PHYSICAL REVIEW B

VOLUME 62, NUMBER 23

15 DECEMBER 2000-I

Microscopic origin of light-induced ESR centers in undoped hydrogenated amorphous silicon
Takahide Umeda1,2,* Satoshi Yamasaki,1 Junichi Isoya,1,3 and Kazunobu Tanaka1,2
1

Joint Research Center for Atom Technology (JRCAT)–National Institute for Advanced Interdisciplinary Research (NAIR),
Tsukuba,305-8562, Japan
2
Institute of Materials Science, University of Tsukuba, Tsukuba, 305-0006, Japan
3
University of Library and Information Science, Tsukuba, 305-0821, Japan
共Received 12 March 1999; revised manuscript received 2 May 2000兲
29
Si hyperfine 共hf兲 structures of light-induced electron-spin-resonance 共LESR兲 centers of g⫽2.004 and 2.01
have been investigated in undoped hydrogenated amorphous silicon (a-Si:H) with different 29Si content 共1.6,
4.7,9.1 at. %兲 by means of pulsed and multifrequency 共3,11,34 GHz兲 ESR techniques. We have experimentallydeconvoluted overlapping LESR signals using the difference in the spin-lattice relaxation time between the two
signals. The deconvoluted 29Si hf structure of g⫽2.004 indicates that the wave function of the g⫽2.004 centerspreads mainly over two Si atoms. Accordingly, we propose that the origin of g⫽2.004 is electrons trapped in
antibonding states of weak Si-Si bonds rather than those trapped at positively charged dangling bonds. The
isotropic hf splittings were estimated to be around 7 mT for g⫽2.004 and below 3 mT for g⫽2.01, which arein good agreement with characteristics of the antibonding and bonding states of the weak Si-Si bond. We
suggest, from our 29Si hf data and other experimental findings, that the g⫽2.004 center is localized spatiallymore than conduction-band-tail electrons detected by photoluminescence.

I. INTRODUCTION

In amorphous semiconductors, there exist band-tail statesin the gap both just below the conduction band and above thevalence band, which have been evidenced by the optical absorption spectrum,1 photoemission spectra,2 drift mobility–
multipletrapping,3
andmodulatedphotocurrent
spectroscopy.4 The band-tail states are characterized as localized states and play an important role in transport and opticalproperties. It is widely accepted that those localized statesoriginate from potential fluctuations due to variation in bondlengths, bond angles, and other topological parameters.
However, there has been no experimental information available on the microscopic structure of the potential fluctuation.
In undoped a-Si:H, two light-induced electron-spinresonance 共LESR兲 signals of g⫽2.004 and 2.01 have been
detected at low temperatures.5 Doped a-Si:H, e.g.,
phosphorus- and boron-doped a-Si:H, also shows g⫽2.004
and 2.01 signals in the dark at low temperatures. In thesesamples the Fermi level shifts up to the conduction- anddown to the valence-band tail in thermal equilibrium.6–8 On
the basis of doping, photoluminescence, and photoconductivity experiments, Street, Biegelsen, and Wiesfield concluded
that the origins of those signals should be ascribed to
conduction-band-tail electrons (g⫽2.004) and valenceband-tail holes (g⫽2.01). 7 Thus, the microscopic origins ofthese ESR centers are directly connected to microscopic information about the potential fluctuation of the band-tailstates.
The microscopic origin of the LESR centers is also important to another unresolved issue: whether undoped a-Si:H
films include a large number of charged dangling bonds
共DB’s兲 or not at thermal equilibrium. For example, chalcogenide glasses also show LESR signals at low temperatures,
but almost no ESR signals are detected in the dark.9 This has
been interpreted in terms of negative effective correlation
0163-1829/2000/62共23兲/15702共9兲/$15.00

PRB 62energy 共U兲 for DB’s, that is all DB’s are considered to form
pairs of positively and negatively charged DB’s in thermal
equilibrium.9–11 In this model, naturally, the origins of the
LESR signals are photoexcited electrons and holes trapped at
the charged DB’s.9 In contrast, a-Si:H shows a pronounced
dark ESR signal of g⫽2.0055 that has been generally identified as a neutral DB signal.12–14 It is therefore believed thata-Si:H is a positive-U material.15 Further, this assignment is
consistent with the sensitivity of the Fermi level to doping in
a-Si:H. 8,16 However, several papers have argued the existence of a large number of charged DB’s in thermal equilibrium, which is associated with the coexistence of negativeand positive U.17–20 In those papers, a carrier-trapped
negative-U DB is one of the candidates for the origin of the
LESR centers and possibly for the precursor of photocreatedneutral DB’s in the Staebler-Wronski effect.17–20 Thus the
LESR centers are related to a major unresolved problem ina-Si:H.
The microscopic origins of the 2.004 and 2.01 centers are
expected to be revealed by detailed analyses of hyperfine 共hf兲structures of 29Si 共nuclear spin of I⫽ 21 , natural abundance of
4.7 at. %兲 in the ESR spectrum. Yamasaki et al. detected
such 29Si hf structures in the LESR spectrum of undopeda-Si:H using a pulsed ESR technique.19 However, it wasdifficult to experimentally deconvolute the two overlapping
LESR signals, which is necessary for extracting conclusive
information about the 29Si hf interactions. On the other hand,no discernible 29Si hf structure has been found in dopeda-Si:H owing to the interference with hf structures of thedopant atoms.11,21
Therefore, we directed our attention to the experimental
deconvolution of 29Si hf structures of LESR spectra in undoped a-Si:H. We found a difference in the spin-lattice relaxation time (T 1 ) between two LESR signals, which enables us to deconvolute the LESR signals experimentally.
For the purpose of precise analysis of 29Si hf interactions,
15 702©2000 The American Physical Society

MICROSCOPIC ORIGIN OF LIGHT-INDUCED ESR . . .

