PHYSICAL REVIEW B

VOLUME 59, NUMBER 7

15 FEBRUARY 1999-I

Electron-spin-resonance center of dangling bonds in undoped a-Si:H
T. Umeda
Joint Research Center for Atom Technology (JRCAT), National Institute for Advanced Interdisciplinary Research (NAIR),
1-1-4, Higashi, Tsukuba, 305, Japanand Institute of Materials Science, University of Tsukuba, Tsukuba, 305, JapanS. Yamasaki
Joint Research Center for Atom Technology (JRCAT), National Institute for Advanced Interdisciplinary Research (NAIR),
1-1-4, Higashi, Tsukuba, 305, Japan

J. Isoya
Joint Research Center for Atom Technology (JRCAT), National Institute for Advanced Interdisciplinary Research (NAIR),
1-1-4, Higashi, Tsukuba, 305, Japanand University of Library and Information Science, 1-2 Kasuga, Tsukuba, 305, Japan

K. Tanaka
Joint Research Center for Atom Technology (JRCAT), National Institute for Advanced Interdisciplinary Research (NAIR),
1-1-4, Higashi, Tsukuba, 305, Japanand Institute of Materials Science, University of Tsukuba, Tsukuba, 305, Japan~Received 5 October 1998!
A variety of electron-spin-resonance ~ESR! spectra of dangling bond (g52.0055) in undoped hydrogenatedamorphous silicon (a-Si:H) have been measured by the echo-detected ESR of pulsed ESR as well as the usual
continuous-wave ~cw! ESR for a wide range of two experimental parameters of microwave frequency ( n
53 – 34 GHz) and 29Si content ~p51.6, 4.7, 9.1 at. %!. Using those spectra, we have carried out spectral
simulations on the whole dangling bond spectrum ~a primary line and 29Si hf structure!, and also havesimulated n and p dependence of the spectra. From detailed simulation analyses, we confirmed a previous
identification of the dangling bond center by Stutzmann and Biegelsen @Phys. Rev. B 40, 9834 ~1989!#, andraised the reliability of ESR parameters; isotropic and anisotropic 29Si hyperfine interactions were determined
to be approximately 7.4 and 2.1 mT, respectively, and g i 52.0039, g' 52.0065. The ESR parameters indicatethat the dangling bond center is localized predominantly on a single Si atom and is characterized as strongly p
like, which are consistent with the case of the dangling bond at the interface between crystalline Si and SiO2,
the P b center. @S0163-1829~99!01307-7#

I. INTRODUCTION

Amorphous silicon (a-Si) and hydrogenated amorphoussilicon (a-Si:H) contain threefold-coordinated Si atoms, i.e.,
dangling bonds ~DB’s! with a density of 1018– 20 and
1015– 18 cm23 for a-Si and a-Si:H, respectively.1,2 The incorporation of a great number of hydrogen ~10–20 at. %! greatly
reduces the DB’s.2 However, low-defect-density(,1017 cm23) a-Si:H responds with the creation of additional metastable DB’s to strong illumination.3–5 The metastable DB’s are created in bulk regions up to a density of1017 cm23 and can be annihilated completely by thermal annealing ~> 150 °C!. The microscopic mechanism of suchcreation and annihilation has not been clarified yet, although
they were discovered more than 20 years ago. Therefore,
microscopic and electronic structures of the DB’s have been
investigated intensively, and further information is still required.
The DB in a-Si:H shows an electron-spin-resonance~ESR! signal with a g value ~g! of 2.0055,1,4 which is shownin Fig. 1. This signal involves weak signals of the hyperfine~hf! structure of 29Si ~natural abundance of 4.7 at. %, nuclear
0163-1829/99/59~7!/4849~9!/$15.00

PRB 59spin of I5 21 ! which are indicated by arrows in the figure, in
addition to a strong primary line. 29Si hf splittings originate
from the magnetic interactions between 29Si nuclei and an
unpaired electron, from which the distribution of the unpaired electron relative to positions of 29Si nuclei can berevealed. For example, for DB’s on the surface of crystalline
Si~111! covered by SiO2, the P b centers also show a 29Si hf
structure in their ESR spectrum. Detailed analyses clarified
that an unpaired electron of the P b center distributes on one
Si atom by 82% where the electron wave function consists of
3s and 3 p orbitals of approximately 10% and 90%,
respectively.6,7 On the other hand, the DB spectrum of
a-Si:H convolutes the powder pattern as well as causes alarge signal broadening due to its amorphous nature. Therefore, it is difficult to determine principal values of the hf andg tensors, unlike the case of the P b center.
A first analysis on 29Si hf interactions of the DB center in
a-Si:H was reported by Biegelsen and Stutzmann.8 They observed doublet 29Si hf lines using a heavily 29Si-enriched ~93
at. %! sample and determined the isotropic part (A iso) of thestrong 29Si hf interaction from which the fraction of the 3s
orbital in the DB wave function was estimated for the first4849©1999 The American Physical Society

4850

T. UMEDA, S. YAMASAKI, J. ISOYA, AND K. TANAKAPRB 59TABLE I. List of our samples and their characters.

SampleT s 5R.T.

