Subcontract Report

NREL/SR-520-46649

September 2009

Innovative Characterization of 

Amorphous and Thin-Film Silicon 

for Improved Module Performance

1 February 2005 – 31 July 2008

P.C. Taylor and G.A. Williams

University of Utah

Salt Lake City, Utah
National Renewable Energy Laboratory

1617 Cole Boulevard, Golden, Colorado 80401-3393

303-275-3000 • www.nrel.gov

NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency and Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

Contract No. DE-AC36-08-GO28308

Subcontract Report

NREL/SR-520-46649

September 2009

Innovative Characterization of 

Amorphous and Thin-Film Silicon 

for Improved Module Performance

1 February 2005 – 31 July 2008

P.C. Taylor and G.A. Williams

University of Utah

Salt Lake City, Utah

NREL Technical Monitor: Name: Bolko von Roedern

Prepared under Subcontract No. XXL-5-44205-09
This publication was reproduced from the best available copy

Submitted by the subcontractor and received no editorial review at NREL

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iii

Table of Contents

I. Introduction ...........................................................................................................1

II. The Hydrogen Doublet Defect ...........................................................................................1

III. Silicon Dihydride and Silicon Doublets.............................................................................6

IV. Hydrogen-Hydrogen Separation at Silicon Dihydride Bonding Sites in a-Si:H..............15

V. Calculations of Silicon Dihydride Bonding Sites in a-Si:H. ............................................19

VI. Defects in Tritiated a-Si:H ...............................................................................................23

VII. Hydrogen Diffusion and Crystallization ..........................................................................31

VIII. Summary ..........................................................................................................................36

References...................................................................................................................................36
iv
1

I. Introduction

Research results during the duration of NREL Subcontract XXL-5-44205-09 are reported. 

We performed collaborative research with United Solar Ovonics Corporation on defects that 

contribute to the Staebler-Wronski effect in modules made using a-Si:H and a-SixGe1-x:H 

intrinsic layers. Specifically, we performed electron spin resonance (ESR) on a set of devicequality samples, half of which were light soaked. We also performed nuclear magnetic 

resonance (NMR) experiments on these samples to investigate hydrogen doublet sites. In 

addition, we investigated the defects generated in tritiated a-Si:H at both 300 and 77 K in 

collaboration with scientists at NREL. Finally, we performed studies of light soaking at 77 K to 

compare the kinetics with those for the creation of defects at 77 K by tritium decay. 

II. The Hydrogen Doublet Defect

We have previously reported an 1H NMR signal in a-Si:H that occurs only after light soaking 

for 600 hours [1]. This signal, which is attributed to a pair of hydrogen atoms, exhibits similar 

annealing kinetics to that of the defects created during light-soaking, and the concentration of 

these sites is comparable to that of the defects measured by electron spin resonance (ESR). The 

distance between the two hydrogen atoms in the pair is about 2.3 Å. Preliminary data on the 

temperature dependence of the lineshape suggested that the pair may undergo some form of local 

motion as the temperature increases [1], but the evidence was not compelling. In addition, our 

earlier measurements could not exclude the possibility that the additional lineshape was due to a 

hydrogen triplet with the central peak masked by the narrow line from bonded hydrogen. We 

have recently investigated the lineshape of this 1H NMR feature in further detail as well as its 

temperature dependence at a magnetic field, B0, of 3.5 T. 

We have found that the spin-lattice relaxation time (T1) of the doublet has a strong 

temperature dependence, which may indicate a thermally activated motion. However, this 

dependence cannot be explained by a simple thermally activated, random diffusive process, such 

as that described by the Bloembergen, Purcell, and Pound model (BPP model). In particular, for 

temperatures between 6.5 and 20 K we find no evidence that the doublet lineshape is narrowed 

due to motional effects as would be expected if the simplest BPP model applied.

These experiments were performed on a light-soaked, thin film of a-Si:H, which was 

originally made at BP Solar in a large area deposition system by DC plasma enhanced chemical 

vapor deposition (PECVD). The film was light-soaked for 600 hr with a solar simulator. We 

have published the details of the sample preparation elsewhere [1,2]. Details of the NMR 

measurements can also be found elsewhere [1]. We have used our standard technique to 

suppress the much stronger signal from hydrogen bonded to silicon atoms, namely, a JeenerBroekaert three-pulse sequence [3]. The NMR line shapes are obtained by recording the 

stimulated echo after the Jeener-Broekaert sequence. The echo intensity I(τ1, τ2) is given by [4]

}exp{ ( ) } 2 ( , ) exp{ 2

1

1

2

2

1

1 2 0 T T D

I I τ τ

τ τ = − − , (1)
2

where τ1 and τ2 are the separations between the first and second pulses, and the second and third 

pulses, respectively. T2 and T1D are the spin-spin relaxation time and the dipolar spin lattice

relaxation time, respectively. A typical pulse width for the 90o pulse is about 2 μs.

At a 1H NMR frequency ω0 = 147.417 MHz and at low temperatures, the values of T1 for the 

hydrogen, which is bonded to silicon (bonded hydrogen), are too long for these hydrogen sites to 

fully recover using a practical pulse repetition rate. Therefore the signal from the bonded 

hydrogen is suppressed due to partial saturation. The dependence of the NMR signal I on the 

delay time between two scans, Td, is,

(1 ) 1 /

0

Td T I I e− = − , (2)

where I0 is the amplitude of the fully relaxed signal. The inverse of Td is the rate at which the 

three-pulse sequence is repeated (repetition rate). When Td << T1 , the relation becomes,

1

0 T

T

I I d = . (3)

Figure 1 shows the temperature dependence of the NMR line shapes at B0 = 3.5 T. The 

lineshape obtained earlier [1] at B0 = 2 T and T = 7 K is also shown for comparison. [In all line 

shapes shown in this report the Zeeman frequency has been subtracted so that the peaks are 

centered about zero.] The composite line shapes contain a narrow line (~ 4 kHz FWHM) and a 

broad line (~ 25 kHz FWHM) as is always seen in typical a-Si:H samples prepared by the 

PECVD technique. The narrow line is attributed to randomly occurring hydrogen atoms that are 

bonded to silicon, hereafter termed “dilute” hydrogen. The broad line is attributed to hydrogen 

atoms bonded to silicon in a clustered configuration, hereafter termed “clustered” hydrogen. In 

addition, a small doublet occurs with a splitting ∆ν = 15 kHz as indicated by the dashed lines. 

As can be seen from Fig. 1, ∆ν is constant for B0 = 2 T and B0 = 3.5 T. At B0 = 3.5 T, ∆ν

remains the same, within the experimental error, at T = 7 K and T = 10 K. The doublet is less 

obvious at T = 6.5 T and T = 20 K. As we will discuss below, this behavior is attributed to the 

different temperature dependences of the T1’s for the bonded hydrogen and the doublet. A 

detailed comparison of the composite lineshape shows that no motional narrowing of the doublet 

occurs for temperatures up to 20 K.

Figure 2 shows the temperature dependence of T1 for both the bonded hydrogen and the 

doublet, plotted as log(T1) against 1000/T. Open circles denote the data for bonded hydrogen. 

Solid circles denote the data for the doublet. The lines are aids to the eye. The value of T1 for 

bonded hydrogen, hereafter denoted as T1(B), at 4.2 K is an extrapolation from the data at 92.5 

MHz [3], assuming a field dependence of T1 as 2 T1 ∝π . As can be seen in Fig. 2, T1 of the 

doublet, hereafter denoted as T1(D), increases much more rapidly than T1(B), as the temperature 

decreases. For temperatures below about 6 K, T1(D) > T1(B). This relationship means that at the
3

Frequency (kHz)

-40 -20 0 20 40

Amplitude (arb. unit)

0

2

4

6

8

T = 6.5K, B0 = 3.5T

Td = 30 s

T = 7 K, B0 = 2 T

Td = 2 s

T = 7 K, B0 = 3.5T

Td = 5 S

T = 10 K, B0 = 3.5T

Td = 1 s

T = 20 K, B0 = 3.5T

Td = 0.5 S

Figure 1. 1H NMR line shapes from the light-soaked sample at different temperatures and at 

two magnetic fields, B0 = 2 T and B0 = 3.5 T. The two dashed lines indicate where the doublet 

appears.

1000/T (K-1)

0 50 100 150 200 250 300

logT1 (s)

-3

-2

-1

0

1

2

3

Paired hydrogen

Bonded hydorgen

10 7.5 7.0 6.5 4.2

Temperature (K)

Figure 2. Temperature dependence of T1 for the hydrogen doublet and the bonded hydrogen. 

The open circles represent the data for bonded hydrogen. The solid circles represent the data 

for the hydrogen doublet. The lines are aids to the eye. The dashed-dotted line is a straight 

line with a slope of 100 K. See text for details. 
4

lowest temperatures the signal from the bonded hydrogen will recover faster than that of the 

doublet, resulting in an apparent suppression of the signal from the doublet. On the other hand, 

at T = 20 K, T1(B) is short enough compared to the pulse repetition rate so that most of the signal 

from bonded hydrogen fully recovers, and once again effectively reduces the signal from the 

doublet. In short, the doublet only becomes visible when the signal from bonded hydrogen is 

drastically reduced by the dipolar echo sequence (due to a much more rapid T1d) and also 

reduced by partial saturation (due to a much longer T1).

Figure 3 shows the comparison of the lineshape at 7 K, with a recovery time Td = 5 s, and the 

lineshape at 20 K with Td = 0.5 s, in which the signal from the bonded hydrogen has relaxed and 

the signal from the doublet is effectively suppressed. Solid circles and open circles represent the 

data at 7 K and 20 K, respectively. The solid line represents a subtraction of the 20 K data from 

the 7 K data, and the dashed line is a fit to this subtraction with a Pake doublet powder pattern 

that is broadened isotropically by a Gaussian whose width is approximately 10% of the splitting 

between the two divergences. The sharp negative spike near the center is an artifact due to small 

phase errors in the complex Fourier transforms. The splitting between the two divergences is 

about 16 kHz. This value is consistent with that previously estimated from measurements at a 

lower frequency [1].

Frequency (kHz)

-40 -20 0 20 40

Amplitude (arb. unit)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Figure 3. 1H NMR line shapes from the light-soaked sample at different temperatures and at a 

magnetic field B0 = 3.5 T. Solid circles represent data at 7 K taken with Td = 5 s. Open circles 

represent data at 20 K taken with Td = 0.5 s. The solid line represents the difference between 

the data at 7 K and 10 K. The dashed line is a fit using a Pake doublet powder pattern 

broadened isotropically by about 2 kHz, with a splitting between the two divergences of 16 

kHz. See text for details.

The most interesting result of this study is the strong temperature dependence of the spinlattice relaxation time of the doublet. In particular, for temperatures between 6.5 K and 20 K, the 

values of T1 for the doublet are shorter than those of the bonded hydrogen. Since most of the 

intensity in the doublet line is well outside the width of the narrow line, the dipole-dipole 

coupling between the doublet and the dilute hydrogen should be rather weak. Therefore, if the 
5

relaxation mechanism were the same (spin diffusion of the energy to a molecular hydrogen 

relaxation center) the T1 for the doublet should, if anything, be longer than that of the bonded 

hydrogen. Since the T1 of the doublet is actually shorter, there must be a different relaxation 

mechanism. Specifically, there must be a relaxation center close to the hydrogen doublet that is 

more efficient than spin diffusion to molecular hydrogen. A paramagnetic “impurity”, such as a 

silicon dangling bond, is one possibility, but in this case one must explain why this paramagnetic 

center does not also shorten the T1d of the doublet and why the doublets occur preferentially near 

such a relaxation center. 

