VOLUME 77, NUMBER 22

PHYSICAL REVIEW LETTERS

25 NOVEMBER 1996

Electronic Structure of Band-Tail Electrons in a Si:H
T. Umeda,1,2 S. Yamasaki,1, * J. Isoya,1,3 A. Matsuda,4 and K. Tanaka1,2
1

Joint Research Center for Atom Technology (JRCAT)– National Institute for Advanced Interdisciplinary Research (NAIR),
1-1-4, Higashi, Tsukuba, 305, Japan
2
Institute of Materials Science, University of Tsukuba, Tsukuba, 305, Japan
3
University of Library and Information Science, 1-2, Kasuga, Tsukuba, 305, Japan
4
Electrotechnical Laboratory, 1-1-4, Umezono, Tsukuba, 305, Japan(Received 1 July 1996)
Electronic structures of the light-induced electron spin resonance (LESR) centers in undoped a-Si:H
have been investigated by means of pulsed ESR techniques. Overlapping LESR signals of g ­ 2.004
and 2.01 have been experimentally deconvoluted by using the difference in spin-lattice relaxation time
between the two signals. The 29Si hyperfine structures of the 2.004 signal clearly show that the wave
function of this center spreads mainly over two Si atoms, which suggests that the origin of g ­ 2.004
is electrons trapped at antibonding states of weak Si-Si bonds. [S0031-9007(96)01759-0]
PACS numbers: 71.55.Jv, 61.43.Dq

In hydrogenated amorphous silicon (a-Si:H), two different light-induced ESR (LESR) signals of g ­ 2.004
and 2.01 have been detected at low temperatures and under illumination [1], in addition to the dark ESR signal ofg ­ 2.0055 that has been generally identified as a neutral
dangling bond signal [2–4]. Street et al. [5] concluded,
on the basis of the study of doping as well as photoluminescence experiments, that the LESR signals in undopeda-Si:H could be ascribed to conduction-band-tail electronssg ­ 2.004d and valence-band-tail holes sg ­ 2.01d. Yamasaki et al. [6] have succeeded in detecting hyperfine
1(hf) structures of 29Si (a nuclear spin of I ­ 2 , naturalabundance of 4.7 at. %) of the LESR spectrum using apulsed ESR technique, and discussed the nature of the
LESR centers. However, due to the overlapping of two
ESR signals of g ­ 2.004 and 2.01 which are broadened by the random orientation and site-to-site variationof structures, the observed spectrum could not be deconvoluted into the two independent hf structures, which isnecessary for more detailed arguments.
In this Letter, we present the first deconvoluted LESR
spectra of g ­ 2.004 and 2.01 signals in undoped a-Si:H,
which were experimentally obtained by a combinationof two different techniques; one is the deconvolution of
the spectra by making use of the difference in a spinlattice relaxation time sT1 d between two signals, and theother being pulsed ESR measurements on a-Si:H samples
involving different amounts of 29Si (9.1, 4.7, 1.6 at .%).
By analyzing the 29Si hf structures of the deconvoluted
spectra of g ­ 2.004 and 2.1 signals, it is demonstrated
that LESR spin centers with g ­ 2.004 originate fromelectrons trapped at the antibonding states of weak SiSi bonds.
Undoped a-Si:H samples were deposited by the rf-glow
discharge technique from SiH 4 with f29 Sig ­ 9.1, 4.7,
and 1.6 at. % on a metal foil at a temperature of 250 ±C.
Deposited flakes (about 1 mm in thickness) were collected