T s 5250 °C

FIG. 1. A typical DB spectrum of undoped a-Si:H with @ 29Si#
54.7 at.% and a spin density of 3.631018 cm23. The spectrum wasmeasured by a standard X-band ~9.4-GHz! continuous wave ~cw!ESR spectrometer with 2.5 h accumulation. Arrows point to hf linesof 29Si.

time.9 In their sample, however, there existed a large numberof 29Si nuclei surrounding a DB site, which caused an extreme broadening of the signal due to weak 29Si hf splittings.
Such a signal broadening smeared out finer features of thestrong 29Si hf interaction. Following the first work, Stutzmann and Biegelsen carried out a detailed simulation of an
X-band ~;10 GHz! ESR spectrum of a natural abundance
sample,9 from which further detailed information was extracted such as the anisotropic hf interaction (A aniso) due tothe 3 p orbital in the DB wave function. As a result, theyreported that the DB center in a-Si:H has approximately
50% of the distribution on one Si atom, which consists of 3s
and 3p orbitals of approximately 10 and 90 %, respectively.
They concluded that the origin of g52.0055 center is welldescribed as the DB, although five-fold-coordinated Si atoms, so-called ‘‘floating bonds’’ ~FB’s!,10 had been suggested for an alternative origin of g52.0055 and the twomodels had been argued intensely.10–18
However, since tails of the strong primary line are superposed on hf lines in Fig. 1, it was very difficult to accurately
deconvolute the 29Si hf structure from the total spectrum. In
order to remove tails of the strong primary line, they made agreat effort to choose a smooth, structureless tail curve thatjoins the main peak of the primary line continuously. The tailcurve was chosen by satisfying three qualifications; ~i! it had
no structure in the second derivative over the region of 29Si
hf lines, and when the tail curve had been subtracted fromthe total spectrum, ~ii! deconvoluted hf lines returned to zerofor separating each hf line, and ~iii! each hf line had an equalarea.9 Choosing a suitable tail curve, they seemed to obtain
the deconvoluted hf structure successfully. We point out,
however, that the best approach is to calculate the whole DB
spectrum ~the primary line and 29Si hf lines! without deconvoluting hf lines, because the results may depend on how thetail curve is chosen. Furthermore, in order to confirm thereliability of ESR parameters determined in the simulation, it
will be necessary to check the simulations for a variety of the
DB spectra; Stutzmann and Biegelsen carried out the spectral
simulation for only one X-band spectrum.
In this paper, we present a detailed simulation study toconfirm the conclusion of Stutzmann and Biegelsen.9 Our

29

Si~at. %!

1

H~at. %!

Ns~cm23!

1.6
4.7
9.1
1.6
4.7
9.1

30.3
11.8
23.7
8.9
6.8
10.7

9.431017
3.631018
1.331018
631015131015431015

simulations have two features: ~a! simulations of the whole
DB spectrum ~a primary line and 29Si hf lines!, and ~b! simulations of the dependence of the DB spectrum on two experimental parameters of microwave frequency ~3–34 GHz! and29
Si content of the sample ~1.6, 4.7, 9.1 at %!. The two experimental parameters can increase ~or reduce! influences ofparticular ESR parameters on the DB spectrum. Furthermore,
we employed the echo-detected ESR technique of pulsed
ESR in order to obtain the ESR spectrum with much flatterbaselines than that of conventional, continuous-wave ~cw!ESR, which is advantageous for analyzing the weak signal of29
Si hf lines. From detailed simulation analyses over a wide
range of the two experimental parameters, principal values of
the g and hf tensors, A iso and A aniso were determined withhigh reliability. Finally, we compare our results with those of
Stutzmann and Biegelsen as well as those for the P b center.
II. EXPERIMENTAL DETAILSMost of the ESR measurements on a-Si:H have been carried out by a standard X-band ~9–10 GHz! spectrometer so
far.1,2,8,9,12,14,19 In the present work, we used microwave frequencies of 3.0–34 GHz. The microwave frequency of n issimply related with the resonance magnetic field of B r by
h n 5g b B r , where h is the Planck constant and b is the Bohrmagneton. Therefore, the primary line, which is broadened
mainly by the anisotropy of principal g values ~i.e., powder
pattern! and fluctuations of g values, can be narrowed bydecreasing n, while the hf splitting does not change.4 Thus,
the degree of overlapping of the primary line and hf lines canbe experimentally controlled by changing n.
Another parameter, the 29Si contents of the sample ~p!,can determine the relative intensity of hf lines in a total spectrum. We varied the value of p to 1.6 ~diluted!, 4.7 ~naturalabundance!, and 9.1 ~enriched! at. %.
Undoped a-Si:H samples were deposited by the standard
rf-glow discharge technique from SiH4 on a metal foil atsubstrate temperatures (T s ) of room temperature ~R.T.! and250 °C. Deposited samples ~10–40 mg! were collected inhigh-purity vitreous-silica tubes for ESR measurements. The
DB densities (N s ) and hydrogen contents of the samples
were determined using ESR and 1H-NMR, which are summarized in Table I.
ESR measurements of the above samples were carried out
by cw- and pulsed-ESR spectrometers. In cw-ESR measurements, we used a BRUKER ESP300E spectrometer, which
can operate with microwave frequencies of 3.0, 6.5, 9.4–9.8,
and 34 GHz. All cw-ESR spectra were measured at room
temperature under the following conditions: microwave