PRB 62TABLE I. List of samples and their properties. Total and distanthydrogen content was determined by 1H NMR measurements. The
distant hydrogen was revealed by a narrow, Lorentzian component
共full width at half maximum 10 kHz兲 in the 1H NMR spectrum.
Activation energy of the dark conductivity of the B-doped sample(E a ) was deduced from our previous data. 共Ref. 23兲

关 29Si兴
共at.%兲

1.6
4.7
9.1

UndopedTotal 关 1 H兴Distant 关 1 H兴共at. %兲
共at. %兲
8.9
6.8
10.7

2.2
1.1
3.3

N dark共cm⫺3兲
6⫻1015
1⫻1015
4⫻1015B doped关 B2H6兴/关SiH4兴 ⫽0.89%

E a ⫽0.25– 0.3 eV

undoped samples with different amounts of the 29Si isotope
共9.1,4.7,1.6 at. %兲 were prepared and subjected to pulsed
ESR measurements. Prior to this paper, we published a briefreport of our work.22 This paper presents more detailed dataand complete descriptions of the experiments and discussion.
After the detailed description of experimental conditions
共Sec. II兲, the spin-lattice relaxation of the LESR centers is
elucidated by time-domain measurements of pulsed ESR
共Sec. III A兲. Then, taking advantage of the difference in T 1 ,experimentally deconvoluted spectra of g⫽2.004 and 2.01
are presented 共Sec. III B兲. From 29Si hf structures of the deconvoluted 2.004 and 2.01 spectra, detailed information
about the electronic structures of the LESR centers is obtained 共Sec. III C兲. Finally, we propose a weak Si-Si bondmodel to account for the origin of the LESR centers 共Sec.
IV A兲, and discuss this model in comparison with previous
photoluminescence data 共Sec. IV B兲.
II. EXPERIMENTAL DETAILS

Undoped a-Si:H samples were deposited by the conventional rf glow-discharge technique on aluminum foil at
250 °C. The ratio of 29Si atoms to total Si atoms, p, wasvaried from 1.6 to 4.7 to 9.1 at. % for our samples. Flaked
samples 共1 to 2 ␮m in thickness, around 30 mg兲 were collected in a high-purity vitreous-silica tube 共2.5 mm in innerdiameter兲 for ESR measurements. We also prepared a borondoped a-Si:H sample from a mixture of SiH4 and B2H6 with
关 B2H6 兴 / 关 SiH4 兴 ⫽0.89% at the deposition temperature of
250 °C. Dark spin densities (N dark) and hydrogen contents ofour samples are listed in Table I.
ESR spectra were measured by the echo-detected ESR
technique of pulsed ESR to perform a variety of deconvolution procedures and to obtain wide-dynamic-range spectra.
In the standard technique of echo-detected ESR, the spectrum is obtained by recording amplitudes of the two-pulse
Hahn spin echo 共90° pulse– ␶ –180° pulse– ␶ –echo, ␶⫽240 nsec) as a function of magnetic-field strength.19 At
each magnetic field, a pulse sequence was repeated 1000 to
4000 times with an interval of RT 共repetition time兲 which is
generally set to be much longer than T 1 . The T 1 value represents a characteristic time for the spin system to recover its
equilibrium state completely. The magnetic-field increments
were 0.04 mT for the center part of the spectrum with a 5 mT

15 703width and 0.04–0.15 mT for the remaining part. The echodetected ESR spectrum is equivalent to the absorption spectrum of conventional continuous-wave 共cw兲 ESR, although
the baselines of echo-detected ESR spectra are much flatterthan those of cw ESR spectra.19,24 This enables us to observe
clear 29Si hf structures of the LESR spectrum. All echodetected ESR spectra were measured with a home-built
pulsed ESR spectrometer with a microwave frequency of 11
GHz. This frequency was more useful for the deconvolution
than the usual 9.2 GHz 共X band兲, because overlapping of thetwo signals of g⫽2.004 and 2.01 decreases as the resonant
microwave frequency increases.6,22 The details of our pulsed
ESR spectrometer were described in previous papers.24,25
The spin echo was generated by microwave pulses 17 and 34
nsec wide for 90° and 180° pulses, respectively, whose
magnetic-field strength was estimated to be about 0.52 mT.
The echo intensity was accumulated with a 50-nsec-wide
boxcar gate and was then digitized with a 12-bit analog-todigital converter.
Sample temperatures were controlled from 4.5 to 300 K
using an Oxford ESR-900 system, and were measured by athermocouple in the sample tube. The LESR intensity increases monotonically with decreasing temperature in addition to the contribution of the Boltzmann factor.19 On theother hand, the number of echo signals accumulated waslimited by the long repetition time due to a rapid increase in
T 1 . The best temperature for getting a high signal-to-noise
ratio was found to be around 30 K.
LESR measurements were carried out using a Ti-sapphirelaser (h ␯ ⫽1.7 eV兲. The laser light was radiated into a microwave cavity through a glass fiber. The light intensity on
the sample was adjusted to be 30 mW/cm2, unless noted
otherwise. We checked the time evolution of the LESR spectra and confirmed that there was no appreciable influence ofphotodegradation on any LESR spectrum.
Some of the ESR spectra were measured using a cw ESR
spectrometer 共Bruker ESP300E兲 with microwave frequenciesof 3 and 34 GHz. These cw ESR measurements were carriedout at 50 K using a field-modulation frequency of 100 kHz,modulation amplitude of 0.3–0.7 mT, and microwave powerof 0.9–7.8 mW.
III. RESULTS
A. Spin-lattice relaxation time

Figure 1共a兲 shows spin-lattice relaxation curves at 30 K of
the undoped sample (p⫽9.1 at. %). Solid and open circles
were measured at magnetic fields of 389.0 and 391.8 mT
where the echo signals originate mainly from g⫽2.004 and2.01 signals, respectively 关see Fig. 1共b兲兴. These curves wereobtained by a pulse sequence of three-pulse inversion recovery 共180° pulse–t–90° pulse– ␶ –180° pulse– ␶ –echo, ␶⫽240 nsec, t is scanned, RT⫽30 msec).24 Solid lines in the
figure represent fitted curves with stretched-exponentialfunctions I(t)/I(0)⫽1⫺2 exp关⫺(t/T1)␤兴, where T 1 is the
spin-lattice relaxation time and ␤ is a dispersion parameter(0⭐ ␤ ⭐1). 24 Values of T 1 and ␤ at 30 K for g⫽2.004 and2.01 are summarized in Table II. It is found that T 1 of g
⫽2.004 is about three times longer than that of g⫽2.01. This
may reflect a difference in electronic structures between
conduction- and valence-band-tail spins, which will be dis-

UMEDA, YAMASAKI, ISOYA, AND TANAKA

15 704

PRB 62

FIG. 2. Temperature dependence of T 1 共circles兲 and ␤ 共triangles兲. The data were obtained for undoped a-Si:H with p⫽4.7 at. %. Solid lines indicate the dependence T ⫺3.4. ‘‘LESR/
dark’’ represents the ratio of peak heights of the LESR spectrum tothe dark ESR spectrum.

