Prompt and delayed secondary excitons in rare gas solids
Direct and indirect creation of excitons in rare gas solids has been investigated with reflectivity and luminescence spectroscopy. For the heavy rare gas solids Kr and Xe, new and more reliable exciton parameters have been deduced. With time-resolved luminescence spectroscopy, fast and delayed secon...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Цитувати: | Prompt and delayed secondary excitons in rare gas solids / M. Kirm, V. Kisand, E. Sombrowski, B. Steeg, S. Vielhauer, G. Zimmerer // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 1081-1092. — Бібліогр.: 38 назв. — англ. |
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Kirm, M. Kisand, V. Sombrowski, E. Steeg, B. Vielhauer, S. Zimmerer, G. 2018-01-14T13:11:24Z 2018-01-14T13:11:24Z 2003 Prompt and delayed secondary excitons in rare gas solids / M. Kirm, V. Kisand, E. Sombrowski, B. Steeg, S. Vielhauer, G. Zimmerer // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 1081-1092. — Бібліогр.: 38 назв. — англ. 0132-6414 PACS: 71.35.Cc, 72.20.Jv, 78.47.+p, 78.55.Hx https://nasplib.isofts.kiev.ua/handle/123456789/128934 Direct and indirect creation of excitons in rare gas solids has been investigated with reflectivity and luminescence spectroscopy. For the heavy rare gas solids Kr and Xe, new and more reliable exciton parameters have been deduced. With time-resolved luminescence spectroscopy, fast and delayed secondary-exciton creation has been established and separated. Thermalization of photocarriers and their delayed recombination have been analyzed, including a first attempt to investigate the influence of excitation density on the carrier dynamics. The existence of excitonic side bands of ionization limits Ei (either band gap or inner-shell ionization limits) in prompt secondary exciton creation has been established. The threshold energies of these side bands are given by Eth≈Ei nEex (n is integer, Eex is exciton energy). The side bands are ascribed to the formation of electronic polaron complexes, superimposed to inelastic scattering of photoelectrons. The work was supported by the Bundesministerium für Bildung und Forschung (grants No. 05 650GUB, 05 ST8GUI 6) and by the Deutsche Forschungsgemeinschaft DFG (grants No. DFG Zi 159/1-4). V. Kisand and G. Zimmerer acknowledge support by the EU — Project «Regional Centre of Excellence in New Functional Materials, their Design, Diagnostics and Exploitation» ( No. ICA1-1999-70086). en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Spectroscopy in Cryocrystals and Matrices Prompt and delayed secondary excitons in rare gas solids Article published earlier |
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Prompt and delayed secondary excitons in rare gas solids |
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Prompt and delayed secondary excitons in rare gas solids Kirm, M. Kisand, V. Sombrowski, E. Steeg, B. Vielhauer, S. Zimmerer, G. Spectroscopy in Cryocrystals and Matrices |
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Prompt and delayed secondary excitons in rare gas solids |
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Prompt and delayed secondary excitons in rare gas solids |
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Prompt and delayed secondary excitons in rare gas solids |
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Prompt and delayed secondary excitons in rare gas solids |
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prompt and delayed secondary excitons in rare gas solids |
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Kirm, M. Kisand, V. Sombrowski, E. Steeg, B. Vielhauer, S. Zimmerer, G. |
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Kirm, M. Kisand, V. Sombrowski, E. Steeg, B. Vielhauer, S. Zimmerer, G. |
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Spectroscopy in Cryocrystals and Matrices |
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Spectroscopy in Cryocrystals and Matrices |
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2003 |
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English |
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Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Direct and indirect creation of excitons in rare gas solids has been investigated with reflectivity and luminescence spectroscopy. For the heavy rare gas solids Kr and Xe, new and more reliable exciton parameters have been deduced. With time-resolved luminescence spectroscopy, fast and delayed secondary-exciton creation has been established and separated. Thermalization of photocarriers and their delayed recombination have been analyzed, including a first attempt to investigate the influence of excitation density on the carrier dynamics. The existence of excitonic side bands of ionization limits Ei (either band gap or inner-shell ionization limits) in prompt secondary exciton creation has been established. The threshold energies of these side bands are given by Eth≈Ei nEex (n is integer, Eex is exciton energy). The side bands are ascribed to the formation of electronic polaron complexes, superimposed to inelastic scattering of photoelectrons.
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0132-6414 |
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https://nasplib.isofts.kiev.ua/handle/123456789/128934 |
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Prompt and delayed secondary excitons in rare gas solids / M. Kirm, V. Kisand, E. Sombrowski, B. Steeg, S. Vielhauer, G. Zimmerer // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 1081-1092. — Бібліогр.: 38 назв. — англ. |
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AT kirmm promptanddelayedsecondaryexcitonsinraregassolids AT kisandv promptanddelayedsecondaryexcitonsinraregassolids AT sombrowskie promptanddelayedsecondaryexcitonsinraregassolids AT steegb promptanddelayedsecondaryexcitonsinraregassolids AT vielhauers promptanddelayedsecondaryexcitonsinraregassolids AT zimmererg promptanddelayedsecondaryexcitonsinraregassolids |
| first_indexed |
2025-11-24T15:49:02Z |
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1850848758636478464 |
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Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1081–1092
Prompt and delayed secondary excitons in rare
gas solids
M. Kirm1, V. Kisand2, E. Sombrowski3, B. Steeg3, S. Vielhauer1,
and G. Zimmerer1
1 Institut für Experimentalphysik, University of Hamburg, 149 Luruper Chaussee,
Hamburg D–22761, Germany
E-mail: Georg.Zimmerer@desy.de
2 Institute of Physics, University of Tartu, 142 Riia, Tartu 51014, Estonia
3 Deutsches Elektronensynchrotron DESY, 85 Notkestrasse, Hamburg 22607, Germany
Direct and indirect creation of excitons in rare gas solids has been investigated with reflectivity
and luminescence spectroscopy. For the heavy rare gas solids Kr and Xe, new and more reliable
exciton parameters have been deduced. With time-resolved luminescence spectroscopy, fast and
delayed secondary-exciton creation has been established and separated. Thermalization of
photocarriers and their delayed recombination have been analyzed, including a first attempt to in-
vestigate the influence of excitation density on the carrier dynamics. The existence of excitonic
side bands of ionization limits Ei (either band gap or inner-shell ionization limits) in prompt sec-
ondary exciton creation has been established. The threshold energies of these side bands are given
by E E nEith ex� � (n is integer, Eex is exciton energy). The side bands are ascribed to the forma-
tion of electronic polaron complexes, superimposed to inelastic scattering of photoelectrons.