in quartz tubes for ESR measurements. The spin densitiesof those samples were in the range from 1 3 1015 to
4 3 1015 cm23 .
LESR spectra were determined by the technique ofelectron spin echo of pulsed ESR in order to obtain awide-dynamic-range ESR signal [7]. In the echo-detected
ESR technique the spectrum is obtained by recording theamplitude of the spin echo as a function of magnetic-fieldstrength. In order to reduce the contribution of the g ­2.0055 signal to a whole LESR signal, LESR spectra were
measured at 30 K under illumination using a Ti-sapphirelaser (hn ­ 1.7 eV, penetration depth for undoped a-Si:H,10 mm, output power ­ 30 mWycm2 ). Under thoseconditions, the peak height of the LESR spectrum wasmore than 20 times larger than that of the dark ESR
spectrum. We used a microwave frequency of 11 GHz
for the ESR measurements so that the overlapping of the
2.004 and 2.01 signals was reduced below the case ofstandard X-band s,9 GHzd measurements [8].
Figure 1 shows the LESR spectra of the samples withdifferent contents of 29Si, which were determined by a twopulse Hahn echo-detected ESR technique (90± pulse-t180± pulse-t-echo) [7]. A repetition time (RT) of 10 ms ofpulse sequences was used for ensuring a complete recoveryof the spin system to the equilibrium state, by which
the obtained spectra become equivalent to the absorption
spectra of a conventional cw-ESR. As is seen in Fig. 1,
base lines of the echo-detected ESR spectra are very
flat because the echo signals can be picked up under amicrowave-free condition, resulting in a wider dynamic
range of the spectra than that of conventional cw-ESR
spectra [7]. In the tail region, where the magnetic field ishigher than 392.5 mT, a long tail is clearly observed, andits intensity increases with the increase of the 29Si content
of each sample. Actually, the integrated area of the tailstructure of each sample was found to be proportional to
the 29Si content of each sample, indicating that the tail4600

© 1996 The American Physical Society

0031-9007y96y77(22)y4600(4)$10.00

VOLUME 77, NUMBER 22

PHYSICAL REVIEW LETTERS

25 NOVEMBER 1996

FIG. 1. LESR spectra at 30 K of undoped a-Si:H with
f29 Sig ­ 9.1, 4.7, and 1.6 at. %, which were determinedby the two-pulse Hahn echo-detected ESR technique st ­240 ns, RT ­ 10 msd. The spectra were normalized to theirpeak heights. Two vertical thin lines indicate the magnetic
fields at which we have measured Tl .

FIG. 2. LESR spectra of the 29Si-enriched sample, whichwere determined by echo-detected ESR using (i) two-pulse
Hahn echo (t ­ 240 ns, RT ­ 0.5 ms) and (ii) three-pulse
stimulated echo (t ­ 240 ns, t 0 ­ 1 ms, RT ­ 0.5 ms). For
comparison, the spectrum of the 29Si-enriched sample in Fig. 1
is also shown by a dashed line.

structure on the higher-field side originates from 29Si hf
interactions.
The spin-lattice relaxation curves of the LESR centers
for the 29Si-enriched sample sf29 Sig ­ 9.1%d were directly
measured by a pulse sequence of three-pulse inversion recovery (180± pulse-t-90± pulse-t-180± pulse-t-echo; t isscanned) at the magnetic field of 388.0 and 391.2 mT corresponding to g ­ 2.004 and 2.01, respectively. The values of T1 at 30 K for g ­ 2.004 and 2.01 were determined
to be 1.3 ms and 0.47 ms, respectively. Thus, the T1 valueof g ­ 2.01 is about one-third of that of g ­ 2.004, which
may be caused by a difference in electronic structure between the 2.01 and 2.004 spin centers.
When we use a RT of 0.5 ms for echo-detected ESR,the 2.01 signal becomes relatively stronger than the
2.004 signal simply because the 2.01 signal has a shorterrecovery time (i.e., T1 ). On the other hand, when we
adopt the three-pulse stimulated echo (90± pulse-t-90±
pulse-t 0 -90± pulse-t-echo, t ­ 240 ns, t 0 ­ 1 ms, RT ­10 ms) for measuring the echo-detected ESR, the 2.01
signal is relatively suppressed because T1 , in this case,gives the decay time of the echo signal with respect tot 0 [7], resulting in a faster decay of the 2.01 signal. In
this way, we obtained two echo-detected ESR spectrawith different relative intensities between 2.01 and 2.004
signals, which are shown in Fig. 2.
The two spectra in Fig. 2 were deconvoluted into two
independent spectra by subtracting one from the other tocancel out either the 2.004 or the 2.01 signal alternatively,
except for the region of strong overlap of the two signals
where a deconvolution is difficult due to complexities
such as T1 distributions and cross relaxation. The resultof deconvolution of the two spectra of Fig. 2 is shown in
Figs. 3(a) and 3(b), respectively.
As is clearly seen in the figure, the hf structure observedon the high-field side belongs mainly to the g ­ 2.004

signal. The area fraction of the hf structure depends on
the number of Si atoms, N, on which an electron spinis mainly located. The probability that all N Si atoms
have no nuclear spin ( 28Si or 30Si) is s1 2 pdN , where

