The performance of photomultipliers exposed to helium

Nuclear Instruments and Methods in Physics Research A269 (1988) 237-245 North-Holland, Amsterdam

THE PERFORMANCE

OF PHOTOMULTIPLIERS

EXPOSED

237

TO HELIUM

J.R. I N C A N D E L A *, S.P. A H L E N , J. B E A T T Y , A. C I O C I O *, M . F E L C I N I , D . F I C E N E C , E. H A Z E N , D. L E V I N , A. M A R I N , J.L. S T O N E , L . R . S U L A K a n d W . W O R S T E L L Physics Department, Boston University, Boston, MA 02215, USA Received 20 August 1987 and in revised form 14 December 1987

We report results of a study to determine how the performance of photomultipliers is affected by exposure to He. In our tests we monitor two 5 in. diameter EMI hemispherical photomultipliers while they are operated in He environments. Initially we observe He + afterpulses, at an approximately constant delay relative to the primary anode pulse. As the He gas pressure in the tubes increases however, strings of pulses typical of Townsend discharges occur. For the glass composition and geometry of the photomultipliers used in our tests, the internal gas concentration as a function of exposure to He is calculated using Fick's law for the permeation of solids by gases. The He permeation constant for the photomultiplier glass is obtained from a semiempirical formula developed by Altemose. We calculate the internal He concentration resulting from the He exposure which is observed to cause the regular occurrence of discharges and find that it is consistent with that required for production of discharges in the Townsend model. Guidelines are presented for using our results to estimate lifetimes of photomultiplier's of different geometries and glass types when operated in He environments.

1. Introduction Small c o n c e n t r a t i o n s of gases inside a p h o t o m u l t i plier (PM) are k n o w n to cause afterpulses [1]. In new PMs, afterpulses can be associated with H2, N2, CO, He, and other gases found in air or p r o d u c e d from water vapor. W h e n P M s have been exposed to air for as little as 2 years however, it has been reported that afterpulses associated with He increase dramatically as c o m p a r e d with those caused by heavier ions [2]. The reason for this is the relatively high permeability of glass to He. In this p a p e r we report results of tests we have done to determine the p e r f o r m a n c e of P M s as a function of exposure to He. As we h a d anticipated, the afterpulse rate is observed to increase with exposure. In addition, as suggested by Paske [3], the c o n c e n t r a t i o n of He inside the P M eventually reaches a level sufficient to cause the sustained p r o d u c t i o n of free electrons typical of T o w n s e n d discharges [4]. These discharges, which are manifested as strings of pulses at the anode, occur with increasing frequency a n d d u r a t i o n as exposure to He increases. Ultimately, strings lasting as long as = 1 0 - 5 0 /~s are observed for most instances in which a p r i m a r y electron is emitted from the photocathode.

* Current address: EP Division, CERN, CH-1211 Gen~ve 23, Switzerland. 0 1 6 8 - 9 0 0 2 / 8 8 / $ 0 3 . 5 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)

W e begin with a brief discussion of afterpulsing in P M s a n d of the T o w n s e n d model for discharges in gases. W e then summarize the results of N o r t o n [5] and Altemose [6] regarding the p e r m e a t i o n of glass b y He. U s i n g Fick's law for the p e r m e a t i o n of solids by gases [7], together with the He p e r m e a t i o n c o n s t a n t for the P M glass as o b t a i n e d from Altemose's semiempirical formula, we estimate the He exposure required for T o w n s e n d discharges to occur. In particular, the Townsend discharge model predicts that sustained dark currents between electrodes are the result of ionization of neutral gas molecules b y ions. The ionic c o n t r i b u t i o n to the p r o d u c t i o n of free electrons will b e c o m e significant w h e n the m e a n free p a t h for ionization of neutral gas molecules by collision with gas ions becomes c o m p a r a ble to the p h o t o c a t h o d e - f i r s t d y n o d e spacing. Finally we discuss the two tests that we performed. In one test a P M is directly exposed to He and operated with a first stage voltage V0 ~ 400 V, while in the other, the P M is s u b m e r g e d in mineral oil during exposure and o p e r a t e d with V0-- 600 V. (The mineral oil has no appreciable effect u p o n the results while the difference in operating voltage is f o u n d to account for a factor of 2 or so difference in the He exposure required for discharges to occur.) W e find that after a time lag of 1.9 d (consistent with that predicted by the t i m e - d e p e n d e n t form of Fick's law), the occurrence of afterpulses begins to rise. T o w n s e n d discharge effects are then observed at s u b s e q u e n t He exposures consistent with those anticipated by our calculations.

J.R. Incandela et al. / Performance of photomultipliers exposed to helium

238

2. Afterpulses and discharges: the effect of gases in photomultipliers Let V(s) be the electric potential at a distance s from the p h o t o c a t h o d e along the direction of the field lines which are focused to the first dynode [8]. If an ion of charge Ze and mass m is produced at s = s 0, then the time it will take to reach a distance s < s o from the cathode is:

• (So, s ) = - ( m / 2 Z e ) l / 2 f i l d s ( V ( s o ) -

V ( s ) ) -1/z.

