Superior optical response of size-controlled silicon nano-crystals in a-Si:H/nc-Si:H superlattice films for multi-junction solar cells

Abstract

In order to facilitate widening in optical band gaps utilizing quantum size-effects in silicon nano-crystals (Si-ncs) of a few nanometers in dimension, self-assembled Si-ncs embedded in an a-Si matrix were grown within a-Si:H/nc-Si:H superlattice (SL) thin films produced by alternating sub-layers of a-Si:H and nc-Si:H from (SiH₄ + H₂)-plasma in PE-CVD at 180 °C, without post-deposition annealing. The growth of Si-ncs extending all through the nc-Si:H sub-layer thickness is terminated by the alternate deposition of an a-Si:H barrier layer during each cycle and the average size of the Si-ncs with a narrow size distribution is tuned by controlling each nc-Si:H sub-layer thickness. Significantly high-density tiny Si-ncs are grown even within an ultra-thin (∼3 nm) nc-Si:H sub-layer and that has been made possible via an ingenious approach, by utilizing the underneath of an a-Si:H sub-layer as the virtual incubation layer at a very specifically chosen parametric condition, during each cycle of periodic deposition. On systematic thinning of the nc-S:H active layer within 8–3 nm, a remarkable increase in optical absorption at near-UV photon energies along with simultaneous optical band gap widening within 1.89–2.04 eV demonstrate that the quantum size-effect in Si-ncs plays a key role. Subsequent lowering in the defect states identifies the nc-Si:H/a-Si:H SL-films as a superior material for use in devices, including as i-layers in triple-junction all-silicon solar cells.

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Introduction

Self-assembled silicon nano-crystals (Si-ncs) embedded in a superlattice structure or in a dielectric matrix is a fascinating area of research in the field of materials science due to the potential applications of such structures in photovoltaics, optoelectronics, light emitting devices and photo-detectors.^1–6 Taking advantage of the quantum confinement effect due to the size reduction of Si-ncs towards a few nanometers, the band gap of the materials can be well tuned. In third generation silicon solar cells with a triple tandem structure, the top cell should have the highest band gap (∼2.0 eV) and the two subsequent cells need to have sequentially lower band gaps in order to enable efficient absorption of the solar spectrum.^7,8 The different band gap for each i-layer can be achieved by modifying the confinement potential of Si-ncs by tuning their average size. In implementing such a scheme, superior control over the size of the Si-ncs and their distribution are prerequisites. In that direction, there are many approaches available in the literature, e.g. forming nano-crystals in a dielectric matrix (a-SiO_x, a-SiC or a-SiN) by plasma enhanced CVD (both capacitively and inductively coupled),^9–12 hotwire CVD or by layer-by-layer deposition mostly using RF magnetron sputtering.⁷ Among those, nano-scaled superlattice structures with alternate Si-rich layers and Si₃N₄/SiO₂/SiC dielectric layers have attracted substantial attention as they provide superior control over the growth of Si-ncs² which, however, proceeds essentially through high temperature post-deposition annealing at ∼1100 °C.^13–16 On annealing, solid-phase crystallization in the Si-rich layer leads to the formation of Si-ncs and their size-evolution is constrained by the thickness of the Si-rich sub-layer within the dielectric barriers on both sides. This inevitable high temperature annealing step imposes a persistent hindrance in its successful application in thin film solar cells and restriction on the use of low cost substrates, and also affects the other pre-deposited layers of the device. In addition, the charge carriers are obstructed by the high dielectric barriers on both sides of the Si-rich layer. In order to minimize the obstruction, the dielectric layers should be thin and the Si-ncs should be closely spaced so as to allow overlapping of the wave functions inbetween the adjacent Si-ncs.² In this regard, low temperature deposition of superlattice films with sub-layers of hydrogenated amorphous silicon (a-Si:H) and nano-crystalline silicon (nc-Si:H) that contains Si-ncs size-controlled by the corresponding sub-layer thickness, without post-deposition annealing, could be significantly important in terms of improving the carrier transport due to the lower dielectric barrier of the a-Si:H sub-layer, and making device fabrication feasible at a low deposition temperature. In addition, the a-Si:H/nc-Si:H superlattice thin films with a quantum-well structure, when used as the active layer in hot carrier solar cells, could be instrumental in cooling down the hot carriers exploiting the band gap difference between its sub-layers.¹⁷

Accordingly, in this investigation, we demonstrate a straightforward synthesis to fabricate superlattice thin films consisting of alternate sub-layers of a-Si:H and nc-Si:H at a low temperature of ∼180 °C, from (SiH₄ + H₂)-plasma in capacitively coupled plasma enhanced CVD. Significant widening in the optical band gap of the superlattice films has been tried to attain the utilization of quantum size-effects on tiny Si-ncs, the size of which are tuned by controlling the thickness of the nc-Si:H active layer within the a-Si:H barrier layers, without any post-deposition annealing.

