Nuclear Instruments and Methods m Physics Research B 82 (1993) 301-309
North-Holland
Beam Interactions
with Materials & Atoms
Exciton-induced desorption and surface-type luminescence
of Kr atoms from Kr-doped solid Ar
M. Runne, J. Becker, W. Laasch, D. Varding and G. Zimmerer
H lnstttut fur Expertmentalphystk der Untversttat Hamburg, 2000 Hamburg 50, Germany
M. Liu and R.E. Johnson
Department of Nuclear Engmeermg and Engineering Physws, Umt,ersttv of Virgmta, Charlottes~'dle, VA 22901, USA
Recewed 26 November 1992 and an revised form 25 January 1993
Selective exotat~on of Kr atoms at the surface of sohd Ar with synchrotron radlatton stimulates the desorptlon of excited Kr
atoms (e g., Kr3P1) as well as the luminescence of Kr-type surface centers at hv = 9 998 eV (3P 1) and at hv = 9.881 eV (3P 2) The
high-resolution luminescence spectra and the yield curves of the radiative decay channels have been measured. They are
interpreted taking into consideration ab imt~o KrAr pair potentmls. A general correlat]on between the desorption mechamsm and
the energetic position of the vacuum level is estabhshed for pure (Ne, Ar, Kr, Xe) and doped rare gas sohds
I. Introduction
The erosion properties of rare gas solids have been
studied in great detail during the last ten years This
occurred because rare gas solids are model systems for
a better understanding of a variety of desorptlon mechanisms. The present state of the art was described in
recent reviews of Johnson and Schou [1] and Brown
and Johnson [2]. Whereas that work mainly concentrates on particle induced erosion, the present paper
deals with desorption induced by excttomc transtttons.
The term "exciton" is used here for any kind of excitation which results in bound e l e c t r o n - h o l e pairs. It
includes not only band-like exciton states but also
excitations localized at lattice distortions, defects, impurities, and at the surface.
Desorption induced by excitonxc excitations results
from the peculiarities of e x c i t o n - p h o n o n interaction in
rare gas solids which lead to trapping of excitons either
at a self-induced lattice distortion (self-trapped exciton, STE) at lattice defects [3-5] or at the surface [6].
Trapping is accompanied by strong lattice relaxation
effects. Thus, concerning desorption, e x c i t o n - p h o n o n
interaction of rare gas solids has two essential properties. It leads to locahzatton of an electromc excitation
and to conversion of electronic energy into mo,onal
energy of atoms.
Correspondence to M Runne, II Instltut ftir Experlmentalphyslk der Unwersltat Hamburg, W-2000 Hamburg 50, Germany
Following creation of surface excltons of the light
rare-gas solids Ar and Ne, desorption of ground state
atoms, electronically excited atoms (3pI, 1P 1) and
metastable atoms [3-5], and even of desorbed
molecules [7] was observed. The desorptlon of excited
atoms results from trapping of an exclton as an atomic
species (so-called a-STE). In the bulk of the solid, the
excited atom repells the lattice. The physical nature of
the repulsive force is short-range repulsion due to the
overlap of the excited state wavefunction with the
closed electronic shells of the surrounding atoms. Short
range repulsion competes with the polarization of the
lattice by the excited atom. In the light rare gas solids
(Ar, Ne), repulsion dominates causing a local distortion of the lattice. The new equilibrium positions of the
ground-state atoms around the excited atom correspond to a balance between repulsion on one side,
elastic forces and polarization on the other side. In
solid Ne, e.g., in this way, a bubble is formed around
the excited atom with a diameter of - - 8 A [8]
(nearest-neighbour distance of the Ne lattice 3.16 A)
It is quite natural that trapping at an atom of the
crystal surface does not lead to the formation of a
bubble but to the ejection of the excited atom [3-5,9]
In the present paper, the results of a systematic
investigation of the desorptlon of Kr atoms from the
surface of solid Ar are presented. The motivation for
this work is as follows. In rare gas solids, a quantitative
measure of the balance between short-range repulsion
and long-range polarization by an electron in the conduction band is given by the so-called V0 value, V0 =
0168-583X/93/$06 00 © 1993 - Elsevier Soence Pubhshers B V All rights reserved
302
M Runne et al / Desorptton of Kr from Kr-doped sohd Ar
Table 1
Correlation between V0-values of pure and doped rare gas
solids [10] with the observation of desorptlon of electronically
excited atoms
In the p r e s e n t study it is shown that surface centers
are also observed for Kr d o p e d solid Ar. Both, for the
luminescence of Kr surface centers a n d for r e s o n a n c e
fluorescence of d e s o r b e d Kr atoms, the yield spectra
could b e m e a s u r e d T h e yield spectra are closely conn e c t e d with the a b s o r p t i o n cross section of the impurity a b s o r p t i o n at the surface of the host. This is an
aspect of great relevance for surface physics However,
it is also a key e x p e r i m e n t to test i n t e r a c t i o n potentials
b e t w e e n the impurity a t o m a n d the atoms of the host.
Thus, the yield spectra provide us with a d e e p u n d e r s t a n d i n g of the microscopic n a t u r e of a particular
desorption mechanism.