FIG. 1. 共a兲 Echo recovery curves of the g⫽2.004, 2.01, and2.0055 signals at 30 K. Echo intensities are scaled from ⫺1 to 1.
LESR spectra of the 共b兲 undoped and 共c兲 B-doped a-Si:H samples.
Dashed lines indicate magnetic fields at which we have measured
the echo recovery curves. Symbols there correspond to those in
1共a兲.

cussed in Sec. IV A. Such a T 1 difference was also observedin the conduction- and valence-band-tail spins of P- andB-doped a-Si:H and a-Ge:H, respectively, although the twocenters were separately observed in different samples.26
As seen in Fig. 1共a兲, the dark ESR signal of g⫽2.0055
has a much longer T 1 than the above two: T 1 ⫽26 msec. The
same relation was also found in illuminated conditions.27 Using B-doped a-Si:H, we measured the 2.0055 signal and its
T 1 under strong 共100 mW/cm2兲 illumination 关Fig. 1共c兲兴. This
2.0055 signal is thought to arise from neutral DB’s via anelectron trapping process at positively charged DB’s. The T 1value of g⫽2.0055 is six times longer than that of the coexistent 2.01 signal 共Table II兲. Taking advantage of this feature, it is quite possible to reduce the 2.0055 component in
TABLE II. Spin-lattice relaxation parameters of the spin centers. B r represents magnetic fields at which we have measured relaxation curves.

Experimental conditions

g

Br
共mT兲

undoped, p⫽9.1 at. % 共30 K兲
In the dark
2.0055
391.1
Under illumination
2.01
389.0
2.004
391.8
B-doped 共50 K兲
Under illumination
2.01
389.0
2.0055391.1

T1
共msec兲

␤

26
0.47
1.3

0.58
0.61
0.59

0.06
0.38

0.59
0.69

the LESR spectrum. The 2.0055 component should be decreased if we apply RT just long enough for the 2.004 and2.01 components to recover to the equilibrium states 共for
example, 10 msec at 30 K兲, because such a RT is not sufficient for full recovery of the longer-T 1 component, g⫽2.0055.
The dispersion parameter ␤ is found in the range from 0.6
to 0.7 for every center 共Table II兲. ␤ values smaller than unity
indicate that T 1 of each center has a distribution in the vicinity of the major value listed in Table II. This is reasonablebecause of the amorphous nature of the material. The distribution of T 1 values did not affect the echo-detected ESR
experiments in the dark, shown by the fact that the shape ofthe dangling-bond signal was unchanged with varying RT.
The shape of the LESR signals, however, was distorted when
we adopted a RT much shorter than T 1 . The distortion of theline shape was detected only in the center part of the spectra
where g⫽2.004 and 2.01 signals have considerable overlap.
Such distortion is predominantly caused by the cross relaxation between the 2.004 and 2.01 spins rather than the T 1
distributions, because the cross relaxation is more effectivein the overlapping region.28
The temperature dependence of T 1 and ␤ is shown in Fig.
2. Generally, T 1 obeys a power-law dependence with respect
to temperature T, i.e., T 1 ⬀T ⫺m . 28 Actually, T 1 for both g⫽2.004 and 2.01 obeyed a similar power law with m⬇3.4
from 15 to 120 K, slightly different from m⫽2 – 3 for dopeda-Si:H from 30 to 100 K.26 The value of 3.4 is difficult tounderstand from simple models for the spin-lattice relaxation
process.28 Peak heights of LESR spectra normalized to thoseof dark ESR spectra are also shown in the figure. Since the
LESR intensity is much greater than the dark ESR intensity,
the contribution of g⫽2.0055 to T 1 is not observable.
B. 29Si hyperfine structure of the LESR spectrum

Figure 3 shows LESR spectra of undoped samples withp⫽1.6, 4.7, and 9.1 at. %, which were obtained by the twopulse Hahn echo sequence with RT of 10 msec. Spin densi-

PRB 62

MICROSCOPIC ORIGIN OF LIGHT-INDUCED ESR . . .

FIG. 3. 29Si concentration dependence of the LESR spectrum of
undoped a-Si:H. Intensities of those spectra are normalized to theirareas. The upper and lower figures are linear and logarithmic plots,
respectively.

ties of these spectra were found to lie within the range from
8⫻1016 to 1.0⫻1017 cm⫺3, more than 20 times larger thanthose of the dark ESR signals obtained by the same pulse
sequence. When the light intensity is sufficiently high, as in
the present case, LESR spectra no longer depend on the relative intensity between the LESR and the dark ESR signals,
although under very weak illumination 共or at relatively hightemperatures兲 LESR spectra seem to be influenced by thedark ESR component.29,30 This means that there is no substantial contribution of the dark ESR component to the observed LESR spectrum for the strong-illumination cases.
With increasing 29Si concentration, it was found that thepeak height of g⫽2.004 was reduced considerably. This isdue to a signal broadening of the g⫽2.004 signal induced byunresolved 29Si hf splittings, which is effective for the g⫽2.004 signal because of its narrow linewidth. An apparent
shift in the peak position of the 2.004 signal is also a consequence of the reduction in the peak height of g⫽2.004 relative to g⫽2.01. The 29Si concentration dependence shown
here indicates that excessive doping of 29Si in the film causes
extreme signal broadening, which smears out the separation
between the 2.004 and 2.01 signals as well as 29Si hf splittings.
As seen in the logarithmic plot of Fig. 3, there is a weak
and broad signal in the tail region of every LESR spectrum.
These signals are high-magnetic-field-side 29Si hf lines, because the area ratio S high-hf , of these lines to the total spectrum increased proportionally to p, as seen in Fig. 4共a兲. The
deconvolution of the high-field-side hf lines was performedby extrapolating a tail curve from the main peak of g
⫽2.004, in which we assumed an exponential decay of thetail.22 Likewise, in Fig. 4共b兲, the S high-hf values are estimatedfor the dangling-bond signal of g⫽2.0055. Solid lines represent the relation S high-hf⫽p/2, which corresponds to thefact that the wave function of the neutral DB center is localized mainly on a single Si atom.12–14 A good coincidence
between the line and plots in Fig. 4共b兲 assures the validity ofthe deconvolution of high-field hf lines. For the LESR spec-