A second possibility is thermally activated local motion of the hydrogen pairs. The simplest 

case is the BPP-type relaxation, in which the atoms jump randomly between different sites due to 

thermal activation. The local dipolar field experienced by the nuclei is modulated, and therefore 

induces relaxation of the nuclei. If one assumes a thermally activated hopping of hydrogen 

atoms, the hopping time τ can be expressed as

Ea kT

e

1 /

0

−1 − − τ = τ , (4)

where Ea is the activation energy and τ0 is a pre-factor that is, on the order of a phonon 

frequency. 

In the BPP model T1 is given as

2

0 /

1 0

E kT a T e ω

τ

ω

 

∝     ∆ , (5)

where ∆ω is on the order of the dipolar line width and ω0 is the Zeeman frequency. In our case, 

eq. 5 does not appear to hold because the dependence of T1on ω0 is weaker than quadratic. In 

addition, for reasonable choices of ∆ω and τ0 the observed values of T1 imply that the doublet 

lineshape should be motionally narrowed, which is also not the case. Earlier works have 

suggested that if there exists a distribution of τ, which is very likely in disordered materials, then 

one might be able to fit the observed temperature dependence of T1 consistently [5,6]; however, 

even if this is the case, the observed lineshape will be a sum of the line shapes with hydrogen 

atoms at different sites, and one would again expect a change in lineshape with temperature. 

Therefore, if the hydrogen pairs are undergoing local motion, it must be some form of correlated 

motion that maintains the distance between the two hydrogen atoms in a pair. 

The second issue is the absence of motional narrowing of the doublet lineshape. From T = 

6.5 K up to T = 20 K, the doublet lineshape remains unchanged. In the case of the random 

hopping of the atoms, motional narrowing of the NMR line occurs when τ = (∆ν)

−1, where ∆ν is 

the line width. For the doublet, ∆ν = 16 kHz, which gives a value of τ between 10 –5 and 10-4

s. 

Our calculation shows that the temperature at which the narrowing should occur is below 6 K, 

but we observe no narrowing between 6.5 K and 20 K. The microscopic mechanism for the spin 

lattice relaxation of the hydrogen doublet is currently unknown. 
6

In summary, we have investigated the temperature dependence of the paired hydrogen site 

that is associated with light-soaking. We find that the spin-lattice relaxation time of these paired 

hydrogen atoms strongly depends on temperature between 6.5 K and 20 K. A simple model 

assuming that hydrogen atoms are hopping randomly between different sites cannot explain this 

dependence. For temperatures between 6.5 K and 20 K, we do not observe motional narrowing. 

A subtraction of the spectra at 7 K and 20 K provides an approximate lineshape for the site 

associated with light soaking and supports the attribution of this site to a pair of hydrogen atoms, 

which are approximately 2.3 Å apart. 

III. Silicon Dihydride and Silicon Doublets

a. Silicon Dihydride Bonding

Since the discovery of the Staebler-Wronski effect (SWE), many studies have contributed to 

our understanding of the role of hydrogen in producing this metastable effect in hydrogenated 

amorphous silicon (a-Si:H). Models of this metastability, such as those of Stutzmann et al. [7] 

and Branz [8], have the common component that hydrogen must play a role in forming or 

stabilizing a metastable site [7,8]. Our recent 1

H NMR studies of device quality a-Si:H have 

found a paired hydrogen site (H-H) with an H-H distance of 2.3 ± 0.2 Å [9]. This previous study 

indicates that the H-H site is probably metastable; however, the study does not identify the 

specific H-H bonding configuration. A natural candidate for the bonding configuration is SiH2, 

which is predicted to have an H-H separation of 2.4 Å, assuming a tetrahedral structure with a SiH bond length of 1.5 Å. Furthermore, a recent calculation by Tasfaye et al. demonstrates the 

existence of SiH2 in the amorphous network with an H-H separation of approximately 2.4 Å [10]. 

Although these results are suggestive, no conclusive measurements of the H-H distance for SiH2

have been performed in the a-Si:H system. 

The difficulty with assuming that SiH2 is the metastable site derives from a stability 

argument. Annealing studies have shown little change in SiH2 concentrations for temperatures 

up to 600 K [11], and yet it is known that annealing of metastable defects occurs at temperatures 

of ~ 200° C. From these disparate temperature dependences it seems unlikely that SiH2 is 

created or destroyed during light soaking and subsequent annealing. It is possible that the 

metastable doublet observed by Su et al. somehow becomes observable in the NMR experiments 

after light soaking, but there are some compelling arguments to suggest that this is not the case 

[9].

These considerations have motivated the current work. In particular, by combining NMR 

and far infrared spectroscopic evidence, we have positively identified a specific NMR lineshape 

as due to SiH2 and presented the first detailed 1

H NMR study of stable SiH2 in a-Si:H. 

 

The sample used for this set of experiments was grown at United Solar Ovonics using 

plasma enhanced chemical vapor deposition (PECVD) of silane (SiH4). The film was grown on 

aluminum foil at 5 Å/s with a substrate temperature of 200 oC. This high growth rate typically 

yields films with a high defect density [12]. Half the sample was then light soaked, with one sun 

intensity, for 200 hours while the other half remained “as grown”. Electron spin resonance 

(ESR) measurements showed the defect densities for silicon dangling bonds to be on the order of 
7

1016

cm-3 for the as-grown sample. For the ESR and NMR measurements, the samples were 

prepared as powders using methods discussed previously [9]. 

 

Since hydrogen exists in a variety of environments in a-Si:H, each having a unique 1H NMR 

signature, it is difficult to separate individual components in a typical spectrum. Therefore it is 

often necessary to use a pulse sequence that can suppress the dominant line shapes with a 

suitable choice of pulse parameters. As mentioned in the previous section, the three-pulse 

Jeener-Brockaert (JB) sequence provides such a filtering method [13]. At a time ~ τ2 after the 

third pulse, a spin echo forms with the an echo intensity given by

1 / 2

1

1

2

2

1

1 2

1 2 1 0 ( , , ) (1 ) 













 − − −

= − d

d

T T T

d I I e e e

τ τ τ

τ τ τ , (6)

where Io is the initial maximum intensity, T1 is the spin-lattice relaxation time, T2 is the spin dephasing time or spin-spin relaxation time, and T1d is the dipolar spin relaxation time. Henceforth 

the pulse separations will be denoted as τ2 and τ1d, and the time over which the three-pulse 

sequence is repeated will be denoted as τ1. The utility of this sequence relies on the fact that 

each hydrogen environment has its own T2 and T1d. For our purposes, it is also necessary to have 

either relaxation parameter, T2 or T1d, longer than those for the more dominant hydrogen 

environments, which are due to SiH that is either randomly placed or clustered in the sample. 

Since τ1 characterizes a signal growth, filtering with parameter τ1 is effective for components 

with T1 shorter than those of the dominant sites. 

Using the Jeener-Brockaert sequence with parameters {7s, 60μs, 20ms} we obtain in the asgrown sample a line shape displaying a doublet feature with peak-to-peak splitting (Δν) of ~ 16

kHz as shown in Fig. 4. For reference, this figure also contains the line shape found by Su et al.

[9], which shows a similar doublet feature having Δν ~ 14 kHz. The dashed lines, which serve as 

aides to the eye, show a qualitative difference in the peak positions. Signatures of the clustered 

and isolated hydrogen sites (existing as SiH) are also present. Past studies have shown these 

clustered and isolated components contribute to the line shape a Gaussian of ~ 25 kHz full width 

half max (FWHM) and a Lorentzian of ~ 4 kHz FWHM, respectively [14]. 

Figure 5 shows the doublet line shape for temperatures between 5 and 20 K. Due to the 

temperature dependence of T1, we vary τ1 accordingly to obtain a similar line shape for 

each temperature. The parameter τ1 is chosen to be roughly one T1 for the line-shape components 

attributed to clustered and isolated SiH sites. 

Going to longer τ1d suppresses the Gaussian and Lorentzian components thereby yielding a 

more accurate line shape for the doublet. Figure 3 shows such a trace (bottom trace). In the top 

trace in Fig. 6 the doublet signal has decayed almost to the noise level, and the remaining two 

components in the line shape are due to molecular hydrogen (H2). Shoulders occurring at ± 90 

kHz are characteristic of H2, which is frozen into the lowest rotational state. The narrow central 

peak is due to H2, which exists in thermally excited rotational states [15]. 
8

Figure 4. Characteristic line shape for a doublet in two different samples. Shown in the top trace 

is the as-grown, high-growth-rate sample. The bottom trace is the light-soaked, low-defectdensity sample from ref. [9]. Vertical lines are aides to the eye.

Figure 5. Line shape of 1H NMR at various temperatures. NMR parameters are {1 T1, 60 μs, 20 ms} 

for each trace. T1 values are T1 = 10s, 8s, 2s, 1s for T = 5K , 8K, 12K, 20K, respectively.

Subtracting the two traces in Fig. 6 yields a good approximation of the doublet line shape. 

Figure 7 shows the result of this subtraction superimposed on a calculated Pake doublet powder 

pattern that is broadened by Gaussian of 15 kHz FWHM. The Pake doublet powder pattern is 

the line shape expected theoretically for an ensemble of paired hydrogen sites that are randomly 

oriented with respect to the magnetic field. Divergences at ± 14.1 kHz in the de-convoluted 

powder pattern (not shown) are related to the dipolar coupling constant, which varies inversely 

as the H-H separation cubed. From the divergences in this particular case, we calculate an H-H

separation of 1.8 Å. 

We note here, that the real Fourier transforms of time domain data are shown. Imperfect 

phase mixing in the quadrature detection scheme, especially for weak signals, results in a 

complex transform that is asymmetric. We stress that the doublet is observed from the full
9

transforms but that the lineshape is distorted in data sets that are not sufficiently well phased 

mixed. 

Figure 6. Bottom trace: NMR line shape for {7 s, 60 μs, and 45 ms}. Bonded SiH has decayed 

leaving only the doublet and H2. Top trace: NMR line shape for {7 s, 60 μs, and 90 ms}. Only the 

H2 signal remains.

Figure 7. Doublet resulting from subtraction of the two traces in Fig. 6. The smooth line is a 

calculated Pake doublet powder pattern broadened by a Gaussian of approximately 15 kHz FWHM. 

See text for details of this calculation.

Besides the qualitatively different peak doublet positions, Fig. 4 suggests that the highgrowth-rate sample contains a large density of H-H sites (large compared to 10-17

cm-3, the 

density of sites seen by Su et al. [8]). To quantify this claim, we have used the NMR methods 

discussed in [15] to estimate a density of at most 3 at. % for this doublet site. Also, we infer a 

minimum density of ~ 1 at. % from vibrational modes observed in Fourier transform infrared 

spectroscopy. Densities this large, ~1021, suggest that this H-H sight is fundamentally different 

from that found only in light-soaked samples in ref. [9]. 
10

The original intent of this work was to investigate in greater detail the metastable hydrogen 

doublet that accompanies the SWE using a sample, which has a large defect density in the lightsoaked state. In this case, the as-grown sample would provide a benchmark line shape for 

comparison with the light soaked sample. Unfortunately, because of the much smaller density of 

the metastable doublet sites, we have to date not succeeded in making this comparison. The 

major complicating fact is the occurrence in the sample of a doublet at much higher densities, 

and therefore comparisons of the as-grown and light-soaked samples (not shown in this quarterly 

status report) show no difference in the line shapes. The stable hydrogen doublet site persists in 

both samples. Therefore, we have concentrated on identifying the hydrogen-hydrogen (H-H) 

arrangement to determine the H-H separation in this site. 