System
V0 [eV]
Desorptlon of
electronically
excited atoms
Refs
Solid Ne
Ar/Ne
Kr/Ne
Xe/Ne
+
+
+
+
13
11
11
10
yes
yes
yes
yes
[3-6]
[11,12] ~
[12] a
[12] a
Solid Ar
Kr/Ar
Xe/Ar
+04
+03
+03
yes
yes
yes
[3-6]
present paper
[13]
Solid Kr
Xe/Kr
- 03
- 02
no
no
[3-6]
[12] a
2. Experiment
Solid Xe
- 04
no
[3-6]
T h e e x p e r i m e n t a l m e t h o d is high-resolution lumin e s c e n c e spectroscopy u n d e r primary selective excitation with vacuum-ultraviolet ( V U V ) light. T h e experim e n t s were p e r f o r m e d at the S U P E R L U M I setup of
the H a m b u r g e r S y n c h r o t r o n s t r a h l u n g s l a b o r H A S Y LAB. T h e setup was described recently in detail [15] It
allows for (i) selective excitation in the V U V (8 _< h v <_
30 eV) with A / A A _< 103, (11) spectral analysis of lumin e s c e n c e in a large spectral r a n g e (1 _< h v <_ 20 eV)
with A / A A < 104, a n d (ili) time resolution from the
sub-ns to the ms regime. In time-resolved experiments,
t h e pulsed n a t u r e of s y n c h r o t r o n r a d i a t i o n is exploited
[16].
Only with high-resolution l u m i n e s c e n c e analysis is it
possible to discriminate b e t w e e n the r e s o n a n c e fluorescence of d e s o r b e d excited Kr atoms (3P 1 ~ is0, h v =
10.033 eV) and, e.g., t h e luminescence line of 3p~-type
Kr c e n t e r s at the surface of the A r host ( h v = 9.998
eV) However, the c o u n t i n g rates are extremely small
(-- 1 cps p e r resolution interval). Note, special e m p h a sis was p u t on primary selective excitation of impurity
atoms at the surface (some 1013 a t o m s / c m 2 ) . T h e high
sensitivity n e e d e d was achieved with a position-sensitive d e t e c t o r at the exit arm of the analyzing V U V
m o n o c h r o m a t o r . T h e d e t e c t o r (Surface Science Lab.
Inc. model 3391A) was sensitized in our laboratory
with CsI for the longer wavelengths.
A n essential i n g r e d i e n t in our e x p e r i m e n t is sample
p r e p a r a t i o n T h e Kr c o n c e n t r a t i o n was c h o s e n as a
c o m p r o m i s e b e t w e e n two r e q u i r e m e n t s A high conc e n t r a t i o n was desirable to increase the c o u n t i n g rates
O n the o t h e r h a n d , a low c o n c e n t r a t i o n was necessary
to avoid pairing or clustering of Kr atoms at the
surface of the host It t u r n e d out, t h a t up to 5 % Kr in
A r could b e used T h e gases were pre-mlxed in a n
u l t r a h i g h v a c u u m gas-handling system T h e samples
were grown from the gas p h a s e at T-= 20 K at a rate of
200 A./s. T h e rate was controlled with a n e e d l e valve
b e t w e e n the gas h a n d l i n g system a n d the growing
a Preliminary results.
E g - E t h [10]. H e r e , Eg m e a n s t h e b a n d gap energy,
Eth the t h r e s h o l d energy for p h o t o e l e c t r o n emission
(zero p o i n t of the energy scale is t h e top of the valence
band). A positive value of V0 c o r r e s p o n d s to a v a c u u m
level below the b o t t o m of the c o n d u c t i o n b a n d , a
negative value above. In table 1, t h e V0 values of rare
gas solids are given. A clear c o r r e l a t i o n is f o u n d bet w e e n the sign of the V0 value a n d the o b s e r v a t i o n of
d e s o r b e d excited atoms u n d e r primary excltonlc excitation. U p to now, this d e s o r p t l o n was only observed for
rare gas solids with V0 > 0
In analogy to p u r e rare gas solids, a V0 value is also
defined for d o p e d systems, V0 : _. .Eg. . Eth [10] H e r e ,
Eg is the impurity gap energy, Eth is t h e t h r e s h o l d of
i m p u r i t y - p h o t o e l e c t r o n emission. B o t h signs of V0 are
observed, too. T h e q u e s t i o n arises w h e t h e r the correlation b e t w e e n d e s o r p t i o n of excited a t o m s a n d t h e sign
of V0 also holds for t h e d o p e d systems. T h e respective
values are i n c l u d e d in table 1 A n t i c i p a t i n g t h e results
of the p r e s e n t p a p e r we p o i n t out t h a t the c o r r e l a t i o n
also holds for Kr d o p e d Ar. Moreover, during the
p r e p a r a t i o n of this paper, the system X e d o p e d A r was
m e a s u r e d a n d t h e c o r r e l a t i o n clearly showed up [13]
T h e results of the o t h e r systems m e n t i o n e d in table 1
are p r e l i m i n a r y results of test e x p e r i m e n t s a n d deserve
detailed e x p e r i m e n t a l c o n f i r m a t i o n in future.
