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 
https://doi.org/10.1051/epjap/2020190257
Regular Article
Lightinduced defect creation processes and lightinduced defects in hydrogenated amorphous silicon^{★}
University of Tokyo, Hongo, Tokyo 1138654, Japan
^{*} email: k.morigaki@yacht.ocn.ne.jp
^{**} Present Address: C305, Wakabadai 212, Inagi, Tokyo 2060824, Japan
Received:
31
August
2019
Received in final form:
18
January
2020
Accepted:
9
March
2020
Published online: 26 June 2020
We have proposed a model of lightinduced defect creation processes and lightinduced defects. Recently, important results using pulsed electronnuclear double resonance (ENDOR) by Fehr et al. [M. Fehr, A. Schnegg, C. Teutloff, R. Bittl, O. Astakhov, F. Finger, B. Rech, K. Lips, Phys. Status Solidi A 207, 552 (2010)] have been reported, so that these results are interpreted on the basis of our model. Fehr et al. have observed ENDOR signals due to hydrogen nuclei distributed around a dangling bond. The ENDOR spectra due to hydrogen nuclei being located with distance of r from the dangling bond have been calculated, taking into accounts the dipolar interaction, and also the Fermitype contact hyperfine interaction for the Hrelated dangling bond (HDB) that is a dangling bond having hydrogen at a nearby site. The typical features of the observed ENDOR spectra are that the spectrum has a shoulder at the low frequency side from the natural NMR frequency of hydrogen and it has a dip in the central part. The calculated ENDOR spectrum of HDB exhibits such a shoulder. This is consistent with our model of lightinduced defects such as HDB. The ENDOR spectra with various values of r are calculated. In this paper, we also deal with the distant ENDOR precisely, using the theory of distant ENDOR by Lambe et al. [J. Lambe, N. Laurance, K.C. McIrvine, R.W. Terhune, Phys. Rev. 122, 1161 (1961)]. The calculated distant ENDOR spectrum shows a dip in the central part. Concerning the dip, Fehr et al. attribute the dip to be due to the suppression of the matrix ENDOR line (this is called the artifact). Thus, it is not obvious whether the dip is due to such an artifact or the central part of the distant ENDOR spectrum.
© EDP Sciences, 2020
1 Introduction
After prolonged illumination, the dark conductivity and photoconductivity of hydrogenated amorphous silicon (aSi:H) decrease compared with their values before illumination [1]. Such a phenomenon is called the StaeblerWronski effect. After then, StaeblerWronski [2] suggested that this may be due to lightinduced 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 lightinduced 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 lightinduced defects in Section 2. From our model of lightinduced defect creation in aSi:H, we have proposed the model of lightinduced 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 hydrogenrelated dangling bond. For evidence for existence of these defects, our ESR measurements [6,7] are reviewed as well as our electronnuclear double resonance (ENDOR) measurements in aSi:H and aSi:D [8,9] in Section 3. Further, recent results of pulsed ENDOR measurements by Fehr et al. [10] are presented and compared with our computerstimulated ENDOR spectra in Section 3 together with a detailed calculation of distant ENDOR in aSi:H. In Section 4, conclusion is drawn. Preliminary reports concerning Section 3 have been published in [11–13].
2 Lightinduced defect creation
First, our model of lightinduced defect creation processes is described below: Under illumination by light with bandtoband energy, electrons and holes are generated. A hole is selftrapped in a specific weak Si–Si bond [14] that is a weak Si–Si bond adjacent to a SiH 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 SiH bond is switched towards the weak Si–Si bond (Fig. 1c). After switching of the SiH 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 hydrogenrelated 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 hydrogenrelated dangling bonds (Fig. 2b), as have been shown by calculations based on the above lightinduced creation processes [16]. Detailed accounts on the lightinduced defect creation mentioned above have been presented in [17,18].
Fig. 1 Atomic configurations involved in the formation of two types of dangling bonds, i.e., normal dangling bonds and hydrogenrelated dangling bonds, under illumination: (a) selftrapping of a hole in a weak Si–Si bond (wb) adjacent to a SiH bond, (b) electronhole recombination at a weak Si–Si bond, (c) switching of a SiH 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). 
Fig. 2 (a) Schematic illustration of the normal dangling bond in aSi:H. (b) Schematic illustration of the hydrogenrelated dangling bond in aSi:H. 
3 ESR and ENDOR measurements in aSi: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 µ_{B}, µ_{n}, S, I, g, g_{n}, 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 zaxis making an angle of θ with the axial symmetric axis of the hyperfine interaction tensor, A is given by its isotropic part, A_{iso}, and anisotropic part, A_{aniso}, as follows:(2)Using A_{} (A_{} with θ = 0) and A_{⊥} (A_{⊥} with θ = π/2), A_{iso} and A_{aniso} are given by(3) (4)respectively. A_{iso} and A_{aniso} arise from the Fermitype contact hyperfine interaction, whose constant is proportional to the electron density at the hydrogen nucleus, and from the dipolar interaction, respectively. A_{aniso} 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 computersimulation 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 Hrelated dangling bonds. From the deconvolution, we estimate the values of A_{iso} and A_{aniso} as well as the density percentage of normal dangling bonds and Hrelated dangling bonds for various samples of aSiH prepared with different conditions [6,7]. The values of R are also estimated for various samples of aSiH prepared with different conditions [6,7].