15 705

FIG. 4. 29Si concentration dependence of the area fraction(S high-hf) of the high-field-side 29Si hf line: 共a兲 for LESR and 共b兲 fordark ESR spectra. S high-hf is given by the area ratio A/B.

trum, S high-hf seems to trace a similar line as in the danglingbond case. Previously, Yamasaki et al.19 tentatively suggested that the wave function of the LESR spin centers is
localized on a single Si atom, simply because the value of
S high-hf was close to p/2 for p⫽4.7 at. % 关see Fig. 4共a兲兴.
However, the data are not sufficient to discuss, because the
LESR spectrum is composed of two signals (g⫽2.004 and2.01兲. In order to obtain more detailed and correct information, it is necessary to deconvolute the LESR spectrum into
the two signals. Fortunately, by taking advantage of the difference in T 1 between the two LESR centers 共see Sec. III A兲,
it is quite possible to experimentally deconvolute the LESR
spectrum, as we reported previously.22
Figure 5 shows the result of the experimental deconvolution for p⫽4.7 at. % 共a natural-abundance sample兲. The ‘‘total’’ spectra in Figs. 5共a兲 and 5共b兲 were measured by echodetected ESR techniques using a two-pulse Hahn echo 共RT⫽
0.5 msec兲 and a three-pulse stimulated echo␶ ⫽240(90° pulse– ␶ – 90° pulse– ␶ ⬘ – 90° pulse– ␶ – echo,
nsec, ␶ ⬘ ⫽1 msec, RT⫽10 msec兲, respectively. ␶ ⬘ longer
than 1 msec was not effective because of a serious reductionof the echo intensity. The details of the deconvolution procedure have been reported in Ref. 22. The center part of the
LESR spectra could not be deconvoluted completely becauseof the distortion of the spectra as discussed in the preceding
section. Figure 5 clearly demonstrates that the 29Si highfield-side hf line of the LESR spectrum is related mainly to
the 2.004 signal, which is the most important feature. Peakpositions of the two deconvoluted signals were found to correspond to g⫽2.004 and 2.01, respectively. The area ratio ofthe deconvoluted two signals was estimated to be关 2.004兴 : 关 2.01兴 ⬇1.3:1 for the normal LESR spectrum shownin Fig. 3. The same results were also obtained for a29
Si-enriched sample (p⫽9.1 at. %). 22 For a 29Si-diluted
sample (p⫽1.6 at. %), it was rather difficult to get sufficient
intensity of the 29Si structure after the deconvolution process.

UMEDA, YAMASAKI, ISOYA, AND TANAKA

15 706

FIG. 5. Experimental deconvolution of two LESR signals forthe case of p⫽4.7 at. %. Solid lines indicate the deconvoluted
2.004 and 2.01 spectra with high reliability in data analyses, while
dashed lines include some ambiguity. Shaded regions show thehigh-field-side hf structure of 29Si. The dark ESR spectrum of
B-doped a-Si:H is also shown by a broken line.
C. Electronic structure of LESR centers

In this section, we extract detailed information about theelectronic structures of LESR centers from the deconvoluted29
Si hf structures. One of the most important pieces of information is the area fraction S hf of the entire 29Si hf structure
共a group of low- and high-field-side hf lines兲 in the deconvoluted signal. The quantity S hf is determined by the number of
Si atoms, N, on which an electron spin is mainly located.
When N⫽1, S hf equals simply p/2⫹p/2⫽p, as is illustrated
in Fig. 6共a兲. For any N, since the probability that all N Si
atoms have no nuclear spin is (1⫺p) N , S hf should be givenby 1⫺(1⫺p) N . Although this includes the small probabilityof 29Si hf lines overlapping on a central line, e.g., a probability of p 2 /2 for the N⫽2 case shown in Fig. 6共b兲, such a small
probability is negligible for the case of small N and p. The
value of S hf is experimentally determined by the area ratio
A/B of the deconvoluted signal, as shown in Fig. 6共c兲. The
area B is calculated using the high-field-side half of the deconvoluted 2.004 spectrum in order to eliminate an ambiguity in the ‘‘dashed-line’’ region 共cf. Fig. 5兲. The high-fieldside 29Si hf structure was estimated by the procedure used inSec. III B. As a result, the S hf values were estimated to be
0.20⫾0.03 and 0.09⫾0.03 for p⫽0.091 and 0.047, respectively. Thus, for the 2.004 center,N⫽

再2.3⫾0.4

for p⫽0.091

2.1⫾0.4

for p⫽0.047.

共1兲

Consequently, it is concluded that the wave function of the
2.004 center spreads mainly over two Si atoms.22 In theabove discussion, we assumed that the wave function of thespin center spreads over N Si atoms uniformly, although theactual wave function may fluctuate among N Si atoms. A
more exact analysis needs to consider variations of 29Si hf

PRB 62

FIG. 6. Schematic views of 29Si hf splitting for cases of 共a兲 N⫽1 and 共b兲 N⫽2, assuming two equivalent hf splittings. 共c兲 Estimation of S hf and A iso for the deconvoluted 2.004 signal.

interactions among N Si atoms. However, the fluctuation
contributes only to the linewidth of the hf structure andtherefore does not affect the above conclusion.
Another interesting feature is the isotropic hf splitting
A iso , which arises mainly from the 3s character in the wave
function of a spin center.12–14 As is shown in Fig. 6共c兲, theisotropic hf splitting is estimated to be
A iso⬇7 mT

for g⫽2.004.

共2兲

In contrast to the 2.004 signal, the 2.01 signal did notappear to show hf structure. Therefore, the isotropic hf splitting of g⫽2.01 should be smaller than that of g⫽2.004. The
2.01 signal in B-doped a-Si:H 关Fig. 5共a兲兴 also shows nodiscernible hf structures.21 Furthermore, both the 2.01 signals
are similar in their asymmetric line shape. The origin of theasymmetric line shape of g⫽2.01 is ascribed either to thepowder pattern31 due to anisotropy of the g value, or to the
convolution of hf structures. To clarify the origin, ESR spectra of g⫽2.01 were measured at microwave frequencies 共␯兲
of 3,11,34 GHz, and are shown in Fig. 7共a兲. In the figure,although the linewidth was reduced by less than 1.0 mT inthe 3 GHz spectrum, distortion of the spectral shape due toisotropic hf interactions was still not observed. This meansthat the isotropic hf splittings of g⫽2.01 are smaller than 3
mT, i.e.,
A iso⬍3 mT

for g⫽2.01,

共3兲and hence the asymmetric line shape of g⫽2.01 originatesfrom the powder pattern. In Fig. 7共b兲, ESR intensities areplotted as a function of g value. The asymmetry in the line
shape is enhanced in the 34 GHz spectrum in Fig. 7共b兲,which clearly indicates a convolution of the powder pattern.
To estimate principal g values of the 2.01 signal, we carriedout a powder-pattern simulation of the 2.01 spectra. In thesimulation, an ideal powder pattern31 was broadened by convoluting the Voigt broadening function with the full width at
half maximum, W, and a shape parameter y.14 We assumed

PRB 62

MICROSCOPIC ORIGIN OF LIGHT-INDUCED ESR . . .

