Secondary electron yield in the Bendix channel electron multiplier

NUCLEAR INSTRUMENTS

AND METHODS

143 ( 1 9 7 7 )

87-92;

©

NORTH-HOLLAND

P U B L I S H I N G CO.

SECONDARY ELECTRON YIELD IN THE BENDIX CHANNEL ELECTRON MULTIPLIER CLAUDE BARAT and JACQUES COUTELIER

Centre d'Etude Spatiale des Rayonnements, Toulouse, France Received 22 November 1976 The secondary emission yield of the emissive layer of a Bendix channel electron multiplier was measured using an electron beam for energies between 100 eV and 1 keV. This yield reaches 6 = 3.6 at about 350 eV in a channel electron multiplier at the end of the desorption phase. The variation of 6 as a function of the electron energy is in agreement with semiquantitative theories using a power law to describe the primary electron energy loss.

1. Introduction

The theory of the electron charge increase in a channel electron multiplier (C.E.M.) is a complex problem which requires a knowledge of the electron paths ~) and the secondary electron emission (SEE) yield. Goodrich and Wiley 2) have measured = 1.48 at 40 eV for the Bendix emissive layer while Streeter et al. 3) give ~ -- 1.38 at the same energy. To date, no measurements above 70eV exist, in spite of the fact that the electrons may reach energies of about 400 eV for the C-shaped C.E.M.4).

The study of 6 as a function of the primary electron (P.E) energy also presents an interest for secondary emission theory. Although the general shape of the function 6(Ep) is the same for all materialsS), noticeable differences have been observed between metals and semiconductors or insulators6). From this standpoint, it is then interesting to check the behaviour of a metal oxide glass. 2. Apparatus

In standard experiments, the S.E.E. yield is deduced from the target current, and from the collector surrounding the target. This method is slow and. involves a beam current regulation for accurate results. Another technique uses the pulse method and, thus, a pulsed electron gun; however, the measurement errors are relatively high (5-10%). These errors are lower if one uses a compensation pulse method, which consists of cancelling the target or collector pulse by means of an opposite polarity synchronous pulse, supplied by a calibrated pulse generator. Furthermore, sophisticated and accurate apparatus use a LEED-Auger systemT). Our experimental apparatus is shown in fig. 1. The electron source is not a pulsed electron gun,

but a 4010 Bendix C.E.M. whose output is centered on the axis of the electrostatic lenses. The C.E.M. input is excited by electrons emitted by a radioactive tritium source whose flux is adjusted for count rates on the order of 5 × 103 c.p.s. This extremely simple method provides a highly stable current whose density is naturally near that of the saturation current density of a C.E.M. On the other hand, the accuracy of the initial electron energy is only fair. The semiconductor glass sample is joined by means of a conducting adhesive to a target with adjustable inclination. This flat 10 × 10 mm 2 sample is cut out over the pyramidal entry input of a Bendix spiraltron RX 3199 identical to those used on the french satellite D2B. A quasi-spherical collector surrounds the sample completely and collects the secondary electrons (S.E.) emitted by the target. The apparatus is placed inside a stainless steel bell jar associated with an ion pump, the operation pressure is on the order of 10 -7 t o r r ; at which the particle background from the ion pump represents 1% of the C.E.M. count rate. The charge resistors R linked to the C.E.M., the target and the collector are 50 ,Q. The resulting time constant makes it possible to insure that the C.E.M. after-pulse rate is negligible. The Rt resistors filter the polarisation voltages of the target and collector, while the C capacitors are used for pulse decoupling (see fig. 1). 3. Procedure

The purpose of this procedure is to determine the S.E.E. yield as a function of the P.E. energy Ep and the angle 0 made by the electrons with the normal at the surface of the sample. The pulses collected on the C.E.M., target, and collector all

88

C. B A R A T

AND J. C O U T E L I E R V (VOLTS) y(mm) e=lo *

CL

....