PACS: 71.35.Cc, 72.20.Jv, 78.47.+p, 78.55.Hx
Introduction
At the onset of optical excitation of rare gas solids
(RGS) in the vacuum ultraviolet spectral range, pro-
nounced absorption lines are found. They arise from
the creation of bound pairs of valence holes and con-
duction electrons in the centre of the Brillouin zone
(�-point) and can be arranged in two series, � ( )3 2/
� ( )3 2/ and � ( )1 2/ , depending on the total angular
momentum j /� 3 2 or j /� 1 2 of the hole. These exci-
tations have been subject of numerous investigations
because rare gas solids are model systems for excitons
in insulators [1–4]. It is not the purpose of this article
to review the field, but to describe some special as-
pects of exciton creation which have been investigated
in recent years. We have to discriminate between di-
rect and indirect creation of excitons. Direct creation
is achieved, e.g., by optical excitation with an appro-
priate photon energy, E Eph ex� (Eph is photon en-
ergy of excitation; Eex is exciton energy). Some as-
pects of direct creation will be discussed in Sec. 2,
because they are necessary for a better understanding
of the indirect creation processes. Indirect exciton cre-
ation arises from (i) recombination of electron-hole
pairs, (ii) inelastic scattering of photoelectrons, and (iii)
excitonic side bands of valence or inner-shell excitations.
All experimental results have been obtained with
synchrotron radiation (SR) excitation at the Ham-
burger Synchrotronstrahlungslabor HASYLAB at DESY,
Hamburg. Two beamlines have been used, namely
beamline «I» with the set-up SUPERLUMI (normal
incidence; range of excitation � 40 eV), and beamline
«BW3» (grazing incidence; range of excitation
30 eV � h� � 1000 eV). As the main part of the present
paper deals with time-resolved data, some details are
given here. SR at HASYLAB consists of pulses with
FWHM � 150 ps, at a repetition rate between 5 and
1 MHz, depending on the mode of operation. For more
details, we refer to the original papers cited. If neces-
sary, in a few cases, more details are given in the text.
1. Direct exciton creation
1.1. Reflectivity and new evaluation of exciton
parameters
Excitons in rare gas solids are ascribed to the «in-
termediate» type [5] which means that the energetic
© M. Kirm, V. Kisand, E. Sombrowski, B. Steeg, S. Vielhauer, and G. Zimmerer, 2003
positions of the lines corresponding to the main quan-
tum numbers n > 1 are well described by the Wannier
formula,
E E
B
n
nj j
j
� �
2 (1)
(Enj is energy of exciton with main quantum number
n; Ej is ionization limit of the exciton series;
E E/ g3 2 � , Eg is band gap energy; Bj is binding en-
ergy of the exciton series). According to former mea-
surements, however, the members with n = 1 yield
more or less pronounced deviations from the Wannier
formula (see, e.g., [3]). The reflectivity curves of Kr
and Xe have been carefully re-measured in the excitonic
range because the preparation of polycrystalline [6,7] or
even monocrystalline rare gas samples [8] with high
structural quality has been developed. Moreover, con-
trary to the early investigations, now a more precise
determination of the energies of n � 1 excitons from
photoluminescence (the so-called free-exciton (FE)
lines) is possible (see Sec. 1.2). As an example, in
Fig. 1, the reflectivity of Kr is presented [9] (for Xe
see Ref. 10). Five members of the � ( )3 2/ series are
observed. The n � 1 band clearly displays an exci-
ton-polariton nature. In the case of Xe, a quantitative
analysis has been performed in terms of the exci-
ton-polariton model [8], showing that the deduced
energy of the transverse exciton agrees with the en-
ergy of the FE line in photoluminescence. In the case
of Kr, a line-shape analysis of the reflectivity curve in
terms of the exciton-polariton model has not been car-
ried out because only the energy of the transverse
exciton, which was taken from luminescence, is re-
quired for the following conclusions.
In Fig. 2, the energies of the Kr excitons are plot-
ted as a function of1 2/n . All energies, including n � 1,
obey the Wannier formula with high accuracy. The
same is true for Xe [10]. In so far, the former discus-
sion of corrections of the n � 1 value (see, e.g., refer-
ences given in Refs. 1–5) is obsolete in the case of Kr
and Xe. This, however, does not mean that the model
of the intermediate exciton is ruled out in general. In
the case of the light rare gas solids Ar and Ne the n � 1
value indeed deviates from the Wannier formula. In-
terestingly, in the light rare gas solids, the excitons
are unstable against exciton-lattice interaction,
whereas they are metastable in the case of the heavier
rare gas solids. Consequently, no FE lines but mainly
the emission of self-trapped excitons (STE) show up
in the luminescence spectra of Ar and Ne, whereas
both types of luminescence coexist in the case of Xe
and Kr. In Table 1, the exciton parameters deduced
from the new reflectivity curves are presented and
compared with former results.
Table 1
Exciton parameters of solid Kr and Xe at T = 6 K
Parameter Unit
Value of the parameter
Kr Xe
Binding
energy
eV
(1.45±0.02)a
1.53b
1.73c
(0.903±0.036)d
1.02b
0.86c
Band gap eV
(11.59±0.01)a
11.61b
11.67c
(9.298±0.005)d
9.33b
9.28c
Reduced mass m
0
(0.377±0.005)a
0.40b
0.41 (with
r
= 1.80)c
(0.327±0.005)d
0.37b
0.31 (with
r
= 2.23)c
Comment: aRef. 9; bRef. 3; cRef. 11; dRefs. 10, 30.
