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In this Letter we discuss two competing explanations for absorption enhancement via randomly nanotextured interfaces (Fig. 1a). The enhanced efficiency is caused either by scattering of light into the active layer (Fig. 1a, top) or by light localization (bottom). Based on statistical ray optics, Eli Yablonovitch predicted an enhancement for thick absorber layers with randomly corrugated interfaces11. Single scattering events of an incident photon into such an absorber layer extend the propagation length and increase the absorption (Fig. 1a, top panel). Physical-optics simulations of thin-film solar cells12,13 have demonstrated absorption enhancements beyond the limit proposed by Yablonovitch11 and raise the hope of efficiency boosts in suitably designed absorbers. Recently, Vynck and colleagues predicted, by means of theoretical simulations, that localization in a randomly perforated thin absorber layer can enhance absorption10, making absorption enhancement via light localization (Fig. 1a, bottom) highly interesting for thin-film solar cells. The localization of waves in disordered systems is a well-known universal phenomenon that was first reported by Philip Anderson for electrons14 and later observed for light and in acoustics15. Recently, interest has shifted from fundamental demonstrations towards applications of localization phenomena in disordered media16, quantum optics with Anderson localized states17, and to nanoscale nonlinear optical phenomena18,19. Theoretical investigations of absorption enhancement via light localization10 are feasible because electric field and absorption calculations provide high spatial resolution. By contrast, experiments are challenging, because typically only indirect evidence of localization is obtained. Thus, a clear demonstration of absorption enhancement via localization is yet to be provided.

Figure 1: Absorption enhancement in nanotextured a-Si:H absorbers.
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a, Enhanced absorption in nanotextured a-Si:H absorber layers based either on single scattering or on localized photonic modes. b, Schematic cross-sections of the different investigated samples. The root-mean-square roughness of the top layers (obtained from AFM) are 12, 42 and 32 nm for the smooth, nanotextured and exposed nanotextured a-Si:H stacks, respectively. c, UV–vis absolute absorption spectra for the samples in b. The centre wavelength of the ultrashort laser pulses used in this investigation is indicated by the vertical red bar.

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Here, we investigate the absorption enhancement mechanism in amorphous silicon (a-Si:H) layers of the type used in commercial thin-film solar cells. Such devices rely on photon management strategies based on nanotextured interfaces to enhance absorption. To distinguish between the two competing absorption enhancement scenarios based on either localization or single scattering (Fig. 1a), we applied the recently developed method of coherent two-dimensional (2D) nanoscopy20 and spectromicroscopy of scattered fields. Coherent 2D nanoscopy combines time-resolved photoemission electron microscopy (TR-PEEM)21 with coherent 2D spectroscopy22. As the localized emission of electrons is detected, the spatial resolution of 2D nanoscopy (<40 nm in our PEEM set-up) is not limited by optical diffraction.

We compared three different layered solar-cell structures of transparent conductive oxides (TCOs) and a-Si:H grown by plasma-enhanced chemical vapour deposition (PECVD) on glass substrates (Fig. 1b). The deposition method and the parameters for the initial TCO layer growth determine the final-stack surface topography and its light scattering properties (see Supplementary Sections 1 and 2 for details about sample preparation, nanotexturing and roughness characterization). Two samples had identical layer stacks: one with smooth and the other with nanotextured interfaces. An additional third sample with an exposed nanotextured a-Si:H layer enabled coherent 2D nanoscopy via electron emission20. Atomic force microscopy (AFM) topographies show that the two nanotextured samples had almost identical surface roughnesses for spatial frequency components larger than 1 µm−1 (Supplementary Fig. 1d). Cross-correlations of the surface topographies reveal a very small concentration (∼1 × 10−2 µm−2) of nanotexture anomalies that might affect light trapping (Supplementary Section 2). The metallization step used for commercial solar cells was omitted for all samples to provide direct optical access to the TCO and a-Si:H absorber layers. In a complete cell, metallization or application of a white paint back-reflector significantly enhances the quantum efficiency, because light that is transmitted in the first pass is redirected onto the absorber layer23.