T h e r e are o t h e r aspects b e h i n d the subject of this
paper. F r o m solid Ne it is k n o w n t h a t - in a d d i t i o n to
d e s o r p t i o n - excited a t o m s can also stay at the surface
a n d emit surface-type l u m i n e s c e n c e lines [14]. Surface
c e n t e r s of 3P 1 a n d of 1P I origin were already observed.
Additionally, l u m i n e s c e n c e of 3p2-type centers shows
up (partly allowed due to the r e d u c t i o n of symmetry
c o m p a r e d with t h e free atom). Such surface centers are
also p r e d i c t e d from theory for solid A r [9].
M Runne et al / Desorptton ofKrfrom Kr-doped sohdAr
1% Kr In Ar
primary excitation
E=IO 19 eV
03% In Ar
ap~ apl
95
10
PHOTON ENERGY (eV)
p r i m a r y excitation
t05
Fig 1 Luminescence spectra of Kr-doped sohd Ar following
selective exotatmn of Kr atoms at the surface with l0 19 eV
photons (upper curve, excltahon energy indicated with an
arrow, T = 5 5 K), and of surface excltons of the host with
11 82 eV photons (T = 12 K)
c h a m b e r . F o r details of sample p r e p a r a t i o n see ref.
[14]. T h e m e a s u r e m e n t s were p e r f o r m e d in a n U H V
e n v i r o n m e n t , p < 10 -9 mbar.
3. Results
3 1 Lummescence spectra
In fig. 1, a n overview of the l u m i n e s c e n c e of Kr
d o p e d solid m r is given for typical - however, substantially different - surface sensitive excitation conditions.
Curve (1) [17] is o b t a i n e d from a sample with 0 3 % Kr
in m r u n d e r p r i m a r y selective excitation of surface
excitons of the host (hv = 11.82 eV). Curve (2) is
o b t a i n e d from a sample with 1% Kr in m r u n d e r
primary selective excitation with hv = 10.19 eV. This
p h o t o n energy t u r n s out to b e optimal for primary
selective excitation of Kr a t o m s at t h e surface.
T h e spectra are drastically different. Curve (1) yields
a b r o a d l u m i n e s c e n c e b a n d c e n t e r e d at ~ 9.7 e V which
stems from host l u m i n e s c e n c e c e n t e r s of the m o l e c u l a r
type (so-called m-STE, a n a l o g o u s to Are* molecules)
[18]. O n top of this b r o a d b a n d , we observe a line in
perfect a g r e e m e n t with the e n e r g e t i c position of Kr 3P 1
IS 0 r e s o n a n c e fluorescence. This line is resolution
limited a n d stems from d e s o r b e d excited Kr atoms.
Slightly red shifted are two p r o n o u n c e d lines (their
widths are not resolution limited). They stem from
Kr3PI (hv = 9.998 eV) and Kr3P2 (hv = 9.881 e V ) surface centers. Additionally, a p e a k at 10.38 e V is observed. It stems from 3P 1 Kr atoms in t h e bulk of t h e
host [17]. T h e n a r r o w p e a k at hv = 10.62 e V originates
303
from Kr 1p1 surface centers. D e s o r p t i o n of Kr 1P1 atoms
is a very w e a k process. Only a tiny indication at hv =
10.644 e V is found.
Curve (2) clearly yields r e s o n a n c e fluorescence of
d e s o r b e d Kr3P1 atoms as well as the l u m i n e s c e n c e
lines which originate from Kr3PI a n d Kr3P2 surface
centers. T h e b r o a d l u m i n e s c e n c e b a c k g r o u n d is different from the o n e observed in curve (1). Its m a x i m u m is
f o u n d at hv = 9.35 eV. In analogy to gas p h a s e fluorescence spectra of h e t e r o n u c l e a r A r K r * molecules
[19,20] it IS ascribed to a h e t e r o n u c l e a r A r K r center.
In fig. 2, l u m i n e s c e n c e spectra of a sample with 3 %
Kr (excitation with hv = 10.19 eV, t e m p e r a t u r e = 6.7
K) are p r e s e n t e d . They were m e a s u r e d in the first a n d
in the second o r d e r of the m o n o c h r o m a t o r . T h e reson a n c e fluorescence line of d e s o r b e d Kr a t o m s is m u c h
n a r r o w e r in second order. Its width (0.5 ,~ ~ 4 m e V )
clearly d e m o n s t r a t e s t h a t a spectral resolution A / A A
= 2500 (at the given wavelength) can b e o b t a i n e d routinely in V U V l u m i n e s c e n c e spectroscopy u n d e r primary state-selective excitation with s y n c h r o t r o n radiation. T h e widths of the l u m i n e s c e n c e lines of the
surface c e n t e r s are nearly the same in first a n d in
second order. This is of relevance from the following
p o i n t of view T h e Kr atoms at t h e surface of the host
most probably occupy different sites, e.g., on top, substltutional etc. W i t h i n the m e a s u r e d widths, n o additional structures showed u p indicating t h a t the transition energies are not sensitive to t h e respective site
Note, however, this s t a t e m e n t only holds for the relaxed lattice.