To characterize further this different H-H site, we have investigated the line shape as a 

function of the temperature, as shown in Fig. 5. Line shape variations due to motional effects 

usually exhibit strong temperature dependences due to thermal activation over barriers to the 

motion. The doublet line shapes in Fig. 5 display no evidence of motional narrowing. Hence we 

conclude that the doublet consists of hydrogen bonded to silicon.

Definitive identification of the identity of this H-H site comes from comparison with 

infrared spectra. This sample exhibits vibrational modes at 900 cm-1 and 850 cm-1

, which

correspond, respectively, to scissors and wagging modes of SiH2. Therefore, based on the 

density of sites, their thermal stability, and their infrared vibrational modes, we attribute the 

doublet line shape to SiH2. 

In summary, we have made the first detailed NMR measurement of stable SiH2 in high 

defect density a-Si:H. By filtering out the bonded SiH signals, and subtracting the remaining H2

signal, we obtain the SiH2 signature: a “doublet” with peak-to-peak splitting of ~ 16 kHz. By 

considering an isolated SiH2 with a well-defined H-H separation, we calculate 1.8 Å for the H-H

separation in SiH2. 

b. Si-H Bonding Sites

The implication of hydrogen in the Staebler-Wronski effect (SWE) in hydrogenated 

amorphous silicon (a-Si:H) has generated enormous interest in understanding the local bonding 

environments of the hydrogen. In particular, recent proton (1

H) nuclear magnetic resonance 

(NMR) experiments have linked a specific metastable, “paired” hydrogen site, in which the 

hydrogen pair is separated by 2.3 ± 0.2 Å, to the SWE [16]. Silicon dihydride (SiH2) is a 

possible candidate for this site since calculations using the conventional tetrahedral silicon 

structure give 2.4 Å as the hydrogen separation [17]. 

Hydrogen environments can be probed using 1H NMR techniques because the hydrogen 

nucleus communicates with the environment through a variety of spin-mediated interactions. In 

a-Si:H, the dipole-dipole interaction between two protons dominates. For these magnetic dipole 

interactions, the strength depends strongly on the proton-proton separation. Exciting the system 

with radiation corresponding to the interaction strength causes the proton system to resonate 

thereby producing a detectable time varying signal. The resulting Fourier-transformed line shape 

yields details of the local hydrogen bonding configurations. For instance, by analysis of dipole 
11

broadened line shapes, it has been determined that in a-Si:H bonded hydrogen in the silicon 

hydride (SiH) configuration exists in both clustered and essentially randomly isolated 

environments [16].

The SiH2 line shape exhibits a well-known form resulting from a dipole interaction between 

two protons. An analytic expression of the intensity of this so-called “Pake doublet” line shape 

can be expressed in terms of the coupling strength, and hence the proton-proton separation, r. It 

is therefore possible to extract the proton-proton separation by fitting simulated line shapes to the 

experimental data. This would suffice if the SiH2 existed as an isolated species with a welldefined r. In the case where modulations to the local field exist, due to nearby hydrogen nuclei, 

the pure Pake doublet is broadened by an amount corresponding to the proximity and number of 

the nearby nuclei. This “isotropic” broadening effect, which is Gaussian for clustered arrays 

[18], can be taken as a fitting parameter in subsequent simulations. 

Broadening of the pure Pake doublet may also result from a distribution of proton-proton 

separations. It is known from scattering experiments that the nearest neighbor, Si-Si bond angles 

vary by ± 10° [19]. Thus it is natural to expect some distribution in r that will reflect the 

amorphous system. The distribution can also be used as a fitting parameter whereby the resulting 

broadened spectrum is a summation of Pake doublets.

Observation of SiH2 in low defect density a-Si:H has eluded 1

H NMR experiments primarily 

for two reasons. The first reason is obvious: in device quality films the SiH2 concentrations are 

usually below the threshold detection limit of conventional 1

H NMR (~ 10 16 cm-3). Moreover, 

SiH occurs in concentrations ~ 10 21cm-3 and therefore dominates the line shape in standard free 

induction decay (FID) experiments. This fact alone suggests that the FID experiments are 

insufficient for observing the low concentrations of SiH2. 

A more subtle reason for the lack of experimental observation of SiH2 in a-Si:H derives 

from the line shape broadening effects discussed above. Isotropic broadening becomes a 

problem when it is of the same the magnitude as the resolved dipolar coupling. In this case the 

Pake doublet is unresolved since its defining features smear to form a nearly Gaussian line shape. 

For instance, the un-broadened proton dipolar coupling in SiH2 with r = 2.4 Å is 13.4 kHz [18]. 

The typical clustered hydrogen environment yields a Gaussian with ~ 25 kHz full width at half 

maximum (denoted henceforth as σ). Thus there will be no resolved SiH2 line shape if it exists 

in an environment that resembles the standard clustered array. 

In the present study, we have used 1

H NMR to obtain the stable SiH2 Pake doublet. 

Simulations of the Pake doublet for various choices of broadening effects were performed. We 

discuss the simulation details and relevant fitting parameters needed to replicate the experimental 

data. 

The a-Si:H sample used in this study was made at United Solar Ovonic Corporation at high 

growth rate (5 Å/s). The film was grown on aluminum foil at a substrate temperature of 200 °C. 

Such samples contain higher defect densities (≥ 1017 cm-3) and are generally not suitable for 

device applications. Fourier transform infrared spectroscopy (FTIR) measurements show IR 

active modes at 900 cm-1 and 850 cm-1, indicative of the scissor and wagging SiH2 modes, 
12

respectively. The presence of these modes in the FTIR spectrum implies an SiH2 concentration 

on the order of 1021

cm-3 – well above the observation threshold for NMR. For subsequent NMR 

measurements, the sample was prepared as a powder according to methods previously discussed 

[16]. 

For spectral simulations, we numerically compute the “powder pattern” using a method 

similar to that described by Slichter [20]. The program was built in C++ using the pre-written 

functions of the GAMMA libraries [21]. For simulations requiring a distribution of r, we chose a 

Gaussian distribution where σ and mean separation, Ro, are the fitting parameters. Thus the full 

spectrum resulting from a distribution in r is the summation of individual powder patterns 

(whose weight depends on the distribution parameters). 

Figure 8 shows the frequency domain spectrum of the experimentally obtained Pake doublet 

with two simulations superimposed. We obtain the experimental Pake doublet by Fourier 

transforming the time domain signal and subtracting the remaining molecular hydrogen signal. 

The Zeeman frequency (147.417 MHz) has been subtracted so that the spectral center occurs at 0 

Hz. The solid line represents the experimental Pake doublet. For comparison we present the 

simulated Pake doublets for r = 1.8 Å (peaks at ± 15 kHz) and 2.4 Å (peaks at 

± 7 kHz). These simulations are broadened by 1 kHz, but they do not include a distribution of 

distances. The areas have been normalized to equal that of the experimental data. 

-75 -50 -25 0 25 50 75

Frequency (kHz)

Figure 8. Frequency domain spectrum of the experimental Pake doublet with simulations for r =

1.8 Å (shoulder peaks at ± 15 kHz ) and r = 2.4 Å (shoulder peaks at ± 7 kHz). The experimental 

data were obtained via a Fourier transform of the time domain data and subsequent subtraction of 

the molecular hydrogen signal. The Zeeman frequency (147.47 MHz) has been subtracted out so 

that the spectral center occurs at 0 Hz.

Figure 9 demonstrates, in frequency space, the separate effects of isotropic broadening by 

clustering and by a distribution in r. The top trace represents the unbroadened powder pattern 

for r = 1.8 Å. Below it, we present a spectrum broadened by 15 kHz (approximately 72% of the 

dipolar coupling). The bottom trace represents the powder pattern for a Gaussian distribution of 
13

r characterized by the parameters Ro = 1.8 Å, σ = 0.52 Å (30% of Ro). The bottom trace has 

been further broadened by 1 kHz. Similarities between the broadened spectra suggest that the set 

of simulation parameters replicating the data is not unique. 

-75 -50 -25 0 25 50 75

Frequency (kHz)

Figure 9. Broadening effects on the simulated Pake doublet for r = 1.8 Å. The top trace is a unique 

Pake doublet broadened by 1 kHz. The middle trace is the Pake doublet for r = 1.8 Å (no 

distribution) with 15 kHz isotropic broadening. The bottom trace represents the Pake doublet 

simulation for Ro = 1. 8 Å, σ = 0.54 Å, and 1 kHz isotropic broadening.

Figure 10 depicts the simulated spectral fits to the experimental data. The top trace is the 

simulated Pake doublet for r = 1.8 Å, broadened by 15 kHz superimposed on the experimental 

data. The bottom trace shows the Pake doublet for Ro = 1.8 Å, σ = 0.52 Å broadened by 1 kHz 

also superimposed on the experimental data. Dashed lines denote the simulated spectra. 

The experimental data of Fig 8 yield important clues for judicious choices of the fitting 

parameters. Of the three fitting parameters, the fit is most sensitive to Ro since it varies as r

-3

. 

Therefore we first choose Ro according to the qualitative agreement between the unbroadened 

spectra and experimental data. For r = 2.4 Å, the standard result for r in SiH2 according to 

theoretical calculations [17], there is a clear discrepancy in the shoulder peaks. Since subsequent 

broadening will only decrease the separation between peaks, it is clear that larger coupling 

constants (smaller r) are favored. With r = 1.8 Å, the shoulder peaks occur just outside of the 

experimental Pake doublet and serve as a good candidate for Ro. 

In accounting for the broadening effects, we note that the resolved peaks in the data require 

the total broadening to be less than the coupling constant—20.6 kHz for r = 1.8 Å. Two 

broadening mechanisms are available and hence any combination of the two satisfying the 

overall broadening requirement will yield a suitable fit. The NMR data are insufficient to answer 

the question of uniqueness. However, by mimicking the clustered and isolated environments 

known to exist for SiH (see for instance [17]), we deduce limits on the range of acceptable 

parameters.

We obtain the first limiting case by assuming that SiH2 exists in hydrogen-clustered regions 

of the amorphous network. We also place the constraint that there exists a well-defined r = 1.8 Å
14

Figure 10. Simulated Pake 

doublets superimposed on the 

experimental data. The dashed line 

in the top trace shows the 

simulation fit r = 1.8 Å (no 

distribution) with 15 kHz isotropic 

broadening. The dashed line in the 

bottom trace shows the simulation 

fit for Ro = 1. 8 Å, σ = 0.54 Å, and 1 

kHz isotropic broadening

for the SiH2 sites. This seems unreasonable in light of the known nearest neighbor bond angle 

variation [19]. In the clustered region, the SiH2 is isotropically broadened. The effect of 15 kHz 

of isotropic broadening is shown as the middle trace in Fig. 9. We present the fit to the data as 

the dashed line in the top trace of Fig. 10. The resulting spectrum sits outside the shoulders in 

the data—a discrepancy that may be accounted for by minor adjustments in Ro and the amount of 

isotropic broadening.