(1) F o r hemispherical p h o t o t u b e s the electric field increases with increasing s. A p p r o x i m a t i n g the potential as V(s) = Vo(s/d) z, where V0 is the voltage difference between the cathode a n d first dynode, ~(s0, s) is then:

.r (So, s) = ( m d ; / 2 eZ Vo )'/2( ~r/2 - sin-1 ( s / s 0 ) ) .

(2) Thus the time required to reach the p h o t o c a t h o d e at s = 0 is;

"ro = ¢r/2 × ( m d 2 / 2 Z e V o )1/2,

(3)

which is i n d e p e n d e n t of s o [9]. T o w n s e n d [4] studied the effects of gases between electrodes a n d f o u n d that for low gas concentrations, the n u m b e r n of electrons arriving at the a n o d e is related to the n u m b e r of electrons emitted from the cathode, n 0, by a simple exponential; n = n o e ~a, where d is the electrode spacing a n d a is the m e a n n u m b e r of gas ions produced per cm per electron traversing the gap. T o w n s e n d also observed that for fixed pressure a n d electric field, the n u m b e r of electrons reaching the a n o d e increases more rapidly than exponentially when the gap size d is m a d e large [10]. T h e a d d e d electrons are the result of the ions themselves c o n t r i b u t i n g to the p r o d u c t i o n of free electrons by collision with - a n d ionization of - neutral gas molecules. F o r these circumstances T o w n s e n d derives the following expression for the total n u m b e r n of electrons at the anode: n = no

(~-B) a-/3e

e~°-'~ (~ B)d '

One expects ions to c o n t r i b u t e significantly to the p r o d u c t i o n of free electrons when the m e a n free path / for collision and ionization of a neutral gas molecule by an ion is c o m p a r a b l e to the electrode spacing d. F o r a kinetic energy of 50 eV to 1 keV, the ionization cross section for He + ions on He atoms [13] is o = ( 1 - 4 ) × 10 17cm2. The n u m b e r density N of He atoms at room t e m p e r a t u r e a n d at pressure p / x m Hg is N = 3.54 × 1013 p cm 3. The m e a n free p a t h l is then

=

(5)

Thus l is c o m p a r a b l e to d at a pressure P0 given by P0 ~ 103d-1- ( N o t e that the ionization cross section in e - - H e collisions is o~ = (1.6-3.5) × 10 17 cm 2 above 50 eV so that He ions will have roughly the same probability of ionizing He atoms as will electrons [14].) F o r the 5 in. diameter P M s used in our tests, d--~ 10 cm so that P0 = 100 /~m Hg. Thus, we estimate that T o w n s e n d discharges will occur regularly at a He pressure inside the p h o t o t u b e of = 100 # m Hg. W h e n the ions p r o d u c e free electrons by ionizing neutral gas molecules, these electrons proceed through the P M to produce an afterpulse which is delayed relative to the p r i m a r y pulse by a time ~-(s0, s) where s > 0 is the p o i n t at which the H e - H e + collision occurs. F o r a m e a n free p a t h l for this process, the probability that the ionization occurs before the ion has travelled a distance s o - s is: P = 1 - e -(s° ~)/t.

(6)

Thus the pulses initiated by electrons freed in these collisions will not necessarily occur at a c o n s t a n t delay relative to the p r i m a r y pulse a n d will typically occur sooner t h a n what is expected for a s t a n d a r d afterpulse (in which He + ions strike the p h o t o c a t h o d e to cause the emission of electrons). T h e occurrence of afterpulses at arbitrary times less t h a n the time at which He afterpulses n o r m a l l y occur is thus characteristic of the production of free electrons via ionization of gas atoms by ions.

3. The permeability of glass to helium (4)

where /3 is the n u m b e r of ions p r o d u c e d per cm by a positive ion in the gas as it is accelerated to the c a t h o d e [11]. This expression is singular at a = f l e (~ ~)d. The singularity corresponds to conditions for which full b r e a k d o w n of the gas occurs - manifested as a spark [12]. As singularity conditions are approached, increasing n u m b e r s of electrons are p r o d u c e d regeneratively so that a current is observed to flow between the electrodes even after the source of photoelectrons emitted from the cathode is removed.

F o r a p l a n e m e m b r a n e with pressure gradient A p , cross sectional area A a n d thickness z, the q u a n t i t y of gas passing t h r o u g h the m e m b r a n e in time t is calculated from the steady state form of Fick's law [7] to be:

q = kAt A p / z

(plane membrane).

