Anomalous isotope effect in the permeation, retention, and reemission at interaction ofenergetic hydrogen with niobium
A.I. Livshits1, M.E. Notkin1, and M. Bacal2
1

Bonch-Bruyevich University of Telecommunications, 61 Moika, St Petersburg 191186,
Russia2

Laboratoire de Physique et de Technologie des Plasmas, U.M.R. 7648 du C.N.R.S.,
École Polytechnique, 91128 Palaiseau, FranceThis includes such phenomena as hydrogen retention,
permeation and reemission responsible for D/T recycling
and tritium safety. Effects of surface chemistry play avery special role in these phenomena, if hydrogenparticles posses a suprathermal energy [4]. A monolayerof nonmetallic impurity that usually covers a metal“real” surface for e.g. may drastically impede reemission,and at the same time radically enhance retention andpermeation. Moreover, permeation even may reach up to
the “superpermeation” due to such a film, meaning that ametal membrane of macroscopic thickness becomesvirtually “transparent” to hydrogen particles whoseenergy exceeds ~ 1eV. The suppressed reemission of
D/T particles as well as their enhanced retention andpermeation at the interaction with plasma facing
materials are extremely undesirable during normal
reactor operation as well as for safety reasons. On theother hand, the superpermeation and enhanced
absorption may be an effective means of D/T pumping[5] and separation from He [6] in fusion reactors andtheir models.
A superpermeable Nb membrane is used as asample in this study. The paper is focused on the morethan an order–of–magnitude difference in Nb
permeability to hydrogen and deuterium at bombarding
the metal by H and D ions within a narrow range of ionenergies (tens of eV) in a definite range of metal
temperatures (~ 900 K). If the authors’ interpretation iscorrect, then, (1) the effect may be a few orders ofmagnitude greater, (2) a similar isotope effect is to be
expected on other metals as well, and, (3) a similar effectdoes appear in hydrogen absorption and reemission.

Abstract
A niobium membrane sample was placed in H
or D plasma and electrically biased. Isotope effects for H
vs. D in factors of 20,

40 and 40, respectively, wereobserved in plasma driven permeation, retention, and in
the reemission, within a narrow range of bias voltages(40–80 V) at the lowest metal temperature investigated(910 K). The phenomenon occurred at the“superpermeation” of suprathermal hydrogen arisingfrom an oxygen monolayer at the metal surface. The
phenomenon is supposed to be caused by dynamics ofthe oxygen monolayer under the action of ion sputteringand surface segregation of dissolved O. Such and evenmuch stronger isotope effects are also expected on othermetals with a similar “real” surface. This isotope effectmay be important for D/T-mixture recycling, retention
and permeation at its interactions with plasma facing
components of fusion reactors as well as for theapplications of superpermeable membranes for pumpingof hydrogen isotopes and their separation from He.
1. INTRODUCTION
Studies involving the simplest atomic particles
such as hydrogen molecules, atoms, and ions, present a
particular significance for the physics of interactions ofatomic particles with solids. Isotope effects inhydrogen/solid systems is a typical subject ofinvestigations, as the effect of particle mass on
phenomena observed is an important feature oftheoretical speculations [1,2]. Of great interest is, e.g.,
the strong isotope effect in the diffusivity of H, D, and T
in V, Nb and Ta at temperatures < –50° C [2,3].
Peculiar isotope effects in hydrogen/solid
systems become particularly important in view of thedevelopment of fusion reactors where energetic D/Tparticles will interact with plasma facing components.

2. EXPERIMENTAL SETUP
The present investigation was carried out at theplasma – membrane setup described in more details in
Refs. [7]. A resistively heated tubular membrane of Nb

1(1 cm in diameter, 18 cm long and 0.01 cm wall
thickness) is immersed into a hydrogen or deuterium
plasma filling a chamber 44 cm in diameter in height and45 cm as shown in Fig. 1 (in fact two of the same
membrane samples are installed simultaneously). The
plasma is generated by an electric discharge between a
set of sixteen hot tantalum cathode filaments locatedclose to the chamber wall in a multicusp magnetic field
and the chamber wall, serving as the anode [8]. The
plasma density is about 5x1010 cm-3, and the electron
temperature is approximately 0.6 eV [8] during thetypical conditions of this experiment (discharge current
25 – 30 A, discharge voltage of 60-70 V, gas pressure

