www.elsevier.com/locate/apsusc
Applied Surface Science 248 (2005) 50–55
Photoexcitation-induced processes in amorphous
semiconductors
Jai Singh *
School of Engineering and Logistics, Charles Darwin University,
Darwin, NT 0909, Australia
Available online 22 March 2005
Abstract
Theories for the mechanism of photo-induced processes of photodarkening (PD), volume expansion (VE) in amorphous
chalcogenides are presented. Rates of spontaneous emission of photons by radiative recombination of excitons in amorphous
semiconductors are also calculated and applied to study the excitonic photoluminescence in a-Si:H. Results are compared with
previous theories.
# 2005 Elsevier B.V. All rights reserved.
PACS: 78.55.Qr; 74.81.Bd; 78.66.Jg
Keywords: Photo-induced processes; Photodarkening; Volume expansion; Radiative recombination; Amorphous semiconductors
1. Introduction
Amorphous semiconductors are used in fabricating
many opto-electronic devices such as solar cells,
sensors, large area thin film transistors (TFT), X-ray
image detectors, memory storage discs, modulators,
etc., and hence, have many industrial applications.
Most of these devices operate on the principle of first
creating electron–hole pairs by optical excitations or
injections and then their separation and collection or
their radiative recombination. On one hand, structures
of such semiconductors do not have any long-range
* Tel.: +61 8 89 466 811; fax: +61 8 89 466 366.
E-mail address: [email protected].
0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved
doi:10.1016/j.apsusc.2005.03.031
order, and hence, tend to hinder the motion of charge
carriers. On the other hand, the lack of long-range
periodicity gives rise to several new phenomena,
which do not occur in crystalline solids. These
phenomena are, for example, photo-induced creation
of dangling bonds (DB), which leads to the well
known Staebler–Wronski effect (SWE) in hydroge-
nated amorphous silicon (a-Si:H), anomalous Hall
effect, photodarkening (PD) and volume expansion
(VE) in amorphous chalcogenides (a-Chs), etc. [1].
Some of these new phenomena are used in new
frontier technologies, for example, future DVDs are
likely to use the phenomena of photodarkening and
volume expansion for storing information in their
optical memory. Light emitting devices of amorphous
.
J. Singh / Applied Surface Science 248 (2005) 50–55 51
organic materials use the concept of radiative
recombination of excitons in a-semiconductors. X-
ray imaging is based on the creation of electron–hole
pairs in a-Chs by X-ray photons and their collection
and detection, etc.
In amorphous chalcogenides, there are two types of
metastabilities: one is defect-related, e.g., the creation
of dangling bonds due to illumination, and the other is
structure-related, i.e., photostructural changes, such as
volume expansion or contraction and photodarkening
or photobleaching. Earlier, the origins of defect-
related and structure-related metastabilities were
thought to be different because of their different
annealing behaviour [1]. However, recently, photo-
structural changes in a-Chs have been simulated with
first-principles type molecular dynamics (MD) [2] as
well as by ab initio molecular orbital calculations [3].
These microscopic calculations suggest that some of
coordination defects are involved in the structural
transformations under optical excitations. Thus, a
careful study of the mechanism of creation of light-
induced metastable defects (LIMD) is still required.
The reduction in the optical band gap due to
illumination observed in amorphous chalcogenides is
called photodarkening [1,4,5], which has been known
to be metastable until recently because it disappears by
annealing but remains even if the illumination is
stopped. Many attempts have been made at under-
standing the phenomenon in the last two decades but
no model has been successful in resolving all issues
observed in materials exhibiting PD. Another photo-
structural change that occurs in a-Chs is the volume
expansion due to illumination [1]. Although VE and
PD are not linearly related, it was demonstrated by
Shimakawa et al. [6] that they are related. They have
also suggested that both PD and VE occur due to the
excessive repulsive Coulomb force among the photo-
excited electrons occupying the localized tail states.
