Temperature dependence in fast-atom diﬀraction at sur- faces Peng Pana Maxime Debiossacaand Philippe Roncina

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Temperature dependence in fast-atom diﬀraction at sur-

faces

Peng Pana, Maxime Debiossacaand Philippe Roncina

Grazing incidence fast atom diﬀraction at crystal surfaces (GIFAD or FAD) has demonstrated coherent

diﬀraction both at eﬀective energies close to one eV (λ⊥≈14 pm for He) and at elevated surface

temperatures oﬀering high topological resolution and real time monitoring of growth processes. This

is explained by a favorable Debye-Waller factor speciﬁc to the multiple collision regime of grazing

incidence. This paper presents the ﬁrst extensive evaluation of the temperature behavior between 177

and 1017 K on a LiF surface. Similarly to diﬀraction at thermal energies, an exponential attenuation

of the elastic intensity is observed but the maximum coherence is hardly limited by the attraction

forces. It is more inﬂuenced by the surface stiﬀness and appears very sensitive to surface defects.

1 Introduction

The characterization of new materials requires a variety of tech-

niques to analyze their physical and chemical properties. These

can be real space microscopic techniques such as scanning tun-

neling microscopy and atomic force microscopy but also recipro-

cal space techniques using X-rays, neutrons, electrons, or atoms.

Since atoms with kinetic energies below a few eV cannot pene-

trate below the surface, thermal energies atom scattering (TEAS),

also known as helium atom scattering (HAS), is a valuable tool to

investigate surfaces and 2D materials1,2. It is insensitive to the

presence of magnetic or electric ﬁelds and does not induce any

direct damage or charging of the surface. However, its geometry

is not compatible with a standard molecular beam epitaxy (MBE)

vessel which requires that no instrument prevents the gas from

the evaporation cells to reach the surface. MBE also requires ele-

vated surface temperatures in order to control the mobility of the

deposited atom or molecule so that these can reach an optimum

location in a reasonable timescale without being trapped too long

in undesirable sites3. In this context, grazing incidence fast atom

diffraction (GIFAD4or FAD5) which is the high energy, grazing

incidence counterpart of TEAS offers decisive advantages; it has

shown to be compatible with a harsh UHV environment and with

the MBE geometry. At variance with TEAS, the full diffraction

image can be recorded in seconds so that it can be used as an

real time diagnostic of the structure of the terminal layer. More

unexpected, diffraction can be recorded on a surface at elevated

temperatures. This is illustrated in Fig.1taken from Ref6and

recorded inside a MBE vessel with a GaAs surface around 850

K, whereas TEAS is mainly performed at low temperatures. This

aAddress, Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d’Orsay

(ISMO), 91405 Orsay, France

interesting aspect of GIFAD to operate at elevated surface temper-

atures is poorly documented7–9and no systematic experimental

investigation has been reported.

zT~850 K

Fig. 1 Schematic view of a GIFAD setup, the well-aligned row of atoms

acts as a grating for the projectile atomic wave. A detector located

almost a meter downstream records the diﬀraction image. The one here,

taken from Ref.6was recorded directly in a MBE vessel on a GaAs(001)

surface at ∼850 K. The bright spots corresponding to elastic diﬀraction

are located on the Laue circle of energy conservation.

This paper presents experimental investigations on tempera-

ture dependence under a wide variety of experimental conditions

of energy, angle of incidence and temperatures for helium atoms

impinging on a LiF surface. The paper is organized as follows, the

experimental setup is described in Sec.2with the protocol used to

transform raw data into transverse and polar scattering proﬁles

from which the coherence ratio is deﬁned. In Sec.3, the strategy

adopted to performed stable temperature variations is presented

before an introduction to theoretical aspects of elastic and inelas-

Journal Name, [year], [vol.],

1–9| 1

arXiv:2210.06555v1 [physics.chem-ph] 23 Sep 2022

- 6 0 6

e x p .

F i t

L a t t e r a l d e f l e c t i o n ( i n G y= 2 . 2 A - 1 )

c o n t r a s t = I e/(Ie+ I ine) = 7 3 %

a )

300 eV 4H e o n L i F < 1 1 0 >

at 1.28 deg.

kf⊥- k i⊥

kf y

I n t e n s i t y ( a r b . u n i t s )

S c a t t e r i n g a n g l e θi n + θout(deg)

e x p

F i t

D W F = I e/(Ie+ I i n e )

D W F = 1 3 . 3 %

c )

b )

d )

d i r e c t b e a m

kf y

kf z

ki z

Fig. 2 a) quasi polar transform of the raw diﬀraction image in panel d).

The polar scattering proﬁle b) corresponds to a full projection of a) onto

the vertical axis. It is ﬁtted by the sum of a narrow Gaussian and a broad

log-normal proﬁle used to evaluate the DWF=Ie/Itot with Itot =Ie+Iine.

Panel c) corresponds to the intensity in a narrow horizontal band centered

at the specular angle. The contrast measured on the Laue circle (c) is

73% much larger than the DWF=13%.

tic diffraction in Sec.4. The results are presented and discussed

in Sec.5.

