PRAMANA
— journal of
c Indian Academy of Sciences
°
physics
Vol. 68, No. 3
March 2007
pp. 507–515
Contribution of backscattered electrons to the total
electron yield produced in collisions of 8–28 keV
electrons with tungsten
R K YADAV and R SHANKER∗
Atomic Physics Laboratory, Department of Physics, Banaras Hindu University,
Varanasi 221 005, India
∗
Corresponding author. E-mail: [email protected]
MS received 2 November 2005; revised 22 September 2006; accepted 4 December 2006
Abstract. It is shown experimentally that under energetic electron bombardment the
backscattered electrons from solid targets contribute significantly (∼80%) to the observed
total electron yield, even for targets of high backscattering coefficients. It is further found
that for tungsten (Z = 74) with a backscattering coefficient of about 0.50, about 20% of
the total electron yield is contributed by the total secondary electrons for impact energies
in the range of 8–28 keV. The yield of true backscattered electrons at normal incidence
(η0 ), total secondary electrons (δ) and the total electron yield (δtot ) produced in collisions
of 8–28 keV electrons with W have been measured and compared with predictions of
available theories. The present results indicate that the constant-loss of primary electrons
in the target plays a significant role in producing the secondary electrons and that it yields
a better fit to the experiment compared to the power-law.
Keywords. Backscattering yields; secondary electron yield; stopping power.
PACS Nos 79.90.+b; 79.20.Hx; 34.80.-i
1. Introduction
When energetic electrons collide with a solid metallic target, they lose their energy
by a variety of mechanisms: secondary electrons (SE) are emitted as a result of
energy transfer process occurring between the incident electrons and the electrons
in the solid. Secondary electrons are generated within their escape depth in the
range of 30–70 Å for metals [1]. These electrons may find their way to the surface and escape from it. Primary electrons which have penetrated deeper into the
target and got subsequently backscattered towards the surface may also generate
secondary electrons within the secondary electron escape depth, which contribute
to the total yield of secondary electrons [2,3]. Considerable interest has arisen in
the use of secondary electrons resulting from bombardment of a solid target with a
focused and highly accelerated beam of electrons in scanning electron microscopy
507
R K Yadav and R Shanker
(SEM). The quantitative analysis of secondary electrons in studies of microscope
images requires a knowledge of the escape depth of secondary electrons inside the
target, and also the contribution of backscattered electrons for generating the secondary electrons. Relevance of the secondary electrons in determining the atomic
structure of a given target has been considered by several workers (see [4–6]). The
emission of secondary electrons is quantified in terms of SE yield from a solid, which
is defined as the number of the secondary electrons emitted per incident charged
particle. In general, the SE emission from metals takes place due to collisions of
both primary and backscattered electrons with the target. This emission strongly
depends on the scattering process of the primary electrons for which no detailed
theory is available as yet. Theoretical treatment of secondary electron emission
is based on many different mechanisms, for example, ion-induced secondary electron emission for incident energy of 1–100 keV (Parilis and Kishinevskii [7] based
on Auger recombination mechanism, Ghosh and Khare [8] based on the relation
of the SE yields to the ionization cross-sections at high energy electron impact).
Electron-induced secondary electron emission has been described by the elementary
theories by Salow [4], Baroody [5] and Bruining [6]. Kanaya and Kawakatsu [1] have
modified these theories using a Lindhard power potential formalism to describe SE
emission from metals due to both primary and backscattered electrons.
In electron-induced SE emission, some of the incident electrons are backscattered
from the solid [9–13]. In this process, secondary electrons may be produced by
incident as well as backscattered electrons and thus, the total secondary electron
yield produced from the target is given by
δ = δsi + δsb ,
(1)
where δsi is the secondary electron yield from the solid due to the incident electrons passing through the surface and δsb is the secondary electron yield due to the
backscattered electrons. Also, the total electron yield from the target is given by
[14]
δtot = δ + ηα ,
(2)
where ηα is the backscattering coefficient which is the number of backscattered
electrons per incident electrons at the incidence angle α.
In the present work, we report on the measured ratio of backscattering coefficients (ηα /η0 ) for a thick tungsten target as a function of the angle of incidence
for electrons having impact energy 10 keV. In addition, results on the secondary
electron and total electron yields due to backscattered and primary electrons from
tungsten for collisions of electrons with impact energies in the range of 8–28 keV
are presented and discussed. Wherever possible, results of the present work have
been compared with other published data and with the predictions of the available
theoretical models.