(7)

F o r a sphere, q is given by:

q = 4~aZkt z ~ p b / a ( b - a )

(spherical m e m b r a n e ) ,

(8) where a a n d b are the inside a n d outside radii, respec-

239

J.R. Incandela et al. / Performance of photomultipliers exposed to helium

10 10 I

400°K~

The b u l b has an area of 410 cm 2 a n d the rest of the tube has an area of 110 cm 2. Thus the bulb accounts for 92% of the steady flow of He into the photomultiplier. T h e volume of the P M is V = 810 cm 3 so that from eq. (7) the pressure of gas accumulated in the P M as a function of He exposure, tz~p, is calculated to be:

~

io-Ii

Ptube = 7.6 x 105 q = (36.8 _+ 12.5) t,.ip [_) C

(13)

/.J 10-12

/"

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200ox/

i

10_t 3

85

87.5

90

025

95

97.5

100

M% Fig. 1. Permeation constant k, eq. (10), as a function of %mol network-forming oxides M, at 200, 300 and 400 K. tively, of the sphere. The p e r m e a t i o n c o n s t a n t k dep e n d s upon t e m p e r a t u r e T as [5,6]: (9)

k = k 0 e -O/RT,

where Q is the activation energy per gram atom, R is the gas c o n s t a n t ( R = 1.986 c a l / m o l K), a n d k 0 is a constant. Altemose [6] has shown for glass that Q is p r o p o r t i o n a l to the %mol c o n c e n t r a t i o n M of networkforming oxides; SiO 2, B203, and P205. He finds the following semiempifical formula for the p e r m e a t i o n constant:

where the units of t a p are d atm, and the units of Ptube are ffm Hg. Thus the internal pressure will reach = 100 t~m Hg (for which we expect to see T o w n s e n d discharges as discussed in the last section) after an exposure of t a p = 3 d atm. So far we have only considered the steady-state form of Fick's law. It turns out that the t i m e - d e p e n d e n t form of this law predicts that there is a finite time required for gas to diffuse t h r o u g h the glass m e m b r a n e a n d begin the steady state flow given b y eqs. (7) a n d (8). This time lag L depends u p o n the initial c o n c e n t r a t i o n s of gas C0, C 1 a n d C2, inside, a n d in the low a n d high pressure regions, o n either side of the glass m e m b r a n e , respectively. It also d e p e n d s u p o n the diffusion c o n s t a n t D a n d the thickness z of the m e m b r a n e [17]: L = O ( C 2 _ C1 )

e (260M

3"OxIO4)/RT,

(bulb).

(11)

F o r the remainder of the tube, the p e r m e a t i o n c o n s t a n t is: k = (6.2_+ 2.1) x 10 - n

(shaft a n d j o i n t ) .

.

(14)

Z2

(15)

(10)

where M is in percent, R is c a l / m o l K, T is in K, a n d the units of k are cm 3 gas ( N T P ) per sec per cm 2 area per m m thickness per cm Hg gas pressure difference. Fig. 1 shows a plot of k vs %tool M of the network-forming oxides at various temperatures. W h e n our tests with the 5 in. E M I P M s were completed, the P M s were shattered to measure the glass thickness. T h e glass composition was o b t a i n e d from T h o r n - E M I corporation [15]. It t u r n e d out t h a t the b u l b a n d shaft were m a n u f a c t u r e d separately from different types of glass a n d joined with three further glass types over a span of 1 cm to avoid a n a b r u p t change in the coefficient of thermal expansion. The shaft thickness is = 1.0 m m a n d the b u l b thickness is = 2.0 mm. The %mol of network-forming oxides in the b u l b and shaft a r e M b u l b = 93.1 a n d M s h a f t = 90.0, respectively. T h e permeation c o n s t a n t for the b u l b at T = 300 K is then [161: k = (2.9 + 1.0) × 10 11

+

C o a n d C 1 are negligible c o m p a r e d with C2 so that the lag is given by: L° = 6-D'

k = 4.8 × 10 . 7

4- ~ -

(12)

i n d e p e n d e n t of C 2. T h e diffusion c o n s t a n t D has units of cm 2 s-1 a n d has a numerical value which is related to the p e r m e a t i o n c o n s t a n t k as D - ( 5 0 0 - 2 0 0 0 ) k [18]. Thus for z = 0.2 cm, we estimate a time lag L 0 o n the order of 1 - 3 d for the P M s used in our tests [19]. For P M s o p e r a t e d in regions which have very high He concentrations, this time can correspond to a considerable He exposure. In our tests, the He pressure outside the PM was initially 5 psi in the case where the P M was directly exposed to He, a n d 24 psi in the case where the P M was submerged in mineral oil. A delay of one day thus c o r r e s p o n d s to exposures of 0.3 d arm a n d 1.6 d arm, respectively. T h e time lag L 0 should therefore have a very p r o n o u n c e d effect in the mineral oil test in particular. In the next section it will be seen that this is in fact the case. U p to now we have not m e n t i o n e d a n y t h i n g a b o u t the effect of the mineral oil in our second test. O u r group is currently involved in the M A C R O experiment at G r a n Sasso (see the M A C R O Technical Proposal, N o v e m b e r 1984, unpublished), which will use a large q u a n t i t y of liquid scintillator having a mineral oil base. W e are particularly c o n c e r n e d a b o u t the effects of He

240

J.R. Incandela et al. / Performance of photomultipliers exposed to helium

on PMs in this experiment because a major part of the experiment will comprise streamer tubes in which He will be the primary c h a m b e r gas. The PMs in this experiment will be immersed in mineral oil in order to m a t c h the index of refraction of the material in the immediate vicinity of the PMs to that of the liquid scintillator. The oil could conceivably add to the time lag L 0 and also reduce the p e r m e a t i o n rate. F o r solid organic polymers having composition similar to that of mineral oil, N o r t o n [5] states values for the p e r m e a t i o n c o n s t a n t o n the order of - - 1 0 s, corresponding to a diffusion c o n s t a n t D ~ 10 -5. F o r liquids, the diffusion c o n s t a n t of even heavy gases, such as nitrogen, at r o o m temperature [20] is as high as 4.0 × 10 -5 a n d so we expect D for He to be at least this large. Thus the mineral oil in our tests, which h a d a d e p t h of several cm, is not expected to add more t h a n = 10% to L 0 and should have negligible effect upon the p e r m e a t i o n rate in the steady state.