1.2. Radiative exciton decay
Following photon excitation of valence excitons of
Kr and Xe, luminescence spectra are observed which
yield (i) narrow lines originating from the free n � 1
(transverse) exciton and (ii) broad, Stokes shifted
bands originating from self-trapped excitons. In Fig. 3,
Kr results are given [9,12] (Xe results are published,
e.g., in Ref. 13). The Kr results are of special impor-
tance because the samples were nearly free from Xe im-
purities which efficiently quench the Kr FE line and
which also modify the STE bands as a consequence of
the luminescence of heteronuclear Kr–Xe* centres [9].
1082 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1081–1092
M. Kirm, V. Kisand, E. Sombrowski, B. Steeg, S. Vielhauer, and G. Zimmerer
10.0 10.4 10.8 11.2 11.6
11.50 11.55
0
n = 2
n = 3
n = 4
n = 5
n= 5
0
n = 4
s
L
Ln = 1
Photon energy, eV
n =1
R
ef
le
ct
iv
it y
ar
b.
un
its
,
Fig. 1. Reflectivity of solid Kr, measured at T = 6 K with
a resolution interval �� � 06. Š[9]. The inset shows the
range of n = 4 and n = 5 excitons in an enlarged scale.
The decay curves in Fig. 3 display the decay of the FE
line and the decay of the STE emission. The decay of
the FE line is rather fast and nonexponential. For Xe,
the details have been discussed in Ref. 13. The STE lu-
minescence decay includes two components, one in the
ns range originating from the singlet state of the STE,
and another one in the
s range originating from the
triplet state, showing up in the figure as a flat back-
ground. An analysis of the fast component shows that it
displays a cascade behavior involving the decay of the
FE line and the lifetime of the STE singlet state [14].
These remarks on the radiative decay of free exci-
tons have been included because the central part of the
present paper will deal with modifications in the case
of indirect exciton creation.
2. Secondary excitons following valence
excitations
2.1. Decay curves following near band-gap
excitation
2.1.1. Xenon and krypton. The decay curves of the
FE line observed under direct excitation are non-
exponential with an approximate decay rate of the or-
der of some 108 1s� and a rise time < 100 ps (experi-
mental time resolution) [12,13]. The situation changes
as soon as the photon energy of excitation exceeds the
band-gap energy. Then, as a result of the primary exci-
tation, free electron-hole pairs are created. Neverthe-
less, the FE line still shows up with nearly the same in-
tensity as under direct excitation of excitons. It is
therefore obvious that recombination of electrons and
holes into free excitons occurs. The decay curves, how-
ever, change dramatically as is shown for Kr [12] and
Xe [15] in Figs. 4 and 5. The parameter of the curves is
the excess energy, Eexcess � �E Egph . It is the sum of
the kinetic energies of both carriers involved. With in-
creasing excess energy, the cascade-type shape gets
more and more pronounced. Apart from the spike near
to time zero, the whole luminescence intensity is
delayed compared to the decay of directly excited
excitons (for comparison, a directly excited curve is in-
cluded in Fig. 5). This delay arises from a convolution
of thermalization of the carriers and their recombina-
Prompt and delayed secondary excitons in rare gas solids
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1081–1092 1083
0 0.2 0.4 0.6 0.8 1.0
10.2
10.4
10.6
10.8
11.0
11.2
11.4
11.6
sample 39
sample 32
sample 25
E
xc
ito
n
e
n
e
rg
y,
e
V
1/n2
Fig. 2. Plot of exciton energies of the �( )3 2/ series of so-
lid Kr, measured at T = 6 K, as a function of 1 2/n (n is
exciton quantum number) [9].
Photon energy, eV
8.0 8.5 9.0 9.5 10.0
.
time, ns
0 5 10 15 20 25
1
10
10
10
10
0 5 10 15 20 25
1
10
10
10
10
STE FE
STE
FE
In
te
n
si
ty
, a
rb
.u
n
its
4
2
3
4
3
2
a
b
c
In
te
n
si
ty
(
lo
g
. s
ca
le
)
In
te
n
si
ty
(
lo
g
. s
ca
le
)
Fig. 3. (a) Luminescence of nearly Xe-free solid Kr, excited by 10.42 eV photons at T = 6 K and measured with a resolu-
tion interval �� � 12. Å. (b) Decay curve of STE luminescence (measured at 8.55 eV), and (c) decay curve of FE lumi-
nescence (measured at 10.14 eV) of the same sample. Both decay curves were obtained with a resolution interval
�� � 9 Šat 6 K under excitation at 10.42 eV [12].
tion. Here, a special aspect of rare gas solids comes into
play: the simple fcc lattice of the rare gas solids allows
only for acoustical phonons which slows down ther-
malization of carriers, compared to, e.g., alkali halides.
It turns out that the bottleneck of recombination is the
thermalization process because the recombination cross
section is a sensitive function of the velocity of the car-
riers [15].
The curves in Figs. 4 and 5 show also spikes at
t � 0. They are ascribed to experimental artefacts. The
monochromators used are single-pass instruments;
therefore, a «white» background of VUV radiation
(primary monochromator � �10 3, secondary mono-
chromator � �10 2) is unavoidable. The background
shows up at t � 0 as scattered light or even leads to di-
rect excitation of excitons, although the photon ener-
gies chosen by the monochromator settings do not al-
low it.