In fig 3, we p r e s e n t a set of spectra which were
o b t a i n e d for different p h o t o n energies of excitation
(given at each curve). T h e abscissa covers only the
r a n g e of t h e surface type l u m i n e s c e n c e lines a n d the
98
99
10
101
PHOTON ENERGY (eV)
Fig. 2 Luminescence spectra of Kr (3%) doped sohd Ar
following selectwe exotatlon of Kr atoms at the surface with
10.19 eV photons, measured m the first and m the second
order of the monochromator (for details see text).
M Runne et al / Desorptton ofKrfrom Kr-doped sohdAr
304
aPs (desorbed)
~I~ I
-
-
.
.
-
~
i0 272
II z
i0 255
cn
238
C
10
I0 221
i
I
0
6
-
4
-
tttt
>.,
b.,
l0 196
Z
r.1
10 163
Spa( s u r f a c e )
Eua.t
z
Z
r,)
r,O
r~
z
~
85
0
~
~
~
....
I ....
! : :~--~' 10080
99
9.95
I0
PHOTON ENERGY ( e V )
Fig. 3. Luminescence spectra of Kr (3 3%) doped solid Ar
(enlarged scale) for different photon energies of excltatlon
(gwen at the right of each curve). The arrow m&cates the
energetic posltlon of Kr3pI resonance fluorescence, emitted
by desorbed atoms The peaks at 9 998 and 9 881 eV stern
from Kr3Pl-type and from Kr3P2-type surface centers (T =
64 K)
r e s o n a n c e fluorescence hne of the d e s o r b e d Kr atoms.
The results w e r e o b t a i n e d in first o r d e r from a sample
with 3.3% Kr at a t e m p e r a t u r e T = 6.4 K. The curves
clearly show that the relative intens~tms of the radiative
decay c h a n n e l s are a sensitive function of p h o t o n energy of excitation. Details will be discussed in the next
section.
3.2. Ymldspectra
In a y~eld spectrum, the intensity o f a spectrally
selected luminescence line is m e a s u r e d as a function of
p h o t o n energy of excitation. Such yield (excitation)
spectra are p r e s e n t e d in fig. 4 for r e s o n a n c e fluores-
2
-
0
~
I
|
x
_
|
x
x
10 1
10 2
x
10 3
PHOTON ENERGY 0F EXCITATION (eV)
Fig. 4. Yield spectra of desorptlon of Kr3pi atoms (upper
curve), of the luminescence of Kr3pl-type and of Kr3p2-type
surface centers (lower curves) of Kr (3.3%) doped solid Ar at
T = 6 4 K Threshold energies are indicated by arrows
cence of d e s o r b e d Kr3Pt atoms (upper curve), for the
3Pl-type luminescence of Kr surface centers (curve in
middle) and for 3p2-type luminescence of Kr surface
centers (3.3% Kr, T = 6 4 K). The yields are normalized to the n u m b e r of p h o t o n s inctdent on the sample
per second. The reflectivity being low around 10 e V
and without p r o n o u n c e d structures, t h e r e is practically
no difference b e t w e e n incident and p e n e t r a t m g intensity.
As a c o n s e q u e n c e of the extremely low counting
rates, the yield spectra were not m e a s u r e d in the
Table 2
Comparison between experimental and theoretical values of peak positions, widths and threshold energies
3P I (atom)
Energetic posmon [eV]
experiment
theory
FWHM [meV]
experiment
Matrtx shift [meV]
experiment
Threshold energy of the yield curve [eV]
experiment
theory
a
Ref. [20].
10 033
a
3P2 (atom)
3P1 (surface)
9 998 + 0 001
9 90
res limited
~P2 (surface)
9.915 a
not observed
desorpnon
10 10
not observed
~ 10.29
~ 10 12
18 9
+_2
9.881 + 0 001
9 82
18 7
- (35 _+1)
- (35 + 1)
luminescence
10.08
< 10.06
_+1 2
M Runne et a l / Desorptton ofKrfrom Kr-dopedsohdAr
scanning mode (fixed wavelength at the analysing
monochromator, excitation wavelength being tuned)
but were constructed from luminescence spectra like
those shown in fig. 3. The peak area of each radiative
decay channel was plotted as a function of photon
energy of excitation. The data in fig. 4 thus represent
the evaluation of more than 20 luminescence spectra.
In the vicinity of the maxima observed, the interval
between adjacent points is only half as large as the
resolution Interval for the exciting light (18 meV) Note
the expanded scale of photon energy of excitation. It
covers only that energy range, in which primary selective excitation of Kr surface states correlating with the
Kr3p1 and the Kr3p2 asymptotes is found.
The yield curves considerably differ one from another concerning (i) the threshold at the low energy
side, (li) the peak position, and (ili) the general shape.
The (lowest) threshold energy for 3P2-type surface luminescence was not covered in our experiment. The
highest threshold energy is found for the desorptlon of
Kr3P1 atoms. Numerical values are given in table 2.
One would like to correlate the yield spectra with
the absorption cross-section ~ of Kr atoms at the
surface of the host. One essential condition to do so is
fulfilled, the surface layer of the atoms (with n approximately equal to some 1013 atoms/cm 2) is certainly
optically thin, trn << 1. However, only the sum of all
partial yields including the nonradiative decay processes would be a direct measure of tr. In the present
case, one very important yield could not be measured,
namely the yield of desorptlon of Kr3p2 atoms. Therefore, ~r cannot be extracted directly. Nevertheless, detailed information concerning the interaction of Kr
atoms with the surface of the Ar host can already be
extracted.