TMP

6
3

IG

7

IG

PG

PG

7

4
5
2

2 to 4 mTorr). H 2+ , H 3+ and D2+ , D3+ are the main ion
species in hydrogen and deuterium plasmas, respectively.
The ion temperature is in a few tenths of eV. The
membrane sample is electrically insulated, and theincident ion energy may be varied up to 250 eV withbiasing the membrane relative to plasma (practically,
relative to the wall-anode whose potential is close to thatof plasma). The ion current density is ~ 3 mA/cm2,
nearly the same over the whole range of negative bias
voltages investigated.
Two turbo-molecular pumps (50 l/s each)continuously operate in the down– and upstream
chambers. The total pressure of impurities in the input
chamber
was
in
the
order
of
-6
10 Torr during plasma operation, and a quadrupole mass
spectrometer indicated that CO was the main impurity,and H2O the next one ( 2x10-7 Torr). The pressure in the
up- and downstream chambers is measured with BayardAlpert, Pirani and Baracell gauges.
The membrane specimen is made of apolycrystalline Nb foil. Auger Electron Spectroscopy(AES) analysis of the membrane material showed thatoxygen and carbon were the main nonmetallic impurities
that remained, in the form of a monolayer coating, on thesurface of specimen after heating (> 550°C) in vacuum.
The same impurities segregated again to the surface fromthe metal bulk after the surface was submitted to Ar+ ion
bombardment followed with heating in UHV. The
membrane sample was subjected to a 1500 K heating in
vacuum prior to the experiment.

1

5
2

8

plasmaBG

H2, D2

MS

TMP

TMP

FIG. 1. Schematic of the plasma-membrane setup. 1 membranes, 2 - filaments, 3 - downstream vacuum
chambers, 4 - insulators, 5 - heavy-current leads, 6 valves, 7 - multicusp magnet system, 8 - electrostatic
probe; IG - ionization gauge, PG - Pirani gauge, BG Baraсell gauge, MS - quadrupole mass spectrometer,
TMP - turbomolecular pump.

different zones: (1) at a low incident energy, thepermeation is energy/bias-independent in the first
approximation; (2) with energy rising, the permeation is
dropping; and, (3) at a further energy increase, thepermeation becomes almost energy-independent again,
but at a lower level. At the lowest temperature, all thethree zones are most pronounced, whereas at the highest
temperature, the high-permeation zone is spreading overthe entire energy range investigated. Note that ion
species bombarding the sample were mainly H 2+ / D2+
and H 3+ / D3+ . The energy per nucleon for these ions issmaller by a factor 2 and 3, respectively, than theincident ion energy indicated.
The isotope effect is quite ordinary everywhere
except for a narrow range of incident energies at thelowest studied temperature (910 K) where jH/jD exhibits a
sharp maximum with a height ~20. The anomaly is due
to a sharp decrease in D permeation between 30 and

3. EXPERIMENTAL RESULTS AND DISCUSSION
Experimental results. Dependencies on bias/energy ofthe steady-state permeation fluxes driven by H and D
plasmas, jH and jD, respectively, and of the isotope effect,
jH / jD, are presented in Fig. 2. One can single out three2

60 eV, while H permeation still remaining at its highest
value (Fig. 2c).

downstream sides that drastically hinder the dissociationof H2/D2 molecules at their thermal absorption in themetal, with the probabilities of these processes (sticking

The role of nonmetallic monolayer. As indicated above,
the Auger Electron Spectroscopy Analysis [7, 9] shows
the presence of a very stable O monolayer on Nb surface
remaining after the dissolution in metal bulk of virginpolyatomic oxide film during heating in high vacuum at
T > 900 K. Such a monolayer gives rise to potential
barriers, Eu and Ed, at the membrane up– andcoefficients), α u and α d , being [4]:α u = Bu exp (−EuE) ; α d = Bd exp (− d ) ,kT
kT

where Bu and Bd are coefficients that are temperature
independent in the first approximation. The barriers

2Permeation flux j H, j D, molecule/(cm s)

Ion energy (eV)
250

150

100

50

Hydrogen16

10

Deuterium(a)T = 1420 K

15

10

10
10

10

16

Hydrogen

(b)
15

16

Deuterium

T = 1230 K

T = 910 K

(c)

10

15

20
Isotope effect, jH / jD

200

(1)

Hydrogen

Deuterium

Nb, 0.1 mm

15

910 K

10

(d)

5 1230 K
0 1420 K-250 -200 -150 -100 -50
Bias voltage (V)0

FIG. 2. Dependence of the plasma driven permeation fluxes jH and jD (a, b and c) and of theisotopic effect in permeation jH/jD (d) on bias voltage (bombarding ion energy) at three membrane
temperatures. The ion current density is ~3 mA/cm2 (mainly H 2+ , H 3+ and D2+ , D3+ [7]). The
incident flux of H/D atoms of near-thermal energy is ~ 1017 cm–2s–1 [7].