4. Tests performed with 5 in. E M I photomultipliers

In the first test, a 5 in. E M I P M was placed in a c h a m b e r that was initially filled to a partial pressure of 5 psi with He [21]. In the second test a 5 in. P M was immersed in a mineral-oil-filled pyrex beaker before placement in the chamber. The He pressure in the second test was 24 psi. The PMs were powered at = + 1 3 5 0 V a n d --- + 2 0 0 0 V respectively (cathode at ground). The P M bases used a resistor network that divided the voltage between stages such that the first stage ( p h o t o c a t h o d e - f i r s t dynode) h a d roughly 4 times the voltage drop of the 10 successive multiplier stages, all of which h a d the same potential drop. Thus the first stage voltages were = 400 V and ~ 600 V in the two tests.For b o t h tests, dark noise a n d afterpulsing were monitored. Primary electrons were p r o d u c e d in the P M s by flashing a green L E D near the photocathode. The L E D pulse was such that = 1 - 3 photoelectrons were produced for each flash. A 100 M H z trace recorder with 32 kbyte m e m o r y unit was stopped when the L E D was flashed to allow the subsequent a n o d e signals, occurring up to ~ 150/~s after the L E D flash, to be digitized a n d written to minidisk for storage. In the mineral oil test, strings of n > 2 afterpulses were also monitored. F o r overnight monitoring, a s c a l e r / t i m e r was used in conj u n c t i o n with a gate generator to produce triggers for the L E D pulser a n d stop signals for the trace recorder every 1000 s. The events were stored on minidisks (these have a capacity of 39 trace recordings and so the 1000 s spacing of triggers insured that data was taken t h r o u g h o u t the night). Dark noise a n d afterpulse rates were measured in the daytime only. F r o m eq. (3), the voltage across the cathode a n d first d y n o d e in the 5 in. E M I PMs leads to an expected

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Fig. 2. The % of LED flashes which are followed by an afterpulse at t _> 500 ns, as a function of exposure to He in the second test (PM in mineral oil and V0 = 600 V). The first data point is taken to represent the initial noise level in the PM prior to exposure to He. The remaining points are fit to a line, as shown, to determine the time lag L 0 before the steady-state flow of He into the PM begins, as predicted by eq. (15).

afterpulse delay of ~ 1.2 _+ 0.3 # s for singly ionized He. F o r this reason the occurrence of afterpulses later than 500 ns after the p r i m a r y pulse were m o n i t o r e d as one measure of He c o n t a m i n a t i o n . Fig. 2 shows a plot of data from the second test, in which the fraction of primary pulses followed by a n afterpulse at 0.5/2s < t < 10.0 /~s relative to the p r i m a r y pulse is counted. After several d a t m of He exposure the occurrence rate begins to rise roughly linearly. The data were least-squares-fit to a line. W e find that if the first data p o i n t is included in the sample, the fit has a X 2 value of 25.0 for 6 degrees of freedom. If the first point is not included, the fit has X 2 = 4.0 for 5 degrees of freedom. W e conclude therefore that the first d a t a p o i n t represents the rate of occurrence of afterpulses in the P M due to gases which were t r a p p e d in the P M before it was exposed to He, a n d the s u b s e q u e n t linear rise is due to the linear a c c u m u l a t i o n of He (see eqs. (7) a n d (8)) with exposure. T h e line which best fits the sample (fig. 2) intersects the initial noise rate at a n exposure of t a p = 3.1 ± 0.1 d arm. F o r A p = 24 psi, this means that the time lag required for He to diffuse through the glass a n d comm e n c e steady state flow into the P M is L 0 = 1.9 + 0.1 d. This is consistent with the time lag that we estimated using eq. (15) (see the discussion above). In most uses of PMs, the a m b i e n t partial pressure of He is Ap << 1 a t m so t h a t the time lag L 0 will corres p o n d to a very small exposure (unless the diffusion c o n s t a n t D is very small so that L 0 >> 1 d). F o r this reason we will s u b t r a c t the He exposures during the

J.R. Incandela et aL / Performance of photomultipliers exposed to helium 100

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I ....