Experimental details

The superlattice (SL) thin films consisting of repeated cycles of alternate sub-layers of hydrogenated amorphous silicon (a-Si:H) and hydrogenated nano-crystalline silicon (nc-Si:H) were fabricated from hydrogen diluted silane (SiH₄ + H₂)-plasma using a 13.56 MHz capacitively coupled plasma enhanced chemical vapor deposition (CC PE-CVD) system. The deposition conditions for each individual sub-layer (a-Si:H and nc-Si:H) were separately optimized in thick layers, prior to the preparation of the superlattice samples. For the deposition of the alternate layers all the deposition parameters were changed except for the substrate temperature which was maintained at 180 °C. The pressure, power, and H₂ and SiH₄ flow were kept as 3 Torr, 15 W, 95 sccm and 5 sccm, respectively for the a-Si:H layer and as 4 Torr, 40 W, 99.5 sccm and 0.5 sccm for the nc-Si:H layer. For different SL-thin films, the thickness of the nc-Si:H layers (t_nc) was changed from 3 nm to 8 nm, by varying the deposition time, while the thickness of the a-Si:H layers remained unchanged at 4.8 nm. The SL-thin films were deposited on Corning® Eagle2000™ glass substrates for various structural and optical studies. Each SL-thin film consisted of a-Si:H sub-layers on both ends and the total thickness of each sample, including the bulk layers, was maintained constant at ∼200 nm, by changing the number of bi-layers. A schematic diagram for the sample preparation steps along with a representative superlattice structure is depicted in Fig. 1(a) and (b).

Fig. 1 (a) A representative deposition scheme of the a-Si:H/nc-Si:H superlattice thin films. (b) Schematic diagram of the superlattice structure with alternate layers of a-Si:H and nc-Si:H.

The thickness of the samples was estimated using a Dektak 6M profilometer. Small angle X-ray diffractometry with the incident beam at a glancing angle (GISAX) was performed with a Cu K_α X-ray radiation (λ = 1.5418 Å) source in a Bruker (D8 Advance) system. The Raman spectrum was obtained at room temperature in a backscattering geometry using a triple Raman spectrometer (J-Y Horiba, model no. T64000) with an excitation wavelength of 514 nm from a water-cooled Ar⁺ laser source (Spectra Physics-made), at a low power density of 2 mW cm⁻². The beam spot was focused inside the SL-thin films by an Olympus open stage microscope and the scattered signal was detected by a TE-cooled CCD camera. The optical density data of the samples were obtained from absorption and reflection measurements in the UV-visible region at room temperature, using a double beam spectrophotometer (Hitachi330, Japan). Transmission electron microscopy was performed using a JEOL JSM 2010 transmission electron microscope operating at 200 kV.

Results

Small angle XRD

The structural periodicity of the a-Si:H/nc-Si:H superlattice (SL) thin films has been estimated from the small angle XRD data obtained within a limited 2Θ-span of 0.5° to 4.0°, at a glancing angle of incidence (GISAX), for a varying thickness of the nc-Si:H active layer (t_nc) while maintaining a constant thickness of the a-Si:H dielectric barrier layer (t_a). Fig. 2 shows the 1^st order (m = 1) diffraction peak at 2Θ = 1.10° of the SL-thin film for t_nc = 3 nm, which arises due to the periodic appearance of the combination of the active layer and barrier layer of t_nc + t_a thickness for a number of repeated cycles, forming a superlattice structure of the thin film. On increasing the periodic thickness of the superlattice by elevating t_nc from 3 to 4 nm, the 1^st order diffraction peak is no longer detectable due to the angular limitation of SAX measurement instruments. The 2^nd order (m = 2) peaks for t_nc = 4 nm, 6 nm and 8 nm are observed at 2Θ = 1.96°, 1.76° and 1.46°, respectively. It is notable that the diffraction peak positions shifted systematically towards a lower diffraction angle (2Θ) because of regular thickening of the periodic layers. Ultimately, the small angle X-ray diffraction results demonstrate the systematic formation of proper superlattice structures in the present set of thin films.

