1 Introduction

In 1977, Staebler and Wronski reported either photoconductivity or dark conductivity of undoped hydrogenated amorphous silicon (a-Si:H) decreases after a prolonged light illumination, interestingly, a brief annealing at a low temperature of about 150 °C can reverse these conductivities close to their initial values [1]. This phenomenon is called Staebler-Wronski effect (SWE). As shown in Fig. 1, the SWE is independent on the doping type, i.e., it applies to intrinsic a-Si:H, phosphorus-doped a-Si:H and boron-doped a-Si:H [2, 3]. Basically, high-energy photons act scissors that cut saturated chemical bonds and produce dangling bonds. These recombination centers shorten the lifetime of photo-generated carriers in a-Si:H. In the meantime, the Fermi level shifts towards the middle position in optical bandgap, as a consequence, the dark conductance is decreased along with an increase of the annealing activation energy [1].

Fig. 1
figure 1

Evolution of dark conductance by light soaking, followed by a brief annealing, (a) intrinsic a-Si:H [1], (b) phosphorus-doped a-Si:H [2] and (c) boron-doped a-Si:H. [3]

Full size image

The SWE occurs with nearly constant efficiency in the photon energy ranging from 1.2 to 2.1 eV [4], where the decay rate of dark conductance depends on the microscopic structure of a-Si:H films and the light intensity, but the threshold of light intensity is not determined, where the decrease of dark conductance was even observed under an illumination of a very weak indoor light. This excludes it is a thermal effect. Recovery rate of dark conductance is strongly dependent on the annealing temperature. The relaxation time at room temperature is estimated to be 3 × 104 years, but a high-temperature annealing can accelerate the recovery of dark conductance in a short duration [5]. In some cases, the annealing can boost the dark conductance to exceed its initial value, followed by a slow decrease to the equilibrium value close to initial state [6]. In contrast to the light induced decrease of photoconductivity and dark conductivity of hydrogenated amorphous silicon (a-Si:H), we discovered an anomalous SWE induced by light soaking. The light soaking can increase dark conductance (σD) of boron-doped a-Si:H films. In the past, many studies about SWE reported the causes of SWE and researched the influence of light intensity, illumination time and sample temperature [7]. The purpose of this letter is to report the anomalous SWE and compare it to the SWE.

2 Discussion

2.1 Structural origin of dangling bonds

In the last half century, researchers proposed many models to elucidate the microscopic mechanism of SWE. Staebler and Wronski prepared a-Si:H diodes to measure their bulk conductance, it was found that both the photoconductance and dark conductance decreased under light exposure [2]. Si–H bonds exist not only on the surface but also in the bulk, and thus SWE is both a surface effect and a bulk effect [8]. Kakinuma et al. surveyed the effect of film thickness on the SWE, by this means they made the same conclusion as that from Staebler and Wronski [9]. With the help of dark electron-spin resonance (ESR), Dersch et al. discovered that light soaking can increase the dangling bond density from 9.2 × 1015 cm−3 to 1.8 × 1016 cm−3, in this regard, they concluded the SWE is caused by dangling bonds. A 30 min annealing at 220 °C then recovered the dangling bond density to the initial value [10]. Moreover, light-induced increase of gap-state density in a-Si:H film can also be confirmed by a measurement of deep level transient spectroscopy (DLTS). Similarly, the gap-state relevant absorption around 1.0–1.3 eV below the conduction band of intrinsic a-Si:H is enhanced after light-soaking exposure, which can also be restored close to initial value after a brief annealing [11].

In the work of Kruhler et al., they reported that metastable defects are also generated when p-type a-Si:H/i-type a-Si:H/p-type a-Si:H stack is biased by voltage [12]. In addition, Nakamura et al. unveiled that a-Si:H thin-film solar cells exhibit similar degradation behavior under an injection of either charge carriers or photon injection [13], indicating that the SWE may alternatively be caused by carriers no matter from carrier injection or light-induced carriers.