FIG. 7. Multifrequency 共3,11,34 GHz兲 ESR measurements on
the g⫽2.01 signal in B-doped a-Si:H 共solid lines兲. ESR intensities are plotted 共a兲 as a function of applied magnetic field B, and 共b兲
as a function of g value, where g⫽ 关 71.4488␯ 共GHz兲兴 / 关 B共mT兲兴 .
The 2.01 spectra are normalized to their peak heights and are vertically shifted for clarity. Dashed lines indicate simulated powderpattern spectra. LESR spectra in undoped a-Si:H (p⫽9.1 at. %)for 34 GHz are also shown by broken lines, with intensities modified to fit their 2.01 signals approximately to the B-doped 2.01
signal.

that the width W is proportional to the g shift (⌬g) from thefree-electron g value 共2.0023兲 as well as the resonant frequency, because such a dependence has been observed in thedangling-bond spectrum in a-Si:H. 14 The fitting parameters
were g 1 , g 2 , and g 3 共principal g values g 1 ⬎g 2 ⬎g 3 ), W 0
and W 1 共width parameters: W⬅W 0 ⫹W 1 ⌬g ␯ ), C 共normalizing constant兲, and y, where g 1 , g 2 , g 3 , W 0 , and W 1 were set
to be common for all the spectra. The simulation minimized
the sum of deviations among three experimental and fitted
spectra using the same algorithm as in previous work.14 The
best-fitted spectra 共dashed lines in Fig. 7兲 were obtained forg 1 ⬇2.019, g 2 ⬇2.012, and g 3 ⬇2.005. One of the g values(g 3 ) was close to g⫽2.004, so the two LESR signals of g
⫽2.004 and 2.01 were not completely separated even in the
34 GHz spectrum, as shown in Fig. 7.
It has been reported that the energetic positions in the gap
are deeper for valence-band-tail holes than for conductionband-tail electrons, resulting in stronger localization for g⫽2.01 centers than g⫽2.004 ones.3,8,32 The stronger localization must cause larger isotropic splitting, unless the wave
function of the spin center has less 3s component. Thus, theweaker isotropic hf interaction of g⫽2.01 means that thewave function of the 2.01 center has much less 3s component compared to the 2.004 center; in other words, it consistsof 3p component predominantly. This difference will be interpreted later in terms of the origin of the LESR centers.
Although the 2.01 center has much 3p component, it is difficult to detect the anisotropic 29Si hf interactions in the 2.01
spectrum, because a 100% localized 3p orbital of the 29Si
atom causes an anisotropic hf splitting of no more than 3.6
mT.33
The electronic levels that are located in the vicinity of themobility gap of a-Si:H are characterized by a combination of
3s and 3p levels of Si atoms. Thus, to consider the electronic structures of band-tail states, it is useful to describe the

15 707wave function ␺ of g⫽2.004 and 2.01 by a linear combination of atomic orbitals. That is ␺ ⫽ 兺 i ␣ i ( ␴ i 兩 3s 典 ⫹ ␲ i 兩 3p 典 ),where 兩 3s 典 and 兩 3 p 典 denote the atomic 3s and 3p orbitals of
Si, i indexes all Si atoms within the extent of ␺, ␣ 2i represents the degree of localization of an unpaired electron onsite i, and ␴ 2i and ␲ 2i are fractions of 3s and 3p orbitals onsite i, respectively.12,14 The projection coefficients satisfy thenormalization conditions 兺 i ␣ 2i ⫽1 and ␴ 2i ⫹ ␲ 2i ⫽1 for all i.
The isotropic hf splitting A iso has been theoretically calculated to be 149.0 mT for a 100% localized 3s orbital of 29Si
atom.33 Comparing Eq. 共2兲 with this value, the 3s component
in the wave function of the 2.004 center is estimated to be
7/149⫽5% on each of the two Si atoms. On all other i sites,the 3s components should be much smaller than 5%. Therefore,␣ 21 ␴ 21 ⬇ ␣ 22 ␴ 22 ⬇0.05,
␣ 2i ␴ 2i ⬍0.05

共 i⫽1,2兲

共4兲

for g⫽2.004, where i⫽1 and 2 represent the two Si atoms
counted in N. For the 2.01 center, all ␣ 2i ␴ 2i should be smaller
than 3/149⫽2%, because A iso⬍3 mT 关Eq. 共3兲兴, namely,␣ 21 ␴ 21 ⬍0.02

for all i

共5兲

for g⫽2.01. The localization coefficients ␣ 21 and ␣ 22 for g⫽2.004 should be larger than those for g⫽2.01, as we mentioned above. Thus, to satisfy Eqs. 共4兲 and 共5兲, ␴ 21 and ␴ 22 forg⫽2.01 should be much smaller than those for g⫽2.004,

␴ 21 , ␴ 22

共 for g⫽2.01兲 Ⰶ ␴ 21 , ␴ 22 共 for g⫽2.004兲 .

共6兲

A further evaluation of the projection coefficients has beenreported in Ref. 22.
IV. DISCUSSION
A. Origin of LESR centers

For the origin of the LESR centers, two models have so
far been proposed. In this section, those models are compared with the ESR results obtained here, in particular, with
Eqs. 共1兲 and 共6兲.
One model is that of electrons or holes trapped at weak
Si-Si bonds.34 In an amorphous network, it is quite possiblethat greatly elongated covalent bonds 共weak bonds兲 arepresent and give rise to the energy levels in the band-tailregions. In this case, an electron is trapped in an antibonding
state and its wave function extends over the two Si atoms
associated with the weak Si-Si bond. In the other model,
electrons and holes are trapped at positively and negatively
charged DB’s with negative U, resulting in neutral DB’s
with g⫽2.004 and 2.01, respectively.17–20 The resultant neutral DB’s are thought to be similar to those observed in thedark. However, a neutral DB state is characterized by anelectron localized on a single Si atom 共namely, N⬇1),12–14
which is clearly inconsistent with the present result of N
⬇2 关Eq. 共1兲兴. Consequently, the present results suggest thatthe origin of the LESR center of g⫽2.004 is electrons
trapped at weak Si-Si bonds located at the conduction-bandtail rather than electrons trapped at positively charged DB’s.