UV–vis absorption measurements (Fig. 1c) for the three different samples show enhanced absorption for nanotextured interfaces (red, green) in the range of interband absorption cutoff (600–700 nm) and tail-state absorption (>700 nm) compared with the sample with smooth interfaces (black). For the sample with smooth interfaces, Fabry–Perot resonances are responsible for the oscillating absorption in the strong absorption band (<550 nm). Nanotextured interfaces wipe out these Fabry–Perot resonances and the cell efficiency is enhanced by up to 35% (Supplementary Section 1). Interestingly, in the long wavelength range, the sample with the exposed nanotextured a-Si:H layer exhibits an absorption twice that of the sample with smooth interfaces, although it has only one-third the absorber thickness.

More insight is obtained from analysis of the scattered radiation. As shown in Fig. 2a, ultrashort laser pulses of 20 fs duration were directed onto the sample at a small incidence angle. Most of the incident light is reflected in the specular direction, absorbed or transmitted through the layer stack. However, a small fraction is backscattered, collected by the focusing mirror, and directed towards a spectrometer. Figure 2b presents a typical spectrum of the backscattered radiation from the sample with nanotextured interfaces. In contrast to the smooth incident laser spectrum (dashed line), the backscattered radiation is composed of distinct spectral peaks. The linewidth of these peaks reflects the lifetime of resonances involved in the light scattering process. A statistical peak analysis in 25 spectra recorded along a 100 µm lateral scan of the sample yielded the lifetime distribution shown as the inset in Fig. 2b. The distribution of resonance lifetimes is centred at ∼100 fs, indicating that the electromagnetic fields reside for about this length of time in the layer stack.

Figure 2: Coherence properties of backscattered radiation from a-Si:H thin-film solar cells.
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a, Spectromicroscopy set-up used to characterize the backscattered light. Ultrashort light pulses (25 fs, 790 nm centre, 80 MHz) are focused onto the sample (15 µm 1/e2 intensity spot diameter) with an incidence angle of 2°. The spectral composition of the scattered light in the backward direction is determined by spectrometry. The total opening angle for scattered light collection is ∼11°. b, Spectral intensity of backscattered light from the sample with nanotextured interface (solid black line) and incident laser spectrum (dashed grey line). The red shaded spectral line has a width of 0.013 rad fs−1, corresponding to a resonance coherence lifetime of τ0 = 160 fs. Inset: lifetime distribution histogram, determined from peaks in 25 spectra recorded along a 100 µm scan of the sample. c, Spatial variation of the backscattered field amplitude for the three different samples as a function of a unidirectional lateral sample displacement (black bar indicates the displacement scale). Time-domain representations of the scattered field amplitudes for the spectra indicated by coloured boxes in the middle panel are provided in Supplementary Fig. 3c.

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The laterally scanned backscattered spectra show characteristic differences for the different samples (Fig. 2c). The smooth sample has unstructured spectra (Fig. 2c, left), the nanotextured sample has varying narrow resonances (Fig. 2c, middle), and the exposed nanotextured a-Si:H sample somewhat broader resonances (Fig. 2c, right). A statistical peak analysis in the latter case yields an average coherence lifetime of ∼70 fs. This lifetime is shorter than the 100 fs observed for the TCO-covered nanotextured sample (Fig. 2b), but still significantly longer than the time required to travel vertically through the dielectric layer stack (7.5 fs). Spectral interferometry24 allowed the temporal field evolution of the backscattered radiation to be reconstructed (Supplementary Fig. 3). Time-domain analysis yielded an average coherence lifetime of 135 fs (Supplementary Fig. 3d, red) for the sample with nanotextured interfaces and 70 fs (Supplementary Fig. 3d, green) for the sample with the exposed nanotextured a-Si:H layer, confirming the coherence lifetimes derived from spectral peak-width analysis.