If the metastable phenomenon is caused by excess carriers, the mechanism should be explained by capture of single carriers in weak bonds and/or the recombination of electron–hole pairs. In the model of Adler, the SWE is caused by the trapping of excess carriers in the equilibrium-state charged-state dangling bond defects, this results in neutral metastable dangling bond defects [14], however, the density of charged dangling bonds in amorphous silicon are not very high [15]. The light-induced degradation behavior was also observed in compensated a-Si:H, it supports the bimolecular electron–hole recombination mechanism [16]. By means of spin resonance (LESR) signal of light-soaked compensated semiconductor, it was demonstrated that the dangling bond density is basically independent on the doping level. The increase of the dangling bond density is very small after illumination in case of a high doping level, and almost no light-induced degradation was observed. This is because the compensation introduces a large density of active phosphorus donors to capture electrons, which spatially separates electron–hole pairs. In this consideration, the nonradiative recombination is effectively limited, leading to a reduction in light-induced metastable defects. This cannot be explained by the single carrier model, as the compensation changes neither the overall excess carrier density nor the rate of single moleculer recombination.

Irradiation to a-Si:H by laser produces recombination centers that declines the carrier lifetimes [17]. This phenomenon is similar to SWE, which can be also reversed by annealing at ~ 200 °C. They proposed a Si-only model, where photons can break Si–Si bonds to create dangling bonds. An annealing can reconstruct these Si–Si bonds, but the exchange narrowed line with respect to dangling bond pair was not found in the ESR spectrum [10]. In addition, the broken weak Si–Si bond has the possibility to reconstruct again, thus it is unlikely to generate metastable dangling bonds. Another Si-only model was proposed by Pantelides [18], the illumination can switch the four-coordinated Si–Si bonds, and results in to five-coordinated silicon atoms, forming floating bonds along with three-coordinated silicon atoms with dangling bonds. This model assigns the characteristic ESR signal g = 2.0055 to the floating bonds. However, other groups demonstrated g = 2.0055 originates from dangling bonds, and the Si hyperfine structure is incompatible with the floating bond model [19, 20].

In 1985, Stutzmann et al. proposed stabilization of dangling bonds can be realized by rearrangement of hydrogen atoms, which is called the SJT model [4], as is shown in Fig. 2a. During illumination, the energy releases from the recombination of excited electrons and holes breaks Si–Si bonds, forming the dangling bonds. The reformation of weak bonds is prevented by switching back-bonded hydrogen atoms into the broken bonds. This process can be reversed by releasing hydrogen atoms at high temperatures.

Fig. 2
figure 2

Different models for the creation of metastable dangling bond defects in a Si–H. a SJT model (1985) [4], (b) Carlson model (1986) [21], (c) Godet model (1996) [22], (d) Hydrogen collision model (1999) [23].

Full size image

In the SJT model, metastable dangling bonds are created by a nonradiative tail-to-tail recombination transition, The generation rate of defects (Ndb) is proportional to the product of photogenerated electron (n) and hole (p) density, and the carrier recombination occurs mainly through defects, this relationship can be described as,

$$\frac{{dN_{{{\text{db}}}} }}{dt} \propto np \propto \left( {\frac{G}{{N_{{{\text{db}}}} }}} \right)^{{2}}$$
(1)

G is the generation rate of electron–hole pairs, t is the illumination time. It is worth noting that the generation rate of dangling bonds decreases with the dangling bond density. This is because the already existed dangling bonds act as recombination centers to trap photogenerated carriers, which in turn affects the generation rate of dangling bonds.

By integrating Eq. (1), we further obtain

$$N_{{{\text{db}}}} \propto G^{2/3} t^{1/3}$$
(2)

Here G2/3 indicates that SWE is related to photogenerated carriers, and t1/3 indicates the self-limiting characteristic of SWE. Since light intensity (I) is proportional to G, Eq. (2) can also be written as,

$$N_{{{\text{db}}}} \propto I^{2/3} t^{1/3}$$
(3)

This relationship has been confirmed in experiments.

Nevertheless, defect recombination can be neglected at low temperature, the carriers in the localized tail states recombine by tunneling, which contradicts the assumptions of the SJT model. Stradins et al. [24] found generation rate of metastable defects are essentially the same at 300 K and 4.2 K. The kinetics of light-induced defect at 4.2 K is \(N_{{{\text{db}}}} \propto G^{0.44} t^{0.35}\). The recombination forms in the range of 4.2 K to 300 K is complicated, and the temperature dependence of light-induced defect generation was not determined.