Accordingly, the repulsive force between the layers of
a-Chs is considered responsible for VE and the same
force is assumed to induce an in-plane slip motion that
causes PD. Recently, the same group [7] has also
observed the transient PD in a-As2S3, a-As2Se3 and a-
Se, which disappears as soon as the illumination is
stopped. It is not clearly understood what causes two
types of PD, metastable and transient. Moreover, the
repulsive Coulomb force model is qualitative and
provides no estimates of the magnitude of the
repulsive forces required for causing PD and VE.
For causing movements in an atomic network, one
requires lattice motion, which surprisingly none of the
models on PD and VE have given any account of.
However, the involvement of lattice vibrations has
recently been considered [8] in inducing photostruc-
tural changes in glassy semiconductors.
In 1988, Singh discovered a large reduction in the
band gap [9] due to pairing of charge carriers in
excitons and exciton–lattice interaction in non-
metallic crystalline solids. The magnitude of the
reduction in the band gap varies with the magnitude of
exciton–phonon interaction which is different for
different materials. The softer the structure, the
stronger is the carrier–phonon interaction. It has been
established that due to the planar structure [1], the
carrier–phonon interaction in a-Chs is stronger than in
a-Si:H, which satisfies the condition for Anderson’s
negative-U [10] in a-Chs but not in a-Si:H. It may be
noted that the concept of negative-U has been applied
to photodarkening before [11–13], but to the author’s
knowledge no quantitative theory has been developed
at least not for VE.
Some controversy has recently arisen on the
magnitude of the radiative lifetime in the photo-
luminescence of a-Si:H. Using time-resolved spectro-
scopy (TRS), Wilson et al. [14] have observed PL
peaks with radiative lifetimes in the nanosecond (ns),
microsecond (ms) and millisecond (ms) time ranges in
a-Si:H at a temperature of 15 K. In contrast to this,
using the quadrature frequency resolved spectroscopy
(QFRS), other groups [15–17] have observed only a
double peak structure PL in a-Si:H at liquid helium
temperature. One peak appears at a short time in the ms
range and the other in the ms range. Using the effective
mass approach, a theory for the excitonic states in
amorphous semiconductors has been developed by
Singh et al. [18] and the occurrence of the double peak
structure has successfully been explained for both a-
Si:H and a-Ge:H.
In the present paper, based on Holstein’s [19]
approach, the energy eigenvalues of positively and
negatively charged polarons and paired charge
carriers, created by illumination, are calculated. It is
found that the energies of the excited electron
(negative charge) and hole (positive charge) polarons
decrease due to the carrier–phonon interaction. Also,
the energy of the paired charge carriers decreases.
J. Singh / Applied Surface Science 248 (2005) 50–5552
Thus, the hole polaronic state and paired hole states
overlap with the lone pair and tail states in a-Chs,
which expands the valence band and reduces the band
gap energy, and hence, causes PD. Formation of
polarons as well as pairing of holes increases the bond
length, on which such localizations occur, which
causes VE. For photoluminescence, using the first
order perturbation theory, rates of spontaneous
emission of photons due to the radiative recombina-
tion of excitons are calculated at the thermal
equilibrium. Assuming that the maximum of the
calculated rates and that of the observed PL intensity
occur at the same photon energy, the radiative lifetime
of excitons is calculated from the inverse of the
maximum rates.
2. Photo-induced changes in a-Ch
Following Holstein’s approach for a linear chain
[19], it is shown that a bond gets stretched when a hole
is localized (hole–polaron) on it due to the strong
hole–phonon interaction and the bond becomes
weaker. The hole energy is lowered by the polaron
binding energy. The expression for the bond length xhp
with one localized hole on it is [1]:
xhp ¼
AhpC�
pC p
Mv2; (1)
where Ahp is the force of vibration of a pth bond with a
localized hole on it and C p is the probability amplitude
coefficient (C�p is its complex conjugate) for a hole
being localized on the bond. M is the atomic mass and
v is the frequency of vibration in the Einstein approx-
imation. A weak bond with a localized hole facilitates
capturing another hole again due to the strong hole–
phonon interaction and then the bond, denoted by xhhp ,
increases to double its size, i.e., xhhp ¼ 2xh
p.