I

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'-'

'

Direct E x p o s u r e

m 80

A\ Z

60

©

4O

03

20 O

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I .... 2

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tap

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Fig. 3. The % of LED flashes which are followed by an afterpulse at t >_500 ns as a function of exposure to He in the first test after correcting for the time lag L 0.

delay time in order to present our results as a function of He exposure during which steady-state flow of He into the P M takes place [22]. Henceforth, " e x p o s u r e " will thus be u n d e r s t o o d to m e a n exposure after subtraction of the time lag L 0. Fig. 3 shows the measured percent of L E D flashes followed by n > 1 afterpulse at t >_ 500 ns for the first test after subtraction of L 0 as m e a s u r e d in the second test. A line fit to the data in the figure has y-intercept consistent (within uncertainty) with a rate of 1 - 2 % as measured in the p m prior to exposure to He. T h e delay time L 0 is calculated to be the same for the P M s used in the two tests to within a n overall m e a s u r e m e n t uncertainty of = 20%. It follows that the He diffusion a n d permeation properties of the tube glass in the two P M s is also the same to within this level of uncertainty. In each test, the m e a n single-photoelectron pulse height was crudely measured to + 50%. Thus a factor of 2 difference in the m e a n n u m b e r of primary electrons (n 0 in eq. (4)) in the two tests is n o t unlikely a n d would explain the factor of 2 difference in the slopes of the rates presented in figs. 2 a n d 3. In fig. 4 data are s h o w n in which the fraction of L E D flashes followed by strings of n > 2 afterpulses of d u r a t i o n zSt > 500 ns were counted in the second test. T h e rate of occurrence of these strings is seen to increase as ( t A p ) m, where m = 1.8 + 0 . 4 . Initially the strings are due to a c o m b i n a t i o n of the recurrence of s t a n d a r d afterpulses, and afterpulses resulting from electrons freed in H e + - H e collisions. This is evidenced by the fact that the delay between some, b u t not all, of the pulses in the string is roughly c o n s t a n t at a b o u t 1-1.5 ~ts (see fig. 5a). A t greater He exposures, the delay between pulses is more frequently shorter t h a n t h a t

241

expected for s t a n d a r d afterpulses, indicating t h a t He + ions are c o n t r i b u t i n g m o r e to the ionization of He atoms [23] (see fig. 5b). As expected, the d u r a t i o n of the strings was observed to grow. Ultimately strings as long as - 1 0 - 5 0 /~s, like that seen in fig. 5c, were seen for the majority of L E D flashes. T h e m e a n n u m b e r of afterpulses per p r i m a r y pulse was m o n i t o r e d b y using a discriminator a n d scaler to c o u n t the n u m b e r of times the a n o d e signal crossed a threshold of 30 mV, ( = 1 / 2 photoelectron), in 10 ~s after the L E D was flashed. (A coincidence unit was used to produce an enable signal for the scaler only w h e n both an L E D pulse trigger and a primary pulse above 30 m V occurred.) Fig. 6 shows plots of d a t a from these measurements. In the first test we see that the multiplicity of afterpulses increases exponentially with exposure. In the second test the n u m b e r of d a t a points is insufficient to say whether the increase here is also exponential [24]. Strong evidence for the occurrence of T o w n s e n d discharges is seen in the plots shown in fig. 7 of the d a r k noise in the PMs. T h e dark noise initially rises exponentially with exposure. With further exposure the rise becomes faster t h a n exponential. This type of behavior is characteristic of the a p p r o a c h to b r e a k d o w n predicted by Townsend. T h e exposure required for this to h a p p e n in the tests is seen to be -- 2 a n d 5 d atm, in r o u g h agreement with our estimate of 3 d a t m as discussed in the last section. T h e difference of ~ 2 - 3 in the exposure required for discharges in the two tests is most likely a t t r i b u t a b l e to the difference in the first stage voltages, V0, used in the two tests. In particular, for a given electrode gap size d, the singularity c o n d i t i o n of eq. (4) is determined b y the

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tap [d-arm] Fig. 4 . T h e % occurrence of LED flashes followed by at least two afterpulses in the second test. Only strings of pulses of duration A t >_ 500 ns were counted. The data rise roughly as a power of the exposure, (tAp )", where m = 1.8 + 0.4.

J.R. Incandela et al. / Performance of photomultipliers exposed to helium

242

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Fig. 5. (a) Primary pulse followed by standard He afterpulses mixed with afterpulses initiated by electrons freed in H e + - H e collisions. (b) An early Townsend discharge occurring after an exposure of = 2 d arm in the second test. In this case it is seen that the afterpulses are almost always separated by times significantly less than 1 Vs. (c) Townsend discharge of duration At = 40 /~s after an exposure of = 3 d atm in the second test. The amplitude and time scales are marked at the left side of the signal traces.