Fig. 2 Small angle X-ray diffraction spectra of a-Si:H/nc-Si:H superlattice thin films with different thicknesses (t_nc) of the nc-Si:H active sub-layer showing 1^st and 2^nd order diffraction peaks.

Raman spectroscopy

Raman spectroscopy is one of the most useful and non-destructive optical tools for the characterization of the nano-crystalline properties of silicon. Fig. 3(a) presents the normalized Raman spectra for the set of films with different t_nc values. In general, each Raman spectrum appears to possess four individual components, viz., three broad components around ∼310 cm⁻¹, ∼420 cm⁻¹ and 480 cm⁻¹, known as the LA, LO and TO Raman modes of amorphous silicon (a-Si)¹⁸ and a fourth sharp peak at ∼518 cm⁻¹ known as the TO Raman mode of crystalline silicon (c-Si). It has been grossly noted that with the systematic increase in the nano-crystalline active layer thickness, t_nc, the intensity of the TO Raman mode of the a-Si component gradually reduced and the reduction appeared quite significant for t_nc > 6 nm, while the peak of the TO Raman mode of the nc-Si component gradually sharpened and shifted towards higher wave numbers. As per the available literature on nc-Si, an intermediate component at around 500–510 cm⁻¹ has been considered which was assigned to the thermodynamically stable very tiny nano-crystallites of Si (ultra-nano-crystalline silicon, unc-Si) and/or the grain boundary region,^19–21 a prominent signature of which is evident in the spectrum for t_nc ≤ 6 nm. A representative deconvolution of all the five satellite components is shown in the inset of Fig. 3(a).

Fig. 3 (a) Normalized Raman spectra for superlattice thin films with different t_nc values. Inset shows the typical deconvolution of the Raman spectra into satellite components. (b) The enhanced crystalline volume fraction on widening of t_nc. (c) The deconvoluted spectra of the nc-Si component, showing a gradual blue-shift at lower t_nc values. Inset shows the variation of the peak position and the FWHM of the nc-Si peak. (d) The average size of the silicon nano-crystals, as calculated from the position of the nc-Si peak, being larger at increasing t_nc values.

The crystalline volume fraction (F_c) has been estimated using the following formula:

where I_nc, I_unc and I_a are the integrated areas of the peaks corresponding to the nc-Si, unc-Si and a-Si components, respectively. Considering the average size of the nano-crystallites in the order of a few nanometers, β, the ratio of cross-sections between the crystalline and amorphous components has been taken as unity.²² Fig. 3(b) demonstrates that a reasonably high crystalline volume fraction (F_c) of ∼42% has been obtained in the SL-film even with a very low periodic thickness of the nc-Si:H active layer, t_nc ∼ 3 nm. With a systematic increase in t_nc, F_c increases gradually and attains a very high magnitude, ∼67.4% for t_nc = 8 nm. Thus the a-Si:H/nc-Si:H SL-film with a periodic thickness (t_a + t_nc) = (4.8 + 8) nm produces an almost continuously grown nc-Si:H network in terms of a sufficiently high degree of the overall crystallinity.

Considering the nc-Si satellite component of the Raman peak, in particular, obtained from the deconvolution of the Raman spectra, Fig. 3(c) demonstrates that the nc-Si peak gradually becomes broader in the FWHM along with a continuous shift towards lower wave numbers, from 518.7 to 513 cm⁻¹ on systematic thinning in t_nc from 8 to 3 nm. This shift of the nc-Si peak position can be attributed to the phonon confinement effect in silicon nano-crystallites.²³ For bulk crystalline silicon (c-Si), the first order Raman scattering process of the excited phonon has been limited at the centre of the Brillouin zone by the momentum conservation law. However, with the formation of Si-ncs, the phonons, dispersed over the Brillouin zone, started contributing in the Raman spectra due to spatial confinement of the phonons within the Si-ncs by the presence of structural defects at nano-crystalline boundaries. This phonon confinement effect caused the shift of the nc-Si peak position towards lower wave numbers, along with the broadening of its line-width. Strong confinement effects occurred when the radius of the Si-ncs approached the Bohr radius of silicon (∼5 nm) and reduced further. Considering the shift of the nc-Si peak arising due to the size-variation of the Si-ncs and assuming a spherical shape of the Si-ncs, their average size can be estimated by the empirical formula:¹⁸