PRB 59

ELECTRON-SPIN-RESONANCE CENTER OF DANGLING . . .

powers of 0.1 ~34 GHz! and 0.9 mW ~3.0, 6.5, 9.8 GHz!,
field modulation amplitudes in a range from 0.1 mT ~3.0
GHz! to 0.7 mT ~34 GHz! and 100 kHz of a modulation
frequency. In order to get a sufficient signal-to-noise ratio,some spectra were accumulated for several hours.
In pulsed-ESR measurements, we used a home-built
pulsed ESR spectrometer that can operate with frequenciesof 8.2, 9.4, 11 GHz. The pulse widths were 17 and 34 nsec
for 90° and 180° microwave pulses, respectively, and themicrowave field B 1 was estimated to be less than 0.52 mT.
The echo intensity was accumulated by a 50-nsec-wide boxcar gate and then was digitized by a 12-bit A/D converter.
Details of other setups of our spectrometer have been described elsewhere.20,21 The echo-detected ESR spectra are
obtained by recording the amplitude of two-pulse Hahn echo
~90° pulse– t –180° pulse– t –echo! as a function ofmagnetic-field strength. The magnetic field increment waseither 0.04 or 0.1 mT. The echo-detected ESR spectrum isequivalent to an integrated spectrum of cw ESR except for
its much flatter baseline than that of cw ESR because themicrowave pulses are not applied at a time of detecting theecho signal and because phase cycling techniques are
employed.20,21 Pulsed-ESR measurements were carried out at
50 K with t 5240 nsec and 1 msec repetition time of pulse
sequences in order to achieve the highest signal-to-noise ratio. The spin echo signal was often smaller than the cw-ESR
signal, so that the longest accumulation time was prolonged
up to three days.
III. RESULTS AND DISCUSSION
A. Simulation method

It is necessary for determining ESR parameters of the
2.0055 center to perform spectral simulation. We considered
the same spin system as the P b center for the present simulation, namely, ~a! the system has an axial symmetry the axisof symmetry of which coincides with the direction of the 3 p
orbital in the DB wave function, ~b! the electron spin S is1
5,22
and ~c! the
2 and DB’s are isolated from each other,28
nuclear spin I is either zero for DB’s on Si and 30Si atoms,
or 21 for DB’s on 29Si atoms.6,7 Although the DB defects inthe amorphous network are likely to have g and 29Si hf tensors which slightly deviate from axial symmetry, such minor
corrections to our simple model seem to be smeared out by
the large signal broadening due to site-to-site variation of
structure. Hence we apply the above simple model of axial
symmetry.
Under conditions of ~a!–~c!, an effective g value g( u ) anda hf splitting K( u ) are given by23
g ~ u ! 2 5g 2i cos2 u 1g'2 sin2 u~1!

K ~ u ! 2 g ~ u ! 2 5A 2i g 2i cos2 u 1A'2 g'2 sin2 u ,

~2!

and

respectively, where g i ,g' and A i ,A' are principal values of
the g and hf tensors parallel ~i! and perpendicular ~'! to thedirection of the axis of symmetry, respectively. u is the angle
between the axis of symmetry and the applied magnetic field.
Line positions are given by
B r ~ u ! 5h n /g ~ u ! b

for the primary line,

~3a!

4851

and
B6
r ~ u ! 5h n /g ~ u ! b 6K ~ u ! /2

for the 29Si hf lines.
~3b!
Although we calculated line positions of the hf lines in termsof the second order in K,23 they were hardly different fromthe first-order result. Signal intensities P( u ) are calculated
as24
P ~ u ! 5g'2 @ g 2i /g ~ u ! 2 cos2 u 11 # .

~4!

Finally, the ESR spectrum of Y (B) is given by
Y ~ B ! 5C

E

p /2

0

F

d u sin u P ~ u ! ~ 12 p ! f „B2B r ~ u ! ,W ~ u ! …

1p
f „B2B 1
r ~ u ! ,W hf~ u ! …
2 hf

1

p
f „B2B 2
r ~ u ! ,W hf~ u ! … ,
2 hf

G

~5!

where B is the strength of the applied magnetic field, C is anormalizing constant, f and f hf are broadening functions forthe primary and hf lines, and W( u ) and W hf( u ) are full widthat half-maximum of those functions, respectively.
Stutzmann and Biegelsen calculated separately the firstterm ~the primary line! and the last two ~hf lines! in Eq. ~5!.9
They deconvoluted the hf lines from a total spectrum using asmooth, structureless tail curve which joins the main peak of
the primary line continuously. On the other hand, in thepresent work, we calculate the whole spectrum from a combination of three terms in Eq. ~5! without deconvoluting thehf lines, and analyze the dependence of the spectrum on two
experimental parameters of n and p. As a result, our spectral
simulation is not affected by the method of choosing the tailcurve and thus the reliability of ESR parameters is increased.
Although Stutzmann and Biegelsen adopted the Gaussianbroadening function for f and f hf because of random fluctuations arising from the amorphous nature, we need to consider
the broadening function in more detail.
It is considered that the signal broadening is caused by
two dominant mechanisms: ~i! distributions of ESR parameters such as g i ,g' ,A i ,A' due to site-to-site variation of
structures, and ~ii! additional hf interactions such as weak29
Si hf interaction from backbonded Si atoms and from moredistant Si atoms and weak 1H hf interactions from nearby H
atoms.
In regard to the contribution ~i!, the broadening function
may be well described by the Gaussian function because of
random fluctuations of parameters. Now, we define W gi ,W'g
and W Ai ,W'A as full widths at half-maximum of Gaussian
distributions of g i ,g' and A i ,A' in a field dimension, respectively. Equations ~3a! and ~3b! mean that fluctuations ofg and K increase the fluctuation of resonance fields linearly,
assuming a small g-shift. Therefore, we assumed simply thatfull widths at half-maximum of the Gaussian broadening
function increase linearly with g and K themselves,9 thenW ~ u ! 2 5 ~ W gi ! 2 cos2 u 1 ~ W'g ! 2 sin2 u ,~6a!