The observation of long-lived coherent contributions in the backscattered light reveals that electromagnetic fields are captured in the nanotextured thin-film a-Si:H solar-cell absorber stack for a substantially long time and thus absorption is enhanced. From the strong spatial variability of the backscattered spectra and the applied confocal detection scheme, we conclude that the resonances are confined to the volume defined by the absorber thickness and the focal spot. However, this does not yet allow identification of the absorption enhancement mechanism. Two possible mechanisms remain to explain this behaviour: (1) the nanotextured interfaces might support spectrally selective diffraction of incident radiation into the absorber layer (Fig. 1a, top panel) or (2) the nanotextured interfaces could lead to the formation of localized standing-wave patterns confined in the absorber layer, and leakage radiation is then responsible for the backscattered radiation (Fig. 1a, bottom).

A higher spatial resolution and sensitivity to absorbing photonic modes is required to distinguish between these two absorption enhancement mechanisms. Using coherent 2D nanoscopy20 (Fig. 3a), a sequence of three laser pulses with variable delays and relative phases was focused onto the sample with the exposed a-Si:H layer and the local electron emission yield was recorded with PEEM (see Supplementary Section 6 for details). The laser intensities remained below the regime where nonlinear absorption in a-Si:H significantly influences light propagation in the medium, and the 2D spectroscopy scheme was applied here to study linear optical absorption. Two-dimensional Fourier transformation of the local electron yield, recorded as a function of both time delays τ and t between the pulses, yielded a 2D spectrum that was then further analysed. These local 2D nanospectra (exemplified in Fig. 3a) are well characterized by a single Lorentzian 2D line-shape function. The emission pattern (Fig. 3b) is rather inhomogeneous and exhibits strong emission spots. From the 2D nanospectra, for each pixel of an emission spot we obtain the characteristic centre frequency ω0 (Fig. 3c) and corresponding lifetime τ0 (Fig. 3d) of the involved resonant mode (see Supplementary Section 9 for details). The emission from any individual hot spot is characterized by a distinct spectral position given by the centre frequency ω0 (Fig. 3c) and a homogeneous lifetime τ0 (Fig. 3d) across the emission spot. The measured local lifetime varies between 40 and 140 fs and thus agrees well with the average lifetime of ∼70 fs measured via optical backscattering (see above). From this agreement we conclude that both methods detect the same spectral features.

Figure 3: Coherent 2D nanoscopy of localized photonic states in nanotextured a-Si:H thin-film solar cells.
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a, Experimental set-up to determine the local electron emission yield for excitation with a sequence of three light pulses (60 fs, 796 nm, 80 MHz, 50 µm 1/e2 intensity spot diameter on the sample surface) with relative delays τ and t between the pulses and relative phases. An ultrahigh-vacuum (UHV) photoemission electron microscope (PEEM) records the electron emission pattern (<40 nm spatial resolution for the chosen field of view). Local 2D nanoscopy spectra are obtained as 2D Fourier transforms (FT) of the yield measured as a function of delays τ and t. b, Electron emission pattern (τ = t = 0) of the sample with an exposed nanotextured a-Si:H layer. c,d, Lorentzian line-shape analysis of the coherent 2D nanoscopy spectra yielding the resonance centre frequency ω0 (c) and the coherence lifetime τ0 of the localized photonic modes (d). e, Local power-law nonlinearity n of the laser-intensity-dependent local electron emission yield shown in b, obtained from fitting the emission yield for single-pulse excitation as a function of incident laser intensity. In the grey shaded regions the yield is lower than 5% of the maximum yield and does not allow reliable determination of n. f, Scheme of thermionic electron emission from laser-excited localized photonic modes. After excitation of the photonic mode and thermalization of the electron gas, thermionic emission dominates the electron yield (for further explanations see main text and Supplementary Section 7). g, Relation between locally absorbed energy density and thermionic emission yield. The black line indicates a nonlinear yield dependence varying with nonlinearity n = 8.