where Δω is the relative shifting of the nc-Si peak position from 520 cm⁻¹ (corresponding to bulk c-Si). Fig. 3(d) demonstrates that the average size (d) of the Si-ncs gradually increased from ∼3.3 to ∼7.5 nm as t_nc was enhanced from 3 to 8 nm. It is notable that the average grain sizes (d), as estimated from Raman spectroscopy, are comparable with the thickness (t_nc) of the nc-Si:H active layer sandwiched between two adjacent a-Si:H barrier layers. According to the phonon confinement effect, the size reduction of the Si-ncs induces shifting of the peak position towards lower wave numbers along with widening in the line-width of the peak. Contrary to that effect, as seen in Fig. 3(c), the FWHM of the nc-Si peak widened from 15.54 to 17.11 cm⁻¹ as t_nc was increased from 6 to 8 nm. Actually, contrary to the effect of phonon confinement mentioned above, a narrower size distribution opposes the peak broadening. The FWHM of the nc-Si peak is thus governed by two competitive factors – the reduction in the average size of the Si-ncs widens the FWHM while the narrow size distribution of the Si-ncs opposes this widening. For 6 nm ≤ t_nc ≤ 8 nm, the average grain size varied in the range 5.7 nm ≤ d ≤ 7.5 nm where quantum confinement has feeble effects on the limit of Bohr’s radius, while size distribution effects may play a significant role.²⁴ It has been identified by the TEM studies mentioned in the next section that the size distribution became narrower when the grain size reduced within a thinner t_nc, which might be supported by similar earlier reports as well.¹⁰ Thus the deviation of the FWHM data-point for t_nc = 8 nm from the regular nature of its variation in Fig. 3(c) is reasonably explained, while for t_nc < 6 nm, the strong phonon confinement effect became dominant over the effect of a narrow size distribution, which finally resulted in prominent broadening of the nc-Si peak.²⁵

TEM analysis

Systematic variations in the evolution of silicon nano-crystals (Si-ncs) in the a-Si:H/nc-Si:H SL-films on an increase in the periodic thickness (t_nc) of the nc-layers have been studied by transmission electron microscopy (TEM). The TEM samples have been prepared on carbon coated Cu-grids with a common initial amorphous layer of thickness t_a = 4.8 nm and the 3 and 2 bi-layers each of t_nc + t_a thickness for films with t_nc = 5 nm and 8 nm, respectively, in order to maintain a gross thickness >30 nm in each case. The plain view TEM micrograph for the SL-thin films with t_nc = 5 nm, in Fig. 4(a-i), identifies the deep dark spots as the Si-ncs which are uniformly distributed in the relatively bright a-Si matrix. On an increase in the nc-layer thickness t_nc to 8 nm, the micrograph in Fig. 4(b-i) shows the growth of relatively large sized Si-ncs which are closely packed and bound by sharp edges with narrow amorphous interconnections. The individual lattice planes of c-Si are clearly identified in the HR-TEM micrographs in Fig. 4(a-ii) and (b-ii). The corresponding selected area electron diffraction (SAED) pattern, shown in the inset of Fig. 4(a-i) exhibits diffraction rings corresponding to the 〈111〉 and 〈220〉 planes of c-Si, while a similar SAED pattern for t_nc = 8 nm, in the inset of Fig. 4(b-i) exhibits relatively sharp diffraction rings implying the formation of relatively enhanced crystallinity with the 〈111〉, 〈220〉 and 〈311〉 planes of Si.

Fig. 4 ((a-i) and (b-i)) The plain view TEM micrographs of the a-Si:H/nc-Si:H superlattice thin films with t_nc = 5 and 8 nm. Insets present the related selected area electron diffraction (SAED) patterns, demonstrating a higher degree of crystallinity at t_nc = 8 nm compared to 5 nm. ((a-ii) and (b-ii)) The high resolution TEM micrographs exhibiting lattice planes of arbitrarily selected Si-ncs. ((a-iii) and (b-iii)) The corresponding histograms illustrating Gaussian-like size distributions of the Si-ncs.

