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: jai.singh@cdu.edu.au.

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.

References

[1] J. Singh, K. Shimakawa, Advances in Amorphous

Semiconductors, Taylor & Francis, London/New York, 2003.[2] D.A. Jun Li, Drabold, Phys. Rev. Lett. 85 (2000) 2785.

[3] T. Uchino, D.C. Clary, S.R. Elliott, Phys. Rev. Lett. 85 (2000)

3305.

[4] K. Shimakawa, A. Kolobov, R. Elliott, Adv. Phys. 44 (1995)

475.

[5] Ke. Tanaka, Phys. Rev. B 57 (1998) 5163.

[6] K. Shimakawa, N. Yoshida, A. Ganjoo, Y. Kuzakawa, J. Singh,

Philos. Mag. Lett. 77 (1998) 153.

[7] A. Ganjoo, K. Shimakawa, K. Kitano, E.A. Davis, J. Non-

Cryst. Solids 299–302 (2002) 917.

[8] M.I. Klinger, V. Halpern, F. Bass, Phys. Status Solidi b 230

(2002) 39.

[9] J. Singh, Chem. Phys. Lett. 149 (1988) 447.

[10] P.W. Anderson, Phys. Rev. Lett. 34 (1975) 953.

[11] N.F. Mott, E.A. Davis, R.A. Street, Philos. Mag. 32 (1975) 961.

[12] R.A. Street, N.F. Mott, Phys. Rev. Lett. 35 (1975) 1293.

[13] M. Kastner, D. Adler, H. Fritzsche, Phys. Rev. Lett. 37 (1976)

1504.

[14] B.A. Wilson, P. Hu, J.P. Harbison, T.M. Jedju, Phys. Rev. Lett.

50 (1983) 1490.

[15] R. Stachowitz, M. Schubert, W. Fuhs, J. Non-Cryst. Solids

227–230 (1998) 190.

[16] S. Ishii, M. Kurihara, T. Aoki, K. Shimakawa, J. Singh, J. Non-

Cryst. Solids 266–269 (1999) 721.

[17] T. Aoki, T. Shimizu, D. Saito, K. Ikeda, Presented at the 13th

International School of Condensed Matter Physics (13 ISCMP),

30 August–3 September, 2004, Varna, Bulgaria, and references

therein, J. Optoelectron. Adv. Mater. 7 (2005) 137.

[18] J. Singh, T. Aoki, K. Shimakawa, Philos. Mag. B 82 (2002)

855.

[19] T. Holstein, Ann. Phys. 8 (1959) 325.

[20] D.G. Stearns, Phys. Rev. B 30 (1984) 6000.