15 708

UMEDA, YAMASAKI, ISOYA, AND TANAKA

It is reasonable to consider for the g⫽2.01 center, by
analogy with the 2.004 center, that it originates from holes
trapped in the bonding states of the weak Si-Si bonds locatedin the valence-band tail. The weak Si-Si bond model can
explain why the 2.01 center has less 3s component in its
wave function than the 2.004 center 关cf. Eq. 共6兲兴. As in crystalline silicon, the top of the valence band and the bottom of
the conduction band in a-Si:H are characterized by 3p orbital (p ␴ state兲 and an admixture of 3s and 3p orbitals(sp ␴ * state兲, respectively.35 The antibonding and bonding
states of the weak Si-Si bond retain essentially similar features to normal Si-Si bonds. Therefore, the wave function ofholes trapped in the bonding states of the weak bonds willconsist of much less 3s component than that of electrons in
the antibonding levels, resulting in smaller isotropic hf splitting of g⫽2.01.
The above discussion is supported by more quantitativeevaluations. Takeda et al. reported a first-principles localdensity-functional calculation of a weak bond with 27%
stretching embedded in polysilane chains (Si4H8 and
Si6H12).36 They showed that holes localize at the center ofthe weak bond and the hole wave function is composed
mainly of 3p orbital, while electrons tend to localize at two
Si atoms of the weak bond and its wave function has a 3s
component. As a result, the isotropic hf splitting of the hole
center was calculated to be less than 701 of that of the electron
center. The energy separation between the two weak-bondlevels was estimated to be 65% of the energy gap for polysilane chains 共⫽3.9 eV兲, which is comparable with the actual
range between 60% and 100% of 1.7 eV in a-Si:H. 1,2,8 Morerecently, Ishii and Shimizu calculated 29Si hf interactions in
negatively and positively charged weak bonds with 50–75%
stretching by means of the density-functional method forclusters with 8–26 Si atoms.37 They found that the isotropic
hf splitting for the negatively charged weak bond becomes
6–11 mT as against 0.1–0.2 mT for the positively charged
one, which is quite consistent with our experimental results.
Note that any s orbitals make little contribution to thespin-orbit interaction, because their orbital angular momentum is zero.38 Thus, due to more 3s component in the wave
function of g⫽2.004, the 2.004 center tends to generate lessspin-orbit coupling, resulting in a longer T 1 and smaller g
shift compared to the 2.01 center. Such a trend is consistent
with the T 1 difference and the g shift observed in the experiment.
In contrast to the weak bond, charged DB’s are unlikely
to adopt different isotropic hf splittings between g⫽2.004
and 2.01. As is seen in Fig. 1共c兲 for the case of positively
charged DB’s, both positively and negatively charged DB’s
are probably converted to neutral DB’s with isotropic hf
splitting close to 7 mT.
A detailed study of the electron-spin-echo envelope
modulation revealed that the LESR centers are spatiallyseparated from hydrogen atoms by approximately 0.4 nm.25
This is quite reasonable for the weak Si-Si bond model, because insertion of hydrogen in a disordered Si network may
relax local stress and prevent the formation of elongated covalent Si-Si bonds near hydrogen atoms. Conventionala-Si:H films contain other impurities such as oxygen, carbon, and nitrogen with concentrations of 1018 – 1020 cm⫺3. 39
However, a high-purity undoped film, which contains no

PRB 62TABLE III. Comparison of data for conduction-band-tail electrons from the present LESR and the previous PL and ODMR
共Refs. 40–42, 44兲 experiments.

Spatial extent
Time constant of decay
g value
Concentration
Energy positions
Origin of trap center

LESR

PL and ODMR

smaller than 1 nm
⬎102 sec
2.004⭐1017 cm⫺3
deep
weak Si-Si bond

⬇1 nm
⬇10⫺3 sec
⬇1.99
⭓1018 cm⫺3
shallow?

more than 1016 cm⫺3 of impurities, still reveals the band-tailstructure in its optical absorption spectrum.39 Therefore, we
speculate that the impurities do not directly relate to the formation of weak bonds, and thus the weak bond may be an
intrinsic structure of the amorphous silicon network.
B. Comparison between LESR centersand other band-tail states

Our experiment revealed that the g⫽2.004 electrons generate only two main isotropic hf interactions of 29Si. On theother hand, previous photoluminescence 共PL兲 and spindependent PL 关the so-called optically detected magnetic
resonance 共ODMR兲兴 experiments suggested that the spatial
extent of the conduction-band-tail electrons is as large as 1
nm.40,41 Those experiments analyzed the PL signal at a photon energy of 1.2–1.4 eV which has been attributed to theradiative recombination between conduction-band-tail electrons and valence-band-tail holes.7,40,42 Normally, a sphere of
1 nm radius in a-Si:H (Si density⬇5⫻1022 atoms/cm⫺3)
contains more than 150 Si atoms.43 Thus, the PL electrons
are considered to have substantial electron densities on several dozen Si atoms and therefore do not adopt the same29
Si hf interactions as the 2.004 electrons.
In order to interpret the difference between the LESR and
PL data, we considered that the band-tail electrons observedin the PL possess relatively higher energetic positions andlarger spatial extent compared to the 2.004 electrons in
LESR. This speculation is consistent with various experimental facts, which are summarized in Table III. 共1兲 The
time constant of the decay is quite different between the two
experiments; below 50 K, the PL intensity decays with atime constant of 10⫺3 sec after excitation,40 but for the LESR
intensity, the constant is larger than 102 sec. The muchslower decay for the LESR may be ascribed to the deeper
energy location of the 2.004 electrons. Since the PL intensity
decreases proportionally with the rate of radiative recombination, it is quite difficult for PL to detect the 2.004 electrons, which have a very long recombination lifetime. 共2兲
The g value is quite different; a time-resolved ODMR measurement under intense pulsed excitations (peak power⬇220 kW/cm2) detected a very weak signal of g⬇1.99
which was tentatively ascribed to band-tail electrons,44 but
such a signal is similar to a conduction-electron resonance inmicrocrystalline silicon45 (g⫽1.998) rather than g⫽2.004.
This suggests that the PL electrons are located in shallow
levels close to the mobility edge. 共3兲 The carrier concentration is different; the concentration of the PL electrons is eas-