The histogram plots in Fig. 4(a-iii) and (b-iii) for t_nc = 5 and 8 nm, respectively, present the nearly Gaussian distribution of the Si-ncs with the corresponding FWHMs as 4.34 and 6.03 nm, respectively, demonstrating the narrower size distribution of the Si-ncs in thinner nc-Si:H layers. On an increase in the nc-Si:H layer thickness (t_nc) from 5 to 8 nm, the average size (d) of the Si-ncs, obtained from the apex of the Gaussian distribution, increases from ∼5.5 to ∼8.1 nm, along with a corresponding increase in the number density from ∼3.5 × 10¹⁰ cm⁻² to ∼7.5 × 10¹⁰ cm⁻², respectively. It is, therefore, significant to infer from the TEM studies that high density (∼10¹⁰ cm⁻²) Si-ncs of size in the order of the thickness of the nc-Si:H active layers (t_nc), bound by a-Si:H barrier layers, could be grown within the very low thickness of a-Si:H/nc-Si:H SL-thin films, while the overall crystallinity of the SL-film increases rapidly and the size distribution broadens with increasing t_nc, which grossly corroborates with the Raman results discussed earlier.

UV-vis spectroscopy and optical band gap

Based on the structural analysis by SAX, Raman and TEM, it is arguably expected that the size reduction of the Si-ncs governed by the reduced stacking thickness (t_nc) of the nc-Si:H active layers would pertinently control the optical properties of the superlattice thin films, e.g., the absorption coefficient (α) and the optical band gap (E_g). In this investigation the optical absorption coefficient spectra of the SL-films with different t_nc values have been obtained utilizing both the reflectance and transmittance data in the UV-vis region and are presented in Fig. 5, along with the same for the bulk nc-Si:H and a-Si:H films when deposited individually. Looking at the absorption spectrum of the a-Si:H film two different energy regions are identified around 2.65 eV. The a-Si:H films do possess the highest optical absorption that increases at higher energies up to 2.65 eV beyond which a virtual saturation in optical absorption is evident. While in the case of bulk nc-Si:H films similar virtual saturation seems to arise at energies above around 3.10 eV, below which the ascending absorption coefficient values remain at magnitudes lower than those of the a-Si:H network.

Fig. 5 The optical absorption coefficient (α) spectra of the a-Si:H/nc-Si:H superlattice thin films with different thicknesses of the nc-Si:H layer (t_nc).

On forming the superlattice structure by introducing thin nc-Si:H layers of t_nc = 3 nm, within identical a-Si:H layers of a constant 4.8 nm thickness on both sides, the absorption coefficient grossly reduced for energies <2.65 eV, beyond which, however, the absorption continues to increase monotonically at similar rate with energy. On a further systematic increase in t_nc to 8 nm, the entire optical absorption coefficient spectrum gradually reduces in intensity, showing a prominent response in the energy regions both below and above 2.65 eV, in a way similar to the nature of optical absorption exhibited by the single-layer nc-Si:H thin film. Accordingly, it has been identified that with the addition of even very thin nc-Si:H layers inbetween two a-Si:H barrier layers, the superlattice structure adopts the nc-Si characteristics in view of the ascending optical absorption at higher energies beyond 2.65 eV, while maintaining the a-Si characteristics considering that its magnitude is higher than that of the nc-Si:H layers all along. A shift in the energy (E_αsat) corresponding to the saturation absorption coefficient (α_sat) related to increasing t_nc, the thickness of the nc-Si:H active layer of the a-Si:H/nc-Si:H SL-films, is shown in Table 1. The results demonstrate that in the case of the superlattice films of increasing t_nc, the energy (E_αsat) corresponding to the saturation absorption coefficient (α_sat) gradually approaches the same as that of the bulk nc-Si:H film and increases even further beyond that for t_nc > 5 nm, while the gradually increasing magnitude of α_sat starts reducing at t_nc > 5 nm. Increasing t_nc beyond 5 nm gradually enhanced the population of the nc-Si:H component in the SL-film, which induces systematic lowering of the overall absorption spectrum, thereby reducing α_sat, while the quantum confinement effects associated to small dimensional Si-ncs in the SL-films of high crystallinity induce an increase in the magnitude of E_αsat beyond the same for the bulk layer nc-Si films.