Pairing of holes on a weak bond results into ‘‘bond
breaking’’ due to removal of covalent electrons and
two dangling bonds are created. The gained energy
DEhh due to a pair of holes localized on a bond and two
electrons localized elsewhere as polarons in a
simplified linear chain is obtained as [1]:
DEhh ¼ 2Ee p þ Ehh; (2)
where Ee p ¼ 148
ðMv2Q20Þ2
T is the lattice relaxation
energy due to localization of an electron (polaron
binding energy); here Q0 is the reaction co-ordinate
at the minimum of the vibrational potential and T is the
carrier transfer matrix element between the nearest
neighbours. Ehh ¼ 16
ðMv2Q20Þ2
T is the lattice relaxation
energy due to localization of a pair of holes (bipolaron
binding energy). DEhh is then obtained as:
DEhh ¼ 5
24
½Mv2Q20�
2
T: (3)
A lattice with strong carrier–phonon interaction
induces pairing of both like charge carriers, and there-
fore, excited electrons can also become paired. The
energy of such a paired electron state with the two
holes localized as polarons is also lowered by
DEee = 2Eh p + Eee, where Eh p is the lattice relaxation
energy due to localization of a hole and Eee that due to
localization of a pair of electrons. For simplification,
assuming that electron–phonon and hole–phonon
interactions are equal, one gets DEh p = DEe p and
DEhh = DEee. The effect of DEhh and DEee on the
energy band gap is to expand the valence band upward
and conduction band downward, and hence, narrowing
the band gap and producing photodarkening.
It may be noted that the pairing of electrons on a
bond does not break the bond and it is not very
probable that in a pair of excitons, both holes and
both electrons will be paired because the effect of
strong carrier–phonon interaction drives unlike
charge carriers far apart. Therefore, here we consider
only the three most probable possibilities: (1) all four
charge carriers in a pair of excitons become four
individual polarons, (2) two holes are paired and two
electrons remain as two polarons and (3) two
electrons are paired and two holes remain as
polarons. A bond gets broken only in the possibility
(2) and it will remain broken even after switching-off
the illumination. However, the effect of the possibi-
lities (1) and (3) will disappear after the illumination
is switched-off and all excitons have either recom-
bined radiatively or non-radiatively. Thus, only
possibility (2) contributes to the metastable photo-
darkening and possibilities (1) and (3) to transient
photodarkening.
The pairing of holes on a bond breaks the bond
causing an increase in interatomic separation. The
localization of a hole on a weak bond also increases
the length of the bond. These two effects contribute to
the increase in volume by illumination.
J. Singh / Applied Surface Science 248 (2005) 50–55 53
3. Photoluminescence
Four possibilities for the excitonic radiative
recombination are considered: (i) both excited
electrons and holes are in their extended states, (ii)
electrons are in the extended and holes in tail states,
(iii) electrons are in tail and hole in extended states and
(iv) both are in their tail states. There are two different
forms of electron–photon, and hence, exciton–photon
transition matrix elements used for amorphous solids
[1]. Using these two different forms and applying
Fermi’s golden rule, two different forms of rates of
spontaneous emission for the possibilities (i)–(iii) are
obtained under thermal equilibrium as:
Rs p1 ¼ e2Lmx
4e0�h3n2ð�hvÞ
ð�hv� E0Þ2
exp�ð�hv� E0Þ
kBT
� �Qð�hv� E0Þ (4)
and
Rs p2 ¼ m3xe2a2
ex
2p2e0n2�h7vrA
�hvð�hv� E0Þ2
exp�ð�hv� E0Þ
kBT
� �Qð�hv� E0Þ; (5)
where E0 ¼ Ec � Ev is the energy difference between
an excited pair of electron and hole prior to their
recombination, e the electronic charge, e0 the permit-
tivity of vacuum, L the average bond length in a
sample, mx and aex the excitonic reduced mass and
Bohr radius, respectively, n the refractive index of the
material, v the coordination number of the valence
electrons per atom, rA the atomic mass density per
unit volume and £v is the energy of the emitted
photon. Q(£v � E0) is a step function used to indicate
that there is no radiative recombination for £v < E0
and kB is the Boltzmann constant.