3

demonstrated on many metals (including Nb) with
controlled chemical composition of the surfaces (e.g.,
Refs. [4, 13]). The plasma driven permeation presented
in Fig. 2 also is superpermeation over the low

prevent the association of absorbed H/D atoms into
H2/D2 molecules at their thermal evolution as well [4,7],
with the desorption rate constants kru and krd related to αuand αd as:

bias/energy range (here, α u ≈ α d ), which is proven, e.g.,

k ru =zz
× α u , k rd = 2 × α d ,S2Sby temperature independence of jH and jD (Fig. 2a-c);that conforms with previous results obtained on the same
apparatus with H plasma [7].

(2)where S is a solubility constant of H2/D2 in metal, and z
is the kinetic gas theory coefficient.
Hydrogen evolution may be inhibited with suchbarriers to such an extent that the absorbed atoms reachthe opposite side of the membrane with a greater
probability than are reemitted back. The downstream
barrier also reflects the absorbed atoms to make them“oscillate” between the two boundaries by way of usual
random-walk diffusion. As a result, the absorbed atoms“forget” their starting position, with their desorption
through the up– or downstream surfaces depending only
on relative values of the desorption rate constants kru andkrd. Hence the steady state permeation flux, j, is givenby:j ≈ j inc ξ ×

1
1 + k ru / k rd

= j inc ξ ×

The role of sputtering. The drop in permeation at higher
energies (Fig. 2b,c) implies an increase of reemission.
The direct ion-induced reemission is negligible at theserather high T [4, 13], but ion bombardment may strongly
enhance the thermal absorption/desorption processes due
to sputtering of the O monolayer [4,7] at ion energies
exceeding the sputtering threshold (just for instance, thedifference in α and in kr for the clean surface of atransition metal and for the surface covered bynonmetallic monolayer is typically in excess of 3 ordersof magnitude [4, 14]). We denote with upper indices H+
and D+ the kinetic coefficients of the thermal boundary
processes occurring under ion bombardment:

1, (3)1 + αu / αdα uH , α uD , k ruH , k ruD (the kinetic coefficients ξ and αd as++

absorption at one impact on the surface. In the specificcase of the Group Va metals (including Nb), such apermeation regime (the so called regime of “strong
internal reflection” [10], or “RR-regime” [11]) occurs
over practically the whole range of temperatures, flux
densities, and membrane thickness of interest [4, 7].
Suprathermal hydrogen particles whose energy(kinetic, internal, or chemical) exceeds ~ 1 eV may passfactor of+j H , D = (0.1 − 1) jinc ×is a function of incident ion

11+ α

H + , D+u(E) / α d

;

(5)

+

j H 1 + α uD ( E ) / α d=.
j D 1 + α uH + ( E ) / α d(6)Thus the idea is that the steep permeation drop
and the anomalous isotope effect observed when theincident energy exceeds a certain value (Fig. 2) are dueto the energy exceeding the threshold of O monolayer
sputtering and to a drastic change in the rate of sputteringin the vicinity of threshold energy, which makes

0.1 − 11+ α u / α dj inc × (0.1 − 1) .

+energy E, with the permeation flux jH,D (i.e., jH or jD)
and the isotope effect, jH /jD given by:independent of T and varies between ~ 0.1 and 1,
conditioned only by reflection coefficient [12].
Accordingly, the permeation of suprathermal particles isgiven by:αu ≤ α2 , which is not the point of this ourtreatment). Then α uH , D

freely into metal in spite of the barrier, i.e., ξ is

d→
⎯⎯ ⎯⎯

+

well as the incident flux jinc in the above equations also
may depend on hydrogen isotope mass. However, such a
difference only may amount to the usual isotope effectwhere jinc is an incident flux, and ξ is a probability ofj ≈ j inc ×+(4)

Thus, due to the barrier generated by anonmetallic film, the permeation flux may becomecomparable
totheincidentone
andtemperature-independent. That is the mentioned above“superpermeation”(e.g.,
Refs. [4,7]).
The
superpermeation of both the H and D atoms of thermal
kinetic energies and of more energetic particles was++

α uH , α uD in eqs. (5) and (6) change dramatically.