W hf~ u ! 2 5W ~ u ! 2 1W K ~ u ! 2 ,~6b!

W K ~ u ! 2 5 ~ W Ai ! 2 cos2 u 1 ~ W'A ! 2 sin2 u .

~6c!

where

4852

T. UMEDA, S. YAMASAKI, J. ISOYA, AND K. TANAKAPRB 59

FIG. 2. Illustration of the isotropic hf splittings, A iso-back , due tothree backbonded Si atoms. Two figures show the cases ~a! before
and ~b! after taking into account A iso-back where q512p.

The validity of Eq. ~6a! has been confirmed in the P bspectrum.25 Two kinds of broadening parameters of W gi ,W'g
and W Ai ,W'A are different in their dependence on n. With
increasing n, the former two should increase linearly, while
the latter two should remain constant.
The contribution ~ii! to W and W hf is classified into twogroups. When additional weak hf splittings are comparablewith or are greater than the sizes of W and W hf , it may beinappropriate to describe f and f hf by a single Gaussian function. Such additional hf splittings will be caused by the isotropic hf interactions due to 29Si atoms at three backbondsites of a DB.8,11 Although a first-principles theoretical calculation reported that the next largest isotropic hf splittings
are yielded at some of the next-nearest-neighbor sites of theDB, the number of such sites was also counted to be 3.18
When A iso-back is defined as the average isotropic hf splitting
due to backbonded 29Si, a single line splits into seven lines,
as is illustrated in Fig. 2. Furthermore, even if additional hf
splittings are rather smaller in size than W and W hf , they will
not only increase the broadening width but also affect theline shape. It is known that the line shape is well describedby the cutoff Lorentzian curve rather than the Gaussian curvewhen the density of nuclear spins surrounding the spin centeris very small.26 In fact, it was reported that the line shape ofthe 2.0055 spectrum as well as the P b spectrum is well givenby the Voigt function, which has a medium curve between
the Gaussian and the Lorentzian curves.14,25 As a result, thebroadening widths of W gi ,W'g have a constant component at
n 50 in addition to the component in proportion to n, and weevaluated Eq. ~5! using a group of seven Voigt functions,f „B2B r ( u ),W( u ),y,A iso-back…, for the broadening functionof the primary line, where y is a shape parameter and details
are described in Ref. 27 ~f →Gaussian when y→0, f→Lorentzian when y→`!. For the broadening function of
hf lines, a group of seven Gaussian functions, f hf„B
2B 6
r ( u ),W hf( u ),A iso-back…, was adopted, because hf lines
should be greatly influenced by the Gaussian distribution due
to large A i and A' fluctuations.
The numerical evaluations of Eq. ~5! were carried out by
a numerical integral with an increment angle d u of 0.45°.
The calculated spectra were fitted into experimental spectra

FIG. 3. Cw-ESR spectra of 29Si-diluted undoped a-Si:H (N s
59.4310 17 cm23! at various frequencies. Solid and dashed lines
indicate experimental and calculated spectra, respectively. The bestfit g parameters are also indicated in the figure.

by non-linear least-squares fitting based on the LevenbergMarquardt algorithm28 and, as a result, we determined ESR
parameters.
B. Principal g values and frequency-dependenceof the DB spectrum

As the first step, we determined principal g values, because they determine the general shape of the spectrum. The
primary line exhibits a slight asymmetry in its line shape thatis ascribed to anisotropy of the g tensor.9 In addition, suchanisotropy causes asymmetry of the 29Si hf structure between
the low-and high-magnetic-field sides ~see Fig. 1!.9
The overlapping of resonance lines with different g values
can be reduced as n increases.4 Thus, our Q-band ~34-GHz!
measurements are more powerful for determining g values
than usual X-band ~10-GHz! measurements; for example, a0.001 difference in the g value makes a 0.6-mT difference inresonance fields at 34 GHz as against a 0.17-mT difference
for X-band measurements.
Figure 3 shows experimental first-derivative spectra of29
Si-diluted (p51.6 at. %) undoped a-Si:H with N s 59.4
31017 cm23, which were obtained by cw-ESR measurements at frequencies of 3.0, 6.5, 9.7, and 34 GHz. This
sample is convenient for determining the g parameters because of a lack of the 29Si hf structure.
First, we analyzed the frequency dependence of the line
shape and width of the primary line. Peak-to-peak widths ofthe observed first-derivative spectra DB pp( n ) linearly increased with an increase of n, as is shown in Fig. 4~a!. A
proportionally increasing component in DB pp originates from

PRB 59

ELECTRON-SPIN-RESONANCE CENTER OF DANGLING . . .