The shape of the delayed FE luminescence was used
to analyze the recombination dynamics of the photo
carriers [15]. The full curves in Figs. 4 and 5 are re-
sults of model calculations in which the carrier dy-
namics have been treated in the following way
[15,16]. The starting point is an initial mean kinetic
energy of the carriers,
E
m
m m
Ee h
h e
e h
0 ,
,�
� excess (2)
(the excess energy is shared among the carriers accord-
ing to the effective masses me, and mh), and a density
of electrons and holes, n ne h, ,0 0� , which has been es-
tablished due to the nearly �-like photo-excitation. As-
suming the carriers achieve a Maxwellian distribution
of temperatures Te and Th , the energy loss of electrons,
e, and holes, h, due to scattering on acoustical pho-
nons, is described by [17]
dE
dt
E m
kT
T T
T
e h d e h
/
/ e h
/ e h L
e
, ,
,
,
,
( )
ac
� �
�8 2 2 5 2
3 2 4
3 2
� �� h
�
�
�
�
�
�
�
�
(3)
with deformation potential Ed, effective masses me,
and mh, mass density �, lattice temperature TL, and
Boltzmann and Planck constants, k and �. For RGS,
mh >> me, therefore the holes relax much faster than
1084 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1081–1092
M. Kirm, V. Kisand, E. Sombrowski, B. Steeg, S. Vielhauer, and G. Zimmerer
Time, ns
0 5 10 15 20 25 30
E excess = 780 meV
340 meV
187 meV
87 meV
In
te
n
si
ty
l
o
g
. s
ca
le
Fig. 4. FE decay curves of Kr, measured at T = 6 K, to-
gether with fitting results (full lines) for the delayed part
[16]. Resolution intervals in excitation 35. Å and in emis-
sion 8 Å. The parameter of the curves is the excess energy.
0 meV
Excitation
0
2
4
6
8
10
27 meV
63 meV
98 meV
135 meV
1.0 eV
12
14
16
18
E = 1.45 eVexcess
Solid Xe
T = 5 K
lo
g
a
ri
th
m
o
f
in
te
si
ty
, a
rb
. u
n
its
0 10 20 30 40
Delay, ns
Fig. 5. FE decay curves of Xe, measured at T = 5 K, to-
gether with fitting results (full curves) for the delayed
part [15]. The parameter of the curves is the excess en-
ergy. For comparison, an «apparatus function» (convolu-
tion of an excitation pulse with the response of the detec-
tor and the electronics) is included (open circles).
the electrons (note the factor me h
/
,
5 2 in the nominator
of equation (3)). For that reason, we assume Th = TL.
For t > 0, the evolution of the carrier densities due
to exciton formation and the exciton density, nex, are
described by the following rate equations
dn
dt
T n n v T
ne h
e e h e
e h
nr
, ,( ) ( )� � ��
�rel and
dn
dt
T n n v T R te e h e
ex
rel� �� ( ) ( ) ( ) (4)
with a temperature dependent cross-section � ( )Te ,
and relative velocity v Terel ( ). The term n /e h nr, � de-
scribes additional nonradiative carrier losses, e.g., at
the surface. The decay of the exciton itself is described
by the decay term R(t), for which experimental FE
decay curves following direct photo-excitation of the
excitons measured at the same sample were used. For
��Te), we use the formula given by Reimand et al.
[15]*,
�
� � �
( )
( ) ( ) (
T
e E m
c
m
m kT k
e
d e
/
s r
e
h L
�
1
4
16 2
3 3
1
3
6 2 5 2
4
0
3
� Te )2
(5)
which is a modification of the formula given by
Avakumov et al. [19] for Te � Th (e is electron charge,
cs is sound velocity, 0 r is dielectric permeability).
In the case of Xe, values for cs, � , ,r mh, and Ed
were taken from the literature [1–4]. TL was mea-
sured. Moreover, the sample quality was sufficiently
good to neglect the nonradiative term in the kinetic
equations. Then the only free adjustable parameter in
the calculations was the initial density. A hidden ap-
proximation is the definition of an electron tempera-
ture of the relaxing system via E = (3/2) kTe (E is
mean value of kinetic energy).
For Xe, the fits are quite acceptable. Nevertheless,
the result has to be taken with care for the following
reason. Among the parameters taken from the litera-
ture there are some which are known with high accu-
racy (cs, � , r) and others which are rather uncertain
(me, mh, and Ed). Concerning the effective masses,
another difficulty has to be mentioned. In the model,
isotropic parabolic bands are assumed, whereas the
band structure of Xe and Kr is anisotropic. Moreover,
the excess energies in the experiment extend to large
values where the parabolic approximation breaks
down. Therefore it is questionable to use the data for a
deduction of more reliable values of, e.g., the mass or
the deformation potential.
In the case of Kr, the model was modified in the fol-
lowing way. The term E md e
/2 5 2 in the nominator of
equation (5) is the most important factor. It is con-
nected with the low field mobility according to [17,20]
� �
0
4 2
2 5 2
2
3
2
�
e v
E m k T k T
l
d e
/
B L B e
�
( )
. (6)
In the case of the low-field mobility, T TL e� , and �vl
2
is sufficienty well known (vl is longitudinal sound ve-
locity). Therefore, E md e
/2 5 2 was calculated from the
mobility measurements of Miller et al. [21]. In other
words, using an experimental result, the most uncer-
tain parameters were eliminated**. The Kr fits were
obtained in this way. Although they are not as good as
for the case of Xe, they are more satisfactory because
the number of parameters has been decreased. The pa-
rameters of the fits are collected in Table 2.
The values of the initial carrier densities are by far
much lower than those estimated from the photon flux
and from the value of the absorption coefficient at the
respective photon energy of excitation [15] for the fol-
lowing reasons. The initial density is the density after
redistribution of the carriers via Coulomb scattering.
During this first stage of relaxation, carrier diffusion
decreases the density. Here, the geometry of excita-
tion comes into play. The size of the spot at the sample
surface is about 0.3�4 mm2. The penetration depth of
light is of the order of a few 100 Å. On the other side,
it was shown that the scattering length of excitons is
of the order of 1000 Å [13]. The scattering lengths of
the carriers should be similar because both is scatter-
ing on acoustic phonons. With a scattering length ex-
ceeding the thickness of the initially excited volume
by an order of magnitude, diffusion of the carriers into
the bulk will rapidly decrease the carrier density.
This, however, raises the question why spatial dif-
fusion has not been taken into account in the rate
equations. Diffusion has been neglected there because
the holes get self-trapped in rare gas solids. Then, the
spatial diffusion of the electrons in a localized posi-
tively charged background is suppressed. It seems as if
Prompt and delayed secondary excitons in rare gas solids
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1081–1092 1085
* Compared to Ref. 15, a factor 1 4 3/( )� was added so that this formula is valid for SI system. This was pointed out to us
by A.N. Vasil’ev [18].