To illustrate the near threshold behavior of thecoefficient of sputtering by H+ and D+ ions, YH + , D + , weused an empirical equation by Bohdansky et al. [15] for
sputtering of metals and their compounds by low-energy4light ions:+

E thD < E < E thH
1

YH + , D + = 0.0064 ⋅ M O γ

5
3
H ,D

7

+

: the D+ bombardment would have+already brought about an orders-of-magnitude α uD rise

⎛ E ⎞ 4 ⎛ E H + ,D+ ⎞ 2⎟
× ⎜ + + ⎟ × ⎜1 − th⎟
⎜ E H ,D ⎟ ⎜
E
⎠
⎠ ⎝
⎝ th

+

up to α uD ≈ 0.1 (clean surface), while H+ bombardment+

would not have yet changed α uH from its undisturbed(7)+value: α uH ≈ α d . Hence one would gethere MO is the mass of O atom in a.m.u., γ H,D is the
reduced mass: γ H,D = 4MH,D⋅MO/(MH,D+MO)2, E thH , D+

thethreshold+

U Nb −O+

E thH , D =energyγ H , D (1 − γ H , D )

of

+

is

+

E thD < E < E thH

effect, though decreasing at higher T (Fig. 4) due to αd, and UNb-O is bonding energy ofrising, still would remain very strong, as αd << 0.1 evenat high T.
Effects of the dynamics of impurities. However, such a
picture is at a variance with the reality (Fig. 2). A more
realistic description must account for that oxygenmonolayer may be dynamically restored during
sputtering.
In the absence of sputtering, O at the surface istrends: a dramatic change in YH + , D + with E changing,

Permeation flux, jH, jD (a.u.)

and a drastic isotope effect in the near threshold energy
range.
The simplest case would be, if one might
disregard a possible continuous repair of sputtered
nonmetallic monolayer even in the near-threshold energy
range where the sputtering coefficient is relatively small(Fig. 3). In such a case, a smallest overstepping ofEwould lead to a complete removal of nonmetallic

monolayer from the upstream surface and, consequently,
H + ,D+to an immense α urise. Thus, according to eq. (5)and as shown in Fig. 4, an orders-of-magnitude stepwise
dropping of jH and jD should have been observed at
and

E≈E

D+
th

,

respectively,

with

an

Sputtering coefficient, YH+,YD+

-2

10
10

D

+

H

-4

10

-5

10

Eth

-6

10 0

20

40

60

10
10
10

-1

D

(a)

H

-2
-4

-3

T2, αu=0.1, αd=10-4

T1, αu=0.1, αd=10

-5

-5

T1

3

10

2

T2

10

(b)

1

10

0

10

D
Eth

-1

0

H
Eth

20
40
60
80
Incident ion energy, E (eV)100

FIG. 4. Energy dependence of the permeation
flux (a) and of the isotopic effect in permeation (b)calculated by eqs. (5) and (6) at two temperatures(T1 < T2) for the case when the rate of replenishmentof the nonmetallic monolayer is negligible comparedto the rate of its sputtering in near-threshold range.
Taken as typical exemplifying values of α d for an
undisturbed downstream surface and of α u for aclean upstream surface are: αd (T1) = 10–5, αd (T2) =10–4 and αu = 0.1.

H

Eth

10

10

+

+

+

D

10

T1, T2, αu= αd04orders-of-magnitude isotope effect manifesting itself at

-3

10

10
Isotope effect, jH / jD

E≈E

H+
th

(eq. (6) and Fig. 4). Such an isotope

sputtering:an O atom. We applied eq. (7) to the sputtering of
surface O atoms from NbO, so we took for the bonding
energy that in NbO: UNb-O = 6.95 eV [16]. The result ispresented in Fig. 3. Though this calculation hardly
describes the sputtering of chemisorbed O atoms (ourcase) quantitatively, Fig. 3 does demonstrate the main

H + , D+
th

+

jH
0.1
at
≈
j D 2α d80 100 120 140

Ion energy, E (eV/nucleon)

FIG. 3. Energy dependence of the sputtering
coefficient of surface O atoms from NbO by H+ andD+ ions at perpendicular incidence calculated byempirical eq. (7).