Table 1 Variation of the saturated absorption coefficient (α_sat) and the corresponding energy (E_αsat) at α_sat

Bulk layer	Superlattice tnc (nm)	Saturation absorption coefficient (αsat in cm^−1)	Energy at αsat (in eV)
a-Si:H		258 793	2.65
	3	377 430	2.91
	4	391 247	2.93
	5	420 234	2.96
	6	377 430	3.00
	8	351 447	3.14
nc-Si:H		193 787	2.96

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The optical gaps (E_g) of the SL-films were calculated using the Tauc equation (αhν)^1/2 = B(hν − E_g) for the allowed indirect transitions, where B is a constant known as the edge width parameter which indicates the sharpness of the band edge.²⁶ It is related to the width of the band tails or disorder in the film in terms of bond angle and bond length distribution.²⁷ The constant B, obtained from the slope of the Tauc’s plot and shown in Fig. 6, has been found to increase monotonically on narrowing of t_nc, however, a sharp increase in B has been identified with t_nc reducing from 8 to 6 nm which incidentally corresponds closely to the Bohr radius of Si. Usually, B is inversely proportional to the width of the tail states, which enlarges with an increase in disorder. Therefore, the enhanced magnitude of B with decreasing t_nc implies the growth of lower defects and disorders, which might be correlated with the overall reduction of the crystalline volume fraction wherein the tiny size of the Si-ncs and their reduced number density altogether reduce the contribution of defects arising from the related grain boundary zone. The lowering of the defects at a thinner t_nc value in SL-thin films appears advantageous in view of their potential application as absorber layers in solar cells.

Fig. 6 The gradual decay of the optical band gap E_g and the slope B of the superlattice thin films at higher t_nc values.

The Tauc band gap, E_g, of the SL-thin film having t_nc = 8 nm has been estimated to be ∼1.89 eV and a gradual decrease in t_nc widens the band gap up to 2.04 eV at t_nc = 3 nm (Fig. 6). It is remarkably noted that the optical band gaps of the superlattice thin films for 3 nm ≤ t_nc ≤ 8 nm are even higher than those of the bulk a-Si:H and nc-Si:H layers when deposited separately, which are ∼1.85 eV for a-Si:H and ∼1.64 eV for nc-Si:H thin films.

Discussions

The optical band gap of the a-Si:H/nc-Si:H SL-thin films could be simply written as:

E_g = E_a + E_nc,

where the E_a term corresponds to the band gap of the amorphous component which depends on its defect distribution and the bonded H-content, while the second term, E_nc, corresponds to the nano-crystalline network with varied crystalline volume fraction and changes in the average sizes of the Si-ncs which are determined by the thickness (t_nc) of the nano-crystalline layer of individual SL-thin films in the present study.¹⁰ It is remarkable to observe that the optical gaps of the SL-thin films are much higher than those of the a-Si:H thin films which usually possess a significant amount of bonded-H that helps widen the optical gap.^28,29 For 3 nm ≤ t_nc ≤ 8 nm, the SL-thin films possess a reasonably high crystallinity in the range 42% ≤ F_c ≤ 67%. The lowering in the overall crystallinity of the SL-film arises due to the lower volume percentage of the nc-Si:H layer in the ensemble because of a reduced t_nc. The a-Si:H component of the SL-film remains unchanged in layer-thickness (t_a), whose changes in the nature of H-bonding and its qualitative involvement in the resultant widening of the optical gap of the SL-film is categorically excluded. Hence, a predominant contribution of the nc-Si component to the optical gap, (E_nc), of the SL-film appears strongly evident. The E_nc component depends on the size of the Si-ncs due to the contribution of the quantum confinement effect.³⁰

Semiconductor nanostructures exhibit increased oscillator strength due to electron–hole wave function overlap. Quantum confinement (QC) is defined as the modification in the free particle dispersion relation as a function of a system’s spatial dimension.³¹ The confinement potential is determined by the alignment of the respective Fermi levels when a material of a band gap E_G1 is surrounded by a material of another band gap E_G2, with E_G1 < E_G2, as in the present case where each nc-Si:H layer is surrounded by the a-Si:H layers on both sides.³²

Si is an indirect gap material, meaning that, in principle, phonon scattering events are essential to maintain momentum and energy conservation during a radiative event. This situation is true in the case of a bulk material; however, as the dimension of the system is reduced, the uncertainty in the momentum k vector is increased. Therefore, it is possible to break the k selection rules making the band gap “pseudo-direct”, allowing for direct e–h recombination.³³ The length scale at which this “pseudo-direct” phenomenon becomes important is typically less than a few nanometers.³⁴ This length scale corresponds to the systems considered here i.e., the thickness of the individual a-Si:H and nc-Si:H layers; therefore, theoretically it is valid to assume direct e–h recombination without phonon-assistance.