[d-aLto]

Fig. 6. The m e a n n u m b e r of afterpulses counted in the time period, 500 ns < t < 10/~s after the primary pulse occurs, as a function of exposure to He in both tests.

c o u l d affect t h e e x p o s u r e r e q u i r e d for d i s c h a r g e s to o c c u r b y a f a c t o r o f 2 or so [25]. T h e d a r k n o i s e r a t e s a r e also s e e n to b e g i n to p l a t e a u a f t e r r o u g h l y 3 a n d 7 d a t m e x p o s u r e s . T h i s is p a r t l y d u e to t h e fact t h a t as t h e m e a n free p a t h for i n e l a s t i c collisions of He + with He becomes much smaller than t h e g a p size d, t h e k i n e t i c e n e r g y g a i n e d b y t h e i o n s b e t w e e n c o l l i s i o n s is m o r e likely to b e b e l o w 100 eV in w h i c h c a s e t h e i o n i z a t i o n c r o s s s e c t i o n s a r e small. A n o t h e r c o n t r i b u t i o n to this effect m a y be t h e c a p t u r e o f p h o t o e l e c t r o n s b y p o s i t i v e i o n s w h i c h a c c u m u l a t e in increasing numbers near the photocathode.

[

[] Vo = 600 Vo = 400

i0 2 0 0 0

T o w n s e n d c o e f f i c i e n t s a a n d 13. T h e s e in t u r n d e p e n d u p o n t h e p r e s s u r e o f t h e H e g a s in t h e p m a n d t h e field s t r e n g t h (see ref. [11]). I n t h e d i s c u s s i o n a b o v e r e g a r d i n g t h e m e a s u r e m e n t o f t h e t i m e l a g L0, we c o n c l u d e d t h a t t h e p e r m e a t i o n p r o p e r t i e s o f t h e t u b e g l a s s in t h e P M s d i f f e r e d b y less t h a n = 20%. T h e a m o u n t of H e in t h e t u b e s as a f u n c t i o n o f e x p o s u r e will t h e r e f o r e b e v e r y n e a r l y t h e s a m e as well. O n t h e o t h e r h a n d , t h e c o m p l e x i t y o f t h e d i s c h a r g e p r o c e s s m a k e s it d i f f i c u l t to c a l c u l a t e t h e effect o f v a r y i n g t h e g a p v o l t a g e V0. S o m e s i m p l e c a l c u l a t i o n s we h a v e p e r f o r m e d do, h o w e v e r , i n d i c a t e t h a t t h e d i f f e r e n t v o l t a g e s u s e d in t h e t w o t e s t s

Y

0

z

i01

o o

K~

o o []

oo ~o oeo

~

oo l i J l l

2

4

tap

J

6

I

i

I

8

[d-atrn]

Fig. 7. Dark noise rates as a function of exposure in both tests. The dark noise is seen to initially rise exponentially and later to rise at a faster than exponential rate as expected for the occurrence of discharges.

J.R. Incandela et al. / Performance of photomultipliers exposed to helium 5. Conclusions

. . . . . . . . . . . . . . .

F r o m our tests we c a n c o n c l u d e that H e p e r m e a t i n g into p h o t o m u l t i p l i e r s c a n r e p r e s e n t a serious source o f d e g r a d a t i o n of p e r f o r m a n c e . F o r t u b e s in w h i c h the %mol c o n c e n t r a t i o n o f n e t w o r k - f o r m i n g oxides in the glass walls is high, even relatively low a m b i e n t H e c o n c e n t r a t i o n s can cause serious d a m a g e to the P M s over p e r i o d s o f several years. T h e n o i s e level resulting f r o m T o w n s e n d d i s c h a r g e s r e n d e r P M s effectively useless for m o s t a p p l i c a t i o n s . T h e e x p o s u r e r e q u i r e d for discharges to o c c u r c a n t h e r e f o r e b e i n t e r p r e t e d as the lifetime of the p m scaled b y the a m b i e n t H e p r e s s u r e Ap. It has b e e n seen in the analysis a b o v e that t h e i m p o r t a n t variables for d e t e r m i n i n g the lifetime o f a P M e x p o s e d to H e are (a) t h e %mol c o n c e n t r a t i o n M of n e t w o r k - f o r m i n g oxides in the t u b e glass, (b) the a m b i e n t H e p r e s s u r e A p , (c) the m e a n i o n i z a t i o n cross section o for H e + collisions with He, a n d (d) the g e o m e t r y of the P M (surface area A, v o l u m e V, thickness z a n d p h o t o c a t h o d e - f i r s t d y n o d e gap size d). G i v e n this i n f o r m a t i o n , the H e e x p o s u r e r e q u i r e d for T o w n s e n d d i s c h a r g e s to b e g i n to o c c u r regularly, c a n b e e s t i m a t e d b y c o m b i n i n g eqs. (5), (7) or (8), (10), a n d (13), i.e.:

tAp=1.2)
3"0 × 1 0 4 ) / R T .

(16) A s seen in our tests, the gap voltage Vo m a y b e r e s p o n -

....

loz

I ....

-

I ....

/

I ....

I ....

I ....

Vo = 400

A '

,.~

5

243 I ....

I ....