5

sputtering in an energy range near the sputtering
threshold. However sputtering coefficients are rather
small here (Fig. 3), and that is why the condition (9)could have been met in the near-threshold energy range
only at the lowest temperature in our experiment (910 K),
and at this T only the anomalous isotope effect wasobserved. Though fairly well pronounced, this isotope
effect is still substantially smaller than that for theidealized case of a practically immobile O, as
exemplified by Fig. 4. However, a permeation
experiment with Nb may be staged at a substantiallylower T, e.g., at ~ 600 [13] rather than 900 K. In such acase, O transport between the surface and lattice will bealmost frozen, and one can approach much closer the
hypothetical case of Fig. 4 with its orders-of-magnitudeisotope effect.

in a dynamic equilibrium with the O dissolved in themetallic lattice [17]:
eq
O
Θ Os
G Nb
=
A
⋅
exp
× Θ Ov ;eq
1 − Θ Os
kT

(8)

eq
here Θ Os
is an equilibrium surface coverage with O,OΘ Ov an atomic ratio of O in the lattice, and G Nb
the heatOof surface segregation of O ( G Nb
> 0). Usually, aeqmonolayer O coverage ( Θ Os

≈ 1) exists even at

Θ Ov << 1 [4,7,17,18] due to surface segregation. However,according to eq. (8), a definite equilibrium concentrationeq, does always exist, with theof O-free sites, Θ eqf ≡ 1 − Θ Os

number of such sites increasing with Т.
The surface segregation [18] continues tomaintain an O coverage even under sputtering. Hence
sputtering never resulted in a complete cleaning of the
upstream surface in our experiment – it damaged, but

The isotope effect in retention and reemission. As it
follows from all the above, the primary underlying causeof the anomalous isotope effect in permeation is a large
difference in the kinetic coefficients of thermal boundary

only slightly, the equilibrium monolayer ( Θ Oeq ≈ 1 was
kept valid) [7,18] to maintain a certain steady-state
+

+

+

+

bombardment may lead to a significant α uH , D increase,

+

(

+

) 1A ⋅ exp⎛⎜⎜ − GkT ⎞⎟⎟ × Θ1 .
⎠j H / j D >> 1 (on assuming+hydrogen obeys the relations c H , D ,T ∝ 1 / k ruH , D ,T

O
Nb

⎝

at

the rate constant of H2 /D2 desorption goes as high as 40
in our experiment at 910 K (Fig. 2). The steady-state
concentration, с, during the interaction with an energetic

and on O diffusivity in Nb, DO, and with using eq. (8),we formulate the condition of the strong effect of ion
bombardment:++

α u ≈ α d without sputtering). Thus the isotope effect in+∆Θ Hf , D depends on E, MH,D, T, ion flux density, i H + , D + ,++k ruD / k ruH ≈ 2 ⋅ j H / j D

and, according to eq. (5), to a decreased permeation of
suprathermal H/D particles. On accounting for that∆Θ Hf , D i H + , D + , E , M H , D , DO , T ≥+important, since these constants are responsible for
H/D/T reemission/recycling and retention in plasma
facing materials in fusion devices. From eqs. (2) and (5),+desorption. Therefore, if ∆Θ Hf , D ≥ Θ eqf , the ion++

constants, k ruH , k ruD and k ruT , seems to be particularly

are centers of a facilitated thermal hydrogen absorption-++

The isotope effect in the desorption/reemission rate

their equilibrium concentration, Θ eqf . The O-free sites++

processes, α uH , α uD , and k ruH , k ruD , at E thD < E < E thH .

+concentration of O-free sites, ∆Θ Hf , D and in addition,

+

[4].

Correspondingly, the isotope effect in retention, cH /cD,

Ovreaches(9)40 .

The anomalous isotope effect in theabsorption/desorption kinetics is by no means related toparticular properties of the O-covered Nb: that must be auniversal phenomenon to appear on all transition metals
with a “real” surface. The anomalous isotope effect in
the permeation of suprathermal gas also should manifest
itself on other metals with a realistic surface composition,
since the strong dependence of permeation on chemicalcomposition of the surface is a universal feature of
non-equilibrium gas–metal systems [4].