By imitating the isolated environment of SiH, we obtain the second limiting case. It is 

known, from hole burning experiments, that isolated SiH sees ~ 1 kHz broadening due to the 

surrounding hydrogen nuclei [18]. Thus we take this as our isotropic broadening parameter. To 

complete the broadening, we include a Gaussian distribution of r. The resulting spectrum with 

parameters Ro = 1.8 Å and σ = 0.54 Å is shown as the bottom trace of Fig. 2. The bottom trace 

of Fig. 10 shows the near perfect fit of these simulations to the data. Simulations with Ro = 1.9 Å 

and 1.7 Å have yielded inferior fits to those presented.

As demonstrated in Fig. 10 the true SiH2 environment cannot be inferred directly from the

NMR results. In either limiting case, Ro = 1.8 Å is the essential ingredient. Thus in light of prior 

1

H NMR results linking a paired hydrogen site with r = 2.4 Å to the SWE, it is unlikely that an 

“average” SiH2 site is involved. However, if the true r distribution includes this value, we cannot 

rule out SiH2 as a candidate. Therefore, if the metastable, paired hydrogen site that stabilizes the 

SWE is indeed a SiH2 site, then it must be a rare embodiment that is not indicative of the average 

site. 

In summary, we have fitted the experimental Pake doublet for stable SiH2 with line shape 

simulations whose fitting parameters reflect the local environment and variation in proton-proton 

separations. Accurate fits of the data are available for fitting parameters that imitate the 

clustered and isolated SiH environments. We take these sets of fitting parameters as the limiting 

cases whereby the true SiH2 environment is a mixture of the two. We find for both extremes that 

an accurate fit is obtainable only when the proton-proton separation in SiH2 is on average 1.8 Å. 

Hence a distribution of proton-proton separations is necessary if SiH2 is to be involved with the 

SWE. 

-75 -50 -25 0 25 50 75

Frequency (kHz)
15

IV. Hydrogen-Hydrogen Separation at Silicon Dihydride Bonding Sites in a-Si:H

The hydrogen bonding environments and their correlation to film quality have been the 

subject of an enormous body of research; see for example ref. [19]. It is generally believed that a 

more ordered a-Si:H matrix leads to smaller void structures and therefore to improved optoelectronic properties. As such, the concentration of large polysilane hydrogen structures, such as 

(SiH2)n , is thought to be small compared to the total hydrogen content for device quality films. 

IR studies seem to support this trend; higher quality films show no evidence of the (SiH2)n 

scissor or wagging modes near 800-900 cm-1. Most of the hydrogen is bonded to silicon and can 

be found either in clusters, such as on the internal surfaces of voids, or in isolated regions of the 

matrix. Since these sites occur in sufficient quantity, >1 atomic percent (at. %), they can be 

detected via their IR modes near 2000 cm-1. Below the IR sensitivity of approximately1 at %, 

the hydrogen bonding structures cannot be observed, and hence the (SiH2)n content is unknown. 

We have discussed above (previous section) the 1H NMR spectra of (SiH2)n in a high defect 

density film. At these sites the average hydrogen-hydrogen separation is 1.8 Å [22]. In this 

section we describe similar (SiH2)n structures in as-grown, higher quality material where the IR 

modes are absent. Of course, n may be unity for these sites; i.e., isolated silicon dihydride sites. 

Using 1H NMR, which is a more sensitive probe of the bonded hydrogen, we have estimated the 

(SiH2)n content for both films. We compare estimates of the (SiH2)n content. Contrary to current 

belief, we find a significant fraction of the total hydrogen content can be bonded in (SiH2)n 

configurations in “device quality” films supplied by United Solar Ovonics. The film has a darkto-photo conductivity ratio of 10-5

. IR absorption measurements show no evidence of the 800-

900 cm-1 wagging or scissor modes characteristic of (SiH2)n. 

The film produced at United Solar that we discussed in the previous section was 

intentionally grown at a high deposition rate by PECVD. As a result, a high defect density (mid 

1017 defects cm-3) film was produced that contained observable 800-900 cm-1 IR wagging or 

scissor modes. From the total intensity of these modes compared to the total 600 cm-1 absorption 

intensity due to bonded silicon monohydride, we estimate that the hydrogen occurring in the 

(SiH2)n configuration is approximately 10% of the total hydrogen. It is generally accepted that 

the 600 cm-1 absorption region contains contributions from all silicon bonded hydrogen sites 

[23,24]. Therefore, we take 10% as an estimate of the total hydrogen bonded in the (SiH2)n

form. 

The growth conditions for both films are summarized in Table 1. Results reported in this 

section are for the as-deposited films that have not been subjected to deliberate light soaking.

To probe the signal decay of each hydrogen component, we used the Jeener-Brockaert threepulse sequence. Details of the pulse sequence and its utility in studying hydrogen bonding in aSi:H can be found in ref. [25]. In this particular application, we measured the stimulated echo 

decay as a function of the time separation between pulse pairs. In general, the total signal 

amplitude, IT, can be written as:
16

∑ 













 − −

= i

T T

T d io

i d

d

i I I e e

1/ 2

1

1

2

2 2

2 1 ( , )

τ τ

τ τ (7)

where Iio represents the initial maximum intensity for the ith component (for a discussion of the 

usual line shapes, see ref. [26]), T2 is the characteristic decay time due to spin de-phasing, and 

T1d is the dipolar spin relaxation time. Pulses 1 and 2 are separated by τ2 (typical values are tens 

of μsec) while pulses 2 and 3 are separated by τ1d (tens of msec typically). We determine these 

parameters separately by measuring the decay of the intensity as a function of τ2 (τ1d) when τ1d

(τ2) is kept constant. 

When the decay times are known, the total maximum intensity for each component is 

computed by correcting the signal intensity, at any time, with the appropriate exponential 

arguments given in Eq. 7. This procedure amounts to extrapolating the component signal 

intensity to zero time. The total signal and the relative concentrations of any component, Ci, are 

then computed by:

= = = ∑

i

T d io I ( 0, 0) I 2 1 τ τ and ( 0, 0) 2 = 1 = =

T d

io

i I

I C

τ τ . (8)

Experimentally, it is quite difficult to obtain perfect line shape fits. The spectral features 

can be artificially distorted by imperfections in the detection scheme. As a result, the fits can 

lead to intensity mismatches that, in turn, affect the error reported in any one component. Since 

the measurement relies on an extrapolation of an exponential function, small uncertainties are 

compounded at τ2 , τ1d = 0. There is also uncertainty in the total intensity incurred from the 

signal to noise ratio of each measurement. Our measurements are reported using the combined, 

additive effects of these uncertainties. This procedure yields a more conservative error estimate 

than the standard quadrature rules of error propagation. 

Because no doublet features are observed in the NMR spectra obtained at τ2 and τ1d = 0 (the 

free induction decay), an upper bound on the concentration of (SiH2)n sites is estimated by 

calculating the total NMR frequency spectra with varying contributions from all known 

components. Figure 11 (bottom trace, solid line) demonstrates one such composite line shape 

that results when the spectra in the upper plot are added in concentrations of (top to bottom, 

respectively) 15%, 15% and 70%. When the percentages are 30%, 30%, and 40%, respectively, 

the doublet is no longer resolved. The top trace of the upper plots is a Lorentzian, corresponding 

to the isolated SiH and characterized by a full width at half maximum (FWHM) of 4.2 kHz. 

Immediately below it is a Gaussian with a FWHM of 25 kHz, which represents the clustered 

SiH. A simulation of the Pake doublet, where the average hydrogen-hydrogen splitting is 1.9 Å 

is drawn immediately below the Gaussian. This spectrum is characteristic of two strongly 

interacting hydrogen atoms as would occur for atoms in the (SiH2)n configuration [22]. The 

percentages are representative of the minimum (SiH2)n contribution necessary to achieve the 

resolved peaks near ±10 kHz shown in the bottom trace. The doublet peaks in Fig. 11 help to 

distinguish it from the other components that mask the doublet’s intensity. When these two 

features are present, the component concentrations can be more accurately determined.
17

Figure 11. Estimate of the 

minimum 1

H NMR signal 

intensity needed to observe 

(SiH2)n. Top: Normalized 1

H 

NMR signals of (top to bottom)

isolated SiH, clustered SiH, and 

(SiH2)n. Bottom: Signal 

resulting from addition of 

differing amounts of the three 

components. Solid line: 15% 

isolated SiH, 15% clustered 

SiH, and 70% (SiH2)n. Dashed 

Line: 30% isolated SiH, 30% 

clustered SiH, and 40% (SiH2)n

Table 1. Summary of (SiH2)n concentration measured from NMR and IR. The reported value is the 

percent concentration relative to the total hydrogen concentration observable by NMR and IR. 

“Min %” refers to the minimum concentration estimate, within experimental uncertainty. Details of 

the growth conditions are also provided.

Sample Min % (SiH2)n 

NMR Estimate

% (SiH2)n 

IR Estimate

Growth Conditions (films grown by PECVD) 

Substrate 

Temp (oC)

Growth Rate 

(Å/sec)

Power

(mW/cm2)

Pressure

(mTorr)

United Solar

(high quality)

12 No Modes 200 2 50 500

United Solar 

(low quality)

15 10 200 5 50 500

Figure 12 shows the decay of the intensity, for the 4 components, as a function of τ1d when 

τ2 = 60 μsec. The data have been scaled such that the extrapolation to τ1d = 0 msec is 100. The 

data are plotted on a log scale vs. (τ1d )

1/2 so the extrapolation to τ1d = 0 can be evaluated by 

inspection. The dashed lines, drawn as aides to the eye, enclose the τ1d = 0 (SiH2)n

concentrations allowed by experimental uncertainties. The upper (lower) bound occurs near 

70% (10%) of the total signal intensity. The combined Lorentzian and Gaussian contributions 

are plotted, since they have essentially the same T1d. At τ1d = 1 msec, the total Lorentzian and 

Gaussian components comprise essentially all of the total intensity. 

-100 -80 -60 -40 -20 0 20 40 60 80 100

-100 -80 -60 -40 -20 0 20 40 60 80 100

Frequency (kHz)

Intensity (Arb. Units)
18

0 1 2 3 4 5 6 7 8

0.1

1

10

100

Log(Intensity) Arb. Units

τ2

1/2 (msec)1/2

Figure 12. Log of the signal intensity as a function of (τ1d)

1/2. For all data points, τ2 = 60 

μsec. “▪” represent total signal intensity, “▲” represent the (SiH2)n intensity , “” 

represent the H2 x 10 intensity, and “” represents the clustered and isolated SiH 

signal intensity. Dashed lines are aides to the eye. These two dashed lines enclose the 

possible (SiH2)n signal intensities for τ1d = 0 msec as allowed by experimental 

uncertainty. 

Figure 13 shows the decay of the total intensity as a function of τ2, when τ1d = 1 msec for an aSi:H sample grown under the same conditions as those listed in Table 1. The data are again 

scaled to read 100 at τ2 = 0 μsec. There are two distinct decay regions, as indicated by the lines. 

The fast (slow) decay region has T2 ≅ 60 μsec (≅ 300 μsec). These T2 values correspond, 

respectively, to the Gaussian and Lorentzian components. 