:

10 0

4.0 3.0

mm

2.0

-

/11 /

/

10-1

/

.... 85

I .... 87.5

I,,, 90

I .... 92.5

I .... 95

I .... 97,5

iO0

M% Fig. 9. The calculated time lag L 0 as a function of the %mol network-forming oxides for four typical PM glass thicknesses, z = 1, 2, 3, and 4 mm. (We assume that the diffusion constant is given by D = 103 k so that actual time lags could differ by a factor of 2 from those indicated by the plot - see the discussion following eq. (15)).

sible for a factor o f 2 or so d i f f e r e n c e in the P M lifetime. Fig. 8 s h o w s p l o t s o f the linearized exposure, t A p ( A d / z V ) , c a l c u l a t e d f r o m eq. (16) as a f u n c t i o n o f %tool c o n c e n t r a t i o n o f n e t w o r k - f o r m i n g oxides, w h e r e w e have e x t r a p o l a t e d f r o m o u r m e a s u r e m e n t s to indicate the p o s s i b l e v a r i a t i o n to b e e x p e c t e d for P M s o p e r a t e d w i t h V0 = 400 a n d 600 V. Fig. 9 p l o t s the lag t i m e L 0 (eq. (15)) also as a f u n c t i o n o f M , for various typical P M glass t h i c k n e s s e s z = 1, 2, 3, a n d 4 m m . F o r a p p l i c a t i o n s in w h i c h the a m b i e n t H e p r e s s u r e is e x p e c t e d to b e high, the time lag c a n c o r r e s p o n d to a significant exposure, as was the case in our tests. In such instances, t h e time lag m u s t be i n c l u d e d to o b t a i n a m o r e a c c u r a t e e s t i m a t e o f the lifetime of the p h o t o m u l t i p l i e r .

lo 1

Acknowledgements 10 0

.... 85

I .... h7.5

I .... 90

I .... 925

I .... 95

I .... 97.5

100

M% Fig. 8. The linearized exposure, (tAp)(Ad/zV), required for the regular occurrence of Townsend discharges to occur in PMs as a function of the %mol of network-forming oxides in the tube glass and for first stage voltages V0 of 400 V and 600 V.

W e like to t h a n k R.A. P h a n e u f o f the O a k R i d g e N a t i o n a l L a b o r a t o r y a n d J. C u e v a s o f the U n i v e r s i t y o f C h i c a g o for their a s s i s t a n c e in l o c a t i n g low energy i o n i z a t i o n cross s e c t i o n d a t a for H e a n d for their insights in r e g a r d to t h e t e c h n i q u e s used to m e a s u r e these cross sections. W e also t h a n k S. O s a k a for h e r assist a n c e in p r e p a r i n g t h e figures for this p a p e r . This res e a r c h was m a d e p o s s i b l y b y g r a n t n u m b e r 6973-5 f r o m t h e U S N a t i o n a l Science F o u n d a t i o n a n d g r a n t n u m b e r 7098-7 f r o m the U S D e p a r t m e n t o f Energy.

244

J.R. lncandela et al. / Performance of photomuhipliers exposed to helium

References [1] G.A. Morton, H.M. Smith and R. Wasserman, IEEE Trans. Nucl. Sci. NS-14 (1967) 443. [2] P.B. Coates, J. Phys. D, Appl. Phys. 6 (1973) 1159. Coates refers specifically to O 2. Morton et al. [1] however, used a valved glass tube system that allowed them to fill the PM with various gases in controlled amounts and found that 02 did not cause afterpulsing even at concentrations as high as 10 5 Torr (for which other gases showed significant afterpulse rates). The afterpulses to which Coates refers are therefore probably the result of N 2 which has mass similar to 02 and therefore will have roughly the same afterpulse delay time %. [3] W.C. Paske, Rev. Sci. Instr. 45 (1974) 1001. [4] J.S. Townsend, The Theory of Ionisation of Gases By Collision (Constable, London, 1910). [5] F.J. Norton, J. Appl. Phys. 28 (1957) 34. [6] V.O. Altemose, J. Appl. Phys. 32 (1961) 1309. [7] See for instance, R.M. Bauer; Diffusion In and Through Solids (Cambridge University Press, New York, 1941). [8] Ions which are produced in later stages are captured by dynodes and do not contribute substantially to afterpulse production. See ref. [2]. [9] For a uniform field: V = V o ( s / d ) ; r = ( 2 m d / Z e V o ) 1/2 (s o - s) 1/2 and % -- Slo/2. In this case, r0 varies little with s o for s o >> 0. Furthermore, the probability that an electron produces an ion upon collision with a neutral gas molecule increases at larger values of s o since it will have more likely attained a kinetic energy above 100 eV at which point the cross section for ionizing He is relatively large (see ref. [14]). Thus, for this potential also, afterpulse times for a given species of ion will be peaked about a fixed value of r0. [10] For a fixed pressure p and, consequently, a fixed mean free path l for ionization of a gas molecule by collision, the number of ionizing collisions per charged particle as it traverses the gap will increase as the gap size d is made larger. The same increase in ionizing collisions can be obtained by decreasing the mean free path as a result of increasing the pressure so long as the cross section for ionization does not decrease appreciably with the decrease in l. This is the case, for instance, in PMs which are ilaitially He free as they are exposed to He since the He pressure in the tube is then sufficiently low that l > d. Thus, as PMs are exposed to He we expect dark noise to rise with He exposure in the same way that Townsend observes currents to rise between electrodes filled with gas at constant pressure as d is increased. [11] The strength of the electric field E will determine the ionization efficiency of the electron-molecule and ion-molecule collisions. The Townsend coefficient a depends upon E and p as a / p = f ( E / p ) . This can be understood by the following simple argument (see ref. [4]). The chance of producing an ion by collision will depend upon the energy of the charged particle, i.e. the electric field E and mean free path l, which is inversely proportional to the pressure p. For an increase in pressure, p ~ cp (c > 1), the mean free path is reduced, l ~ l / c . If E is unchanged, the energy of the electron at collision is then reduced. If E ~ cE, then the energy is restored but