= V3

80 25 ~

:

50 ~

c

V1

V2

• V4

Ep=100eV

*

\

,

d':

~

oo

40 35

V3

30_

\

\

Fig. 1. Experimental set-up.

have the same width; so the different currents are proportional to the corresponding pulse height, and the experimental technique consists of measuring the pulse height after amplification. The measurements were begun after a C.E.M. desorption phase of 1 x 108 counts in order to assure the stability of the P.E. beam and to reduce the gas adsorption on the surface of the sample (without bombardment of P.E., the absorption rate is about equal to one monoatomic layer deposited per second at 1 x 10 -7 torr). The P.E. energy at the point of impact on the target is determined by the potential of the target (the C.E.M. output is grounded) and by the average initial energy of the electrons emerging from the C.E.M., i.e. 75 eV for a C.E.M. voltage of 2800 V4). Since the currents on the target and collector are known, the S.E.E. yield is defined by (see fig. 2): 6 = i, io

i o - ic io

1

ic io

where i0 is the P.E. current, ic the target current, and is the S.E. current. This expression shows that a knowledge of is is not necessary if i0 can be measured (e.g. by means of a Faraday cup, lined with carbon black to prevent a stray secondary emission).

t~L

0

10-

,

',

\

',

o°

,

°o

5 ~ ' 1 0

10

20

30

40

SO

60

70

80 v(VOLTS)

Fig. 3. Equipotentials.

Furthermore, we can also write: c5=

i~ i¢ + i~

with i~ =

/sphere --

A is -

irerl ,

where iren is the elastically scattered electron current and Ais the current of the S.E. lost in the collector opening. The current of the elastically scattered electrons was neglected for P.E. energies between 100 eV and 1 keV, while this approximation is no longer possible for Ep<100eV. On the other hand, Ais is high for 0 values near 0 °. In15 14-13 12

I

11 10-

I oEp ~ Ep + Ep ,,En = Ep~

I I = 50eV = 100eV = 200eV = 300eV =400eV

I

I

I

I

I

I

I

I 70

I 80

I 90

I 100

9 e-

6 4 ÷

2 1 0

10

20

I

30

I 40

I 50

60

e (DEGREES)

Fig. 2. Diagram o f currents.

Fig. 4. Aq~ as a function of 0 for various energies Ep.

110

SECONDARY

ELECTRON

YIELD

6

4Fq.-++ 4p +.+

3

tg zqSo =

+

89

(2el)/(2e~) vo2v--m

svdy

Vo2x--m

exdx ,

with

++

+

f ( e r dy + ex dx) = Vt (target) - Vc (collector), ,--,I-, ,--,F-, m

,-~ e = 0 * ~|~ e=60 ° • STREETER ET AL (REE 3) I 100

I 200

I 300

I

[

I

t.O0 500 600 E p (ev)

I

I

'700 800

Fig. 5. S.E.E. yield as a function of Ep.

I

900

I

I

1.000 11100

where Voy and v0~ are the components of the P.E. velocity at the collector input. These calculations show that A q ~ = O i - - O 0 is about 5° for E p = 100eV (i.e. Ep= 180eV at the collector input) but does not go above 2° for Ep>300 eV (fig. 4). One also notes that the determination of 00 is inaccurate at low energies for 101>70 °, since many P.E. may miss the target. 4. Results

The maximum S.E.E. yield ranges from 2.9 to 3 for 0 = 0 ° (fig. 5). In the absence of similar resuits on the Bendix glass, it may be noted that the maximum S.E.E. is 3.5 for a lead glass reduced in hydrogen and 2.4-3.6 for a SnO2 layer depending on the method of layer preparation and thermal treatment). The P.E. energy Epm for which 6 = 6m ranges from 200-250 eV. This value should be compared with that of silicium [250 eV for Dekker 8) and

deed, the S.E. energy is below 50 eV while the modal value is about 1 eV at the sample surface for any P.E. energy. Furthermore, the S.E. angular distribution is approximately a cosine distribution, without an electric field. The application of a potential difference between the collector and the target modifies the S.E. angular distribution by curving the S.E. paths inward, towards a direction perpendicular to the equipotentials (fig. 3). As a result, Ai s is negligible for [01 >40 °, which makes E p - 1 2 5 tV it possible to find the value of is, thus io=is+ic. a E p = 2"/5 eV EXPERIMENTAL The potentials are applied to the electrodes in DATA o Ep = 975 eV order to maintain a constant electric field in the 6 THEORETICAL space between electrode 3, the collector, and the . . . . . APPROXIHATION 4sample (see fig. 1), independent of the target potential. This method makes it possible to keep a constant electric pattern in the collector target ",,,.. 3,5space for all P.E. energies. The results have been checked, for certain energies, by fixing the poten' ', i ' ' + ' " ~ . . + . tial of acceleration V3 and varying the retarding ',,, "+--+_+_,..-;_+_ potential of the sample. In this case, the P.E. current i0 is constant, but the potential gradient of + + + + the sample-collector space may vary. The pitch angle 00 formed by the P.E. with the target was calculated as a function of the P.E. en§-,, 2ergy at the collector input for different injection angles ¢~ = 90 ° - 0 (fig. 3). In the first phase, the equipotentials and the components of the electric 1.5field e were determined at all points by a numerical method of relaxation, taking into account the real I I I I I I I I i I I I I 1 geometry of the collector-target space. In addition, -90-80 - 7 0 - 6 0 - 5 0 - 4 0 - 3 0 - 2 0 - 1 0 0 10 20 30 /,0 50 the equation for the motion of an electron placed O ( DEGREES ) within an electric field give the pitch angle ¢0, i.e.: Fig. 6. S.E.E. yield as a function of 0.