Carlson [21] proposed a model for long-range hydrogen diffusion, which is called the Carlson model, as shown in Fig. 2b. First, the holes are trapped in the Si–Si bonds nearby the internal surface of microvoids, then holes move towards the adjacent Si–H bond, these hydrogen atoms become weakly bonded, their movements further break nearby weak Si–Si bonds, consequently, dangling bonds are generated. By annealing, the original configuration can be restored. Similarly, Santos and co-workers [25] also proposed hydrogen is emitted from Si–H bonds, inserting into weak Si–Si bonds, eventually leading to the formation of dangling bonds, via measuring the deuterium depth profile of a-Si:H/a-Si:H:D/a-Si:H stack before and after illumination by secondary-ion mass spectroscopy. Under light soaking, the hydrogen diffusion is improved, as proved by Both Fehr et al. [26] and Melskens et al. [27], there exist two types of defects in a-Si:H, one related to microvoid (21%), the other is randomly distributed (79%), measured by electron-spin echoes decay. In their experiment, the defect concentration significantly increased during light soaking with the help of hydrogen atoms, mainly from internal surfaces of microvoids.

Figure 2c shows the model suggested by Godet et al. [22] During illumination, instead of breaking a Si–H bond or a Si–Si bond, the energy from electron–hole pair recombination is transferred to the Si–H H-Si configuration, hydrogen hopping forms two Si–H-Si metastable configurations, in the meantime a Si–Si bond is reconstructed, this reaction is described as below,

$$\left(\text{Si-H} \text{H-Si}\right)\to 2\left(\text{Si-H-Si}\right)+\left(\text{Si-Si}\right)$$
(4)

The activation energy is 1.44 eV, much lower than 2.40 eV for the breakage of an isolated Si–H bond. When the H in Si–H-Si configuration hop back to their initial sites, or further hop in the amorphous lattice, they have a probability to encounter Si–H bonds, dangling bonds are created as below,

$$\left( {\text{Si - H - Si}} \right){ + }\left( {\text{Si - H}} \right) \to \left( {\text{Si - DB}} \right){ + }\left( {{\text{Si - H}}\begin{array}{*{20}c} {} \\ \end{array} {\text{H - Si}}} \right)$$
(5)

But the ESR hyperfine results indicate the dangling bonds are formed in the hydrogen depletion region, where dangling bonds are about 4.2 Å away from the closest hydrogen atoms. [28] This is inconsistent with Carlson and Godet models, as hydrogen atoms are trapped very close to the dangling bonds in their models.

Branz proposed a hydrogen collision model [23], as schematic in Fig. 2d. First, recombination of photogenerated carriers leads to emission of hydrogen from Si–H bonds. Then the mobile hydrogen diffuses rapidly in the amorphous lattice by hopping between Si–Si bonds. Finally, the collision of two mobile H atoms form an immobile metastable complex containing two Si–H bonds, M(Si–H)2. The metastable dangling bonds are created,

$${\text{2(Si - H)}} \to 2({\text{Si - DB)}} + 2{\text{H}} \to 2({\text{Si - DB)}} + {\text{M}}\left( {\text{Si - H}} \right)_{2}$$
(6)

In an annealing process, hydrogen atoms are emitted from the M(Si–H)2, and hop back to saturate the dangling bonds.

In this hydrogen collision model, the creation rate of dangling bonds is mainly controlled by the mobile H density Nm,

$$\frac{{dN_{{{\text{db}}}} }}{dt} \propto N_{m}^{2}$$
(7)

where Nm is proportional to G, but inversely proportional to Ndb,

$$N_{{\text{m}}} \propto \frac{G}{{N_{{{\text{db}}}} }}$$
(8)

Therefore, Ndb is expressed as below,

$$N_{{{\text{db}}}} \propto G^{2/3} t^{1/3}$$
(9)

It is interesting to see that the hydrogen collision model and the SJT model describe the creation kinetics of dangling bonds in the same mathematical expression, but their physical picture is different from each other.

The hydrogen collision model explains the formation of dangling bonds at 4.2 K. Mobile hydrogen-related bandgap states trap photogenerated carriers to drive the diffusion of hydrogen atoms [29]. The ratio of mobile hydrogen captured by dangling bonds to those captured by collisions is not affected by temperature, thus it explains to the t1/3 kinetics.

