2 16: ..

This requirement is fulfilled under mostoperational conditions.

Since h < d, the nest collision will bewith the outside wall,

and integrating (1) we find

R @c - .. .. .. (7)o c 2

where e( is the angle between collisions.

From (4) we have

2 12a R 2/3

(\A2

hence R o = R 36-o c o\ V

0

) 1/3.... ... (8)

and the energy of collision V is given by

VV2 1/3V = (36-s.)c p

.... ... (9)

Let us assume that the secondary emission co-efficient 6 obeys the relation

6 = K Vc

The gain G is then given by

G = 6n

where n is the number of collisions and

c

hence

h 81 ~2 V21/h = R0 16 2

0

..(.... (5)G = K(36

Wv2 1/33v62\36V

1/3

... . (10)

where V is the initial energy of the electronin volts.

VO is the applied voltage.3 is the ratio of channel length to

radius of curvature.

(for a full circle 3 = 2XL)If we write

0Rd =

APPENDIX Ill

Probability of lonisation of Residual Gas

Consider two planes a distance dL apart inthe gap of total length L. Electrons areaccelerated and may ionise the residual gas.The number of ions found in distance dL is givenby

92 June


dN = np f (v) dL

where dN is the number of ionsn is the number of electronsp is the pressure in torr

f(v) is the efficiency of ionisationwhich is a function of V theelectron energy.

If the field is uniform

dL Ldv V

dN = np v f(v) dV

The total number of ions formed as an electronaccelerates from 0 to V volts in a distance Lis then given by

V

N npL f(v) dV

The function f(v) is given for a number of gasesby Meek and Craggs6 and the correspondingfunction

V

| f(v) dV

0

can be obtained numerically. Since its valuedoes not vary widely among a number of the morecomnon gases, one can obtain an estimate off(v) by assuming the residual gas is oxygen andthat the effective ionisation takes place in thelast stage of multiplication. Since the energyof the emerging electrons has a peak of about100 eV, we take V = 100 volts in f(v), and wefind its value is about 6. Hence

N = 6 n p L

As an example, if the channel is 10 cm longand the applied voltage is 4000 V then L, thefinal stage is 0.25 cm. If n, the gain in thestarter pulse is 106, and the pressure is 10-5torr, then N = 15.

This means that each starter electronpulse produces 15 positive ions. If the gain ishigher then of course more positive ions areproduced.

Figure 15 shows that one third of allstarter pulses did not produce ionic feedbacktrains under the particular experimentalconditions.

The most favourable conditions for feedbackare high gain, high pressure and long channels.

REFERENCES

1. WILEY., W.C. and HENDEE, C.F., I.R.E.Trans. Nuclear Science, NS-9, 103, (1962)

2. ADAMS, J. and MANLEY, B.W., ElectronEng. 37, 180, (1965)

3. EVANS, D.S., Rev. Sci. Instr. 36,375, (1965)

4. BRYANT, D.A. and JOHNSTONE, A.D.,Rev. Sci. Instr. 36, 1662, (1965)

5. LOMBARD, F.J. and MARTIN, F.,Rev. Sci. Instr. 32, 200 (1961)

6. MEEK and CRAGGS., "Electrical Break-down of Gases", 13, (Oxford, ClarendonPress, 1953)

Fig. 1-Channel Electron Multiplier

93


CEa(0

VO, Multiplying voltage (kilovolts)

Fig. 2-Comparison of Theoretical and ExperimentalGain versus voltage characteristics for achannel multiplier

-_ a

-~~~~~~~- b

Fig. 4-Ionic feedback pulses produced by (a) argon,(b) xenon, and (c) mercury. Pressure ofargon and xenon 4.5 x 10-5 torr. Pressureof mercury 8 x 10-4 torr. Scale 0.5 ,u S/largedivision. The channel used for (a) and @) was10 cm long, that for (c) 5 cm.

Fig. 3-Ionic feedback pulses from a channel multi-plier. Pressure 4 x 10-6 torr. Scale 0.5pusec./large division, 0.01 volts/largedivision

June94


10'

' 0

10

In

K -ISO

SxlOSTorr

Total

/ pulse

/ 5x10 Torr

5xlO Torr

- 4 5Multiplying voltage (kilovolts)

Starter pulse .5C,

Fig. 5-Gain as a function of voltage in starter pulseand total pulse

Fig. 6-Gain as a function of pressure at a givenvoltage

Fig. 7-Output pulse from a curved channel multiplierScale 0.02 uS/Aarge division

'v l f w -ln l /

95P


0-Theory I

K-0-017 0

10e-o 14 _ 0V.IVolt 0

0

eo Experiment withMullard B300A(Non standard)A =14

10o

106 ,

I,

lo' _~~

le02 ~

V0 Multiplying voltage (iilovolts)5 0

4-0 4.3 i5n0 556(0Multiplying voltage (kilovolts)

65 70

Fig. 9-Experimental gain versus voltage curve forlarge diameter curved channel. Length todiameter ratio = 18

Fig. 8-Theoretical gain versus voltage characteristicfor Mullard B300A channel multiplier. Exper-imental points are also shown

Fig. 10-Large diameter curved channel multiplier.Length to diameter ratio = 18. Angle sub-tended at centre of curvature = 5.2 radians

96 June

et IsA-52

2elCs Torr

O' _1_ I:__I_I

0f '..,

ea,.

I

.S13

1,

I


Fig. 11-Output pulses from straight channel illus-trating time dependence of pulse height.Applied voltage 7 kV. Pressure 2 x 10-5torr. Gain: about 109. Scale 2 msecs./large division. 0.1 volts/large division

|_ ~~~~a

Notional

~/Cho ~~~~~~~Beamswitch Electrodes

Fig. 13-Equivalent circuit of channel multiplier.The output pulse is obtained when the finalcapacity is discharged by the abeam switch'

Fig. 14-Output pulses from curved channel showinglack of dependence of height on time. Appliedvoltage 7 kV, gain about 108. Scale 100msecs./large division, 0.2 volts/largedivision

b

2000V- 2100V- 2200V

GAIN

Fig. 12-Effect of channel resistance on recoverytime of straight channel multiplier. (a)Resistance 7 x 1010.Q. Time scale 50 Msec./large division. (b) Resistance 109Q. Timescale 10 p sec./large division

Fig. 15-Pulse height distribution from a straightchannel showing distinction between thestarter pulse and the total pulse.

97


/I I 102

/I /

I IAAA i ,I .1a I I a I . . I I I . --- .

Peak PeakI I I

1-16mm. OID.x12mm. VDR~~~~~~1II--W4mm

Mullard B300A

4Kvi08 and 2xlO0

5Kv1.6xlO8and 3-2xl08

-4 t - i

Fig. 16-Pulse height distributions from a Mullard B300A curvred chanmel at various applied voltages.Abscissae logarithmic but not continuous.

_ E~~~

, 4 / tra

Channel walls\

Fig. 17-Electron trajectory in a straight channel

1 25Kv2x 05

2-5Kv3x107

1-2

uc

0-6 *w

a

Threshold Peak

0

c

0

u

L

10

dd /s-oE

w as I-- lfJl.^f-

L

It ft i i .% I OsX X *i i ,i

98 June

.. a

A.a I I I I I I

Ictronijectory

Fig. 18-Electron trajectory in a curved channel


dL

0 volts V volts_ L r

Fig. 19-Gas ionisation by accelerated electrons

99

mechanism of channel electron...

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