3.3. Temperature dependence
For a sample with 3% Kr, in fig. 5 the intensities of
the different radiative decay channels are plotted as a
function of temperature. The photon energy of excitation, hv = 10.19 eV, approximately corresponds to the
peak positions of the yield curves of fig. 4. Additionally
to the Intensities of the narrow lines, the values for the
broad ArKr band (peak position at 9.35 eV, see fig. 1)
are included. Due to the large width, the wavelength
integrated intensity (peak area) is much larger than the
intensities of the narrow lines.
The intensities of all radiative decay channels decrease with increasing temperature The decrease is
most pronounced for the 3p2-center. In an Arrhenlus
plot, a straight line is found, indicating an (approximate) temperature dependence of the type exp
( - A E / k T ) with an activation energy A E = 3 meV
(not shown here).
'
6
~'
'
'
I
305
. . . .
I
\.
0
I
+ Spz-surf
\
_
. . . .
T x~ ~
~
x
T~T
10
Temperature
apl-surf
o ap1-desorbed
o molecular . 1/:
15
20
[K]
Fig 5 Temperature dependence of the yields of the different
decay channels of Kr (3%) doped sohd Ar following pnmary
selectwe exotatlon of Kr surface atoms with 10 19 eV photons The hnes are only a grade for the eye
Though the results of this section are not well
understood, they are reported here for the following
reason. A decrease of intensity of all the observed
decay channels indicates that not all eyasting decay
channels are observed. At least, desorptlon of Kr3p2
atoms should be taken into account. From pure rare
gas solids (Ne, Ar), this decay channel is well known
and could be analysed with time-of-flight methods and
a metastable detector [5,6]. Similar measurements will
be performed for the doped systems in the future.
4.
Discussion
As a guide line for a first attempt to understand the
results, the ab lnitio pair potentials of the heteronuclear molecule ArKr may be used. The result of
Spiegeimann et al. [21] is reproduced in fig. 6. The
ground state is strongly repulsive apart from a shallow
Van der Waals minimum. Each of the excited states
terminating at the Kr 3P1 and Kr 3P2 asymptote exhibits
a similar shallow minimum at somewhat larger internuclear distance. At shorter internuclear distance, strongly
repulsive potential curves are found, some of them,
however, include an additional narrow inner minimum.
The double-well nature of the respective states was
corroborated by fluorescence spectra in the gas phase
[19].
The observed luminescence lines of those Kr atoms
staying at the surface obviously originate from minima
correlated with the shallow minima of the ArKr pair
potentials at rather large internuclear distance. The
transitions are indicated in fig. 6. The ab initio curves
predict that the energetic difference of the transition
energies equals the energetic difference in the asymptone hmit (atomic values). Indeed, the experimental
306
M Runne et al / Desorpnon o f Kr from Kr-doped sohd A r
10 15
.......
I ....
I ....
. . . .
~
I ....
against each other. Therefore, direct excitation of the
bound excited state well below the desorption threshold is unfavourable due to negligible F r a n c k - C o n d o n
overlap. A similar behaviour is known from the gas
phase. In absorption experiments on Kr doped Ar gas
in the vicinity of the first Kr resonance line, only a
" b l u e " wing and no " r e d " wing is found [19,23].
Next we want to interprete the branching rauo
between desorption of Kr3PI atoms and luminescence
of Kr3Pa-type surface centers. For this purpose, we
calculated the ratio
I ....
I0 10
0=I
0=0 +
10 O5
Kr(aPl)
- -
10 O0
0=2
fl=l
--
,~ 9 9 5
~ 990
~sK
(S
(rIPz)
ft=0-
08
Yoe~(3P,)
06
04
P = Ydes(3pl ) + Y,um(3Pi )
(1)
O2
00
0
025
05
075
I
INTb2RNUCLEARDISTANCE (nm)
1 :~5
15
Fig. 6. Reproductlon of ab mmo calculatlons [21] of the
potential energy curves of ArKr molecules terminating at
KrlSo (ground state) and at Kr3P2, Kr3P1 (lowest excited
states) The arrow upwards indicates the origin of the threshold energy, Eth,d, for the desorption yield of Kr3P1 atoms
The downward arrows Indicate the origin of the surface-type
luminescence lines.
from the yield curves of fig. 4. Assuming that the
primary excitation leading to either 3P 1 desorption or
3Pl-type luminescence does not feed into other decay
channels, the quantity P then is the probability for
desorption, ( 1 - P )
however the probability for the
creation of the emitting surface center In fig. 7, p2 is
plotted as a function of photon energy of excitation.
Surprisingly enough, a straight line is found which
indicates
(2)
P a ~/hr, - Eth,d
results are in perfect agreement with this prediction.