Nevertheless, the hydrogen collision model does not apply to a-SiGe:H, Palinginis et al. implemented modulated photocurrent measurements to investigate the generation and annihilation process of light-induced defects in a-SiGe:H [30]. In annealing process, Si dangling bonds and the density of Ge dangling bonds are coupled with each other. This is a global reconstruction, likely involves long-range hydrogen diffusion, in agreement with the collision model. But the generation rates of these two types of dangling bonds are not coupled anymore and thus cannot be explained by the hydrogen collision model, instead, can be explained by the SJT model.

There exists some experimental evidence to support the light-induced metastable H pairs. From NMR signals, Su et al. demonstrated illumination produces hydrogen pairs, which can be removed by an annealing process [31]. Detail calculation reveals hydrogen pairs separate about 2.3 Å apart, this excludes the configuration of H2 because the bond length of H2 is much shorter than 2.3 Å. Tuttle suggested two hydrogen atoms break one weak Si–Si bond to form (Si–H H-Si), these hydrogen atoms spaced approximately 2.2 Å apart [32], in well agreement to the experimental 2.3 Å. Table 1 summarizes advantages and disadvantages of these proposed models.

Table 1 The experimental observations that the models could explain and could not explain
Full size table

2.2 Dangling bond annihilation in SWE

The reversible process in annealing is dependent on the temperature during light soaking. Zhang et al. studied the annealing activation energy of a-Si:H after light exposure [33], they reported that when the a-Si:H was light soaked at 77 K, its defect density reduced by 50% after room temperature annealing, and reduced by 97% at 393 K; but when the a-Si:H was light soaked at room temperature, only 45% of the defects were eliminated after annealing at 393 K, and 100% were eliminated after annealing at 470 K.

The light-induced defect density N(Ea,t) decreases as a function of annealing activation energy (Ea) and annealing time (t) in the following form,

$$N(E_{{\text{a}}} ,t) \propto \exp \left[ { - \frac{t}{{\tau (E_{{\text{a}}} )}}} \right]$$
(10)

where τ(Ea) is the metastable defect lifetime, and t(Ea) is

$$\tau (E_{{\text{a}}} ) \propto \exp \left( {\frac{{E_{{\text{a}}} }}{kT}} \right)$$
(11)

The annealing activation energies are 0.2 eV, 0.7 eV and 1.1 eV respectively generated by light soaking at 77 K, room temperature and 393 K.

2.3 Other changes in SWE

The SWE is usually accompanied with some other metastable structural changes. For example, the light induced change of the compressive stress ΔS in the a-Si:H film was reported, that is, the material volume change ΔV/V [34,35,36]. This expansion effect is similar to SWE and is also reversible by annealing. Under illumination, ΔS(t) increases significantly and gradually saturates. The relative volume expansion is about 10–3 when isotropic optical expansion is assumed. In initial stage, ΔS(t) is proportional to t0.5. Stratakis et al. analyzed and compared SWE and light-induced expansion, they demonstrated the dangling bonds make no contribution to the volume expansion [34], because the dangling bond density saturated after 1 h illumination, but ΔV/V did not saturate even after 72 h illumination. They also speculated the microscopic origin of light-induced volume expansion is caused by bimolecular recombination [36].

To date, the mechanism of SWE is still under debate. The SJT, Carlson and hydrogen collision models are widely used. They all suggest the recombination of photogenerated carriers and the redistribution of bonded hydrogen play significant roles in the generation and annihilation of dangling bond defects. Despite of this, all these models still have difficulties to explain some specific experimental observations, a more convincing and complete model is yet to be developed.

2.4 Light-induced anomalous SWE

In contrast to the SWE, we recently reported an anomalous Staebler-Wronski effect [37], i.e., light soaking can increase dark conductance (σD) of boron-doped a-Si:H films. After illumination, the σD gradually decays to the initial value in the dark, and the decay behavior conforms to a combination of the Debye model and the Williams-Watts model,

$$\Delta \sigma_{{{\text{dark}}}} \left( t \right) = \Delta \sigma_{{\text{D}}} \exp \left[ { - \left( {{t \mathord{\left/ {\vphantom {t {\tau_{{\text{D}}} }}} \right. \kern-0pt} {\tau_{{\text{D}}} }}} \right)^{{\beta_{{\text{D}}} }} } \right] + \Delta \sigma_{{{\text{WW}}}} \exp \left[ { - \left( {{t \mathord{\left/ {\vphantom {t \tau }} \right. \kern-0pt} \tau }_{{{\text{WW}}}} } \right)^{{\beta_{{{\text{WW}}}} }} } \right]$$
(12)

ΔσD, ΔσWW and τD, τWW are constant coefficients and characteristic time constants of the Debye model and the Williams-Watts model respectively. βD and βWW are dispersive factors.

