Issue
Eur. Phys. J. Appl. Phys.
Volume 90, Number 2, May 2020
Disordered Semiconductors: Physics and Applications
Article Number 20101
Number of page(s) 7
Section Semiconductors and Devices
DOI https://doi.org/10.1051/epjap/2020190257
Published online 26 June 2020

© EDP Sciences, 2020

1 Introduction

After prolonged illumination, the dark conductivity and photoconductivity of hydrogenated amorphous silicon (a-Si:H) decrease compared with their values before illumination [1]. Such a phenomenon is called the Staebler-Wronski effect. After then, Staebler-Wronski [2] suggested that this may be due to light-induced creation of Si dangling bonds. This suggestion has been confirmed by electron spin resonance (ESR) measurements by Hirabayashi et al. [3] and Dersch et al. [4]. Since then, the models of light-induced defect creation have been proposed by several authors (see [5] for a review article). In this paper, our model is presented as well as the model of light-induced defects in Section 2. From our model of light-induced defect creation in a-Si:H, we have proposed the model of light-induced defects, that is, two types of dangling bonds which are a normal dangling bond and a dangling bond having hydrogen in a nearby site that is called hydrogen-related dangling bond. For evidence for existence of these defects, our ESR measurements [6,7] are reviewed as well as our electron-nuclear double resonance (ENDOR) measurements in a-Si:H and a-Si:D [8,9] in Section 3. Further, recent results of pulsed ENDOR measurements by Fehr et al. [10] are presented and compared with our computer-stimulated ENDOR spectra in Section 3 together with a detailed calculation of distant ENDOR in a-Si:H. In Section 4, conclusion is drawn. Preliminary reports concerning Section 3 have been published in [1113].

2 Light-induced defect creation

First, our model of light-induced defect creation processes is described below: Under illumination by light with band-to-band energy, electrons and holes are generated. A hole is self-trapped in a specific weak Si–Si bond [14] that is a weak Si–Si bond adjacent to a Si-H bond (Fig. 1a) and then is recombined with an electron most nonradiatively (Fig. 1b) and eventually the weak bond is broken. Using the recombination energy associated with nonradiative recombination between the electron and the hole, the Si-H bond is switched towards the weak Si–Si bond (Fig. 1c). After switching of the Si-H bond (Fig. 1c) and breaking of the weak Si–Si bond, the two close dangling bonds created under illumination [15] are separated by movement of hydrogen due to hopping and/or tunneling (Fig. 1d) and eventually two separate dangling bonds (Fig. 1d), i.e., a normal dangling bond and a hydrogen-related dangling bond are created under illumination, as shown in Figure 1d. Some of such two separate dangling bonds become more separate so as to be isolated normal dangling bonds (Fig. 2a) and isolated hydrogen-related dangling bonds (Fig. 2b), as have been shown by calculations based on the above light-induced creation processes [16]. Detailed accounts on the light-induced defect creation mentioned above have been presented in [17,18].

thumbnail Fig. 1

Atomic configurations involved in the formation of two types of dangling bonds, i.e., normal dangling bonds and hydrogen-related dangling bonds, under illumination: (a) self-trapping of a hole in a weak Si–Si bond (wb) adjacent to a Si-H bond, (b) electron-hole recombination at a weak Si–Si bond, (c) switching of a Si-H bond towards the weak Si–Si bond, leaving a dangling bond behind, (d) formation of two separate dangling bonds through hydrogen movement after repeating the processes shown in (a)–(c).

thumbnail Fig. 2

(a) Schematic illustration of the normal dangling bond in a-Si:H. (b) Schematic illustration of the hydrogen-related dangling bond in a-Si:H.

3 ESR and ENDOR measurements in a-Si:H

First, we present the Hamiltonian of Zeeman energy and hyperfine interaction responsible for ESR and ENDOR in Section 3.1. Secondly, a detailed account of the results of ENDOR measurements is presented in Section 3.2.