0 20 40 60 80 100 120

10

20

30

40

50

60

70

80

90

100

Log(Intensity) Arb. Units

τ

2 (μsec)

Figure 13. Log of the total signal intensity as a function of τ2 (τ1d = 1 msec for all 

data points) for a typical a-Si:H film. The solid lines are aides to the eye and 

indicate the values of T2 for the clustered and isolated SiH. For the clustered 

SiH, T2 ≅ 60 μsec. The isolated SiH has a T2 ≅ 300 μsec.
19

The data in figs. 12 and 13 are sufficient to determine the component concentrations from 

Eq. 8. Since T2 is directly related to the component line width, we take 60 μsec as an 

approximation of T2 for the (SiH2)n. The specific (SiH2)n bonding environment and distribution 

of hydrogen-hydrogen separations is presently unknown and hence a more accurate evaluation of 

T2 is unavailable. Using T2 = 60 μsec to correct for the τ1d = 0 msec (SiH2)n signal intensity, we 

calculate a minimum relative (SiH2)n concentration, C(SiH2)n = 12 %. In the same calculation, 

about 70 % of the total hydrogen is in the clustered configuration, 15 % exists in the isolated 

phase, and 1 % exists as ortho-H2 (para-H2 has total spin of 0 and is unobservable by NMR). 

The existence of a minimum 12 % C(SiH2)n in the higher quality film is a bit surprising in 

light of the large body of NMR research on a-Si:H. However, Fig. 11 shows that (SiH2)n must 

contribute a considerable fraction (~ 70 %) to the total spectrum before its features can be 

distinguished from the usual line shapes. If we take this as an upper bound on C(SiH2)n , then the 

(SiH2)n spectrum would not be observed by conventional free induction decay, or solid echo 

NMR techniques. The actual concentration of hydrogen in (SiH2)n sites is clearly less than 70 % 

since no definitive evidence of (SiH2)n from these conventional methods has been reported. As 

the dashed lines in Fig.11 demonstrate, the combined Gaussian and Lorentzian line shapes can 

mask a considerable fraction of (SiH2)n.

We have previously made similar measurements of C(SiH2)n in a high defect density sample 

of a-Si:H. The growth conditions are provided in Table 1. The NMR measurements of C(SiH2)n 

yield a range between 15 % and 60 %, consistent with C(SiH2)n estimates based on IR data. 

Within the NMR experimental error, C(SiH2)n can be the same for both films or, at most, differ by 

a factor of 6. To be consistent with the IR data for the defective film, the higher quality C(SiH2)n 

can be at most equal to the minimum detectable signal in the IR measurements. In either case, 

the (SiH2)n densities differ by less than an order of magnitude in these two films. 

Concentration measurements from NMR can clearly be used as a more sensitive probe of 

hydrogen bonding sites than the standard IR measurements. This NMR analysis will 

undoubtedly be useful in future film characterizations, if specific hydrogen sites are related to the 

metastabilities commonly observed in a-Si:H. Presently, the role of (SiH2)n in any metastability

is unclear, and a correlation between the (SiH2)n concentration and film quality has yet to be 

established.

In summary, we have compared the concentration of hydrogen in (SiH2)n sites occurring in 

higher quality and high defect density a-Si:H films. Our results show that, despite the large 

difference in film quality, the hydrogen concentrations in (SiH2)n sites are within an order of 

magnitude of each other. We have shown that when compared to the usual silicon bonded 

hydrogen sites, 40% of the total hydrogen content can exist in (SiH2)n structures before being 

visible by conventional nuclear magnetic resonance methods. 

V. Calculations of Silicon Dihydride Bonding Sites in a-Si:H

In 1977 Staebler and Wronski reported a fundamental experiment on hydrogenated 

amorphous silicon (a-Si:H) [27], which revealed marked decreases in both the dark and 

photoconductivities after light soaking. Subsequent work showed that light soaking created 
20

defects, most probably dangling bonds. Because hydrogenated amorphous silicon (a-Si:H) is a 

material with technological applications, understanding the phenomenon of light-induced 

degradation, i.e., the Staebler-Wronski effect (SWE), has been a major focus [28]. In the 

intervening thirty years, extensive work in experiment and modeling has been carried out to 

obtain the microscopic origin and fundamental understanding of light-induced degradation. 

Disorder in the network, hydrogen concentration and its complex bonding structure, and 

concentrations of impurities are some of the material properties that play a role in the SWE. We 

have reported an experimental clue of some importance [16] where we performed nuclear 

magnetic resonance (NMR) experiments on protons in a-Si:H and found that the NMR spectrum 

of light-soaked a-Si:H films shows the preferential creation of a hydrogen doublet where the H-H 

distance is 2.3 ± 0.2 Å. This experiment appears to directly connect light soaking to creation of a 

specific new structure (or family of structures) in the amorphous matrix. In our collaborative 

efforts with the group at the Ohio University, we have shown that SiH2 is a possible candidate 

for the observed proton separation. Zhang, Jackson, and Chadi [29] and Chadi [30] have shown 

in careful calculations in c-Si:H that a two H interstitial complex, ** H2 , is another potential 

candidate for the observed defect. Both proposals have the merit that they do not rely on an 

unlikely conformation found only in specific models, and appear to occur with significant 

reproducibility, consistent with the reasonably well-defined experimental distance.

There have been various proposals for the microscopic origins of the SWE. One class of 

models involves breaking of “weak bonds” whose microscopic properties are often unspecified 

[31]. Another class of models proposes the creation of new defects as a result of movement or 

diffusion of an original defect [32]. Zafar and Schiff [33] considered a metastability model 

based upon transfer of H between clustered and isolated phases seen by NMR. Bonding in each 

of these phases was presumed to be monohydride. In their subsequent work Zafar and Schiff 

showed that the 2-phase picture closely accounted for experiments on thermal changes in the 

spin-density and also the changes caused by evolving hydrogen [34]. Some current theories 

combine the electronic and hydrogen energy states and hydrogen diffusion as in the hydrogen 

collision model of Branz [35], and the hydrogen flip model of Biswas and Li [36]. Kopidakis 

and Schiff [37] have proposed that clustered-phase sites can bind either one or two hydrogen 

pairs (dihydride bonding). Using this line of argument, Zhang and Branz [38] proposed a model 

that vacancies that produce missing Si atoms, at which the remaining Si atoms are fully 

terminated with Si-H bonds eliminate DB’s and strained Si-Si bonds and provide the paired-H 

reservoir and metastability sites in a-Si:H. There are also new findings that reveal a lack of 

spatial correlation between the defects and hydrogen, the realization that the effectiveness of 

light induced defects as recombination centers depends on the light exposure conditions, and the 

observation that it is not only defects that are produced by extended light exposure but also larger 

structural changes in the material involving the Si network [28].

There are two possible interpretations of our previous NMR results [16]. The simplest 

interpretation is that some metastable, paired-hydrogen site, perhaps, but not necessarily SiH2, is 

formed after the exposure to light. A second interpretation, which cannot be ruled out by the 

experiments to date, is that some changes in the various NMR relaxation rates after exposure to 

light allow existing paired-hydrogen sites, such as SiH2, to become observable in the NMR 

spectra. Of particular importance to the latter interpretation, Stutzmann, Jackson, and Tsai [31] 

have argued that the breaking of weak Si-Si bonds will also promote the diffusion of dangling 
21

bonds away from their original sites. If the presence of such a dangling bond near a stable, 

paired-hydrogen site, for which the most logical candidate is SiH2, allows this site to be seen in 

the H NMR, then the results of Su et al. are also logically explained. Although there are 

technical reasons why this explanation is not as probable as the formation of metastable, pairedhydrogen sites, it cannot be ruled out. The simulations in collaboration with the Ohio University 

group support either of these two interpretations. 

In these simulations we used the ab initio code, SIESTA [39,40,41], within the local density 

approximation (LDA). Details of these simulations are available elsewhere [42].

The calculations began with a defect-free 64-atom a-Si model [43] and removed two Si 

atoms and added 8 H atoms to create defect-free (that is, gap state free) structures with SiH2 

present. This model is denoted as aSiH-70. Another model is obtained in the same way except 

that one more Si atom is removed to form aSiH-72 (61 Si atoms and 11 H atoms), which 

includes one dangling bond [44]. This supercell surgery was repeated at other sites to generate 

an ensemble of models to obtain some insight into the bonding statistics of SiH2 conformations 

in the solid state. The SiH2 confirmations obtained in the two models are shown in Fig. 14(a) 

and Fig. 14(b). Four configurations were considered for each model in our calculation. Each 

configuration in the respective models was constructed by selecting different (typically 

tetrahedral) sites of the SiH2 conformations in the cell. Calculations of the SiH2 structures and 

dynamics on each of the four configurations of the aSiH-70 model and also on each of the four 

configurations of the aSiH-72 model were performed. The system was then relaxed. Details of 

the relaxation procedures are available elsewhere [42]. There is a consistent pattern that in the 

amorphous matrix the proton-proton separation is significantly reduced relative to a gas phase 

silane molecule with tetrahedral bonds (which produces a separation of 2.45 Å).

Figure 14. (a) SiH2 conformation in aSiH-70 

model and (b) SiH2 conformation in aSiH-72 

model with a dangling bond. In the figure the 

hydrogen atoms are shown in red (smaller in 

size) and the silicon atoms are shown in cyan 

(larger in size).
22

Thermal molecular dynamics (MD) simulations were performed to estimate the H-H 

distance at room temperature and to compare to T=0. The cells evolved freely for 250 fs (within 

a time step of 0.05 fs) at a temperature of T = 300 K. Thermal fluctuations in the bond lengths 

were observed as indicated in Fig. 15(a), and from 

Fig. 15(b). Over 5000 step MD runs, the average HH distance becomes 2.41 Å in the case of the LDA 

calculations and 2.34 Å for the GGA calculations for 

an initial H-H distance of 2.27 Å.

Figure 15. Thermal MD simulation for the 

H-H distance in aSiH-72 model using a) 

LDA calculations and b) GGA calculations 

[36].

The same calculation has also been done for the 

aSiH-72 model. Consistent with the first 

configuration, the aSiH-72 model also gives proton 

separations well within the tolerance of the 

experiments of Su et al. [16].

Most of the aforementioned models of the SWE invoke paired-hydrogen sites. These models 

associate the SWE with the conversion of isolated H into paired-hydrogen sites, for which SiH2

must be considered a prime candidate. The experiments of Su et al. [16] provide direct evidence 

that light soaking creates structures with a proton-proton separation of about 2.3 Å. Given the 

remarkably well-defined nature of the observed proton separation, it is natural to expect that the 

structure(s) causing the feature must not be a very rare conformation. Something like the 

complex of Chadi [30], or the SiH2 proposal presented here, appear to fulfill that condition – one 

certainly expects a priori that both of these configurations should occur in a-Si:H, although it is 

not initially obvious with what probability.

Given that the various models proposed [24−38] all appear to be at least consistent with our 

calculations for SiH2, the link between these calculations and the NMR experiments could be a 

very important step. On the other hand, what has not been done is to provide any explanation of 

the light-induced formation of SiH2, which is certainly a key missing piece to the puzzle. This is 

not an easy process to simulate, since the (diffusive) time-scales for creation are presumably 

vastly longer than what is directly accessible from our simulation. 

In summary, using accurate methods and supercells properly representing the disorder of aSi:H, we have seen that SiH2 is a credible candidate for the proton-proton distance inferred from 

the work of Su et al. [16]. The results indicate clearly that rather accurate methods are needed to 

properly describe the bonding in this system. 