4853

Figure 4~a! also shows full widths at half maximum ofintegrated ~i.e., absorption! spectra, DB 1/2 . DB 1/2 increased
with the same slope as DB pp , while the ratio of DB pp to
DB 1/2 decreased as n increased. This means that as n increases, the shape of the primary line changes from theLorentzian curve (DB 1/2 /DB pp51.73) to the Gaussian curve(DB 1/2 /DB pp51.18). In other words, at low n, the line shapeis determined to be the Lorentzian curve due to the influenceof weak hf splittings. On the contrary, the Gaussian fluctuations of g values dominate at high n.
In order to determine principal g values from the observed
spectra in Fig. 3, we carried out the simulation of the spectra
as follows. In this sample, we could simulate the ESR spectrum without including the discernible 29Si hf structure andby neglecting the line splittings due to 29Si hf interactions ofbackbonded Si atoms. Namely, the first term in Eq. ~5! wasonly calculated and we need not consider a number of small
hf lines as shown in Fig. 2~b!. Fitting parameters wereg i ,g' , W gi , W'g ,C,y, where both g i and g' were set to becommon for all the spectra. In Fig. 3, the simulated spectra
are shown by dashed lines. The simulation minimized thesum of deviations among four experimental and fitted spectra, the so-called x-square method. Figure 4~b! shows thelinearity of W gi and W'g with respect to n, in which residualcomponents at n 50 are thought to arise from unresolved
weak hf splittings. The angular dependence of the unresolved
weak hf splittings seems to be very small because of W gi
;W'g at n 50. Finally, principal values of the g tensor were
determined to be
g i 52.0037– 2.0042~ 2.0039! ,~7a!

g' 52.0060– 2.0067~ 2.0065! ,~7b!

respectively, where values in brackets produced the best fitting. The deviations from the best values correspond to about
a 50% increase in the x-square value from its minimum
value.
Further discussion will appear in the last section in connection with the discussion on other ESR parameters.
FIG. 4. ~a! Frequency dependence of the width and shape of the
DB spectra in Fig. 3. Solid lines represent a linearity of DB pp ~opencircles! and DB 1/2 ~closed circles! against n. A dashed line is a
guide to the eyes for DB 1/2 /DB pp ~crosses!. ~b! Frequency dependence of fitting parameters W gi ~open squares!, W'g ~solid squares!,and y ~plus symbols!. ~c! DB pp( n 50) plotted against the 29Si contents, p. Solid and open circles correspond to samples with high~20–30 at. %! and low- ~around 10 at. %! hydrogen densities, respectively.

the fluctuations of g values and anisotropy of the g tensor,
while a residual component, namely, DB pp( n 50), originates
mainly from weak hf interactions. We estimated DB pp( n50) of all our samples from the frequency dependence ofDB pp and plotted them against 29Si contents of the samples
p, as shown in Fig. 4~c!. The figure clearly shows an appreciable contribution of weak 29Si hf interactions to DB pp( n50). A contribution of 1H hf interactions to the signal
broadening was not found, because hydrogen atoms are morethan 0.4 nm from the DB site, which corresponds to 0.05 mTof dipolar magnetic fields of 1H. 8,20,29,30

C. 29Si hyperfine interactions

In order to determine principal values of the hf tensor A i
and A' , we simulated the whole DB spectra of 29Si enriched(p59.1 at. %) sample by fully calculating Eq. ~5!. The DB
spectra were obtained by the echo-detected ESR technique of
pulsed ESR instead of cw ESR. Since the 29Si hf structures
for high- and low-spin-density samples are believed to bealmost the same,5,8,9,12 we analyzed the 29Si hf structure of
the sample with N s 51.331018 cm23.
In Fig. 5, solid lines indicate the echo-detected ESR spectra at frequencies of 8.2 and 11 GHz in the first-derivative
form. Those spectra were differentiated in order to clarify thedetailed features of the 29Si hf structure. As is shown in the
figure, two spectra were different in the degree of overlapping of the primary and hf lines. Our simulation calculated
two spectra simultaneously in order to reduce arbitrariness inthe determination of hf parameters. In the procedure of thesimulation, g i and g' were fixed to values given by Eqs. ~7a!
and ~7b!, and fitting parameters were W gi , W'g , y, A iso-back ,4854

T. UMEDA, S. YAMASAKI, J. ISOYA, AND K. TANAKAPRB 59

FIG. 6. Echo-detected ESR spectra of 29Si-diluted sample ~p51.6 at. %, N s 59.431017 cm23! and natural abundance sample~p54.7 at. %, N s 53.631018 cm23! with a magnetic-field increment of 0.1 mT ~solid lines!. Simulated spectra are also shown bydashed lines.

29

FIG. 5. Echo-detected ESR spectra of Si-enriched undopeda-Si:H with N s 51.331018 cm23 at frequencies of 8.2 and 11, GHz~solid lines! and corresponding simulated spectra ~dashed lines!.
The best-fit hf parameters are also indicated in the figure.