3.1 Zeeman energy and hyperfine interaction

The Hamiltonian responsible for ENDOR is given below:(1)

where µB, µn, S, I, g, gn, H and A are the Bohr magneton, the nuclear magneton, the electron spin, the nuclear spin (proton spin), the g tensor, the nuclear g factor, applied magnetic field and the hyperfine interaction tensor, respectively. The first and second terms in equation (1) represent the electronic and nuclear Zeeman energies, respectively, while the third term in equation (1) expresses the hyperfine interaction. We consider the third term of equation (1), i.e., hyperfine interaction with axial symmetry between electron spin and proton spin. When the static magnetic field is applied along the z-axis making an angle of θ with the axial symmetric axis of the hyperfine interaction tensor, A is given by its isotropic part, Aiso, and anisotropic part, Aaniso, as follows:(2)Using A|| (A|| with θ = 0) and A (A with θ = π/2), Aiso and Aaniso are given by(3) (4)respectively. Aiso and Aaniso arise from the Fermi-type contact hyperfine interaction, whose constant is proportional to the electron density at the hydrogen nucleus, and from the dipolar interaction, respectively. Aaniso is given by(5)where R is the distance between the dangling bond site and a hydrogen nuclear spin.

A typical anisotropic hyperfine structure is illustrated in Figure 3. The computer-simulation of hyperfine structure has been performed, using the program of FESRSDS (Fitting of Electron Spin Resonance Spectrum for Disordered System) [19]. The line shape of ESR signals is deconvoluted into two components due to normal dangling bonds and H-related dangling bonds. From the deconvolution, we estimate the values of Aiso and Aaniso as well as the density percentage of normal dangling bonds and H-related dangling bonds for various samples of a-Si-H prepared with different conditions [6,7]. The values of R are also estimated for various samples of a-Si-H prepared with different conditions [6,7].

thumbnail Fig. 3

The computer-simulated hyperfine structure with the values of ESR parameters shown below: giso = 2.004, A|| = 93 G, A = 51 G and σiso = 2 G. The isotropic g-value and the isotropic σ value are assumed for simplicity [11]. σ is the standard deviation of the spin-packet Gaussian shape function.

3.2 ENDOR measurements

Electron-nuclear double resonance (ENDOR) is normally characterized by the nuclear site, that is, (i) nearby nuclei to unpaired electron spin (local ENDOR), (ii) nuclear spins connected through dipolar interaction with unpaired electron spin (matrix ENDOR), and (iii) distant nuclei from unpaired electron spin (distant ENDOR).

3.2.1 Local ENDOR

The computer-simulated ENDOR spectrum due to the hydrogen-related dangling bond (HDB) is shown in Figure 4. The hydrogen nucleus nearby a site of dangling bond is located at a site with r = 2.5 Å. r is the distance corresponding to R in equation (5). The values of parameter used in the computer-simulation are given in the figure caption. The ENDOR spectrum is obtained from a transformation of the ESR spectrum involving hyperfine structure with hydrogen nucleus. The figure also shows the observed ENDOR spectrum by Fehr et al., in which a shoulder is seen around rr0 = -5 MHz. Such a shoulder is also seen in the computer-simulated ENDOR spectrum shown in Figure 4. This suggests for the hydrogen-related dangling bond to exist in a-Si:H. Further evidence for existence of the hydrogen-related dangling bond has been obtained from our ENDOR measurements in a-Si:H and a-Si:D [8,9].

thumbnail Fig. 4

The computer-simulated ENDOR spectra in a-Si:H. HDB(blue): The values of the parameters are given below. g|| = 2.0050 and g = 2.0056, A|| = 19.6 MHz, A = 2.80 MHz, σ|| = 2.24 MHz, and σ= 3.36 MHz. The matrix ENDOR spectra for various distance between the dangling bond site and the hydrogen, r, are shown as follows: r = 3.20 Å (red). The values of the parameters are given below. g|| = 2.0050 and g⊥ = 2.0056, A|| = 4.68 MHz and A =2.34 MHz, σ|| = 1.12 MHz, and σ= 1.68 MHz. r = 3.40 Å (sky blue), r = 3.72 Å (magenta), r = 4.80 Å (yellow brown), r = 5.12 Å (olive): The values of the parameters for these r are given in Table 1. The Fehr ENDOR spectrum [10] is also shown. (Reproduced from [11]).