[12]

[13] [14]

[15] [16]

[17] [18] [19]

[20] [21]

[22]

[23]

the situation is not as it was to begin with because the increase in p means that the number of gas molecules present is now larger by a factor of c. Thus a has increased by this factor. A similar argument can of course be made for the coefficient /~. The argument has to be modified somewhat at very low pressures (see ref. [10]). Furthermore, in the above discussion a constant electric field E has been assumed. When the field varies with distance s from the cathode as in the PMs used in our tests, it follows that the Townsend coefficients will also depend on s. The Townsend theory does not hold for all conditions, e.g. appreciable overvoltages etc. This led to the development of the streamer theory of breakdown. Both theories have singularity conditions. See, Electrical Breakdown in Gases, ed. J,A. Rees (Wiley, New York, 1973). H.B. Gilbody and J.B. Hasted, Proc. Phys. Soc. 240A (1957) 382. P.T. Smith, Phys. Rev, 36 (1930) 1293. See also N.F. Mott and H.S.W. Massey, The Theory of Atomic Collisions, 3rd ed. (Oxford University Press, London, 1956) p. 501. M. Avery, T h o r n - E M I Gen. Com. Inc., 23 Madison rd., Fairfield, NJ 07006, USA. The error in k is estimated from the variance of data points with respect to the empirical formula (see fig. 6 of ref. [6]). See ref. [7], pp. 18, 19. Compare tables 2 and 3 on p. 1312 of ref. [6]. In general, L 0 is determined by the region with the highest value of D / z 2. In the PMs used in our tests, the values differ by ~ 25% in the two regions, with the larger value corresponding to the bulb region for which M -- 93%. Note that the lag time L 0 also corresponds to the amount of time it takes for the flow of He through the membrane to cease once the PM is removed from the region containing He. This explains the observation by S.P. Ahlen of Boston University and by R. McAlpine of T h o r n - E M l Corp, of continued increases in noise currents after exposure to He has stopped. S.P. Ahlen and R. McAlpine, private communications. W. Jost, Diffusion in Solids, Liquids, Gases (Academic Press, New York, 1952) p. 475. In our first test, the pressure of the He in the containment vessel was changed twice - to 8 psi and then to 10 psi. In each case a time lag occurs before the increased steady state flow into the pm is established. This has been taken into account in presenting the data from this test. Thus if our data, presented in this manner, indicate a certain noise level after an exposure of x d atm, it can be stated that the same tube exposed to He at a partial pressure Ap << 1 atm will have noise at this level after x / A p d. E.g. for Ap = 1 0 -3 atm and x =1 d atm, x / A p = 1000 d = 2.7 yr. Afterpulses therefore occur in most instances in which a He + is formed - whether as a result of an electron freed from the cathode or from a He atom as a result of the impact of a He + ion. The probability that an afterpulse occurs at low internal gas pressures therefore depends upon whether or not an electron ionizes a He atom en route to the first dynode. The probability that at least two afterpulses occur in a string is then expected to be roughly

J.R. Incandela et al. / Performance of photomultipliers exposed to helium the square of the probability for the occurrence of a single afterpulse. Note that the exponent m calculated from the data in fig. 4 is consistent with a value of 2.0. [24] Because the He pressure and high voltage were greater in the second test, the effects of He after the lag time L 0 were observed much more rapidly than in the first test. As a consequence there were, in general, fewer data points obtained in the mineral oil test. Furthermore, the most dramatic changes in the performance of the PM in this test look place over an eight hour period in one night when careful pulse counting measurements were not being performed. Nevertheless, the data are sufficient to confirm that the effects of the He are as expected. [25] We used the e - H e and H e + - H e ionization cross sections (refs. [13] and [14]), in a Monte Carlo calculation of the rate at which a He ion produced by collision with a primary electron goes on to produce an additional He ion

245

by collision with a neutral He atom. With V0 = 600 V, we calculate a rate of = 10% when the partial pressure of He in the tube is chosen so that the mean free path for ionization of He by He + is comparable to the gap size d. For V0 - 4 0 0 V, we do not calculate a similar rate until the He pressure in the tube is doubled. The calculation does not take into account the effect of inelastic collisions of He + with He (in which the ion will give up half of its kinetic energy to the He atom on average), or other details of the discharge process (e.g. electron-ion recombination, space charge effects etc.). The results of the calculation are thus only interpreted as an indication that the voltage VU may play a role at the "factor of 2" level in determining the exposure required for discharges to occur. In hindsight it would have been useful to vary the operating voltage in an individual test to better understand its effect on discharging.