** This is not completely true because there is still the factor m /me h in the equation. However, the errors introduced
by this square root are much less than those introduced by E md e
/2 5 2.
the fitting parameter characterizes the distribution af-
ter hole-trapping.
2.1.2. Argon and neon. In the light RGS, free
excitons are rapidly self-trapped. Therefore, the
method used in the case of Kr and Xe to study
thermalization and recombination of free carriers can-
not be used. In the case of Ar, we succeeded in
analyzing recombination with the luminescence of
self-trapped excitons. The STE emission of Ar consists
of a singlet and a triplet band [1–4]. The lifetime of
the singlet emission is 1.8 ns [23]. The formation
should therefore be observable in the decay curves of
the singlet component.
The singlet and the triplet STE bands overlap spec-
trally, and the singlet contribution is much weaker
than the triplet one. Therefore, at first a photon energy
of luminescence had to be found to get an optimal sin-
glet / triplet ratio and sufficiently high counting rates.
The chosen photon energies were 9.76 and 10.21 eV
(for comparison: maximum of the triplet STE band
9.72 eV, of the singlet band 9.83 eV [24]).
In Fig. 6, decay curves of the singlet luminescence
are shown. Most of the photon energies of excitation
are above the band gap energy, Eg � 14.16 eV. With
increasing photon energy of excitation, up to a value
E E Egth ex� � (which will be discussed below; Eex
is energy of the n = 1 exciton), the curves get more
and more cascadelike. They were fitted with the sum
of two exponentials,
I t I A t/ A t/( ) exp( ) exp( )� � � � �0 1 1 2 2� � (7)
(A A1 2, with opposite sign). The results of the fits ��1
and �2) are shown in Fig. 7 as a function of photon en-
ergy of excitation [24]. Apart from the range where
the values of both time constants are comparable, the
decay time is independent from photon energy of exci-
tation*. This time corresponds to the lifetime of the
1086 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1081–1092
M. Kirm, V. Kisand, E. Sombrowski, B. Steeg, S. Vielhauer, and G. Zimmerer
5 50 10 15 20 25
Time, ns
27.21 eV
23.62 eV
20.00 eV
16.00 eV
= 13.40 eVE ph
In
te
n
si
ty
(
lo
g
. s
ca
le
)
Fig. 6. Decay curves of the STE luminescence of Ar, mea-
sured at T = 8 K at a luminescence photon energy 10.21 eV
[24]. The resolution intervals are �� � 175. Šin excitation
and �� � 11 Šin emission. The photon energy of excitation
is given at each curve.
Table 2
The values of the parameters used for the fits of the time
dependence of delayed FE luminescence in solid Kr and Xe
shown in Figs. 4 and 5. The values for m m v ce h l s, , , ,� and
r are taken from [1–4]. Ed was taken from [22]. For Cexp
see text
Parameter Unit
Value of the parameter
Kr Xe
Effective electron mass, m
e
m
0
0.42 0.35
Effective hole mass, m
h
m
0
3.6 2.1
Initial carrier density, N
0
* 1/m3 3.6�1014 6�����
Initial excess energy, E
excess
meV 780 1450
Deformation potential, E
d
eV not needed 0.79
C E md e
/
exp � 2 5 2 J2�kg5/2 4.83�10–114 not used
Longitudinal sound
velocity, v
l
m/s 1370*** not needed
Averaged sound velocity, c
s
m/s 830****
Crystal temperature, T
L
K 5.5
Nonradiative losses,
�nr / nr� 1 �
1/s 0** 0**
Density of solid Kr at 5 K, � kg/m3 3092.6 3781
Relative dielectric
permeability, r
1.88 2.22
*The values were obtained neglecting the correction pointed out to
us by A.N. Vasil’ev (see footnote 1). Including the correction
means, the values have to be multiplied by a factor ( )4 3� .
**If the value of nonradiative losses is smaller than � � �5 107 1s ,
its influence on the fits can be neglected.
***In the case of Kr, for the whole calculation, the longitudinal
sound velocity was used.
****For the Xe calculations, the averaged sound velocity was
used.
* For mathematical reasons, the accuracy of the fits is lower for nearly equal time constans � �1 2� .
STE singlet, and the value is in good agreement with
the one reported by Roick et al. [23]. The rise times
for excitation below the band gap correspond to the
experimental time resolution. For excitation above the
band gap, we observe a linear increase of the rise time
until it reaches the value of the lifetime of the singlet
state*. Above Eth , the rise time drops to the value it
has in the excitonic range of excitation. There, the de-
cay curves are nearly identical with those observed
under excitation with a photon energy below the
band-gap energy (see Fig. 6).
In view of Sec. 2.1.1, the increase of the rise time is
ascribed to the thermalization of the electrons. From
the slope of the linear increase of �2, a loss rate of ap-
proximately 5 eV/ns (slope of the straight line:
0.2 ns/eV) is obtained. With an average phonon
energy 5 meV this corresponds to a loss of one phonon
energy per one ps, in other words, an average scatter-
ing rate of 1012 s–1 has been observed.
Concerning Ne, systematic measurements like in
the case of Ar were not possible up to now due to ex-
perimental difficulties.
2.2. Time-resolved excitation spectra and «prompt»
secondary exciton formation
2.2.1. FE line of Kr and Xe. Under pulsed excita-
tion with a sufficiently large interpulse period, the re-
combination-type luminescence at t = 0 (defined by
the excitation pulse) starts from zero. On the other
hand, excitons created at t = 0 start emitting at t = 0
with maximum intensity. Based on these ideas, time-
resolved excitation spectra can be used to discriminate
between «prompt» (within the experimental time re-
solution) secondary excitons and delayed recombi-
nation-type secondary excitons. In a time-resolved ex-
citation spectrum, following pulsed excitation, the
luminescence intensity is measured within a time-in-
terval (called time-window) of length �t with a delay
�t with respect to the exciting pulse. Without delay
and with a short time-window, we are sensitive for
prompt secondary excitons. With a delay much larger
than the lifetime of prompt excitons, we are sensitive
for recombination-type excitons. If the delay is zero,
the time-window accepts scattered light of the excit-
ing light pulse. Therefore sometimes a slight delay is
chosen to suppress scattered light, however at the ex-
pense of sensitivity for prompt luminescence. Some re-
sults have already been published [10,12,25–27].