FIG. 3. Deconvoluted spectra of the LESR (g ­ 2.004, 2.01)
of undoped a-Si:H. The solid lines indicate the deconvoluted
2.004 and 2.01 spectra with a high reliability in data analyses, while the dashed lines include some ambiguity. (a) Deconvolution of the spectrum (i) in Fig. 2 and the dark ESR
spectrum of boron (0.89 at. %)-doped a-Si:H (Ts ­ 200 ±C,
measured at 50 K). (b) Deconvolution of the spectrum (ii)in Fig. 2. Shadow regions show the high-field-side hyperfine
structure of 29Si.

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VOLUME 77, NUMBER 22

PHYSICAL REVIEW LETTERS

p is the number fraction of 29Si atoms in the total Si
atoms. Therefore, the fraction of hf structure for the caseof small N and p ø 1 should be 1 2 s1 2 pdN , although
this includes the small probability for two or more 29Si
atoms to be members of N Si atoms. The area of the highfield-side hf structure, which should correspond to onehalf of the area of the entire hf structure, was estimatedto be 20 6 3% [9] of the total area of the high-field-side
spectrum of g ­ 2.004,(1)
1 2 s1 2 pdN ­ 0.2 6 0.03 .
Using the actual value of p in this experiment, p ­ 0.091,
N ­ 2.3 6 0.4(2)
is obtained, and therefore it is concluded that the wave
function of the 2.004 center spreads mainly over two Si
atoms. The obtained value of N seems to be larger than
2 within some fluctuation. One possible origin might be
the contribution from a slight spreading of the wave function on back-bonded Si atoms, but the present experimental data is insufficient for more detailed discussion. We
also confirmed this result for the case of p ­ 4.7%. For
p ­ 1.6%, it was rather difficult to analyze the spectrum
because of a small fraction of 29Si. In this discussion weassumed that the electron wave function spreads over N Si
atoms uniformly, although the actual wave function may
fluctuate among N Si atoms. However, the fluctuation contributes only to the linewdith of the hf structure and does
not affect the above conclusion. Previously, Yamasaki etal. [6] were the first to report the hf structure of LESR
spectra in undoped a-Si:H, and tentatively speculated thatthe wave function of the LESR spin centers is localized
on a single Si atom simply because a ratio of the area ofthe hf structure to a total area of the whole LESR spectrum (2.004 1 2.01 signals) was close to the 29Si content.
However, by the present detailed study of the spectrum deconvolution, it has been clarified for the first time that the2.01 signal does not contribute to the high-magnetic-fieldside hf structure; only the 2.004 signal does.
The isotropic hf splitting which arises mainly from the
3s character in the wave function of the g ­ 2.004 center
was estimated to be about 7 mT which is almost as large
as that of the neutral dangling bond signal (g ­ 2.004)[2,4]. Since the isotropic hf splitting due to the 3s orbitalon 29Si has been theoretically calculated to be 149.0 mT[2], the component of the 3s orbital in the wave functionof the 2.004 center is estimated to be about 5%. In
contrast to the g ­ 2.004 signal, the g ­ 2.01 signal
apparently does not show any hf structure, from which
the isotropic hf splitting of the 2.01 signal was roughly
estimated to be below 5 mT; in other words, the isotropic
hf splitting of the 2.01 signal should be smaller than thatof the 2.004 signal. Furthermore, it should be pointed
out that the deconvoluted 2.01 signal is quite similar tothe dark ESR signal of g ­ 2.01 in boron (0.89 at. %)doped a-Si:H, as is also shown by the dashed curve in
Fig. 3(a). The 2.01 signal of B-doped a-Si:H does not
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25 NOVEMBER 1996