The higher Т, the harder to satisfy condition (9); that is
so not only due to an exponential rise of the right-handpart with T, but also because of a decrease of the left partdue to a faster filling of over-equilibrium O-free sites
with migrating O atoms. Hence, the higher Т, the farther
superpermeation is spreading into the region of higher E(cf. Fig. 2a,b,c).
The same background seems to determine thedisappearance of the anomalous isotope effect at higher
T (Fig. 2d). The crucial point for the effect to take placeconsists in that the steady-state concentration of O-freesites is to be effectively augmented (eq. (9)) by ion

6

(1979)
10. A. I. Livshits, Sov. Phys. Tech. Phys. 20, 1207
(1975), 21, 187 (1976)
11. D. K. Brice and B. L. Doyle, J. Vac. Sci. Technlol.,
A5 2311 (1987).
12. W. Eckstein, Nucl. Fusion Suppl. 1, 17 (1991)
13. A. I. Livshits, M. E. Notkin, A. A. Samartsev, and
I. P. Grigoriadi, J. Nucl. Mater. 178, 1 (1991)
14. M. W. Roberts and C. S. McKee, Chemistry of
Metal – Gas Interface, (Clarendon Press, Oxford,
1978)
15. J. Bohdansky, J. Roth, and H. Bay, J. Appl. Phys.
52, 1610 (1981)
16. Gase und Kohlenstoff in Metallen, eds. E. Fromm
and E. Gebhardt (Springer, Berlin, 1976)
17. Blakely and J. C. Shelton, in: Surface Physics ofMaterials 1, ed. J. M. Blakely (Academic Press,
New York, 1975)
18. Y. Nakamura, A. Busnyuk, H. Suzuki, Y. Nakahara,
N. Ohyabu, and A. Livshits, J. Appl. Phys., 89, 760(2001)

4. CONCLUSIONSIsotope effects for H vs. D in factors of 20,

40 and 40,

respectively, were observed in plasma driven permeation,
retention, and in the reemission, at the interactions of Nbwith H and D plasmas within a narrow range of bias
voltages (40–80 V) at the lowest metal temperatureinvestigated (910 K). The phenomenon occurred at the“superpermeation” of suprathermal hydrogen arisingfrom an oxygen monolayer at the metal surface. The
phenomenon is supposed to be due to the oxygenmonolayer dynamics under the action of ion sputteringand surface segregation of dissolved O. Such and evenmuch stronger isotope effects are also expected on othermetals having a similar “real” surface. This isotope effectshould be taken into account at consideration of D/Tmixture recycling, retention and permeation at its
interactions with plasma facing components of fusion
reactors as well as at the applications of superpermeable
membranes for pumping of hydrogen isotopes and theirseparation from He.
ACKNOWLEDGEMENTS
This work was partly supported by International
Science and Technology Center (ISTC), Project #1110.
Authors are grateful to Dr. Samartsev for his help in the
manuscript preparation.
REFERENCES
1.
2.
3.
4.
5.

6.

7.
8.
9.

Hydrogen in Metals, eds. G. Alefeld and J. Volkl(Springer, Berlin, 1978)
R. Lasser, Tritium and Helium-3 in Metals,(Springer, Berlin, 1989)
K. Fujii, K. Hashizume, Y. Hatano, and M. Sugisaki,
J. Alloys and Compounds, 282, 38 (1999)
A. I. Livshits, M. E. Notkin and A. A. Samartsev, J.
Nucl. Mater. 170, 74 (1990)
Y. Nakamura, S. Sengoku, Y. Nakahara, N. Suzuki,
H. Suzuki, N. Ohyabu, A. Busnyuk, M. Notkin, A.
Livshits, J. Nucl. Mater. 278, 312 (2000)
A. I. Livshits, M. E. Notkin, V. I. Pistunovich,
M. Bacal, and A. O. Busnyuk, J. Nucl Mater.,
220&222, 259 (1995)
A. Livshits, F. Sube, M. Notkin, M. Soloviev and M.
Bacal, J. Appl. Phys. 84, 2558 (1998)
C. Courteille, A.-M. Bruneteau, and M. Bacal,
Rev. Sci. Instr. 66, 2533 (1995)
M. P. H. Dawson and W.-C. Tam, Surf. Sci. 81, 4647