3.2.2 Matrix ENDOR

Dipolar interaction between the electron spin and hydrogen nuclei separated from the DB site with the distance r is calculated. The ENDOR spectrum is obtained, taking into account the dipolar interaction mentioned above. For various values of r (see Fig. 5), the computer-simulated ENDOR spectra are shown in Figure 4. Figure 5 has been obtained by Bellisent et al. [20], using the neutron-scattering measurement in sputtered a-Si:H samples. These samples have poor qualities compared to those used by Fehr et al. The values of parameters used in the simulation are given in the figure caption and in Table 1.

thumbnail Fig. 5

Schematic illustration of the local structure being composed of silicon atoms and hydrogen atoms. The distances 1, 2, and 3 are cited from Bellisent et al. [20] as follows: 1 = 3.3–4.3 Å, 2 = 3.2 Å, and 3 = 3.72–5.12 Å. (Reproduced from [11]].

Table 1

The values of parameters used in the calculation.

3.2.3 Distant ENDOR

We consider distant ENDOR observed in a-Si:H in terms of Lambe et al.'s theory [23] which is based on the dynamical nuclear polarization [2426]. In this theory, forbidden double spin-flip transition of electron and nuclear spins (I = 1/2) is excited. We summarize Lambe et al.'s theory. below: The difference in electron spin population is defined as follows:(6)

where h(ω' − ω0) is a local field distribution of microwave frequency ω' with a central ESR frequency ω0 and N(ω ') and N +( ω ') are the part of electrons with spin down and the part of electrons with spin up.

n ( ω') is given by(7) (8)

where T1, T2, g', γ, H1 and n0(ω') are the spin-lattice relaxation time of electrons, the spin-spin relaxation time of electrons (the inverse of the width of a spin-packet), the relative strength of forbidden and allowed transitions, the gyromagnetic ratio of electrons, the magnitude of the microwave field and the equilibrium value of n(ω') in the absence of fields, respectively. g (ω–Δ–ω') is the natural line shape function, in which Δ is the nuclear Zeeman splitting.

When microwave power is applied at a resonance frequency of a normal dangling bond and RF power at an ENDOR frequency (nuclear magnetic resonance (NMR) frequency) is further applied, the difference in nuclear spin polarization is defined as m = M − M+, in which M+ and M are the fraction of nuclei with spin up and spin down, respectively. They obtain the approximate result of m, as follows:(9)where TN and T2* are the nuclear spin-lattice relaxation time, the inverse of the line width of a local field distribution, respectively. When the ESR line is inhomogeneously broadened about its center ω0 with 1/T2*, the line shape function is defined as h(ωω0) that is normalized with(10)

The pulsed ENDOR measurement by Fehr et al. [10] has been carried out with a pulse sequence, using the Davies method [27]. Further, the ENDOR signal is detected as a change in the ESR signal associated with NMR, so that the change is the z-component of magnetization associated with NMR may be observed as the ENDOR signal. Thus, change in the z-component of magnetization is related to Δn = nn0.

Further, for comparison, Δχ' and Δχ” are given by(11) (12) (13) (14)

The calculated curves of the local field distribution curves, Δn, Δχ' and Δχ' are shown in Figure 6a–d for r = 4.80 Å and in Figure 7a–d for r = 5.12 Å, respectively. The computer-simulated ENDOR spectra for r = 4.80 Å and 5.12 Å shown in Figure 4 should be replaced by Figures 6b and 7b, respectively. Because Figure 4 is obtained from a transformation of the ESR spectrum involving hyperfine structure (dipolar interaction) with hydrogen nuclei, taking into account for distribution of hydrogen. A dip centered at the natural NMR frequency is seen in Figures 6b and 7b. This may contribute to the dip seen in the observed ENDOR spectrum by Fehr et al. [10], as seen in Figure 4. However, the dip also appears as a result of the suppression of the matrix ENDOR line (this is called the artifact) [10]. Thus, it is not obvious whether the dip is due to the artifact or the central part of the distant ENDOR spectrum, but a deep dip may arise in the latter case compared to in the former csse.

thumbnail Fig. 6

The calculated curves of the local field distribution curves (the central frequency = ω0): (a), Δn: (b), Δχ': (c), and Δχ”: (d) for r = 4.8 Å (Fig. 5).

thumbnail Fig. 7

The calculated curves of the local field distribution curves (the central frequency = ω0): (a), Δn: (b), Δχ': (c), and Δχ”: (d) for r = 5.12 Å (Fig. 5). (Reproduced from [13]).

4 Discussion

The computer-simulated ENDOR spectra are shown in Figure 4 for various values of r, but the relative intensities of each calculated ENDOR spectra have not yet been determined. Thus, the composite spectrum has not been obtained to compare with the ENDOR spectra observed by Fehr et al. [10]. This is a future problem. However, as has already been pointed out, the feature of the observed ENDOR spectra can be explained in term of our model.