 
23

VI. Defects in Tritiated a-Si:H

a. Growth of ESR and PDS at 300 K

The most important metastable effect in the prototypical amorphous semiconductor, 

hydrogenated amorphous silicon (a-Si:H), is the so-called silicon dangling bond defect 

associated with a threefold coordinated silicon atom. It is this defect that is thought to control 

the decreases in the conductivity and photoconductivity that occur due to exposure to visible 

light. These changes are collectively known as the Staebler-Wronski effect [45], which is the 

major factor in determining the stability of photovoltaic devices and detectors made from a-Si:H.

In this section we describe recent results using a novel method for producing silicon 

dangling-bond defects by replacing some of the hydrogen 1

H with tritium 3H. When the tritium, 

which is radioactive and decays to 3He with a half-life of approximately 12 years, is bonded to 

silicon its decay leaves behind a silicon dangling bond and an inert helium atom. [Tritium 

decays to helium-3 emitting an antineutrino and a beta particle with an average energy of 5.7 

keV]. The great advantage of this method for producing silicon dangling bonds is that one can 

calculate accurately the number that is produced as a function of time. 

For many years hydrogen diffusion has been invoked to explain the kinetics for the 

production and annealing of the Staebler-Wronski effect [46-54]. Although there is recent 

evidence that hydrogen pairing plays a role in stabilizing the Staebler-Wronski defects [55], the 

assumption of significant diffusion of hydrogen at room temperature is supported only by 

circumstantial evidence. In addition, there has been speculation for many years that the StaeblerWronski effect involves the creation of far more extensive changes in the local structural order 

[56] than might be expected from the simple production of a small number (approximately 1017

cm-3

) of silicon dangling-bond defects. In this section we provide direct evidence for the 

diffusion of hydrogen to heal the production of a large density (approximately 1021cm-3) of 

silicon dangling bonds. Some of the diffusion might be essentially athermal and occur even at 

very low temperatures. Together these two results – the diffusion of hydrogen and the annealing 

of a large density of silicon dangling bonds – greatly enhance our understanding of the StaeblerWronski effect, which is the quintessential metastability in all of the tetrahedrally coordinated 

amorphous semiconductors. Our results have a major impact on the two classes of models [51, 

52] that have been proposed to explain the Staebler-Wronski effect because both classes invoke 

the motion of only a small density of hydrogen atoms, about one per defect created, to stabilize 

the defects.

We present results on two samples, deposited by plasma-enhanced chemical vapor 

deposition (PECVD) from SiH4 and tritium gas mixtures, under conditions described 

elsewhere[57]. The first sample was grown at a substrate temperature of 225 oC. This sample is 

similar to those used in devices, in which the initial defect densities are the lowest 

experimentally obtainable (film thickness of 0.26 μm). The second sample was grown at 150 o

C. 

This sample, which is representative of a more defective material (film thickness of 1.5 μm), 

showed considerable dihydride bonding (silicon bonded to two Si and two H atoms) as measured 

by Fourier transform infrared (FTIR) spectroscopy. Because of the presence of silicon-tritium 
24

bonds, one expects the tritium decay to accumulate Si dangling bond defects after the samples 

have been deposited. The density of these defects should follow approximately the number of 

decayed tritium atoms per unit volume. Since our first measurements were made seven years 

after deposition, the density of decayed tritium was about 6x1020 cm-3 or a few at. %. 

Surprisingly, both electron spin resonance (ESR) measurements of the neutral silicon dangling 

bond density and photothermal deflection spectroscopy (PDS) measurements of the absorption of 

both neutral and charged defects yielded densities that were lower by about 3 orders of 

magnitude (5 x 1017 cm-3 and 4 x 1017cm-3 for films deposited at 150 oC and 225 oC, 

respectively). In addition, most of these defects annealed at temperatures between about 150 and 

200 oC with kinetics similar to that observed for the optically induced defects created in the 

Staebler-Wronski effect. The residual spin densities in the samples after annealing at the highest 

temperatures, near the deposition temperatures, were 9 x 1016 cm-3 and 2 x 1016 cm-3 for samples 

deposited at 150 and 225 oC, respectively. For the film deposited at 225 oC, Fig. 16 shows the 

fraction of metastable defects that remains after 30 min at several stepwise annealing 

temperatures, TA (open circles). The defect densities are normalized to their saturated values 

before annealing. This annealing behavior is quite similar to annealing of the optically induced 

defects in non-tritiated PECVD a-Si:H, performed at the University of Chicago [58] at room T 

for a week and stepwise annealed afterwards. The similarity of the annealing curves for tritiated 

and non-tritiated samples suggests similar distributions of defect annealing energies. 

Figure 16. Fraction of defects, NS, remaining after stepwise annealing for 30 min at each 

temperature TA . Open circles represent the annealing of a tritiated sample of a-Si:H made at a 

substrate temperature of 225 o

C and stored 7 years at room temperature (MRS 2004).

After the final annealing, new defects begin to accumulate in these tritiated samples in 

the dark. The accumulation kinetics depends on the temperature at which the samples are stored. 

Figures 17 and 18 show the number of newly created defects as functions of time after the final 

annealing for the samples grown at 225 oC and 150 oC, respectively. Data are shown for the 

accumulation of defects at 25, 77, 300, and 353 K (the last temperature is only shown for the 

sample grown at 150 oC). PDS measurements were performed for the samples kept at room 

temperature. Because the sample deposited at 225 0C was only 0.26 μm thick, a considerable 

portion of the spin density in the annealed state is likely due to surface or interface defects [52, 

59]. Therefore, the annealed spin density was subtracted from the total spin density to get the 

TA (K)

300 350 400 450

Ns (rel. un.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2
25

concentrations ∆NS of newly created defects shown in Figs. 9 and 10. The large scatter in the 

300 K data at short times in Fig. 17 is indicative of the inherent error in the measurements.

Figure 17. Kinetics of the accumulation of

new defects, ΔNS, after annealing at 180 o

C in 

a sample of tritiated a-Si:H deposited at 225 o

C. Open circles and triangles represent ESR 

measurements on the sample kept at 77 K 

and 25 K, respectively. Solid symbols 

indicate the same sample kept at room 

temperature, with the solid circles and 

diamonds representing ESR and PDS 

measurements, respectively. The dashed 

curve is a linear fit to the 77 K data, and the 

solid curve show the calculated number of 

tritium decays in the sample after the 

annealing. The measurement error in ΔNS is 

approximately ±2 x 1016 cm-3 (MRS 2004).

Figure 18. Kinetics of the accumulation of 

new defects after annealing at 150 o

C in a 

sample deposited at 150 o

C. The symbols 

represent same quantities as those 

described in the caption to Fig.2. The solid 

line is the calculated tritium decay (1.7x1016

cm-3

/h), and the dashed line is a linear fit to 

the 77K data. Large and small solid circles 

denote two separate experiments at room 

temperature. The relative error in ΔNS is 

about 5x1015 cm3

. (MRS 2004).

Two distinct features are apparent from the data in Figs. 17 and 18. At short times the 

growth is nearly linear, within experimental error, but much slower than the estimated 

production of silicon dangling bonds. Therefore the first general feature is that the initial growth 

rate is essentially independent of temperature (athermal) over the entire range of temperatures 

studied. At the higher temperatures (300 K and above) the defects accumulate more slowly at 

longer times and eventually saturate, and the saturated densities increase with decreasing 

temperature consistent with the data shown in Fig. 16. At 300 K the growth roughly follows a 

stretched exponential rise to a saturation that occurs after approximately 104 hours in the sample 

grown at 225 oC and at shorter times (and higher densities) in the sample grown at 150 oC. This 

behavior is very similar to that which is observed under optical excitation. In contrast, when the 

sample is kept at 77 K, there is no sign of saturation even after 104 hours. Therefore, the second 

general feature is a saturation level, which is strongly temperature dependent. If these saturation 

levels are thermally activated, they suggest an activation energy of approximately 0.3 eV.

Because the nuclear reaction for tritium decay also creates an energetic electron (beta

particle) and a much less energetic 3

He, we must first rule out any annealing (or generating) 

Time (h)

10-1 100 101 102 103 104 105

Delta NS (10

16

 cm

-3

)

100

101

102

103

Time (h)

100 101 102 103 104 105

Delta NS (1016 cm-3)

100

101

102

103
26

effects of these two particles. The 3

He has a recoil energy of only a few eV, which is unlikely to 

have much effect in either annealing or generating defects. The electrons are emitted with an 

average energy of approximately 6 keV, and the average distance they travel through the film is 

approximately 0.6 μm. During this process each electron produces about 103 electron-hole pairs, 

which can in principle generate additional defects; however, this production rate of electron-hole 

pairs is equivalent to illumination by only about 10-6 W/cm2 of visible light, which implies the 

production of about one defect for 50 electrons [60]. This production rate is too small to be of 

any consequence. 

It is conceivable that the energetic electrons locally heat up the lattice in such a way as to 

anneal defects, but calculations suggest that the probability is low. Nonetheless, we tested this 

defect annealing hypothesis by exposing the film grown at 225 o

C, after saturation of the defect 

density, to a 7 keV electron flux in an electron microscope. The average incident current density 

was 10-8 A/cm2 and the exposure time was 1.5 h. This flux is about 200 times larger than the 

effective beta particle flux, which bombards any small volume element in the film (~ 10-11

A/cm2

). Thus, the 1.5 h e-beam exposure is equivalent to 10 days of intrinsic beta particle 

exposure. In the saturated steady state, the annealing rate is equal to the defect creation rate of 

about 1016 cm-3 h-1. If the beta particles were responsible for annealing of defects, we would see 

a decrease of the saturated defect density by about 1018 cm-3 after the e-beam exposure, but we 

observed no measurable change. We conclude that the emission of beta particles (energetic 

electrons) during the decay of tritium has no significant influence on the production or annealing 

of defects in tritiated a-Si:H.

In addition, it is conceivable that there is a large density of positively and negatively 

charged defects that are unseen by ESR. Figs. 17 and 18 show clearly that this is not the case at 

room temperature; here the defect densities measured by PDS (optical absorption), which is 

believed to measure both neutral and charged defects, match those measured by ESR. At 25 and 

77K, the growth of the ESR signal is remarkably similar to that seen at short times at room 

temperature, which strongly suggests that charged defects are not important at any temperature. 

It remains to explain the two general features of the growth curves – an annealing of defects 

at short times that is essentially athermal, and an annealing at long times (saturation) that is 

strongly temperature dependent. Because we have tested the saturation over time scales 

approaching seven years, this feature requires a significant reservoir of hydrogen sites on the 

order of an atomic percent. In a typical sample of a-Si:H, such as our tritiated one grown at 225 o

C, there is approximately 10 at. % hydrogen that 1H nuclear magnetic resonance (NMR) 

measurements show [61, 62] exists in three primary forms: ~ 7 at. % bonded to silicon in small 

clustered environments, ~ 3 at. % bonded to silicon at isolated (randomly distributed) sites, and ~ 

1 at. % interstitial molecular hydrogen (H2), of which approximately half is HT (hydrogentritium) and one quarter is T2 (tritium-tritium) in the tritiated sample. 

The most obvious candidate to provide the mobile hydrogen necessary for annealing [63] is 

the decay of hydrogen–tritium (HT) or T2 molecules, which leaves behind an unbonded H (or T). 