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The observation of distinct and highly localized emission spots with unique spectroscopic properties, that is, distinct resonances with specific centre frequencies and lifetimes, rules out propagating modes (Fig. 1a, top) to be responsible for the enhanced absorption. This identification is further supported by a detailed analysis of the electron emission mechanism. Key information is retrieved from the highly nonlinear intensity dependence of the electron yield as it is measured by recording the yield for different incident laser intensities and fitting a power-law nonlinearity n (Fig. 3e). The strongest emission spots exhibit nonlinearities around n = 8. For threshold multiphoton photoemission, that is, when the total delivered energy of n times the photon energy just overcomes the material workfunction, one would expect n = 4 to efficiently emit photoelectrons assuming a workfunction of 5.8 eV. Note that above-threshold photoemission25,26 and strong-field emission processes27 also cannot account for such high nonlinearities of the total yield. In addition, the maximum emission yield is chosen to remain well below the onset of the space-charge effects that might influence the emission yield. By contrast, the thermionic emission model (Fig. 3f) accounts for such high nonlinearities. The enhanced absorption of radiation in localized modes heats the electron gas in the absorber layer to sufficiently high temperatures that thermionic emission dominates. Using the heat capacity of the electron gas for a-Si:H and the Richardson–Dushman equation for thermionic emission, the electron emission yield is obtained as a function of the locally absorbed energy density (Fig. 3g, red line; see Supplementary Section 7 for details). The yield varies over 15 orders of magnitude for absorbed energy densities between 0.02 and 1.1 eV nm−3 and exhibits a continuously changing slope in the double logarithmic plot. Note that thermionic emission after short pulse excitation is a transient process and, as discussed in Supplementary Section 7, lateral hot carrier transport influences the emission pattern only marginally.

The slope of the thermionic emission yield (Fig. 3g, red line) matches the experimentally observed nonlinearity n = 8 (Fig. 3g, black line) for absorbed energy densities between 0.1 and 0.2 eV nm−3. We thus see the excess energy density in the electron gas reflecting the local absorption in the a-Si:H layer. Based on the accordingly determined absorbed energy density (Supplementary Fig. 5b) and assuming homogeneous excitation across the a-Si:H film thickness, an average absorbed fluence of 100 µJ cm−2 is determined, which corresponds to 75% absolute absorption in the a-Si:H layer. Taking into account the uncertainties of the assumptions, this estimated absorption via localized photonic modes agrees well with the measured 40% absorption for the exposed nanotextured a-Si:H layer (green line in Fig. 1c). From this we conclude that the absorption in the layer is dominated by light trapping in localized states, and hence absorption in propagating modes can only play a marginal role; that is, the mechanism shown in Fig. 1a (top) does not contribute significantly to the total absorption in the investigated wavelength range. This is of interest, because the coexistence of localized and delocalized modes has been observed for disordered 2D systems and provides qualitative information about the localization mechanism28,29.

The spatial extent of the localized photonic modes provides insight into the localization mechanism. Scattering of waves in disordered media gives rise to various localization phenomena15. For strong scattering—that is, for a mean free propagation path length shorter or on the order of the wavelength—Anderson or strong localization occurs. For relatively weak scattering, the waves propagate over larger spatial domains and the associated localization is conceived as self-intersecting multiple scattering pathways that still support transport in finite disordered systems. As discussed in detail in Supplementary Section 8, the localized modes observed here have a diameter (full-width at half-maximum (FWHM) of the intensity profile) of ∼1 µm.

Among other factors, absorption in the material might limit the localization length. However, the dominant absorption in modes localized on the micrometre scale indicates that the experimentally determined localization length is not influenced by absorption in the a-Si:H layer (the absorption length for 800 nm is larger than 10 µm30). Closed scattering pathways that would form in a non-absorbing layer appear as propagating modes if the path length exceeds the absorption length. Because the excitation of such propagating modes does not significantly contribute to the total absorption, the experimentally determined localization length indeed reflects the localization length for a non-absorbing nanotextured layer. Finite-difference time-domain (FDTD) calculations for absorbing and non-absorbing nanotextured a-Si:H layers reveal identical mode sizes (Supplementary Fig. 8, lower two panels) and thus corroborate that the weak absorption does not affect the localization length in the present case.