In Fig. 8, time-resolved excitation spectra of the
FE line of Kr and Xe, measured in short time-windows
are presented. The details of the time-windows are
given in the figure caption. The special photon energy
scale is well suited to illuminate the physics behind
the phenomena observed. The unit of the scale is the
exciton energy (Xe: 8.36 eV, Kr: 10.14 eV). As
zero-point, the band-gap energy is chosen. In both
curves, we observe (i) low intensity, until a threshold
Eth at point 1 is reached, and (ii) a dramatic increase
of intensity above Eth .
The low intensity underlines the slow formation of
secondary excitons via recombination. The increase of
the signal above the threshold underlines, that in this
range of excitation, «prompt» secondary excitons are
created. In Kr as well as in Xe, an analysis [10,12] of
the threshold energy shows that it is given within
0 2. eV by
E E Egth ex� � . (8)
This is the energy required (from point of view of en-
ergy conservation) to obtain one electron-hole pair
with negligible kinetic energy and one exciton. In
both cases, the time-resolved excitation spectrum
yields a broad maximum above Eth . It does not drop
to the low value as on the low energy side but levels
off. At higher photon energies, another increase is
found, starting approximately at an energy
E Eg � 2 ex.
There are two mechanisms for the prompt secondary
exciton creation observed above threshold Eth , (i) in-
elastic scattering of photoelectrons at a valence electron
resulting in an additional exciton, and (ii) simultaneous
creation of an electron-hole pair and an exciton (elec-
tronic polaron complex [28]). Contrary to the electronic
Prompt and delayed secondary excitons in rare gas solids
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1081–1092 1087
12 14 16 18 20 22 24 26 28 30
Excitation energy, eV
E+E g ex
E g
T
im
e
, n
s
2.5
2.0
1.5
1.0
0.5
0
rise time
decay time
�1
�2
Fig. 7. Plot of the characteristic times of the cascade-type
fits of decay curves of the STE singlet state of Ar as a
function of photon energy of excitation [24]. The band
gap at 14.15 eV and the threshold energy E E Egth ex� �
are marked.
* Of course, it is an accidental coincidence of both values.
polaron complex, the scattering mechanism is a sequen-
tial process. The scattering time in the fs regime cannot
be resolved in our experiments, therefore, these second-
ary excitons are called prompt as well. On the other
hand, excitons created simultaneously with an elec-
tron-hole pair could also be called «direct» because they
are the result of a primary excitation process.
From an experimental point of view it is difficult to
discriminate between both mechanisms. At first, it
was pointed out that a discrimination should be possi-
ble via the threshold energy because the simplest scat-
tering model predicts a threshold considerably larger
than the one predicted for the electronic polaron com-
plex [10]. The simple model assumes parabolic bands,
neglecting Bragg reflection across the Brillouin zone
boundaries. With the so-called mutiple-parabolic-
branch-band (MPPB) model by Vasil’ev et al. [29] it
was shown that the threshold is practically the same
for both mechanisms [12,30]. An argument in favour
of the electronic polaron complex is the fact that the-
ory predicts a resonance as it is observed, whereas the
scattering process leads to a more stepwise increase of
the excitation spectrum. Summing up, the curves are
ascribed to inelastic scattering with a resonant en-
hancement near threshold due to the formation of elec-
tronic polaron complexes. In a certain sense, the
time-resolved excitation spectra bring about excitonic
sidebands of valence ionization as they were predicted
by theory, E E nEgres ex� � , n is integer [28].
2.2.2. The special case of argon and neon. In the
light RGS, FE luminescence is missing. Time-resolved
(Ar) and time-integrated (Ne) excitation spectra of
the STE emission, however, yield similar results as in
the case of Xe and Kr. The drop of the rise time �2
(see Fig. 7) around Eth also shows that above Eth
prompt secondary excitons are created. In Figs. 9 and
10, data are presented for Ar [24,31] and Ne [24]. In
the case of Ar, the singlet component of the STE has
been chosen as a fast decay channel for time-resolved
excitation spectra (observation at 10.21 eV), in the
case of Ne, the emissions of the atomic-type STE at
16.75 eV and of the so-called W-band at 15.5 eV were
used for time-integrated measurements. Nevertheless,
the threshold of prompt secondary exciton creation at
E E Egth ex� � was observed. In the case of Ar, a
broad resonance like in the heavy rare gases shows up,
in the case of Ne (time-integrated spectrum), a more
step-like increase was found. It has to be admitted
that the spectral range of the Ne-measurements is un-
favorable for both beamlines used. The interesting fea-
tures are close to the limits of the working ranges of
the respective monochromators (left part of Fig. 10:
normal-incidence monochromator, right part of Fig.
10: grazing-incidence monochromator) where the exci-
tation intensity is small. The threshold itself and the
creation of prompt secondary excitons is well
established.
1088 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1081–1092
M. Kirm, V. Kisand, E. Sombrowski, B. Steeg, S. Vielhauer, and G. Zimmerer
0
0
0.5
0.5
1.0
1.0
1.5
1.5
2.0
2.0
2.5
2.5
Xenon
In
te
n
si
ty
, a
rb
. u
n
its
In
te
n
si
ty
, a
rb
. u
n
its
(E E )/Eg ex
Krypton
Fig. 8. Time-resolved excitation spectra of the FE lumines-
cence of solid Kr [12] and Xe [30], plotted in an energy
scale which is described in the text. The time windows and
time delays are: �t � 0.94 ns, �t � 0 ns (Kr); �t � 0.8 ns,
�t � 0.6 ns (Xe). The sharp maxima arise from scattered
light.