2 Grazing incidence fast atom diﬀraction

(GIFAD)

The grazing incidence fast atom diffraction at crystal surfaces uses

atoms in the keV energy range as probed with incidence angles θi

around 1 deg. so that the full diffraction pattern can be recorded

in one take on a position-sensitive detector10–13 as sketched in

Fig.1. A commercial ion source delivers ions at the desired energy,

they pass inside a charge exchange cell ﬁlled with the same gas,

where a signiﬁcant fraction is neutralized by resonant electron

capture, see e.g. Ref.14. After this cell, the ion fraction is deﬂected

away and the spatial extent and angular divergence of the neu-

tral beam is controlled by two co-linear diaphragms adjustable

between 20 and 100 µm, separated by a distance close to half

a meter before entering into the UHV chamber with the target.

If the projectile encounters a large enough terrace, it undergoes

quasi-specular reﬂection and the projectiles are scattered within

a cone with an opening angle of θi. Since keV atoms are easily

detected and imaged by micro-channel plates, GIFAD was able to

record a few images per second15,16 with an old ion source.

GIFAD offers a high topological resolution of a few pm on

atomic structure, e.g. surface rumpling17 or charge transfer18,

simple semi-quantitative interpretation14 and, when compared

with exact quantum scattering code4,19–21, a parameter free ac-

curacy6,22. The temperature of the surface affects both its nuclear

and electronic systems. We use the well-documented system of

helium on LiF(001), where the large band-gap prevents electronic

contributions allowing interpretations of inelastic effects only in

terms of thermal motion of the surface atoms.

A deﬁnition of the (x,y,z)axis is displayed in Fig.1together

177 K 687 K 1017 K

qout

a) c)

Fig. 3 Three diﬀraction images recorded with 500 eV helium impinging

with θin=0.75 deg. on LiF [100] at temperatures of 177 K a), 687 K

b) and 1017 K c). The images are normalized to the maximum inten-

sity corresponding here to the elastic specular spot. The rainbow color

palettes are identical with a threshold at 3% of the maximum intensity.

with a typical raw diffraction image on GaAs at elevated temper-

atures. Another raw diffraction image is plotted in Fig.2d) for

a LiF crystal and a helium beam oriented along the [110] direc-

tion. These images correspond to a direct mapping of the ﬁnal

velocity or wave vector (kf y,kf z) of the scattered projectile per-

pendicular to the crystal axis. Bright elastic diffraction spots are

clearly visible and located on a single circle corresponding to en-

ergy conservation of the motion in the (y,z) plane perpendicu-

lar to the crystal axis probed : k2

f y +k2

f z =k2

⊥=cst. A polar-like

transformation23 brings this Laue circle into a straight line dis-

played in (Fig.2a)). The intensity in this narrow stripe of max-

imum intensity is reported on Fig.2c) and shows well-resolved

diffraction peaks equally separated by multiples of the Bragg an-

gle θB=arctan(Gy/}k//), where }k// =}kcos θin is the projectile

momentum parallel to the crystal axis. Gy=2π/ayis the recipro-

cal lattice vector associated with the distance aybetween atomic

rows perpendicular to the probed crystal axis, taken here as the x

direction. To derive the structure factor, only the elastic intensi-

ties should be considered, however, when elastic intensity is sig-

niﬁcant, the elastic and inelastic relative intensities on the Laue

circle Imwere found identical24 so that Fig.2c) can be directly

exploited.

The projection of Fig.2a) on the vertical axis produces the po-

lar scattering proﬁle in Fig.2b) showing a narrow elastic peak on

top of a broader inelastic scattering proﬁle. The relative weight of

the elastic peak can be estimated using a simple ﬁt where the elas-

tic component is represented by a narrow Gaussian peak and the

inelastic one by a broader, slightly asymmetric log-normal pro-

ﬁle f(θ) = 1

wθ√2πexp(−(lnθ−ln θs)2

2w2)25–27. Assuming that the im-

age contains only the gently scattered projectile that did not en-

counter major surface defects, this ratio DWF=Ie/Itot is believed

to be a direct measurement of the Debye-Waller factor. It is differ-

ent from the standard deﬁnition used in TEAS DWF=Ie/I0where

I0would be the intensity of the direct beam which, in practice,

is never measured directly with the same detector. In GIFAD, the

direct beam is always measured, either directly or through a cal-

ibrated attenuation grid, because both the exact beam position

and line-proﬁle are mandatory for accurate analysis. It reveals

that for the present cleaved LiF sample, the intensity scattered by

2 | 1–9

Journal Name, [year], [vol.],

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摘要：

Temperaturedependenceinfast-atomdiractionatsur-facesPengPana,MaximeDebiossacaandPhilippeRoncinaGrazingincidencefastatomdiractionatcrystalsurfaces(GIFADorFAD)hasdemonstratedcoherentdiractionbothateectiveenergiesclosetooneeV(l?14pmforHe)andatelevatedsurfacetemperaturesoeringhightopologicalresolu...

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Temperature dependence in fast-atom diﬀraction at sur- faces Peng Pana Maxime Debiossacaand Philippe Roncina

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