2. Experimental
Measurements were carried out on a recently developed experimental set-up, the
details of which are given and discussed elsewhere [15]. Briefly, a mono-energetic
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Collisions of 8–28 keV electrons with tungsten
beam of electrons was generated from a custom-built electron gun (M/s P.Staib
GmbH, Germany) and was focused onto a 3 mm spot size on the target (20 mm
× 14 mm × 0.5 mm) situated at about 500 mm away from the gun. The accuracy
of positioning the beam spot on the target was estimated to be about ±1 mm.
During the measurements, the incident beam current was kept at about 10 nA.
The base pressure of the scattering chamber was maintained at 1.6 × 10−6 Torr.
The chamber is equipped with a movable target holder in the vertical plane at
its center to position the target in front of the beam. A high purity (99.90%)
tungsten target with 0.5 mm thickness was mounted on the target holder. In order
to measure the secondary electrons, we have used a suppressor grid biased at −50
V with respect to the target. A semi-spherical aluminum collector plate (0.5 mm
thick) placed behind the grid was used to monitor the current produced by the
scattered electrons from the target. Both the suppressor grid and the collector
plate were fixed in front of the target. The integrated assembly of the target holder
and the target could be moved up or down or rotated with respect to the direction
of the beam. The angular positioning of the target with respect to the direction of
the incident beam was made between α = 0◦ and 60◦ with an accuracy of ±1◦ . All
measurements were carried out under a high vacuum (< 2.0 × 10−6 Torr) condition.
For conditioning the specimen, one of its faces was mechanically polished until it
reflected light specularly. This face was made to interact with the beam. It was
cleaned with acetone repeatedly and degreased in the alcohol vapor bath before
being transferred to the scattering chamber.
The backscattered electrons reach the collector plate kept at earth potential
through a high precision resistance of 33 MΩ. The plate and the target current
were measured through a dual switch with the help of a digital voltmeter (DVM)
connected across a precision resistance. Relative calibration of the two measuring
devices was insured before recording the actual corresponding currents. It may be
pointed out here that three successive measurements of η0 and δtot were made in
our experiments for each impact energy E. The average of these measurements
finally was taken. The statistical uncertainty of measurements was found to be
about 5%. The electron energy of impact E was varied from 8 to 28 keV. At an
angle of incidence higher than 60◦ , the accuracy of measurements for ηα becomes
less reliable as at these angles the electron beam does not necessarily fall fully onto
the surface of the target, rather a large fraction of it scatters at a grazing angle.
3. Results and discussion
The variation of ratio (ηα /η0 ) as a function of angle of incidence α for impact energy
E = 10 keV for W and Au targets has been studied and shown in figure 1. The
ratio is seen to increase smoothly with α. The nature of angular variation of the
data from our results for W is found to be similar to that for Au from other workers
(Fitting et al [16] and Staub [17]). From this comparison, it is noted that our data
for W are in satisfactory agreement with those of Staub for Au [17] but the data
for Au from Fitting et al [16] are seen to lie slightly lower than ours. However, on
comparing the above data for W and Au, it is concluded that three sets of data for
not too different Z-elements are in a good agreement with each other within the
Pramana – J. Phys., Vol. 68, No. 3, March 2007
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R K Yadav and R Shanker
Figure 1. Variation of the ratio (ηα /η0 ) as a function of incidence angle α
for W and Au at E = 10 keV.
experimental uncertainties. The angular dependence of the backscattered electrons
for W at 8 keV electron impact has been measured recently in our laboratory and
the results are reported (see, ref. [15]).
In order to predict the variation of η with α, two simple theories of backscattering
are available: one due to Everhart [18] and other due to Archard [19]. Bruining
[6] derived a relation for emission of secondary electrons according to which the
expression for angle-dependent backscattering coefficient ηα is given as
ηα = η0 exp[γxd (1 − cos α)],
(3)
where ηα and η0 are the backscattering coefficients for angle of incidence α and for
α = 0◦ respectively, γ is the absorption coefficient and xd is the diffusion range.
The constant γxd in eq. (3) is then found to be a simple function of η0 for all
elements and for all impact energies [20],
γxd = − ln η0 − 0.119.
(4)
Combining the above relation with Bruining’s expression (see, eq. (3)), one obtains
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Collisions of 8–28 keV electrons with tungsten
Figure 2. Plot of δ, η0 and δtot as a function of impact energy E (8–28 keV).