PRB 62

MICROSCOPIC ORIGIN OF LIGHT-INDUCED ESR . . .

ily higher than 1018 cm⫺3, 40 while that of the 2.004 electrons
did not exceed 1017 cm⫺3. 30 It also leads to higher-energy
positions for the PL electrons. Further, this fact suggests thatthe 2.004 centers relate to only a part of the conductionband-tail states, although the PL electrons may be responsible for the major part.
The reason that LESR and PL revealed different
conduction-band-tail electrons is tentatively ascribed to thefollowing features of the LESR. The LESR measurements
are efficient in detecting band-tail electrons having a longrecombination lifetime ( ␶ r ), because the steady-state density
N of band-tail electrons should increase as ␶ r increases 共notethat the steady-state rate equation dN/dt⫽G⫺N/ ␶ r ⫽0,
where G is the generation rate of band-tail electrons, resultsin N⫽G ␶ r ). In addition, it is also required that unpaired
spins have a T 1 long enough to avoid a serious reduction in
the ESR signal intensity due to lifetime broadening. Naturally, localized electrons in deeper band-tail levels have
longer ␶ r 共and may also have longer T 1 ) as compared todelocalized electrons in shallower band-tail levels. Therefore, LESR will be increasingly effective for deeper band-taillevels, resulting in smaller spatial extent for the LESR electrons than for the PL ones.
As mentioned earlier, the 29Si hf structure of the PL electrons may be different from that of the LESR electrons. For
example, discernible 29Si hf splitting might be absent in the
ODMR spectrum due to the delocalization of unpaired electrons. Unfortunately, previous experimental results as well as
the present work are not sufficient to determine what sort ofstructural fluctuation causes such weakly localized centers,with a spatial extent of 1 nm, having a density of stateshigher than 1018 cm⫺3. For the weak-bond center, theoretical
calculations suggest 0.3–0.4 nm for the Si-Si bondlength.36,37,46 Weak Si-Si bonds whose Si-Si bond length iscloser to a normal Si-Si length 共0.235 nm兲 than to 0.3 to 0.4
nm might be one of the origins of the weakly localized centers. But even so, many kinds of structural fluctuation willcontribute to the formation of the centers because of theirlarge spatial extent. For example, it was reported that fluctuations of either bond-angle or ring statistics rather thanbond length are effective in generating band-tail states.47
Thus, the nature of the weakly localized centers is probably
different from that of the 2.004 center.
V. SUMMARY

This paper follows up our previous work22 with more
complete experimental data and discussion. We have inves-*Present address: System Devices and Fundamental Research,
NEC Corporation, Tsukuba, 305-8501, Japan.
1
S. Yamasaki, Philos. Mag. B 56, 79 共1987兲.
2
S. Aljishi, J. D. Cohen, S. Jin, and L. Ley, Phys. Rev. Lett. 64,
2811 共1990兲.
3
T. Tiedje, J. M. Cebulka, D. L. Morel, and B. Abels, Phys. Rev.
Lett. 46, 1425 共1981兲; W. E. Spear and C. S. Cloude, Philos.
Mag. B 58, 467 共1988兲; M. Kemp and M. Silver, ibid. 63, 437
共1991兲.
4
K. Hattori, H. Okamoto, and Y. Hamakawa, J. Non-Cryst. Solids
198-200, 288 共1996兲.

15 709tigated the electronic and microscopic structures of the
LESR centers of g⫽2.004 共conduction-band-tail electrons兲
and 2.01 共valence-band-tail holes兲 in undoped a-Si:H on thebasis of detailed analyses of their 29Si hf structures. In thisstudy, we took advantage of pulsed ESR techniques, samples
with different content of 29Si 共1.6, 4.7, 9.1 at. %兲, and multifrequency 共3–34 GHz兲 ESR studies, and obtained experimental results as follows.
共1兲 The T 1 of the g⫽2.004 center is about three times
longer than that of g⫽2.01 共Sec. III A兲. Using the T 1 difference, the LESR spectra can be experimentally deconvoluted
into two independent signals for g⫽2.004 and 2.01 共Sec.
III B兲.
共2兲 The fractional intensity of the 29Si hf structure in thedeconvoluted signal of g⫽2.004 revealed that the wave
function of the 2.004 center spreads mainly over two Si atoms 共Sec. III C兲. This suggests that the origin of the 2.004
center is electrons trapped in the antibonding states of the
weak Si-Si bond rather than those trapped in the positively
charged DB’s 共Sec. IV A兲. By analogy, we suggested that the2.01 center arises from holes trapped in the bonding states of
the weak Si-Si bond.
共3兲 The 29Si isotropic hf splitting of g⫽2.004 was estimated to be around 7 mT, while that of g⫽2.01 was below 3
mT 共Sec. III C兲. This indicates that the wave function of g
⫽2.01 consists mainly of the 3p component, while the wave
function of g⫽2.004 has more 3s component compared to
the 2.01 center. The difference can be accounted for within
the framework of the weak-bond model 共Sec. IV A兲.
共4兲 The anisotropic line shape of g⫽2.01 originates froma large anisotropy of the g value 共Sec. III C兲.
共5兲 We discussed the difference in the nature of band-tailelectrons observed in LESR and PL experiments on the basisof our results and other experimental findings 共Sec. IV B兲.
The discussion pointed out that the 2.004 electrons are presumably more localized and are located in deeper band-taillevels than the PL electrons.
ACKNOWLEDGMENTS

The authors thank Dr. A. Matsuda, Dr. H. Okushi, Dr. H.
Katagiri, and Dr. N. Ishii for valuable suggestions, and weare also grateful to Dr. S. Hayashi for NMR analyses of oursamples. This work, partly supported by NEDO, was performed in the Joint Research Center for Atom Technology
共JRCAT兲 under the joint research agreement between the National Institute for Advanced Interdisciplinary Research
共NAIR兲 and the Angstrom Technology Partnership 共ATP兲.
5

J. C. Knights, D. K. Biegelsen, and I. Solomon, Solid State Commun. 22, 133 共1977兲.
6
H. Dersh, J. Stuke, and J. Bachelor, Phys. Status Solidi B 105,
265 共1981兲.
7
R. A. Street, D. K. Biegelsen, and R. L. Weisfield, Phys. Rev. B
30, 5861 共1984兲.
8
M. Stutzmann, D. K. Biegelsen, and R. A. Street, Phys. Rev. B
35, 5666 共1987兲.
9
S. G. Bishop, U. Strom, and P. C. Taylor, Phys. Rev. Lett. 34,
1346 共1975兲; 36, 543 共1976兲.
10
R. A. Street and N. F. Mott, Phys. Rev. Lett. 35, 1293 共1975兲.