22
0
24 26 28 30 32 34
In
te
n
si
ty
, a
rb
. u
n
its
Photon energy, eV
26.22 eV
E + E =g ex
Short time window
�t = 0.69 ns, �t = 1.07 ns
Fig. 9. Time-resolved excitation spectrum of STE lumines-
cence of Ar [24,31]. Due to the photon energy of observa-
tion chosen (10.21 eV), the main contribution in the time
window �t � 1.07 ns and �t � 0.69 ns arises from the sin-
glet STE. T = 8 K. Resolution intervals as in Fig. 6.
3. Secondary excitons following inner-shell
excitation
3.1. Excitonic sidebands of inner shell ionization
limits
Here, we start with a presentation of time-resolved
excitation spectra of FE luminescence in the vicinity of
the Kr 3d and Xe 4d inner-shell excitation (Fig. 11
[34]). The (spin-orbit split) ionization energies are
Kr 3d5/2: 92.32 eV, Kr 3d3/2: 93.50 eV; Xe 4d5/2:
65.59 eV, Xe 4d3/2: 67.54 eV (averages of the values
given by Resca et al. [32] and Kassühlke [33]). For
comparison purposes, the spectra are aligned for the re-
spective d5/2 ionization limits, and the spread of the
scales corresponds to the respective exciton energies
(vertical lines). The numbers given at the abscissa,
however, are electron-volts. Similar to the valence
case, strong resonances with a threshold energy
E E Ed /th ex� �
5 2
are observed. In the case of Xe, the
resonance is split. The second peak is ascribed to a reso-
nance with a threshold E Ed /3 2
� ex . Experiments with
higher spectral resolution show that the Kr resonance
also contains two contributions, one of them being cor-
related to the d /3 2 ionization limit*. Moreover, a sec-
ond resonance with a threshold E E Ed /th ex� �
5 2
2 is
observed. In conclusion, excitonic side bands exist not
only in the range of valence excitations but also in the
range of inner-shell excitations.
In the case of light rare gas solids, up to now only
the Ar 2p excitations have been investigated [24,35].
The results yield an excitonic sideband as well, how-
ever, degradation of the samples due to radiation dam-
age is severe, therefore the excitation spectra suffer
from an overall decrease of intensity during the mea-
surements.
Prompt and delayed secondary excitons in rare gas solids
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1081–1092 1089
SUPERLUMI
E + E = 38.94 eVg ex E + E = 38.94 eVg ex
0
20 25 30 35 40 40
2
4
In
te
n
si
ty
, a
rb
.u
n
its
Excitation energy, eV Excitation energy, eV
1.5
1.0
0.5
30 35 45 50
BW3
a-STE
W-STE
Fig. 10. Time-integrated luminescence excitation spectra of Ne [24]. Left part measured at the SUPERLUMI station (nor-
mal incidence range) at 16.75 eV (atomic-type STE). The curves in the right part were measured at the undulator beamline
BW3 at 16.4 eV (a-STE) and at 15.5 eV (W-band). T = 6 K. The resolution interval in excitation was 0.01 eV (a-STE) and
0.02 eV (W-band).
90 95 100 105 110 115 120
5
6
7
8
9
10
11
E 3d5 / 2
+ E ex
Kr FE
Excitation energy, eV
E 3d5 / 2
65 70 75 80 85 90
20
25
30
35
40 Xe FE
E4d,5/2
E 4d5 / 2
+ 2E ex
E 4d5 / 2
+ Eex
E3d5 / 2
+ 2E ex
P
ro
m
p
t
lu
m
in
e
sc
e
n
ce
, a
rb
. u
n
its
Fig. 11. Time-resolved excitation spectra of FE lumines-
cence of Kr and Xe in the vicinity of the Kr 3d and the
Xe 4d inner shell excitations [34]. The time windows are
Kr: �t � 1.6 ns, �t � 0; Xe: �t � 1.2 ns, �t � 0. For de-
tails, especially for the scale used, see text.
* In Fig. 11 we preferred to present a quick scan. During high-resolution scans, which take some hours, the samples degrade
due to defect formation. This leads to a continuous decrease of FE luminescence. High-resolution scans are given in [34].
4. Carrier recombination and density effects
The influence of inner-shell excitation on the decay
curves is illustrated in Fig. 12 with a set of decay
curves of the FE line of Xe, presented as a function of
time and photon energy of excitation around the
excitonic sideband of 4d5/2 ionisation. Prompt and
delayed FE luminescence is observed [36]. As soon as
the photon energy of excitation crosses the threshold
of the excitonic sideband, the prompt part increases at
the expense of the delayed part, indicating a redistri-
bution among prompt and delayed secondary excitons.
The prompt part below threshold originates from in-
elastic scattering of photoelectrons originating from
valence excitations. The superposition of valence and
inner-shell excitations makes a quantitative analysis
difficult. Therefore, we restrict ourselves to present
these qualitative results.
Excitation in the same range of excitation made
feasible another type of investigation. The measure-
ments have been carried out at the undulator beamline
BW3 of HASYLAB with its high excitation intensity
[37]. By tuning the undulator gap the spectral posi-
tion of the first harmonic is tuned. With fixed settings
of photon energy, it means that the intensity is tuned
across the first harmonic. In this way, the excitation
density can be varied by a factor of 50. This was used
to establish density effects in the carrier dynamics.
The models used to analyze the delayed FE decay pre-
dict such effects (Eq. (4)). An excitation below the
thresholds of the sidebands was chosen to avoid inter-
ference with the strong contribution of prompt
secondary excitons originating from the sideband.
In Fig. 13, decay curves of the FE lines of Kr (exci-
tation 85.3 eV) and Xe (excitation 66.1 eV) are pre-
sented [38]. The parameter of the curves is the initial
carrier density at t = 0, obtained from the fits. With
increasing carrier density, the delayed part of the de-
cay curves changes. The maximum shifts to smaller
times. The full curves are fits with equations (3)–(5).
The variation of the excitation density by a factor of
50 leads to relatively small changes in the shape of the
decay curves, although the product of the initial car-
rier densities in the rate Eq. (4) varies by a factor of
2500. This is explained by the fast increase of the re-
combination cross-section � ( )Te (Eq. (5)) within the
first nanoseconds [15], which strongly influences the
shape of the decay curves independently from the
carrier densities.