Concerning the absolute values of the transition energies, a calculation of the energy surface of a Kr atom
interacting with the A r host is necessary. Such calculations including molecular dynamics calculations are in
progress now. First results are already reported in
section 5 of this paper and included in table 2. The
calculated transition energies are in slight disagreement ( = 7 0 . . . 100 meV) with experiment, indicating
that the well depth of the Van der Waals minima are
overestimated in the work of Spiegelmann et al. [21].
For the ground state, this is quite obvious and explicitely discussed in ref. [21].
Next we discuss the threshold energies for Kr3P1
desorptlon and K r 3 p l - t y p e surface luminescence.
Again, the absolute values can only be checked with
detailed calculations. However, a lower limit of the
threshold of the 3P I desorption yield (experiment: 10.10
eV) can be estimated. Obviously the lower limit is
given by the sum of the atomic transition energy (10.033
eV) and the binding energy of the Kr atom at the A r
host The binding energy must be in between the value
of pure Ar (80 m e V [22]) and pure Kr (116 m e V [22])
Taking as an estimate 96 meV, we obtain Eth.d > 10.12
eV. This is In surprisingly good agreement with the
measured value. The threshold energy, Eth,l, of Kr3PI type surface luminescence is only slightly below Eth,d
(see table 2 and fig 4) As it turned out in the theoretical calculations (section 5), the minima of the ground
state and of the excited state are considerably shifted
Eth.d 1S the intercept with the energy axis and corresponds to the threshold of desorption. The quantity
h u - Eth is the energy above the dissociation limit. It is
a measure of the velocity of the Kr atom above the
surface,
- Eth,d a V a 1 ~ A t .
(3)
The velocity can be interpreted as a ( A t ) -1, At being
a measure of the time of the interaction of the Kr atom
with the surface. The experimental result corresponds
to what we intuitively expect: the probability of an
085
I
. . . .
l
. . . .
0 20
I
××/¢J
x
~~
015
x
X
/
0 I0
v
%
005
o oo
/
J/
.
.
.
.
l
,
.
,
,
I01
I0 £
PHOTON ENERGYOF EXC[TATI0N (eV)
,
l
,
,
I03
Fig. 7 Plot of the square of the relative desorpnon yleld of
Kr3PI atoms from Kr (3.3%) doped solid Ar at T = 6 4 K as a
function of photon energy of excitatlon For details see text
M Runne et al / Desorptzon ofKrfrom Kr-doped sohdAr
energy loss stabilizing the outward moving Kr atom in
the shallow well scales with At. The probabihty of
desorption, however, increases with increasing velocity
of the outward moving Kr atom.
The clear and simple interpretation of the branching ratio has some hidden assumptions. Though there
is a spectral overlap, the 3Pl-type yields have obviously
nothing to do with the 3P2-type yield. In other words,
electronic relaxation from the 3Pi-type potential energy
curves to the manifold correlated with the 3P 2 limit can
be neglected. In an indirect way, this is also established
by the temperature dependences in fig. 5. Only the
yield of 3P2-type surface luminescence is strongly
quenched in favour of Kr3P2 desorption. The other
yields show only a comparatively weak temperature
dependence.
A n o t h e r hidden assumption concerns the formation
of A r K r centers emitting the broad band at 9 35 eV.
The existence of this strong band was neglected in the
discussion of the branching ratio. At first sight, this
seems to be a strong point against our interpretation.
However, from the gas-phase date it is known that the
inner minima of the double-well potentials are the
source of the broad luminescence features. Obviously,
direct excitation to the inner minima are responsible
for the molecular-type luminescence. Branching between 3P 1 desorptlon and 3Pl-type surface luminescence is a property of the outer repulsive part of the
potentml curves
5. Molecular dynamics calculations
Using the molecular dynamics scheme described in
ref. [9] for A r and ref. [24] for Kr, we formed an fee
cubic sample containing 500 atoms with the surface
(100) atoms relaxed. This defines z = 0 in fig. 8, where
z is the axis perpendicular to the surface A surface A r
is then replaced by a Kr atom in the ground state
(substitution) or a Kr atom is added onto the surface
(adsorption), after which the sample IS cooled to its
relaxed position. A L e n n a r d - J o n e s (6-12) potential is
used for the A r - K r interaction potential (to e = 113.9
cm 1, r0 = 3.88 ,~.) [25]. The substitutional Kr atom
relaxes to a position -= 0.6 .~ inside the surface, and
the A r nearest neighbors relax slightly inwards, ~ 0.04
.A. An approximate net ground state interaction potential is then constructed by stepping the Kr atom along
the z-direction with the A r fixed In their relaxed positions. The potential thus constructed is shown in fig. 8.
The resulting minimum is found to be shifted slightly
outward from the relaxed Kr position, because the Ar
positions were fixed (i.e. this is not the adiabatic potential).
A n excitation is produced (viz. refs. [9,24], assuming
the F r a n c k - C o n d o n principle, by switching to the A r -
307
3O0
,,
200
i
,,
L
100
I
,'i..