It is unlikely that molecular hydrogen is the only source given the very different temperature 

dependences for the short-time and long-time annealing processes and the need for a very large 

reservoir of potential hydrogen sites. A second possible candidate is the replacement of two near 

neighbor bonds in the clustered phase [64] (e.g., Si-H and Si-T) with silicon-silicon bonds on 
27

formation of a silicon dangling bond by tritium decay. This reconstruction eliminates the newly 

created Si dangling bond and at the same time, produces an extra H (or T) atom that can easily 

diffuse and passivate another defect nearby. 

The low rates of defect production in the linear regime show there is some tritium decay that 

does not produce defects: some athermal process circumvents this defect production. Either the 

diffusion of at least some of the hydrogen is athermal or the replacement of some of the siliconhydrogen bonds with silicon-silicon bonds, as discussed above, is athermal. The latter appears to 

be the more likely possibility if the lattice relaxation is strong enough at the clustered H sites. 

This explanation requires that the H produced in the same process has no ESR signal. With this 

mechanism, the metastable defects are created essentially at the isolated tritium sites, which 

represent only a fraction of the total tritium sites. Thus, tritium decay produces both Si danglingbond defects at isolated tritium sites and “mobile” hydrogen at clustered tritium and hydrogen 

sites. In the saturation regime at higher temperatures, the hydrogen released at clustered sites 

can thermally diffuse to passivate defects. Saturation is possible when the annealing rate due to 

diffusion of interstitial hydrogen is equal to the defect production rate.

What are the implications of these results for understanding the Staebler-Wronski effect in 

a-Si:H? The similarity of the annealing of the defects induced by tritium decay and the optically 

induced defects at room temperature (Fig.16) suggests that the annealing in both cases is likely to 

be governed by the same mechanism. The annealing of light-induced defects has been 

extensively studied and is characterized by a wide distribution of annealing activation energies 

[52, 65]. There is much circumstantial evidence that the annealing of optically induced defects is 

mediated by mobile hydrogen [50, 66]. Both classes of model for the Staebler-Wronski effect 

suggest [51, 52] that defect annealing is mediated by a metastable configuration that is created 

together with the defects and can reverse the creation process during anneal. In both models, 

however, only a small density (1017 cm-3 in device quality films) of such metastable species is 

created after prolonged optical excitation. In the tritiated samples, however, the tritium bonded 

to silicon is converted into inert 3He and therefore plays no role in the formation of metastable 

configurations capable of annealing Si dangling bond defects. As discussed above, the 

metastability must be mediated by hydrogen from a large reservoir of already existing metastable 

sites (a few at. %). As no new defects are created by the tritium decay at these metastable sites, 

an isolated Si-H could not fill this role, but molecular hydrogen and clustered hydrogen bonded 

to silicon could. We therefore conclude that the annealing of optically induced defects that are 

created in the Staebler-Wronski effect at room temperature and elevated temperatures might also 

take place from a large, pre-existing reservoir of annealing species rather than from stabilization 

mechanisms of a small density of defects that are created by the light. 

Finally, we address the growth of defects created by tritium decay and those created by 

optical excitation at temperatures below 300 K. The optically induced defect densities are 

difficult to measure at low temperatures by ESR [67] or by the constant photocurrent method 

[56, 58], but neither of these experiments has observed saturation at temperatures much below 

300 K. Unless the presence of optical excitation plays a role in the saturation process, one can 

speculate that the behavior at low temperatures is similar to that observed in the tritiated samples. 

Some of the network healing mechanisms, which follow tritium decay, are essentially 

athermal and occur even at very low temperatures.

 
28

b. Growth of ESR at 77 K

The appearance of optically or electrically induced defects in hydrogenated amorphous 

silicon (a-Si: H), especially those that contribute to the Staebler-Wronski effect [68], has been 

the topic of numerous studies, yet the mechanism of defect creation and annealing is far from 

clarified. This quarterly status report describes our recent progress using another method to 

induce silicon dangling-bond defects by replacing some of the hydrogen, 1

H, with tritium, 3H. 

Tritium decays to 3He, emitting a beta particle (average energy of 5.7 keV) and an antineutrino. 

This reaction has a half –life of 12.5 years. The samples contain approximately 7 and 10.4 at.% 

tritium. In these tritium-doped a-Si: H samples each beta decay will create a defect by converting 

a tritium, which is bonded to silicon, to an interstitial helium, leaving behind a silicon dangling 

bond.

We have tracked these defects through electron spin resonance (ESR) and photothermal 

deflection spectroscopy (PDS) [69]. The densities we measured at room temperature were 

smaller by orders of magnitude than the number of tritium decays – only about 5x1017cm-3. 

Therefore, there must exist a mechanism of defect annealing that is capable of healing ~ 1020 

cm-3 defects at room temperature. In the present report, we extend these studies to 77K, in order 

to establish the thermal stability of the Si dangling bond defects introduced by tritium decay.

Both samples studied were made at the University of Toronto in 1996. The samples used in 

this experiment were deposited at glass substrate temperatures of 150oC (further referred to as 

G181) and 225 oC (referred to as G83). Shortly after deposition high temperature tritium 

effusion experiments determined the tritium concentration to be approximately 7 and 10 at. % in 

the two samples, respectively. 

We expect the tritium decay to accumulate Si dangling bond defects because of the silicontritium bonds. The density of these defects is related to the number of tritium atoms that have 

decayed per unit volume. We first measured the samples 7 years after deposition, where the 

density of tritium atoms that had decayed since making the films was about 6x1020 cm-3 [69]. 

However, both ESR and PDS measurements of the defect densities were lower by about 3 orders 

of magnitude because the defect density saturates at room temperature [69]. Next, we annealed 

the samples near the deposition temperature and kept the two samples at liquid nitrogen 

temperature for almost two years. During this time we used ESR to track the defect densities. 

After two years, the defect densities were about 1019 cm-3 for both samples. After two years in 

liquid nitrogen, we annealed the two samples. We step-wise annealed the G83 sample at 

successive temperatures up to 473 K isochronally while the G181 sample was annealed 

isothermally at 300 K.

After annealing the films, the defects began to accumulate in the dark at 77 K. The spin 

densities as functions of time stored at 77K are shown in Figs. 19 and 20 for the samples G181 

and G83, respectively. The data at the shortest times are the defect densities just after annealing. 

These densities are about 1016 cm-3 and 1017 cm-3 for G181 and G83, respectively. In both cases, 

the densities are probably due to surface or interface defects. The spin densities increase linearly 

with time. The final data points are the defect densities after about two years. In Fig.19, the 

final density is about 3x1019 cm-3

, which is about 4 times lower than 1.4x1020 cm-3, the density of 
29

tritium atoms, which have decayed since the sample was annealed. In Fig. 20, the final density is 

about 2x1019 cm-3. In both samples there is no saturation in the growth in contrast to the case at 

300 K. [69].

Figure 21 shows the decrease in defect densities after sample G181 was heated to room 

temperature and then kept at room temperature for several months. The defect densities were 

tracked by ESR. At 300 K the defects created at 77 K anneal slowly. Even after several months, 

the density is still higher t han the saturation density for defects created at room temperature, 

which is 6x1017 cm-3

. Only after about one year does the defect density reach the saturated value 

at 300 K[2]. Because PDS measures both charged and uncharged defects in the sample, we used 

this technique to check that the ESR was measuring all of the defects. The densities of defects, 

as measured by ESR in these samples of a-Si: H, are the same as those measured by PDS within 

a factor of two.

Figure 22 shows data for stepwise annealing of the G83 sample up to 380 K. The sample 

was kept for 30 minutes at each annealing temperature, Ta. We continued annealing step by step 

up to 380 K, and after each annealing step we measured the spin densities at 20 K. The data 

show that the defects are fully annealed at 473 K. The final density of approximately 1017 cm-3 

matches the number after we annealed the sample at the start of the 77 K experiments.

At 77 K the defects accumulate almost linearly with the time. The spin density after two 

years is smaller than the density of tritium atoms that have decayed. This result possibly 

suggests that the tritium decay in a clustered hydrogen environment does not produce a dangling 

bond due to bond reconstruction as a result of emission of hydrogen from nearly Si atom. This 

Time(hrs)

10-1 100 101 102 103 104 105 106

Spin Density (1016 cm-3)

10-1

100

101

102

103

104

105

Time(hrs)

10-1 100 101 102 103 104 105

Spin density(1016cm-3) 101

102

103

104

105

Figure 19. Increase of the defect 

densities of G181 as a function of 

time at 77 K. (MRS 2007)

Figure 20. Increase of the defect 

density of G83 as a function of time at 

77 K. (MRS 2007).
30

suggestion is similar to the previous suggestion of thermal emission of hydrogen from the 

clustered phase [70, 74]. In addition, some tritium decays do not produce a silicon dangling 

bond because the tritium occurs in molecular form (trapped 1H1H or 3H3H). The sample G83 

Time(hrs)

10-2 10-1 100 101 102 103 104 105

Spin density(1017cm-3)

1

10

100

Figure 21. Decrease in the defect density after the sample G181 was heated to room 

temperature and then kept at room temperature for several months of isothermal 

annealing. (MRS 2007)

Annealing Temperature Ta(K)

0 50 100 150 200 250 300 350 400

N

D/N

0

0.2

0.4

0.6

0.8

1.2

0.0

1.0

Figure 22. Relative decreases in defect density in sample G83 after stepwise annealing

for 30 minutes at each successive annealing temperature, Ta. (MRS 2007).
31

was annealed step-by-step up to 200 oC. Annealing results are similar to those that are observed 

when defects are created with light (Staebler-Wronski effect) at low temperatures. Two thirds of 

the defects are annealed at around 300 K in our tritium sample. In some a-Si:H samples light 

soaked at 77 K essentially the same annealing kinetics is observed [71, 72]. 

In summary, we have shown that the defect densities of two tritiated amorphous silicon 

samples at 77 K increase linearly in time up to 1019cm-3

. The final densities, however, are 

factors of 4 to 8 smaller than the density of tritium atoms that have decayed. From NMR 

experiments, we know that 3 at. % of the atoms in the sample exists as hydrogen in the dilute 

phase and the rest is in the clustered phase [76]. Therefore, some of the clustered tritium atoms 

probably do not produce silicon dangling bonds at 77 K due to reconstruction. There is no 

evidence of saturation at 77 K. These results provide further hints for the role of hydrogen in 

creating defects in light soaked samples at low temperature as suggested in [73-75].

VII. Hydrogen Diffusion and Crystallization

We have investigated the evolution of the defects created during hydrogen effusion and the 

crystallization process, using magnetic resonance techniques such as nuclear magnetic resonance 

(NMR) and electron spin resonance (ESR). In this section, we show the results from ESR during 

the annealing and crystallization and present a simple model of the exchange interaction in the 

disordered a-Si.

Amorphous silicon samples were deposited by both HWCVD and PECVD at the facility at 

National Renewable Energy Laboratory (NREL). Information of the samples is listed in Table 2. 

One HWCVD sample (H2029) and one PECVD sample (L1477) were annealed at the same time 

at T C

 = 560 in nitrogen gas. A second PECVD sample was annealed at T C = 580 for 1300 

min, and reflectance measurements show that the film crystallized after t ~ 1050 min. The 

annealing is monitored by a n&k reflectance and transmittance spectrometer.

Table 2. Growth conditions of the HWCVD and PECVD a-Si:H samples.