Fig. 3 The computersimulated hyperfine structure with the values of ESR parameters shown below: g_{iso} = 2.004, A_{} = 93 G, A_{⊥} = 51 G and σ_{iso} = 2 G. The isotropic gvalue and the isotropic σ value are assumed for simplicity [11]. σ is the standard deviation of the spinpacket Gaussian shape function. 
3.2 ENDOR measurements
Electronnuclear 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 computersimulated ENDOR spectrum due to the hydrogenrelated 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 computersimulation 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 r − r_{0} = 5 MHz. Such a shoulder is also seen in the computersimulated ENDOR spectrum shown in Figure 4. This suggests for the hydrogenrelated dangling bond to exist in aSi:H. Further evidence for existence of the hydrogenrelated dangling bond has been obtained from our ENDOR measurements in aSi:H and aSi:D [8,9].
Fig. 4 The computersimulated ENDOR spectra in aSi: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 computersimulated ENDOR spectra are shown in Figure 4. Figure 5 has been obtained by Bellisent et al. [20], using the neutronscattering measurement in sputtered aSi: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.
Fig. 5 Schematic illustration of the local structure being composed of silicon atoms and hydrogen atoms. The distances ℓ_{1}, ℓ_{2}, and ℓ_{3} are cited from Bellisent et al. [20] as follows: ℓ_{1} = 3.3–4.3 Å, ℓ_{2} = 3.2 Å, and ℓ_{3 }= 3.72–5.12 Å. (Reproduced from [11]]. 
The values of parameters used in the calculation.
3.2.3 Distant ENDOR
We consider distant ENDOR observed in aSi:H in terms of Lambe et al.'s theory [23] which is based on the dynamical nuclear polarization [24–26]. In this theory, forbidden double spinflip 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' − ω_{0}) is a local field distribution of microwave frequency ω' with a central ESR frequency ω_{0} and N^{–}(ω ^{'}) and N ^{+}( ω ^{'}) are the part of electrons with spin down and the part of electrons with spin up.
where T_{1}, T_{2}, g', γ, H_{1} and n_{0}(ω') are the spinlattice relaxation time of electrons, the spinspin relaxation time of electrons (the inverse of the width of a spinpacket), 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 T_{N} and T_{2}^{*} are the nuclear spinlattice relaxation time, the inverse of the line width of a local field distribution, respectively. When the ESR line is inhomogeneously broadened about its center ω_{0} with 1/T_{2}*, the line shape function is defined as h(ω − ω_{0}) 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 zcomponent of magnetization associated with NMR may be observed as the ENDOR signal. Thus, change in the zcomponent of magnetization is related to Δn = n − n_{0}.
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 computersimulated 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.
Fig. 6 The calculated curves of the local field distribution curves (the central frequency = ω_{0}): (a), Δn: (b), Δχ': (c), and Δχ”: (d) for r = 4.8 Å (Fig. 5). 
Fig. 7 The calculated curves of the local field distribution curves (the central frequency = ω_{0}): (a), Δn: (b), Δχ': (c), and Δχ”: (d) for r = 5.12 Å (Fig. 5). (Reproduced from [13]). 
4 Discussion
The computersimulated 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 hydrogenrelated dangling bond. Further, isolated normal dangling bonds and isolated hydrogenrelated 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 computersimulated ENDOR spectra, it is assumed that the gtensor and the hyperfine interaction of dangling bonds have axial symmetry. However, Fehr et al. [29] obtained the parameters of the gtensor with rhombic symmetry. So, the computersimulated ENDOR spectra taking into accounts the gtensor 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 lightinduced defect creation processes and of lightinduced defects in aSi: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, Lightinduced defect creation processes and lightinduced defects in hydrogenated amorphous silicon, Eur. Phys. J. Appl. Phys. 90, 20101 (2020)
All Tables
All Figures
Fig. 1 Atomic configurations involved in the formation of two types of dangling bonds, i.e., normal dangling bonds and hydrogenrelated dangling bonds, under illumination: (a) selftrapping of a hole in a weak Si–Si bond (wb) adjacent to a SiH bond, (b) electronhole recombination at a weak Si–Si bond, (c) switching of a SiH 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 
Fig. 2 (a) Schematic illustration of the normal dangling bond in aSi:H. (b) Schematic illustration of the hydrogenrelated dangling bond in aSi:H. 

In the text 
Fig. 3 The computersimulated hyperfine structure with the values of ESR parameters shown below: g_{iso} = 2.004, A_{} = 93 G, A_{⊥} = 51 G and σ_{iso} = 2 G. The isotropic gvalue and the isotropic σ value are assumed for simplicity [11]. σ is the standard deviation of the spinpacket Gaussian shape function. 

In the text 
Fig. 4 The computersimulated ENDOR spectra in aSi: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 
Fig. 5 Schematic illustration of the local structure being composed of silicon atoms and hydrogen atoms. The distances ℓ_{1}, ℓ_{2}, and ℓ_{3} are cited from Bellisent et al. [20] as follows: ℓ_{1} = 3.3–4.3 Å, ℓ_{2} = 3.2 Å, and ℓ_{3 }= 3.72–5.12 Å. (Reproduced from [11]]. 

In the text 
Fig. 6 The calculated curves of the local field distribution curves (the central frequency = ω_{0}): (a), Δn: (b), Δχ': (c), and Δχ”: (d) for r = 4.8 Å (Fig. 5). 

In the text 
Fig. 7 The calculated curves of the local field distribution curves (the central frequency = ω_{0}): (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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