sj

s

"S

- +_4.-+ -'+''+" +,', ¢

-

I

1

•

I

60 70 80 50

90

C.

0.8

I

I

I

I

I

100

200

300

400

I

BARAT

AND

0.6 0.5 e. 0.4 0.3 0.2 0.1

Fig. 7. p a s a f u n c t i o n

500 600 Ep (eV)

700

800

I 900

I 1.000

I~00

o f Ep.

215 eV for Henrich7)] as long as there is a correlation between Epm and a material density ~°) (the densities of the Si and SiO2 are close to each other). It is well known that the secondary yield is greater for a primary beam at an oblique angle with the surface than for perpendicular incidence (0 = 0). However, this effect is very small for low P.E. (fig. 6). This experimental result, dependent on depth of the P.E. penetration, can be expressed by the relation: 30 = 3o exp{p(1-cos0)}, 4[

,

I

F

I

I

I

COUTELIER

where p is a function of the P.E. energy (fig. 7). The decrease of p when Ep decreases can be explained by the fact that the P.E. progressively loses its initial direction in the material since the cross section of electron scattering increases. In addition, p seems to tend towards an asymptotic value (-0.75) for E~>I keV. As for the C.E.M., the impact angle 00 of the S.E. with the emissive layer varies according to the type of trajectory, the applied voltage on the tube, and the initial S.E. energy. If we consider that the average angle 00 is between 10° and 15° 1) the S.E.E. yield can go above 3.6 for P.E. energies of about 350 eV (fig. 8).

I

0.7

0.0

J.

5. D i s c u s s i o n

Elementary S.E. theories are limited to a semiquantitative comparison with the experiment, and do not take into account details of the S.E. production nor of the escape mechanism. One generally assumes that 6 is given by the relation 6 =

n (x, Ep) f (x) dx, 0

where n(x, Ep)dx represents the number of S.E. produced by P.E. in a layer of thickness dx at a depth x below the surface; f ( x ) is the probability that a S.E. produced at x escapes from the surface. One also assumes that n(x, Ep) is proportional to the energy lost by the P.E. per unit path length, i.e., n (x, Ep) = - K dEp/dx.

I

Furthermore f ( x ) is considered to be given by e x p ( - a x ) where 1/~ is the effective S.E. range. Applying Widdington's law i.e., dEp/dx = - A / E p ( x ) ,

2[--

/

where A is a characteristic constant of the solid. Baroody s) obtained a reduced yield curve where 6/6m is expressed as a function of Ep/Epm, independent of the characteristic parameters of the solid:

1 0 ' ' : ~ < 15"

'k/

6/6m -

1

- F(0.92Ep/Epm), F(0.92)

(1)

with F(r) = e x p ( - r 2) 0

100

200

300

400

500

600

700

Ep (eV) Fig. 8. S.E.E. yield as a f u n c t i o n o f Ep for | 0 ° < ~ < 1 5 °.

fo

exp(y 2) dy.

A comparison of expression (1) with the experimental results reveals an important discrepancy

SECONDARY

ELECTRON

for Ep>Epm. In fact, Widdington's law does not correctly describe the losses of energy of the primary electrons. Experimental measurements on low-energy electron transmission by different materials have led Lye et al. 6) to define a generalised power law, i.e. d E p / d x = - A / E ; (x) .

The agreement with the experimental results is made for n = 0.35. For this reason, the P.E. range is no longer proportional to the square of the energy (Widdington's law), but to E~,+1. If f ( x ) is given by exp(-agc), the expression for the reduced yield curve for the power law becomes 6)

G.(r)

'1~

I

.....