V (mev)
,
0
--
'
\
~
'
-100
V
1
-200 ----.-~.__.L
-5
0
"
5"
",".'"/
~/
o5
Z(A)
t
10
__
15
Fig 8 Interaction potentials of a substitutional Kr atom with
the Ar matrix. Ar atoms are fLxed In their relaxed positions
when the Kr atom ~s In the ground state The z-axis is
outward from the (100) surface and z = 0 is the position of
the Ar atom prior to the substitution of the Kr atom Full
line. ground state, dashed line: potential energy curve terminating at Kr3P1; dotted line' potential energy curve terminating at Kr3P2
Kr excited state interaction potentials. We first constructed spherically symmetric excited state K r - A r pair
interactions, as in ref. [9] for an excited A r in an A r
matrix. Such states are, roughly, correct within the pair
approximation when an excited atomic species is
trapped in the bulk. However, we also used such states
to describe surface desorptlon. These pair interaction
potentials were based on the gas-phase pair potentials
of Spiegelmann et al. [21] shown in fig. 6. For the 3P 1
and 3P 2 states we used the weighted mixtures /2 = 0,1
and 12 = 0,1,2, respectively. Results based on the interactions were compared with those calculations shown
in figs. 8 and 9 in which we simply used the 12 = 1
states in fig. 6. For atoms trapped far from the surface,
as was found to occur when exciting pure Kr, a description based on pair potentials can be justified. However,
using simultaneously the same interaction of the excited Kr with Ar in different positions is a very rough
approximation for this nonspherically symmetric excited state wave function and lattice geometry. New
calculations are in progress to deal with this, and the
calculations described below are examples for discusslon.
O n exciting Kr, using one of the pair potentials
discussed above, we can again construct approximate
net interaction potentials along the z-axis, again fixing
the Ar. This is done to visualize the effect produced on
selectively exoting the Kr. Such potentials are shown
in fig. 8, constructed using the 12 = 1 states only Additional structure is seen in these potentials compared to
308
M Runne et al / Desorptton of Kr from Kr-doped sohd Ar
25
20
z (A)
lo
6
_50
i
2
I
I
4
6
i
8
10
t[ps)
Fig. 9 Position In z-direction of the excited atoms vs rime
following excitation of the Kr m its ground state relaxed
posmon (curve 1 3Pa, curve 2. 3P I) or shifted reward (curve 4"
3P1, curve 6' 3P2)oand outward (curve 3 3P2, curve 5 3P 1)
from that by 01 A. Trapping is seen at the outer mlmmum
and the tuner minimum and desorpt~on ~s also seen to occur
t h a t shown in fig. 6 since t h e r e are l n t e r a c t m g A r
atoms at a n u m b e r of different distances from the Kr.
F o r the potentials c o n s t r u c t e d using the average of the
angular m o m e n t u m states the s t r u c t u r e at the o u t e r
m i n i m u m is f o u n d to b e very similar, which is not
surprising b a s e d on fig. 6. However, at the i n n e r repulsive wall, w h e r e repulsive states a n d states having an
i n n e r m i n i m u m are mixed, the differences are large.
This is especially so for the 3P 2 i n t e r a c t i o n w h e n the
O = 2 state is included. T h e r e f o r e , the p r e s e n t set of
e x p e r i m e n t s a n d calculations provide a m o r e s t r i n g e n t
test of our ability to construct " s o l i d - s t a t e " p o t e n t i a l s
from gas-phase p o t e n t i a l s t h a n did the previous calculations for p u r e A r [9] a n d p u r e Kr [24].
Allowing t h e excited Kr to relax into t h e m i n i m u m
at - 4 A. a n d the i n n e r m i n i m u m for the 3P 2 state, new
potentials are again calculated for the excited state Kr
using the A r locations associated with e a c h new relaxed lattice. F o r each set of relaxed positions a corres p o n d i n g n e t g r o u n d state i n t e r a c t i o n p o t e n t i a l is also
calculated F o r the g r o u n d state a n d the o u t e r minim u m these curves are only slightly shifted from those
in fig. 8, w h e r e a s relaxation into the i n n e r m i n i m u m
d e e p e n s this well considerably forming a d i m e r - h k e
state T h e p o t e n t i a l s so c o n s t r u c t e d are t h e n used to
calculate the l u m i n e s c e n c e shifts, the " t h e o r e t i c a l " line
energies given in table 2, using the 12 = 1 state interaction potentials. T h e shifts from the atomic emission of
the expected l u m i n e s c e n c e are seen to b e in the right
direction in b o t h cases. This is t h e case for b o t h the
spherically symmetric a n d O = 1 states. However, the
shifts o b t a i n e d using these potentials are too large. A t
the i n n e r m i n i m u m (using O = 1 only) the shift also is
too large (-= 2.5 e V vs the e x p e r i m e n t a l value of -- 0.7
eV) primarily due to the repulsive wall b e i n g too steep
in the g r o u n d state p o t e n t i a l R e p l a c i n g the L e n n a r d J o n e s g r o u n d state interaction p o t e n t i a l by the g r o u n d
state potential of S p i e g e l m a n n et al. [21] m a k e s the
c o m p a r i s o n to e x p e r i m e n t worse at b o t h the Inner a n d
o u t e r m i n i m u m , and, in fact, at the o u t e r m i n i m u m the
shifts are in the w r o n g direction. A l t h o u g h differences
from e x p e r i m e n t are expected, b e c a u s e the same pair
potentials are used for the Kr interacting with all of
the Ar, the size of the differences f o u n d in table 2 are
primarily due to t h e long-range well b e i n g too d e e p for
the gas-phase pair potentials used
Following the ideas in ref. [9] a sample was also
c o n s t r u c t e d in which a surface n e i g h b o u r was removed,
i.e. a " d a m a g e d " crystal. Allowing the substitional Kr
to relax the new net i n t e r a c t i o n potentials were f o u n d
to b e similar but, not surprisingly, the o u t e r m i n i m u m
was s o m e w h a t shallower. U p o n relaxation to the o u t e r
m i m m u m the t r a p p e d Kr m o v e d above the vacancy a n d
the repulsive wall shifted outward. T h e calculated line
shifts were in the same direction showing a slightly
b e t t e r a g r e e m e n t with e x p e r i m e n t for the 3P 1 state
using the O = 1 i n t e r a c t i o n only, b u t a p o o r e r agreem e n t for the 3P 2 state.