By SIMS measurements, we demonstrated the hydrogen content in boron-doped a-Si:H decreased by more than 20% after annealing at 180 °C for 2 h. In contrast, the Si–H density remained almost unchanged. This indicates there exists huge amounts of weak hydrogen atoms in doped a-Si:H materials, they are inactive in the infrared absorption. Theoretical simulations demonstrate these weak hydrogen atoms can ‘poison’ effective doping of boron and phosphorus in a-Si:H [38]. In the a-Si:H, A portion of the hydrogen atoms occupies near the doping sites of a-Si:H, reducing their effective doping. Fortunately, light soaking can promote these metastable H atoms move away from the doping sites. As a consequence, related B and P are activated, and improve the σD. This improvement is reversed after annealing, suggesting weakly-bound hydrogen atoms in a-Si:H play an important role in the anomalous SWE [39].

Here we showcase this anomalous effect also takes place in phosphors-doped a-Si:H [40, 41]. Figure 3 shows σD of the phosphors-doped a-Si:H film is more sensitive to one-sun illumination than boron-doped a-Si:H film, its value improves as high as more than 100 times. After annealing, the σD reverses to the initial value. According to the NMR data, a large amount of hydrogen atoms locates at the second-nearest or more distant neighbors from phosphors atoms [42]. In this consideration, we speculate the weakly-bound hydrogen in the phosphors-doped a-Si:H film is attracted to form P-Si–H-Si metastable configurations, consistent with the simulated result of Pandey et al. [38], they also discovered the P-Si–H-Si structure can ‘poison’ effective doping. The binding energy of Si–H-Si is smaller than that of B-H-Si, thus phosphors-doped a-Si:H is more sensitive to light soaking, this explains why its σD improves more than that of boron-doped a-Si:H (Fig. 3).

Fig. 3
figure 3

Dark conductance changes in anomalous SWE. a boron-doped amorphous silicon, (b) phosphorus-doped amorphous silicon

Full size image

Next we illustrate the microscopic dynamics, as shown in Fig. 4, to activate the B or P doping, the hopping steps of weakly bonded hydrogen in phosphorus-doped a-Si:H films are less than those in boron-doped a-Si:H films. The energy required for the first-step H hopping in boron-doped a-Si:H films is about 0.9 eV, while the energy required for the second-step H hopping is about 0.64 eV [37]. The energy required for H hopping in phosphorus-doped a-Si:H is much less than 0.9 eV. This explains why the light-induced dark conductance improvement of phosphorus-doped a-Si:H film is much higher than that of boron-doped a-Si:H films.

Fig. 4
figure 4

The mechanism of anomalous SWE in (a) boron-doped a-Si:H films [37] and (b) phosphorus-doped a-Si:H films. The H needs to hop at least 2 steps to activate the B doping, while it only needs to hop one step to activate the P doping

Full size image

The binding energy of hydrogen captured in B-H-Si and P-Si–H-Si are about 0.96–1.51 eV and 0.5eV respectively [37], which is significantly lower than that of Si–H bond (3.2–3.6eV) [43], so when the photo energy is higher than 0.96–1.51eV, Anomalous SWE will appear in amorphous/crystalline silicon heterojunction (SHJ) solar cells. According to the relation between the wavelength and energy, the corresponding wavelength of light applied to solar cells is approximately between 820 and 1290nm. When using the light with wavelengths in this range to illuminate the SHJ solar cells, the efficiency of the SHJ solar cells will be greatly improved, in contrast, when the wavelength of light is less than 340nm, it will destroy the normal Si–H passivation in the SHJ solar cells, resulting in the SWE, which will reduce the conductivity of the material. Therefore, the efficiency of thin-film solar cells will be greatly reduced. Comparison of the above two phenomena will give a clue to the design of equipment. In order to maximize the efficiency of SHJ cells, we suggest to use intensive light soaking between 820 to 1290nm to illuminate the SHJ solar cells/modules.