15 710
11

UMEDA, YAMASAKI, ISOYA, AND TANAKA

M. Kastner, D. Adler, and H. Fritzsche, Phys. Rev. Lett. 37, 1504
共1976兲.
12
M. Stutzmann and D. K. Biegelsen, Phys. Rev. B 40, 9834
共1989兲; in Amorphous Silicon and Related Materials, edited by
H. Fritzsche 共World Scientific, Singapore, 1988兲, pp. 557–594.
13
N. Ishii and T. Shimizu, Phys. Rev. B 42, 9697 共1990兲.
14
T. Umeda, S. Yamasaki, J. Isoya, and K. Tanaka, Phys. Rev. B
59, 4849 共1999兲.
15
J. D. Cohen, J. P. Harbison, and K. W. Wecht, Phys. Rev. Lett.
48, 109 共1982兲.
16
H. Okamoto and Y. Hamakawa, Solid State Commun. 24, 1197
共1977兲.
17
D. Adler, Sol. Cells 9, 133 共1983兲.
18
K. Morigaki, J. Phys. Soc. Jpn. 50, 2279 共1981兲.
19
S. Yamasaki, H. Okushi, A. Matsuda, K. Tanaka, and J. Isoya,
Phys. Rev. Lett. 65, 756 共1990兲.
20
N. Orita, T. Matsumura, and H. Katayama-Yoshida, J. Non-Cryst.
Solids 198-200, 347 共1996兲.
21
S. Yamasaki, S. Kuroda, J. Isoya, and K. Tanaka, J. Non-Cryst.
Solids 97-98, 691 共1987兲.
22
T. Umeda, S. Yamasaki, J. Isoya, A. Matsuda, and K. Tanaka,
Phys. Rev. Lett. 77, 4600 共1996兲.
23
S. Yamasaki, Electrotecnical Laboratory Research Report No.
883, 1987 共unpublished兲.
24
J. Isoya, S. Yamasaki, A. Matsuda, and K. Tanaka, Philos. Mag.
B 69, 263 共1994兲.
25
J. Isoya, S. Yamasaki, H. Okushi, A. Matsuda, and K. Tanaka,
Phys. Rev. B 47, 7013 共1993兲.
26
M. Stutzmann and D. K. Biegelsen, Phys. Rev. B 28, 6256
共1983兲.
27
Under illumination, T 1 of g⫽2.0055 can be decreased due toconversion between neutral and charged DB states, and also dueto the cross relaxation between 2.0055 and 2.01 spins, whichwere discussed in Refs. 26 and 28, respectively.
28
M. K. Bowman and L. Kevan, in Time Domain Electron Spin
Resonance, edited by L. Kevan and R. N. Schwartz 共Wiley, New
York, 1979兲, pp. 67–106.

29

PRB 62

G. Schumm, W. B. Jackson, and R. A. Street, Phys. Rev. B 48,
14 198 共1993兲.
30
T. Umeda, S. Yamasaki, J. Isoya, A. Matsuda, and K. Tanaka, J.
Non-Cryst. Solids 227-230, 353 共1998兲.
31
P. C. Taylor, J. F. Baugher, and H. M. Kriz, Chem. Rev. 75, 203
共1975兲.
32
H. Dersh, J. Stuke, and J. Beichler, Phys. Status Solidi B 107, 307
共1981兲.
33
G. D. Watkins and J. W. Corbett, Phys. Rev. A 134, 1359 共1964兲.
34
M. Stutzmann, W. B. Jackson, and C. C. Tsai, Phys. Rev. B 32,
23 共1985兲.
35
W. B. Jackson, S. M. Kelso, C. C. Tsai, J. W. Allen, and S.-J. Oh,
Phys. Rev. B 31, 5187 共1985兲.
36
K. Takeda, K. Shiraishi, M. Fujiki, M. Kondo, and K. Morigaki,
Phys. Rev. B 50, 5171 共1994兲.
37
N. Ishii and T. Shimizu, Solid State Commun. 102, 647 共1997兲.
38
A. J. Stone, Proc. R. Soc. London, Ser. A 271, 424 共1963兲.
39
T. Kamei, N. Hata, A. Matsuda, T. Uchiyama, S. Amano, K.
Tsukamoto, Y. Yoshioka, and T. Hirao, Appl. Phys. Lett. 68,
2380 共1996兲.
40
C. Tsang and R. A. Street, Phys. Rev. B 19, 3027 共1979兲.
41
M. Yoshida and K. Morigaki, J. Phys. Soc. Jpn. 58, 3371 共1989兲.
42
F. Boulitrop, Phys. Rev. B 28, 6192 共1983兲.
43
D. Weaire, N. Higgins, P. Moore, and I. Marshall, Philos. Mag. B
40, 243 共1979兲.
44
H. Takenaka, C. Ogihara, and K. Morigaki, J. Phys. Soc. Jpn. 57,
3858 共1988兲.
45
J. H. Zhou, S. Yamasaki, J. Isoya, K. Ikuta, M. Kondo, A. Matsuda, and K. Tanaka, in Advances in Microcrystalline and Nanocrystalline Semiconductors—1996, edited by R. W. Collins, P.
M. Fauchet, I. Shimizu, J.-C. Vial, T. Shimada, and P. A. Alivisatos, MRS Symposia Proceedings No. 452 共Materials ResearchSociety, Pittsburgh, 1997兲, p. 821.
46
N. Ishii, M. Kumeda, and T. Shimizu, Phys. Status Solidi B 116,
91 共1983兲.
47
F. Yonezawa and M. H. Cohen, in Fundamental Physics of Amorphous Semiconductors, edited by F. Yonezawa 共SpringerVerlag, Singapore, 1981兲, pp. 119–144.