A i , A' , W Ai , W'A , and C. Among those parameters,
frequency-independent parameters, A i , A' , W Ai , W'A , andA iso-back were set to be common for two spectra. As is shownin Fig. 5, an excellent fitting was obtained, from which principal values of the hf tensor were determined to be
A i 510.8– 12.3 ~ 11.9! mT,~8a!

A' 54.9– 5.6 ~ 5.1! mT,~8b!

respectively, where the best-fit values are in the brackets anddeviations of parameters were obtained by the same procedure as the case of g principal values. A iso-back was estimatedto be 1–2 mT. The broadening widths W Ai and W'A wereapproximately 2.6 and 2.0 mT, respectively. In addition, we
have examined the parameters given in Eqs. ~8a! and ~8b!
employing samples with ~p54.7 at. %, N s 53.631018 cm23!
and ~p51.6 at. %, N s 59.631017 cm23!, which is shown in
Fig. 6. Even for the case of p50.016, the echo-detected
spectra involve the 29Si hf structure clearly at the tail region,
although it was not detected by cw ESR. Dashed lines in the
figure indicate the simulated spectra that were calculated using the values of g i ,g' ,A i ,A' ,A iso-back determined above.
As is seen in the figure, the simulations are successful
enough to ensure a high reliability of the hf parameters obtained here.
The linear combination of atomic orbitals ~LCAO! pictureis quite useful for describing the wave function of localized
centers in covalently bonded semiconductors.6–9 When the

DB wave function is composed of 3s and 3 p orbitals of the
Si atom, the hf splitting K( u ) is written as K( u )5A iso
1A aniso(3 cos2 u21),9 where A iso and A aniso are the isotropic
and anisotropic 29Si hf splittings due to 3s and 3 p orbitals of
the DB, respectively. Thus, A iso and A aniso are given in termsof A i and A' as
A iso5 ~ A i 12A' ! /356.9– 7.9 mT~9a!

A aniso5 ~ A i 2A' ! /351.8– 2.5 mT.

~9b!

and

Full widths at half maximum of the distributions of A iso andA aniso were estimated to be W Aiso5 31 @ (W Ai ) 2 14(W'A ) 2 # 1/2
51.6 mT and W Aaniso5 31 @ (W Ai ) 2 1(W'A ) 2 # 1/251.1 mT, respectively.
D. ESR parameters—present versus previous work

Up to now, we have determined various ESR parameters.
In this section, we compare the present results with previous
works of Stutzmann and Biegelsen as well as theories.
Table II summarizes ESR parameters of the 2.0055 centeras well as the P b center obtained by ESR ~and related methods! and theoretical calculations. On the whole, each ESR
parameter obtained here is similar to that of Stutzmann andBiegelsen.8,9 Note that A iso and A aniso , which are the mostimportant ESR parameters for determining electronic andmicroscopic structures of the center, were quite consistent
with their previous conclusions. Therefore, with high reliability over a wide range of microwave frequency and 29Si
content, our experiments support a previous conclusion of
Stutzmann and Biegelsen, namely, that the origin of the
2.0055 center is well identified as the DB. Due to the natureof the DB, the DB center should have a unique Si atom
where an unpaired electron is mainly localized and causes

ELECTRON-SPIN-RESONANCE CENTER OF DANGLING . . .

PRB 594855

TABLE II. ESR parameters of the 2.0055 center and the P b center reported by ESR and theoreticalworks. N and N back represent a number of Si atoms accompanied with the largest and the next largest
isotropic 29Si hf interaction, respectively. For atoms counted into N back , their positions are referred to either
NN ~the nearest-neighbor sites, i.e., backbond sites! or NNN ~the next-nearest-neighbor sites!. The otherparameters are defined in the text. Values in brackets were given by assumptions.

Ref.

gi

g'

N

A iso
~mT!

A aniso~mT!

N back &position

A iso-pact~mT!

The 2.0055 center in undoped a-Si:H~ESR, etc.!
Present
Refs. 8, 9
Ref. 11a~Theory!
Ref. 18b
Ref. 18c
Ref. 33d

2.0037–2.0042
2.0038–2.0042

2.00232.0060–2.0067
2.0076–2.0084

~1!
~1!

6.9–7.9
7.0–7.5
6.9–7.3

1.8–2.5
1.5–2.0

~3!
~3!

1–2
2–3
2.4–2.8

12

10.1
6.0–8.9

1.8–2.9
0.3–0.5

3 NNN
2 NN

1.5
3.2–4.8

2.0037–2.0049
The P b center at Si~111!-SiO2 interface~ESR!
Refs. 6, 7e~Theory!
Ref. 34f

2.0011–2.0019

2.0080–2.0093

~1!