For possibility (iv), where both electrons and holes
have relaxed down in the tail states before their
radiative recombination, their envelope wave func-
tions become localized [1]. Therefore, the transition
matrix element changes and then the corresponding
two rates of spontaneous emission are obtained as:
Rspti ¼ Rs piexp ð�2t0eaexÞ; i ¼ 1; 2; (6)
where the subscript spt stands for the spontaneous emi-
ssion from tail-to-tail states, t0e ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2m�
eðEc � EeÞp
=�hwith m�
e being the effective mass of electron and
aex = (5mea0)/(4mx) is the excitonic Bohr radius in
the tail states, where m is the reduced mass of electron
in the hydrogen atom, e the static dielectric constant and
a0 = 0.529 A is the Bohr radius.
4. Results
To estimate the photodarkening, we use the phonon
energy = 344 cm�1 for the symmetric stretching mode
of AsS3/2 units [1] and applying Toyozawa’s criteria
[1] of strong electron–phonon interaction as Ee p � T,
we get T = 12.3 meV and DEhh = 0.12 eV for a-As2S3,
which agrees well with the value of 0.16 eV estimated
from experiments [1].
The effective masses of electron and hole, required
for calculating the rates in Eqs. (4)–(6), have recently
been derived for amorphous solids [1]. Accordingly,
one gets different effective masses for a charge carrier
in its extended and tail states, and for sp3 hybrid
systems the electron effective mass is found to be the
same as the hole effective mass. Thus, in a sample of a-
Si:H with 1 at.% weak bonds contributing to the tail
states, we get the effective mass of a charge carrier in
the extended states as m�ex ¼ m�
hx ¼ 0:34 me and in the
tail states as m�et ¼ m�
ht ¼ 7:1 me.
For determining E0, it is assumed that the peak of
the observed PL intensity occurs at the same energy as
that of the rate of spontaneous emission obtained in
Eqs. (4) and (5). The PL intensity as a function of 9v
has been measured in a-Si:H [14,17,20]. From these
measurements, the photon energy corresponding to the
PL peak maximum can be determined. By comparing
the experimental energy thus obtained with the energy
corresponding to the maximum of the rate of
spontaneous emission, one can determine E0. Wilson
et al. [14] have measured the PL intensity as a function
of the emission energy in a-Si:H at 15 K, Stearns [20]
at 20 K and Aoki et al. [17] at 3.7 K. The values of Emx
estimated from these three measurements at 3.7, 15
and 20 K are obtained as 1.360, 1.428 and 1.450 eV,
respectively. The values of Emx are well below the
mobility edge Ec by about 0.44 eVat 3.7 K and 0.4 eV
at 15 and 20 K. This means that most excited charge
carriers have relaxed down below their mobility edges
in these experiments. Using these values of Emx and
the corresponding lattice temperature in Eqs. (4) and
(5), the values of E01 and E02 are found to be the same,
J. Singh / Applied Surface Science 248 (2005) 50–5554
i.e., E01 = E01 = E0 = 1.359, 1.398 and 1.447 eVat 3.7,
15 and 20 K, respectively.