The fact that localized modes form in a disordered 2D waveguide structure, together with the directly measured localization length of ∼1 µm and the observation that absorption in propagating modes is marginal, allow us to conclude that Anderson localization of light in the absorber layer indeed occurs. This is independently supported by the analysis of spectral and intensity correlations in the scattered radiation yielding dimensionless conductance values of g = 0.82 ± 0.08 and g = 0.76 ± 0.07 (Supplementary Fig. 4b) for the nanotextured and exposed nanotextured a-Si:H samples, respectively. The observation of a dimensionless conductance of g < 1 for both nanotextured samples establishes that Anderson localization occurs in both cases. However, we can claim only for the exposed nanotextured a-Si:H sample that Anderson localization is responsible for the absorption enhancement, as only for this sample does thermionic emission microscopy provide a quantitative measure of the local absorption.

Scaling theory for Anderson localized modes in disordered 2D systems relates the localization length ξ to the mean free path l* and the wavevector in the medium k by ξ = l*exp(0.5πkl*)31. Using this, a mean free path of ∼60 nm is obtained in the present case; that is, l* is significantly smaller than the wavelength λa-Si of the radiation in the medium (refractive index na-Si ≈ 4, λa-Si ≈ 200 nm). Note that an a-Si:H layer thickness of 100 nm was intentionally chosen to match the fundamental transverse mode in the layer and thus the absorber indeed acts laterally as a disordered 2D waveguide. Based on the reduced propagation speed of light in a-Si:H, this small l* means that a photon is scattered on average every 0.8 fs. Hence, within the 100 fs lifetime of a photon in a localized mode (Fig. 3d), more than 100 scattering events occur and the regime of strong multiple scattering is fulfilled. Thus, our study shows clearly that absorption enhancement works far away from the conventionally assumed single-scattering regime (Fig. 1a, top).

The structural correlation length of the exposed nanotextured a-Si:H interface, as obtained from AFM topographies, is ∼400 nm. For light propagating in the corrugated 100-nm-thick a-Si:H layer, mean free path lengths below 100 nm are conceivable. Anderson localization of light in disordered 2D systems has already been demonstrated for acoustic waves32, microwaves33 and in the infrared9, yielding similar localization length values normalized to the wavelength in the media. In contrast to those investigations, we demonstrate that Anderson localized modes dominate the absorption of radiation in the investigated wavelength range. Efficient absorption in localized states at first glance seems counterintuitive, because efficient localization requires small losses and thus weak coupling to the incident radiation. However, as discussed below, high or even perfect absorption can occur in a resonator, even under weak coupling conditions.

Thermionic emission microscopy using PEEM, as demonstrated here, represents a fascinating new tool for studying photonic phenomena in disordered systems with high spatial resolution below the optical diffraction limit. Because electrons are detected, this method yields information that is complementary and additional to that obtained with near-field optical methods29,34,35. For example, a perfectly absorbing mode would be clearly visible, but it is invisible in the scattered radiation because the incident light is completely absorbed. Beyond the direct detection of locally absorbed energy densities, the present method yields spectroscopic information with high spatial resolution, limited by the electron optics of the used PEEM set-up reaching a few nanometres for aberration-corrected designs. Interestingly, the thermionic emission signal is also influenced by relaxation and transport phenomena of the hot electron gas, and so future experiments will provide detailed information about absorption and local electron dynamics—crucial information for photonic applications.

The demonstrated enhanced absorption via Anderson localization has consequences for designing future light absorbers. Even for weakly absorbing materials, localized modes operating under critical coupling conditions, that is, resonators with internal losses equal to the loss from coupling to external fields, offer the possibility of achieving extraordinarily high absorptions36. The absorption cross-section for the observed localized photonic modes is similar to their geometric cross-section (see Supplementary Section 8 for details). Roughly speaking, every photon hitting the localized mode is absorbed, making these modes perfect absorbers. The combination of different resonant absorption strategies might allow the absorbers to be tuned further towards the critical coupling regime, possibly leading to an even higher concentration of perfect absorbers. With respect to large-scale fabrication of absorbers it is important to note that such resonators do not require sophisticated top-down nanostructuring, but form by ‘chance’ in randomly nanotextured, layered materials, and yet still significantly enhance absorption.