Sample # Deposition

method

Substrate

temperature (°C)

Deposition rate

(Å/s)

Thickness

(μm)

L1447 PECVD 250 1-2 ~1

H2029 HWCVD 400 7 ~1

ESR measurements of the defect densities were carried out on a Bruker Elex 500 

Spectrometer at room temperature. The defect densities were obtained by comparing the double 

integrated intensity in the samples to that in a standard weak pitch sample measured under the 

same conditions.

Figure 23 shows the evolution of the defect densities in H2029 and L1477 as a function 

of the annealing time at T C

 = 560 . In the HWCVD sample (H2029), the defect density begins 

to decrease after about 60 min, and the film is fully crystallized after about 750 min. Reflectance 

measurements show that crystallization occurs during the same time period. After the film is 
32

crystallized, the defect density deceases to about 17 4×10 cm-3 and remains at this value through 

the rest of the annealing.

annealing time (min)

0 200 400 600 800 1000 1200 1400

n

D (x 1017 cm-3)

0

20

40

60

80

L1447

H2029

L1447 crystalized

Figure 23. The defect densities in HWCVD (H2029) and PECVD (L4774) samples as a function of 

annealing time at T C

 = 560 . Open squares and solid circles indicate data for HWCVD and 

PECVD samples, respectively. The open triangle indicates defect the density of the PECVD sample 

after annealing at T C

 = 580 for t~1300 min.

The defect density in PECVD sample (L4774) shows an initial sharp increase to about 

18 4×10 cm-3

, followed by a decease to 18 3×10 cm-3, and a gradual increase over the remainder of 

the annealing. This sample does not show any evidence of crystallization, which is consistent 

with the reflectance measurements. Due to the lack of detailed data on the HWCVD sample, we 

will focus our discussion in the PECVD sample.

Figure 24 shows the comparison of the lineshapes of the ESR signals in H-effused and 

crystallized samples to that in a typical a-Si:H sample. In trace (a), which is from a typical aSi:H sample, the peak-to-peak width is about 7 G. Trace (b) is from the sample in the H-effused 

state before crystallization, the line-width is about 5 G. The line-width of the crystallized sample 

(6.5 G) is much smaller than previously reported values in micro-crystalline silicon (μc-Si:H) 

samples [77, 78, 79]. The lineshape changes can be attributed to exchange-narrowing that is well 

known for high defect density films [80]. This narrowing effect will be discussed in detail later. 

Figure 24 also shows a slight difference in the g-values as calculated from the field of zero 

crossing, which could be due to the difference in ESR resonance frequency or to a slight change 

in g-value of the defect signal.
33

Field (G)

3340 3350 3360 3370 3380

Amplitude (arb. Unit)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

(c)

(b)

(a)

Figure 24. Comparison of the ESR lineshapes in H-effused and crystallized samples to a typical aSi:H sample. (a) typical a-Si:H, (b) H-effused, before crystallization ( 18 nD = 3.6×10 cm-3

), and (c) 

after crystallization ( 17 nD = 4.3×10 cm-3

). The amplitudes are scaled to show the difference in 

line-width.

Since only the total number of spins is measured in typical ESR spin count measurements, 

these measurements do not determine whether or not the spins are clustered. The bulk defect 

density is only accurate based on the assumption that the defects are randomly distributed within 

the sample. This is unlikely during the crystallization, as well as right before and after 

crystallization. To investigate the potential clustering of the spins, we compared the lineshape in 

the hydrogen effused PECVD sample to that in an a-Si:HT sample. In a-Si:HT, the defects are 

crested by decay of the tritium toms that are bonded to silicon atoms,

3

H --> 3He + ß- + anti-neutrino + 5.7 keV (9)

The resulting 3

He atom will detach from the silicon atom and leave a dangling bond on the 

Si atom. The energy of the β particle is ~ 5.7 keV. Irradiating the sample with an electron beam 

with the same energy and dosage shows that no significant amount of defects are created [81, 

82]. Therefore the main mechanism for defect creation is due to the reaction in Eq. (9). This 

process does not involve large-scale lattice reconstruction, due to the slow decay rate of the 

tritium nuclei, and therefore this process presumably creates defects that are more likely to be 

randomly distributed. Figure 25 shows the dependence of the line-width on the defect densities 

in one a-Si:HT sample. For comparison, the line-width of the H-effused PECVD sample with a 

bulk defect density of 18 nD = 3.6×10 cm-3 and the line-width in an a-Si sample prepared by RF 

sputtering [80] are also shown.
34

ND (x 1018 cm-3)

1 10 100 1000

Line-width (G)

3

4

5

6

7

8

9

a-Si:HT

H-effused

PECVD

a-Si by

Sputtering

Figure 25 The dependence of the ESR line-width on the defect densities in a-Si:HT sample 

and in H-effused a-Si:H sample prepared by PECVD. Solid circles represent the data from the aSi:HT sample, the open square represents the line-width for the defect density of 

18 nD = 3.6×10 cm-3 in the H-effused PECVD sample. The open triangle is the line-width from Ref. 

[80] in a-Si sample prepared by RF sputtering.

Figure 25 clearly shows the discrepancy in line-width between the H-effused PECVD 

sample and the a-Si:HT sample with the same bulk defect density. The defect density in a-Si:HT 

is about one order of magnitude higher with the same line-width (~5 G). If we assume the defects 

are randomly distributed in a-Si:HT, then there must be significant clustering in the H-effused 

sample to have a comparable line-width, with a much lower bulk defect density. This result will 

be further discussed below.

It is well known that at high spin densities, the observed ESR line-width is narrower due to 

the so-called exchange-narrowing effect [83]. This effect arises from the exchange interaction 

between the spins, and has the form

S1 S2 H J ex

  = ⋅ , (10)

where 1 S

 and 2 S

 are the spins of the two defects. J is the coupling constant. This interaction 

allows the spin-pair to undergo rapid mutual flipping and effectively average out the broadening 

due to other interactions, such as the dipole-dipole interaction between the spins and g-tensor 

anisotropy. The exchange interaction deceases rapidly as the distance between the two spins 

increases, and therefore this interaction does not affect the line-width at low spin densities. 

Although this effect has been extensively studied in crystalline materials, no details to estimate 

the coupling constant have been reported. Here we develop a rather simple method to estimate 

the interaction in a-Si:H.

Consider two defects (dangling bonds) that are separated by n Si atoms. In this case, the 

exchange-interaction will be through the n-1 bonds in between. The dangling bond, which is a 

singly occupied sp

3 hybrid on a Si atom, interacts with another dangling bond by coupling to the 

Si-Si bond on the same atom, which in turn couples to another Si-Si bond, and so on. If we only 
35

consider the coupling through the bonding orbitals, the matrix of the total Hamiltonian is an 

(n +1)× (n +1) matrix,





































































⋅

⋅ ⋅ ⋅

⋅ −

⋅ ⋅ ⋅ ⋅

⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

⋅ ⋅ ⋅ ⋅

− ⋅ ⋅

⋅ ⋅ ⋅

0

2

0 0

2 2

0

0

2

2

0

2 2

0 0

2

0

1

1

2

1

1

1

1

2

1

1

V

V V V

V

V

V V V

V

(11)

where 

2

V1 is the coupling between the dangling bond and the Si-Si bond, 2

V1 is the coupling 

between two hybrids within a bond, and V2 is the energy gained by forming the bonding orbital. 

Diagonalization of this matrix results in n+1 energy levels, of which n-1 levels are close to V2

(bonding orbitals). The other two energy levels are higher and are separated only by a small 

energy, which is due to the exchange interaction between the two dangling bonds.

To estimate the onset of the exchange-narrowing of the lineshape, we assume that the 

narrowing will be measurable when the exchange interaction is about the same as the line-width 

of the ESR signal. By choosing V1 = 1.8 eV and V2 = 4.4 eV for Si [84], we numerically 

diagonalized the Hamiltonian (Eq. 11), and obtained a value of the exchange interaction of 

8 5.4 10− ∆Eex = × eV when the two dangling bonds are separated by 12 atoms. This value of ∆Eex

corresponds to an ESR line-width of about 4.6 G. The defect density is calculated to be about 

19 3×10 cm-3

, with an average distance between two defects of 12 inter-atomic distances of Si. 

This is consistent with the experimentally observed relation between defect density and the ESR 

line-width in a-Si:HT, in which we assume the defects are randomly distributed, and not 

significant clustered. 

We found that ∆Eex decreases exponentially with an increasing number of bonds between 

the two dangling bonds. Therefore, the exchange interaction is effectively a short-range 

interaction. As a consequence, our results do not distinguish between the case in which more 

than two defects are close to each other and the case in which only paired defects are present.

In summary, we have performed ESR measurements in H-effused a-Si:H thin films made by 

both HWCVD and PECVD. The evolution of the defect density as a function of annealing time 

is consistent with that found in optical measurements. Analysis of the line-width shows that in Heffused states, the defects are either clustered or exist in pairs. A simple model of the exchange 

interaction in a-Si can account for the difference in line shapes observed in these films as 

compared to a-Si:HT samples described in the previous section.
36

VIII. Summary

During the sub-contract we have made significant progress in understanding the 

metastable, hydrogen-doublet defect that may be responsible for stabilizing the silicon dangling 

bond defects that occur during optical excitation (Staebler-Wronski effect). Also, we have made 

the first definitive measurement of the H-H separation at silicon doublet bonding sites in a-Si:H. 

These sites are probably not silicon dihydride but rather hydrogen atoms on nearest neighbor 

silicon atoms on the surfaces of voids. Also, we have discovered some interesting features 

concerning the production and annealing of silicon dangling bonds by studying their creation 

through the decay of tritium in tritiated samples of a-Si:H. We have made significant progress in 

understanding the role of SiH2 in both high and low defect-density films of a-Si:H. In addition, 

we have calculated the H-H separation at SiH2 sites that may be consistent with that observed in 

NMR light-soaking experiments. Finally, we have studied annealing and crystallization in films 

of a-Si:H.

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F1146-E(10/2008)

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September 2009

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Subcontract report

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1 February 2005 - 31 July 2008

4. TITLE AND SUBTITLE

Innovative Characterization of Amorphous and Thin-Film Silicon for 

Improved Module Performance: 1 February 2005 – 31 July 2008

5a. CONTRACT NUMBER

DE-AC36-08-GO28308

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6. AUTHOR(S)

P.C. Taylor and G.A. Williams

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NREL/SR-520-46649

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PVB91110

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University of Utah

Salt Lake City, Utah

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XXL-5-44205-09

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NREL

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14. ABSTRACT (Maximum 200 Words)

We performed collaborative research with United Solar Ovonics Corporation on defects that contribute to the 

Staebler-Wronski effect in modules made using a-Si:H and a-SixGe1-x:H intrinsic layers. Specifically, we performed 

electron spin resonance on a set of device-quality samples, half of which were light-soaked. We also performed 

nuclear magnetic resonance experiments on these samples to investigate hydrogen doublet sites. In addition, we 

investigated the defects generated in tritiated a-Si:H at both 300 and 77 K in collaboration with scientists at NREL. 

Finally, we performed studies of light-soaking at 77 K to compare the kinetics with those for the creation of defects at 

77 K by tritium decay.

15. SUBJECT TERMS

PV; amorphous; thin film; silicon; module performance; innovative characterization; electronic spin resonance; 

nuclear magnetic; Satebler-Wronski effect;

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