3 Conclusions and future directions

The SWE hinders the application of thin-film a-Si:H solar cells. As shown in Fig. 5a, the cell efficiency decays under prolonged light exposure, and the light-induced degradation can be partially reversed by an annealing [44,45,46,47,48,49,50]. Moreover, the reverse process can be accelerated at moderate temperatures by applying a strong electric field and exposure to intense illumination, because an electric field can reduce the activation energy of a-Si:H solar cells [51, 52].

Fig. 5
figure 5

a Schematic of a-Si:H thin-film solar cell. Also shown are the light-induced degradation and annealing recovery of its efficiency [44,45,46,47,48,49,50]; b Schematic of SHJ solar cell. Also shown are the light-induced improvement and annealing reverse of its efficiency. The same color circles indicate they are the same samples

Full size image

Because of this adverse effect, it is important to improve the light-soaked stability of a-Si:H solar cells. Nishimoto et al. [53] proved light-induced degradation can be reduced by decreasing the content of Si-H2 in the film. Matsui et al. [48, 50] reported the content of Si-H2 bonds in a-Si:H prepared by triode PECVD is less than that in film prepared by conventional diode PECVD. Fabrication of a-Si:H solar cells by triode PECVD achieved a stabilized efficiency of 10.2%, being the record stabilized efficiency of single-junction thin-film a-Si:H solar cells [45].

Anomalous SWE exists in amorphous/crystalline silicon heterojunction (SHJ) solar cells. Taking advantage of this effect, the efficiency of SHJ solar cells is improved by about 0.3% after light soaking (Fig. 5b), but reverses to initial value after an annealing. By capping the cell with an antireflection layer, we achieved certificated efficiencies of 25.10% and 25.45% on 6-inch wafers [37]. Here the improvement stems from several factors, (1) the conductance improvement declines the solar cell’s series resistance, (2) activation of the doping efficiency improves the carrier selectivity, and (3) the improved doping concentration can decrease the depletion region in doped a-Si:H at the TCO/a-Si:H interface, thus improve the carrier’s tunneling efficiency.

The efficiency developments of single-junction SHJ solar cells and single-junction thin-film a-Si:H solar cells are summarized in Fig. 6. The measured efficiency of thin-film a-Si:H solar cells is the stabilized value after long-term illumination. The highest efficiency of single-junction SHJ solar cells is 27.09% (https://www.longi.com/cn/news/heterojunction-back-contact-battery/.), which is much higher than 10.22% of the thin-film a-Si:H solar cells [45]. Since the efficiency of the latter is difficult to further improve, this technology route has been gradually obsoleted. SHJ solar cells not only possess high efficiency and good stability [54], but also exhibit better performance under illumination and good flexible fabrication [39], thus have a big promising to establish its position in next-generation photovoltaic market.

Fig. 6
figure 6

Efficiency developments of SHJ solar cells and thin-film a-Si:H solar cells [45, 55,56,57]. The former shows high efficiencies of more than 26% for both double-side contacted [58,59,60,61,62,63,64,65,66,67] and interdigitated back-contacted structures [68,69,70] (https://www.longi.com/cn/news/heterojunction-back-contact-battery/). The latter shows a low efficiency of slightly higher than 10%

Full size image

To conclude, a-Si:H thin films exhibit two opposite effects under illumination, in which hydrogen atoms play an important role. The hydrogen atoms can be roughly divided into Si–H configurations and bridge configurations of B-H-Si, P-Si–H-Si and Si–H-Si. Light soaking can promote H movements in a-Si:H network. On the one hand, H diffusion can induce breakage of weak bonds, leading to the SWE. On the other hand, bridge H atoms nearby B and P doping sites can ‘poison’ the effective doping, light soaking can promote their departure from these doping sites via hopping movements between bonds, consequently, the doping efficiency is improved, leading to the anomalous SWE. At the device level, when SWE dominates, light soaking declines the efficiency of a-Si:H thin-film solar cells; in contrast, when anomalous SWE dominates, the light soaking improves the efficiency of SHJ solar cells. For both cases, a brief annealing at ~ 200 °C can reverse the efficiency (close) to the initial value. Implementation of anomalous SWE can improve efficiency of SHJ solar cells, which are promising to become the mainstream product of next-generation silicon photovoltaics.