show any discernible hf structures, being almost identicalto the present deconvoluted 2.01 signal.
So far, two models have been proposed for the originsof the LESR signals. The first one pictures electrons orholes trapped at band-tail states originating from weak
Si-Si bonds [10]. In an amorphous network, it is quitepossible that largely elongated covalent bonds (weakbonds) are present and give rise to energy levels in the
tail regions of the conduction and valence bands. In
this case, when an electron is trapped in an antibonding
state, its wave function is expected to extend over thetwo Si atoms associated with the weak Si-Si bond. In
the second model for LESR centers, electrons and holes
are trapped at positively and negatively charged dangling
bonds, resulting in the formation of neutral dangling
bonds with g ­ 2.004 and 2.01, respectively [6,11], which
are thought to be similar to the neutral dangling bondobserved in the dark. This model essentially originatedfrom the charged defect model for chalcogenide glasses,
where negative correlation energy plays an importantrole [12]. However, a neutral dangling bond state ischaracterized by an electron localized on a single Si atom
[2–4], which is inconsistent with the present results on
the g ­ 2.004 LESR signal.
Consequently, the present results suggest that the origin of the LESR signal of g ­ 2.004 is electrons trappedat weak Si-Si bonds whose antibonding states are located at the conduction-band tail, rather than electrons
trapped at positively charged dangling bonds.
Although detailed information on the g ­ 2.01 center
was not obtained in this study, it is reasonable to consider,by analogy with the g ­ 2.004 signal, that it originatesfrom holes trapped in the bonding states of the weakbonds located in the valence-band tail. Katagiri calculated
electronic structures of negatively and positively charged
weak bonds using the ab initio method, in which a bondlength of the positively charged weak bond was shorter
than that of the negatively charged one [13]. From that
result, it is speculated that the wave function of the 2.01
center may be shifted towards the bond center of the weakbond compared to that of the 2.004 center, resulting inless density of an unpaired electron of the 2.01 center at
Si nuclei associated with the weak bond. This might be
the reason why the hf splitting of the 2.01 signal is smaller
than that of the 2.004 signal.
The deconvoluted signal of g ­ 2.004 shows hf splittingof about 7 mT, which is similar to the value for neutral
dangling bonds [2,4]. Using the linear combination of
atomic orbitals (LCAO) expansion, the wave
P function jcl
of an unpaired electron is written as jcl ­ i ai ssi j3sl 1
pi j3pld, where j3sl and j3pl denote the atomic 3s and3p orbitals of Si, i indexes all atoms within the extent of
the wave function jcl, and the projection coefficientsai ,P
si , and pi , obey the normalization conditions i ai2 ­1, si2 1 pi2 ­ 1 for all i. The experimental value of 7 mT
for hf splitting means a12 s12 , 0.05 for neutral dangling

VOLUME 77, NUMBER 22

PHYSICAL REVIEW LETTERS

bonds sg ­ 2.0055d, where an atom of i ­ 1 represents athreefold-coordinated Si atom, and(3)
a12 s12 , a22 s22 , 0.05
for the 2.004 center, where atoms of i ­ 1 and 2 represent
Si atoms associated with the weak bond, respectively.
For the case of the neutral dangling bond, Stutzmann
and Biegelsen [2] reported that a12 , 50% and s12 ,10% [4], and the ratio of 3s to 3p character ss12 yp12 d
1
is estimated to be about 9 . As compared with strongly
localized dangling bonds, for the signal of g ­ 2.004, it
is reasonable to consider that the densities of the wave
function of this center on two Si atoms, i.e., a12 and a22
are rather less than 50%. Therefore, to satisfy Eq. (3),s12 and s22 should be higher than 10%. Namely, the 3sto 3p-character ratio for the 2.004 center should be higher
than that for the dangling bond.
The ratio of s 2 yp 2 is related to the angle between adangling (or weak) bond and back bonds, i.e., a ratioof zero means a p electron on a sp 2 -network planer
1
structure, while a ratio of 3 means a tetrahedral structure.
In the case of the 2.004 center, s12 yp12 and s22 yp22 should
be higher than s12 yp12 for the neutral dangling bond.
Therefore, it is speculated that the bonding structure of the
2.004 center is closer to a tetrahedral structure than thatof the neutral dangling bond which may be characterized
as a planar structure since its wave function consists ofmostly p character [2–4]. Likewise, the smaller isotropic
hf splitting of the 2.01 signal in comparison to thatof the 2.004 signal seems to indicate that the atomic
configuration of the 2.01 center is closer to a planar
structure than that of the 2.004 center [14].
In conclusion, LESR spectra in 29Si enriched a-Si:H(9.1 at. %) were deconvoluted into two signals of g ­2.004 and g ­ 2.01 centers by pulsed ESR techniques
using the difference in the spin-lattice relaxation time
between the two signals. It was pointed out that the hf
structure at the high-magnetic-field side of LESR spectra
originates mainly from the signal of g ­ 2.004. On thebasis of careful data analyses it was demonstrated thatthe wave function of the 2.004 center is spread mainly
over two Si atoms, which suggests that the origin of the
2.004 center is electrons trapped at antibonding statesof the weak Si-Si bonds located at the conduction-band
tail rather than those trapped at the positively charged
dangling bonds.
We thank H. Katagiri and N. Ishii for valuable suggestions regarding the theoretical aspect. This work, partly
supported by NEDO, was performed at the Joint Re-