B o t h for the " u n d a m a g e d " a n d the " d a m a g e d "
surface, excitation was t h e n carried out a n d the m o t i o n
of t h e system was allowed to r e s p o n d to the excited
state i n t e r a c t i o n potentials. This was d o n e for Kr in
the relaxed g r o u n d state position a n d for shifts in t h a t
positions associated with g r o u n d a n d possible excited
vibrational states. T h e resulting m o t i o n of the Kr along
the z-direction is shown in fig. 9 ( " u n d a m a g e d " surface) W h e n t h e r e is no shift in the z-position for the
fully cooled crystal (approximately a few Kelvin, o u r
usual starting point) excitation 3 to the 3P 2 state leads
to desorptlon, w h e r e a s excitation to the 3P 1 state leads
to t r a p p i n g at the o u t e r m i n i m u m , due to the somew h a t d e e p e r well for that state a n d t h e r e s p o n s e of the
surface Ar. Fortuitously, this b e h a v i o r is also the case
w h e n t h e spherically averaged states are used, even
t h o u g h the structure of the net interaction potentials
differs from that o b t a i n e d using the I2 = 1 interactions
only. W h e n the Kr position is shifted inwards or outwards by 0 1 ,~ or by 0.3 ,~ for the Kr in a 3P 2 state,
using t h e O = 1 interactions, t h e n t r a p p i n g occurs for
this a t o m also, b o t h at the i n n e r and o u t e r m i n i m u m
respectively (For the spherically averaged 3P 2 interaction t r a p p i n g does not occur at the i n n e r m i n i m u m for
t h e reasons discussed above) This sensitivity to the
initial position of the Kr a t o m in the lattice is, roughly,
consistent with the sensitivity of the 3P 2 luminescence
yield to t e m p e r a t u r e , as seen in fig. 5
3Pl-type excitation of a Kr a t o m displaced outwards
always leads to trapping. F o r an inward shift of the Kr
a t o m by 0.1 ,~, t r a p p i n g still occurs. If the Kr atom is
shifted inwards by 0 3 ,& during 3Pl-type excitation, the
excited a t o m desorbs promptly due to t h e increase in
M Runne et al / Desorptton ofKrfrom Kr-doped sohdAr
p o t e n t i a l energy, h e n c e , larger o u t w a r d repulsion velocity (VlZ. eq. (3)). B e c a u s e t h e excitation occurs to a
steep repulsive wall (fig. 8), t h e r e is a transition to
desorption. This is c o n s i s t e n t with t h e fact t h a t t h e r e is
a t h r e s h o l d for d e s o r p t l o n as shown in fig. 7. B a s e d o n
t h e s e sample calculation, a n d t h e potentials in fig. 8,
this t h r e s h o l d b e h a v i o r will differ from t h a t for substit u t i o n a l Kr excited to the 3P 2 state.
T h e above results should b e c o n s i d e r e d as d e m o n strative only. Clearly using pa~r p o t e n t i a l s and the
same pair i n t e r a c t i o n with every A r for th~s n o n s p h e n cally symmetric g e o m e t r y ~s not correct. F u r t h e r , t h e
spherically a v e r a g e d p o t e n t i a l s of the type used m ref.
[9] miss the i m p o r t a n t case of t r a p p i n g at the i n n e r
m i n i m u m . However, the results show the correct t r e n d
in the l u m i n e s c e n c e shift a n d a b e h a v i o r ( t r a p p i n g vs
d e s o r p t i o n ) roughly consistent with what we f o u n d
experimentally. Because t r a p p i n g at the o u t e r minim u m should be r e a s o n a b l y well described by long-range
pair m t e r a c h o n s b e t w e e n the excited Kr a n d the g r o u n d
state Ar, t h e errors in the theoretical h n e shifts are
primarily d u e to t h e deficiencies in the gas-phase interaction potentials used.
Acknowledgements
T h e e x p e r i m e n t a l p a r t of t h e work has b e e n supp o r t e d by the M i n i s t e r of Science a n d T e c h n o l o g y of
G e r m a n y u n d e r B M F T g r a n t 05 405 A X B 6 TP7. T h e
t h e o r e t i c a l p a r t has b e e n s u p p o r t e d by t h e N a t i o n a l
Science F o u n d a t i o n (NSF), A s t r o n o m y Division.
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