Concerning the parameters, the situation is more
complex than in the case of excitations into states near
to the bottom of the conduction band. The initial ki-
netic energy of the photoelectrons (we still assume
fast hole relaxation to the top of the valence band) is
an open question because a broad distribution as a
consequence of inelastic scattering of the initially cre-
ated photoelectrons is expected. The time scale for
this redistribution is far below the experimental time
resolution. Therefore, a mean kinetic energy of the
electrons after redistribution, E0, was introduced as a
fit parameter to replace the well-defined energy for
valence excitations, E0, of Eq. (2).
It turned out that the nonradiative channel in the
rate equations can not be neglected. The nonradiative
rate, 1/ nr� has a more phenomenological character and
strongly depends on sample conditions. As in the case
of valence excitations, the initial carrier densities
n ne h0 0� (after the fast redistributions due to elastic
and inelastic scattering) have to be included as fitting
parameters. They were introduced with the constraint
that they are proportional to the measured excitation
density. As three fitting parameters were unavoidable,
a fourth one, namely the effective mass of the electrons,
was tolerated. Values are given in Table 3 [36,38].
The me values are within reasonable limits, but can-
not be taken as definite, since they are coupled to Ed in
the model via Ed
2 me
5/2. The E0-values seem to be in
contradiction to photoemission data which show that
the bulk of the photoelectrons have kinetic energies be-
tween zero and 2 eV in the range of Xe 4d and Kr 3d
excitation [33]. Note, however, the electrons below the
vacuum level are not observed in photoemission. E0 ob-
viously does not correspond to the mean kinetic energy
after redistribution via electron-electron scattering as it
is observed in photoemission. It is ascribed to that
1090 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1081–1092
M. Kirm, V. Kisand, E. Sombrowski, B. Steeg, S. Vielhauer, and G. Zimmerer
Fig. 12. Set of decay curves of the FE luminescence of Xe
in the vicinity of the excitonic sideband of 5d5/2 ioniza-
tion [36]. For details see text.
range of kinetic energy, in which the rates for elec-
tron-hole recombination and further phonon-relaxation
get comparable. An estimate for the excitation density
based on absolute flux measurements is about two or-
ders of magnitude higher than the results of the fits.
This discrepancy corresponds to the small values of E0
insofar as diffusion processes during the first stage of
relaxation to E0 may considerably reduce the density.
Although significant simplifications have been applied,
both for Kr and Xe the whole set of data can be de-
scribed with a reasonable and consistent set of parame-
ter values.
Conclusions
It was shown that time-resolved luminescence spec-
troscopy on rare gas solids is a powerful tool to inves-
tigate the dynamics of photocarriers, namely elec-
tronic relaxation, thermalization and recombination
into secondary excitons. The time-evolution of free
excitons following primary valence excitation and to a
certain extend also following inner-shell excitation
can be explained in terms of the «classical» theory of
the relaxation processes mentioned, with values of the
various physical quantities involved, as they are re-
ported in the literature. One of the main results is the
proof that there exist excitonic sidebands of ionization
Prompt and delayed secondary excitons in rare gas solids
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1081–1092 1091
10
10
10 KrXe
4.38·109 cm 3
1.26·1010 cm 3
6.60·10
10
cm 3
9.42·10
9
cm 3
n e,0 = 1.53·1011
cm 3ne,0 = 2.02·10
11
cm 3
3.79·10
9
cm 3
10
10
10
10
4.51·10
10
cm 3
10
10
10
lo
g.
in
te
ns
ity
ar
b.
un
its
0 5 10 15 20 25 30
1
10
10
10
Decay time, ns
10
10
10
10
10
10
10
10
10
10
0 5 10 15 20 25 30
1
10
10
10
Decay time, ns
,
4 4
44
3
3
3
3
3
2
2
2
2
2
22
2
lo
g.
in
te
ns
ity
ar
b.
un
its
,
3
3
3
Fig. 13. Decay curves of the FE luminescence of Kr and Xe, measured with different excitation densities (circles), to-
gether with fitting results for the delayed part (full curves) [38]. The initial electron densities for the calculations are
given at each curve, the other fit parameters are given in Table 3. The Kr curves were measured for 85.3 eV excitation at
12.5 K, the Xe curves were measured at 66.1 eV excitation at 10.8 eV.
Table 3
The values of the parameters used for the fits of delayed
FE luminescence in solid Kr and Xe shown in Fig. 13. The
values of m n Ee e, ,,0 0, and �nr are fit-results. m v ck l s, , ,�,
and r are taken from [1–4]. Ed of Kr was calculated from
the low field mobility [21] with the literature value of the
effective electron mass given in Table 2. Ed of Xe was taken
from [22]
Parameter Unit
Value of the parameter
Kr Xe
Effective electron mass, m
e
m
0
0.36 0.73
Effective hole mass, m
h
m
0
3.6 2.1
Initial carrier density, n
e,0
1/m3 1.53 �1017 2.02 ����!
Mean electron energy, E
0
meV 56 24
Deformation potential, E
d
eV 1.44 0.79
Longitudinal sound
velocity, v
l
m/s 1370 1300
Averaged sound velocity, c
s
m/s 845 830
Crystal temperature, T
L
K 12.5 10.8
Nonradiative losses,
�nr / nr� 1 �
1/s 1/25.9��0–9 1/13.1���–9
Density of solid Kr at 5K, � kg/m3 3092.6 3781
Relative dielectric
permeability, r
1.88 2.22
limits (either band gap or inner shell ionization)
which are ascribed to electronic polaron complexes.
Due to the fact that thermalization is slow in rare gas
solids, a moderate time resolution is sufficient to carry
out the experiments.
Acknowledgments
The work was supported by the Bundesministerium
für Bildung und Forschung (grants No. 05 650GUB, 05
ST8GUI 6) and by the Deutsche Forschungsgemein-
schaft DFG (grants No. DFG Zi 159/1-4). V. Kisand
and G. Zimmerer acknowledge support by the EU —
Project «Regional Centre of Excellence in New Func-
tional Materials, their Design, Diagnostics and Exploi-
tation» ( No. ICA1-1999-70086).
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