(•, N, H): present experiment; ◦: Al [24]. Theory: solid curves (δ: [14], η0 :
[21], δtot : [14,21]).
ηα = B(η0 /B)cos α ,
(5)
which yields the value of B (a constant) to be 0.891. The least squares fit to our
experimental data and those of Staub with eq. (5) is made and shown in figure 1.
The comparison between theory and experiment shows a good agreement among
themselves within the experimental errors. Further, a plot of our measured values
of η0 as a function of E is shown in figure 2, which exhibits a linear dependence.
Hunger and Kuchler [21] have also made a theoretical study of this variation in the
range of 4–40 keV. The curve shown in the figure is the prediction of their theoretical
calculations which is found to be in a good agreement with our experimental data.
For studying the behavior of electrons penetrating a solid target, there are two
theories available: (i) diffusion and (ii) large-angle elastic scattering. Two sources
of energy loss, one due to nuclear and other due to electronic stopping, affect the
electron beam. The corresponding momentum transfers are small because electrons
are light particles, but the relative energy loss is very large. Thus, the range of
Pramana – J. Phys., Vol. 68, No. 3, March 2007
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R K Yadav and R Shanker
penetrating electrons is given by the electronic stopping power wherein the incident
electron excites or ejects the atomic electrons with an energy-loss defined as [22],
·
¸
dE
Z
E
= −ρ × 78500
ln 1.166
keV/cm,
(6)
dx
AE
I
where E is the impact energy; I = (9.76 + 58.8Z −1.19 )Z eV [23] is the mean excitation potential of the target material and electron energy range x = E0 /(dE/dx)
and ρ is the density of the target material.
The yield of secondary electrons produced by the incident electrons of energy E
from W can be calculated [14] as
δsi =
1.046
[ln(5.69)E − 1.2329]
E
(7)
and the yield of secondary electrons produced by the backscattered electrons is
obtained as [14],
µ
¶
η
b
δs = 130.75
103 E − Emax
·
¸
3
10 E 1.6 × 104 EEmax
E
3
× ln
ln
− 2.4658 ln
10 ,
(8)
Emax
I2
Emax
where Emax = 800 eV (for Z = 79), is the energy at which the maximum of dE/dx
curves occurs.
The measured yield of true backscattered electrons (η0 ), total secondary electrons
(δ) and the total electron yield (δtot ) produced by the collisions of 8–28 keV electrons with W are shown in figure 2. The theoretical curve for secondary electrons
produced by primary plus backscattered electrons is obtained using eqs (7) and (8).
From the figure, it is seen that the backscattered electrons contribute significantly
to the observed total secondary electrons (δ). For targets of high Z such as tungsten, the backscattering coefficients are found to be about 50% and the contribution
of total secondary electrons to the total electron yield is seen to range from 29 to
10% for impact energies ranging from 8 to 28 keV, that is, on an average about
20% of the total electron yield is contributed by the total secondary electrons. This
finding agrees approximately with what one would expect from the smaller rate of
energy loss and from the smaller path lengths traveled by the backscattered electrons in the secondary electrons escape region compared to that by the incoming
primaries. In figure 2, the open circles represent the total secondary electron yield
for Al (Z = 13) [24] wherein the data are normalized at E = 20 keV. It is also
noted that the total secondary yield increases as E decreases; this happens because
increasing amount of energy is dissipated by the primary electrons in the region
close enough to the surface for a large fraction of the excited internal secondary
electrons to escape. For a sufficiently high impact energy, the penetration depth of
the primary beam becomes large compared to the escape depth of secondary electrons, and since the number of secondary electrons created per unit path length is
a decreasing function of energy, the number of internal secondary electrons created
within the escape depth of the surface decreases with increasing primary energy.
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Collisions of 8–28 keV electrons with tungsten
Figure 2 also shows the increasing trend of η0 with impact energy E. The reason
why η0 increases with E for high Z targets such as W and Au can be understood by
noting the fact that for these elements, the elastic and nuclear scattering of incident
electrons become more dominant with increasing impact energies.
From the yield curves of elements W, Ti and Pt, a universal yield curve can be
obtained by plotting values of δ/δmax vs. E/Emax (see figure 3) following the procedure of Baroody [5], where δmax is the maximum secondary emission coefficient.