Considering the effective mass approximation (EMA) based on the Bloch periodic function, the exciton Bohr radius of Si is ∼4.5 nm. The Bohr radius defines the spatial dimension of the particles, which determines the range of sizes for which QC can be observed. When the Si-nc size is larger than the corresponding Bohr radius, the optical gap depends only on the energy difference between the conduction and valance bands. However, when the particle size is close to the Bohr radius of the material (<5 nm), quantum confinement and Coulomb correlation effects begin to influence the excitation energy across the band gap. As a result, the optical band gap is no longer independent of particle size; rather it is inversely proportional to the square of the radius of the Si-ncs. This confinement effect leads to the sharp widening of the E_nc component for the tiny size of the Si-ncs which is a consequence of the decreasing t_nc.^35,36 Similar changes in the optical absorption and the corresponding widening in the optical gap due to the quantum size-effects were identified in the Si-ncs obtained from stacked layer Si:H films deposited by interrupted growth and H-plasma treatment.^37,38

Considering the experimentally obtained constants e.g., the saturation absorption coefficient (α_sat), the corresponding energy (E_αsat), the edge width parameter (B) and the estimated optical gap (E_g), and in view of the quantum confinement effects controlling the optical phenomena, the effective density of states distributions and their relative nature of variations on the periodic stacking thickness (t_nc) of the nc-Si:H active layers in the a-Si:H/nc-Si:H superlattice thin films can be empirically presented as in Fig. 7. In a quantum mechanical pseudo-potential calculation, Wang et al. have shown that the magnitude of the local density of states increases beyond the band edges with a simultaneous increase in the energy corresponding to its virtual saturation when the silicon quantum dots become larger in size.³⁹ In reliance with that report an elevated magnitude of the saturation optical absorption coefficient, α_sat, with increasing t_nc in our superlattice films demonstrates an enhanced effective density of states along with the increase in the corresponding E_αsat. However, for t_nc ≥ 8 nm, the magnitude of the saturation density of states has reduced with a simultaneous lowering in E_αsat, because of the effectively feeble confinement effects with the size of the Si-ncs of ∼7.5 nm.

Fig. 7 Empirical density of states distribution and their nature of variations on the stacking thickness (t_nc) of the nc-Si:H active layers in the a-Si:H/nc-Si:H superlattice thin films.

Optimization of the optical properties of a-Si:H/nc-Si:H superlattice structures, discarding the conventional post-deposition high-temperature annealing steps, will be of immense importance in further developments in all-silicon solar cells. In this regard, there are only very few reports available in the literature.^40,41 In such a work by Liu et al., alternate layers of μc-Si:H and a-Si:H were deposited within capacitively and inductively coupled electrodes, respectively which certainly made the deposition steps more complicated.

In the present investigation, a single-step low temperature yet simple and most popular capacitively coupled PECVD technique has been utilized to fabricate a-Si:H/nc-Si:H in superlattice structures. While preparing silicon nano-crystals embedded within an amorphous silicon matrix at a low temperature, the re-etching of the growing film surface by the atomic hydrogen present in the plasma is the predominant factor. The growth of silicon thin films, from SiH_n radicals in the plasma, begins with an incubation layer on the substrate surface and that happens to be mostly defective and amorphous in nature, because of the inherent lattice mismatch between the substrate material and the interacting Si precursors.⁴² The typical thickness for such an incubation layer on a glass substrate, at the most crystalline-prone deposition conditions, varies between several tens of nanometers beyond which nano-crystallization starts occurring. This incubation layer usually becomes the perpetual hindrance for the formation of the nc-Si:H network within layers of thickness ∼3–8 nm. In the present set of samples, this obstacle has been surpassed by the initial deposition of an amorphous silicon sub-layer on the substrate, followed by the deposition of the nc-Si:H layer. This initial a-Si:H sub-layer acts as the virtual incubation layer for the growth of the Si-ncs and that effectively eliminates the real incubation layer for the growth of the Si-ncs within the nc-Si:H sub-layer, in the present parametric deposition conditions. As a result, a significantly high crystallinity was attained even within its very low thickness as low as 3 nm. The size of the Si-ncs has been controlled by the interruption of the growth of the nc-Si:H sub-layer, by allowing the next cycle of the a-Si:H sub-layer to grow. This process of crystallization by providing a virtual incubation layer from the a-Si:H barrier layer and interruption of the growth of the nc-Si:H layer was repeated to fabricate the superlattice structure. While the diffraction peaks of SAX validate the formation of a superlattice structure consisting of alternate layers of a-Si:H and nc-Si:H, the Raman studies have shown a consistent reduction of the Si-nc size from 7.5 nm to 3.9 nm, as t_nc is reduced from 8 nm to 3 nm. Thus, in layer-by-layer deposition the a-Si:H layers of identical thickness provide the amorphous virtual incubation layer and the growth interruption of the nc-Si:H layers of a limiting layer-thickness controls the size of the Si-ncs and the overall crystallinity of the superlattice structure.