25 NOVEMBER 1996

search Center for Atom Technology (JRCAT) under thejoint research agreement between the National Institutefor Advanced Interdisciplinary Research (NAIR) and theAngstrom Technology Partnership (ATP).

*Permanent address: Electrotechnical Laboratory, 1-1-4,
Umezono, Tsukuba, 305, Japan.
[1] J. C. Knights, D. K. Biegelsen, and I. Solomon, Solid State
Commun. 22, 133 (1977).
[2] M. Stutzmann and D. K. Biegelsen, Phys. Rev. B 40, 9834
(1989), and references therein.
[3] N. Ishii and T. Shimizu, Phys. Rev. B 42, 9697 (1990).
[4] We have also confirmed this conclusion from analysesof echo-detected ESR measurements, which will be
published elsewhere.
[5] R. A. Street, D. K. Biegelsen, and R. L. Weisfield, Phys.
Rev. B 30, 5861 (1984).
[6] S. Yamasaki, H. Okushi, A. Matsuda, K. Tanaka, and
J. Isoya, Phys. Rev. Lett. 65, 756 (1990).
[7] J. Isoya, S. Yamasaki, A. Matsuda, and K. Tanaka, Philos.
Mag. B 69, 263 (1994); J. Isoya, S. Yamasaki, H. Okushi,
A. Matsuda, and K. Tanaka, Phys. Rev. B 47, 7013 (1993).
[8] When two signals have a constant (­ frequencyindependent) width or a constant component in theirwidth, in higher frequency the overlapping of two signals
corresponding to different g values should be reduced.
In the present case, as is shown in Fig. 1, there areappreciable frequency-independent contributions to thesignal width by small 29Si hf splittings.
[9] The value of 20 6 3% was obtained on the assumptionthat the tail region of the main peak of g ­ 2.004 decays
exponentially with respect to the magnetic field. In orderto check the validity of this assumption we applied thesame procedure to a dangling bond ESR spectrum of thesample enriched by 9.1 at. % of 29Si. As a result, the ratioof 29Si hf structure to the total signal area was obtained as
9 6 2%, which indicates that the assumption is reasonablebecause the wave function of this spin center is locatedmainly on a single Si atom [2–4].
[10] M. Stutzmann, W. B. Jackson, and C. C. Tsai, Phys. Rev.
B 32, 23 (1985).
[11] K. Morigaki, J. Phys. Soc. Jpn. 50, 2279 (1981); D. Adler,
Solar Cells 9, 133 (1983); H. M. Branz, Phys. Rev. B 41,
7887 (1990).
[12] R. A. Street and N. F. Mott, Phys. Rev. Lett. 35, 1293
(1975); S. G. Bishop, U. Strom, and P. C. Taylor, Phys.
Rev. Lett. 34, 1346 (1975); S. G. Bishop, U. Strom, andP. C. Taylor, Phys. Rev. Lett. 36, 543 (1976).
[13] H. Katagiri, Solid State Commun. 95, 143 (1995).
[14] N. Ishii, Solid State Commun. (to be published).

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