11

2.2

1

15.2

2.1

1.3
3 NNN

1.0

a

Measured by ENDOR.
Calculated for the DB center in a relaxed a-Si110 cluster.
c
Calculated for the FB center in relaxed a-Si81–86 clusters.
dCalculated for the DB center in relaxed a-Si10–22H15–27 clusters.
eConverted by A iso , A aniso (mT)50.10683A iso , A aniso (1024 cm21).
f
Calculated for the DB center in an unrelaxed Si22H21 /Si6O18H6 cluster with spin polarization.
b

the main 29Si hf interactions.18 Thus, there will be two identifications for the DB center: ~i! the doublet 29Si hf structure
should be observed in a p5100 at. % sample, and ~ii! theintensity ratio of 29Si hf lines and a primary line shouldamount to p:12p. The observation of the doublet 29Si hf
structure in a 93 at. % 29Si-enriched sample was consistent
with the former identification.8 In addition, our spectral
simulations present the latter identification for the range of
p51.6– 9.1 at. %. In contrast to the DB model, the FB
model anticipated that there are two or three Si atoms wherean unpaired electron is mainly located.25 Therefore, the FB
picture is inappropriate for explaining the present as well as
previous results.
Different from the present study, Hikita et al. reported
from spectral simulations on X-band ESR spectra that the
primary line includes the 1H hf structure with an isotropic hf
splitting of 0.6 mT.19 However, ESR measurements at quite
low frequencies ~,1 GHz! clarified that the hf splitting due
to 1H was estimated to be less than 0.1 mT.8,29,30 In addition,
we demonstrated that the whole DB spectrum and its dependence on n and p can be calculated without a convolution ofsuch a peculiar hf structure. Therefore, such a 1H hf structureis unlikely to exist.
We found some differences in ESR parameters between
the present and previous works on ESR. ~i! Our g' wassmaller than that of Stutzmann and Biegelsen by about0.0015.9 The 0.0015 difference in the g anisotropy yields a
0.9-mT difference in the width of spectrum at the Q band, so
we could detect this difference. Accordingly, both g i and g'
were different from the case of the P b center, which will be

discussed in terms of the electronic structure of the defectlater on. ~ii! The estimated value of A iso-back was smaller thanthat obtained by electron-nuclear-double-resonance ~ENDOR! measurement as well as an analysis on the signal
broadening of 29Si hf lines in a p593 at. % sample.8,11 Although estimations of A iso-back fluctuated among experiments
because of the difficulty of estimating it accurately, thepresent and previous experiments agreed that A iso-back ismuch smaller than the main isotropic hf splitting A iso of approximately 7.5 mT,8,9,11 which also agrees with the theoretical simulation for the DB case.18
E. Microscopic structures of the DB

ESR parameters, especially hf parameters, are closely
connected with the electronic and microscopic structures of
the DB. For the cases of pure 3s and 3 p orbitals of the Siatom, which are denoted by us& and up&, respectively, A iso andA aniso have been theoretically calculated to be 149.0 and 3.6
mT, respectively.31 Applying the LCAO expansion, the wave
function uc& of an unpaired electron is written as
uc&5(i a i~ s iu s & 1 p iu p & ),~10!

where i indexes all atoms within the extent of uc& and the
projection coefficients a i , s i , and p i obey the normalization conditions S i a 2i 51, s 2i 1 p 2i 51 for all i.6–9 The localization strength at a threefold coordinated Si site (i51) a 21 ,

4856

T. UMEDA, S. YAMASAKI, J. ISOYA, AND K. TANAKA

and 3s and 3p components on the site s 21 and p 21 , respectively, are approximately calculated asa 21 547– 67 %,~11a!

s 21 56 – 9 %,

~11b!

and

p 21 591– 94%,

~11c!
6,7,9

Namely, theby the same manner as previous studies.
unpaired electron of the 2.0055 center is localized on athreefold-coordinated Si atom by more than one half of thetotal density and its character is almost p like.
For the case of the P b center, it was concluded that a 21
580– 84%, s 21 511– 12%, and p 21 588– 89%. 6,7 A very
similar s-p hybridization ratio in g52.0055 and the P b centers indicates a similarity of the microscopic structure between the two centers. On the other hand, the two DB centers
are different in regard to the localization strength, i.e., a 21 ;the 2.0055 center is much more delocalized than the P b center.
When f is defined to be the angle between the directionof 3 p orbital of the DB and three backbonds, the value of f
is approximately given by cos f52s/p3s1 /p1 , wheres 2 / p 2 represents the s-p hybridization ratio of paired electrons of backbonds and now s 2 / p 2 ; 31 . From this relation, fis estimated to be about 100°, which is smaller than a normal
tetrahedral angle of 109.27°. Thus, it is considered that the
local structure of DB’s is close to a planar structure such asa p electron on an s p 2 network plane rather than a normal
tetrahedral structure in an s p 3 network. Likewise, the P bcenter should have a similar structure to that of DB’s ina-Si:H. Namely, it is considered that the threefold coordination in the Si network prefers such a planar configuration of
Si atoms rather than the normal tetrahedral structure.
We recall the result that W Aiso;1.6 mT and W Aaniso;1.1 mT, which are different only by a factor of 2 from thecase of 29Si hf lines in the P b spectrum where W Aiso
;1.0 mT and W Aaniso;0.7 mT. 6,29 W Aiso and W Aaniso , which
represent the size of fluctuations of A iso and A aniso , will indicate the degree of site-to-site variation of microscopic
structure of DB’s. Thus, in the vicinity of DB’s, the degreeof disorder seems to be similar between amorphous network
and well-ordered Si~111!-SiO2 interfaces.
The electronic structures of the DB are also considered interms of the g shift. The g shift from a free-electron g value~2.0023! can be calculated by
Dg m n 52

( (i

mÞ0

^ c u L ~mi ! u m &^ m u l i ~ ri ! L ~ni ! u c &« 0 2« m,~12!