However, the prediction of Baroody’s theoretical universal yield curve has assumed
the Whiddington’s law. This curve is found to deviate considerably from the experimental data for various materials. A better fit to the experimental data but
still using simple secondary electron emission theory, has been obtained by Lye and
Dekker [25], assuming the range–energy relationship of electrons given by Young
[26]. From the transmission experiments of Young, it is found that the practical
range R of electrons follows the relationship R = CE n+1 , where C is a constant
and n = 0.35. It may be pointed out here that the Whiddington’s law assumes
n = 1 in the power-law theory. However, a better agreement of the experimental
data for W from our experiment and the data from Baroody’s paper for Ti and Pt
metals is obtained if n = 0.15 is used in the expression given by Lye and Dekker
[25]. The universal yield curve of Lye and Dekker is written as follows:
µ
¶
δ
1
Zm E
=
gn
,
(9)
δmax
gn (Zm )
Emax
gn (Z) =
1 − exp(−Z n+1 )
,
Zn
(10)
where Z n+1 = γR, Zm represents the value of Z when gn (Z) becomes maximum. A
curve is plotted between δ/δmax and E/Emax using eq. (9) for the value of n = 0.15.
The resulting curve is shown by a solid line in figure 3. In this context, it may be
mentioned here that the range–energy results are described quite accurately by
Young using the relation R = 0.0115E 1.35 for aluminum oxide for which the value
of n = 0.35, where R is expressed in mg/cm2 and E in keV. Lye and Dekker [25]
compared their experimental results by taking n = 0.35 in theory and found a
satisfactory agreement with the experiment. It may be pointed out here that the
value used by Young for n = 0.35 was for aluminum oxide and not for a metal. It
is interesting to note that the value of n = 0.15 is found to yield a good agreement
with ours as well as with Baroody’s experimental data for metallic elements. At
still higher energies, where data for metals are not readily available, we have found
that the yields for W, Pt and Ti vary as E −0.15 which fit the experimental data
reasonably well. The smaller value of n (n = 0.15) compared to n = 0.35 [25] is
indicative of the fact that the yields of secondary electrons in metals vary more
slowly with E compared to that in metal oxides. This may be because of the fact
that the stopping powers of electrons in metals [27] and metal oxides [25] vary
differently. In figure 3, the experimental data are seen to follow the ‘constant-loss
principle’ and not the ‘power law’. In contrast, the constant-loss indicates the
importance of straggling of the primaries in the target, which is usually neglected
in the power-law theory [25]. As a consequence of this, the effective energy loss per
Pramana – J. Phys., Vol. 68, No. 3, March 2007
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R K Yadav and R Shanker
Figure 3. Variation of the reduced secondary electron yields (δ/δmax ) with
the reduced primary energy (E/Emax ), where δmax and Emax are defined in
the text. Different symbols show the experimental data points for various
elements; •: W, ◦: Pt, O: Ti. The solid curve represents the prediction from
Lye and Dekker [25] for a case of constant-loss while the dotted line curve
represents the prediction for power-law.
unit depth per incident electron will also be different from the calculated values on
the basis of a single range for all primaries. In fact, if all primaries are assumed
to have the same range, most of the energy losses will occur near the end of the
range and thus the production of secondary electrons will be a function of depth
as indicated by ‘power-law’. In straggling, the act of equalizing the energy losses
leads to essentially a constant value over the entire range.
4. Conclusions
The present work deals with the contribution of backscattered electrons to the
secondary electron yields by the collisions of 8–28 keV electrons with tungsten. It
is shown that the backscattered electrons contribute significantly to the observed
total electron yield δtot . For targets of high Z, the contribution of total secondary
electrons to the total electron yield is seen to range from 29 to 10% for the impact
energies from 8 keV to 28 keV, i.e. on average, about 20% of the total electron yield
forms the total secondary electrons. The total secondary electron yield increases
as the impact energy E decreases; this is because increasing amount of energy is
dissipated by the primary electrons in the region close enough to the surface for
a large fraction of the excited internal secondary electron to escape. The plotted
curve (solid line in figure 3) for δ/δmax vs. E/Emax for n = 0.15 gives a better fit to
the experimental data for W from our experiment and to the data from Baroody’s
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Collisions of 8–28 keV electrons with tungsten
paper for Ti and Pt materials. The experimental data follow the constant-loss
principle. The constant-loss indicates the importance of straggling of the primaries
in the target. In straggling, the tendency of equalizing the energy losses brings
essentially a constant value over the entire range.
Acknowledgements
The work presented here has been financially supported by the Department of
Science and Technology (DST), New Delhi, under a research project, SP/S2/L08/2001. The authors would like to thank Mr S Mondal for his help in the experiment and for fruitful discussions.
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