The miniaturization of the size of the Si-ncs has been found to be very effective in tuning the optical properties (absorption coefficient and optical band gap) of the SL-thin films without any inclusion of foreign elements (O/C/N) in the pristine crystalline silicon network. For thin films with 3 ≤ t_nc (nm) ≤ 6, the optical absorption coefficients have a very high magnitude at a higher photon energy which ensures better light absorption compared to its amorphous part. Moreover, the existence of nano-crystallites can diminish the light induced degradation and enhance the quantum efficiency at the infra-red range. Although the band gap is widened with the reduction of the size of the Si-ncs, the presence of nano-crystallites can enable the conduction charge carriers through tunnelling between the Si-ncs. In addition, the a-S:H/nc-Si:H SL-thin films do possess a low concentration of defects which altogether facilitate their potential applications in solar cells.

Conclusions

Superlattice films consisting of repeated cycles of an alternate a-Si:H barrier layer and nc-Si:H active layer of stacking thickness t_a and t_nc, respectively have been prepared from (SiH₄ + H₂)-plasma in a capacitively coupled PE-CVD system at a moderately low temperature of 180 °C. Formation of the superlattice structure has been confirmed by the small angle XRD data, while the average size of the Si-ncs along with the gross crystalline volume fraction of the films have been estimated from the Raman spectroscopy data. The crystallographic orientations of the Si-ncs have been identified from the X-ray diffraction results and the electron diffraction pattern, while the sizes of the Si nano-crystallites are further confirmed from the histogram plot in the TEM data. It has been demonstrated how the variation in the stacking thickness (t_nc) of the nc-Si:H layer can grossly modify the overall structural and optical properties of the superlattice thin films. The average size (d in nm) of the Si-ncs closely matches the nc-S:H active layer thickness (t_nc in nm), whereas the width of the size distribution of the Si-ncs and their crystalline volume fraction change proportionally with t_nc. With the thinning of the nc-Si:H layer from 8 nm to 3 nm the crystalline volume fraction reduces from 67.4% to 42%, while the optical absorption grossly increased at photon energies above 2.65 eV along with a simultaneous widening in the optical band gap from 1.89 eV to 2.04 eV as contributed by the quantum size-effect on the Si nano-crystallites. The changing slope of the optical absorption edge identifies the lowering of defects in the superlattice thin films at a lower thickness of the nc-Si:H sub-layer which also has been corroborated from the Raman studies. High optical absorption in the towards-UV part of the solar spectrum with simultaneous widening in the optical gap and lowering in the defect states identifies the nc-Si:H/a-Si:H superlattice thin films as a superior material for use in different i-layers in the triple-junction all-silicon solar cells. The successful formation of the Si-ncs even within very thin nc-Si:H layers has been instrumented by the initial deposition of an a-Si:H layer which acts as a virtual incubation layer for the growth of the nano-crystalline sub-layer under chosen parametric conditions. The ensuing plasma deposition technique for the fabrication of Si-ncs within superlattice thin films by a plasma enhanced CVD system at low temperature is significantly effective in tuning their structural and optical characteristics as an advanced material for prospective applications in numerous photonic and optoelectronic devices.

Acknowledgements

The work has been done under nano-silicon projects funded by the Department of Science and Technology (Nano-Mission Program) and the Council of Scientific and Industrial Research, Government of India. The HR-TEM studies have been performed using facilities of the Unit on Nano-Science at IACS.

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