where uc& is the DB wave function of the ground state, i.e.,
Eq. ~10!, and um& represent that of excited states, « 0 and « m
are energies of the ground and excited states, respectively, l iis the spin-orbit coupling constant of an i atom, ri is the
position of the unpaired electron relative to an atom of i, andL m(i), n are components ( m , n 5x,y,z) of orbital angular momentum operator with respect to a position of an i atom .32
Immediately, it is clear that s orbitals do not contribute to theg shift because L m u s & 50. Now, we consider the axis of sym-

PRB 59metry to be the z axis. For the case of P b center, Dg i
(5Dg zz ) was almost zero, while Dg' (5Dg xx 5Dg y y ) was
as large as 0.007 ~see Table II!.6,7 The fact that Dg i 50 canbe easily obtained from Eq. ~12!, because wave function uc&of the P b center consists almost of a localized 3 p z -orbitalu p z & and L z u p z & 50. On the other hand, Dg' will have anonzero value because L x,y u p z & Þ0. A quantitative evaluationof Eq. ~12! for a DB in Si clusters led to the result Dg i ;0and Dg' .Dg i . 33 For the 2.0055 center, we can find a similar relation in the g shift; Dg i ;0.002 and Dg' ;0.004.
Therefore, the DB picture was also suggested in terms of theg shift. The difference between Dg i and Dg' reflects on the
distribution widths of g i and g' , i.e., W gi and W'g , respectively. The fluctuation of Dg i is not affected by the distribution of « 0 2« m u c & and um&, in contrast to the case of Dg' , 29
which brings about the relation W gi ,W'g . In fact, it wasreported for the P b signal that W gi was three times larger thanW'g . 6,29 Likewise, in a-Si:H, W gi was estimated to be larger
than W'g @see Fig. 4~b!#. The reason why Dg i deviates fromzero in a-Si:H might be related with delocalization of the
wave function of DB’s. Since the DB wave function ofa-Si:H is more spread out, we have to take into account thecontributions of L z u p x,y & ~Þ0! for atoms of iÞ1, which willbring a nonzero contribution to Dg i . Furthermore, smaller
Dg' in a-Si:H might be also ascribed to the smaller densityof u p z & at the DB site.
In estimating the unpaired electron populations on 3s and3 p orbitals of a Si atom in the singly occupied DB wave
function, we did not consider the hf contribution from thespin densities, which might be induced by the effect of thespin polarization of bonding electrons and core electrons.
The sign of hf interactions arising from the spin polarization
is not necessarily the same as that of hf interactions due tothe singly occupied DB wave function. For both cases ofa-Si:H and the Si~111!/SiO2 interface, the spin-dependent
first-principles theoretical calculations predicted that the spinpolarization increases the isotropic hf splitting,34,35 so thatthe component of 3s orbital in the wave function s 21 may beeven smaller. Namely, the local structure of the DB may be amore planar structure, when the spin polarization is taken
into account. In fact, a recent molecular dynamics simulation
found completely planar DB’s ( f ;90°) in an amorphous
Si64H8 supercell.36
IV. SUMMARY

Our objective was to confirm a previous conclusion on thedangling bond center (g52.0055) in undoped a-Si:H ofStutzmann and Biegelsen,9 which was based on a simulation
analysis of the spectrum obtained only by n 510 GHz andp54.7 at. %, and was affected by a deconvolution procedureof 29Si hf lines. For that purpose, we measured a variety ofDB spectra using n 53 – 34 GHz and samples with p51.6,
4.7, and 9.1 at. %, and also employed the echo-detected ESR
technique of pulsed ESR as well as cw ESR. Using those
ESR spectra, we carried out the spectral simulations on thewhole dangling bond spectrum ~a primary line and 29Si hflines! without the deconvolution of hf lines, and successfully
reproduced the n and p dependence of the DB spectra. The
principal g values were obtained to be g i 52.0039, g'

PRB 59

ELECTRON-SPIN-RESONANCE CENTER OF DANGLING . . .

4857

52.0065, and 29Si hf splittings were determined to be A iso56.9– 7.9 mT, A aniso51.8– 2.5 mT, and A iso-back51 – 2 mT.
The present ESR parameters were almost in good agreementwith the results of Stutzmann and Biegelsen. Therefore, we
confirmed their identification of g52.0055 center for a wide
range of two experimental parameters as well as free fromthe deconvolution problem. We pointed out that the dangling
bond center of g52.0055 has a quite similar bonding structure, electronic structure, and site-to-site variation to the dangling bond at Si~111!/SiO2 interfaces ~the P b center! except
for a much weaker localization of the g52.0055 center.

The authors are grateful to Dr. A. Matsuda for a variety ofassistance and also Dr. S. Hayashi for his 1H-NMR measurements. We thank Dr. N. Ishii and Dr. H. Katagiri for valuable
discussions from a theoretical view point, and also Dr. J. K.
Lee for his kindly help. This work, partly supported by
NEDO, was performed in the Joint Research Center for
Atom Technology ~JRCAT! under the joint research agreement between the National Institute for Advanced Interdisciplinary Research ~NAIR! and the Angstrom Technology
Partnership ~ATP!.

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ACKNOWLEDGMENTS