Our model is based on a couple of two types of dangling bonds, i.e., a normal dangling bond and a hydrogen-related dangling bond. Further, isolated normal dangling bonds and isolated hydrogen-related dangling bonds are also created in the matrix. On the other hand, Fehr et al. [10] and Melskens et al. [28] postulate the existence of microvoids (Fehr et al.) and open volume deficiencies (Melskens et al.). Further discussions will be performed in a future publication.

In the computer-simulated ENDOR spectra, it is assumed that the g-tensor and the hyperfine interaction of dangling bonds have axial symmetry. However, Fehr et al. [29] obtained the parameters of the g-tensor with rhombic symmetry. So, the computer-simulated ENDOR spectra taking into accounts the g-tensor with rhombic symmetry will be obtained in a future publication.

5 Conclusion

In this paper, we interpret reasonably the results of ENDOR measurements in terms of our model of light-induced defect creation processes and of light-induced defects in a-Si:H. Thus, we conclude that the measurement may support our model.

Acknowledgments

The author acknowledges Professor H. Hikita and Dr K. Takeda for their collaboration in this study.

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Cite this article as: Kazuo Morigaki, Light-induced defect creation processes and light-induced defects in hydrogenated amorphous silicon, Eur. Phys. J. Appl. Phys. 90, 20101 (2020)

All Tables

Table 1

The values of parameters used in the calculation.

All Figures

thumbnail Fig. 1

Atomic configurations involved in the formation of two types of dangling bonds, i.e., normal dangling bonds and hydrogen-related dangling bonds, under illumination: (a) self-trapping of a hole in a weak Si–Si bond (wb) adjacent to a Si-H bond, (b) electron-hole recombination at a weak Si–Si bond, (c) switching of a Si-H bond towards the weak Si–Si bond, leaving a dangling bond behind, (d) formation of two separate dangling bonds through hydrogen movement after repeating the processes shown in (a)–(c).

In the text
thumbnail Fig. 2

(a) Schematic illustration of the normal dangling bond in a-Si:H. (b) Schematic illustration of the hydrogen-related dangling bond in a-Si:H.

In the text
thumbnail Fig. 3

The computer-simulated hyperfine structure with the values of ESR parameters shown below: giso = 2.004, A|| = 93 G, A = 51 G and σiso = 2 G. The isotropic g-value and the isotropic σ value are assumed for simplicity [11]. σ is the standard deviation of the spin-packet Gaussian shape function.

In the text
thumbnail Fig. 4

The computer-simulated ENDOR spectra in a-Si:H. HDB(blue): The values of the parameters are given below. g|| = 2.0050 and g = 2.0056, A|| = 19.6 MHz, A = 2.80 MHz, σ|| = 2.24 MHz, and σ= 3.36 MHz. The matrix ENDOR spectra for various distance between the dangling bond site and the hydrogen, r, are shown as follows: r = 3.20 Å (red). The values of the parameters are given below. g|| = 2.0050 and g⊥ = 2.0056, A|| = 4.68 MHz and A =2.34 MHz, σ|| = 1.12 MHz, and σ= 1.68 MHz. r = 3.40 Å (sky blue), r = 3.72 Å (magenta), r = 4.80 Å (yellow brown), r = 5.12 Å (olive): The values of the parameters for these r are given in Table 1. The Fehr ENDOR spectrum [10] is also shown. (Reproduced from [11]).

In the text
thumbnail Fig. 5

Schematic illustration of the local structure being composed of silicon atoms and hydrogen atoms. The distances 1, 2, and 3 are cited from Bellisent et al. [20] as follows: 1 = 3.3–4.3 Å, 2 = 3.2 Å, and 3 = 3.72–5.12 Å. (Reproduced from [11]].

In the text
thumbnail Fig. 6

The calculated curves of the local field distribution curves (the central frequency = ω0): (a), Δn: (b), Δχ': (c), and Δχ”: (d) for r = 4.8 Å (Fig. 5).

In the text
thumbnail Fig. 7

The calculated curves of the local field distribution curves (the central frequency = ω0): (a), Δn: (b), Δχ': (c), and Δχ”: (d) for r = 5.12 Å (Fig. 5). (Reproduced from [13]).

In the text

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