For calculating the maximum rate for the possi-
bility (i), the required excitonic reduced mass is
obtained as mx = 0.17me and the excitonic Bohr radius
as 4.67 nm. For the possibilities (ii) and (iii), where
one of the charge carriers of an exciton is in its
extended states and the other in its tail states, we get
mex = 0.32me and the corresponding excitonic Bohr
radius is 2.5 nm. The rates for all three of these
possibilities calculated from Eqs. (4) and (5) are found
to be of the same order of magnitude �108 s�1 at 15–
20 K and �107 s�1 at 3.7 K. For the possibility (iv),
we get mex = 3.55me, aex = 2.23 A and
t0e = 1.29 1010 m�1. Using these in Eq. (6), we get
rates one to two orders of magnitude lower than those
of possibilities (i)–(iii). The corresponding radiative
lifetime, ti = 1/Rs pi for the possibilities (i)–(iii) is
found in the ns time range at 15–20 K and in the ms
range at 3.7 K. For the possibility (iv), the radiative
lifetime is much slower in the ms range.
5. Discussion
It is shown that the excited like charge carriers pair
on a bond due to strong carrier–lattice interactions in
a-Chs because energetically such an excited state is
more stable. Thus, the energy of paired holes on a
bond moves up further in the lone-pair orbitals and tail
states, which expands the valence bands. A similar
situation occurs by pairing of electrons in the anti-
bonding orbitals that lowers the conduction mobility
edge. These two effects together reduce the band gap.
The reduction calculated here in a-As2S3 is about
0.12 eV, which agrees quite well with 0.16 eV
estimated experimentally.
It has been established [1] that pairing of holes on a
bond breaks the bond as soon as two excited holes get
localized on it. This is the essence of the pairing-hole
theory of creating light-induced defects in a-Chs,
which are reversible by annealing. However, pairing of
excited electrons does not break a bond, it only
reduces the band gap and such an excited state will be
reversed back to the normal after switching the
illumination off. This can be applied to explain the
metastable and transient PD. The former occurs due to
pairing of holes that breaks the bond and that cannot
be recovered by stopping the illumination. It remains
metastable. The latter occurs due to pairing of
electrons and formation of polarons which reverse
back to normal after the illumination is stopped.
Usually, the transient PD is observed more in
percentage than metastable PD at higher temperatures.
This is because there are three processes contributing
to the transient PD: pairing of electrons, formation of
positive charge polarons and negative charge polarons,
in comparison with only one channel of pairing holes
contributing to metastable PD.
The breaking of bonds expands the interatomic
separation, and hence, can expand the volume of a
flexible structure like those of a-Chs. Thus, all three
processes, bond breaking, photodarkening and volume
expansion, occur in a flexible structure due to very
strong carrier–phonon interaction.
For the photoluminescence, rates of spontaneous
emission due to radiative recombinations of excitons
are derived and found to be independent of the
excitation density but they increase as the PL energy
increases, and hence, the radiative lifetime becomes
shorter, which is quite consistent with the observed
results [16,17]. We have calculated different values of
E0 at different values of Emx. Such a change in E0 can
only be possible in amorphous solids, which do not
have well defined energy gap, and therefore, the
excited charge carriers can relax down to different E0
through the four different possibilities.
According to the above results of the present theory
and taking into account the Stokes shift of about
0.4 eV, the radiative lifetime measured in the ns range
by Wilson et al. [14] at 15 K, by Stearns [20] at 20 K,
and that in the ms range by Aoki et al. [17] at 3.7 K
may be attributed to the radiative recombination of
singlet excitons through the possibility (ii).
Wilson et al. [14] and Aoki et al. [17] have also
observed slower lifetimes but in the ms range, which
may be attributed to the radiative recombination of
geminate pairs through the possibility (iv). As an
exciton relaxes to the tail states, its Bohr radius is
retained but not its excitonic motion due to localiza-
tion. It becomes a geminate pair. Thus, in a-Si:H two
types of geminate pairs are possible: (i) from excitons
and (ii) from other excited electrons and holes. Latter
are likely to have larger separation, and hence, slower
radiative lifetime. Such slower lifetime has recently
been observed [17].
J. Singh / Applied Surface Science 248 (2005) 50–55 55
Acknowledgements
This work is supported by the ARC large Grant
(2000–2003) and ARC IREX (2001–2003) Grant
Schemes.
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