;o

I

I

BAROOOY(REF5).MgO (REF6) "POWER LAW" + Ge (REF6) . . . . -'CONSTANTLOSS"| OUR RESULTSFOR BENDIX LAYER

~

(3)

Zn(rmEp/Epm),

Ln(rm)

with

o ~,;

~

~

.

2) d z .

dr

d E p f d x = - Epl R ( Ep) .

toE

1 (~/(~m = - -

E r f c y = (2/zc ½) i °° e x p ( - z

exp(y "+1) dy.

This expression corresponds to that of Baroody for n = 1. The power law implicitly assumes that the P.E. range R is the same for all. In other words, most of the energy is lost at the end of the range and n(x, Ep) is maximum at x ~ - R . In fact, the loss of energy by P.E. tends to equal out over the entire distance due to the straggling of the primary range. This "constant loss" law is written

[_

where r is the maximum age of the secondaries, proportional to the square of the diffusion length. Under these conditions the expression for the universal reduced yield curve is written:

and

G,(r) = e x p ( - r "+1)

~-

[ ( x ) = Erfc(x/2T'r),

(2)

Gn(l"mEp/Epm)

with

1.5

In the case of a semiconductor or an insulator, it is necessary to consider the interaction of the S.E. with lattice vibrations. In this case, the escape probability f ( x ) becomes 11)

L.(r) = r {Erfcr "+t + n ~ r 1"+1 [ 1 - e x p ( - r2"+2)]}

1 ~/~m = - -

91

YIELD

I

REGIONOF EXPERIMENTAL RESULTS__ FOR METALS

Let us note that the use o f f ( x ) = - exp (-a:x) would have led to an expression numerically similar to relation (3). Expressions (1), (2) and (3) were compared with the experimental results in fig. 9, the theoretical curves given by relations (2) and (3) are close to each other but different from Baroody's relation. The behaviour of the Bendix glass clearly differs from that of the metals and our experimental points lie within those of an intrinsic semiconductor (Ge) and those of an insulator (Mgo). This confirms that there is no reduced yield curve common to all materials, since the mechanisms of production or escape may differ; specifically, in the case of the semiconductor Bendix glass, the S.E. may interact with lattice electrons, lattice vibrations, traps, and occupied donor levels. However, the S.E.E. yield of this glass may be correctly described by the power law for n = 0 . 3 5 up to Ep/Epm = 3.

0.5~- g'./ L /,!/

0

0

"\.

I

1

\

I

2

I

3

I

4

Ep /Epr n

Fig. 9. Comparison of eqs. (1), (2) and (3) with experimental results.

Our experimental results were obtained after a sample desorption under conditions identical to those of a C.E.M. Under experimental conditions, we measured 6 = 3.5 for Ep = 250 eV-~Epr n a t the onset of bombardment (0=0°). The difference with the value found after surface desorption emphasizes the importance of the surface states on the secondary emission and explains the drop in gain during the desorption phase. In the same vein, a surface sputtering by ions or the action of

92

C. BARAT AND J. COUTELIER

radiation damage may modify the value of the S.E.E. yield. O n the other hand, we noted at the end of the desorption that 6 no longer depends on the pressure between 10-7 and 10-5 torr, and of the P.E. current density between 10 -6 and 10 -7 A / c m 2. These values of current density remain, however, below the saturation density, i.e. about 10-5 A / c m 2, beyond which the S.E.E. yield decreases9).

The authors are indebted to Prof. F. Cambou for his encouragement and interest in this work. We would also like to thank J. Hurley and M. Laffont for technical contributions.

References

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) ll)

D. Loubet and C. Barat, Nucl. Instr. and Meth. I11 (1973) 441. G. W. Goodrich and W. C. Wiley, Rev. Sci. Instr. 32 (1961) 846. j. K. Streeter, W. W. Hunt and K. E. McGee, Rev. Sci. Instr. 40 (1969) 307. D. Loubet and C. Barat, Nucl. Instr. and Meth. 118 (1974) 259. E. M. Baroody, Phys. Rev. 78 (1950) 780. R. G. Lye and A. J. Dekker, Phys. Rev. 107 (1957) 977. V. E. Henrich, Rev. Sci. Instr. 44 (1973) 456. A. J. Dekker, SoOd state physics (Academic Press, New York, 1958). A. M. Tyutikov and M. N. Toyseva, Radiotekhn. I. Electron. 12 (1967) 1347. A. O. Barut, Phys. Rev. 93 (1954) 981. A. J. Dekker, Physica 21 (1954) 29.